libm crate v0.2.1 am: fb178dc981
Original change: https://android-review.googlesource.com/c/platform/external/rust/crates/libm/+/1517420
Change-Id: I0d26fa8783e9ae79d98e672ce72f99dd672aa584
diff --git a/.cargo_vcs_info.json b/.cargo_vcs_info.json
new file mode 100644
index 0000000..f2062d3
--- /dev/null
+++ b/.cargo_vcs_info.json
@@ -0,0 +1,5 @@
+{
+ "git": {
+ "sha1": "3d729b7a85daad3b4d54b22e02d00681762bc602"
+ }
+}
diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
new file mode 100644
index 0000000..80ce4eb
--- /dev/null
+++ b/.github/workflows/main.yml
@@ -0,0 +1,67 @@
+name: CI
+on: [push, pull_request]
+
+jobs:
+ docker:
+ name: Docker
+ runs-on: ubuntu-latest
+ strategy:
+ matrix:
+ target:
+ - aarch64-unknown-linux-gnu
+ - arm-unknown-linux-gnueabi
+ - arm-unknown-linux-gnueabihf
+ - armv7-unknown-linux-gnueabihf
+ - i686-unknown-linux-gnu
+ - mips-unknown-linux-gnu
+ - mips64-unknown-linux-gnuabi64
+ - mips64el-unknown-linux-gnuabi64
+ - powerpc-unknown-linux-gnu
+ - powerpc64-unknown-linux-gnu
+ - powerpc64le-unknown-linux-gnu
+ - x86_64-unknown-linux-gnu
+ steps:
+ - uses: actions/checkout@master
+ - name: Install Rust
+ run: rustup update nightly && rustup default nightly
+ - run: rustup target add ${{ matrix.target }}
+ - run: rustup target add x86_64-unknown-linux-musl
+ - run: cargo generate-lockfile
+ - run: ./ci/run-docker.sh ${{ matrix.target }}
+
+ rustfmt:
+ name: Rustfmt
+ runs-on: ubuntu-latest
+ steps:
+ - uses: actions/checkout@master
+ - name: Install Rust
+ run: rustup update stable && rustup default stable && rustup component add rustfmt
+ - run: cargo fmt -- --check
+
+ wasm:
+ name: WebAssembly
+ runs-on: ubuntu-latest
+ steps:
+ - uses: actions/checkout@master
+ - name: Install Rust
+ run: rustup update nightly && rustup default nightly
+ - run: rustup target add wasm32-unknown-unknown
+ - run: cargo build --target wasm32-unknown-unknown
+
+ cb:
+ name: "The compiler-builtins crate works"
+ runs-on: ubuntu-latest
+ steps:
+ - uses: actions/checkout@master
+ - name: Install Rust
+ run: rustup update nightly && rustup default nightly
+ - run: cargo build -p cb
+
+ benchmarks:
+ name: Benchmarks
+ runs-on: ubuntu-latest
+ steps:
+ - uses: actions/checkout@master
+ - name: Install Rust
+ run: rustup update nightly && rustup default nightly
+ - run: cargo bench --all
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..3995091
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,8 @@
+**/*.rs.bk
+.#*
+/bin
+/math/src
+/math/target
+/target
+/tests
+Cargo.lock
diff --git a/CHANGELOG.md b/CHANGELOG.md
new file mode 100644
index 0000000..28e2705
--- /dev/null
+++ b/CHANGELOG.md
@@ -0,0 +1,97 @@
+# Change Log
+
+All notable changes to this project will be documented in this file.
+This project adheres to [Semantic Versioning](http://semver.org/).
+
+## [Unreleased]
+
+...
+
+## [v0.1.4] - 2019-06-12
+
+### Fixed
+- Restored compatibility with Rust 1.31.0
+
+## [v0.1.3] - 2019-05-14
+
+### Added
+
+- minf
+- fmin
+- fmaxf
+- fmax
+
+## [v0.1.2] - 2018-07-18
+
+### Added
+
+- acosf
+- asin
+- asinf
+- atan
+- atan2
+- atan2f
+- atanf
+- cos
+- cosf
+- cosh
+- coshf
+- exp2
+- expm1
+- expm1f
+- expo2
+- fmaf
+- pow
+- sin
+- sinf
+- sinh
+- sinhf
+- tan
+- tanf
+- tanh
+- tanhf
+
+## [v0.1.1] - 2018-07-14
+
+### Added
+
+- acos
+- acosf
+- asin
+- asinf
+- atanf
+- cbrt
+- cbrtf
+- ceil
+- ceilf
+- cosf
+- exp
+- exp2
+- exp2f
+- expm1
+- expm1f
+- fdim
+- fdimf
+- floorf
+- fma
+- fmod
+- log
+- log2
+- log10
+- log10f
+- log1p
+- log1pf
+- log2f
+- roundf
+- sinf
+- tanf
+
+## v0.1.0 - 2018-07-13
+
+- Initial release
+
+[Unreleased]: https://github.com/japaric/libm/compare/v0.1.4...HEAD
+[v0.1.4]: https://github.com/japaric/libm/compare/0.1.3...v0.1.4
+[v0.1.3]: https://github.com/japaric/libm/compare/v0.1.2...0.1.3
+[v0.1.2]: https://github.com/japaric/libm/compare/v0.1.1...v0.1.2
+[v0.1.1]: https://github.com/japaric/libm/compare/v0.1.0...v0.1.1
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
new file mode 100644
index 0000000..59c37a6
--- /dev/null
+++ b/CONTRIBUTING.md
@@ -0,0 +1,95 @@
+# How to contribute
+
+- Pick your favorite math function from the [issue tracker].
+- Look for the C implementation of the function in the [MUSL source code][src].
+- Copy paste the C code into a Rust file in the `src/math` directory and adjust
+ `src/math/mod.rs` accordingly. Also, uncomment the corresponding trait method
+ in `src/lib.rs`.
+- Write some simple tests in your module (using `#[test]`)
+- Run `cargo test` to make sure it works
+- Run `cargo test --features musl-reference-tests` to compare your
+ implementation against musl's
+- Send us a pull request! Make sure to run `cargo fmt` on your code before
+ sending the PR. Also include "closes #42" in the PR description to close the
+ corresponding issue.
+- :tada:
+
+[issue tracker]: https://github.com/rust-lang/libm/issues
+[src]: https://git.musl-libc.org/cgit/musl/tree/src/math
+[`src/math/truncf.rs`]: https://github.com/rust-lang/libm/blob/master/src/math/truncf.rs
+
+Check [PR #65] for an example.
+
+[PR #65]: https://github.com/rust-lang/libm/pull/65
+
+## Tips and tricks
+
+- *IMPORTANT* The code in this crate will end up being used in the `core` crate so it can **not**
+ have any external dependencies (other than `core` itself).
+
+- Only use relative imports within the `math` directory / module, e.g. `use self::fabs::fabs` or
+`use super::k_cos`. Absolute imports from core are OK, e.g. `use core::u64`.
+
+- To reinterpret a float as an integer use the `to_bits` method. The MUSL code uses the
+ `GET_FLOAT_WORD` macro, or a union, to do this operation.
+
+- To reinterpret an integer as a float use the `f32::from_bits` constructor. The MUSL code uses the
+ `SET_FLOAT_WORD` macro, or a union, to do this operation.
+
+- You may use other methods from core like `f64::is_nan`, etc. as appropriate.
+
+- If you're implementing one of the private double-underscore functions, take a look at the
+ "source" name in the comment at the top for an idea for alternate naming. For example, `__sin`
+ was renamed to `k_sin` after the FreeBSD source code naming. Do `use` these private functions in
+ `mod.rs`.
+
+- You may encounter weird literals like `0x1p127f` in the MUSL code. These are hexadecimal floating
+ point literals. Rust (the language) doesn't support these kind of literals. The best way I have
+ found to deal with these literals is to turn them into their integer representation using the
+ [`hexf!`] macro and then turn them back into floats. See below:
+
+[`hexf!`]: https://crates.io/crates/hexf
+
+``` rust
+// Step 1: write a program to convert the float into its integer representation
+#[macro_use]
+extern crate hexf;
+
+fn main() {
+ println!("{:#x}", hexf32!("0x1.0p127").to_bits());
+}
+```
+
+``` console
+$ # Step 2: run the program
+$ cargo run
+0x7f000000
+```
+
+``` rust
+// Step 3: copy paste the output into libm
+let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 12
+```
+
+- Rust code panics on arithmetic overflows when not optimized. You may need to use the [`Wrapping`]
+ newtype to avoid this problem.
+
+[`Wrapping`]: https://doc.rust-lang.org/std/num/struct.Wrapping.html
+
+## Testing
+
+Normal tests can be executed with:
+
+```
+cargo test
+```
+
+If you'd like to run tests with randomized inputs that get compared against musl
+itself, you'll need to be on a Linux system and then you can execute:
+
+```
+cargo test --features musl-reference-tests
+```
+
+Note that you may need to pass `--release` to Cargo if there are errors related
+to integer overflow.
diff --git a/Cargo.toml b/Cargo.toml
new file mode 100644
index 0000000..e75fbba
--- /dev/null
+++ b/Cargo.toml
@@ -0,0 +1,33 @@
+# THIS FILE IS AUTOMATICALLY GENERATED BY CARGO
+#
+# When uploading crates to the registry Cargo will automatically
+# "normalize" Cargo.toml files for maximal compatibility
+# with all versions of Cargo and also rewrite `path` dependencies
+# to registry (e.g., crates.io) dependencies
+#
+# If you believe there's an error in this file please file an
+# issue against the rust-lang/cargo repository. If you're
+# editing this file be aware that the upstream Cargo.toml
+# will likely look very different (and much more reasonable)
+
+[package]
+edition = "2018"
+name = "libm"
+version = "0.2.1"
+authors = ["Jorge Aparicio <jorge@japaric.io>"]
+description = "libm in pure Rust"
+documentation = "https://docs.rs/libm"
+keywords = ["libm", "math"]
+categories = ["no-std"]
+license = "MIT OR Apache-2.0"
+repository = "https://github.com/rust-lang/libm"
+[dev-dependencies.no-panic]
+version = "0.1.8"
+[build-dependencies.rand]
+version = "0.6.5"
+optional = true
+
+[features]
+default = []
+musl-reference-tests = ["rand"]
+unstable = []
diff --git a/Cargo.toml.orig b/Cargo.toml.orig
new file mode 100644
index 0000000..d9d6680
--- /dev/null
+++ b/Cargo.toml.orig
@@ -0,0 +1,34 @@
+[package]
+authors = ["Jorge Aparicio <jorge@japaric.io>"]
+categories = ["no-std"]
+description = "libm in pure Rust"
+documentation = "https://docs.rs/libm"
+keywords = ["libm", "math"]
+license = "MIT OR Apache-2.0"
+name = "libm"
+repository = "https://github.com/rust-lang/libm"
+version = "0.2.1"
+edition = "2018"
+
+[features]
+default = []
+
+# This tells the compiler to assume that a Nightly toolchain is being used and
+# that it should activate any useful Nightly things accordingly.
+unstable = []
+
+# Generate tests which are random inputs and the outputs are calculated with
+# musl libc.
+musl-reference-tests = ['rand']
+
+[workspace]
+members = [
+ "crates/compiler-builtins-smoke-test",
+ "crates/libm-bench",
+]
+
+[dev-dependencies]
+no-panic = "0.1.8"
+
+[build-dependencies]
+rand = { version = "0.6.5", optional = true }
diff --git a/LICENSE b/LICENSE
new file mode 120000
index 0000000..6b579aa
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1 @@
+LICENSE-APACHE
\ No newline at end of file
diff --git a/LICENSE-APACHE b/LICENSE-APACHE
new file mode 100644
index 0000000..16fe87b
--- /dev/null
+++ b/LICENSE-APACHE
@@ -0,0 +1,201 @@
+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
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diff --git a/LICENSE-MIT b/LICENSE-MIT
new file mode 100644
index 0000000..432fbea
--- /dev/null
+++ b/LICENSE-MIT
@@ -0,0 +1,25 @@
+Copyright (c) 2018 Jorge Aparicio
+
+Permission is hereby granted, free of charge, to any
+person obtaining a copy of this software and associated
+documentation files (the "Software"), to deal in the
+Software without restriction, including without
+limitation the rights to use, copy, modify, merge,
+publish, distribute, sublicense, and/or sell copies of
+the Software, and to permit persons to whom the Software
+is furnished to do so, subject to the following
+conditions:
+
+The above copyright notice and this permission notice
+shall be included in all copies or substantial portions
+of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
+ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
+TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
+PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
+SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
+CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
+OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
+IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+DEALINGS IN THE SOFTWARE.
diff --git a/METADATA b/METADATA
new file mode 100644
index 0000000..8b844f0
--- /dev/null
+++ b/METADATA
@@ -0,0 +1,19 @@
+name: "libm"
+description: "libm in pure Rust"
+third_party {
+ url {
+ type: HOMEPAGE
+ value: "https://crates.io/crates/libm"
+ }
+ url {
+ type: ARCHIVE
+ value: "https://static.crates.io/crates/libm/libm-0.2.1.crate"
+ }
+ version: "0.2.1"
+ license_type: NOTICE
+ last_upgrade_date {
+ year: 2020
+ month: 11
+ day: 26
+ }
+}
diff --git a/MODULE_LICENSE_APACHE2 b/MODULE_LICENSE_APACHE2
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/MODULE_LICENSE_APACHE2
diff --git a/OWNERS b/OWNERS
new file mode 100644
index 0000000..46fc303
--- /dev/null
+++ b/OWNERS
@@ -0,0 +1 @@
+include platform/prebuilts/rust:/OWNERS
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..5d9e9bd
--- /dev/null
+++ b/README.md
@@ -0,0 +1,51 @@
+# `libm`
+
+A port of [MUSL]'s libm to Rust.
+
+[MUSL]: https://www.musl-libc.org/
+
+## Goals
+
+The short term goal of this library is to [enable math support (e.g. `sin`, `atan2`) for the
+`wasm32-unknown-unknown` target][wasm] (cf. [rust-lang/compiler-builtins][pr]). The longer
+term goal is to enable [math support in the `core` crate][core].
+
+[wasm]: https://github.com/rust-lang/libm/milestone/1
+[pr]: https://github.com/rust-lang/compiler-builtins/pull/248
+[core]: https://github.com/rust-lang/libm/milestone/2
+
+## Already usable
+
+This crate is [on crates.io] and can be used today in stable `#![no_std]` programs.
+
+The API documentation can be found [here](https://docs.rs/libm).
+
+[on crates.io]: https://crates.io/crates/libm
+
+## Benchmark
+[benchmark]: #benchmark
+
+The benchmarks are located in `crates/libm-bench` and require a nightly Rust toolchain.
+To run all benchmarks:
+
+> cargo +nightly bench --all
+
+## Contributing
+
+Please check [CONTRIBUTING.md](CONTRIBUTING.md)
+
+## License
+
+Licensed under either of
+
+- Apache License, Version 2.0 ([LICENSE-APACHE](LICENSE-APACHE) or
+ http://www.apache.org/licenses/LICENSE-2.0)
+- MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
+
+at your option.
+
+### Contribution
+
+Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the
+work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any
+additional terms or conditions.
diff --git a/build.rs b/build.rs
new file mode 100644
index 0000000..9af6dec
--- /dev/null
+++ b/build.rs
@@ -0,0 +1,444 @@
+use std::env;
+
+fn main() {
+ println!("cargo:rerun-if-changed=build.rs");
+
+ #[cfg(feature = "musl-reference-tests")]
+ musl_reference_tests::generate();
+
+ if !cfg!(feature = "checked") {
+ let lvl = env::var("OPT_LEVEL").unwrap();
+ if lvl != "0" {
+ println!("cargo:rustc-cfg=assert_no_panic");
+ }
+ }
+}
+
+#[cfg(feature = "musl-reference-tests")]
+mod musl_reference_tests {
+ use rand::seq::SliceRandom;
+ use rand::Rng;
+ use std::fs;
+ use std::process::Command;
+
+ // Number of tests to generate for each function
+ const NTESTS: usize = 500;
+
+ // These files are all internal functions or otherwise miscellaneous, not
+ // defining a function we want to test.
+ const IGNORED_FILES: &[&str] = &["fenv.rs"];
+
+ struct Function {
+ name: String,
+ args: Vec<Ty>,
+ ret: Vec<Ty>,
+ tests: Vec<Test>,
+ }
+
+ enum Ty {
+ F32,
+ F64,
+ I32,
+ Bool,
+ }
+
+ struct Test {
+ inputs: Vec<i64>,
+ outputs: Vec<i64>,
+ }
+
+ pub fn generate() {
+ let files = fs::read_dir("src/math")
+ .unwrap()
+ .map(|f| f.unwrap().path())
+ .collect::<Vec<_>>();
+
+ let mut math = Vec::new();
+ for file in files {
+ if IGNORED_FILES.iter().any(|f| file.ends_with(f)) {
+ continue;
+ }
+
+ println!("generating musl reference tests in {:?}", file);
+
+ let contents = fs::read_to_string(file).unwrap();
+ let mut functions = contents.lines().filter(|f| f.starts_with("pub fn"));
+ while let Some(function_to_test) = functions.next() {
+ math.push(parse(function_to_test));
+ }
+ }
+
+ // Generate a bunch of random inputs for each function. This will
+ // attempt to generate a good set of uniform test cases for exercising
+ // all the various functionality.
+ generate_random_tests(&mut math, &mut rand::thread_rng());
+
+ // After we have all our inputs, use the x86_64-unknown-linux-musl
+ // target to generate the expected output.
+ generate_test_outputs(&mut math);
+ //panic!("Boo");
+ // ... and now that we have both inputs and expected outputs, do a bunch
+ // of codegen to create the unit tests which we'll actually execute.
+ generate_unit_tests(&math);
+ }
+
+ /// A "poor man's" parser for the signature of a function
+ fn parse(s: &str) -> Function {
+ let s = eat(s, "pub fn ");
+ let pos = s.find('(').unwrap();
+ let name = &s[..pos];
+ let s = &s[pos + 1..];
+ let end = s.find(')').unwrap();
+ let args = s[..end]
+ .split(',')
+ .map(|arg| {
+ let colon = arg.find(':').unwrap();
+ parse_ty(arg[colon + 1..].trim())
+ })
+ .collect::<Vec<_>>();
+ let tail = &s[end + 1..];
+ let tail = eat(tail, " -> ");
+ let ret = parse_retty(tail.replace("{", "").trim());
+
+ return Function {
+ name: name.to_string(),
+ args,
+ ret,
+ tests: Vec::new(),
+ };
+
+ fn parse_ty(s: &str) -> Ty {
+ match s {
+ "f32" => Ty::F32,
+ "f64" => Ty::F64,
+ "i32" => Ty::I32,
+ "bool" => Ty::Bool,
+ other => panic!("unknown type `{}`", other),
+ }
+ }
+
+ fn parse_retty(s: &str) -> Vec<Ty> {
+ match s {
+ "(f32, f32)" => vec![Ty::F32, Ty::F32],
+ "(f32, i32)" => vec![Ty::F32, Ty::I32],
+ "(f64, f64)" => vec![Ty::F64, Ty::F64],
+ "(f64, i32)" => vec![Ty::F64, Ty::I32],
+ other => vec![parse_ty(other)],
+ }
+ }
+
+ fn eat<'a>(s: &'a str, prefix: &str) -> &'a str {
+ if s.starts_with(prefix) {
+ &s[prefix.len()..]
+ } else {
+ panic!("{:?} didn't start with {:?}", s, prefix)
+ }
+ }
+ }
+
+ fn generate_random_tests<R: Rng>(functions: &mut [Function], rng: &mut R) {
+ for function in functions {
+ for _ in 0..NTESTS {
+ function.tests.push(generate_test(function, rng));
+ }
+ }
+
+ fn generate_test<R: Rng>(function: &Function, rng: &mut R) -> Test {
+ let mut inputs = function
+ .args
+ .iter()
+ .map(|ty| ty.gen_i64(rng))
+ .collect::<Vec<_>>();
+
+ // First argument to this function appears to be a number of
+ // iterations, so passing in massive random numbers causes it to
+ // take forever to execute, so make sure we're not running random
+ // math code until the heat death of the universe.
+ if function.name == "jn" || function.name == "jnf" {
+ inputs[0] &= 0xffff;
+ }
+
+ Test {
+ inputs,
+ // zero output for now since we'll generate it later
+ outputs: vec![],
+ }
+ }
+ }
+
+ impl Ty {
+ fn gen_i64<R: Rng>(&self, r: &mut R) -> i64 {
+ use std::f32;
+ use std::f64;
+
+ return match self {
+ Ty::F32 => {
+ if r.gen_range(0, 20) < 1 {
+ let i = *[f32::NAN, f32::INFINITY, f32::NEG_INFINITY]
+ .choose(r)
+ .unwrap();
+ i.to_bits().into()
+ } else {
+ r.gen::<f32>().to_bits().into()
+ }
+ }
+ Ty::F64 => {
+ if r.gen_range(0, 20) < 1 {
+ let i = *[f64::NAN, f64::INFINITY, f64::NEG_INFINITY]
+ .choose(r)
+ .unwrap();
+ i.to_bits() as i64
+ } else {
+ r.gen::<f64>().to_bits() as i64
+ }
+ }
+ Ty::I32 => {
+ if r.gen_range(0, 10) < 1 {
+ let i = *[i32::max_value(), 0, i32::min_value()].choose(r).unwrap();
+ i.into()
+ } else {
+ r.gen::<i32>().into()
+ }
+ }
+ Ty::Bool => r.gen::<bool>() as i64,
+ };
+ }
+
+ fn libc_ty(&self) -> &'static str {
+ match self {
+ Ty::F32 => "f32",
+ Ty::F64 => "f64",
+ Ty::I32 => "i32",
+ Ty::Bool => "i32",
+ }
+ }
+
+ fn libc_pty(&self) -> &'static str {
+ match self {
+ Ty::F32 => "*mut f32",
+ Ty::F64 => "*mut f64",
+ Ty::I32 => "*mut i32",
+ Ty::Bool => "*mut i32",
+ }
+ }
+
+ fn default(&self) -> &'static str {
+ match self {
+ Ty::F32 => "0_f32",
+ Ty::F64 => "0_f64",
+ Ty::I32 => "0_i32",
+ Ty::Bool => "false",
+ }
+ }
+
+ fn to_i64(&self) -> &'static str {
+ match self {
+ Ty::F32 => ".to_bits() as i64",
+ Ty::F64 => ".to_bits() as i64",
+ Ty::I32 => " as i64",
+ Ty::Bool => " as i64",
+ }
+ }
+ }
+
+ fn generate_test_outputs(functions: &mut [Function]) {
+ let mut src = String::new();
+ let dst = std::env::var("OUT_DIR").unwrap();
+
+ // Generate a program which will run all tests with all inputs in
+ // `functions`. This program will write all outputs to stdout (in a
+ // binary format).
+ src.push_str("use std::io::Write;");
+ src.push_str("fn main() {");
+ src.push_str("let mut result = Vec::new();");
+ for function in functions.iter_mut() {
+ src.push_str("unsafe {");
+ src.push_str("extern { fn ");
+ src.push_str(&function.name);
+ src.push_str("(");
+
+ let (ret, retptr) = match function.name.as_str() {
+ "sincos" | "sincosf" => (None, &function.ret[..]),
+ _ => (Some(&function.ret[0]), &function.ret[1..]),
+ };
+ for (i, arg) in function.args.iter().enumerate() {
+ src.push_str(&format!("arg{}: {},", i, arg.libc_ty()));
+ }
+ for (i, ret) in retptr.iter().enumerate() {
+ src.push_str(&format!("argret{}: {},", i, ret.libc_pty()));
+ }
+ src.push_str(")");
+ if let Some(ty) = ret {
+ src.push_str(" -> ");
+ src.push_str(ty.libc_ty());
+ }
+ src.push_str("; }");
+
+ src.push_str(&format!("static TESTS: &[[i64; {}]]", function.args.len()));
+ src.push_str(" = &[");
+ for test in function.tests.iter() {
+ src.push_str("[");
+ for val in test.inputs.iter() {
+ src.push_str(&val.to_string());
+ src.push_str(",");
+ }
+ src.push_str("],");
+ }
+ src.push_str("];");
+
+ src.push_str("for test in TESTS {");
+ for (i, arg) in retptr.iter().enumerate() {
+ src.push_str(&format!("let mut argret{} = {};", i, arg.default()));
+ }
+ src.push_str("let output = ");
+ src.push_str(&function.name);
+ src.push_str("(");
+ for (i, arg) in function.args.iter().enumerate() {
+ src.push_str(&match arg {
+ Ty::F32 => format!("f32::from_bits(test[{}] as u32)", i),
+ Ty::F64 => format!("f64::from_bits(test[{}] as u64)", i),
+ Ty::I32 => format!("test[{}] as i32", i),
+ Ty::Bool => format!("test[{}] as i32", i),
+ });
+ src.push_str(",");
+ }
+ for (i, _) in retptr.iter().enumerate() {
+ src.push_str(&format!("&mut argret{},", i));
+ }
+ src.push_str(");");
+ if let Some(ty) = &ret {
+ src.push_str(&format!("let output = output{};", ty.to_i64()));
+ src.push_str("result.extend_from_slice(&output.to_le_bytes());");
+ }
+
+ for (i, ret) in retptr.iter().enumerate() {
+ src.push_str(&format!(
+ "result.extend_from_slice(&(argret{}{}).to_le_bytes());",
+ i,
+ ret.to_i64(),
+ ));
+ }
+ src.push_str("}");
+
+ src.push_str("}");
+ }
+
+ src.push_str("std::io::stdout().write_all(&result).unwrap();");
+
+ src.push_str("}");
+
+ let path = format!("{}/gen.rs", dst);
+ fs::write(&path, src).unwrap();
+
+ // Make it somewhat pretty if something goes wrong
+ drop(Command::new("rustfmt").arg(&path).status());
+
+ // Compile and execute this tests for the musl target, assuming we're an
+ // x86_64 host effectively.
+ let status = Command::new("rustc")
+ .current_dir(&dst)
+ .arg(&path)
+ .arg("--target=x86_64-unknown-linux-musl")
+ .status()
+ .unwrap();
+ assert!(status.success());
+ let output = Command::new("./gen").current_dir(&dst).output().unwrap();
+ assert!(output.status.success());
+ assert!(output.stderr.is_empty());
+
+ // Map all the output bytes back to an `i64` and then shove it all into
+ // the expected results.
+ let mut results = output.stdout.chunks_exact(8).map(|buf| {
+ let mut exact = [0; 8];
+ exact.copy_from_slice(buf);
+ i64::from_le_bytes(exact)
+ });
+
+ for f in functions.iter_mut() {
+ for test in f.tests.iter_mut() {
+ test.outputs = (0..f.ret.len()).map(|_| results.next().unwrap()).collect();
+ }
+ }
+ assert!(results.next().is_none());
+ }
+
+ /// Codegens a file which has a ton of `#[test]` annotations for all the
+ /// tests that we generated above.
+ fn generate_unit_tests(functions: &[Function]) {
+ let mut src = String::new();
+ let dst = std::env::var("OUT_DIR").unwrap();
+
+ for function in functions {
+ src.push_str("#[test]");
+ src.push_str("fn ");
+ src.push_str(&function.name);
+ src.push_str("_matches_musl() {");
+ src.push_str(&format!(
+ "static TESTS: &[([i64; {}], [i64; {}])]",
+ function.args.len(),
+ function.ret.len(),
+ ));
+ src.push_str(" = &[");
+ for test in function.tests.iter() {
+ src.push_str("([");
+ for val in test.inputs.iter() {
+ src.push_str(&val.to_string());
+ src.push_str(",");
+ }
+ src.push_str("],");
+ src.push_str("[");
+ for val in test.outputs.iter() {
+ src.push_str(&val.to_string());
+ src.push_str(",");
+ }
+ src.push_str("],");
+ src.push_str("),");
+ }
+ src.push_str("];");
+
+ src.push_str("for (test, expected) in TESTS {");
+ src.push_str("let output = ");
+ src.push_str(&function.name);
+ src.push_str("(");
+ for (i, arg) in function.args.iter().enumerate() {
+ src.push_str(&match arg {
+ Ty::F32 => format!("f32::from_bits(test[{}] as u32)", i),
+ Ty::F64 => format!("f64::from_bits(test[{}] as u64)", i),
+ Ty::I32 => format!("test[{}] as i32", i),
+ Ty::Bool => format!("test[{}] as i32", i),
+ });
+ src.push_str(",");
+ }
+ src.push_str(");");
+
+ for (i, ret) in function.ret.iter().enumerate() {
+ let get = if function.ret.len() == 1 {
+ String::new()
+ } else {
+ format!(".{}", i)
+ };
+ src.push_str(&(match ret {
+ Ty::F32 => format!("if _eqf(output{}, f32::from_bits(expected[{}] as u32)).is_ok() {{ continue }}", get, i),
+ Ty::F64 => format!("if _eq(output{}, f64::from_bits(expected[{}] as u64)).is_ok() {{ continue }}", get, i),
+ Ty::I32 => format!("if output{} as i64 == expected[{}] {{ continue }}", get, i),
+ Ty::Bool => unreachable!(),
+ }));
+ }
+
+ src.push_str(
+ r#"
+ panic!("INPUT: {:?} EXPECTED: {:?} ACTUAL {:?}", test, expected, output);
+ "#,
+ );
+ src.push_str("}");
+
+ src.push_str("}");
+ }
+
+ let path = format!("{}/musl-tests.rs", dst);
+ fs::write(&path, src).unwrap();
+
+ // Try to make it somewhat pretty
+ drop(Command::new("rustfmt").arg(&path).status());
+ }
+}
diff --git a/ci/docker/aarch64-unknown-linux-gnu/Dockerfile b/ci/docker/aarch64-unknown-linux-gnu/Dockerfile
new file mode 100644
index 0000000..9e2559f
--- /dev/null
+++ b/ci/docker/aarch64-unknown-linux-gnu/Dockerfile
@@ -0,0 +1,10 @@
+FROM ubuntu:18.04
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ gcc libc6-dev ca-certificates \
+ gcc-aarch64-linux-gnu libc6-dev-arm64-cross \
+ qemu-user-static
+ENV CARGO_TARGET_AARCH64_UNKNOWN_LINUX_GNU_LINKER=aarch64-linux-gnu-gcc \
+ CARGO_TARGET_AARCH64_UNKNOWN_LINUX_GNU_RUNNER=qemu-aarch64-static \
+ QEMU_LD_PREFIX=/usr/aarch64-linux-gnu \
+ RUST_TEST_THREADS=1
diff --git a/ci/docker/arm-unknown-linux-gnueabi/Dockerfile b/ci/docker/arm-unknown-linux-gnueabi/Dockerfile
new file mode 100644
index 0000000..afab874
--- /dev/null
+++ b/ci/docker/arm-unknown-linux-gnueabi/Dockerfile
@@ -0,0 +1,9 @@
+FROM ubuntu:18.04
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ gcc libc6-dev ca-certificates \
+ gcc-arm-linux-gnueabi libc6-dev-armel-cross qemu-user-static
+ENV CARGO_TARGET_ARM_UNKNOWN_LINUX_GNUEABI_LINKER=arm-linux-gnueabi-gcc \
+ CARGO_TARGET_ARM_UNKNOWN_LINUX_GNUEABI_RUNNER=qemu-arm-static \
+ QEMU_LD_PREFIX=/usr/arm-linux-gnueabi \
+ RUST_TEST_THREADS=1
diff --git a/ci/docker/arm-unknown-linux-gnueabihf/Dockerfile b/ci/docker/arm-unknown-linux-gnueabihf/Dockerfile
new file mode 100644
index 0000000..3ed3602
--- /dev/null
+++ b/ci/docker/arm-unknown-linux-gnueabihf/Dockerfile
@@ -0,0 +1,9 @@
+FROM ubuntu:18.04
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ gcc libc6-dev ca-certificates \
+ gcc-arm-linux-gnueabihf libc6-dev-armhf-cross qemu-user-static
+ENV CARGO_TARGET_ARM_UNKNOWN_LINUX_GNUEABIHF_LINKER=arm-linux-gnueabihf-gcc \
+ CARGO_TARGET_ARM_UNKNOWN_LINUX_GNUEABIHF_RUNNER=qemu-arm-static \
+ QEMU_LD_PREFIX=/usr/arm-linux-gnueabihf \
+ RUST_TEST_THREADS=1
diff --git a/ci/docker/armv7-unknown-linux-gnueabihf/Dockerfile b/ci/docker/armv7-unknown-linux-gnueabihf/Dockerfile
new file mode 100644
index 0000000..6617af1
--- /dev/null
+++ b/ci/docker/armv7-unknown-linux-gnueabihf/Dockerfile
@@ -0,0 +1,9 @@
+FROM ubuntu:18.04
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ gcc libc6-dev ca-certificates \
+ gcc-arm-linux-gnueabihf libc6-dev-armhf-cross qemu-user-static
+ENV CARGO_TARGET_ARMV7_UNKNOWN_LINUX_GNUEABIHF_LINKER=arm-linux-gnueabihf-gcc \
+ CARGO_TARGET_ARMV7_UNKNOWN_LINUX_GNUEABIHF_RUNNER=qemu-arm-static \
+ QEMU_LD_PREFIX=/usr/arm-linux-gnueabihf \
+ RUST_TEST_THREADS=1
diff --git a/ci/docker/i686-unknown-linux-gnu/Dockerfile b/ci/docker/i686-unknown-linux-gnu/Dockerfile
new file mode 100644
index 0000000..5783e28
--- /dev/null
+++ b/ci/docker/i686-unknown-linux-gnu/Dockerfile
@@ -0,0 +1,4 @@
+FROM ubuntu:18.04
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ gcc-multilib libc6-dev ca-certificates
diff --git a/ci/docker/mips-unknown-linux-gnu/Dockerfile b/ci/docker/mips-unknown-linux-gnu/Dockerfile
new file mode 100644
index 0000000..f47e8f5
--- /dev/null
+++ b/ci/docker/mips-unknown-linux-gnu/Dockerfile
@@ -0,0 +1,12 @@
+FROM ubuntu:18.04
+
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ gcc libc6-dev ca-certificates \
+ gcc-mips-linux-gnu libc6-dev-mips-cross \
+ binfmt-support qemu-user-static qemu-system-mips
+
+ENV CARGO_TARGET_MIPS_UNKNOWN_LINUX_GNU_LINKER=mips-linux-gnu-gcc \
+ CARGO_TARGET_MIPS_UNKNOWN_LINUX_GNU_RUNNER=qemu-mips-static \
+ QEMU_LD_PREFIX=/usr/mips-linux-gnu \
+ RUST_TEST_THREADS=1
diff --git a/ci/docker/mips64-unknown-linux-gnuabi64/Dockerfile b/ci/docker/mips64-unknown-linux-gnuabi64/Dockerfile
new file mode 100644
index 0000000..8fa77c7
--- /dev/null
+++ b/ci/docker/mips64-unknown-linux-gnuabi64/Dockerfile
@@ -0,0 +1,15 @@
+FROM ubuntu:18.04
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ ca-certificates \
+ gcc \
+ gcc-mips64-linux-gnuabi64 \
+ libc6-dev \
+ libc6-dev-mips64-cross \
+ qemu-user-static \
+ qemu-system-mips
+ENV CARGO_TARGET_MIPS64_UNKNOWN_LINUX_GNUABI64_LINKER=mips64-linux-gnuabi64-gcc \
+ CARGO_TARGET_MIPS64_UNKNOWN_LINUX_GNUABI64_RUNNER=qemu-mips64-static \
+ CC_mips64_unknown_linux_gnuabi64=mips64-linux-gnuabi64-gcc \
+ QEMU_LD_PREFIX=/usr/mips64-linux-gnuabi64 \
+ RUST_TEST_THREADS=1
diff --git a/ci/docker/mips64el-unknown-linux-gnuabi64/Dockerfile b/ci/docker/mips64el-unknown-linux-gnuabi64/Dockerfile
new file mode 100644
index 0000000..c6611d9
--- /dev/null
+++ b/ci/docker/mips64el-unknown-linux-gnuabi64/Dockerfile
@@ -0,0 +1,14 @@
+FROM ubuntu:18.04
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ ca-certificates \
+ gcc \
+ gcc-mips64el-linux-gnuabi64 \
+ libc6-dev \
+ libc6-dev-mips64el-cross \
+ qemu-user-static
+ENV CARGO_TARGET_MIPS64EL_UNKNOWN_LINUX_GNUABI64_LINKER=mips64el-linux-gnuabi64-gcc \
+ CARGO_TARGET_MIPS64EL_UNKNOWN_LINUX_GNUABI64_RUNNER=qemu-mips64el-static \
+ CC_mips64el_unknown_linux_gnuabi64=mips64el-linux-gnuabi64-gcc \
+ QEMU_LD_PREFIX=/usr/mips64el-linux-gnuabi64 \
+ RUST_TEST_THREADS=1
diff --git a/ci/docker/mipsel-unknown-linux-gnu/Dockerfile b/ci/docker/mipsel-unknown-linux-gnu/Dockerfile
new file mode 100644
index 0000000..0bc6956
--- /dev/null
+++ b/ci/docker/mipsel-unknown-linux-gnu/Dockerfile
@@ -0,0 +1,12 @@
+FROM ubuntu:18.04
+
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ gcc libc6-dev ca-certificates \
+ gcc-mipsel-linux-gnu libc6-dev-mipsel-cross \
+ binfmt-support qemu-user-static
+
+ENV CARGO_TARGET_MIPSEL_UNKNOWN_LINUX_GNU_LINKER=mipsel-linux-gnu-gcc \
+ CARGO_TARGET_MIPSEL_UNKNOWN_LINUX_GNU_RUNNER=qemu-mipsel-static \
+ QEMU_LD_PREFIX=/usr/mipsel-linux-gnu \
+ RUST_TEST_THREADS=1
diff --git a/ci/docker/powerpc-unknown-linux-gnu/Dockerfile b/ci/docker/powerpc-unknown-linux-gnu/Dockerfile
new file mode 100644
index 0000000..2d39fef
--- /dev/null
+++ b/ci/docker/powerpc-unknown-linux-gnu/Dockerfile
@@ -0,0 +1,12 @@
+FROM ubuntu:18.04
+
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ gcc libc6-dev qemu-user-static ca-certificates \
+ gcc-powerpc-linux-gnu libc6-dev-powerpc-cross \
+ qemu-system-ppc
+
+ENV CARGO_TARGET_POWERPC_UNKNOWN_LINUX_GNU_LINKER=powerpc-linux-gnu-gcc \
+ CARGO_TARGET_POWERPC_UNKNOWN_LINUX_GNU_RUNNER=qemu-ppc-static \
+ QEMU_LD_PREFIX=/usr/powerpc-linux-gnu \
+ RUST_TEST_THREADS=1
diff --git a/ci/docker/powerpc64-unknown-linux-gnu/Dockerfile b/ci/docker/powerpc64-unknown-linux-gnu/Dockerfile
new file mode 100644
index 0000000..653cd35
--- /dev/null
+++ b/ci/docker/powerpc64-unknown-linux-gnu/Dockerfile
@@ -0,0 +1,13 @@
+FROM ubuntu:18.04
+
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ gcc libc6-dev ca-certificates \
+ gcc-powerpc64-linux-gnu libc6-dev-ppc64-cross \
+ binfmt-support qemu-user-static qemu-system-ppc
+
+ENV CARGO_TARGET_POWERPC64_UNKNOWN_LINUX_GNU_LINKER=powerpc64-linux-gnu-gcc \
+ CARGO_TARGET_POWERPC64_UNKNOWN_LINUX_GNU_RUNNER=qemu-ppc64-static \
+ CC_powerpc64_unknown_linux_gnu=powerpc64-linux-gnu-gcc \
+ QEMU_LD_PREFIX=/usr/powerpc64-linux-gnu \
+ RUST_TEST_THREADS=1
diff --git a/ci/docker/powerpc64le-unknown-linux-gnu/Dockerfile b/ci/docker/powerpc64le-unknown-linux-gnu/Dockerfile
new file mode 100644
index 0000000..63ea9af
--- /dev/null
+++ b/ci/docker/powerpc64le-unknown-linux-gnu/Dockerfile
@@ -0,0 +1,13 @@
+FROM ubuntu:18.04
+
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ gcc libc6-dev qemu-user-static ca-certificates \
+ gcc-powerpc64le-linux-gnu libc6-dev-ppc64el-cross \
+ qemu-system-ppc
+
+ENV CARGO_TARGET_POWERPC64LE_UNKNOWN_LINUX_GNU_LINKER=powerpc64le-linux-gnu-gcc \
+ CARGO_TARGET_POWERPC64LE_UNKNOWN_LINUX_GNU_RUNNER=qemu-ppc64le-static \
+ QEMU_CPU=POWER8 \
+ QEMU_LD_PREFIX=/usr/powerpc64le-linux-gnu \
+ RUST_TEST_THREADS=1
diff --git a/ci/docker/x86_64-unknown-linux-gnu/Dockerfile b/ci/docker/x86_64-unknown-linux-gnu/Dockerfile
new file mode 100644
index 0000000..98000f4
--- /dev/null
+++ b/ci/docker/x86_64-unknown-linux-gnu/Dockerfile
@@ -0,0 +1,4 @@
+FROM ubuntu:18.04
+RUN apt-get update && \
+ apt-get install -y --no-install-recommends \
+ gcc libc6-dev ca-certificates
diff --git a/ci/run-docker.sh b/ci/run-docker.sh
new file mode 100755
index 0000000..e7b80c7
--- /dev/null
+++ b/ci/run-docker.sh
@@ -0,0 +1,37 @@
+# Small script to run tests for a target (or all targets) inside all the
+# respective docker images.
+
+set -ex
+
+run() {
+ local target=$1
+
+ echo $target
+
+ # This directory needs to exist before calling docker, otherwise docker will create it but it
+ # will be owned by root
+ mkdir -p target
+
+ docker build -t $target ci/docker/$target
+ docker run \
+ --rm \
+ --user $(id -u):$(id -g) \
+ -e CARGO_HOME=/cargo \
+ -e CARGO_TARGET_DIR=/target \
+ -v $(dirname $(dirname `which cargo`)):/cargo \
+ -v `pwd`/target:/target \
+ -v `pwd`:/checkout:ro \
+ -v `rustc --print sysroot`:/rust:ro \
+ --init \
+ -w /checkout \
+ $target \
+ sh -c "HOME=/tmp PATH=\$PATH:/rust/bin exec ci/run.sh $target"
+}
+
+if [ -z "$1" ]; then
+ for d in `ls ci/docker/`; do
+ run $d
+ done
+else
+ run $1
+fi
diff --git a/ci/run.sh b/ci/run.sh
new file mode 100755
index 0000000..ed253ab
--- /dev/null
+++ b/ci/run.sh
@@ -0,0 +1,18 @@
+#!/usr/bin/env sh
+
+set -ex
+TARGET=$1
+
+CMD="cargo test --all --target $TARGET"
+
+# stable by default
+$CMD
+$CMD --release
+
+# unstable with a feature
+$CMD --features 'unstable'
+$CMD --release --features 'unstable'
+
+# also run the reference tests
+$CMD --features 'unstable musl-reference-tests'
+$CMD --release --features 'unstable musl-reference-tests'
diff --git a/src/lib.rs b/src/lib.rs
new file mode 100644
index 0000000..e228af9
--- /dev/null
+++ b/src/lib.rs
@@ -0,0 +1,58 @@
+//! libm in pure Rust
+#![deny(warnings)]
+#![no_std]
+#![cfg_attr(
+ all(target_arch = "wasm32", feature = "unstable"),
+ feature(core_intrinsics)
+)]
+#![allow(clippy::unreadable_literal)]
+#![allow(clippy::many_single_char_names)]
+#![allow(clippy::needless_return)]
+#![allow(clippy::int_plus_one)]
+#![allow(clippy::deprecated_cfg_attr)]
+#![allow(clippy::mixed_case_hex_literals)]
+#![allow(clippy::float_cmp)]
+#![allow(clippy::eq_op)]
+#![allow(clippy::assign_op_pattern)]
+
+mod math;
+
+use core::{f32, f64};
+
+pub use self::math::*;
+
+/// Approximate equality with 1 ULP of tolerance
+#[doc(hidden)]
+#[inline]
+pub fn _eqf(a: f32, b: f32) -> Result<(), u32> {
+ if a.is_nan() && b.is_nan() {
+ Ok(())
+ } else {
+ let err = (a.to_bits() as i32).wrapping_sub(b.to_bits() as i32).abs();
+
+ if err <= 1 {
+ Ok(())
+ } else {
+ Err(err as u32)
+ }
+ }
+}
+
+#[doc(hidden)]
+#[inline]
+pub fn _eq(a: f64, b: f64) -> Result<(), u64> {
+ if a.is_nan() && b.is_nan() {
+ Ok(())
+ } else {
+ let err = (a.to_bits() as i64).wrapping_sub(b.to_bits() as i64).abs();
+
+ if err <= 1 {
+ Ok(())
+ } else {
+ Err(err as u64)
+ }
+ }
+}
+
+#[cfg(all(test, feature = "musl-reference-tests"))]
+include!(concat!(env!("OUT_DIR"), "/musl-tests.rs"));
diff --git a/src/math/acos.rs b/src/math/acos.rs
new file mode 100644
index 0000000..23b1325
--- /dev/null
+++ b/src/math/acos.rs
@@ -0,0 +1,112 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* acos(x)
+ * Method :
+ * acos(x) = pi/2 - asin(x)
+ * acos(-x) = pi/2 + asin(x)
+ * For |x|<=0.5
+ * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
+ * For x>0.5
+ * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
+ * = 2asin(sqrt((1-x)/2))
+ * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
+ * = 2f + (2c + 2s*z*R(z))
+ * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
+ * for f so that f+c ~ sqrt(z).
+ * For x<-0.5
+ * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
+ * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ *
+ * Function needed: sqrt
+ */
+
+use super::sqrt;
+
+const PIO2_HI: f64 = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
+const PIO2_LO: f64 = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
+const PS0: f64 = 1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */
+const PS1: f64 = -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */
+const PS2: f64 = 2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */
+const PS3: f64 = -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */
+const PS4: f64 = 7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */
+const PS5: f64 = 3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */
+const QS1: f64 = -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */
+const QS2: f64 = 2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */
+const QS3: f64 = -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */
+const QS4: f64 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+fn r(z: f64) -> f64 {
+ let p: f64 = z * (PS0 + z * (PS1 + z * (PS2 + z * (PS3 + z * (PS4 + z * PS5)))));
+ let q: f64 = 1.0 + z * (QS1 + z * (QS2 + z * (QS3 + z * QS4)));
+ p / q
+}
+
+/// Arccosine (f64)
+///
+/// Computes the inverse cosine (arc cosine) of the input value.
+/// Arguments must be in the range -1 to 1.
+/// Returns values in radians, in the range of 0 to pi.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn acos(x: f64) -> f64 {
+ let x1p_120f = f64::from_bits(0x3870000000000000); // 0x1p-120 === 2 ^ -120
+ let z: f64;
+ let w: f64;
+ let s: f64;
+ let c: f64;
+ let df: f64;
+ let hx: u32;
+ let ix: u32;
+
+ hx = (x.to_bits() >> 32) as u32;
+ ix = hx & 0x7fffffff;
+ /* |x| >= 1 or nan */
+ if ix >= 0x3ff00000 {
+ let lx: u32 = x.to_bits() as u32;
+
+ if ((ix - 0x3ff00000) | lx) == 0 {
+ /* acos(1)=0, acos(-1)=pi */
+ if (hx >> 31) != 0 {
+ return 2. * PIO2_HI + x1p_120f;
+ }
+ return 0.;
+ }
+ return 0. / (x - x);
+ }
+ /* |x| < 0.5 */
+ if ix < 0x3fe00000 {
+ if ix <= 0x3c600000 {
+ /* |x| < 2**-57 */
+ return PIO2_HI + x1p_120f;
+ }
+ return PIO2_HI - (x - (PIO2_LO - x * r(x * x)));
+ }
+ /* x < -0.5 */
+ if (hx >> 31) != 0 {
+ z = (1.0 + x) * 0.5;
+ s = sqrt(z);
+ w = r(z) * s - PIO2_LO;
+ return 2. * (PIO2_HI - (s + w));
+ }
+ /* x > 0.5 */
+ z = (1.0 - x) * 0.5;
+ s = sqrt(z);
+ // Set the low 4 bytes to zero
+ df = f64::from_bits(s.to_bits() & 0xff_ff_ff_ff_00_00_00_00);
+
+ c = (z - df * df) / (s + df);
+ w = r(z) * s + c;
+ 2. * (df + w)
+}
diff --git a/src/math/acosf.rs b/src/math/acosf.rs
new file mode 100644
index 0000000..1a60479
--- /dev/null
+++ b/src/math/acosf.rs
@@ -0,0 +1,79 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_acosf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::sqrtf::sqrtf;
+
+const PIO2_HI: f32 = 1.5707962513e+00; /* 0x3fc90fda */
+const PIO2_LO: f32 = 7.5497894159e-08; /* 0x33a22168 */
+const P_S0: f32 = 1.6666586697e-01;
+const P_S1: f32 = -4.2743422091e-02;
+const P_S2: f32 = -8.6563630030e-03;
+const Q_S1: f32 = -7.0662963390e-01;
+
+fn r(z: f32) -> f32 {
+ let p = z * (P_S0 + z * (P_S1 + z * P_S2));
+ let q = 1. + z * Q_S1;
+ p / q
+}
+
+/// Arccosine (f32)
+///
+/// Computes the inverse cosine (arc cosine) of the input value.
+/// Arguments must be in the range -1 to 1.
+/// Returns values in radians, in the range of 0 to pi.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn acosf(x: f32) -> f32 {
+ let x1p_120 = f32::from_bits(0x03800000); // 0x1p-120 === 2 ^ (-120)
+
+ let z: f32;
+ let w: f32;
+ let s: f32;
+
+ let mut hx = x.to_bits();
+ let ix = hx & 0x7fffffff;
+ /* |x| >= 1 or nan */
+ if ix >= 0x3f800000 {
+ if ix == 0x3f800000 {
+ if (hx >> 31) != 0 {
+ return 2. * PIO2_HI + x1p_120;
+ }
+ return 0.;
+ }
+ return 0. / (x - x);
+ }
+ /* |x| < 0.5 */
+ if ix < 0x3f000000 {
+ if ix <= 0x32800000 {
+ /* |x| < 2**-26 */
+ return PIO2_HI + x1p_120;
+ }
+ return PIO2_HI - (x - (PIO2_LO - x * r(x * x)));
+ }
+ /* x < -0.5 */
+ if (hx >> 31) != 0 {
+ z = (1. + x) * 0.5;
+ s = sqrtf(z);
+ w = r(z) * s - PIO2_LO;
+ return 2. * (PIO2_HI - (s + w));
+ }
+ /* x > 0.5 */
+ z = (1. - x) * 0.5;
+ s = sqrtf(z);
+ hx = s.to_bits();
+ let df = f32::from_bits(hx & 0xfffff000);
+ let c = (z - df * df) / (s + df);
+ w = r(z) * s + c;
+ 2. * (df + w)
+}
diff --git a/src/math/acosh.rs b/src/math/acosh.rs
new file mode 100644
index 0000000..ac7a5f1
--- /dev/null
+++ b/src/math/acosh.rs
@@ -0,0 +1,26 @@
+use super::{log, log1p, sqrt};
+
+const LN2: f64 = 0.693147180559945309417232121458176568; /* 0x3fe62e42, 0xfefa39ef*/
+
+/// Inverse hyperbolic cosine (f64)
+///
+/// Calculates the inverse hyperbolic cosine of `x`.
+/// Is defined as `log(x + sqrt(x*x-1))`.
+/// `x` must be a number greater than or equal to 1.
+pub fn acosh(x: f64) -> f64 {
+ let u = x.to_bits();
+ let e = ((u >> 52) as usize) & 0x7ff;
+
+ /* x < 1 domain error is handled in the called functions */
+
+ if e < 0x3ff + 1 {
+ /* |x| < 2, up to 2ulp error in [1,1.125] */
+ return log1p(x - 1.0 + sqrt((x - 1.0) * (x - 1.0) + 2.0 * (x - 1.0)));
+ }
+ if e < 0x3ff + 26 {
+ /* |x| < 0x1p26 */
+ return log(2.0 * x - 1.0 / (x + sqrt(x * x - 1.0)));
+ }
+ /* |x| >= 0x1p26 or nan */
+ return log(x) + LN2;
+}
diff --git a/src/math/acoshf.rs b/src/math/acoshf.rs
new file mode 100644
index 0000000..0879e1e
--- /dev/null
+++ b/src/math/acoshf.rs
@@ -0,0 +1,25 @@
+use super::{log1pf, logf, sqrtf};
+
+const LN2: f32 = 0.693147180559945309417232121458176568;
+
+/// Inverse hyperbolic cosine (f32)
+///
+/// Calculates the inverse hyperbolic cosine of `x`.
+/// Is defined as `log(x + sqrt(x*x-1))`.
+/// `x` must be a number greater than or equal to 1.
+pub fn acoshf(x: f32) -> f32 {
+ let u = x.to_bits();
+ let a = u & 0x7fffffff;
+
+ if a < 0x3f800000 + (1 << 23) {
+ /* |x| < 2, invalid if x < 1 or nan */
+ /* up to 2ulp error in [1,1.125] */
+ return log1pf(x - 1.0 + sqrtf((x - 1.0) * (x - 1.0) + 2.0 * (x - 1.0)));
+ }
+ if a < 0x3f800000 + (12 << 23) {
+ /* |x| < 0x1p12 */
+ return logf(2.0 * x - 1.0 / (x + sqrtf(x * x - 1.0)));
+ }
+ /* x >= 0x1p12 */
+ return logf(x) + LN2;
+}
diff --git a/src/math/asin.rs b/src/math/asin.rs
new file mode 100644
index 0000000..3e4b7c5
--- /dev/null
+++ b/src/math/asin.rs
@@ -0,0 +1,119 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_asin.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* asin(x)
+ * Method :
+ * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
+ * we approximate asin(x) on [0,0.5] by
+ * asin(x) = x + x*x^2*R(x^2)
+ * where
+ * R(x^2) is a rational approximation of (asin(x)-x)/x^3
+ * and its remez error is bounded by
+ * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
+ *
+ * For x in [0.5,1]
+ * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
+ * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
+ * then for x>0.98
+ * asin(x) = pi/2 - 2*(s+s*z*R(z))
+ * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
+ * For x<=0.98, let pio4_hi = pio2_hi/2, then
+ * f = hi part of s;
+ * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
+ * and
+ * asin(x) = pi/2 - 2*(s+s*z*R(z))
+ * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
+ * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ *
+ */
+
+use super::{fabs, get_high_word, get_low_word, sqrt, with_set_low_word};
+
+const PIO2_HI: f64 = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
+const PIO2_LO: f64 = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
+/* coefficients for R(x^2) */
+const P_S0: f64 = 1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */
+const P_S1: f64 = -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */
+const P_S2: f64 = 2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */
+const P_S3: f64 = -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */
+const P_S4: f64 = 7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */
+const P_S5: f64 = 3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */
+const Q_S1: f64 = -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */
+const Q_S2: f64 = 2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */
+const Q_S3: f64 = -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */
+const Q_S4: f64 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+fn comp_r(z: f64) -> f64 {
+ let p = z * (P_S0 + z * (P_S1 + z * (P_S2 + z * (P_S3 + z * (P_S4 + z * P_S5)))));
+ let q = 1.0 + z * (Q_S1 + z * (Q_S2 + z * (Q_S3 + z * Q_S4)));
+ p / q
+}
+
+/// Arcsine (f64)
+///
+/// Computes the inverse sine (arc sine) of the argument `x`.
+/// Arguments to asin must be in the range -1 to 1.
+/// Returns values in radians, in the range of -pi/2 to pi/2.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn asin(mut x: f64) -> f64 {
+ let z: f64;
+ let r: f64;
+ let s: f64;
+ let hx: u32;
+ let ix: u32;
+
+ hx = get_high_word(x);
+ ix = hx & 0x7fffffff;
+ /* |x| >= 1 or nan */
+ if ix >= 0x3ff00000 {
+ let lx: u32;
+ lx = get_low_word(x);
+ if ((ix - 0x3ff00000) | lx) == 0 {
+ /* asin(1) = +-pi/2 with inexact */
+ return x * PIO2_HI + f64::from_bits(0x3870000000000000);
+ } else {
+ return 0.0 / (x - x);
+ }
+ }
+ /* |x| < 0.5 */
+ if ix < 0x3fe00000 {
+ /* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */
+ if ix < 0x3e500000 && ix >= 0x00100000 {
+ return x;
+ } else {
+ return x + x * comp_r(x * x);
+ }
+ }
+ /* 1 > |x| >= 0.5 */
+ z = (1.0 - fabs(x)) * 0.5;
+ s = sqrt(z);
+ r = comp_r(z);
+ if ix >= 0x3fef3333 {
+ /* if |x| > 0.975 */
+ x = PIO2_HI - (2. * (s + s * r) - PIO2_LO);
+ } else {
+ let f: f64;
+ let c: f64;
+ /* f+c = sqrt(z) */
+ f = with_set_low_word(s, 0);
+ c = (z - f * f) / (s + f);
+ x = 0.5 * PIO2_HI - (2.0 * s * r - (PIO2_LO - 2.0 * c) - (0.5 * PIO2_HI - 2.0 * f));
+ }
+ if hx >> 31 != 0 {
+ -x
+ } else {
+ x
+ }
+}
diff --git a/src/math/asinf.rs b/src/math/asinf.rs
new file mode 100644
index 0000000..6ec61b6
--- /dev/null
+++ b/src/math/asinf.rs
@@ -0,0 +1,72 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_asinf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::fabsf::fabsf;
+use super::sqrt::sqrt;
+
+const PIO2: f64 = 1.570796326794896558e+00;
+
+/* coefficients for R(x^2) */
+const P_S0: f32 = 1.6666586697e-01;
+const P_S1: f32 = -4.2743422091e-02;
+const P_S2: f32 = -8.6563630030e-03;
+const Q_S1: f32 = -7.0662963390e-01;
+
+fn r(z: f32) -> f32 {
+ let p = z * (P_S0 + z * (P_S1 + z * P_S2));
+ let q = 1. + z * Q_S1;
+ p / q
+}
+
+/// Arcsine (f32)
+///
+/// Computes the inverse sine (arc sine) of the argument `x`.
+/// Arguments to asin must be in the range -1 to 1.
+/// Returns values in radians, in the range of -pi/2 to pi/2.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn asinf(mut x: f32) -> f32 {
+ let x1p_120 = f64::from_bits(0x3870000000000000); // 0x1p-120 === 2 ^ (-120)
+
+ let hx = x.to_bits();
+ let ix = hx & 0x7fffffff;
+
+ if ix >= 0x3f800000 {
+ /* |x| >= 1 */
+ if ix == 0x3f800000 {
+ /* |x| == 1 */
+ return ((x as f64) * PIO2 + x1p_120) as f32; /* asin(+-1) = +-pi/2 with inexact */
+ }
+ return 0. / (x - x); /* asin(|x|>1) is NaN */
+ }
+
+ if ix < 0x3f000000 {
+ /* |x| < 0.5 */
+ /* if 0x1p-126 <= |x| < 0x1p-12, avoid raising underflow */
+ if (ix < 0x39800000) && (ix >= 0x00800000) {
+ return x;
+ }
+ return x + x * r(x * x);
+ }
+
+ /* 1 > |x| >= 0.5 */
+ let z = (1. - fabsf(x)) * 0.5;
+ let s = sqrt(z as f64);
+ x = (PIO2 - 2. * (s + s * (r(z) as f64))) as f32;
+ if (hx >> 31) != 0 {
+ -x
+ } else {
+ x
+ }
+}
diff --git a/src/math/asinh.rs b/src/math/asinh.rs
new file mode 100644
index 0000000..1429535
--- /dev/null
+++ b/src/math/asinh.rs
@@ -0,0 +1,39 @@
+use super::{log, log1p, sqrt};
+
+const LN2: f64 = 0.693147180559945309417232121458176568; /* 0x3fe62e42, 0xfefa39ef*/
+
+/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
+/// Inverse hyperbolic sine (f64)
+///
+/// Calculates the inverse hyperbolic sine of `x`.
+/// Is defined as `sgn(x)*log(|x|+sqrt(x*x+1))`.
+pub fn asinh(mut x: f64) -> f64 {
+ let mut u = x.to_bits();
+ let e = ((u >> 52) as usize) & 0x7ff;
+ let sign = (u >> 63) != 0;
+
+ /* |x| */
+ u &= (!0) >> 1;
+ x = f64::from_bits(u);
+
+ if e >= 0x3ff + 26 {
+ /* |x| >= 0x1p26 or inf or nan */
+ x = log(x) + LN2;
+ } else if e >= 0x3ff + 1 {
+ /* |x| >= 2 */
+ x = log(2.0 * x + 1.0 / (sqrt(x * x + 1.0) + x));
+ } else if e >= 0x3ff - 26 {
+ /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */
+ x = log1p(x + x * x / (sqrt(x * x + 1.0) + 1.0));
+ } else {
+ /* |x| < 0x1p-26, raise inexact if x != 0 */
+ let x1p120 = f64::from_bits(0x4770000000000000);
+ force_eval!(x + x1p120);
+ }
+
+ if sign {
+ -x
+ } else {
+ x
+ }
+}
diff --git a/src/math/asinhf.rs b/src/math/asinhf.rs
new file mode 100644
index 0000000..e22a291
--- /dev/null
+++ b/src/math/asinhf.rs
@@ -0,0 +1,38 @@
+use super::{log1pf, logf, sqrtf};
+
+const LN2: f32 = 0.693147180559945309417232121458176568;
+
+/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
+/// Inverse hyperbolic sine (f32)
+///
+/// Calculates the inverse hyperbolic sine of `x`.
+/// Is defined as `sgn(x)*log(|x|+sqrt(x*x+1))`.
+pub fn asinhf(mut x: f32) -> f32 {
+ let u = x.to_bits();
+ let i = u & 0x7fffffff;
+ let sign = (u >> 31) != 0;
+
+ /* |x| */
+ x = f32::from_bits(i);
+
+ if i >= 0x3f800000 + (12 << 23) {
+ /* |x| >= 0x1p12 or inf or nan */
+ x = logf(x) + LN2;
+ } else if i >= 0x3f800000 + (1 << 23) {
+ /* |x| >= 2 */
+ x = logf(2.0 * x + 1.0 / (sqrtf(x * x + 1.0) + x));
+ } else if i >= 0x3f800000 - (12 << 23) {
+ /* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */
+ x = log1pf(x + x * x / (sqrtf(x * x + 1.0) + 1.0));
+ } else {
+ /* |x| < 0x1p-12, raise inexact if x!=0 */
+ let x1p120 = f32::from_bits(0x7b800000);
+ force_eval!(x + x1p120);
+ }
+
+ if sign {
+ -x
+ } else {
+ x
+ }
+}
diff --git a/src/math/atan.rs b/src/math/atan.rs
new file mode 100644
index 0000000..4259dc7
--- /dev/null
+++ b/src/math/atan.rs
@@ -0,0 +1,184 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* atan(x)
+ * Method
+ * 1. Reduce x to positive by atan(x) = -atan(-x).
+ * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
+ * is further reduced to one of the following intervals and the
+ * arctangent of t is evaluated by the corresponding formula:
+ *
+ * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
+ * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
+ * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
+ * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
+ * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+use super::fabs;
+use core::f64;
+
+const ATANHI: [f64; 4] = [
+ 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
+ 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
+ 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
+ 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
+];
+
+const ATANLO: [f64; 4] = [
+ 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
+ 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
+ 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
+ 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
+];
+
+const AT: [f64; 11] = [
+ 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
+ -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
+ 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
+ -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
+ 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
+ -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
+ 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
+ -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
+ 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
+ -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
+ 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
+];
+
+/// Arctangent (f64)
+///
+/// Computes the inverse tangent (arc tangent) of the input value.
+/// Returns a value in radians, in the range of -pi/2 to pi/2.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn atan(x: f64) -> f64 {
+ let mut x = x;
+ let mut ix = (x.to_bits() >> 32) as u32;
+ let sign = ix >> 31;
+ ix &= 0x7fff_ffff;
+ if ix >= 0x4410_0000 {
+ if x.is_nan() {
+ return x;
+ }
+
+ let z = ATANHI[3] + f64::from_bits(0x0380_0000); // 0x1p-120f
+ return if sign != 0 { -z } else { z };
+ }
+
+ let id = if ix < 0x3fdc_0000 {
+ /* |x| < 0.4375 */
+ if ix < 0x3e40_0000 {
+ /* |x| < 2^-27 */
+ if ix < 0x0010_0000 {
+ /* raise underflow for subnormal x */
+ force_eval!(x as f32);
+ }
+
+ return x;
+ }
+
+ -1
+ } else {
+ x = fabs(x);
+ if ix < 0x3ff30000 {
+ /* |x| < 1.1875 */
+ if ix < 0x3fe60000 {
+ /* 7/16 <= |x| < 11/16 */
+ x = (2. * x - 1.) / (2. + x);
+ 0
+ } else {
+ /* 11/16 <= |x| < 19/16 */
+ x = (x - 1.) / (x + 1.);
+ 1
+ }
+ } else if ix < 0x40038000 {
+ /* |x| < 2.4375 */
+ x = (x - 1.5) / (1. + 1.5 * x);
+ 2
+ } else {
+ /* 2.4375 <= |x| < 2^66 */
+ x = -1. / x;
+ 3
+ }
+ };
+
+ let z = x * x;
+ let w = z * z;
+ /* break sum from i=0 to 10 AT[i]z**(i+1) into odd and even poly */
+ let s1 = z * (AT[0] + w * (AT[2] + w * (AT[4] + w * (AT[6] + w * (AT[8] + w * AT[10])))));
+ let s2 = w * (AT[1] + w * (AT[3] + w * (AT[5] + w * (AT[7] + w * AT[9]))));
+
+ if id < 0 {
+ return x - x * (s1 + s2);
+ }
+
+ let z = i!(ATANHI, id as usize) - (x * (s1 + s2) - i!(ATANLO, id as usize) - x);
+
+ if sign != 0 {
+ -z
+ } else {
+ z
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::atan;
+ use core::f64;
+
+ #[test]
+ fn sanity_check() {
+ for (input, answer) in [
+ (3.0_f64.sqrt() / 3.0, f64::consts::FRAC_PI_6),
+ (1.0, f64::consts::FRAC_PI_4),
+ (3.0_f64.sqrt(), f64::consts::FRAC_PI_3),
+ (-3.0_f64.sqrt() / 3.0, -f64::consts::FRAC_PI_6),
+ (-1.0, -f64::consts::FRAC_PI_4),
+ (-3.0_f64.sqrt(), -f64::consts::FRAC_PI_3),
+ ]
+ .iter()
+ {
+ assert!(
+ (atan(*input) - answer) / answer < 1e-5,
+ "\natan({:.4}/16) = {:.4}, actual: {}",
+ input * 16.0,
+ answer,
+ atan(*input)
+ );
+ }
+ }
+
+ #[test]
+ fn zero() {
+ assert_eq!(atan(0.0), 0.0);
+ }
+
+ #[test]
+ fn infinity() {
+ assert_eq!(atan(f64::INFINITY), f64::consts::FRAC_PI_2);
+ }
+
+ #[test]
+ fn minus_infinity() {
+ assert_eq!(atan(f64::NEG_INFINITY), -f64::consts::FRAC_PI_2);
+ }
+
+ #[test]
+ fn nan() {
+ assert!(atan(f64::NAN).is_nan());
+ }
+}
diff --git a/src/math/atan2.rs b/src/math/atan2.rs
new file mode 100644
index 0000000..fb2ea4e
--- /dev/null
+++ b/src/math/atan2.rs
@@ -0,0 +1,126 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ */
+/* atan2(y,x)
+ * Method :
+ * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
+ * 2. Reduce x to positive by (if x and y are unexceptional):
+ * ARG (x+iy) = arctan(y/x) ... if x > 0,
+ * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
+ *
+ * Special cases:
+ *
+ * ATAN2((anything), NaN ) is NaN;
+ * ATAN2(NAN , (anything) ) is NaN;
+ * ATAN2(+-0, +(anything but NaN)) is +-0 ;
+ * ATAN2(+-0, -(anything but NaN)) is +-pi ;
+ * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
+ * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
+ * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
+ * ATAN2(+-INF,+INF ) is +-pi/4 ;
+ * ATAN2(+-INF,-INF ) is +-3pi/4;
+ * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+use super::atan;
+use super::fabs;
+
+const PI: f64 = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
+const PI_LO: f64 = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
+
+/// Arctangent of y/x (f64)
+///
+/// Computes the inverse tangent (arc tangent) of `y/x`.
+/// Produces the correct result even for angles near pi/2 or -pi/2 (that is, when `x` is near 0).
+/// Returns a value in radians, in the range of -pi to pi.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn atan2(y: f64, x: f64) -> f64 {
+ if x.is_nan() || y.is_nan() {
+ return x + y;
+ }
+ let mut ix = (x.to_bits() >> 32) as u32;
+ let lx = x.to_bits() as u32;
+ let mut iy = (y.to_bits() >> 32) as u32;
+ let ly = y.to_bits() as u32;
+ if ((ix.wrapping_sub(0x3ff00000)) | lx) == 0 {
+ /* x = 1.0 */
+ return atan(y);
+ }
+ let m = ((iy >> 31) & 1) | ((ix >> 30) & 2); /* 2*sign(x)+sign(y) */
+ ix &= 0x7fffffff;
+ iy &= 0x7fffffff;
+
+ /* when y = 0 */
+ if (iy | ly) == 0 {
+ return match m {
+ 0 | 1 => y, /* atan(+-0,+anything)=+-0 */
+ 2 => PI, /* atan(+0,-anything) = PI */
+ _ => -PI, /* atan(-0,-anything) =-PI */
+ };
+ }
+ /* when x = 0 */
+ if (ix | lx) == 0 {
+ return if m & 1 != 0 { -PI / 2.0 } else { PI / 2.0 };
+ }
+ /* when x is INF */
+ if ix == 0x7ff00000 {
+ if iy == 0x7ff00000 {
+ return match m {
+ 0 => PI / 4.0, /* atan(+INF,+INF) */
+ 1 => -PI / 4.0, /* atan(-INF,+INF) */
+ 2 => 3.0 * PI / 4.0, /* atan(+INF,-INF) */
+ _ => -3.0 * PI / 4.0, /* atan(-INF,-INF) */
+ };
+ } else {
+ return match m {
+ 0 => 0.0, /* atan(+...,+INF) */
+ 1 => -0.0, /* atan(-...,+INF) */
+ 2 => PI, /* atan(+...,-INF) */
+ _ => -PI, /* atan(-...,-INF) */
+ };
+ }
+ }
+ /* |y/x| > 0x1p64 */
+ if ix.wrapping_add(64 << 20) < iy || iy == 0x7ff00000 {
+ return if m & 1 != 0 { -PI / 2.0 } else { PI / 2.0 };
+ }
+
+ /* z = atan(|y/x|) without spurious underflow */
+ let z = if (m & 2 != 0) && iy.wrapping_add(64 << 20) < ix {
+ /* |y/x| < 0x1p-64, x<0 */
+ 0.0
+ } else {
+ atan(fabs(y / x))
+ };
+ match m {
+ 0 => z, /* atan(+,+) */
+ 1 => -z, /* atan(-,+) */
+ 2 => PI - (z - PI_LO), /* atan(+,-) */
+ _ => (z - PI_LO) - PI, /* atan(-,-) */
+ }
+}
+
+#[test]
+fn sanity_check() {
+ assert_eq!(atan2(0.0, 1.0), 0.0);
+ assert_eq!(atan2(0.0, -1.0), PI);
+ assert_eq!(atan2(-0.0, -1.0), -PI);
+ assert_eq!(atan2(3.0, 2.0), atan(3.0 / 2.0));
+ assert_eq!(atan2(2.0, -1.0), atan(2.0 / -1.0) + PI);
+ assert_eq!(atan2(-2.0, -1.0), atan(-2.0 / -1.0) - PI);
+}
diff --git a/src/math/atan2f.rs b/src/math/atan2f.rs
new file mode 100644
index 0000000..eae3b00
--- /dev/null
+++ b/src/math/atan2f.rs
@@ -0,0 +1,91 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2f.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::atanf;
+use super::fabsf;
+
+const PI: f32 = 3.1415927410e+00; /* 0x40490fdb */
+const PI_LO: f32 = -8.7422776573e-08; /* 0xb3bbbd2e */
+
+/// Arctangent of y/x (f32)
+///
+/// Computes the inverse tangent (arc tangent) of `y/x`.
+/// Produces the correct result even for angles near pi/2 or -pi/2 (that is, when `x` is near 0).
+/// Returns a value in radians, in the range of -pi to pi.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn atan2f(y: f32, x: f32) -> f32 {
+ if x.is_nan() || y.is_nan() {
+ return x + y;
+ }
+ let mut ix = x.to_bits();
+ let mut iy = y.to_bits();
+
+ if ix == 0x3f800000 {
+ /* x=1.0 */
+ return atanf(y);
+ }
+ let m = ((iy >> 31) & 1) | ((ix >> 30) & 2); /* 2*sign(x)+sign(y) */
+ ix &= 0x7fffffff;
+ iy &= 0x7fffffff;
+
+ /* when y = 0 */
+ if iy == 0 {
+ return match m {
+ 0 | 1 => y, /* atan(+-0,+anything)=+-0 */
+ 2 => PI, /* atan(+0,-anything) = pi */
+ 3 | _ => -PI, /* atan(-0,-anything) =-pi */
+ };
+ }
+ /* when x = 0 */
+ if ix == 0 {
+ return if m & 1 != 0 { -PI / 2. } else { PI / 2. };
+ }
+ /* when x is INF */
+ if ix == 0x7f800000 {
+ return if iy == 0x7f800000 {
+ match m {
+ 0 => PI / 4., /* atan(+INF,+INF) */
+ 1 => -PI / 4., /* atan(-INF,+INF) */
+ 2 => 3. * PI / 4., /* atan(+INF,-INF)*/
+ 3 | _ => -3. * PI / 4., /* atan(-INF,-INF)*/
+ }
+ } else {
+ match m {
+ 0 => 0., /* atan(+...,+INF) */
+ 1 => -0., /* atan(-...,+INF) */
+ 2 => PI, /* atan(+...,-INF) */
+ 3 | _ => -PI, /* atan(-...,-INF) */
+ }
+ };
+ }
+ /* |y/x| > 0x1p26 */
+ if (ix + (26 << 23) < iy) || (iy == 0x7f800000) {
+ return if m & 1 != 0 { -PI / 2. } else { PI / 2. };
+ }
+
+ /* z = atan(|y/x|) with correct underflow */
+ let z = if (m & 2 != 0) && (iy + (26 << 23) < ix) {
+ /*|y/x| < 0x1p-26, x < 0 */
+ 0.
+ } else {
+ atanf(fabsf(y / x))
+ };
+ match m {
+ 0 => z, /* atan(+,+) */
+ 1 => -z, /* atan(-,+) */
+ 2 => PI - (z - PI_LO), /* atan(+,-) */
+ _ => (z - PI_LO) - PI, /* case 3 */ /* atan(-,-) */
+ }
+}
diff --git a/src/math/atanf.rs b/src/math/atanf.rs
new file mode 100644
index 0000000..73f3352
--- /dev/null
+++ b/src/math/atanf.rs
@@ -0,0 +1,112 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::fabsf;
+
+const ATAN_HI: [f32; 4] = [
+ 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
+ 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
+ 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
+ 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
+];
+
+const ATAN_LO: [f32; 4] = [
+ 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
+ 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
+ 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
+ 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
+];
+
+const A_T: [f32; 5] = [
+ 3.3333328366e-01,
+ -1.9999158382e-01,
+ 1.4253635705e-01,
+ -1.0648017377e-01,
+ 6.1687607318e-02,
+];
+
+/// Arctangent (f32)
+///
+/// Computes the inverse tangent (arc tangent) of the input value.
+/// Returns a value in radians, in the range of -pi/2 to pi/2.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn atanf(mut x: f32) -> f32 {
+ let x1p_120 = f32::from_bits(0x03800000); // 0x1p-120 === 2 ^ (-120)
+
+ let z: f32;
+
+ let mut ix = x.to_bits();
+ let sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+
+ if ix >= 0x4c800000 {
+ /* if |x| >= 2**26 */
+ if x.is_nan() {
+ return x;
+ }
+ z = ATAN_HI[3] + x1p_120;
+ return if sign { -z } else { z };
+ }
+ let id = if ix < 0x3ee00000 {
+ /* |x| < 0.4375 */
+ if ix < 0x39800000 {
+ /* |x| < 2**-12 */
+ if ix < 0x00800000 {
+ /* raise underflow for subnormal x */
+ force_eval!(x * x);
+ }
+ return x;
+ }
+ -1
+ } else {
+ x = fabsf(x);
+ if ix < 0x3f980000 {
+ /* |x| < 1.1875 */
+ if ix < 0x3f300000 {
+ /* 7/16 <= |x| < 11/16 */
+ x = (2. * x - 1.) / (2. + x);
+ 0
+ } else {
+ /* 11/16 <= |x| < 19/16 */
+ x = (x - 1.) / (x + 1.);
+ 1
+ }
+ } else if ix < 0x401c0000 {
+ /* |x| < 2.4375 */
+ x = (x - 1.5) / (1. + 1.5 * x);
+ 2
+ } else {
+ /* 2.4375 <= |x| < 2**26 */
+ x = -1. / x;
+ 3
+ }
+ };
+ /* end of argument reduction */
+ z = x * x;
+ let w = z * z;
+ /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+ let s1 = z * (A_T[0] + w * (A_T[2] + w * A_T[4]));
+ let s2 = w * (A_T[1] + w * A_T[3]);
+ if id < 0 {
+ return x - x * (s1 + s2);
+ }
+ let id = id as usize;
+ let z = ATAN_HI[id] - ((x * (s1 + s2) - ATAN_LO[id]) - x);
+ if sign {
+ -z
+ } else {
+ z
+ }
+}
diff --git a/src/math/atanh.rs b/src/math/atanh.rs
new file mode 100644
index 0000000..79a989c
--- /dev/null
+++ b/src/math/atanh.rs
@@ -0,0 +1,36 @@
+use super::log1p;
+
+/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
+/// Inverse hyperbolic tangent (f64)
+///
+/// Calculates the inverse hyperbolic tangent of `x`.
+/// Is defined as `log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2`.
+pub fn atanh(x: f64) -> f64 {
+ let u = x.to_bits();
+ let e = ((u >> 52) as usize) & 0x7ff;
+ let sign = (u >> 63) != 0;
+
+ /* |x| */
+ let mut y = f64::from_bits(u & 0x7fff_ffff_ffff_ffff);
+
+ if e < 0x3ff - 1 {
+ if e < 0x3ff - 32 {
+ /* handle underflow */
+ if e == 0 {
+ force_eval!(y as f32);
+ }
+ } else {
+ /* |x| < 0.5, up to 1.7ulp error */
+ y = 0.5 * log1p(2.0 * y + 2.0 * y * y / (1.0 - y));
+ }
+ } else {
+ /* avoid overflow */
+ y = 0.5 * log1p(2.0 * (y / (1.0 - y)));
+ }
+
+ if sign {
+ -y
+ } else {
+ y
+ }
+}
diff --git a/src/math/atanhf.rs b/src/math/atanhf.rs
new file mode 100644
index 0000000..7b2f34d
--- /dev/null
+++ b/src/math/atanhf.rs
@@ -0,0 +1,36 @@
+use super::log1pf;
+
+/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
+/// Inverse hyperbolic tangent (f32)
+///
+/// Calculates the inverse hyperbolic tangent of `x`.
+/// Is defined as `log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2`.
+pub fn atanhf(mut x: f32) -> f32 {
+ let mut u = x.to_bits();
+ let sign = (u >> 31) != 0;
+
+ /* |x| */
+ u &= 0x7fffffff;
+ x = f32::from_bits(u);
+
+ if u < 0x3f800000 - (1 << 23) {
+ if u < 0x3f800000 - (32 << 23) {
+ /* handle underflow */
+ if u < (1 << 23) {
+ force_eval!((x * x) as f32);
+ }
+ } else {
+ /* |x| < 0.5, up to 1.7ulp error */
+ x = 0.5 * log1pf(2.0 * x + 2.0 * x * x / (1.0 - x));
+ }
+ } else {
+ /* avoid overflow */
+ x = 0.5 * log1pf(2.0 * (x / (1.0 - x)));
+ }
+
+ if sign {
+ -x
+ } else {
+ x
+ }
+}
diff --git a/src/math/cbrt.rs b/src/math/cbrt.rs
new file mode 100644
index 0000000..b4e77ea
--- /dev/null
+++ b/src/math/cbrt.rs
@@ -0,0 +1,113 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrt.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ * Optimized by Bruce D. Evans.
+ */
+/* cbrt(x)
+ * Return cube root of x
+ */
+
+use core::f64;
+
+const B1: u32 = 715094163; /* B1 = (1023-1023/3-0.03306235651)*2**20 */
+const B2: u32 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */
+
+/* |1/cbrt(x) - p(x)| < 2**-23.5 (~[-7.93e-8, 7.929e-8]). */
+const P0: f64 = 1.87595182427177009643; /* 0x3ffe03e6, 0x0f61e692 */
+const P1: f64 = -1.88497979543377169875; /* 0xbffe28e0, 0x92f02420 */
+const P2: f64 = 1.621429720105354466140; /* 0x3ff9f160, 0x4a49d6c2 */
+const P3: f64 = -0.758397934778766047437; /* 0xbfe844cb, 0xbee751d9 */
+const P4: f64 = 0.145996192886612446982; /* 0x3fc2b000, 0xd4e4edd7 */
+
+// Cube root (f64)
+///
+/// Computes the cube root of the argument.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn cbrt(x: f64) -> f64 {
+ let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54
+
+ let mut ui: u64 = x.to_bits();
+ let mut r: f64;
+ let s: f64;
+ let mut t: f64;
+ let w: f64;
+ let mut hx: u32 = (ui >> 32) as u32 & 0x7fffffff;
+
+ if hx >= 0x7ff00000 {
+ /* cbrt(NaN,INF) is itself */
+ return x + x;
+ }
+
+ /*
+ * Rough cbrt to 5 bits:
+ * cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3)
+ * where e is integral and >= 0, m is real and in [0, 1), and "/" and
+ * "%" are integer division and modulus with rounding towards minus
+ * infinity. The RHS is always >= the LHS and has a maximum relative
+ * error of about 1 in 16. Adding a bias of -0.03306235651 to the
+ * (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE
+ * floating point representation, for finite positive normal values,
+ * ordinary integer divison of the value in bits magically gives
+ * almost exactly the RHS of the above provided we first subtract the
+ * exponent bias (1023 for doubles) and later add it back. We do the
+ * subtraction virtually to keep e >= 0 so that ordinary integer
+ * division rounds towards minus infinity; this is also efficient.
+ */
+ if hx < 0x00100000 {
+ /* zero or subnormal? */
+ ui = (x * x1p54).to_bits();
+ hx = (ui >> 32) as u32 & 0x7fffffff;
+ if hx == 0 {
+ return x; /* cbrt(0) is itself */
+ }
+ hx = hx / 3 + B2;
+ } else {
+ hx = hx / 3 + B1;
+ }
+ ui &= 1 << 63;
+ ui |= (hx as u64) << 32;
+ t = f64::from_bits(ui);
+
+ /*
+ * New cbrt to 23 bits:
+ * cbrt(x) = t*cbrt(x/t**3) ~= t*P(t**3/x)
+ * where P(r) is a polynomial of degree 4 that approximates 1/cbrt(r)
+ * to within 2**-23.5 when |r - 1| < 1/10. The rough approximation
+ * has produced t such than |t/cbrt(x) - 1| ~< 1/32, and cubing this
+ * gives us bounds for r = t**3/x.
+ *
+ * Try to optimize for parallel evaluation as in __tanf.c.
+ */
+ r = (t * t) * (t / x);
+ t = t * ((P0 + r * (P1 + r * P2)) + ((r * r) * r) * (P3 + r * P4));
+
+ /*
+ * Round t away from zero to 23 bits (sloppily except for ensuring that
+ * the result is larger in magnitude than cbrt(x) but not much more than
+ * 2 23-bit ulps larger). With rounding towards zero, the error bound
+ * would be ~5/6 instead of ~4/6. With a maximum error of 2 23-bit ulps
+ * in the rounded t, the infinite-precision error in the Newton
+ * approximation barely affects third digit in the final error
+ * 0.667; the error in the rounded t can be up to about 3 23-bit ulps
+ * before the final error is larger than 0.667 ulps.
+ */
+ ui = t.to_bits();
+ ui = (ui + 0x80000000) & 0xffffffffc0000000;
+ t = f64::from_bits(ui);
+
+ /* one step Newton iteration to 53 bits with error < 0.667 ulps */
+ s = t * t; /* t*t is exact */
+ r = x / s; /* error <= 0.5 ulps; |r| < |t| */
+ w = t + t; /* t+t is exact */
+ r = (r - t) / (w + r); /* r-t is exact; w+r ~= 3*t */
+ t = t + t * r; /* error <= 0.5 + 0.5/3 + epsilon */
+ t
+}
diff --git a/src/math/cbrtf.rs b/src/math/cbrtf.rs
new file mode 100644
index 0000000..9d70305
--- /dev/null
+++ b/src/math/cbrtf.rs
@@ -0,0 +1,75 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Debugged and optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* cbrtf(x)
+ * Return cube root of x
+ */
+
+use core::f32;
+
+const B1: u32 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */
+const B2: u32 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
+
+/// Cube root (f32)
+///
+/// Computes the cube root of the argument.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn cbrtf(x: f32) -> f32 {
+ let x1p24 = f32::from_bits(0x4b800000); // 0x1p24f === 2 ^ 24
+
+ let mut r: f64;
+ let mut t: f64;
+ let mut ui: u32 = x.to_bits();
+ let mut hx: u32 = ui & 0x7fffffff;
+
+ if hx >= 0x7f800000 {
+ /* cbrt(NaN,INF) is itself */
+ return x + x;
+ }
+
+ /* rough cbrt to 5 bits */
+ if hx < 0x00800000 {
+ /* zero or subnormal? */
+ if hx == 0 {
+ return x; /* cbrt(+-0) is itself */
+ }
+ ui = (x * x1p24).to_bits();
+ hx = ui & 0x7fffffff;
+ hx = hx / 3 + B2;
+ } else {
+ hx = hx / 3 + B1;
+ }
+ ui &= 0x80000000;
+ ui |= hx;
+
+ /*
+ * First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In
+ * double precision so that its terms can be arranged for efficiency
+ * without causing overflow or underflow.
+ */
+ t = f32::from_bits(ui) as f64;
+ r = t * t * t;
+ t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
+
+ /*
+ * Second step Newton iteration to 47 bits. In double precision for
+ * efficiency and accuracy.
+ */
+ r = t * t * t;
+ t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
+
+ /* rounding to 24 bits is perfect in round-to-nearest mode */
+ t as f32
+}
diff --git a/src/math/ceil.rs b/src/math/ceil.rs
new file mode 100644
index 0000000..eda28b9
--- /dev/null
+++ b/src/math/ceil.rs
@@ -0,0 +1,63 @@
+use core::f64;
+
+const TOINT: f64 = 1. / f64::EPSILON;
+
+/// Ceil (f64)
+///
+/// Finds the nearest integer greater than or equal to `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn ceil(x: f64) -> f64 {
+ // On wasm32 we know that LLVM's intrinsic will compile to an optimized
+ // `f64.ceil` native instruction, so we can leverage this for both code size
+ // and speed.
+ llvm_intrinsically_optimized! {
+ #[cfg(target_arch = "wasm32")] {
+ return unsafe { ::core::intrinsics::ceilf64(x) }
+ }
+ }
+ let u: u64 = x.to_bits();
+ let e: i64 = (u >> 52 & 0x7ff) as i64;
+ let y: f64;
+
+ if e >= 0x3ff + 52 || x == 0. {
+ return x;
+ }
+ // y = int(x) - x, where int(x) is an integer neighbor of x
+ y = if (u >> 63) != 0 {
+ x - TOINT + TOINT - x
+ } else {
+ x + TOINT - TOINT - x
+ };
+ // special case because of non-nearest rounding modes
+ if e < 0x3ff {
+ force_eval!(y);
+ return if (u >> 63) != 0 { -0. } else { 1. };
+ }
+ if y < 0. {
+ x + y + 1.
+ } else {
+ x + y
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use core::f64::*;
+
+ #[test]
+ fn sanity_check() {
+ assert_eq!(ceil(1.1), 2.0);
+ assert_eq!(ceil(2.9), 3.0);
+ }
+
+ /// The spec: https://en.cppreference.com/w/cpp/numeric/math/ceil
+ #[test]
+ fn spec_tests() {
+ // Not Asserted: that the current rounding mode has no effect.
+ assert!(ceil(NAN).is_nan());
+ for f in [0.0, -0.0, INFINITY, NEG_INFINITY].iter().copied() {
+ assert_eq!(ceil(f), f);
+ }
+ }
+}
diff --git a/src/math/ceilf.rs b/src/math/ceilf.rs
new file mode 100644
index 0000000..f1edbd0
--- /dev/null
+++ b/src/math/ceilf.rs
@@ -0,0 +1,63 @@
+use core::f32;
+
+/// Ceil (f32)
+///
+/// Finds the nearest integer greater than or equal to `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn ceilf(x: f32) -> f32 {
+ // On wasm32 we know that LLVM's intrinsic will compile to an optimized
+ // `f32.ceil` native instruction, so we can leverage this for both code size
+ // and speed.
+ llvm_intrinsically_optimized! {
+ #[cfg(target_arch = "wasm32")] {
+ return unsafe { ::core::intrinsics::ceilf32(x) }
+ }
+ }
+ let mut ui = x.to_bits();
+ let e = (((ui >> 23) & 0xff).wrapping_sub(0x7f)) as i32;
+
+ if e >= 23 {
+ return x;
+ }
+ if e >= 0 {
+ let m = 0x007fffff >> e;
+ if (ui & m) == 0 {
+ return x;
+ }
+ force_eval!(x + f32::from_bits(0x7b800000));
+ if ui >> 31 == 0 {
+ ui += m;
+ }
+ ui &= !m;
+ } else {
+ force_eval!(x + f32::from_bits(0x7b800000));
+ if ui >> 31 != 0 {
+ return -0.0;
+ } else if ui << 1 != 0 {
+ return 1.0;
+ }
+ }
+ f32::from_bits(ui)
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use core::f32::*;
+
+ #[test]
+ fn sanity_check() {
+ assert_eq!(ceilf(1.1), 2.0);
+ assert_eq!(ceilf(2.9), 3.0);
+ }
+
+ /// The spec: https://en.cppreference.com/w/cpp/numeric/math/ceil
+ #[test]
+ fn spec_tests() {
+ // Not Asserted: that the current rounding mode has no effect.
+ assert!(ceilf(NAN).is_nan());
+ for f in [0.0, -0.0, INFINITY, NEG_INFINITY].iter().copied() {
+ assert_eq!(ceilf(f), f);
+ }
+ }
+}
diff --git a/src/math/copysign.rs b/src/math/copysign.rs
new file mode 100644
index 0000000..1527fb6
--- /dev/null
+++ b/src/math/copysign.rs
@@ -0,0 +1,11 @@
+/// Sign of Y, magnitude of X (f64)
+///
+/// Constructs a number with the magnitude (absolute value) of its
+/// first argument, `x`, and the sign of its second argument, `y`.
+pub fn copysign(x: f64, y: f64) -> f64 {
+ let mut ux = x.to_bits();
+ let uy = y.to_bits();
+ ux &= (!0) >> 1;
+ ux |= uy & (1 << 63);
+ f64::from_bits(ux)
+}
diff --git a/src/math/copysignf.rs b/src/math/copysignf.rs
new file mode 100644
index 0000000..3514856
--- /dev/null
+++ b/src/math/copysignf.rs
@@ -0,0 +1,11 @@
+/// Sign of Y, magnitude of X (f32)
+///
+/// Constructs a number with the magnitude (absolute value) of its
+/// first argument, `x`, and the sign of its second argument, `y`.
+pub fn copysignf(x: f32, y: f32) -> f32 {
+ let mut ux = x.to_bits();
+ let uy = y.to_bits();
+ ux &= 0x7fffffff;
+ ux |= uy & 0x80000000;
+ f32::from_bits(ux)
+}
diff --git a/src/math/cos.rs b/src/math/cos.rs
new file mode 100644
index 0000000..db8bc49
--- /dev/null
+++ b/src/math/cos.rs
@@ -0,0 +1,73 @@
+// origin: FreeBSD /usr/src/lib/msun/src/s_cos.c */
+//
+// ====================================================
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+//
+// Developed at SunPro, a Sun Microsystems, Inc. business.
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+
+use super::{k_cos, k_sin, rem_pio2};
+
+// cos(x)
+// Return cosine function of x.
+//
+// kernel function:
+// k_sin ... sine function on [-pi/4,pi/4]
+// k_cos ... cosine function on [-pi/4,pi/4]
+// rem_pio2 ... argument reduction routine
+//
+// Method.
+// Let S,C and T denote the sin, cos and tan respectively on
+// [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+// in [-pi/4 , +pi/4], and let n = k mod 4.
+// We have
+//
+// n sin(x) cos(x) tan(x)
+// ----------------------------------------------------------
+// 0 S C T
+// 1 C -S -1/T
+// 2 -S -C T
+// 3 -C S -1/T
+// ----------------------------------------------------------
+//
+// Special cases:
+// Let trig be any of sin, cos, or tan.
+// trig(+-INF) is NaN, with signals;
+// trig(NaN) is that NaN;
+//
+// Accuracy:
+// TRIG(x) returns trig(x) nearly rounded
+//
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn cos(x: f64) -> f64 {
+ let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
+
+ /* |x| ~< pi/4 */
+ if ix <= 0x3fe921fb {
+ if ix < 0x3e46a09e {
+ /* if x < 2**-27 * sqrt(2) */
+ /* raise inexact if x != 0 */
+ if x as i32 == 0 {
+ return 1.0;
+ }
+ }
+ return k_cos(x, 0.0);
+ }
+
+ /* cos(Inf or NaN) is NaN */
+ if ix >= 0x7ff00000 {
+ return x - x;
+ }
+
+ /* argument reduction needed */
+ let (n, y0, y1) = rem_pio2(x);
+ match n & 3 {
+ 0 => k_cos(y0, y1),
+ 1 => -k_sin(y0, y1, 1),
+ 2 => -k_cos(y0, y1),
+ _ => k_sin(y0, y1, 1),
+ }
+}
diff --git a/src/math/cosf.rs b/src/math/cosf.rs
new file mode 100644
index 0000000..424fa42
--- /dev/null
+++ b/src/math/cosf.rs
@@ -0,0 +1,83 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_cosf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{k_cosf, k_sinf, rem_pio2f};
+
+use core::f64::consts::FRAC_PI_2;
+
+/* Small multiples of pi/2 rounded to double precision. */
+const C1_PIO2: f64 = 1. * FRAC_PI_2; /* 0x3FF921FB, 0x54442D18 */
+const C2_PIO2: f64 = 2. * FRAC_PI_2; /* 0x400921FB, 0x54442D18 */
+const C3_PIO2: f64 = 3. * FRAC_PI_2; /* 0x4012D97C, 0x7F3321D2 */
+const C4_PIO2: f64 = 4. * FRAC_PI_2; /* 0x401921FB, 0x54442D18 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn cosf(x: f32) -> f32 {
+ let x64 = x as f64;
+
+ let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120
+
+ let mut ix = x.to_bits();
+ let sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+
+ if ix <= 0x3f490fda {
+ /* |x| ~<= pi/4 */
+ if ix < 0x39800000 {
+ /* |x| < 2**-12 */
+ /* raise inexact if x != 0 */
+ force_eval!(x + x1p120);
+ return 1.;
+ }
+ return k_cosf(x64);
+ }
+ if ix <= 0x407b53d1 {
+ /* |x| ~<= 5*pi/4 */
+ if ix > 0x4016cbe3 {
+ /* |x| ~> 3*pi/4 */
+ return -k_cosf(if sign { x64 + C2_PIO2 } else { x64 - C2_PIO2 });
+ } else if sign {
+ return k_sinf(x64 + C1_PIO2);
+ } else {
+ return k_sinf(C1_PIO2 - x64);
+ }
+ }
+ if ix <= 0x40e231d5 {
+ /* |x| ~<= 9*pi/4 */
+ if ix > 0x40afeddf {
+ /* |x| ~> 7*pi/4 */
+ return k_cosf(if sign { x64 + C4_PIO2 } else { x64 - C4_PIO2 });
+ } else if sign {
+ return k_sinf(-x64 - C3_PIO2);
+ } else {
+ return k_sinf(x64 - C3_PIO2);
+ }
+ }
+
+ /* cos(Inf or NaN) is NaN */
+ if ix >= 0x7f800000 {
+ return x - x;
+ }
+
+ /* general argument reduction needed */
+ let (n, y) = rem_pio2f(x);
+ match n & 3 {
+ 0 => k_cosf(y),
+ 1 => k_sinf(-y),
+ 2 => -k_cosf(y),
+ _ => k_sinf(y),
+ }
+}
diff --git a/src/math/cosh.rs b/src/math/cosh.rs
new file mode 100644
index 0000000..2fb568a
--- /dev/null
+++ b/src/math/cosh.rs
@@ -0,0 +1,38 @@
+use super::exp;
+use super::expm1;
+use super::k_expo2;
+
+/// Hyperbolic cosine (f64)
+///
+/// Computes the hyperbolic cosine of the argument x.
+/// Is defined as `(exp(x) + exp(-x))/2`
+/// Angles are specified in radians.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn cosh(mut x: f64) -> f64 {
+ /* |x| */
+ let mut ix = x.to_bits();
+ ix &= 0x7fffffffffffffff;
+ x = f64::from_bits(ix);
+ let w = ix >> 32;
+
+ /* |x| < log(2) */
+ if w < 0x3fe62e42 {
+ if w < 0x3ff00000 - (26 << 20) {
+ let x1p120 = f64::from_bits(0x4770000000000000);
+ force_eval!(x + x1p120);
+ return 1.;
+ }
+ let t = expm1(x); // exponential minus 1
+ return 1. + t * t / (2. * (1. + t));
+ }
+
+ /* |x| < log(DBL_MAX) */
+ if w < 0x40862e42 {
+ let t = exp(x);
+ /* note: if x>log(0x1p26) then the 1/t is not needed */
+ return 0.5 * (t + 1. / t);
+ }
+
+ /* |x| > log(DBL_MAX) or nan */
+ k_expo2(x)
+}
diff --git a/src/math/coshf.rs b/src/math/coshf.rs
new file mode 100644
index 0000000..e7b6845
--- /dev/null
+++ b/src/math/coshf.rs
@@ -0,0 +1,38 @@
+use super::expf;
+use super::expm1f;
+use super::k_expo2f;
+
+/// Hyperbolic cosine (f64)
+///
+/// Computes the hyperbolic cosine of the argument x.
+/// Is defined as `(exp(x) + exp(-x))/2`
+/// Angles are specified in radians.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn coshf(mut x: f32) -> f32 {
+ let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120
+
+ /* |x| */
+ let mut ix = x.to_bits();
+ ix &= 0x7fffffff;
+ x = f32::from_bits(ix);
+ let w = ix;
+
+ /* |x| < log(2) */
+ if w < 0x3f317217 {
+ if w < (0x3f800000 - (12 << 23)) {
+ force_eval!(x + x1p120);
+ return 1.;
+ }
+ let t = expm1f(x);
+ return 1. + t * t / (2. * (1. + t));
+ }
+
+ /* |x| < log(FLT_MAX) */
+ if w < 0x42b17217 {
+ let t = expf(x);
+ return 0.5 * (t + 1. / t);
+ }
+
+ /* |x| > log(FLT_MAX) or nan */
+ k_expo2f(x)
+}
diff --git a/src/math/erf.rs b/src/math/erf.rs
new file mode 100644
index 0000000..a2c617d
--- /dev/null
+++ b/src/math/erf.rs
@@ -0,0 +1,317 @@
+use super::{exp, fabs, get_high_word, with_set_low_word};
+/* origin: FreeBSD /usr/src/lib/msun/src/s_erf.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* double erf(double x)
+ * double erfc(double x)
+ * x
+ * 2 |\
+ * erf(x) = --------- | exp(-t*t)dt
+ * sqrt(pi) \|
+ * 0
+ *
+ * erfc(x) = 1-erf(x)
+ * Note that
+ * erf(-x) = -erf(x)
+ * erfc(-x) = 2 - erfc(x)
+ *
+ * Method:
+ * 1. For |x| in [0, 0.84375]
+ * erf(x) = x + x*R(x^2)
+ * erfc(x) = 1 - erf(x) if x in [-.84375,0.25]
+ * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375]
+ * where R = P/Q where P is an odd poly of degree 8 and
+ * Q is an odd poly of degree 10.
+ * -57.90
+ * | R - (erf(x)-x)/x | <= 2
+ *
+ *
+ * Remark. The formula is derived by noting
+ * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
+ * and that
+ * 2/sqrt(pi) = 1.128379167095512573896158903121545171688
+ * is close to one. The interval is chosen because the fix
+ * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is
+ * near 0.6174), and by some experiment, 0.84375 is chosen to
+ * guarantee the error is less than one ulp for erf.
+ *
+ * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and
+ * c = 0.84506291151 rounded to single (24 bits)
+ * erf(x) = sign(x) * (c + P1(s)/Q1(s))
+ * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0
+ * 1+(c+P1(s)/Q1(s)) if x < 0
+ * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06
+ * Remark: here we use the taylor series expansion at x=1.
+ * erf(1+s) = erf(1) + s*Poly(s)
+ * = 0.845.. + P1(s)/Q1(s)
+ * That is, we use rational approximation to approximate
+ * erf(1+s) - (c = (single)0.84506291151)
+ * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
+ * where
+ * P1(s) = degree 6 poly in s
+ * Q1(s) = degree 6 poly in s
+ *
+ * 3. For x in [1.25,1/0.35(~2.857143)],
+ * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1)
+ * erf(x) = 1 - erfc(x)
+ * where
+ * R1(z) = degree 7 poly in z, (z=1/x^2)
+ * S1(z) = degree 8 poly in z
+ *
+ * 4. For x in [1/0.35,28]
+ * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0
+ * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0
+ * = 2.0 - tiny (if x <= -6)
+ * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else
+ * erf(x) = sign(x)*(1.0 - tiny)
+ * where
+ * R2(z) = degree 6 poly in z, (z=1/x^2)
+ * S2(z) = degree 7 poly in z
+ *
+ * Note1:
+ * To compute exp(-x*x-0.5625+R/S), let s be a single
+ * precision number and s := x; then
+ * -x*x = -s*s + (s-x)*(s+x)
+ * exp(-x*x-0.5626+R/S) =
+ * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
+ * Note2:
+ * Here 4 and 5 make use of the asymptotic series
+ * exp(-x*x)
+ * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
+ * x*sqrt(pi)
+ * We use rational approximation to approximate
+ * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625
+ * Here is the error bound for R1/S1 and R2/S2
+ * |R1/S1 - f(x)| < 2**(-62.57)
+ * |R2/S2 - f(x)| < 2**(-61.52)
+ *
+ * 5. For inf > x >= 28
+ * erf(x) = sign(x) *(1 - tiny) (raise inexact)
+ * erfc(x) = tiny*tiny (raise underflow) if x > 0
+ * = 2 - tiny if x<0
+ *
+ * 7. Special case:
+ * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
+ * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
+ * erfc/erf(NaN) is NaN
+ */
+
+const ERX: f64 = 8.45062911510467529297e-01; /* 0x3FEB0AC1, 0x60000000 */
+/*
+ * Coefficients for approximation to erf on [0,0.84375]
+ */
+const EFX8: f64 = 1.02703333676410069053e+00; /* 0x3FF06EBA, 0x8214DB69 */
+const PP0: f64 = 1.28379167095512558561e-01; /* 0x3FC06EBA, 0x8214DB68 */
+const PP1: f64 = -3.25042107247001499370e-01; /* 0xBFD4CD7D, 0x691CB913 */
+const PP2: f64 = -2.84817495755985104766e-02; /* 0xBF9D2A51, 0xDBD7194F */
+const PP3: f64 = -5.77027029648944159157e-03; /* 0xBF77A291, 0x236668E4 */
+const PP4: f64 = -2.37630166566501626084e-05; /* 0xBEF8EAD6, 0x120016AC */
+const QQ1: f64 = 3.97917223959155352819e-01; /* 0x3FD97779, 0xCDDADC09 */
+const QQ2: f64 = 6.50222499887672944485e-02; /* 0x3FB0A54C, 0x5536CEBA */
+const QQ3: f64 = 5.08130628187576562776e-03; /* 0x3F74D022, 0xC4D36B0F */
+const QQ4: f64 = 1.32494738004321644526e-04; /* 0x3F215DC9, 0x221C1A10 */
+const QQ5: f64 = -3.96022827877536812320e-06; /* 0xBED09C43, 0x42A26120 */
+/*
+ * Coefficients for approximation to erf in [0.84375,1.25]
+ */
+const PA0: f64 = -2.36211856075265944077e-03; /* 0xBF6359B8, 0xBEF77538 */
+const PA1: f64 = 4.14856118683748331666e-01; /* 0x3FDA8D00, 0xAD92B34D */
+const PA2: f64 = -3.72207876035701323847e-01; /* 0xBFD7D240, 0xFBB8C3F1 */
+const PA3: f64 = 3.18346619901161753674e-01; /* 0x3FD45FCA, 0x805120E4 */
+const PA4: f64 = -1.10894694282396677476e-01; /* 0xBFBC6398, 0x3D3E28EC */
+const PA5: f64 = 3.54783043256182359371e-02; /* 0x3FA22A36, 0x599795EB */
+const PA6: f64 = -2.16637559486879084300e-03; /* 0xBF61BF38, 0x0A96073F */
+const QA1: f64 = 1.06420880400844228286e-01; /* 0x3FBB3E66, 0x18EEE323 */
+const QA2: f64 = 5.40397917702171048937e-01; /* 0x3FE14AF0, 0x92EB6F33 */
+const QA3: f64 = 7.18286544141962662868e-02; /* 0x3FB2635C, 0xD99FE9A7 */
+const QA4: f64 = 1.26171219808761642112e-01; /* 0x3FC02660, 0xE763351F */
+const QA5: f64 = 1.36370839120290507362e-02; /* 0x3F8BEDC2, 0x6B51DD1C */
+const QA6: f64 = 1.19844998467991074170e-02; /* 0x3F888B54, 0x5735151D */
+/*
+ * Coefficients for approximation to erfc in [1.25,1/0.35]
+ */
+const RA0: f64 = -9.86494403484714822705e-03; /* 0xBF843412, 0x600D6435 */
+const RA1: f64 = -6.93858572707181764372e-01; /* 0xBFE63416, 0xE4BA7360 */
+const RA2: f64 = -1.05586262253232909814e+01; /* 0xC0251E04, 0x41B0E726 */
+const RA3: f64 = -6.23753324503260060396e+01; /* 0xC04F300A, 0xE4CBA38D */
+const RA4: f64 = -1.62396669462573470355e+02; /* 0xC0644CB1, 0x84282266 */
+const RA5: f64 = -1.84605092906711035994e+02; /* 0xC067135C, 0xEBCCABB2 */
+const RA6: f64 = -8.12874355063065934246e+01; /* 0xC0545265, 0x57E4D2F2 */
+const RA7: f64 = -9.81432934416914548592e+00; /* 0xC023A0EF, 0xC69AC25C */
+const SA1: f64 = 1.96512716674392571292e+01; /* 0x4033A6B9, 0xBD707687 */
+const SA2: f64 = 1.37657754143519042600e+02; /* 0x4061350C, 0x526AE721 */
+const SA3: f64 = 4.34565877475229228821e+02; /* 0x407B290D, 0xD58A1A71 */
+const SA4: f64 = 6.45387271733267880336e+02; /* 0x40842B19, 0x21EC2868 */
+const SA5: f64 = 4.29008140027567833386e+02; /* 0x407AD021, 0x57700314 */
+const SA6: f64 = 1.08635005541779435134e+02; /* 0x405B28A3, 0xEE48AE2C */
+const SA7: f64 = 6.57024977031928170135e+00; /* 0x401A47EF, 0x8E484A93 */
+const SA8: f64 = -6.04244152148580987438e-02; /* 0xBFAEEFF2, 0xEE749A62 */
+/*
+ * Coefficients for approximation to erfc in [1/.35,28]
+ */
+const RB0: f64 = -9.86494292470009928597e-03; /* 0xBF843412, 0x39E86F4A */
+const RB1: f64 = -7.99283237680523006574e-01; /* 0xBFE993BA, 0x70C285DE */
+const RB2: f64 = -1.77579549177547519889e+01; /* 0xC031C209, 0x555F995A */
+const RB3: f64 = -1.60636384855821916062e+02; /* 0xC064145D, 0x43C5ED98 */
+const RB4: f64 = -6.37566443368389627722e+02; /* 0xC083EC88, 0x1375F228 */
+const RB5: f64 = -1.02509513161107724954e+03; /* 0xC0900461, 0x6A2E5992 */
+const RB6: f64 = -4.83519191608651397019e+02; /* 0xC07E384E, 0x9BDC383F */
+const SB1: f64 = 3.03380607434824582924e+01; /* 0x403E568B, 0x261D5190 */
+const SB2: f64 = 3.25792512996573918826e+02; /* 0x40745CAE, 0x221B9F0A */
+const SB3: f64 = 1.53672958608443695994e+03; /* 0x409802EB, 0x189D5118 */
+const SB4: f64 = 3.19985821950859553908e+03; /* 0x40A8FFB7, 0x688C246A */
+const SB5: f64 = 2.55305040643316442583e+03; /* 0x40A3F219, 0xCEDF3BE6 */
+const SB6: f64 = 4.74528541206955367215e+02; /* 0x407DA874, 0xE79FE763 */
+const SB7: f64 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
+
+fn erfc1(x: f64) -> f64 {
+ let s: f64;
+ let p: f64;
+ let q: f64;
+
+ s = fabs(x) - 1.0;
+ p = PA0 + s * (PA1 + s * (PA2 + s * (PA3 + s * (PA4 + s * (PA5 + s * PA6)))));
+ q = 1.0 + s * (QA1 + s * (QA2 + s * (QA3 + s * (QA4 + s * (QA5 + s * QA6)))));
+
+ 1.0 - ERX - p / q
+}
+
+fn erfc2(ix: u32, mut x: f64) -> f64 {
+ let s: f64;
+ let r: f64;
+ let big_s: f64;
+ let z: f64;
+
+ if ix < 0x3ff40000 {
+ /* |x| < 1.25 */
+ return erfc1(x);
+ }
+
+ x = fabs(x);
+ s = 1.0 / (x * x);
+ if ix < 0x4006db6d {
+ /* |x| < 1/.35 ~ 2.85714 */
+ r = RA0 + s * (RA1 + s * (RA2 + s * (RA3 + s * (RA4 + s * (RA5 + s * (RA6 + s * RA7))))));
+ big_s = 1.0
+ + s * (SA1
+ + s * (SA2 + s * (SA3 + s * (SA4 + s * (SA5 + s * (SA6 + s * (SA7 + s * SA8)))))));
+ } else {
+ /* |x| > 1/.35 */
+ r = RB0 + s * (RB1 + s * (RB2 + s * (RB3 + s * (RB4 + s * (RB5 + s * RB6)))));
+ big_s =
+ 1.0 + s * (SB1 + s * (SB2 + s * (SB3 + s * (SB4 + s * (SB5 + s * (SB6 + s * SB7))))));
+ }
+ z = with_set_low_word(x, 0);
+
+ exp(-z * z - 0.5625) * exp((z - x) * (z + x) + r / big_s) / x
+}
+
+/// Error function (f64)
+///
+/// Calculates an approximation to the “error function”, which estimates
+/// the probability that an observation will fall within x standard
+/// deviations of the mean (assuming a normal distribution).
+pub fn erf(x: f64) -> f64 {
+ let r: f64;
+ let s: f64;
+ let z: f64;
+ let y: f64;
+ let mut ix: u32;
+ let sign: usize;
+
+ ix = get_high_word(x);
+ sign = (ix >> 31) as usize;
+ ix &= 0x7fffffff;
+ if ix >= 0x7ff00000 {
+ /* erf(nan)=nan, erf(+-inf)=+-1 */
+ return 1.0 - 2.0 * (sign as f64) + 1.0 / x;
+ }
+ if ix < 0x3feb0000 {
+ /* |x| < 0.84375 */
+ if ix < 0x3e300000 {
+ /* |x| < 2**-28 */
+ /* avoid underflow */
+ return 0.125 * (8.0 * x + EFX8 * x);
+ }
+ z = x * x;
+ r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));
+ s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));
+ y = r / s;
+ return x + x * y;
+ }
+ if ix < 0x40180000 {
+ /* 0.84375 <= |x| < 6 */
+ y = 1.0 - erfc2(ix, x);
+ } else {
+ let x1p_1022 = f64::from_bits(0x0010000000000000);
+ y = 1.0 - x1p_1022;
+ }
+
+ if sign != 0 {
+ -y
+ } else {
+ y
+ }
+}
+
+/// Error function (f64)
+///
+/// Calculates the complementary probability.
+/// Is `1 - erf(x)`. Is computed directly, so that you can use it to avoid
+/// the loss of precision that would result from subtracting
+/// large probabilities (on large `x`) from 1.
+pub fn erfc(x: f64) -> f64 {
+ let r: f64;
+ let s: f64;
+ let z: f64;
+ let y: f64;
+ let mut ix: u32;
+ let sign: usize;
+
+ ix = get_high_word(x);
+ sign = (ix >> 31) as usize;
+ ix &= 0x7fffffff;
+ if ix >= 0x7ff00000 {
+ /* erfc(nan)=nan, erfc(+-inf)=0,2 */
+ return 2.0 * (sign as f64) + 1.0 / x;
+ }
+ if ix < 0x3feb0000 {
+ /* |x| < 0.84375 */
+ if ix < 0x3c700000 {
+ /* |x| < 2**-56 */
+ return 1.0 - x;
+ }
+ z = x * x;
+ r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));
+ s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));
+ y = r / s;
+ if sign != 0 || ix < 0x3fd00000 {
+ /* x < 1/4 */
+ return 1.0 - (x + x * y);
+ }
+ return 0.5 - (x - 0.5 + x * y);
+ }
+ if ix < 0x403c0000 {
+ /* 0.84375 <= |x| < 28 */
+ if sign != 0 {
+ return 2.0 - erfc2(ix, x);
+ } else {
+ return erfc2(ix, x);
+ }
+ }
+
+ let x1p_1022 = f64::from_bits(0x0010000000000000);
+ if sign != 0 {
+ 2.0 - x1p_1022
+ } else {
+ x1p_1022 * x1p_1022
+ }
+}
diff --git a/src/math/erff.rs b/src/math/erff.rs
new file mode 100644
index 0000000..3840522
--- /dev/null
+++ b/src/math/erff.rs
@@ -0,0 +1,229 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_erff.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{expf, fabsf};
+
+const ERX: f32 = 8.4506291151e-01; /* 0x3f58560b */
+/*
+ * Coefficients for approximation to erf on [0,0.84375]
+ */
+const EFX8: f32 = 1.0270333290e+00; /* 0x3f8375d4 */
+const PP0: f32 = 1.2837916613e-01; /* 0x3e0375d4 */
+const PP1: f32 = -3.2504209876e-01; /* 0xbea66beb */
+const PP2: f32 = -2.8481749818e-02; /* 0xbce9528f */
+const PP3: f32 = -5.7702702470e-03; /* 0xbbbd1489 */
+const PP4: f32 = -2.3763017452e-05; /* 0xb7c756b1 */
+const QQ1: f32 = 3.9791721106e-01; /* 0x3ecbbbce */
+const QQ2: f32 = 6.5022252500e-02; /* 0x3d852a63 */
+const QQ3: f32 = 5.0813062117e-03; /* 0x3ba68116 */
+const QQ4: f32 = 1.3249473704e-04; /* 0x390aee49 */
+const QQ5: f32 = -3.9602282413e-06; /* 0xb684e21a */
+/*
+ * Coefficients for approximation to erf in [0.84375,1.25]
+ */
+const PA0: f32 = -2.3621185683e-03; /* 0xbb1acdc6 */
+const PA1: f32 = 4.1485610604e-01; /* 0x3ed46805 */
+const PA2: f32 = -3.7220788002e-01; /* 0xbebe9208 */
+const PA3: f32 = 3.1834661961e-01; /* 0x3ea2fe54 */
+const PA4: f32 = -1.1089469492e-01; /* 0xbde31cc2 */
+const PA5: f32 = 3.5478305072e-02; /* 0x3d1151b3 */
+const PA6: f32 = -2.1663755178e-03; /* 0xbb0df9c0 */
+const QA1: f32 = 1.0642088205e-01; /* 0x3dd9f331 */
+const QA2: f32 = 5.4039794207e-01; /* 0x3f0a5785 */
+const QA3: f32 = 7.1828655899e-02; /* 0x3d931ae7 */
+const QA4: f32 = 1.2617121637e-01; /* 0x3e013307 */
+const QA5: f32 = 1.3637083583e-02; /* 0x3c5f6e13 */
+const QA6: f32 = 1.1984500103e-02; /* 0x3c445aa3 */
+/*
+ * Coefficients for approximation to erfc in [1.25,1/0.35]
+ */
+const RA0: f32 = -9.8649440333e-03; /* 0xbc21a093 */
+const RA1: f32 = -6.9385856390e-01; /* 0xbf31a0b7 */
+const RA2: f32 = -1.0558626175e+01; /* 0xc128f022 */
+const RA3: f32 = -6.2375331879e+01; /* 0xc2798057 */
+const RA4: f32 = -1.6239666748e+02; /* 0xc322658c */
+const RA5: f32 = -1.8460508728e+02; /* 0xc3389ae7 */
+const RA6: f32 = -8.1287437439e+01; /* 0xc2a2932b */
+const RA7: f32 = -9.8143291473e+00; /* 0xc11d077e */
+const SA1: f32 = 1.9651271820e+01; /* 0x419d35ce */
+const SA2: f32 = 1.3765776062e+02; /* 0x4309a863 */
+const SA3: f32 = 4.3456588745e+02; /* 0x43d9486f */
+const SA4: f32 = 6.4538726807e+02; /* 0x442158c9 */
+const SA5: f32 = 4.2900814819e+02; /* 0x43d6810b */
+const SA6: f32 = 1.0863500214e+02; /* 0x42d9451f */
+const SA7: f32 = 6.5702495575e+00; /* 0x40d23f7c */
+const SA8: f32 = -6.0424413532e-02; /* 0xbd777f97 */
+/*
+ * Coefficients for approximation to erfc in [1/.35,28]
+ */
+const RB0: f32 = -9.8649431020e-03; /* 0xbc21a092 */
+const RB1: f32 = -7.9928326607e-01; /* 0xbf4c9dd4 */
+const RB2: f32 = -1.7757955551e+01; /* 0xc18e104b */
+const RB3: f32 = -1.6063638306e+02; /* 0xc320a2ea */
+const RB4: f32 = -6.3756646729e+02; /* 0xc41f6441 */
+const RB5: f32 = -1.0250950928e+03; /* 0xc480230b */
+const RB6: f32 = -4.8351919556e+02; /* 0xc3f1c275 */
+const SB1: f32 = 3.0338060379e+01; /* 0x41f2b459 */
+const SB2: f32 = 3.2579251099e+02; /* 0x43a2e571 */
+const SB3: f32 = 1.5367296143e+03; /* 0x44c01759 */
+const SB4: f32 = 3.1998581543e+03; /* 0x4547fdbb */
+const SB5: f32 = 2.5530502930e+03; /* 0x451f90ce */
+const SB6: f32 = 4.7452853394e+02; /* 0x43ed43a7 */
+const SB7: f32 = -2.2440952301e+01; /* 0xc1b38712 */
+
+fn erfc1(x: f32) -> f32 {
+ let s: f32;
+ let p: f32;
+ let q: f32;
+
+ s = fabsf(x) - 1.0;
+ p = PA0 + s * (PA1 + s * (PA2 + s * (PA3 + s * (PA4 + s * (PA5 + s * PA6)))));
+ q = 1.0 + s * (QA1 + s * (QA2 + s * (QA3 + s * (QA4 + s * (QA5 + s * QA6)))));
+ return 1.0 - ERX - p / q;
+}
+
+fn erfc2(mut ix: u32, mut x: f32) -> f32 {
+ let s: f32;
+ let r: f32;
+ let big_s: f32;
+ let z: f32;
+
+ if ix < 0x3fa00000 {
+ /* |x| < 1.25 */
+ return erfc1(x);
+ }
+
+ x = fabsf(x);
+ s = 1.0 / (x * x);
+ if ix < 0x4036db6d {
+ /* |x| < 1/0.35 */
+ r = RA0 + s * (RA1 + s * (RA2 + s * (RA3 + s * (RA4 + s * (RA5 + s * (RA6 + s * RA7))))));
+ big_s = 1.0
+ + s * (SA1
+ + s * (SA2 + s * (SA3 + s * (SA4 + s * (SA5 + s * (SA6 + s * (SA7 + s * SA8)))))));
+ } else {
+ /* |x| >= 1/0.35 */
+ r = RB0 + s * (RB1 + s * (RB2 + s * (RB3 + s * (RB4 + s * (RB5 + s * RB6)))));
+ big_s =
+ 1.0 + s * (SB1 + s * (SB2 + s * (SB3 + s * (SB4 + s * (SB5 + s * (SB6 + s * SB7))))));
+ }
+ ix = x.to_bits();
+ z = f32::from_bits(ix & 0xffffe000);
+
+ expf(-z * z - 0.5625) * expf((z - x) * (z + x) + r / big_s) / x
+}
+
+/// Error function (f32)
+///
+/// Calculates an approximation to the “error function”, which estimates
+/// the probability that an observation will fall within x standard
+/// deviations of the mean (assuming a normal distribution).
+pub fn erff(x: f32) -> f32 {
+ let r: f32;
+ let s: f32;
+ let z: f32;
+ let y: f32;
+ let mut ix: u32;
+ let sign: usize;
+
+ ix = x.to_bits();
+ sign = (ix >> 31) as usize;
+ ix &= 0x7fffffff;
+ if ix >= 0x7f800000 {
+ /* erf(nan)=nan, erf(+-inf)=+-1 */
+ return 1.0 - 2.0 * (sign as f32) + 1.0 / x;
+ }
+ if ix < 0x3f580000 {
+ /* |x| < 0.84375 */
+ if ix < 0x31800000 {
+ /* |x| < 2**-28 */
+ /*avoid underflow */
+ return 0.125 * (8.0 * x + EFX8 * x);
+ }
+ z = x * x;
+ r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));
+ s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));
+ y = r / s;
+ return x + x * y;
+ }
+ if ix < 0x40c00000 {
+ /* |x| < 6 */
+ y = 1.0 - erfc2(ix, x);
+ } else {
+ let x1p_120 = f32::from_bits(0x03800000);
+ y = 1.0 - x1p_120;
+ }
+
+ if sign != 0 {
+ -y
+ } else {
+ y
+ }
+}
+
+/// Error function (f32)
+///
+/// Calculates the complementary probability.
+/// Is `1 - erf(x)`. Is computed directly, so that you can use it to avoid
+/// the loss of precision that would result from subtracting
+/// large probabilities (on large `x`) from 1.
+pub fn erfcf(x: f32) -> f32 {
+ let r: f32;
+ let s: f32;
+ let z: f32;
+ let y: f32;
+ let mut ix: u32;
+ let sign: usize;
+
+ ix = x.to_bits();
+ sign = (ix >> 31) as usize;
+ ix &= 0x7fffffff;
+ if ix >= 0x7f800000 {
+ /* erfc(nan)=nan, erfc(+-inf)=0,2 */
+ return 2.0 * (sign as f32) + 1.0 / x;
+ }
+
+ if ix < 0x3f580000 {
+ /* |x| < 0.84375 */
+ if ix < 0x23800000 {
+ /* |x| < 2**-56 */
+ return 1.0 - x;
+ }
+ z = x * x;
+ r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));
+ s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));
+ y = r / s;
+ if sign != 0 || ix < 0x3e800000 {
+ /* x < 1/4 */
+ return 1.0 - (x + x * y);
+ }
+ return 0.5 - (x - 0.5 + x * y);
+ }
+ if ix < 0x41e00000 {
+ /* |x| < 28 */
+ if sign != 0 {
+ return 2.0 - erfc2(ix, x);
+ } else {
+ return erfc2(ix, x);
+ }
+ }
+
+ let x1p_120 = f32::from_bits(0x03800000);
+ if sign != 0 {
+ 2.0 - x1p_120
+ } else {
+ x1p_120 * x1p_120
+ }
+}
diff --git a/src/math/exp.rs b/src/math/exp.rs
new file mode 100644
index 0000000..5b163f9
--- /dev/null
+++ b/src/math/exp.rs
@@ -0,0 +1,154 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_exp.c */
+/*
+ * ====================================================
+ * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* exp(x)
+ * Returns the exponential of x.
+ *
+ * Method
+ * 1. Argument reduction:
+ * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
+ * Given x, find r and integer k such that
+ *
+ * x = k*ln2 + r, |r| <= 0.5*ln2.
+ *
+ * Here r will be represented as r = hi-lo for better
+ * accuracy.
+ *
+ * 2. Approximation of exp(r) by a special rational function on
+ * the interval [0,0.34658]:
+ * Write
+ * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
+ * We use a special Remez algorithm on [0,0.34658] to generate
+ * a polynomial of degree 5 to approximate R. The maximum error
+ * of this polynomial approximation is bounded by 2**-59. In
+ * other words,
+ * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
+ * (where z=r*r, and the values of P1 to P5 are listed below)
+ * and
+ * | 5 | -59
+ * | 2.0+P1*z+...+P5*z - R(z) | <= 2
+ * | |
+ * The computation of exp(r) thus becomes
+ * 2*r
+ * exp(r) = 1 + ----------
+ * R(r) - r
+ * r*c(r)
+ * = 1 + r + ----------- (for better accuracy)
+ * 2 - c(r)
+ * where
+ * 2 4 10
+ * c(r) = r - (P1*r + P2*r + ... + P5*r ).
+ *
+ * 3. Scale back to obtain exp(x):
+ * From step 1, we have
+ * exp(x) = 2^k * exp(r)
+ *
+ * Special cases:
+ * exp(INF) is INF, exp(NaN) is NaN;
+ * exp(-INF) is 0, and
+ * for finite argument, only exp(0)=1 is exact.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * Misc. info.
+ * For IEEE double
+ * if x > 709.782712893383973096 then exp(x) overflows
+ * if x < -745.133219101941108420 then exp(x) underflows
+ */
+
+use super::scalbn;
+
+const HALF: [f64; 2] = [0.5, -0.5];
+const LN2HI: f64 = 6.93147180369123816490e-01; /* 0x3fe62e42, 0xfee00000 */
+const LN2LO: f64 = 1.90821492927058770002e-10; /* 0x3dea39ef, 0x35793c76 */
+const INVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
+const P1: f64 = 1.66666666666666019037e-01; /* 0x3FC55555, 0x5555553E */
+const P2: f64 = -2.77777777770155933842e-03; /* 0xBF66C16C, 0x16BEBD93 */
+const P3: f64 = 6.61375632143793436117e-05; /* 0x3F11566A, 0xAF25DE2C */
+const P4: f64 = -1.65339022054652515390e-06; /* 0xBEBBBD41, 0xC5D26BF1 */
+const P5: f64 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
+
+/// Exponential, base *e* (f64)
+///
+/// Calculate the exponential of `x`, that is, *e* raised to the power `x`
+/// (where *e* is the base of the natural system of logarithms, approximately 2.71828).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn exp(mut x: f64) -> f64 {
+ let x1p1023 = f64::from_bits(0x7fe0000000000000); // 0x1p1023 === 2 ^ 1023
+ let x1p_149 = f64::from_bits(0x36a0000000000000); // 0x1p-149 === 2 ^ -149
+
+ let hi: f64;
+ let lo: f64;
+ let c: f64;
+ let xx: f64;
+ let y: f64;
+ let k: i32;
+ let sign: i32;
+ let mut hx: u32;
+
+ hx = (x.to_bits() >> 32) as u32;
+ sign = (hx >> 31) as i32;
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* special cases */
+ if hx >= 0x4086232b {
+ /* if |x| >= 708.39... */
+ if x.is_nan() {
+ return x;
+ }
+ if x > 709.782712893383973096 {
+ /* overflow if x!=inf */
+ x *= x1p1023;
+ return x;
+ }
+ if x < -708.39641853226410622 {
+ /* underflow if x!=-inf */
+ force_eval!((-x1p_149 / x) as f32);
+ if x < -745.13321910194110842 {
+ return 0.;
+ }
+ }
+ }
+
+ /* argument reduction */
+ if hx > 0x3fd62e42 {
+ /* if |x| > 0.5 ln2 */
+ if hx >= 0x3ff0a2b2 {
+ /* if |x| >= 1.5 ln2 */
+ k = (INVLN2 * x + HALF[sign as usize]) as i32;
+ } else {
+ k = 1 - sign - sign;
+ }
+ hi = x - k as f64 * LN2HI; /* k*ln2hi is exact here */
+ lo = k as f64 * LN2LO;
+ x = hi - lo;
+ } else if hx > 0x3e300000 {
+ /* if |x| > 2**-28 */
+ k = 0;
+ hi = x;
+ lo = 0.;
+ } else {
+ /* inexact if x!=0 */
+ force_eval!(x1p1023 + x);
+ return 1. + x;
+ }
+
+ /* x is now in primary range */
+ xx = x * x;
+ c = x - xx * (P1 + xx * (P2 + xx * (P3 + xx * (P4 + xx * P5))));
+ y = 1. + (x * c / (2. - c) - lo + hi);
+ if k == 0 {
+ y
+ } else {
+ scalbn(y, k)
+ }
+}
diff --git a/src/math/exp10.rs b/src/math/exp10.rs
new file mode 100644
index 0000000..9537f76
--- /dev/null
+++ b/src/math/exp10.rs
@@ -0,0 +1,21 @@
+use super::{exp2, modf, pow};
+
+const LN10: f64 = 3.32192809488736234787031942948939;
+const P10: &[f64] = &[
+ 1e-15, 1e-14, 1e-13, 1e-12, 1e-11, 1e-10, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1,
+ 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15,
+];
+
+pub fn exp10(x: f64) -> f64 {
+ let (mut y, n) = modf(x);
+ let u: u64 = n.to_bits();
+ /* fabs(n) < 16 without raising invalid on nan */
+ if (u >> 52 & 0x7ff) < 0x3ff + 4 {
+ if y == 0.0 {
+ return P10[((n as isize) + 15) as usize];
+ }
+ y = exp2(LN10 * y);
+ return y * P10[((n as isize) + 15) as usize];
+ }
+ return pow(10.0, x);
+}
diff --git a/src/math/exp10f.rs b/src/math/exp10f.rs
new file mode 100644
index 0000000..d45fff3
--- /dev/null
+++ b/src/math/exp10f.rs
@@ -0,0 +1,21 @@
+use super::{exp2, exp2f, modff};
+
+const LN10_F32: f32 = 3.32192809488736234787031942948939;
+const LN10_F64: f64 = 3.32192809488736234787031942948939;
+const P10: &[f32] = &[
+ 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7,
+];
+
+pub fn exp10f(x: f32) -> f32 {
+ let (mut y, n) = modff(x);
+ let u = n.to_bits();
+ /* fabsf(n) < 8 without raising invalid on nan */
+ if (u >> 23 & 0xff) < 0x7f + 3 {
+ if y == 0.0 {
+ return P10[((n as isize) + 7) as usize];
+ }
+ y = exp2f(LN10_F32 * y);
+ return y * P10[((n as isize) + 7) as usize];
+ }
+ return exp2(LN10_F64 * (x as f64)) as f32;
+}
diff --git a/src/math/exp2.rs b/src/math/exp2.rs
new file mode 100644
index 0000000..8ea434d
--- /dev/null
+++ b/src/math/exp2.rs
@@ -0,0 +1,394 @@
+// origin: FreeBSD /usr/src/lib/msun/src/s_exp2.c */
+//-
+// Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
+// All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions
+// are met:
+// 1. Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+// 2. Redistributions in binary form must reproduce the above copyright
+// notice, this list of conditions and the following disclaimer in the
+// documentation and/or other materials provided with the distribution.
+//
+// THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+// OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+// OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+// SUCH DAMAGE.
+
+use super::scalbn;
+
+const TBLSIZE: usize = 256;
+
+#[cfg_attr(rustfmt, rustfmt_skip)]
+static TBL: [u64; TBLSIZE * 2] = [
+ // exp2(z + eps) eps
+ 0x3fe6a09e667f3d5d, 0x3d39880000000000,
+ 0x3fe6b052fa751744, 0x3cd8000000000000,
+ 0x3fe6c012750bd9fe, 0xbd28780000000000,
+ 0x3fe6cfdcddd476bf, 0x3d1ec00000000000,
+ 0x3fe6dfb23c651a29, 0xbcd8000000000000,
+ 0x3fe6ef9298593ae3, 0xbcbc000000000000,
+ 0x3fe6ff7df9519386, 0xbd2fd80000000000,
+ 0x3fe70f7466f42da3, 0xbd2c880000000000,
+ 0x3fe71f75e8ec5fc3, 0x3d13c00000000000,
+ 0x3fe72f8286eacf05, 0xbd38300000000000,
+ 0x3fe73f9a48a58152, 0xbd00c00000000000,
+ 0x3fe74fbd35d7ccfc, 0x3d2f880000000000,
+ 0x3fe75feb564267f1, 0x3d03e00000000000,
+ 0x3fe77024b1ab6d48, 0xbd27d00000000000,
+ 0x3fe780694fde5d38, 0xbcdd000000000000,
+ 0x3fe790b938ac1d00, 0x3ce3000000000000,
+ 0x3fe7a11473eb0178, 0xbced000000000000,
+ 0x3fe7b17b0976d060, 0x3d20400000000000,
+ 0x3fe7c1ed0130c133, 0x3ca0000000000000,
+ 0x3fe7d26a62ff8636, 0xbd26900000000000,
+ 0x3fe7e2f336cf4e3b, 0xbd02e00000000000,
+ 0x3fe7f3878491c3e8, 0xbd24580000000000,
+ 0x3fe80427543e1b4e, 0x3d33000000000000,
+ 0x3fe814d2add1071a, 0x3d0f000000000000,
+ 0x3fe82589994ccd7e, 0xbd21c00000000000,
+ 0x3fe8364c1eb942d0, 0x3d29d00000000000,
+ 0x3fe8471a4623cab5, 0x3d47100000000000,
+ 0x3fe857f4179f5bbc, 0x3d22600000000000,
+ 0x3fe868d99b4491af, 0xbd32c40000000000,
+ 0x3fe879cad931a395, 0xbd23000000000000,
+ 0x3fe88ac7d98a65b8, 0xbd2a800000000000,
+ 0x3fe89bd0a4785800, 0xbced000000000000,
+ 0x3fe8ace5422aa223, 0x3d33280000000000,
+ 0x3fe8be05bad619fa, 0x3d42b40000000000,
+ 0x3fe8cf3216b54383, 0xbd2ed00000000000,
+ 0x3fe8e06a5e08664c, 0xbd20500000000000,
+ 0x3fe8f1ae99157807, 0x3d28280000000000,
+ 0x3fe902fed0282c0e, 0xbd1cb00000000000,
+ 0x3fe9145b0b91ff96, 0xbd05e00000000000,
+ 0x3fe925c353aa2ff9, 0x3cf5400000000000,
+ 0x3fe93737b0cdc64a, 0x3d17200000000000,
+ 0x3fe948b82b5f98ae, 0xbd09000000000000,
+ 0x3fe95a44cbc852cb, 0x3d25680000000000,
+ 0x3fe96bdd9a766f21, 0xbd36d00000000000,
+ 0x3fe97d829fde4e2a, 0xbd01000000000000,
+ 0x3fe98f33e47a23a3, 0x3d2d000000000000,
+ 0x3fe9a0f170ca0604, 0xbd38a40000000000,
+ 0x3fe9b2bb4d53ff89, 0x3d355c0000000000,
+ 0x3fe9c49182a3f15b, 0x3d26b80000000000,
+ 0x3fe9d674194bb8c5, 0xbcec000000000000,
+ 0x3fe9e86319e3238e, 0x3d17d00000000000,
+ 0x3fe9fa5e8d07f302, 0x3d16400000000000,
+ 0x3fea0c667b5de54d, 0xbcf5000000000000,
+ 0x3fea1e7aed8eb8f6, 0x3d09e00000000000,
+ 0x3fea309bec4a2e27, 0x3d2ad80000000000,
+ 0x3fea42c980460a5d, 0xbd1af00000000000,
+ 0x3fea5503b23e259b, 0x3d0b600000000000,
+ 0x3fea674a8af46213, 0x3d38880000000000,
+ 0x3fea799e1330b3a7, 0x3d11200000000000,
+ 0x3fea8bfe53c12e8d, 0x3d06c00000000000,
+ 0x3fea9e6b5579fcd2, 0xbd29b80000000000,
+ 0x3feab0e521356fb8, 0x3d2b700000000000,
+ 0x3feac36bbfd3f381, 0x3cd9000000000000,
+ 0x3fead5ff3a3c2780, 0x3ce4000000000000,
+ 0x3feae89f995ad2a3, 0xbd2c900000000000,
+ 0x3feafb4ce622f367, 0x3d16500000000000,
+ 0x3feb0e07298db790, 0x3d2fd40000000000,
+ 0x3feb20ce6c9a89a9, 0x3d12700000000000,
+ 0x3feb33a2b84f1a4b, 0x3d4d470000000000,
+ 0x3feb468415b747e7, 0xbd38380000000000,
+ 0x3feb59728de5593a, 0x3c98000000000000,
+ 0x3feb6c6e29f1c56a, 0x3d0ad00000000000,
+ 0x3feb7f76f2fb5e50, 0x3cde800000000000,
+ 0x3feb928cf22749b2, 0xbd04c00000000000,
+ 0x3feba5b030a10603, 0xbd0d700000000000,
+ 0x3febb8e0b79a6f66, 0x3d0d900000000000,
+ 0x3febcc1e904bc1ff, 0x3d02a00000000000,
+ 0x3febdf69c3f3a16f, 0xbd1f780000000000,
+ 0x3febf2c25bd71db8, 0xbd10a00000000000,
+ 0x3fec06286141b2e9, 0xbd11400000000000,
+ 0x3fec199bdd8552e0, 0x3d0be00000000000,
+ 0x3fec2d1cd9fa64ee, 0xbd09400000000000,
+ 0x3fec40ab5fffd02f, 0xbd0ed00000000000,
+ 0x3fec544778fafd15, 0x3d39660000000000,
+ 0x3fec67f12e57d0cb, 0xbd1a100000000000,
+ 0x3fec7ba88988c1b6, 0xbd58458000000000,
+ 0x3fec8f6d9406e733, 0xbd1a480000000000,
+ 0x3feca3405751c4df, 0x3ccb000000000000,
+ 0x3fecb720dcef9094, 0x3d01400000000000,
+ 0x3feccb0f2e6d1689, 0x3cf0200000000000,
+ 0x3fecdf0b555dc412, 0x3cf3600000000000,
+ 0x3fecf3155b5bab3b, 0xbd06900000000000,
+ 0x3fed072d4a0789bc, 0x3d09a00000000000,
+ 0x3fed1b532b08c8fa, 0xbd15e00000000000,
+ 0x3fed2f87080d8a85, 0x3d1d280000000000,
+ 0x3fed43c8eacaa203, 0x3d01a00000000000,
+ 0x3fed5818dcfba491, 0x3cdf000000000000,
+ 0x3fed6c76e862e6a1, 0xbd03a00000000000,
+ 0x3fed80e316c9834e, 0xbd0cd80000000000,
+ 0x3fed955d71ff6090, 0x3cf4c00000000000,
+ 0x3feda9e603db32ae, 0x3cff900000000000,
+ 0x3fedbe7cd63a8325, 0x3ce9800000000000,
+ 0x3fedd321f301b445, 0xbcf5200000000000,
+ 0x3fede7d5641c05bf, 0xbd1d700000000000,
+ 0x3fedfc97337b9aec, 0xbd16140000000000,
+ 0x3fee11676b197d5e, 0x3d0b480000000000,
+ 0x3fee264614f5a3e7, 0x3d40ce0000000000,
+ 0x3fee3b333b16ee5c, 0x3d0c680000000000,
+ 0x3fee502ee78b3fb4, 0xbd09300000000000,
+ 0x3fee653924676d68, 0xbce5000000000000,
+ 0x3fee7a51fbc74c44, 0xbd07f80000000000,
+ 0x3fee8f7977cdb726, 0xbcf3700000000000,
+ 0x3feea4afa2a490e8, 0x3ce5d00000000000,
+ 0x3feeb9f4867ccae4, 0x3d161a0000000000,
+ 0x3feecf482d8e680d, 0x3cf5500000000000,
+ 0x3feee4aaa2188514, 0x3cc6400000000000,
+ 0x3feefa1bee615a13, 0xbcee800000000000,
+ 0x3fef0f9c1cb64106, 0xbcfa880000000000,
+ 0x3fef252b376bb963, 0xbd2c900000000000,
+ 0x3fef3ac948dd7275, 0x3caa000000000000,
+ 0x3fef50765b6e4524, 0xbcf4f00000000000,
+ 0x3fef6632798844fd, 0x3cca800000000000,
+ 0x3fef7bfdad9cbe38, 0x3cfabc0000000000,
+ 0x3fef91d802243c82, 0xbcd4600000000000,
+ 0x3fefa7c1819e908e, 0xbd0b0c0000000000,
+ 0x3fefbdba3692d511, 0xbcc0e00000000000,
+ 0x3fefd3c22b8f7194, 0xbd10de8000000000,
+ 0x3fefe9d96b2a23ee, 0x3cee430000000000,
+ 0x3ff0000000000000, 0x0,
+ 0x3ff00b1afa5abcbe, 0xbcb3400000000000,
+ 0x3ff0163da9fb3303, 0xbd12170000000000,
+ 0x3ff02168143b0282, 0x3cba400000000000,
+ 0x3ff02c9a3e77806c, 0x3cef980000000000,
+ 0x3ff037d42e11bbca, 0xbcc7400000000000,
+ 0x3ff04315e86e7f89, 0x3cd8300000000000,
+ 0x3ff04e5f72f65467, 0xbd1a3f0000000000,
+ 0x3ff059b0d315855a, 0xbd02840000000000,
+ 0x3ff0650a0e3c1f95, 0x3cf1600000000000,
+ 0x3ff0706b29ddf71a, 0x3d15240000000000,
+ 0x3ff07bd42b72a82d, 0xbce9a00000000000,
+ 0x3ff0874518759bd0, 0x3ce6400000000000,
+ 0x3ff092bdf66607c8, 0xbd00780000000000,
+ 0x3ff09e3ecac6f383, 0xbc98000000000000,
+ 0x3ff0a9c79b1f3930, 0x3cffa00000000000,
+ 0x3ff0b5586cf988fc, 0xbcfac80000000000,
+ 0x3ff0c0f145e46c8a, 0x3cd9c00000000000,
+ 0x3ff0cc922b724816, 0x3d05200000000000,
+ 0x3ff0d83b23395dd8, 0xbcfad00000000000,
+ 0x3ff0e3ec32d3d1f3, 0x3d1bac0000000000,
+ 0x3ff0efa55fdfa9a6, 0xbd04e80000000000,
+ 0x3ff0fb66affed2f0, 0xbd0d300000000000,
+ 0x3ff1073028d7234b, 0x3cf1500000000000,
+ 0x3ff11301d0125b5b, 0x3cec000000000000,
+ 0x3ff11edbab5e2af9, 0x3d16bc0000000000,
+ 0x3ff12abdc06c31d5, 0x3ce8400000000000,
+ 0x3ff136a814f2047d, 0xbd0ed00000000000,
+ 0x3ff1429aaea92de9, 0x3ce8e00000000000,
+ 0x3ff14e95934f3138, 0x3ceb400000000000,
+ 0x3ff15a98c8a58e71, 0x3d05300000000000,
+ 0x3ff166a45471c3df, 0x3d03380000000000,
+ 0x3ff172b83c7d5211, 0x3d28d40000000000,
+ 0x3ff17ed48695bb9f, 0xbd05d00000000000,
+ 0x3ff18af9388c8d93, 0xbd1c880000000000,
+ 0x3ff1972658375d66, 0x3d11f00000000000,
+ 0x3ff1a35beb6fcba7, 0x3d10480000000000,
+ 0x3ff1af99f81387e3, 0xbd47390000000000,
+ 0x3ff1bbe084045d54, 0x3d24e40000000000,
+ 0x3ff1c82f95281c43, 0xbd0a200000000000,
+ 0x3ff1d4873168b9b2, 0x3ce3800000000000,
+ 0x3ff1e0e75eb44031, 0x3ceac00000000000,
+ 0x3ff1ed5022fcd938, 0x3d01900000000000,
+ 0x3ff1f9c18438cdf7, 0xbd1b780000000000,
+ 0x3ff2063b88628d8f, 0x3d2d940000000000,
+ 0x3ff212be3578a81e, 0x3cd8000000000000,
+ 0x3ff21f49917ddd41, 0x3d2b340000000000,
+ 0x3ff22bdda2791323, 0x3d19f80000000000,
+ 0x3ff2387a6e7561e7, 0xbd19c80000000000,
+ 0x3ff2451ffb821427, 0x3d02300000000000,
+ 0x3ff251ce4fb2a602, 0xbd13480000000000,
+ 0x3ff25e85711eceb0, 0x3d12700000000000,
+ 0x3ff26b4565e27d16, 0x3d11d00000000000,
+ 0x3ff2780e341de00f, 0x3d31ee0000000000,
+ 0x3ff284dfe1f5633e, 0xbd14c00000000000,
+ 0x3ff291ba7591bb30, 0xbd13d80000000000,
+ 0x3ff29e9df51fdf09, 0x3d08b00000000000,
+ 0x3ff2ab8a66d10e9b, 0xbd227c0000000000,
+ 0x3ff2b87fd0dada3a, 0x3d2a340000000000,
+ 0x3ff2c57e39771af9, 0xbd10800000000000,
+ 0x3ff2d285a6e402d9, 0xbd0ed00000000000,
+ 0x3ff2df961f641579, 0xbcf4200000000000,
+ 0x3ff2ecafa93e2ecf, 0xbd24980000000000,
+ 0x3ff2f9d24abd8822, 0xbd16300000000000,
+ 0x3ff306fe0a31b625, 0xbd32360000000000,
+ 0x3ff31432edeea50b, 0xbd70df8000000000,
+ 0x3ff32170fc4cd7b8, 0xbd22480000000000,
+ 0x3ff32eb83ba8e9a2, 0xbd25980000000000,
+ 0x3ff33c08b2641766, 0x3d1ed00000000000,
+ 0x3ff3496266e3fa27, 0xbcdc000000000000,
+ 0x3ff356c55f929f0f, 0xbd30d80000000000,
+ 0x3ff36431a2de88b9, 0x3d22c80000000000,
+ 0x3ff371a7373aaa39, 0x3d20600000000000,
+ 0x3ff37f26231e74fe, 0xbd16600000000000,
+ 0x3ff38cae6d05d838, 0xbd0ae00000000000,
+ 0x3ff39a401b713ec3, 0xbd44720000000000,
+ 0x3ff3a7db34e5a020, 0x3d08200000000000,
+ 0x3ff3b57fbfec6e95, 0x3d3e800000000000,
+ 0x3ff3c32dc313a8f2, 0x3cef800000000000,
+ 0x3ff3d0e544ede122, 0xbd17a00000000000,
+ 0x3ff3dea64c1234bb, 0x3d26300000000000,
+ 0x3ff3ec70df1c4ecc, 0xbd48a60000000000,
+ 0x3ff3fa4504ac7e8c, 0xbd3cdc0000000000,
+ 0x3ff40822c367a0bb, 0x3d25b80000000000,
+ 0x3ff4160a21f72e95, 0x3d1ec00000000000,
+ 0x3ff423fb27094646, 0xbd13600000000000,
+ 0x3ff431f5d950a920, 0x3d23980000000000,
+ 0x3ff43ffa3f84b9eb, 0x3cfa000000000000,
+ 0x3ff44e0860618919, 0xbcf6c00000000000,
+ 0x3ff45c2042a7d201, 0xbd0bc00000000000,
+ 0x3ff46a41ed1d0016, 0xbd12800000000000,
+ 0x3ff4786d668b3326, 0x3d30e00000000000,
+ 0x3ff486a2b5c13c00, 0xbd2d400000000000,
+ 0x3ff494e1e192af04, 0x3d0c200000000000,
+ 0x3ff4a32af0d7d372, 0xbd1e500000000000,
+ 0x3ff4b17dea6db801, 0x3d07800000000000,
+ 0x3ff4bfdad53629e1, 0xbd13800000000000,
+ 0x3ff4ce41b817c132, 0x3d00800000000000,
+ 0x3ff4dcb299fddddb, 0x3d2c700000000000,
+ 0x3ff4eb2d81d8ab96, 0xbd1ce00000000000,
+ 0x3ff4f9b2769d2d02, 0x3d19200000000000,
+ 0x3ff508417f4531c1, 0xbd08c00000000000,
+ 0x3ff516daa2cf662a, 0xbcfa000000000000,
+ 0x3ff5257de83f51ea, 0x3d4a080000000000,
+ 0x3ff5342b569d4eda, 0xbd26d80000000000,
+ 0x3ff542e2f4f6ac1a, 0xbd32440000000000,
+ 0x3ff551a4ca5d94db, 0x3d483c0000000000,
+ 0x3ff56070dde9116b, 0x3d24b00000000000,
+ 0x3ff56f4736b529de, 0x3d415a0000000000,
+ 0x3ff57e27dbe2c40e, 0xbd29e00000000000,
+ 0x3ff58d12d497c76f, 0xbd23080000000000,
+ 0x3ff59c0827ff0b4c, 0x3d4dec0000000000,
+ 0x3ff5ab07dd485427, 0xbcc4000000000000,
+ 0x3ff5ba11fba87af4, 0x3d30080000000000,
+ 0x3ff5c9268a59460b, 0xbd26c80000000000,
+ 0x3ff5d84590998e3f, 0x3d469a0000000000,
+ 0x3ff5e76f15ad20e1, 0xbd1b400000000000,
+ 0x3ff5f6a320dcebca, 0x3d17700000000000,
+ 0x3ff605e1b976dcb8, 0x3d26f80000000000,
+ 0x3ff6152ae6cdf715, 0x3d01000000000000,
+ 0x3ff6247eb03a5531, 0xbd15d00000000000,
+ 0x3ff633dd1d1929b5, 0xbd12d00000000000,
+ 0x3ff6434634ccc313, 0xbcea800000000000,
+ 0x3ff652b9febc8efa, 0xbd28600000000000,
+ 0x3ff6623882553397, 0x3d71fe0000000000,
+ 0x3ff671c1c708328e, 0xbd37200000000000,
+ 0x3ff68155d44ca97e, 0x3ce6800000000000,
+ 0x3ff690f4b19e9471, 0xbd29780000000000,
+];
+
+// exp2(x): compute the base 2 exponential of x
+//
+// Accuracy: Peak error < 0.503 ulp for normalized results.
+//
+// Method: (accurate tables)
+//
+// Reduce x:
+// x = k + y, for integer k and |y| <= 1/2.
+// Thus we have exp2(x) = 2**k * exp2(y).
+//
+// Reduce y:
+// y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE.
+// Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]),
+// with |z - eps[i]| <= 2**-9 + 2**-39 for the table used.
+//
+// We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via
+// a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61.
+// The values in exp2t[] and eps[] are chosen such that
+// exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such
+// that exp2t[i] is accurate to 2**-64.
+//
+// Note that the range of i is +-TBLSIZE/2, so we actually index the tables
+// by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are
+// virtual tables, interleaved in the real table tbl[].
+//
+// This method is due to Gal, with many details due to Gal and Bachelis:
+//
+// Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library
+// for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991).
+
+/// Exponential, base 2 (f64)
+///
+/// Calculate `2^x`, that is, 2 raised to the power `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn exp2(mut x: f64) -> f64 {
+ let redux = f64::from_bits(0x4338000000000000) / TBLSIZE as f64;
+ let p1 = f64::from_bits(0x3fe62e42fefa39ef);
+ let p2 = f64::from_bits(0x3fcebfbdff82c575);
+ let p3 = f64::from_bits(0x3fac6b08d704a0a6);
+ let p4 = f64::from_bits(0x3f83b2ab88f70400);
+ let p5 = f64::from_bits(0x3f55d88003875c74);
+
+ // double_t r, t, z;
+ // uint32_t ix, i0;
+ // union {double f; uint64_t i;} u = {x};
+ // union {uint32_t u; int32_t i;} k;
+ let x1p1023 = f64::from_bits(0x7fe0000000000000);
+ let x1p52 = f64::from_bits(0x4330000000000000);
+ let _0x1p_149 = f64::from_bits(0xb6a0000000000000);
+
+ /* Filter out exceptional cases. */
+ let ui = f64::to_bits(x);
+ let ix = ui >> 32 & 0x7fffffff;
+ if ix >= 0x408ff000 {
+ /* |x| >= 1022 or nan */
+ if ix >= 0x40900000 && ui >> 63 == 0 {
+ /* x >= 1024 or nan */
+ /* overflow */
+ x *= x1p1023;
+ return x;
+ }
+ if ix >= 0x7ff00000 {
+ /* -inf or -nan */
+ return -1.0 / x;
+ }
+ if ui >> 63 != 0 {
+ /* x <= -1022 */
+ /* underflow */
+ if x <= -1075.0 || x - x1p52 + x1p52 != x {
+ force_eval!((_0x1p_149 / x) as f32);
+ }
+ if x <= -1075.0 {
+ return 0.0;
+ }
+ }
+ } else if ix < 0x3c900000 {
+ /* |x| < 0x1p-54 */
+ return 1.0 + x;
+ }
+
+ /* Reduce x, computing z, i0, and k. */
+ let ui = f64::to_bits(x + redux);
+ let mut i0 = ui as u32;
+ i0 = i0.wrapping_add(TBLSIZE as u32 / 2);
+ let ku = i0 / TBLSIZE as u32 * TBLSIZE as u32;
+ let ki = ku as i32 / TBLSIZE as i32;
+ i0 %= TBLSIZE as u32;
+ let uf = f64::from_bits(ui) - redux;
+ let mut z = x - uf;
+
+ /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */
+ let t = f64::from_bits(TBL[2 * i0 as usize]); /* exp2t[i0] */
+ z -= f64::from_bits(TBL[2 * i0 as usize + 1]); /* eps[i0] */
+ let r = t + t * z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * p5))));
+
+ scalbn(r, ki)
+}
+
+#[test]
+fn i0_wrap_test() {
+ let x = -3.0 / 256.0;
+ assert_eq!(exp2(x), f64::from_bits(0x3fefbdba3692d514));
+}
diff --git a/src/math/exp2f.rs b/src/math/exp2f.rs
new file mode 100644
index 0000000..8a890b8
--- /dev/null
+++ b/src/math/exp2f.rs
@@ -0,0 +1,135 @@
+// origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c
+//-
+// Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
+// All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions
+// are met:
+// 1. Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+// 2. Redistributions in binary form must reproduce the above copyright
+// notice, this list of conditions and the following disclaimer in the
+// documentation and/or other materials provided with the distribution.
+//
+// THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+// OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+// OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+// SUCH DAMAGE.
+
+const TBLSIZE: usize = 16;
+
+static EXP2FT: [u64; TBLSIZE] = [
+ 0x3fe6a09e667f3bcd,
+ 0x3fe7a11473eb0187,
+ 0x3fe8ace5422aa0db,
+ 0x3fe9c49182a3f090,
+ 0x3feae89f995ad3ad,
+ 0x3fec199bdd85529c,
+ 0x3fed5818dcfba487,
+ 0x3feea4afa2a490da,
+ 0x3ff0000000000000,
+ 0x3ff0b5586cf9890f,
+ 0x3ff172b83c7d517b,
+ 0x3ff2387a6e756238,
+ 0x3ff306fe0a31b715,
+ 0x3ff3dea64c123422,
+ 0x3ff4bfdad5362a27,
+ 0x3ff5ab07dd485429,
+];
+
+// exp2f(x): compute the base 2 exponential of x
+//
+// Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.
+//
+// Method: (equally-spaced tables)
+//
+// Reduce x:
+// x = k + y, for integer k and |y| <= 1/2.
+// Thus we have exp2f(x) = 2**k * exp2(y).
+//
+// Reduce y:
+// y = i/TBLSIZE + z for integer i near y * TBLSIZE.
+// Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
+// with |z| <= 2**-(TBLSIZE+1).
+//
+// We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
+// degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.
+// Using double precision for everything except the reduction makes
+// roundoff error insignificant and simplifies the scaling step.
+//
+// This method is due to Tang, but I do not use his suggested parameters:
+//
+// Tang, P. Table-driven Implementation of the Exponential Function
+// in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989).
+
+/// Exponential, base 2 (f32)
+///
+/// Calculate `2^x`, that is, 2 raised to the power `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn exp2f(mut x: f32) -> f32 {
+ let redux = f32::from_bits(0x4b400000) / TBLSIZE as f32;
+ let p1 = f32::from_bits(0x3f317218);
+ let p2 = f32::from_bits(0x3e75fdf0);
+ let p3 = f32::from_bits(0x3d6359a4);
+ let p4 = f32::from_bits(0x3c1d964e);
+
+ // double_t t, r, z;
+ // uint32_t ix, i0, k;
+
+ let x1p127 = f32::from_bits(0x7f000000);
+
+ /* Filter out exceptional cases. */
+ let ui = f32::to_bits(x);
+ let ix = ui & 0x7fffffff;
+ if ix > 0x42fc0000 {
+ /* |x| > 126 */
+ if ix > 0x7f800000 {
+ /* NaN */
+ return x;
+ }
+ if ui >= 0x43000000 && ui < 0x80000000 {
+ /* x >= 128 */
+ x *= x1p127;
+ return x;
+ }
+ if ui >= 0x80000000 {
+ /* x < -126 */
+ if ui >= 0xc3160000 || (ui & 0x0000ffff != 0) {
+ force_eval!(f32::from_bits(0x80000001) / x);
+ }
+ if ui >= 0xc3160000 {
+ /* x <= -150 */
+ return 0.0;
+ }
+ }
+ } else if ix <= 0x33000000 {
+ /* |x| <= 0x1p-25 */
+ return 1.0 + x;
+ }
+
+ /* Reduce x, computing z, i0, and k. */
+ let ui = f32::to_bits(x + redux);
+ let mut i0 = ui;
+ i0 += TBLSIZE as u32 / 2;
+ let k = i0 / TBLSIZE as u32;
+ let ukf = f64::from_bits(((0x3ff + k) as u64) << 52);
+ i0 &= TBLSIZE as u32 - 1;
+ let mut uf = f32::from_bits(ui);
+ uf -= redux;
+ let z: f64 = (x - uf) as f64;
+ /* Compute r = exp2(y) = exp2ft[i0] * p(z). */
+ let r: f64 = f64::from_bits(EXP2FT[i0 as usize]);
+ let t: f64 = r as f64 * z;
+ let r: f64 = r + t * (p1 as f64 + z * p2 as f64) + t * (z * z) * (p3 as f64 + z * p4 as f64);
+
+ /* Scale by 2**k */
+ (r * ukf) as f32
+}
diff --git a/src/math/expf.rs b/src/math/expf.rs
new file mode 100644
index 0000000..47c1b2c
--- /dev/null
+++ b/src/math/expf.rs
@@ -0,0 +1,101 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_expf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::scalbnf;
+
+const HALF: [f32; 2] = [0.5, -0.5];
+const LN2_HI: f32 = 6.9314575195e-01; /* 0x3f317200 */
+const LN2_LO: f32 = 1.4286067653e-06; /* 0x35bfbe8e */
+const INV_LN2: f32 = 1.4426950216e+00; /* 0x3fb8aa3b */
+/*
+ * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
+ * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
+ */
+const P1: f32 = 1.6666625440e-1; /* 0xaaaa8f.0p-26 */
+const P2: f32 = -2.7667332906e-3; /* -0xb55215.0p-32 */
+
+/// Exponential, base *e* (f32)
+///
+/// Calculate the exponential of `x`, that is, *e* raised to the power `x`
+/// (where *e* is the base of the natural system of logarithms, approximately 2.71828).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn expf(mut x: f32) -> f32 {
+ let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
+ let x1p_126 = f32::from_bits(0x800000); // 0x1p-126f === 2 ^ -126 /*original 0x1p-149f ??????????? */
+ let mut hx = x.to_bits();
+ let sign = (hx >> 31) as i32; /* sign bit of x */
+ let signb: bool = sign != 0;
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* special cases */
+ if hx >= 0x42aeac50 {
+ /* if |x| >= -87.33655f or NaN */
+ if hx > 0x7f800000 {
+ /* NaN */
+ return x;
+ }
+ if (hx >= 0x42b17218) && (!signb) {
+ /* x >= 88.722839f */
+ /* overflow */
+ x *= x1p127;
+ return x;
+ }
+ if signb {
+ /* underflow */
+ force_eval!(-x1p_126 / x);
+ if hx >= 0x42cff1b5 {
+ /* x <= -103.972084f */
+ return 0.;
+ }
+ }
+ }
+
+ /* argument reduction */
+ let k: i32;
+ let hi: f32;
+ let lo: f32;
+ if hx > 0x3eb17218 {
+ /* if |x| > 0.5 ln2 */
+ if hx > 0x3f851592 {
+ /* if |x| > 1.5 ln2 */
+ k = (INV_LN2 * x + HALF[sign as usize]) as i32;
+ } else {
+ k = 1 - sign - sign;
+ }
+ let kf = k as f32;
+ hi = x - kf * LN2_HI; /* k*ln2hi is exact here */
+ lo = kf * LN2_LO;
+ x = hi - lo;
+ } else if hx > 0x39000000 {
+ /* |x| > 2**-14 */
+ k = 0;
+ hi = x;
+ lo = 0.;
+ } else {
+ /* raise inexact */
+ force_eval!(x1p127 + x);
+ return 1. + x;
+ }
+
+ /* x is now in primary range */
+ let xx = x * x;
+ let c = x - xx * (P1 + xx * P2);
+ let y = 1. + (x * c / (2. - c) - lo + hi);
+ if k == 0 {
+ y
+ } else {
+ scalbnf(y, k)
+ }
+}
diff --git a/src/math/expm1.rs b/src/math/expm1.rs
new file mode 100644
index 0000000..4260850
--- /dev/null
+++ b/src/math/expm1.rs
@@ -0,0 +1,144 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use core::f64;
+
+const O_THRESHOLD: f64 = 7.09782712893383973096e+02; /* 0x40862E42, 0xFEFA39EF */
+const LN2_HI: f64 = 6.93147180369123816490e-01; /* 0x3fe62e42, 0xfee00000 */
+const LN2_LO: f64 = 1.90821492927058770002e-10; /* 0x3dea39ef, 0x35793c76 */
+const INVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
+/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */
+const Q1: f64 = -3.33333333333331316428e-02; /* BFA11111 111110F4 */
+const Q2: f64 = 1.58730158725481460165e-03; /* 3F5A01A0 19FE5585 */
+const Q3: f64 = -7.93650757867487942473e-05; /* BF14CE19 9EAADBB7 */
+const Q4: f64 = 4.00821782732936239552e-06; /* 3ED0CFCA 86E65239 */
+const Q5: f64 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
+
+/// Exponential, base *e*, of x-1 (f64)
+///
+/// Calculates the exponential of `x` and subtract 1, that is, *e* raised
+/// to the power `x` minus 1 (where *e* is the base of the natural
+/// system of logarithms, approximately 2.71828).
+/// The result is accurate even for small values of `x`,
+/// where using `exp(x)-1` would lose many significant digits.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn expm1(mut x: f64) -> f64 {
+ let hi: f64;
+ let lo: f64;
+ let k: i32;
+ let c: f64;
+ let mut t: f64;
+ let mut y: f64;
+
+ let mut ui = x.to_bits();
+ let hx = ((ui >> 32) & 0x7fffffff) as u32;
+ let sign = (ui >> 63) as i32;
+
+ /* filter out huge and non-finite argument */
+ if hx >= 0x4043687A {
+ /* if |x|>=56*ln2 */
+ if x.is_nan() {
+ return x;
+ }
+ if sign != 0 {
+ return -1.0;
+ }
+ if x > O_THRESHOLD {
+ x *= f64::from_bits(0x7fe0000000000000);
+ return x;
+ }
+ }
+
+ /* argument reduction */
+ if hx > 0x3fd62e42 {
+ /* if |x| > 0.5 ln2 */
+ if hx < 0x3FF0A2B2 {
+ /* and |x| < 1.5 ln2 */
+ if sign == 0 {
+ hi = x - LN2_HI;
+ lo = LN2_LO;
+ k = 1;
+ } else {
+ hi = x + LN2_HI;
+ lo = -LN2_LO;
+ k = -1;
+ }
+ } else {
+ k = (INVLN2 * x + if sign != 0 { -0.5 } else { 0.5 }) as i32;
+ t = k as f64;
+ hi = x - t * LN2_HI; /* t*ln2_hi is exact here */
+ lo = t * LN2_LO;
+ }
+ x = hi - lo;
+ c = (hi - x) - lo;
+ } else if hx < 0x3c900000 {
+ /* |x| < 2**-54, return x */
+ if hx < 0x00100000 {
+ force_eval!(x);
+ }
+ return x;
+ } else {
+ c = 0.0;
+ k = 0;
+ }
+
+ /* x is now in primary range */
+ let hfx = 0.5 * x;
+ let hxs = x * hfx;
+ let r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
+ t = 3.0 - r1 * hfx;
+ let mut e = hxs * ((r1 - t) / (6.0 - x * t));
+ if k == 0 {
+ /* c is 0 */
+ return x - (x * e - hxs);
+ }
+ e = x * (e - c) - c;
+ e -= hxs;
+ /* exp(x) ~ 2^k (x_reduced - e + 1) */
+ if k == -1 {
+ return 0.5 * (x - e) - 0.5;
+ }
+ if k == 1 {
+ if x < -0.25 {
+ return -2.0 * (e - (x + 0.5));
+ }
+ return 1.0 + 2.0 * (x - e);
+ }
+ ui = ((0x3ff + k) as u64) << 52; /* 2^k */
+ let twopk = f64::from_bits(ui);
+ if k < 0 || k > 56 {
+ /* suffice to return exp(x)-1 */
+ y = x - e + 1.0;
+ if k == 1024 {
+ y = y * 2.0 * f64::from_bits(0x7fe0000000000000);
+ } else {
+ y = y * twopk;
+ }
+ return y - 1.0;
+ }
+ ui = ((0x3ff - k) as u64) << 52; /* 2^-k */
+ let uf = f64::from_bits(ui);
+ if k < 20 {
+ y = (x - e + (1.0 - uf)) * twopk;
+ } else {
+ y = (x - (e + uf) + 1.0) * twopk;
+ }
+ y
+}
+
+#[cfg(test)]
+mod tests {
+ #[test]
+ fn sanity_check() {
+ assert_eq!(super::expm1(1.1), 2.0041660239464334);
+ }
+}
diff --git a/src/math/expm1f.rs b/src/math/expm1f.rs
new file mode 100644
index 0000000..3fc2a24
--- /dev/null
+++ b/src/math/expm1f.rs
@@ -0,0 +1,134 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+const O_THRESHOLD: f32 = 8.8721679688e+01; /* 0x42b17180 */
+const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */
+const LN2_LO: f32 = 9.0580006145e-06; /* 0x3717f7d1 */
+const INV_LN2: f32 = 1.4426950216e+00; /* 0x3fb8aa3b */
+/*
+ * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
+ * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
+ * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
+ */
+const Q1: f32 = -3.3333212137e-2; /* -0x888868.0p-28 */
+const Q2: f32 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
+
+/// Exponential, base *e*, of x-1 (f32)
+///
+/// Calculates the exponential of `x` and subtract 1, that is, *e* raised
+/// to the power `x` minus 1 (where *e* is the base of the natural
+/// system of logarithms, approximately 2.71828).
+/// The result is accurate even for small values of `x`,
+/// where using `exp(x)-1` would lose many significant digits.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn expm1f(mut x: f32) -> f32 {
+ let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
+
+ let mut hx = x.to_bits();
+ let sign = (hx >> 31) != 0;
+ hx &= 0x7fffffff;
+
+ /* filter out huge and non-finite argument */
+ if hx >= 0x4195b844 {
+ /* if |x|>=27*ln2 */
+ if hx > 0x7f800000 {
+ /* NaN */
+ return x;
+ }
+ if sign {
+ return -1.;
+ }
+ if x > O_THRESHOLD {
+ x *= x1p127;
+ return x;
+ }
+ }
+
+ let k: i32;
+ let hi: f32;
+ let lo: f32;
+ let mut c = 0f32;
+ /* argument reduction */
+ if hx > 0x3eb17218 {
+ /* if |x| > 0.5 ln2 */
+ if hx < 0x3F851592 {
+ /* and |x| < 1.5 ln2 */
+ if !sign {
+ hi = x - LN2_HI;
+ lo = LN2_LO;
+ k = 1;
+ } else {
+ hi = x + LN2_HI;
+ lo = -LN2_LO;
+ k = -1;
+ }
+ } else {
+ k = (INV_LN2 * x + (if sign { -0.5 } else { 0.5 })) as i32;
+ let t = k as f32;
+ hi = x - t * LN2_HI; /* t*ln2_hi is exact here */
+ lo = t * LN2_LO;
+ }
+ x = hi - lo;
+ c = (hi - x) - lo;
+ } else if hx < 0x33000000 {
+ /* when |x|<2**-25, return x */
+ if hx < 0x00800000 {
+ force_eval!(x * x);
+ }
+ return x;
+ } else {
+ k = 0;
+ }
+
+ /* x is now in primary range */
+ let hfx = 0.5 * x;
+ let hxs = x * hfx;
+ let r1 = 1. + hxs * (Q1 + hxs * Q2);
+ let t = 3. - r1 * hfx;
+ let mut e = hxs * ((r1 - t) / (6. - x * t));
+ if k == 0 {
+ /* c is 0 */
+ return x - (x * e - hxs);
+ }
+ e = x * (e - c) - c;
+ e -= hxs;
+ /* exp(x) ~ 2^k (x_reduced - e + 1) */
+ if k == -1 {
+ return 0.5 * (x - e) - 0.5;
+ }
+ if k == 1 {
+ if x < -0.25 {
+ return -2. * (e - (x + 0.5));
+ }
+ return 1. + 2. * (x - e);
+ }
+ let twopk = f32::from_bits(((0x7f + k) << 23) as u32); /* 2^k */
+ if (k < 0) || (k > 56) {
+ /* suffice to return exp(x)-1 */
+ let mut y = x - e + 1.;
+ if k == 128 {
+ y = y * 2. * x1p127;
+ } else {
+ y = y * twopk;
+ }
+ return y - 1.;
+ }
+ let uf = f32::from_bits(((0x7f - k) << 23) as u32); /* 2^-k */
+ if k < 23 {
+ (x - e + (1. - uf)) * twopk
+ } else {
+ (x - (e + uf) + 1.) * twopk
+ }
+}
diff --git a/src/math/expo2.rs b/src/math/expo2.rs
new file mode 100644
index 0000000..82e9b36
--- /dev/null
+++ b/src/math/expo2.rs
@@ -0,0 +1,14 @@
+use super::{combine_words, exp};
+
+/* exp(x)/2 for x >= log(DBL_MAX), slightly better than 0.5*exp(x/2)*exp(x/2) */
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn expo2(x: f64) -> f64 {
+ /* k is such that k*ln2 has minimal relative error and x - kln2 > log(DBL_MIN) */
+ const K: i32 = 2043;
+ let kln2 = f64::from_bits(0x40962066151add8b);
+
+ /* note that k is odd and scale*scale overflows */
+ let scale = combine_words(((0x3ff + K / 2) as u32) << 20, 0);
+ /* exp(x - k ln2) * 2**(k-1) */
+ exp(x - kln2) * scale * scale
+}
diff --git a/src/math/fabs.rs b/src/math/fabs.rs
new file mode 100644
index 0000000..b2255ad
--- /dev/null
+++ b/src/math/fabs.rs
@@ -0,0 +1,41 @@
+use core::u64;
+
+/// Absolute value (magnitude) (f64)
+/// Calculates the absolute value (magnitude) of the argument `x`,
+/// by direct manipulation of the bit representation of `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fabs(x: f64) -> f64 {
+ // On wasm32 we know that LLVM's intrinsic will compile to an optimized
+ // `f64.abs` native instruction, so we can leverage this for both code size
+ // and speed.
+ llvm_intrinsically_optimized! {
+ #[cfg(target_arch = "wasm32")] {
+ return unsafe { ::core::intrinsics::fabsf64(x) }
+ }
+ }
+ f64::from_bits(x.to_bits() & (u64::MAX / 2))
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use core::f64::*;
+
+ #[test]
+ fn sanity_check() {
+ assert_eq!(fabs(-1.0), 1.0);
+ assert_eq!(fabs(2.8), 2.8);
+ }
+
+ /// The spec: https://en.cppreference.com/w/cpp/numeric/math/fabs
+ #[test]
+ fn spec_tests() {
+ assert!(fabs(NAN).is_nan());
+ for f in [0.0, -0.0].iter().copied() {
+ assert_eq!(fabs(f), 0.0);
+ }
+ for f in [INFINITY, NEG_INFINITY].iter().copied() {
+ assert_eq!(fabs(f), INFINITY);
+ }
+ }
+}
diff --git a/src/math/fabsf.rs b/src/math/fabsf.rs
new file mode 100644
index 0000000..6655c4c
--- /dev/null
+++ b/src/math/fabsf.rs
@@ -0,0 +1,39 @@
+/// Absolute value (magnitude) (f32)
+/// Calculates the absolute value (magnitude) of the argument `x`,
+/// by direct manipulation of the bit representation of `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fabsf(x: f32) -> f32 {
+ // On wasm32 we know that LLVM's intrinsic will compile to an optimized
+ // `f32.abs` native instruction, so we can leverage this for both code size
+ // and speed.
+ llvm_intrinsically_optimized! {
+ #[cfg(target_arch = "wasm32")] {
+ return unsafe { ::core::intrinsics::fabsf32(x) }
+ }
+ }
+ f32::from_bits(x.to_bits() & 0x7fffffff)
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use core::f32::*;
+
+ #[test]
+ fn sanity_check() {
+ assert_eq!(fabsf(-1.0), 1.0);
+ assert_eq!(fabsf(2.8), 2.8);
+ }
+
+ /// The spec: https://en.cppreference.com/w/cpp/numeric/math/fabs
+ #[test]
+ fn spec_tests() {
+ assert!(fabsf(NAN).is_nan());
+ for f in [0.0, -0.0].iter().copied() {
+ assert_eq!(fabsf(f), 0.0);
+ }
+ for f in [INFINITY, NEG_INFINITY].iter().copied() {
+ assert_eq!(fabsf(f), INFINITY);
+ }
+ }
+}
diff --git a/src/math/fdim.rs b/src/math/fdim.rs
new file mode 100644
index 0000000..0149300
--- /dev/null
+++ b/src/math/fdim.rs
@@ -0,0 +1,22 @@
+use core::f64;
+
+/// Positive difference (f64)
+///
+/// Determines the positive difference between arguments, returning:
+/// * x - y if x > y, or
+/// * +0 if x <= y, or
+/// * NAN if either argument is NAN.
+///
+/// A range error may occur.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fdim(x: f64, y: f64) -> f64 {
+ if x.is_nan() {
+ x
+ } else if y.is_nan() {
+ y
+ } else if x > y {
+ x - y
+ } else {
+ 0.0
+ }
+}
diff --git a/src/math/fdimf.rs b/src/math/fdimf.rs
new file mode 100644
index 0000000..ea0b592
--- /dev/null
+++ b/src/math/fdimf.rs
@@ -0,0 +1,22 @@
+use core::f32;
+
+/// Positive difference (f32)
+///
+/// Determines the positive difference between arguments, returning:
+/// * x - y if x > y, or
+/// * +0 if x <= y, or
+/// * NAN if either argument is NAN.
+///
+/// A range error may occur.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fdimf(x: f32, y: f32) -> f32 {
+ if x.is_nan() {
+ x
+ } else if y.is_nan() {
+ y
+ } else if x > y {
+ x - y
+ } else {
+ 0.0
+ }
+}
diff --git a/src/math/fenv.rs b/src/math/fenv.rs
new file mode 100644
index 0000000..652e603
--- /dev/null
+++ b/src/math/fenv.rs
@@ -0,0 +1,33 @@
+// src: musl/src/fenv/fenv.c
+/* Dummy functions for archs lacking fenv implementation */
+
+pub(crate) const FE_UNDERFLOW: i32 = 0;
+pub(crate) const FE_INEXACT: i32 = 0;
+
+pub(crate) const FE_TONEAREST: i32 = 0;
+pub(crate) const FE_TOWARDZERO: i32 = 0;
+
+#[inline]
+pub(crate) fn feclearexcept(_mask: i32) -> i32 {
+ 0
+}
+
+#[inline]
+pub(crate) fn feraiseexcept(_mask: i32) -> i32 {
+ 0
+}
+
+#[inline]
+pub(crate) fn fetestexcept(_mask: i32) -> i32 {
+ 0
+}
+
+#[inline]
+pub(crate) fn fegetround() -> i32 {
+ FE_TONEAREST
+}
+
+#[inline]
+pub(crate) fn fesetround(_r: i32) -> i32 {
+ 0
+}
diff --git a/src/math/floor.rs b/src/math/floor.rs
new file mode 100644
index 0000000..b2b7605
--- /dev/null
+++ b/src/math/floor.rs
@@ -0,0 +1,62 @@
+use core::f64;
+
+const TOINT: f64 = 1. / f64::EPSILON;
+
+/// Floor (f64)
+///
+/// Finds the nearest integer less than or equal to `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn floor(x: f64) -> f64 {
+ // On wasm32 we know that LLVM's intrinsic will compile to an optimized
+ // `f64.floor` native instruction, so we can leverage this for both code size
+ // and speed.
+ llvm_intrinsically_optimized! {
+ #[cfg(target_arch = "wasm32")] {
+ return unsafe { ::core::intrinsics::floorf64(x) }
+ }
+ }
+ let ui = x.to_bits();
+ let e = ((ui >> 52) & 0x7ff) as i32;
+
+ if (e >= 0x3ff + 52) || (x == 0.) {
+ return x;
+ }
+ /* y = int(x) - x, where int(x) is an integer neighbor of x */
+ let y = if (ui >> 63) != 0 {
+ x - TOINT + TOINT - x
+ } else {
+ x + TOINT - TOINT - x
+ };
+ /* special case because of non-nearest rounding modes */
+ if e < 0x3ff {
+ force_eval!(y);
+ return if (ui >> 63) != 0 { -1. } else { 0. };
+ }
+ if y > 0. {
+ x + y - 1.
+ } else {
+ x + y
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use core::f64::*;
+
+ #[test]
+ fn sanity_check() {
+ assert_eq!(floor(1.1), 1.0);
+ assert_eq!(floor(2.9), 2.0);
+ }
+
+ /// The spec: https://en.cppreference.com/w/cpp/numeric/math/floor
+ #[test]
+ fn spec_tests() {
+ // Not Asserted: that the current rounding mode has no effect.
+ assert!(floor(NAN).is_nan());
+ for f in [0.0, -0.0, INFINITY, NEG_INFINITY].iter().copied() {
+ assert_eq!(floor(f), f);
+ }
+ }
+}
diff --git a/src/math/floorf.rs b/src/math/floorf.rs
new file mode 100644
index 0000000..287f086
--- /dev/null
+++ b/src/math/floorf.rs
@@ -0,0 +1,64 @@
+use core::f32;
+
+/// Floor (f32)
+///
+/// Finds the nearest integer less than or equal to `x`.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn floorf(x: f32) -> f32 {
+ // On wasm32 we know that LLVM's intrinsic will compile to an optimized
+ // `f32.floor` native instruction, so we can leverage this for both code size
+ // and speed.
+ llvm_intrinsically_optimized! {
+ #[cfg(target_arch = "wasm32")] {
+ return unsafe { ::core::intrinsics::floorf32(x) }
+ }
+ }
+ let mut ui = x.to_bits();
+ let e = (((ui >> 23) as i32) & 0xff) - 0x7f;
+
+ if e >= 23 {
+ return x;
+ }
+ if e >= 0 {
+ let m: u32 = 0x007fffff >> e;
+ if (ui & m) == 0 {
+ return x;
+ }
+ force_eval!(x + f32::from_bits(0x7b800000));
+ if ui >> 31 != 0 {
+ ui += m;
+ }
+ ui &= !m;
+ } else {
+ force_eval!(x + f32::from_bits(0x7b800000));
+ if ui >> 31 == 0 {
+ ui = 0;
+ } else if ui << 1 != 0 {
+ return -1.0;
+ }
+ }
+ f32::from_bits(ui)
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use core::f32::*;
+
+ #[test]
+ fn sanity_check() {
+ assert_eq!(floorf(0.5), 0.0);
+ assert_eq!(floorf(1.1), 1.0);
+ assert_eq!(floorf(2.9), 2.0);
+ }
+
+ /// The spec: https://en.cppreference.com/w/cpp/numeric/math/floor
+ #[test]
+ fn spec_tests() {
+ // Not Asserted: that the current rounding mode has no effect.
+ assert!(floorf(NAN).is_nan());
+ for f in [0.0, -0.0, INFINITY, NEG_INFINITY].iter().copied() {
+ assert_eq!(floorf(f), f);
+ }
+ }
+}
diff --git a/src/math/fma.rs b/src/math/fma.rs
new file mode 100644
index 0000000..3219dbc
--- /dev/null
+++ b/src/math/fma.rs
@@ -0,0 +1,223 @@
+use core::{f32, f64};
+
+use super::scalbn;
+
+const ZEROINFNAN: i32 = 0x7ff - 0x3ff - 52 - 1;
+
+struct Num {
+ m: u64,
+ e: i32,
+ sign: i32,
+}
+
+fn normalize(x: f64) -> Num {
+ let x1p63: f64 = f64::from_bits(0x43e0000000000000); // 0x1p63 === 2 ^ 63
+
+ let mut ix: u64 = x.to_bits();
+ let mut e: i32 = (ix >> 52) as i32;
+ let sign: i32 = e & 0x800;
+ e &= 0x7ff;
+ if e == 0 {
+ ix = (x * x1p63).to_bits();
+ e = (ix >> 52) as i32 & 0x7ff;
+ e = if e != 0 { e - 63 } else { 0x800 };
+ }
+ ix &= (1 << 52) - 1;
+ ix |= 1 << 52;
+ ix <<= 1;
+ e -= 0x3ff + 52 + 1;
+ Num { m: ix, e, sign }
+}
+
+fn mul(x: u64, y: u64) -> (u64, u64) {
+ let t1: u64;
+ let t2: u64;
+ let t3: u64;
+ let xlo: u64 = x as u32 as u64;
+ let xhi: u64 = x >> 32;
+ let ylo: u64 = y as u32 as u64;
+ let yhi: u64 = y >> 32;
+
+ t1 = xlo * ylo;
+ t2 = xlo * yhi + xhi * ylo;
+ t3 = xhi * yhi;
+ let lo = t1.wrapping_add(t2 << 32);
+ let hi = t3 + (t2 >> 32) + (t1 > lo) as u64;
+ (hi, lo)
+}
+
+/// Floating multiply add (f64)
+///
+/// Computes `(x*y)+z`, rounded as one ternary operation:
+/// Computes the value (as if) to infinite precision and rounds once to the result format,
+/// according to the rounding mode characterized by the value of FLT_ROUNDS.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fma(x: f64, y: f64, z: f64) -> f64 {
+ let x1p63: f64 = f64::from_bits(0x43e0000000000000); // 0x1p63 === 2 ^ 63
+ let x0_ffffff8p_63 = f64::from_bits(0x3bfffffff0000000); // 0x0.ffffff8p-63
+
+ /* normalize so top 10bits and last bit are 0 */
+ let nx = normalize(x);
+ let ny = normalize(y);
+ let nz = normalize(z);
+
+ if nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN {
+ return x * y + z;
+ }
+ if nz.e >= ZEROINFNAN {
+ if nz.e > ZEROINFNAN {
+ /* z==0 */
+ return x * y + z;
+ }
+ return z;
+ }
+
+ /* mul: r = x*y */
+ let zhi: u64;
+ let zlo: u64;
+ let (mut rhi, mut rlo) = mul(nx.m, ny.m);
+ /* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */
+
+ /* align exponents */
+ let mut e: i32 = nx.e + ny.e;
+ let mut d: i32 = nz.e - e;
+ /* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */
+ if d > 0 {
+ if d < 64 {
+ zlo = nz.m << d;
+ zhi = nz.m >> (64 - d);
+ } else {
+ zlo = 0;
+ zhi = nz.m;
+ e = nz.e - 64;
+ d -= 64;
+ if d == 0 {
+ } else if d < 64 {
+ rlo = rhi << (64 - d) | rlo >> d | ((rlo << (64 - d)) != 0) as u64;
+ rhi = rhi >> d;
+ } else {
+ rlo = 1;
+ rhi = 0;
+ }
+ }
+ } else {
+ zhi = 0;
+ d = -d;
+ if d == 0 {
+ zlo = nz.m;
+ } else if d < 64 {
+ zlo = nz.m >> d | ((nz.m << (64 - d)) != 0) as u64;
+ } else {
+ zlo = 1;
+ }
+ }
+
+ /* add */
+ let mut sign: i32 = nx.sign ^ ny.sign;
+ let samesign: bool = (sign ^ nz.sign) == 0;
+ let mut nonzero: i32 = 1;
+ if samesign {
+ /* r += z */
+ rlo = rlo.wrapping_add(zlo);
+ rhi += zhi + (rlo < zlo) as u64;
+ } else {
+ /* r -= z */
+ let t = rlo;
+ rlo = rlo.wrapping_sub(zlo);
+ rhi = rhi.wrapping_sub(zhi.wrapping_sub((t < rlo) as u64));
+ if (rhi >> 63) != 0 {
+ rlo = (-(rlo as i64)) as u64;
+ rhi = (-(rhi as i64)) as u64 - (rlo != 0) as u64;
+ sign = (sign == 0) as i32;
+ }
+ nonzero = (rhi != 0) as i32;
+ }
+
+ /* set rhi to top 63bit of the result (last bit is sticky) */
+ if nonzero != 0 {
+ e += 64;
+ d = rhi.leading_zeros() as i32 - 1;
+ /* note: d > 0 */
+ rhi = rhi << d | rlo >> (64 - d) | ((rlo << d) != 0) as u64;
+ } else if rlo != 0 {
+ d = rlo.leading_zeros() as i32 - 1;
+ if d < 0 {
+ rhi = rlo >> 1 | (rlo & 1);
+ } else {
+ rhi = rlo << d;
+ }
+ } else {
+ /* exact +-0 */
+ return x * y + z;
+ }
+ e -= d;
+
+ /* convert to double */
+ let mut i: i64 = rhi as i64; /* i is in [1<<62,(1<<63)-1] */
+ if sign != 0 {
+ i = -i;
+ }
+ let mut r: f64 = i as f64; /* |r| is in [0x1p62,0x1p63] */
+
+ if e < -1022 - 62 {
+ /* result is subnormal before rounding */
+ if e == -1022 - 63 {
+ let mut c: f64 = x1p63;
+ if sign != 0 {
+ c = -c;
+ }
+ if r == c {
+ /* min normal after rounding, underflow depends
+ on arch behaviour which can be imitated by
+ a double to float conversion */
+ let fltmin: f32 = (x0_ffffff8p_63 * f32::MIN_POSITIVE as f64 * r) as f32;
+ return f64::MIN_POSITIVE / f32::MIN_POSITIVE as f64 * fltmin as f64;
+ }
+ /* one bit is lost when scaled, add another top bit to
+ only round once at conversion if it is inexact */
+ if (rhi << 53) != 0 {
+ i = (rhi >> 1 | (rhi & 1) | 1 << 62) as i64;
+ if sign != 0 {
+ i = -i;
+ }
+ r = i as f64;
+ r = 2. * r - c; /* remove top bit */
+
+ /* raise underflow portably, such that it
+ cannot be optimized away */
+ {
+ let tiny: f64 = f64::MIN_POSITIVE / f32::MIN_POSITIVE as f64 * r;
+ r += (tiny * tiny) * (r - r);
+ }
+ }
+ } else {
+ /* only round once when scaled */
+ d = 10;
+ i = ((rhi >> d | ((rhi << (64 - d)) != 0) as u64) << d) as i64;
+ if sign != 0 {
+ i = -i;
+ }
+ r = i as f64;
+ }
+ }
+ scalbn(r, e)
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ #[test]
+ fn fma_segfault() {
+ // These two inputs cause fma to segfault on release due to overflow:
+ assert_eq!(
+ fma(
+ -0.0000000000000002220446049250313,
+ -0.0000000000000002220446049250313,
+ -0.0000000000000002220446049250313
+ ),
+ -0.00000000000000022204460492503126,
+ );
+
+ assert_eq!(fma(-0.992, -0.992, -0.992), -0.00793599999988632,);
+ }
+}
diff --git a/src/math/fmaf.rs b/src/math/fmaf.rs
new file mode 100644
index 0000000..03d371c
--- /dev/null
+++ b/src/math/fmaf.rs
@@ -0,0 +1,106 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_fmaf.c */
+/*-
+ * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+use core::f32;
+use core::ptr::read_volatile;
+
+use super::fenv::{
+ feclearexcept, fegetround, feraiseexcept, fesetround, fetestexcept, FE_INEXACT, FE_TONEAREST,
+ FE_TOWARDZERO, FE_UNDERFLOW,
+};
+
+/*
+ * Fused multiply-add: Compute x * y + z with a single rounding error.
+ *
+ * A double has more than twice as much precision than a float, so
+ * direct double-precision arithmetic suffices, except where double
+ * rounding occurs.
+ */
+
+/// Floating multiply add (f32)
+///
+/// Computes `(x*y)+z`, rounded as one ternary operation:
+/// Computes the value (as if) to infinite precision and rounds once to the result format,
+/// according to the rounding mode characterized by the value of FLT_ROUNDS.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaf(x: f32, y: f32, mut z: f32) -> f32 {
+ let xy: f64;
+ let mut result: f64;
+ let mut ui: u64;
+ let e: i32;
+
+ xy = x as f64 * y as f64;
+ result = xy + z as f64;
+ ui = result.to_bits();
+ e = (ui >> 52) as i32 & 0x7ff;
+ /* Common case: The double precision result is fine. */
+ if (
+ /* not a halfway case */
+ ui & 0x1fffffff) != 0x10000000 ||
+ /* NaN */
+ e == 0x7ff ||
+ /* exact */
+ (result - xy == z as f64 && result - z as f64 == xy) ||
+ /* not round-to-nearest */
+ fegetround() != FE_TONEAREST
+ {
+ /*
+ underflow may not be raised correctly, example:
+ fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f)
+ */
+ if e < 0x3ff - 126 && e >= 0x3ff - 149 && fetestexcept(FE_INEXACT) != 0 {
+ feclearexcept(FE_INEXACT);
+ // prevent `xy + vz` from being CSE'd with `xy + z` above
+ let vz: f32 = unsafe { read_volatile(&z) };
+ result = xy + vz as f64;
+ if fetestexcept(FE_INEXACT) != 0 {
+ feraiseexcept(FE_UNDERFLOW);
+ } else {
+ feraiseexcept(FE_INEXACT);
+ }
+ }
+ z = result as f32;
+ return z;
+ }
+
+ /*
+ * If result is inexact, and exactly halfway between two float values,
+ * we need to adjust the low-order bit in the direction of the error.
+ */
+ fesetround(FE_TOWARDZERO);
+ // prevent `vxy + z` from being CSE'd with `xy + z` above
+ let vxy: f64 = unsafe { read_volatile(&xy) };
+ let mut adjusted_result: f64 = vxy + z as f64;
+ fesetround(FE_TONEAREST);
+ if result == adjusted_result {
+ ui = adjusted_result.to_bits();
+ ui += 1;
+ adjusted_result = f64::from_bits(ui);
+ }
+ z = adjusted_result as f32;
+ z
+}
diff --git a/src/math/fmax.rs b/src/math/fmax.rs
new file mode 100644
index 0000000..93c97bc
--- /dev/null
+++ b/src/math/fmax.rs
@@ -0,0 +1,12 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmax(x: f64, y: f64) -> f64 {
+ // IEEE754 says: maxNum(x, y) is the canonicalized number y if x < y, x if y < x, the
+ // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
+ // is either x or y, canonicalized (this means results might differ among implementations).
+ // When either x or y is a signalingNaN, then the result is according to 6.2.
+ //
+ // Since we do not support sNaN in Rust yet, we do not need to handle them.
+ // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
+ // multiplying by 1.0. Should switch to the `canonicalize` when it works.
+ (if x.is_nan() || x < y { y } else { x }) * 1.0
+}
diff --git a/src/math/fmaxf.rs b/src/math/fmaxf.rs
new file mode 100644
index 0000000..6077466
--- /dev/null
+++ b/src/math/fmaxf.rs
@@ -0,0 +1,12 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmaxf(x: f32, y: f32) -> f32 {
+ // IEEE754 says: maxNum(x, y) is the canonicalized number y if x < y, x if y < x, the
+ // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
+ // is either x or y, canonicalized (this means results might differ among implementations).
+ // When either x or y is a signalingNaN, then the result is according to 6.2.
+ //
+ // Since we do not support sNaN in Rust yet, we do not need to handle them.
+ // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
+ // multiplying by 1.0. Should switch to the `canonicalize` when it works.
+ (if x.is_nan() || x < y { y } else { x }) * 1.0
+}
diff --git a/src/math/fmin.rs b/src/math/fmin.rs
new file mode 100644
index 0000000..ab1509f
--- /dev/null
+++ b/src/math/fmin.rs
@@ -0,0 +1,12 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmin(x: f64, y: f64) -> f64 {
+ // IEEE754 says: minNum(x, y) is the canonicalized number x if x < y, y if y < x, the
+ // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
+ // is either x or y, canonicalized (this means results might differ among implementations).
+ // When either x or y is a signalingNaN, then the result is according to 6.2.
+ //
+ // Since we do not support sNaN in Rust yet, we do not need to handle them.
+ // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
+ // multiplying by 1.0. Should switch to the `canonicalize` when it works.
+ (if y.is_nan() || x < y { x } else { y }) * 1.0
+}
diff --git a/src/math/fminf.rs b/src/math/fminf.rs
new file mode 100644
index 0000000..0049e71
--- /dev/null
+++ b/src/math/fminf.rs
@@ -0,0 +1,12 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fminf(x: f32, y: f32) -> f32 {
+ // IEEE754 says: minNum(x, y) is the canonicalized number x if x < y, y if y < x, the
+ // canonicalized number if one operand is a number and the other a quiet NaN. Otherwise it
+ // is either x or y, canonicalized (this means results might differ among implementations).
+ // When either x or y is a signalingNaN, then the result is according to 6.2.
+ //
+ // Since we do not support sNaN in Rust yet, we do not need to handle them.
+ // FIXME(nagisa): due to https://bugs.llvm.org/show_bug.cgi?id=33303 we canonicalize by
+ // multiplying by 1.0. Should switch to the `canonicalize` when it works.
+ (if y.is_nan() || x < y { x } else { y }) * 1.0
+}
diff --git a/src/math/fmod.rs b/src/math/fmod.rs
new file mode 100644
index 0000000..d892ffd
--- /dev/null
+++ b/src/math/fmod.rs
@@ -0,0 +1,80 @@
+use core::u64;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmod(x: f64, y: f64) -> f64 {
+ let mut uxi = x.to_bits();
+ let mut uyi = y.to_bits();
+ let mut ex = (uxi >> 52 & 0x7ff) as i64;
+ let mut ey = (uyi >> 52 & 0x7ff) as i64;
+ let sx = uxi >> 63;
+ let mut i;
+
+ if uyi << 1 == 0 || y.is_nan() || ex == 0x7ff {
+ return (x * y) / (x * y);
+ }
+ if uxi << 1 <= uyi << 1 {
+ if uxi << 1 == uyi << 1 {
+ return 0.0 * x;
+ }
+ return x;
+ }
+
+ /* normalize x and y */
+ if ex == 0 {
+ i = uxi << 12;
+ while i >> 63 == 0 {
+ ex -= 1;
+ i <<= 1;
+ }
+ uxi <<= -ex + 1;
+ } else {
+ uxi &= u64::MAX >> 12;
+ uxi |= 1 << 52;
+ }
+ if ey == 0 {
+ i = uyi << 12;
+ while i >> 63 == 0 {
+ ey -= 1;
+ i <<= 1;
+ }
+ uyi <<= -ey + 1;
+ } else {
+ uyi &= u64::MAX >> 12;
+ uyi |= 1 << 52;
+ }
+
+ /* x mod y */
+ while ex > ey {
+ i = uxi.wrapping_sub(uyi);
+ if i >> 63 == 0 {
+ if i == 0 {
+ return 0.0 * x;
+ }
+ uxi = i;
+ }
+ uxi <<= 1;
+ ex -= 1;
+ }
+ i = uxi.wrapping_sub(uyi);
+ if i >> 63 == 0 {
+ if i == 0 {
+ return 0.0 * x;
+ }
+ uxi = i;
+ }
+ while uxi >> 52 == 0 {
+ uxi <<= 1;
+ ex -= 1;
+ }
+
+ /* scale result */
+ if ex > 0 {
+ uxi -= 1 << 52;
+ uxi |= (ex as u64) << 52;
+ } else {
+ uxi >>= -ex + 1;
+ }
+ uxi |= (sx as u64) << 63;
+
+ f64::from_bits(uxi)
+}
diff --git a/src/math/fmodf.rs b/src/math/fmodf.rs
new file mode 100644
index 0000000..c53dc18
--- /dev/null
+++ b/src/math/fmodf.rs
@@ -0,0 +1,89 @@
+use core::f32;
+use core::u32;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn fmodf(x: f32, y: f32) -> f32 {
+ let mut uxi = x.to_bits();
+ let mut uyi = y.to_bits();
+ let mut ex = (uxi >> 23 & 0xff) as i32;
+ let mut ey = (uyi >> 23 & 0xff) as i32;
+ let sx = uxi & 0x80000000;
+ let mut i;
+
+ if uyi << 1 == 0 || y.is_nan() || ex == 0xff {
+ return (x * y) / (x * y);
+ }
+
+ if uxi << 1 <= uyi << 1 {
+ if uxi << 1 == uyi << 1 {
+ return 0.0 * x;
+ }
+
+ return x;
+ }
+
+ /* normalize x and y */
+ if ex == 0 {
+ i = uxi << 9;
+ while i >> 31 == 0 {
+ ex -= 1;
+ i <<= 1;
+ }
+
+ uxi <<= -ex + 1;
+ } else {
+ uxi &= u32::MAX >> 9;
+ uxi |= 1 << 23;
+ }
+
+ if ey == 0 {
+ i = uyi << 9;
+ while i >> 31 == 0 {
+ ey -= 1;
+ i <<= 1;
+ }
+
+ uyi <<= -ey + 1;
+ } else {
+ uyi &= u32::MAX >> 9;
+ uyi |= 1 << 23;
+ }
+
+ /* x mod y */
+ while ex > ey {
+ i = uxi.wrapping_sub(uyi);
+ if i >> 31 == 0 {
+ if i == 0 {
+ return 0.0 * x;
+ }
+ uxi = i;
+ }
+ uxi <<= 1;
+
+ ex -= 1;
+ }
+
+ i = uxi.wrapping_sub(uyi);
+ if i >> 31 == 0 {
+ if i == 0 {
+ return 0.0 * x;
+ }
+ uxi = i;
+ }
+
+ while uxi >> 23 == 0 {
+ uxi <<= 1;
+ ex -= 1;
+ }
+
+ /* scale result up */
+ if ex > 0 {
+ uxi -= 1 << 23;
+ uxi |= (ex as u32) << 23;
+ } else {
+ uxi >>= -ex + 1;
+ }
+ uxi |= sx;
+
+ f32::from_bits(uxi)
+}
diff --git a/src/math/frexp.rs b/src/math/frexp.rs
new file mode 100644
index 0000000..badad78
--- /dev/null
+++ b/src/math/frexp.rs
@@ -0,0 +1,20 @@
+pub fn frexp(x: f64) -> (f64, i32) {
+ let mut y = x.to_bits();
+ let ee = ((y >> 52) & 0x7ff) as i32;
+
+ if ee == 0 {
+ if x != 0.0 {
+ let x1p64 = f64::from_bits(0x43f0000000000000);
+ let (x, e) = frexp(x * x1p64);
+ return (x, e - 64);
+ }
+ return (x, 0);
+ } else if ee == 0x7ff {
+ return (x, 0);
+ }
+
+ let e = ee - 0x3fe;
+ y &= 0x800fffffffffffff;
+ y |= 0x3fe0000000000000;
+ return (f64::from_bits(y), e);
+}
diff --git a/src/math/frexpf.rs b/src/math/frexpf.rs
new file mode 100644
index 0000000..2919c0a
--- /dev/null
+++ b/src/math/frexpf.rs
@@ -0,0 +1,21 @@
+pub fn frexpf(x: f32) -> (f32, i32) {
+ let mut y = x.to_bits();
+ let ee: i32 = ((y >> 23) & 0xff) as i32;
+
+ if ee == 0 {
+ if x != 0.0 {
+ let x1p64 = f32::from_bits(0x5f800000);
+ let (x, e) = frexpf(x * x1p64);
+ return (x, e - 64);
+ } else {
+ return (x, 0);
+ }
+ } else if ee == 0xff {
+ return (x, 0);
+ }
+
+ let e = ee - 0x7e;
+ y &= 0x807fffff;
+ y |= 0x3f000000;
+ (f32::from_bits(y), e)
+}
diff --git a/src/math/hypot.rs b/src/math/hypot.rs
new file mode 100644
index 0000000..da458ea
--- /dev/null
+++ b/src/math/hypot.rs
@@ -0,0 +1,74 @@
+use core::f64;
+
+use super::sqrt;
+
+const SPLIT: f64 = 134217728. + 1.; // 0x1p27 + 1 === (2 ^ 27) + 1
+
+fn sq(x: f64) -> (f64, f64) {
+ let xh: f64;
+ let xl: f64;
+ let xc: f64;
+
+ xc = x * SPLIT;
+ xh = x - xc + xc;
+ xl = x - xh;
+ let hi = x * x;
+ let lo = xh * xh - hi + 2. * xh * xl + xl * xl;
+ (hi, lo)
+}
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn hypot(mut x: f64, mut y: f64) -> f64 {
+ let x1p700 = f64::from_bits(0x6bb0000000000000); // 0x1p700 === 2 ^ 700
+ let x1p_700 = f64::from_bits(0x1430000000000000); // 0x1p-700 === 2 ^ -700
+
+ let mut uxi = x.to_bits();
+ let mut uyi = y.to_bits();
+ let uti;
+ let ex: i64;
+ let ey: i64;
+ let mut z: f64;
+
+ /* arrange |x| >= |y| */
+ uxi &= -1i64 as u64 >> 1;
+ uyi &= -1i64 as u64 >> 1;
+ if uxi < uyi {
+ uti = uxi;
+ uxi = uyi;
+ uyi = uti;
+ }
+
+ /* special cases */
+ ex = (uxi >> 52) as i64;
+ ey = (uyi >> 52) as i64;
+ x = f64::from_bits(uxi);
+ y = f64::from_bits(uyi);
+ /* note: hypot(inf,nan) == inf */
+ if ey == 0x7ff {
+ return y;
+ }
+ if ex == 0x7ff || uyi == 0 {
+ return x;
+ }
+ /* note: hypot(x,y) ~= x + y*y/x/2 with inexact for small y/x */
+ /* 64 difference is enough for ld80 double_t */
+ if ex - ey > 64 {
+ return x + y;
+ }
+
+ /* precise sqrt argument in nearest rounding mode without overflow */
+ /* xh*xh must not overflow and xl*xl must not underflow in sq */
+ z = 1.;
+ if ex > 0x3ff + 510 {
+ z = x1p700;
+ x *= x1p_700;
+ y *= x1p_700;
+ } else if ey < 0x3ff - 450 {
+ z = x1p_700;
+ x *= x1p700;
+ y *= x1p700;
+ }
+ let (hx, lx) = sq(x);
+ let (hy, ly) = sq(y);
+ z * sqrt(ly + lx + hy + hx)
+}
diff --git a/src/math/hypotf.rs b/src/math/hypotf.rs
new file mode 100644
index 0000000..576eebb
--- /dev/null
+++ b/src/math/hypotf.rs
@@ -0,0 +1,43 @@
+use core::f32;
+
+use super::sqrtf;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn hypotf(mut x: f32, mut y: f32) -> f32 {
+ let x1p90 = f32::from_bits(0x6c800000); // 0x1p90f === 2 ^ 90
+ let x1p_90 = f32::from_bits(0x12800000); // 0x1p-90f === 2 ^ -90
+
+ let mut uxi = x.to_bits();
+ let mut uyi = y.to_bits();
+ let uti;
+ let mut z: f32;
+
+ uxi &= -1i32 as u32 >> 1;
+ uyi &= -1i32 as u32 >> 1;
+ if uxi < uyi {
+ uti = uxi;
+ uxi = uyi;
+ uyi = uti;
+ }
+
+ x = f32::from_bits(uxi);
+ y = f32::from_bits(uyi);
+ if uyi == 0xff << 23 {
+ return y;
+ }
+ if uxi >= 0xff << 23 || uyi == 0 || uxi - uyi >= 25 << 23 {
+ return x + y;
+ }
+
+ z = 1.;
+ if uxi >= (0x7f + 60) << 23 {
+ z = x1p90;
+ x *= x1p_90;
+ y *= x1p_90;
+ } else if uyi < (0x7f - 60) << 23 {
+ z = x1p_90;
+ x *= x1p90;
+ y *= x1p90;
+ }
+ z * sqrtf((x as f64 * x as f64 + y as f64 * y as f64) as f32)
+}
diff --git a/src/math/ilogb.rs b/src/math/ilogb.rs
new file mode 100644
index 0000000..0a380b7
--- /dev/null
+++ b/src/math/ilogb.rs
@@ -0,0 +1,31 @@
+const FP_ILOGBNAN: i32 = -1 - 0x7fffffff;
+const FP_ILOGB0: i32 = FP_ILOGBNAN;
+
+pub fn ilogb(x: f64) -> i32 {
+ let mut i: u64 = x.to_bits();
+ let e = ((i >> 52) & 0x7ff) as i32;
+
+ if e == 0 {
+ i <<= 12;
+ if i == 0 {
+ force_eval!(0.0 / 0.0);
+ return FP_ILOGB0;
+ }
+ /* subnormal x */
+ let mut e = -0x3ff;
+ while (i >> 63) == 0 {
+ e -= 1;
+ i <<= 1;
+ }
+ e
+ } else if e == 0x7ff {
+ force_eval!(0.0 / 0.0);
+ if (i << 12) != 0 {
+ FP_ILOGBNAN
+ } else {
+ i32::max_value()
+ }
+ } else {
+ e - 0x3ff
+ }
+}
diff --git a/src/math/ilogbf.rs b/src/math/ilogbf.rs
new file mode 100644
index 0000000..b384fa4
--- /dev/null
+++ b/src/math/ilogbf.rs
@@ -0,0 +1,31 @@
+const FP_ILOGBNAN: i32 = -1 - 0x7fffffff;
+const FP_ILOGB0: i32 = FP_ILOGBNAN;
+
+pub fn ilogbf(x: f32) -> i32 {
+ let mut i = x.to_bits();
+ let e = ((i >> 23) & 0xff) as i32;
+
+ if e == 0 {
+ i <<= 9;
+ if i == 0 {
+ force_eval!(0.0 / 0.0);
+ return FP_ILOGB0;
+ }
+ /* subnormal x */
+ let mut e = -0x7f;
+ while (i >> 31) == 0 {
+ e -= 1;
+ i <<= 1;
+ }
+ e
+ } else if e == 0xff {
+ force_eval!(0.0 / 0.0);
+ if (i << 9) != 0 {
+ FP_ILOGBNAN
+ } else {
+ i32::max_value()
+ }
+ } else {
+ e - 0x7f
+ }
+}
diff --git a/src/math/j0.rs b/src/math/j0.rs
new file mode 100644
index 0000000..c4258cc
--- /dev/null
+++ b/src/math/j0.rs
@@ -0,0 +1,422 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_j0.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* j0(x), y0(x)
+ * Bessel function of the first and second kinds of order zero.
+ * Method -- j0(x):
+ * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
+ * 2. Reduce x to |x| since j0(x)=j0(-x), and
+ * for x in (0,2)
+ * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x;
+ * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
+ * for x in (2,inf)
+ * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
+ * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ * as follow:
+ * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
+ * = 1/sqrt(2) * (cos(x) + sin(x))
+ * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
+ * = 1/sqrt(2) * (sin(x) - cos(x))
+ * (To avoid cancellation, use
+ * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ * to compute the worse one.)
+ *
+ * 3 Special cases
+ * j0(nan)= nan
+ * j0(0) = 1
+ * j0(inf) = 0
+ *
+ * Method -- y0(x):
+ * 1. For x<2.
+ * Since
+ * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
+ * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
+ * We use the following function to approximate y0,
+ * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
+ * where
+ * U(z) = u00 + u01*z + ... + u06*z^6
+ * V(z) = 1 + v01*z + ... + v04*z^4
+ * with absolute approximation error bounded by 2**-72.
+ * Note: For tiny x, U/V = u0 and j0(x)~1, hence
+ * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
+ * 2. For x>=2.
+ * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
+ * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ * by the method mentioned above.
+ * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
+ */
+
+use super::{cos, fabs, get_high_word, get_low_word, log, sin, sqrt};
+const INVSQRTPI: f64 = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */
+const TPI: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
+
+/* common method when |x|>=2 */
+fn common(ix: u32, x: f64, y0: bool) -> f64 {
+ let s: f64;
+ let mut c: f64;
+ let mut ss: f64;
+ let mut cc: f64;
+ let z: f64;
+
+ /*
+ * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x-pi/4)-q0(x)*sin(x-pi/4))
+ * y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x-pi/4)+q0(x)*cos(x-pi/4))
+ *
+ * sin(x-pi/4) = (sin(x) - cos(x))/sqrt(2)
+ * cos(x-pi/4) = (sin(x) + cos(x))/sqrt(2)
+ * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ */
+ s = sin(x);
+ c = cos(x);
+ if y0 {
+ c = -c;
+ }
+ cc = s + c;
+ /* avoid overflow in 2*x, big ulp error when x>=0x1p1023 */
+ if ix < 0x7fe00000 {
+ ss = s - c;
+ z = -cos(2.0 * x);
+ if s * c < 0.0 {
+ cc = z / ss;
+ } else {
+ ss = z / cc;
+ }
+ if ix < 0x48000000 {
+ if y0 {
+ ss = -ss;
+ }
+ cc = pzero(x) * cc - qzero(x) * ss;
+ }
+ }
+ return INVSQRTPI * cc / sqrt(x);
+}
+
+/* R0/S0 on [0, 2.00] */
+const R02: f64 = 1.56249999999999947958e-02; /* 0x3F8FFFFF, 0xFFFFFFFD */
+const R03: f64 = -1.89979294238854721751e-04; /* 0xBF28E6A5, 0xB61AC6E9 */
+const R04: f64 = 1.82954049532700665670e-06; /* 0x3EBEB1D1, 0x0C503919 */
+const R05: f64 = -4.61832688532103189199e-09; /* 0xBE33D5E7, 0x73D63FCE */
+const S01: f64 = 1.56191029464890010492e-02; /* 0x3F8FFCE8, 0x82C8C2A4 */
+const S02: f64 = 1.16926784663337450260e-04; /* 0x3F1EA6D2, 0xDD57DBF4 */
+const S03: f64 = 5.13546550207318111446e-07; /* 0x3EA13B54, 0xCE84D5A9 */
+const S04: f64 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
+
+pub fn j0(mut x: f64) -> f64 {
+ let z: f64;
+ let r: f64;
+ let s: f64;
+ let mut ix: u32;
+
+ ix = get_high_word(x);
+ ix &= 0x7fffffff;
+
+ /* j0(+-inf)=0, j0(nan)=nan */
+ if ix >= 0x7ff00000 {
+ return 1.0 / (x * x);
+ }
+ x = fabs(x);
+
+ if ix >= 0x40000000 {
+ /* |x| >= 2 */
+ /* large ulp error near zeros: 2.4, 5.52, 8.6537,.. */
+ return common(ix, x, false);
+ }
+
+ /* 1 - x*x/4 + x*x*R(x^2)/S(x^2) */
+ if ix >= 0x3f200000 {
+ /* |x| >= 2**-13 */
+ /* up to 4ulp error close to 2 */
+ z = x * x;
+ r = z * (R02 + z * (R03 + z * (R04 + z * R05)));
+ s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * S04)));
+ return (1.0 + x / 2.0) * (1.0 - x / 2.0) + z * (r / s);
+ }
+
+ /* 1 - x*x/4 */
+ /* prevent underflow */
+ /* inexact should be raised when x!=0, this is not done correctly */
+ if ix >= 0x38000000 {
+ /* |x| >= 2**-127 */
+ x = 0.25 * x * x;
+ }
+ return 1.0 - x;
+}
+
+const U00: f64 = -7.38042951086872317523e-02; /* 0xBFB2E4D6, 0x99CBD01F */
+const U01: f64 = 1.76666452509181115538e-01; /* 0x3FC69D01, 0x9DE9E3FC */
+const U02: f64 = -1.38185671945596898896e-02; /* 0xBF8C4CE8, 0xB16CFA97 */
+const U03: f64 = 3.47453432093683650238e-04; /* 0x3F36C54D, 0x20B29B6B */
+const U04: f64 = -3.81407053724364161125e-06; /* 0xBECFFEA7, 0x73D25CAD */
+const U05: f64 = 1.95590137035022920206e-08; /* 0x3E550057, 0x3B4EABD4 */
+const U06: f64 = -3.98205194132103398453e-11; /* 0xBDC5E43D, 0x693FB3C8 */
+const V01: f64 = 1.27304834834123699328e-02; /* 0x3F8A1270, 0x91C9C71A */
+const V02: f64 = 7.60068627350353253702e-05; /* 0x3F13ECBB, 0xF578C6C1 */
+const V03: f64 = 2.59150851840457805467e-07; /* 0x3E91642D, 0x7FF202FD */
+const V04: f64 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
+
+pub fn y0(x: f64) -> f64 {
+ let z: f64;
+ let u: f64;
+ let v: f64;
+ let ix: u32;
+ let lx: u32;
+
+ ix = get_high_word(x);
+ lx = get_low_word(x);
+
+ /* y0(nan)=nan, y0(<0)=nan, y0(0)=-inf, y0(inf)=0 */
+ if ((ix << 1) | lx) == 0 {
+ return -1.0 / 0.0;
+ }
+ if (ix >> 31) != 0 {
+ return 0.0 / 0.0;
+ }
+ if ix >= 0x7ff00000 {
+ return 1.0 / x;
+ }
+
+ if ix >= 0x40000000 {
+ /* x >= 2 */
+ /* large ulp errors near zeros: 3.958, 7.086,.. */
+ return common(ix, x, true);
+ }
+
+ /* U(x^2)/V(x^2) + (2/pi)*j0(x)*log(x) */
+ if ix >= 0x3e400000 {
+ /* x >= 2**-27 */
+ /* large ulp error near the first zero, x ~= 0.89 */
+ z = x * x;
+ u = U00 + z * (U01 + z * (U02 + z * (U03 + z * (U04 + z * (U05 + z * U06)))));
+ v = 1.0 + z * (V01 + z * (V02 + z * (V03 + z * V04)));
+ return u / v + TPI * (j0(x) * log(x));
+ }
+ return U00 + TPI * log(x);
+}
+
+/* The asymptotic expansions of pzero is
+ * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
+ * For x >= 2, We approximate pzero by
+ * pzero(x) = 1 + (R/S)
+ * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
+ * S = 1 + pS0*s^2 + ... + pS4*s^10
+ * and
+ * | pzero(x)-1-R/S | <= 2 ** ( -60.26)
+ */
+const PR8: [f64; 6] = [
+ /* for x in [inf, 8]=1/[0,0.125] */
+ 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+ -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
+ -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
+ -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
+ -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
+ -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
+];
+const PS8: [f64; 5] = [
+ 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
+ 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
+ 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
+ 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
+ 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
+];
+
+const PR5: [f64; 6] = [
+ /* for x in [8,4.5454]=1/[0.125,0.22001] */
+ -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
+ -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
+ -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
+ -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
+ -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
+ -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
+];
+const PS5: [f64; 5] = [
+ 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
+ 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
+ 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
+ 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
+ 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
+];
+
+const PR3: [f64; 6] = [
+ /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+ -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
+ -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
+ -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
+ -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
+ -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
+ -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
+];
+const PS3: [f64; 5] = [
+ 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
+ 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
+ 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
+ 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
+ 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
+];
+
+const PR2: [f64; 6] = [
+ /* for x in [2.8570,2]=1/[0.3499,0.5] */
+ -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
+ -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
+ -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
+ -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
+ -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
+ -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
+];
+const PS2: [f64; 5] = [
+ 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
+ 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
+ 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
+ 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
+ 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
+];
+
+fn pzero(x: f64) -> f64 {
+ let p: &[f64; 6];
+ let q: &[f64; 5];
+ let z: f64;
+ let r: f64;
+ let s: f64;
+ let mut ix: u32;
+
+ ix = get_high_word(x);
+ ix &= 0x7fffffff;
+ if ix >= 0x40200000 {
+ p = &PR8;
+ q = &PS8;
+ } else if ix >= 0x40122E8B {
+ p = &PR5;
+ q = &PS5;
+ } else if ix >= 0x4006DB6D {
+ p = &PR3;
+ q = &PS3;
+ } else
+ /*ix >= 0x40000000*/
+ {
+ p = &PR2;
+ q = &PS2;
+ }
+ z = 1.0 / (x * x);
+ r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+ s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
+ return 1.0 + r / s;
+}
+
+/* For x >= 8, the asymptotic expansions of qzero is
+ * -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
+ * We approximate pzero by
+ * qzero(x) = s*(-1.25 + (R/S))
+ * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
+ * S = 1 + qS0*s^2 + ... + qS5*s^12
+ * and
+ * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
+ */
+const QR8: [f64; 6] = [
+ /* for x in [inf, 8]=1/[0,0.125] */
+ 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+ 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
+ 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
+ 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
+ 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
+ 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
+];
+const QS8: [f64; 6] = [
+ 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
+ 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
+ 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
+ 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
+ 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
+ -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
+];
+
+const QR5: [f64; 6] = [
+ /* for x in [8,4.5454]=1/[0.125,0.22001] */
+ 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
+ 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
+ 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
+ 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
+ 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
+ 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
+];
+const QS5: [f64; 6] = [
+ 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
+ 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
+ 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
+ 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
+ 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
+ -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
+];
+
+const QR3: [f64; 6] = [
+ /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+ 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
+ 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
+ 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
+ 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
+ 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
+ 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
+];
+const QS3: [f64; 6] = [
+ 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
+ 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
+ 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
+ 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
+ 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
+ -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
+];
+
+const QR2: [f64; 6] = [
+ /* for x in [2.8570,2]=1/[0.3499,0.5] */
+ 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
+ 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
+ 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
+ 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
+ 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
+ 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
+];
+const QS2: [f64; 6] = [
+ 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
+ 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
+ 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
+ 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
+ 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
+ -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
+];
+
+fn qzero(x: f64) -> f64 {
+ let p: &[f64; 6];
+ let q: &[f64; 6];
+ let s: f64;
+ let r: f64;
+ let z: f64;
+ let mut ix: u32;
+
+ ix = get_high_word(x);
+ ix &= 0x7fffffff;
+ if ix >= 0x40200000 {
+ p = &QR8;
+ q = &QS8;
+ } else if ix >= 0x40122E8B {
+ p = &QR5;
+ q = &QS5;
+ } else if ix >= 0x4006DB6D {
+ p = &QR3;
+ q = &QS3;
+ } else
+ /*ix >= 0x40000000*/
+ {
+ p = &QR2;
+ q = &QS2;
+ }
+ z = 1.0 / (x * x);
+ r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+ s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
+ return (-0.125 + r / s) / x;
+}
diff --git a/src/math/j0f.rs b/src/math/j0f.rs
new file mode 100644
index 0000000..91c03db
--- /dev/null
+++ b/src/math/j0f.rs
@@ -0,0 +1,359 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_j0f.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{cosf, fabsf, logf, sinf, sqrtf};
+
+const INVSQRTPI: f32 = 5.6418961287e-01; /* 0x3f106ebb */
+const TPI: f32 = 6.3661974669e-01; /* 0x3f22f983 */
+
+fn common(ix: u32, x: f32, y0: bool) -> f32 {
+ let z: f32;
+ let s: f32;
+ let mut c: f32;
+ let mut ss: f32;
+ let mut cc: f32;
+ /*
+ * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
+ * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
+ */
+ s = sinf(x);
+ c = cosf(x);
+ if y0 {
+ c = -c;
+ }
+ cc = s + c;
+ if ix < 0x7f000000 {
+ ss = s - c;
+ z = -cosf(2.0 * x);
+ if s * c < 0.0 {
+ cc = z / ss;
+ } else {
+ ss = z / cc;
+ }
+ if ix < 0x58800000 {
+ if y0 {
+ ss = -ss;
+ }
+ cc = pzerof(x) * cc - qzerof(x) * ss;
+ }
+ }
+ return INVSQRTPI * cc / sqrtf(x);
+}
+
+/* R0/S0 on [0, 2.00] */
+const R02: f32 = 1.5625000000e-02; /* 0x3c800000 */
+const R03: f32 = -1.8997929874e-04; /* 0xb947352e */
+const R04: f32 = 1.8295404516e-06; /* 0x35f58e88 */
+const R05: f32 = -4.6183270541e-09; /* 0xb19eaf3c */
+const S01: f32 = 1.5619102865e-02; /* 0x3c7fe744 */
+const S02: f32 = 1.1692678527e-04; /* 0x38f53697 */
+const S03: f32 = 5.1354652442e-07; /* 0x3509daa6 */
+const S04: f32 = 1.1661400734e-09; /* 0x30a045e8 */
+
+pub fn j0f(mut x: f32) -> f32 {
+ let z: f32;
+ let r: f32;
+ let s: f32;
+ let mut ix: u32;
+
+ ix = x.to_bits();
+ ix &= 0x7fffffff;
+ if ix >= 0x7f800000 {
+ return 1.0 / (x * x);
+ }
+ x = fabsf(x);
+
+ if ix >= 0x40000000 {
+ /* |x| >= 2 */
+ /* large ulp error near zeros */
+ return common(ix, x, false);
+ }
+ if ix >= 0x3a000000 {
+ /* |x| >= 2**-11 */
+ /* up to 4ulp error near 2 */
+ z = x * x;
+ r = z * (R02 + z * (R03 + z * (R04 + z * R05)));
+ s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * S04)));
+ return (1.0 + x / 2.0) * (1.0 - x / 2.0) + z * (r / s);
+ }
+ if ix >= 0x21800000 {
+ /* |x| >= 2**-60 */
+ x = 0.25 * x * x;
+ }
+ return 1.0 - x;
+}
+
+const U00: f32 = -7.3804296553e-02; /* 0xbd9726b5 */
+const U01: f32 = 1.7666645348e-01; /* 0x3e34e80d */
+const U02: f32 = -1.3818567619e-02; /* 0xbc626746 */
+const U03: f32 = 3.4745343146e-04; /* 0x39b62a69 */
+const U04: f32 = -3.8140706238e-06; /* 0xb67ff53c */
+const U05: f32 = 1.9559013964e-08; /* 0x32a802ba */
+const U06: f32 = -3.9820518410e-11; /* 0xae2f21eb */
+const V01: f32 = 1.2730483897e-02; /* 0x3c509385 */
+const V02: f32 = 7.6006865129e-05; /* 0x389f65e0 */
+const V03: f32 = 2.5915085189e-07; /* 0x348b216c */
+const V04: f32 = 4.4111031494e-10; /* 0x2ff280c2 */
+
+pub fn y0f(x: f32) -> f32 {
+ let z: f32;
+ let u: f32;
+ let v: f32;
+ let ix: u32;
+
+ ix = x.to_bits();
+ if (ix & 0x7fffffff) == 0 {
+ return -1.0 / 0.0;
+ }
+ if (ix >> 31) != 0 {
+ return 0.0 / 0.0;
+ }
+ if ix >= 0x7f800000 {
+ return 1.0 / x;
+ }
+ if ix >= 0x40000000 {
+ /* |x| >= 2.0 */
+ /* large ulp error near zeros */
+ return common(ix, x, true);
+ }
+ if ix >= 0x39000000 {
+ /* x >= 2**-13 */
+ /* large ulp error at x ~= 0.89 */
+ z = x * x;
+ u = U00 + z * (U01 + z * (U02 + z * (U03 + z * (U04 + z * (U05 + z * U06)))));
+ v = 1.0 + z * (V01 + z * (V02 + z * (V03 + z * V04)));
+ return u / v + TPI * (j0f(x) * logf(x));
+ }
+ return U00 + TPI * logf(x);
+}
+
+/* The asymptotic expansions of pzero is
+ * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
+ * For x >= 2, We approximate pzero by
+ * pzero(x) = 1 + (R/S)
+ * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
+ * S = 1 + pS0*s^2 + ... + pS4*s^10
+ * and
+ * | pzero(x)-1-R/S | <= 2 ** ( -60.26)
+ */
+const PR8: [f32; 6] = [
+ /* for x in [inf, 8]=1/[0,0.125] */
+ 0.0000000000e+00, /* 0x00000000 */
+ -7.0312500000e-02, /* 0xbd900000 */
+ -8.0816707611e+00, /* 0xc1014e86 */
+ -2.5706311035e+02, /* 0xc3808814 */
+ -2.4852163086e+03, /* 0xc51b5376 */
+ -5.2530439453e+03, /* 0xc5a4285a */
+];
+const PS8: [f32; 5] = [
+ 1.1653436279e+02, /* 0x42e91198 */
+ 3.8337448730e+03, /* 0x456f9beb */
+ 4.0597855469e+04, /* 0x471e95db */
+ 1.1675296875e+05, /* 0x47e4087c */
+ 4.7627726562e+04, /* 0x473a0bba */
+];
+const PR5: [f32; 6] = [
+ /* for x in [8,4.5454]=1/[0.125,0.22001] */
+ -1.1412546255e-11, /* 0xad48c58a */
+ -7.0312492549e-02, /* 0xbd8fffff */
+ -4.1596107483e+00, /* 0xc0851b88 */
+ -6.7674766541e+01, /* 0xc287597b */
+ -3.3123129272e+02, /* 0xc3a59d9b */
+ -3.4643338013e+02, /* 0xc3ad3779 */
+];
+const PS5: [f32; 5] = [
+ 6.0753936768e+01, /* 0x42730408 */
+ 1.0512523193e+03, /* 0x44836813 */
+ 5.9789707031e+03, /* 0x45bad7c4 */
+ 9.6254453125e+03, /* 0x461665c8 */
+ 2.4060581055e+03, /* 0x451660ee */
+];
+
+const PR3: [f32; 6] = [
+ /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+ -2.5470459075e-09, /* 0xb12f081b */
+ -7.0311963558e-02, /* 0xbd8fffb8 */
+ -2.4090321064e+00, /* 0xc01a2d95 */
+ -2.1965976715e+01, /* 0xc1afba52 */
+ -5.8079170227e+01, /* 0xc2685112 */
+ -3.1447946548e+01, /* 0xc1fb9565 */
+];
+const PS3: [f32; 5] = [
+ 3.5856033325e+01, /* 0x420f6c94 */
+ 3.6151397705e+02, /* 0x43b4c1ca */
+ 1.1936077881e+03, /* 0x44953373 */
+ 1.1279968262e+03, /* 0x448cffe6 */
+ 1.7358093262e+02, /* 0x432d94b8 */
+];
+
+const PR2: [f32; 6] = [
+ /* for x in [2.8570,2]=1/[0.3499,0.5] */
+ -8.8753431271e-08, /* 0xb3be98b7 */
+ -7.0303097367e-02, /* 0xbd8ffb12 */
+ -1.4507384300e+00, /* 0xbfb9b1cc */
+ -7.6356959343e+00, /* 0xc0f4579f */
+ -1.1193166733e+01, /* 0xc1331736 */
+ -3.2336456776e+00, /* 0xc04ef40d */
+];
+const PS2: [f32; 5] = [
+ 2.2220300674e+01, /* 0x41b1c32d */
+ 1.3620678711e+02, /* 0x430834f0 */
+ 2.7047027588e+02, /* 0x43873c32 */
+ 1.5387539673e+02, /* 0x4319e01a */
+ 1.4657617569e+01, /* 0x416a859a */
+];
+
+fn pzerof(x: f32) -> f32 {
+ let p: &[f32; 6];
+ let q: &[f32; 5];
+ let z: f32;
+ let r: f32;
+ let s: f32;
+ let mut ix: u32;
+
+ ix = x.to_bits();
+ ix &= 0x7fffffff;
+ if ix >= 0x41000000 {
+ p = &PR8;
+ q = &PS8;
+ } else if ix >= 0x409173eb {
+ p = &PR5;
+ q = &PS5;
+ } else if ix >= 0x4036d917 {
+ p = &PR3;
+ q = &PS3;
+ } else
+ /*ix >= 0x40000000*/
+ {
+ p = &PR2;
+ q = &PS2;
+ }
+ z = 1.0 / (x * x);
+ r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+ s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
+ return 1.0 + r / s;
+}
+
+/* For x >= 8, the asymptotic expansions of qzero is
+ * -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
+ * We approximate pzero by
+ * qzero(x) = s*(-1.25 + (R/S))
+ * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
+ * S = 1 + qS0*s^2 + ... + qS5*s^12
+ * and
+ * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
+ */
+const QR8: [f32; 6] = [
+ /* for x in [inf, 8]=1/[0,0.125] */
+ 0.0000000000e+00, /* 0x00000000 */
+ 7.3242187500e-02, /* 0x3d960000 */
+ 1.1768206596e+01, /* 0x413c4a93 */
+ 5.5767340088e+02, /* 0x440b6b19 */
+ 8.8591972656e+03, /* 0x460a6cca */
+ 3.7014625000e+04, /* 0x471096a0 */
+];
+const QS8: [f32; 6] = [
+ 1.6377603149e+02, /* 0x4323c6aa */
+ 8.0983447266e+03, /* 0x45fd12c2 */
+ 1.4253829688e+05, /* 0x480b3293 */
+ 8.0330925000e+05, /* 0x49441ed4 */
+ 8.4050156250e+05, /* 0x494d3359 */
+ -3.4389928125e+05, /* 0xc8a7eb69 */
+];
+
+const QR5: [f32; 6] = [
+ /* for x in [8,4.5454]=1/[0.125,0.22001] */
+ 1.8408595828e-11, /* 0x2da1ec79 */
+ 7.3242180049e-02, /* 0x3d95ffff */
+ 5.8356351852e+00, /* 0x40babd86 */
+ 1.3511157227e+02, /* 0x43071c90 */
+ 1.0272437744e+03, /* 0x448067cd */
+ 1.9899779053e+03, /* 0x44f8bf4b */
+];
+const QS5: [f32; 6] = [
+ 8.2776611328e+01, /* 0x42a58da0 */
+ 2.0778142090e+03, /* 0x4501dd07 */
+ 1.8847289062e+04, /* 0x46933e94 */
+ 5.6751113281e+04, /* 0x475daf1d */
+ 3.5976753906e+04, /* 0x470c88c1 */
+ -5.3543427734e+03, /* 0xc5a752be */
+];
+
+const QR3: [f32; 6] = [
+ /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+ 4.3774099900e-09, /* 0x3196681b */
+ 7.3241114616e-02, /* 0x3d95ff70 */
+ 3.3442313671e+00, /* 0x405607e3 */
+ 4.2621845245e+01, /* 0x422a7cc5 */
+ 1.7080809021e+02, /* 0x432acedf */
+ 1.6673394775e+02, /* 0x4326bbe4 */
+];
+const QS3: [f32; 6] = [
+ 4.8758872986e+01, /* 0x42430916 */
+ 7.0968920898e+02, /* 0x44316c1c */
+ 3.7041481934e+03, /* 0x4567825f */
+ 6.4604252930e+03, /* 0x45c9e367 */
+ 2.5163337402e+03, /* 0x451d4557 */
+ -1.4924745178e+02, /* 0xc3153f59 */
+];
+
+const QR2: [f32; 6] = [
+ /* for x in [2.8570,2]=1/[0.3499,0.5] */
+ 1.5044444979e-07, /* 0x342189db */
+ 7.3223426938e-02, /* 0x3d95f62a */
+ 1.9981917143e+00, /* 0x3fffc4bf */
+ 1.4495602608e+01, /* 0x4167edfd */
+ 3.1666231155e+01, /* 0x41fd5471 */
+ 1.6252708435e+01, /* 0x4182058c */
+];
+const QS2: [f32; 6] = [
+ 3.0365585327e+01, /* 0x41f2ecb8 */
+ 2.6934811401e+02, /* 0x4386ac8f */
+ 8.4478375244e+02, /* 0x44533229 */
+ 8.8293585205e+02, /* 0x445cbbe5 */
+ 2.1266638184e+02, /* 0x4354aa98 */
+ -5.3109550476e+00, /* 0xc0a9f358 */
+];
+
+fn qzerof(x: f32) -> f32 {
+ let p: &[f32; 6];
+ let q: &[f32; 6];
+ let s: f32;
+ let r: f32;
+ let z: f32;
+ let mut ix: u32;
+
+ ix = x.to_bits();
+ ix &= 0x7fffffff;
+ if ix >= 0x41000000 {
+ p = &QR8;
+ q = &QS8;
+ } else if ix >= 0x409173eb {
+ p = &QR5;
+ q = &QS5;
+ } else if ix >= 0x4036d917 {
+ p = &QR3;
+ q = &QS3;
+ } else
+ /*ix >= 0x40000000*/
+ {
+ p = &QR2;
+ q = &QS2;
+ }
+ z = 1.0 / (x * x);
+ r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+ s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
+ return (-0.125 + r / s) / x;
+}
diff --git a/src/math/j1.rs b/src/math/j1.rs
new file mode 100644
index 0000000..02a65ca
--- /dev/null
+++ b/src/math/j1.rs
@@ -0,0 +1,414 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_j1.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* j1(x), y1(x)
+ * Bessel function of the first and second kinds of order zero.
+ * Method -- j1(x):
+ * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
+ * 2. Reduce x to |x| since j1(x)=-j1(-x), and
+ * for x in (0,2)
+ * j1(x) = x/2 + x*z*R0/S0, where z = x*x;
+ * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 )
+ * for x in (2,inf)
+ * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
+ * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
+ * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
+ * as follow:
+ * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+ * = 1/sqrt(2) * (sin(x) - cos(x))
+ * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+ * = -1/sqrt(2) * (sin(x) + cos(x))
+ * (To avoid cancellation, use
+ * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ * to compute the worse one.)
+ *
+ * 3 Special cases
+ * j1(nan)= nan
+ * j1(0) = 0
+ * j1(inf) = 0
+ *
+ * Method -- y1(x):
+ * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
+ * 2. For x<2.
+ * Since
+ * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
+ * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
+ * We use the following function to approximate y1,
+ * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
+ * where for x in [0,2] (abs err less than 2**-65.89)
+ * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
+ * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5
+ * Note: For tiny x, 1/x dominate y1 and hence
+ * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
+ * 3. For x>=2.
+ * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
+ * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
+ * by method mentioned above.
+ */
+
+use super::{cos, fabs, get_high_word, get_low_word, log, sin, sqrt};
+
+const INVSQRTPI: f64 = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */
+const TPI: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
+
+fn common(ix: u32, x: f64, y1: bool, sign: bool) -> f64 {
+ let z: f64;
+ let mut s: f64;
+ let c: f64;
+ let mut ss: f64;
+ let mut cc: f64;
+
+ /*
+ * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x-3pi/4)-q1(x)*sin(x-3pi/4))
+ * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x-3pi/4)+q1(x)*cos(x-3pi/4))
+ *
+ * sin(x-3pi/4) = -(sin(x) + cos(x))/sqrt(2)
+ * cos(x-3pi/4) = (sin(x) - cos(x))/sqrt(2)
+ * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ */
+ s = sin(x);
+ if y1 {
+ s = -s;
+ }
+ c = cos(x);
+ cc = s - c;
+ if ix < 0x7fe00000 {
+ /* avoid overflow in 2*x */
+ ss = -s - c;
+ z = cos(2.0 * x);
+ if s * c > 0.0 {
+ cc = z / ss;
+ } else {
+ ss = z / cc;
+ }
+ if ix < 0x48000000 {
+ if y1 {
+ ss = -ss;
+ }
+ cc = pone(x) * cc - qone(x) * ss;
+ }
+ }
+ if sign {
+ cc = -cc;
+ }
+ return INVSQRTPI * cc / sqrt(x);
+}
+
+/* R0/S0 on [0,2] */
+const R00: f64 = -6.25000000000000000000e-02; /* 0xBFB00000, 0x00000000 */
+const R01: f64 = 1.40705666955189706048e-03; /* 0x3F570D9F, 0x98472C61 */
+const R02: f64 = -1.59955631084035597520e-05; /* 0xBEF0C5C6, 0xBA169668 */
+const R03: f64 = 4.96727999609584448412e-08; /* 0x3E6AAAFA, 0x46CA0BD9 */
+const S01: f64 = 1.91537599538363460805e-02; /* 0x3F939D0B, 0x12637E53 */
+const S02: f64 = 1.85946785588630915560e-04; /* 0x3F285F56, 0xB9CDF664 */
+const S03: f64 = 1.17718464042623683263e-06; /* 0x3EB3BFF8, 0x333F8498 */
+const S04: f64 = 5.04636257076217042715e-09; /* 0x3E35AC88, 0xC97DFF2C */
+const S05: f64 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
+
+pub fn j1(x: f64) -> f64 {
+ let mut z: f64;
+ let r: f64;
+ let s: f64;
+ let mut ix: u32;
+ let sign: bool;
+
+ ix = get_high_word(x);
+ sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+ if ix >= 0x7ff00000 {
+ return 1.0 / (x * x);
+ }
+ if ix >= 0x40000000 {
+ /* |x| >= 2 */
+ return common(ix, fabs(x), false, sign);
+ }
+ if ix >= 0x38000000 {
+ /* |x| >= 2**-127 */
+ z = x * x;
+ r = z * (R00 + z * (R01 + z * (R02 + z * R03)));
+ s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * (S04 + z * S05))));
+ z = r / s;
+ } else {
+ /* avoid underflow, raise inexact if x!=0 */
+ z = x;
+ }
+ return (0.5 + z) * x;
+}
+
+const U0: [f64; 5] = [
+ -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
+ 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
+ -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
+ 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
+ -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
+];
+const V0: [f64; 5] = [
+ 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
+ 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
+ 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
+ 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
+ 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
+];
+
+pub fn y1(x: f64) -> f64 {
+ let z: f64;
+ let u: f64;
+ let v: f64;
+ let ix: u32;
+ let lx: u32;
+
+ ix = get_high_word(x);
+ lx = get_low_word(x);
+
+ /* y1(nan)=nan, y1(<0)=nan, y1(0)=-inf, y1(inf)=0 */
+ if (ix << 1 | lx) == 0 {
+ return -1.0 / 0.0;
+ }
+ if (ix >> 31) != 0 {
+ return 0.0 / 0.0;
+ }
+ if ix >= 0x7ff00000 {
+ return 1.0 / x;
+ }
+
+ if ix >= 0x40000000 {
+ /* x >= 2 */
+ return common(ix, x, true, false);
+ }
+ if ix < 0x3c900000 {
+ /* x < 2**-54 */
+ return -TPI / x;
+ }
+ z = x * x;
+ u = U0[0] + z * (U0[1] + z * (U0[2] + z * (U0[3] + z * U0[4])));
+ v = 1.0 + z * (V0[0] + z * (V0[1] + z * (V0[2] + z * (V0[3] + z * V0[4]))));
+ return x * (u / v) + TPI * (j1(x) * log(x) - 1.0 / x);
+}
+
+/* For x >= 8, the asymptotic expansions of pone is
+ * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
+ * We approximate pone by
+ * pone(x) = 1 + (R/S)
+ * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
+ * S = 1 + ps0*s^2 + ... + ps4*s^10
+ * and
+ * | pone(x)-1-R/S | <= 2 ** ( -60.06)
+ */
+
+const PR8: [f64; 6] = [
+ /* for x in [inf, 8]=1/[0,0.125] */
+ 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+ 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
+ 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
+ 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
+ 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
+ 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
+];
+const PS8: [f64; 5] = [
+ 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
+ 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
+ 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
+ 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
+ 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
+];
+
+const PR5: [f64; 6] = [
+ /* for x in [8,4.5454]=1/[0.125,0.22001] */
+ 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
+ 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
+ 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
+ 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
+ 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
+ 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
+];
+const PS5: [f64; 5] = [
+ 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
+ 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
+ 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
+ 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
+ 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
+];
+
+const PR3: [f64; 6] = [
+ 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
+ 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
+ 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
+ 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
+ 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
+ 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
+];
+const PS3: [f64; 5] = [
+ 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
+ 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
+ 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
+ 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
+ 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
+];
+
+const PR2: [f64; 6] = [
+ /* for x in [2.8570,2]=1/[0.3499,0.5] */
+ 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
+ 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
+ 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
+ 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
+ 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
+ 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
+];
+const PS2: [f64; 5] = [
+ 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
+ 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
+ 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
+ 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
+ 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
+];
+
+fn pone(x: f64) -> f64 {
+ let p: &[f64; 6];
+ let q: &[f64; 5];
+ let z: f64;
+ let r: f64;
+ let s: f64;
+ let mut ix: u32;
+
+ ix = get_high_word(x);
+ ix &= 0x7fffffff;
+ if ix >= 0x40200000 {
+ p = &PR8;
+ q = &PS8;
+ } else if ix >= 0x40122E8B {
+ p = &PR5;
+ q = &PS5;
+ } else if ix >= 0x4006DB6D {
+ p = &PR3;
+ q = &PS3;
+ } else
+ /*ix >= 0x40000000*/
+ {
+ p = &PR2;
+ q = &PS2;
+ }
+ z = 1.0 / (x * x);
+ r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+ s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
+ return 1.0 + r / s;
+}
+
+/* For x >= 8, the asymptotic expansions of qone is
+ * 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
+ * We approximate pone by
+ * qone(x) = s*(0.375 + (R/S))
+ * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
+ * S = 1 + qs1*s^2 + ... + qs6*s^12
+ * and
+ * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
+ */
+
+const QR8: [f64; 6] = [
+ /* for x in [inf, 8]=1/[0,0.125] */
+ 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+ -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
+ -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
+ -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
+ -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
+ -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
+];
+const QS8: [f64; 6] = [
+ 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
+ 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
+ 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
+ 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
+ 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
+ -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
+];
+
+const QR5: [f64; 6] = [
+ /* for x in [8,4.5454]=1/[0.125,0.22001] */
+ -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
+ -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
+ -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
+ -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
+ -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
+ -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
+];
+const QS5: [f64; 6] = [
+ 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
+ 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
+ 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
+ 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
+ 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
+ -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
+];
+
+const QR3: [f64; 6] = [
+ -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
+ -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
+ -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
+ -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
+ -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
+ -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
+];
+const QS3: [f64; 6] = [
+ 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
+ 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
+ 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
+ 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
+ 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
+ -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
+];
+
+const QR2: [f64; 6] = [
+ /* for x in [2.8570,2]=1/[0.3499,0.5] */
+ -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
+ -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
+ -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
+ -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
+ -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
+ -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
+];
+const QS2: [f64; 6] = [
+ 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
+ 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
+ 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
+ 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
+ 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
+ -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
+];
+
+fn qone(x: f64) -> f64 {
+ let p: &[f64; 6];
+ let q: &[f64; 6];
+ let s: f64;
+ let r: f64;
+ let z: f64;
+ let mut ix: u32;
+
+ ix = get_high_word(x);
+ ix &= 0x7fffffff;
+ if ix >= 0x40200000 {
+ p = &QR8;
+ q = &QS8;
+ } else if ix >= 0x40122E8B {
+ p = &QR5;
+ q = &QS5;
+ } else if ix >= 0x4006DB6D {
+ p = &QR3;
+ q = &QS3;
+ } else
+ /*ix >= 0x40000000*/
+ {
+ p = &QR2;
+ q = &QS2;
+ }
+ z = 1.0 / (x * x);
+ r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+ s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
+ return (0.375 + r / s) / x;
+}
diff --git a/src/math/j1f.rs b/src/math/j1f.rs
new file mode 100644
index 0000000..5095894
--- /dev/null
+++ b/src/math/j1f.rs
@@ -0,0 +1,372 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{cosf, fabsf, logf, sinf, sqrtf};
+
+const INVSQRTPI: f32 = 5.6418961287e-01; /* 0x3f106ebb */
+const TPI: f32 = 6.3661974669e-01; /* 0x3f22f983 */
+
+fn common(ix: u32, x: f32, y1: bool, sign: bool) -> f32 {
+ let z: f64;
+ let mut s: f64;
+ let c: f64;
+ let mut ss: f64;
+ let mut cc: f64;
+
+ s = sinf(x) as f64;
+ if y1 {
+ s = -s;
+ }
+ c = cosf(x) as f64;
+ cc = s - c;
+ if ix < 0x7f000000 {
+ ss = -s - c;
+ z = cosf(2.0 * x) as f64;
+ if s * c > 0.0 {
+ cc = z / ss;
+ } else {
+ ss = z / cc;
+ }
+ if ix < 0x58800000 {
+ if y1 {
+ ss = -ss;
+ }
+ cc = (ponef(x) as f64) * cc - (qonef(x) as f64) * ss;
+ }
+ }
+ if sign {
+ cc = -cc;
+ }
+ return (((INVSQRTPI as f64) * cc) / (sqrtf(x) as f64)) as f32;
+}
+
+/* R0/S0 on [0,2] */
+const R00: f32 = -6.2500000000e-02; /* 0xbd800000 */
+const R01: f32 = 1.4070566976e-03; /* 0x3ab86cfd */
+const R02: f32 = -1.5995563444e-05; /* 0xb7862e36 */
+const R03: f32 = 4.9672799207e-08; /* 0x335557d2 */
+const S01: f32 = 1.9153760746e-02; /* 0x3c9ce859 */
+const S02: f32 = 1.8594678841e-04; /* 0x3942fab6 */
+const S03: f32 = 1.1771846857e-06; /* 0x359dffc2 */
+const S04: f32 = 5.0463624390e-09; /* 0x31ad6446 */
+const S05: f32 = 1.2354227016e-11; /* 0x2d59567e */
+
+pub fn j1f(x: f32) -> f32 {
+ let mut z: f32;
+ let r: f32;
+ let s: f32;
+ let mut ix: u32;
+ let sign: bool;
+
+ ix = x.to_bits();
+ sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+ if ix >= 0x7f800000 {
+ return 1.0 / (x * x);
+ }
+ if ix >= 0x40000000 {
+ /* |x| >= 2 */
+ return common(ix, fabsf(x), false, sign);
+ }
+ if ix >= 0x39000000 {
+ /* |x| >= 2**-13 */
+ z = x * x;
+ r = z * (R00 + z * (R01 + z * (R02 + z * R03)));
+ s = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * (S04 + z * S05))));
+ z = 0.5 + r / s;
+ } else {
+ z = 0.5;
+ }
+ return z * x;
+}
+
+const U0: [f32; 5] = [
+ -1.9605709612e-01, /* 0xbe48c331 */
+ 5.0443872809e-02, /* 0x3d4e9e3c */
+ -1.9125689287e-03, /* 0xbafaaf2a */
+ 2.3525259166e-05, /* 0x37c5581c */
+ -9.1909917899e-08, /* 0xb3c56003 */
+];
+const V0: [f32; 5] = [
+ 1.9916731864e-02, /* 0x3ca3286a */
+ 2.0255257550e-04, /* 0x3954644b */
+ 1.3560879779e-06, /* 0x35b602d4 */
+ 6.2274145840e-09, /* 0x31d5f8eb */
+ 1.6655924903e-11, /* 0x2d9281cf */
+];
+
+pub fn y1f(x: f32) -> f32 {
+ let z: f32;
+ let u: f32;
+ let v: f32;
+ let ix: u32;
+
+ ix = x.to_bits();
+ if (ix & 0x7fffffff) == 0 {
+ return -1.0 / 0.0;
+ }
+ if (ix >> 31) != 0 {
+ return 0.0 / 0.0;
+ }
+ if ix >= 0x7f800000 {
+ return 1.0 / x;
+ }
+ if ix >= 0x40000000 {
+ /* |x| >= 2.0 */
+ return common(ix, x, true, false);
+ }
+ if ix < 0x33000000 {
+ /* x < 2**-25 */
+ return -TPI / x;
+ }
+ z = x * x;
+ u = U0[0] + z * (U0[1] + z * (U0[2] + z * (U0[3] + z * U0[4])));
+ v = 1.0 + z * (V0[0] + z * (V0[1] + z * (V0[2] + z * (V0[3] + z * V0[4]))));
+ return x * (u / v) + TPI * (j1f(x) * logf(x) - 1.0 / x);
+}
+
+/* For x >= 8, the asymptotic expansions of pone is
+ * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
+ * We approximate pone by
+ * pone(x) = 1 + (R/S)
+ * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
+ * S = 1 + ps0*s^2 + ... + ps4*s^10
+ * and
+ * | pone(x)-1-R/S | <= 2 ** ( -60.06)
+ */
+
+const PR8: [f32; 6] = [
+ /* for x in [inf, 8]=1/[0,0.125] */
+ 0.0000000000e+00, /* 0x00000000 */
+ 1.1718750000e-01, /* 0x3df00000 */
+ 1.3239480972e+01, /* 0x4153d4ea */
+ 4.1205184937e+02, /* 0x43ce06a3 */
+ 3.8747453613e+03, /* 0x45722bed */
+ 7.9144794922e+03, /* 0x45f753d6 */
+];
+const PS8: [f32; 5] = [
+ 1.1420736694e+02, /* 0x42e46a2c */
+ 3.6509309082e+03, /* 0x45642ee5 */
+ 3.6956207031e+04, /* 0x47105c35 */
+ 9.7602796875e+04, /* 0x47bea166 */
+ 3.0804271484e+04, /* 0x46f0a88b */
+];
+
+const PR5: [f32; 6] = [
+ /* for x in [8,4.5454]=1/[0.125,0.22001] */
+ 1.3199052094e-11, /* 0x2d68333f */
+ 1.1718749255e-01, /* 0x3defffff */
+ 6.8027510643e+00, /* 0x40d9b023 */
+ 1.0830818176e+02, /* 0x42d89dca */
+ 5.1763616943e+02, /* 0x440168b7 */
+ 5.2871520996e+02, /* 0x44042dc6 */
+];
+const PS5: [f32; 5] = [
+ 5.9280597687e+01, /* 0x426d1f55 */
+ 9.9140142822e+02, /* 0x4477d9b1 */
+ 5.3532670898e+03, /* 0x45a74a23 */
+ 7.8446904297e+03, /* 0x45f52586 */
+ 1.5040468750e+03, /* 0x44bc0180 */
+];
+
+const PR3: [f32; 6] = [
+ 3.0250391081e-09, /* 0x314fe10d */
+ 1.1718686670e-01, /* 0x3defffab */
+ 3.9329774380e+00, /* 0x407bb5e7 */
+ 3.5119403839e+01, /* 0x420c7a45 */
+ 9.1055007935e+01, /* 0x42b61c2a */
+ 4.8559066772e+01, /* 0x42423c7c */
+];
+const PS3: [f32; 5] = [
+ 3.4791309357e+01, /* 0x420b2a4d */
+ 3.3676245117e+02, /* 0x43a86198 */
+ 1.0468714600e+03, /* 0x4482dbe3 */
+ 8.9081134033e+02, /* 0x445eb3ed */
+ 1.0378793335e+02, /* 0x42cf936c */
+];
+
+const PR2: [f32; 6] = [
+ /* for x in [2.8570,2]=1/[0.3499,0.5] */
+ 1.0771083225e-07, /* 0x33e74ea8 */
+ 1.1717621982e-01, /* 0x3deffa16 */
+ 2.3685150146e+00, /* 0x401795c0 */
+ 1.2242610931e+01, /* 0x4143e1bc */
+ 1.7693971634e+01, /* 0x418d8d41 */
+ 5.0735230446e+00, /* 0x40a25a4d */
+];
+const PS2: [f32; 5] = [
+ 2.1436485291e+01, /* 0x41ab7dec */
+ 1.2529022980e+02, /* 0x42fa9499 */
+ 2.3227647400e+02, /* 0x436846c7 */
+ 1.1767937469e+02, /* 0x42eb5bd7 */
+ 8.3646392822e+00, /* 0x4105d590 */
+];
+
+fn ponef(x: f32) -> f32 {
+ let p: &[f32; 6];
+ let q: &[f32; 5];
+ let z: f32;
+ let r: f32;
+ let s: f32;
+ let mut ix: u32;
+
+ ix = x.to_bits();
+ ix &= 0x7fffffff;
+ if ix >= 0x41000000 {
+ p = &PR8;
+ q = &PS8;
+ } else if ix >= 0x409173eb {
+ p = &PR5;
+ q = &PS5;
+ } else if ix >= 0x4036d917 {
+ p = &PR3;
+ q = &PS3;
+ } else
+ /*ix >= 0x40000000*/
+ {
+ p = &PR2;
+ q = &PS2;
+ }
+ z = 1.0 / (x * x);
+ r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+ s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
+ return 1.0 + r / s;
+}
+
+/* For x >= 8, the asymptotic expansions of qone is
+ * 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
+ * We approximate pone by
+ * qone(x) = s*(0.375 + (R/S))
+ * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
+ * S = 1 + qs1*s^2 + ... + qs6*s^12
+ * and
+ * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
+ */
+
+const QR8: [f32; 6] = [
+ /* for x in [inf, 8]=1/[0,0.125] */
+ 0.0000000000e+00, /* 0x00000000 */
+ -1.0253906250e-01, /* 0xbdd20000 */
+ -1.6271753311e+01, /* 0xc1822c8d */
+ -7.5960174561e+02, /* 0xc43de683 */
+ -1.1849806641e+04, /* 0xc639273a */
+ -4.8438511719e+04, /* 0xc73d3683 */
+];
+const QS8: [f32; 6] = [
+ 1.6139537048e+02, /* 0x43216537 */
+ 7.8253862305e+03, /* 0x45f48b17 */
+ 1.3387534375e+05, /* 0x4802bcd6 */
+ 7.1965775000e+05, /* 0x492fb29c */
+ 6.6660125000e+05, /* 0x4922be94 */
+ -2.9449025000e+05, /* 0xc88fcb48 */
+];
+
+const QR5: [f32; 6] = [
+ /* for x in [8,4.5454]=1/[0.125,0.22001] */
+ -2.0897993405e-11, /* 0xadb7d219 */
+ -1.0253904760e-01, /* 0xbdd1fffe */
+ -8.0564479828e+00, /* 0xc100e736 */
+ -1.8366960144e+02, /* 0xc337ab6b */
+ -1.3731937256e+03, /* 0xc4aba633 */
+ -2.6124443359e+03, /* 0xc523471c */
+];
+const QS5: [f32; 6] = [
+ 8.1276550293e+01, /* 0x42a28d98 */
+ 1.9917987061e+03, /* 0x44f8f98f */
+ 1.7468484375e+04, /* 0x468878f8 */
+ 4.9851425781e+04, /* 0x4742bb6d */
+ 2.7948074219e+04, /* 0x46da5826 */
+ -4.7191835938e+03, /* 0xc5937978 */
+];
+
+const QR3: [f32; 6] = [
+ -5.0783124372e-09, /* 0xb1ae7d4f */
+ -1.0253783315e-01, /* 0xbdd1ff5b */
+ -4.6101160049e+00, /* 0xc0938612 */
+ -5.7847221375e+01, /* 0xc267638e */
+ -2.2824453735e+02, /* 0xc3643e9a */
+ -2.1921012878e+02, /* 0xc35b35cb */
+];
+const QS3: [f32; 6] = [
+ 4.7665153503e+01, /* 0x423ea91e */
+ 6.7386511230e+02, /* 0x4428775e */
+ 3.3801528320e+03, /* 0x45534272 */
+ 5.5477290039e+03, /* 0x45ad5dd5 */
+ 1.9031191406e+03, /* 0x44ede3d0 */
+ -1.3520118713e+02, /* 0xc3073381 */
+];
+
+const QR2: [f32; 6] = [
+ /* for x in [2.8570,2]=1/[0.3499,0.5] */
+ -1.7838172539e-07, /* 0xb43f8932 */
+ -1.0251704603e-01, /* 0xbdd1f475 */
+ -2.7522056103e+00, /* 0xc0302423 */
+ -1.9663616180e+01, /* 0xc19d4f16 */
+ -4.2325313568e+01, /* 0xc2294d1f */
+ -2.1371921539e+01, /* 0xc1aaf9b2 */
+];
+const QS2: [f32; 6] = [
+ 2.9533363342e+01, /* 0x41ec4454 */
+ 2.5298155212e+02, /* 0x437cfb47 */
+ 7.5750280762e+02, /* 0x443d602e */
+ 7.3939318848e+02, /* 0x4438d92a */
+ 1.5594900513e+02, /* 0x431bf2f2 */
+ -4.9594988823e+00, /* 0xc09eb437 */
+];
+
+fn qonef(x: f32) -> f32 {
+ let p: &[f32; 6];
+ let q: &[f32; 6];
+ let s: f32;
+ let r: f32;
+ let z: f32;
+ let mut ix: u32;
+
+ ix = x.to_bits();
+ ix &= 0x7fffffff;
+ if ix >= 0x41000000 {
+ p = &QR8;
+ q = &QS8;
+ } else if ix >= 0x409173eb {
+ p = &QR5;
+ q = &QS5;
+ } else if ix >= 0x4036d917 {
+ p = &QR3;
+ q = &QS3;
+ } else
+ /*ix >= 0x40000000*/
+ {
+ p = &QR2;
+ q = &QS2;
+ }
+ z = 1.0 / (x * x);
+ r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
+ s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
+ return (0.375 + r / s) / x;
+}
+
+#[cfg(test)]
+mod tests {
+ use super::{j1f, y1f};
+ #[test]
+ fn test_j1f_2488() {
+ // 0x401F3E49
+ assert_eq!(j1f(2.4881766_f32), 0.49999475_f32);
+ }
+ #[test]
+ fn test_y1f_2002() {
+ assert_eq!(y1f(2.0000002_f32), -0.10703229_f32);
+ }
+}
diff --git a/src/math/jn.rs b/src/math/jn.rs
new file mode 100644
index 0000000..1be167f
--- /dev/null
+++ b/src/math/jn.rs
@@ -0,0 +1,343 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_jn.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/*
+ * jn(n, x), yn(n, x)
+ * floating point Bessel's function of the 1st and 2nd kind
+ * of order n
+ *
+ * Special cases:
+ * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
+ * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
+ * Note 2. About jn(n,x), yn(n,x)
+ * For n=0, j0(x) is called,
+ * for n=1, j1(x) is called,
+ * for n<=x, forward recursion is used starting
+ * from values of j0(x) and j1(x).
+ * for n>x, a continued fraction approximation to
+ * j(n,x)/j(n-1,x) is evaluated and then backward
+ * recursion is used starting from a supposed value
+ * for j(n,x). The resulting value of j(0,x) is
+ * compared with the actual value to correct the
+ * supposed value of j(n,x).
+ *
+ * yn(n,x) is similar in all respects, except
+ * that forward recursion is used for all
+ * values of n>1.
+ */
+
+use super::{cos, fabs, get_high_word, get_low_word, j0, j1, log, sin, sqrt, y0, y1};
+
+const INVSQRTPI: f64 = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */
+
+pub fn jn(n: i32, mut x: f64) -> f64 {
+ let mut ix: u32;
+ let lx: u32;
+ let nm1: i32;
+ let mut i: i32;
+ let mut sign: bool;
+ let mut a: f64;
+ let mut b: f64;
+ let mut temp: f64;
+
+ ix = get_high_word(x);
+ lx = get_low_word(x);
+ sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+
+ // -lx == !lx + 1
+ if (ix | (lx | ((!lx).wrapping_add(1))) >> 31) > 0x7ff00000 {
+ /* nan */
+ return x;
+ }
+
+ /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
+ * Thus, J(-n,x) = J(n,-x)
+ */
+ /* nm1 = |n|-1 is used instead of |n| to handle n==INT_MIN */
+ if n == 0 {
+ return j0(x);
+ }
+ if n < 0 {
+ nm1 = -(n + 1);
+ x = -x;
+ sign = !sign;
+ } else {
+ nm1 = n - 1;
+ }
+ if nm1 == 0 {
+ return j1(x);
+ }
+
+ sign &= (n & 1) != 0; /* even n: 0, odd n: signbit(x) */
+ x = fabs(x);
+ if (ix | lx) == 0 || ix == 0x7ff00000 {
+ /* if x is 0 or inf */
+ b = 0.0;
+ } else if (nm1 as f64) < x {
+ /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+ if ix >= 0x52d00000 {
+ /* x > 2**302 */
+ /* (x >> n**2)
+ * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Let s=sin(x), c=cos(x),
+ * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+ *
+ * n sin(xn)*sqt2 cos(xn)*sqt2
+ * ----------------------------------
+ * 0 s-c c+s
+ * 1 -s-c -c+s
+ * 2 -s+c -c-s
+ * 3 s+c c-s
+ */
+ temp = match nm1 & 3 {
+ 0 => -cos(x) + sin(x),
+ 1 => -cos(x) - sin(x),
+ 2 => cos(x) - sin(x),
+ 3 | _ => cos(x) + sin(x),
+ };
+ b = INVSQRTPI * temp / sqrt(x);
+ } else {
+ a = j0(x);
+ b = j1(x);
+ i = 0;
+ while i < nm1 {
+ i += 1;
+ temp = b;
+ b = b * (2.0 * (i as f64) / x) - a; /* avoid underflow */
+ a = temp;
+ }
+ }
+ } else {
+ if ix < 0x3e100000 {
+ /* x < 2**-29 */
+ /* x is tiny, return the first Taylor expansion of J(n,x)
+ * J(n,x) = 1/n!*(x/2)^n - ...
+ */
+ if nm1 > 32 {
+ /* underflow */
+ b = 0.0;
+ } else {
+ temp = x * 0.5;
+ b = temp;
+ a = 1.0;
+ i = 2;
+ while i <= nm1 + 1 {
+ a *= i as f64; /* a = n! */
+ b *= temp; /* b = (x/2)^n */
+ i += 1;
+ }
+ b = b / a;
+ }
+ } else {
+ /* use backward recurrence */
+ /* x x^2 x^2
+ * J(n,x)/J(n-1,x) = ---- ------ ------ .....
+ * 2n - 2(n+1) - 2(n+2)
+ *
+ * 1 1 1
+ * (for large x) = ---- ------ ------ .....
+ * 2n 2(n+1) 2(n+2)
+ * -- - ------ - ------ -
+ * x x x
+ *
+ * Let w = 2n/x and h=2/x, then the above quotient
+ * is equal to the continued fraction:
+ * 1
+ * = -----------------------
+ * 1
+ * w - -----------------
+ * 1
+ * w+h - ---------
+ * w+2h - ...
+ *
+ * To determine how many terms needed, let
+ * Q(0) = w, Q(1) = w(w+h) - 1,
+ * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+ * When Q(k) > 1e4 good for single
+ * When Q(k) > 1e9 good for double
+ * When Q(k) > 1e17 good for quadruple
+ */
+ /* determine k */
+ let mut t: f64;
+ let mut q0: f64;
+ let mut q1: f64;
+ let mut w: f64;
+ let h: f64;
+ let mut z: f64;
+ let mut tmp: f64;
+ let nf: f64;
+
+ let mut k: i32;
+
+ nf = (nm1 as f64) + 1.0;
+ w = 2.0 * nf / x;
+ h = 2.0 / x;
+ z = w + h;
+ q0 = w;
+ q1 = w * z - 1.0;
+ k = 1;
+ while q1 < 1.0e9 {
+ k += 1;
+ z += h;
+ tmp = z * q1 - q0;
+ q0 = q1;
+ q1 = tmp;
+ }
+ t = 0.0;
+ i = k;
+ while i >= 0 {
+ t = 1.0 / (2.0 * ((i as f64) + nf) / x - t);
+ i -= 1;
+ }
+ a = t;
+ b = 1.0;
+ /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+ * Hence, if n*(log(2n/x)) > ...
+ * single 8.8722839355e+01
+ * double 7.09782712893383973096e+02
+ * long double 1.1356523406294143949491931077970765006170e+04
+ * then recurrent value may overflow and the result is
+ * likely underflow to zero
+ */
+ tmp = nf * log(fabs(w));
+ if tmp < 7.09782712893383973096e+02 {
+ i = nm1;
+ while i > 0 {
+ temp = b;
+ b = b * (2.0 * (i as f64)) / x - a;
+ a = temp;
+ i -= 1;
+ }
+ } else {
+ i = nm1;
+ while i > 0 {
+ temp = b;
+ b = b * (2.0 * (i as f64)) / x - a;
+ a = temp;
+ /* scale b to avoid spurious overflow */
+ let x1p500 = f64::from_bits(0x5f30000000000000); // 0x1p500 == 2^500
+ if b > x1p500 {
+ a /= b;
+ t /= b;
+ b = 1.0;
+ }
+ i -= 1;
+ }
+ }
+ z = j0(x);
+ w = j1(x);
+ if fabs(z) >= fabs(w) {
+ b = t * z / b;
+ } else {
+ b = t * w / a;
+ }
+ }
+ }
+
+ if sign {
+ -b
+ } else {
+ b
+ }
+}
+
+pub fn yn(n: i32, x: f64) -> f64 {
+ let mut ix: u32;
+ let lx: u32;
+ let mut ib: u32;
+ let nm1: i32;
+ let mut sign: bool;
+ let mut i: i32;
+ let mut a: f64;
+ let mut b: f64;
+ let mut temp: f64;
+
+ ix = get_high_word(x);
+ lx = get_low_word(x);
+ sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+
+ // -lx == !lx + 1
+ if (ix | (lx | ((!lx).wrapping_add(1))) >> 31) > 0x7ff00000 {
+ /* nan */
+ return x;
+ }
+ if sign && (ix | lx) != 0 {
+ /* x < 0 */
+ return 0.0 / 0.0;
+ }
+ if ix == 0x7ff00000 {
+ return 0.0;
+ }
+
+ if n == 0 {
+ return y0(x);
+ }
+ if n < 0 {
+ nm1 = -(n + 1);
+ sign = (n & 1) != 0;
+ } else {
+ nm1 = n - 1;
+ sign = false;
+ }
+ if nm1 == 0 {
+ if sign {
+ return -y1(x);
+ } else {
+ return y1(x);
+ }
+ }
+
+ if ix >= 0x52d00000 {
+ /* x > 2**302 */
+ /* (x >> n**2)
+ * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+ * Let s=sin(x), c=cos(x),
+ * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+ *
+ * n sin(xn)*sqt2 cos(xn)*sqt2
+ * ----------------------------------
+ * 0 s-c c+s
+ * 1 -s-c -c+s
+ * 2 -s+c -c-s
+ * 3 s+c c-s
+ */
+ temp = match nm1 & 3 {
+ 0 => -sin(x) - cos(x),
+ 1 => -sin(x) + cos(x),
+ 2 => sin(x) + cos(x),
+ 3 | _ => sin(x) - cos(x),
+ };
+ b = INVSQRTPI * temp / sqrt(x);
+ } else {
+ a = y0(x);
+ b = y1(x);
+ /* quit if b is -inf */
+ ib = get_high_word(b);
+ i = 0;
+ while i < nm1 && ib != 0xfff00000 {
+ i += 1;
+ temp = b;
+ b = (2.0 * (i as f64) / x) * b - a;
+ ib = get_high_word(b);
+ a = temp;
+ }
+ }
+
+ if sign {
+ -b
+ } else {
+ b
+ }
+}
diff --git a/src/math/jnf.rs b/src/math/jnf.rs
new file mode 100644
index 0000000..360f62e
--- /dev/null
+++ b/src/math/jnf.rs
@@ -0,0 +1,259 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_jnf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{fabsf, j0f, j1f, logf, y0f, y1f};
+
+pub fn jnf(n: i32, mut x: f32) -> f32 {
+ let mut ix: u32;
+ let mut nm1: i32;
+ let mut sign: bool;
+ let mut i: i32;
+ let mut a: f32;
+ let mut b: f32;
+ let mut temp: f32;
+
+ ix = x.to_bits();
+ sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+ if ix > 0x7f800000 {
+ /* nan */
+ return x;
+ }
+
+ /* J(-n,x) = J(n,-x), use |n|-1 to avoid overflow in -n */
+ if n == 0 {
+ return j0f(x);
+ }
+ if n < 0 {
+ nm1 = -(n + 1);
+ x = -x;
+ sign = !sign;
+ } else {
+ nm1 = n - 1;
+ }
+ if nm1 == 0 {
+ return j1f(x);
+ }
+
+ sign &= (n & 1) != 0; /* even n: 0, odd n: signbit(x) */
+ x = fabsf(x);
+ if ix == 0 || ix == 0x7f800000 {
+ /* if x is 0 or inf */
+ b = 0.0;
+ } else if (nm1 as f32) < x {
+ /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+ a = j0f(x);
+ b = j1f(x);
+ i = 0;
+ while i < nm1 {
+ i += 1;
+ temp = b;
+ b = b * (2.0 * (i as f32) / x) - a;
+ a = temp;
+ }
+ } else {
+ if ix < 0x35800000 {
+ /* x < 2**-20 */
+ /* x is tiny, return the first Taylor expansion of J(n,x)
+ * J(n,x) = 1/n!*(x/2)^n - ...
+ */
+ if nm1 > 8 {
+ /* underflow */
+ nm1 = 8;
+ }
+ temp = 0.5 * x;
+ b = temp;
+ a = 1.0;
+ i = 2;
+ while i <= nm1 + 1 {
+ a *= i as f32; /* a = n! */
+ b *= temp; /* b = (x/2)^n */
+ i += 1;
+ }
+ b = b / a;
+ } else {
+ /* use backward recurrence */
+ /* x x^2 x^2
+ * J(n,x)/J(n-1,x) = ---- ------ ------ .....
+ * 2n - 2(n+1) - 2(n+2)
+ *
+ * 1 1 1
+ * (for large x) = ---- ------ ------ .....
+ * 2n 2(n+1) 2(n+2)
+ * -- - ------ - ------ -
+ * x x x
+ *
+ * Let w = 2n/x and h=2/x, then the above quotient
+ * is equal to the continued fraction:
+ * 1
+ * = -----------------------
+ * 1
+ * w - -----------------
+ * 1
+ * w+h - ---------
+ * w+2h - ...
+ *
+ * To determine how many terms needed, let
+ * Q(0) = w, Q(1) = w(w+h) - 1,
+ * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+ * When Q(k) > 1e4 good for single
+ * When Q(k) > 1e9 good for double
+ * When Q(k) > 1e17 good for quadruple
+ */
+ /* determine k */
+ let mut t: f32;
+ let mut q0: f32;
+ let mut q1: f32;
+ let mut w: f32;
+ let h: f32;
+ let mut z: f32;
+ let mut tmp: f32;
+ let nf: f32;
+ let mut k: i32;
+
+ nf = (nm1 as f32) + 1.0;
+ w = 2.0 * (nf as f32) / x;
+ h = 2.0 / x;
+ z = w + h;
+ q0 = w;
+ q1 = w * z - 1.0;
+ k = 1;
+ while q1 < 1.0e4 {
+ k += 1;
+ z += h;
+ tmp = z * q1 - q0;
+ q0 = q1;
+ q1 = tmp;
+ }
+ t = 0.0;
+ i = k;
+ while i >= 0 {
+ t = 1.0 / (2.0 * ((i as f32) + nf) / x - t);
+ i -= 1;
+ }
+ a = t;
+ b = 1.0;
+ /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+ * Hence, if n*(log(2n/x)) > ...
+ * single 8.8722839355e+01
+ * double 7.09782712893383973096e+02
+ * long double 1.1356523406294143949491931077970765006170e+04
+ * then recurrent value may overflow and the result is
+ * likely underflow to zero
+ */
+ tmp = nf * logf(fabsf(w));
+ if tmp < 88.721679688 {
+ i = nm1;
+ while i > 0 {
+ temp = b;
+ b = 2.0 * (i as f32) * b / x - a;
+ a = temp;
+ i -= 1;
+ }
+ } else {
+ i = nm1;
+ while i > 0 {
+ temp = b;
+ b = 2.0 * (i as f32) * b / x - a;
+ a = temp;
+ /* scale b to avoid spurious overflow */
+ let x1p60 = f32::from_bits(0x5d800000); // 0x1p60 == 2^60
+ if b > x1p60 {
+ a /= b;
+ t /= b;
+ b = 1.0;
+ }
+ i -= 1;
+ }
+ }
+ z = j0f(x);
+ w = j1f(x);
+ if fabsf(z) >= fabsf(w) {
+ b = t * z / b;
+ } else {
+ b = t * w / a;
+ }
+ }
+ }
+
+ if sign {
+ -b
+ } else {
+ b
+ }
+}
+
+pub fn ynf(n: i32, x: f32) -> f32 {
+ let mut ix: u32;
+ let mut ib: u32;
+ let nm1: i32;
+ let mut sign: bool;
+ let mut i: i32;
+ let mut a: f32;
+ let mut b: f32;
+ let mut temp: f32;
+
+ ix = x.to_bits();
+ sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+ if ix > 0x7f800000 {
+ /* nan */
+ return x;
+ }
+ if sign && ix != 0 {
+ /* x < 0 */
+ return 0.0 / 0.0;
+ }
+ if ix == 0x7f800000 {
+ return 0.0;
+ }
+
+ if n == 0 {
+ return y0f(x);
+ }
+ if n < 0 {
+ nm1 = -(n + 1);
+ sign = (n & 1) != 0;
+ } else {
+ nm1 = n - 1;
+ sign = false;
+ }
+ if nm1 == 0 {
+ if sign {
+ return -y1f(x);
+ } else {
+ return y1f(x);
+ }
+ }
+
+ a = y0f(x);
+ b = y1f(x);
+ /* quit if b is -inf */
+ ib = b.to_bits();
+ i = 0;
+ while i < nm1 && ib != 0xff800000 {
+ i += 1;
+ temp = b;
+ b = (2.0 * (i as f32) / x) * b - a;
+ ib = b.to_bits();
+ a = temp;
+ }
+
+ if sign {
+ -b
+ } else {
+ b
+ }
+}
diff --git a/src/math/k_cos.rs b/src/math/k_cos.rs
new file mode 100644
index 0000000..49b2fc6
--- /dev/null
+++ b/src/math/k_cos.rs
@@ -0,0 +1,62 @@
+// origin: FreeBSD /usr/src/lib/msun/src/k_cos.c
+//
+// ====================================================
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+//
+// Developed at SunSoft, a Sun Microsystems, Inc. business.
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+
+const C1: f64 = 4.16666666666666019037e-02; /* 0x3FA55555, 0x5555554C */
+const C2: f64 = -1.38888888888741095749e-03; /* 0xBF56C16C, 0x16C15177 */
+const C3: f64 = 2.48015872894767294178e-05; /* 0x3EFA01A0, 0x19CB1590 */
+const C4: f64 = -2.75573143513906633035e-07; /* 0xBE927E4F, 0x809C52AD */
+const C5: f64 = 2.08757232129817482790e-09; /* 0x3E21EE9E, 0xBDB4B1C4 */
+const C6: f64 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
+
+// kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
+// Input x is assumed to be bounded by ~pi/4 in magnitude.
+// Input y is the tail of x.
+//
+// Algorithm
+// 1. Since cos(-x) = cos(x), we need only to consider positive x.
+// 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
+// 3. cos(x) is approximated by a polynomial of degree 14 on
+// [0,pi/4]
+// 4 14
+// cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
+// where the remez error is
+//
+// | 2 4 6 8 10 12 14 | -58
+// |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
+// | |
+//
+// 4 6 8 10 12 14
+// 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
+// cos(x) ~ 1 - x*x/2 + r
+// since cos(x+y) ~ cos(x) - sin(x)*y
+// ~ cos(x) - x*y,
+// a correction term is necessary in cos(x) and hence
+// cos(x+y) = 1 - (x*x/2 - (r - x*y))
+// For better accuracy, rearrange to
+// cos(x+y) ~ w + (tmp + (r-x*y))
+// where w = 1 - x*x/2 and tmp is a tiny correction term
+// (1 - x*x/2 == w + tmp exactly in infinite precision).
+// The exactness of w + tmp in infinite precision depends on w
+// and tmp having the same precision as x. If they have extra
+// precision due to compiler bugs, then the extra precision is
+// only good provided it is retained in all terms of the final
+// expression for cos(). Retention happens in all cases tested
+// under FreeBSD, so don't pessimize things by forcibly clipping
+// any extra precision in w.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn k_cos(x: f64, y: f64) -> f64 {
+ let z = x * x;
+ let w = z * z;
+ let r = z * (C1 + z * (C2 + z * C3)) + w * w * (C4 + z * (C5 + z * C6));
+ let hz = 0.5 * z;
+ let w = 1.0 - hz;
+ w + (((1.0 - w) - hz) + (z * r - x * y))
+}
diff --git a/src/math/k_cosf.rs b/src/math/k_cosf.rs
new file mode 100644
index 0000000..e99f234
--- /dev/null
+++ b/src/math/k_cosf.rs
@@ -0,0 +1,29 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/k_cosf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Debugged and optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */
+const C0: f64 = -0.499999997251031003120; /* -0x1ffffffd0c5e81.0p-54 */
+const C1: f64 = 0.0416666233237390631894; /* 0x155553e1053a42.0p-57 */
+const C2: f64 = -0.00138867637746099294692; /* -0x16c087e80f1e27.0p-62 */
+const C3: f64 = 0.0000243904487962774090654; /* 0x199342e0ee5069.0p-68 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn k_cosf(x: f64) -> f32 {
+ let z = x * x;
+ let w = z * z;
+ let r = C2 + z * C3;
+ (((1.0 + z * C0) + w * C1) + (w * z) * r) as f32
+}
diff --git a/src/math/k_expo2.rs b/src/math/k_expo2.rs
new file mode 100644
index 0000000..7345075
--- /dev/null
+++ b/src/math/k_expo2.rs
@@ -0,0 +1,14 @@
+use super::exp;
+
+/* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */
+const K: i32 = 2043;
+
+/* expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5f*expf(x/2)*expf(x/2) */
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn k_expo2(x: f64) -> f64 {
+ let k_ln2 = f64::from_bits(0x40962066151add8b);
+ /* note that k is odd and scale*scale overflows */
+ let scale = f64::from_bits(((((0x3ff + K / 2) as u32) << 20) as u64) << 32);
+ /* exp(x - k ln2) * 2**(k-1) */
+ exp(x - k_ln2) * scale * scale
+}
diff --git a/src/math/k_expo2f.rs b/src/math/k_expo2f.rs
new file mode 100644
index 0000000..fbd7b27
--- /dev/null
+++ b/src/math/k_expo2f.rs
@@ -0,0 +1,14 @@
+use super::expf;
+
+/* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */
+const K: i32 = 235;
+
+/* expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5f*expf(x/2)*expf(x/2) */
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn k_expo2f(x: f32) -> f32 {
+ let k_ln2 = f32::from_bits(0x4322e3bc);
+ /* note that k is odd and scale*scale overflows */
+ let scale = f32::from_bits(((0x7f + K / 2) as u32) << 23);
+ /* exp(x - k ln2) * 2**(k-1) */
+ expf(x - k_ln2) * scale * scale
+}
diff --git a/src/math/k_sin.rs b/src/math/k_sin.rs
new file mode 100644
index 0000000..9dd96c9
--- /dev/null
+++ b/src/math/k_sin.rs
@@ -0,0 +1,57 @@
+// origin: FreeBSD /usr/src/lib/msun/src/k_sin.c
+//
+// ====================================================
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+//
+// Developed at SunSoft, a Sun Microsystems, Inc. business.
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+
+const S1: f64 = -1.66666666666666324348e-01; /* 0xBFC55555, 0x55555549 */
+const S2: f64 = 8.33333333332248946124e-03; /* 0x3F811111, 0x1110F8A6 */
+const S3: f64 = -1.98412698298579493134e-04; /* 0xBF2A01A0, 0x19C161D5 */
+const S4: f64 = 2.75573137070700676789e-06; /* 0x3EC71DE3, 0x57B1FE7D */
+const S5: f64 = -2.50507602534068634195e-08; /* 0xBE5AE5E6, 0x8A2B9CEB */
+const S6: f64 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
+
+// kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
+// Input x is assumed to be bounded by ~pi/4 in magnitude.
+// Input y is the tail of x.
+// Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
+//
+// Algorithm
+// 1. Since sin(-x) = -sin(x), we need only to consider positive x.
+// 2. Callers must return sin(-0) = -0 without calling here since our
+// odd polynomial is not evaluated in a way that preserves -0.
+// Callers may do the optimization sin(x) ~ x for tiny x.
+// 3. sin(x) is approximated by a polynomial of degree 13 on
+// [0,pi/4]
+// 3 13
+// sin(x) ~ x + S1*x + ... + S6*x
+// where
+//
+// |sin(x) 2 4 6 8 10 12 | -58
+// |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
+// | x |
+//
+// 4. sin(x+y) = sin(x) + sin'(x')*y
+// ~ sin(x) + (1-x*x/2)*y
+// For better accuracy, let
+// 3 2 2 2 2
+// r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
+// then 3 2
+// sin(x) = x + (S1*x + (x *(r-y/2)+y))
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn k_sin(x: f64, y: f64, iy: i32) -> f64 {
+ let z = x * x;
+ let w = z * z;
+ let r = S2 + z * (S3 + z * S4) + z * w * (S5 + z * S6);
+ let v = z * x;
+ if iy == 0 {
+ x + v * (S1 + z * r)
+ } else {
+ x - ((z * (0.5 * y - v * r) - y) - v * S1)
+ }
+}
diff --git a/src/math/k_sinf.rs b/src/math/k_sinf.rs
new file mode 100644
index 0000000..88d10ca
--- /dev/null
+++ b/src/math/k_sinf.rs
@@ -0,0 +1,30 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/k_sinf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */
+const S1: f64 = -0.166666666416265235595; /* -0x15555554cbac77.0p-55 */
+const S2: f64 = 0.0083333293858894631756; /* 0x111110896efbb2.0p-59 */
+const S3: f64 = -0.000198393348360966317347; /* -0x1a00f9e2cae774.0p-65 */
+const S4: f64 = 0.0000027183114939898219064; /* 0x16cd878c3b46a7.0p-71 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn k_sinf(x: f64) -> f32 {
+ let z = x * x;
+ let w = z * z;
+ let r = S3 + z * S4;
+ let s = z * x;
+ ((x + s * (S1 + z * S2)) + s * w * r) as f32
+}
diff --git a/src/math/k_tan.rs b/src/math/k_tan.rs
new file mode 100644
index 0000000..d177010
--- /dev/null
+++ b/src/math/k_tan.rs
@@ -0,0 +1,105 @@
+// origin: FreeBSD /usr/src/lib/msun/src/k_tan.c */
+//
+// ====================================================
+// Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
+//
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+
+// kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
+// Input x is assumed to be bounded by ~pi/4 in magnitude.
+// Input y is the tail of x.
+// Input odd indicates whether tan (if odd = 0) or -1/tan (if odd = 1) is returned.
+//
+// Algorithm
+// 1. Since tan(-x) = -tan(x), we need only to consider positive x.
+// 2. Callers must return tan(-0) = -0 without calling here since our
+// odd polynomial is not evaluated in a way that preserves -0.
+// Callers may do the optimization tan(x) ~ x for tiny x.
+// 3. tan(x) is approximated by a odd polynomial of degree 27 on
+// [0,0.67434]
+// 3 27
+// tan(x) ~ x + T1*x + ... + T13*x
+// where
+//
+// |tan(x) 2 4 26 | -59.2
+// |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
+// | x |
+//
+// Note: tan(x+y) = tan(x) + tan'(x)*y
+// ~ tan(x) + (1+x*x)*y
+// Therefore, for better accuracy in computing tan(x+y), let
+// 3 2 2 2 2
+// r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
+// then
+// 3 2
+// tan(x+y) = x + (T1*x + (x *(r+y)+y))
+//
+// 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
+// tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
+// = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
+static T: [f64; 13] = [
+ 3.33333333333334091986e-01, /* 3FD55555, 55555563 */
+ 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */
+ 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */
+ 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */
+ 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */
+ 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */
+ 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */
+ 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */
+ 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */
+ 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */
+ 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */
+ -1.85586374855275456654e-05, /* BEF375CB, DB605373 */
+ 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */
+];
+const PIO4: f64 = 7.85398163397448278999e-01; /* 3FE921FB, 54442D18 */
+const PIO4_LO: f64 = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn k_tan(mut x: f64, mut y: f64, odd: i32) -> f64 {
+ let hx = (f64::to_bits(x) >> 32) as u32;
+ let big = (hx & 0x7fffffff) >= 0x3FE59428; /* |x| >= 0.6744 */
+ if big {
+ let sign = hx >> 31;
+ if sign != 0 {
+ x = -x;
+ y = -y;
+ }
+ x = (PIO4 - x) + (PIO4_LO - y);
+ y = 0.0;
+ }
+ let z = x * x;
+ let w = z * z;
+ /*
+ * Break x^5*(T[1]+x^2*T[2]+...) into
+ * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
+ * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
+ */
+ let r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + w * T[11]))));
+ let v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + w * T[12])))));
+ let s = z * x;
+ let r = y + z * (s * (r + v) + y) + s * T[0];
+ let w = x + r;
+ if big {
+ let sign = hx >> 31;
+ let s = 1.0 - 2.0 * odd as f64;
+ let v = s - 2.0 * (x + (r - w * w / (w + s)));
+ return if sign != 0 { -v } else { v };
+ }
+ if odd == 0 {
+ return w;
+ }
+ /* -1.0/(x+r) has up to 2ulp error, so compute it accurately */
+ let w0 = zero_low_word(w);
+ let v = r - (w0 - x); /* w0+v = r+x */
+ let a = -1.0 / w;
+ let a0 = zero_low_word(a);
+ a0 + a * (1.0 + a0 * w0 + a0 * v)
+}
+
+fn zero_low_word(x: f64) -> f64 {
+ f64::from_bits(f64::to_bits(x) & 0xFFFF_FFFF_0000_0000)
+}
diff --git a/src/math/k_tanf.rs b/src/math/k_tanf.rs
new file mode 100644
index 0000000..af8db53
--- /dev/null
+++ b/src/math/k_tanf.rs
@@ -0,0 +1,46 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/k_tan.c */
+/*
+ * ====================================================
+ * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
+ *
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
+const T: [f64; 6] = [
+ 0.333331395030791399758, /* 0x15554d3418c99f.0p-54 */
+ 0.133392002712976742718, /* 0x1112fd38999f72.0p-55 */
+ 0.0533812378445670393523, /* 0x1b54c91d865afe.0p-57 */
+ 0.0245283181166547278873, /* 0x191df3908c33ce.0p-58 */
+ 0.00297435743359967304927, /* 0x185dadfcecf44e.0p-61 */
+ 0.00946564784943673166728, /* 0x1362b9bf971bcd.0p-59 */
+];
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn k_tanf(x: f64, odd: bool) -> f32 {
+ let z = x * x;
+ /*
+ * Split up the polynomial into small independent terms to give
+ * opportunities for parallel evaluation. The chosen splitting is
+ * micro-optimized for Athlons (XP, X64). It costs 2 multiplications
+ * relative to Horner's method on sequential machines.
+ *
+ * We add the small terms from lowest degree up for efficiency on
+ * non-sequential machines (the lowest degree terms tend to be ready
+ * earlier). Apart from this, we don't care about order of
+ * operations, and don't need to to care since we have precision to
+ * spare. However, the chosen splitting is good for accuracy too,
+ * and would give results as accurate as Horner's method if the
+ * small terms were added from highest degree down.
+ */
+ let mut r = T[4] + z * T[5];
+ let t = T[2] + z * T[3];
+ let w = z * z;
+ let s = z * x;
+ let u = T[0] + z * T[1];
+ r = (x + s * u) + (s * w) * (t + w * r);
+ (if odd { -1. / r } else { r }) as f32
+}
diff --git a/src/math/ldexp.rs b/src/math/ldexp.rs
new file mode 100644
index 0000000..e46242e
--- /dev/null
+++ b/src/math/ldexp.rs
@@ -0,0 +1,4 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn ldexp(x: f64, n: i32) -> f64 {
+ super::scalbn(x, n)
+}
diff --git a/src/math/ldexpf.rs b/src/math/ldexpf.rs
new file mode 100644
index 0000000..95b27fc
--- /dev/null
+++ b/src/math/ldexpf.rs
@@ -0,0 +1,4 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn ldexpf(x: f32, n: i32) -> f32 {
+ super::scalbnf(x, n)
+}
diff --git a/src/math/lgamma.rs b/src/math/lgamma.rs
new file mode 100644
index 0000000..5bc87e8
--- /dev/null
+++ b/src/math/lgamma.rs
@@ -0,0 +1,5 @@
+use super::lgamma_r;
+
+pub fn lgamma(x: f64) -> f64 {
+ lgamma_r(x).0
+}
diff --git a/src/math/lgamma_r.rs b/src/math/lgamma_r.rs
new file mode 100644
index 0000000..9533e88
--- /dev/null
+++ b/src/math/lgamma_r.rs
@@ -0,0 +1,319 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_lgamma_r.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ */
+/* lgamma_r(x, signgamp)
+ * Reentrant version of the logarithm of the Gamma function
+ * with user provide pointer for the sign of Gamma(x).
+ *
+ * Method:
+ * 1. Argument Reduction for 0 < x <= 8
+ * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
+ * reduce x to a number in [1.5,2.5] by
+ * lgamma(1+s) = log(s) + lgamma(s)
+ * for example,
+ * lgamma(7.3) = log(6.3) + lgamma(6.3)
+ * = log(6.3*5.3) + lgamma(5.3)
+ * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
+ * 2. Polynomial approximation of lgamma around its
+ * minimun ymin=1.461632144968362245 to maintain monotonicity.
+ * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
+ * Let z = x-ymin;
+ * lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
+ * where
+ * poly(z) is a 14 degree polynomial.
+ * 2. Rational approximation in the primary interval [2,3]
+ * We use the following approximation:
+ * s = x-2.0;
+ * lgamma(x) = 0.5*s + s*P(s)/Q(s)
+ * with accuracy
+ * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71
+ * Our algorithms are based on the following observation
+ *
+ * zeta(2)-1 2 zeta(3)-1 3
+ * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ...
+ * 2 3
+ *
+ * where Euler = 0.5771... is the Euler constant, which is very
+ * close to 0.5.
+ *
+ * 3. For x>=8, we have
+ * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
+ * (better formula:
+ * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
+ * Let z = 1/x, then we approximation
+ * f(z) = lgamma(x) - (x-0.5)(log(x)-1)
+ * by
+ * 3 5 11
+ * w = w0 + w1*z + w2*z + w3*z + ... + w6*z
+ * where
+ * |w - f(z)| < 2**-58.74
+ *
+ * 4. For negative x, since (G is gamma function)
+ * -x*G(-x)*G(x) = PI/sin(PI*x),
+ * we have
+ * G(x) = PI/(sin(PI*x)*(-x)*G(-x))
+ * since G(-x) is positive, sign(G(x)) = sign(sin(PI*x)) for x<0
+ * Hence, for x<0, signgam = sign(sin(PI*x)) and
+ * lgamma(x) = log(|Gamma(x)|)
+ * = log(PI/(|x*sin(PI*x)|)) - lgamma(-x);
+ * Note: one should avoid compute PI*(-x) directly in the
+ * computation of sin(PI*(-x)).
+ *
+ * 5. Special Cases
+ * lgamma(2+s) ~ s*(1-Euler) for tiny s
+ * lgamma(1) = lgamma(2) = 0
+ * lgamma(x) ~ -log(|x|) for tiny x
+ * lgamma(0) = lgamma(neg.integer) = inf and raise divide-by-zero
+ * lgamma(inf) = inf
+ * lgamma(-inf) = inf (bug for bug compatible with C99!?)
+ *
+ */
+
+use super::{floor, k_cos, k_sin, log};
+
+const PI: f64 = 3.14159265358979311600e+00; /* 0x400921FB, 0x54442D18 */
+const A0: f64 = 7.72156649015328655494e-02; /* 0x3FB3C467, 0xE37DB0C8 */
+const A1: f64 = 3.22467033424113591611e-01; /* 0x3FD4A34C, 0xC4A60FAD */
+const A2: f64 = 6.73523010531292681824e-02; /* 0x3FB13E00, 0x1A5562A7 */
+const A3: f64 = 2.05808084325167332806e-02; /* 0x3F951322, 0xAC92547B */
+const A4: f64 = 7.38555086081402883957e-03; /* 0x3F7E404F, 0xB68FEFE8 */
+const A5: f64 = 2.89051383673415629091e-03; /* 0x3F67ADD8, 0xCCB7926B */
+const A6: f64 = 1.19270763183362067845e-03; /* 0x3F538A94, 0x116F3F5D */
+const A7: f64 = 5.10069792153511336608e-04; /* 0x3F40B6C6, 0x89B99C00 */
+const A8: f64 = 2.20862790713908385557e-04; /* 0x3F2CF2EC, 0xED10E54D */
+const A9: f64 = 1.08011567247583939954e-04; /* 0x3F1C5088, 0x987DFB07 */
+const A10: f64 = 2.52144565451257326939e-05; /* 0x3EFA7074, 0x428CFA52 */
+const A11: f64 = 4.48640949618915160150e-05; /* 0x3F07858E, 0x90A45837 */
+const TC: f64 = 1.46163214496836224576e+00; /* 0x3FF762D8, 0x6356BE3F */
+const TF: f64 = -1.21486290535849611461e-01; /* 0xBFBF19B9, 0xBCC38A42 */
+/* tt = -(tail of TF) */
+const TT: f64 = -3.63867699703950536541e-18; /* 0xBC50C7CA, 0xA48A971F */
+const T0: f64 = 4.83836122723810047042e-01; /* 0x3FDEF72B, 0xC8EE38A2 */
+const T1: f64 = -1.47587722994593911752e-01; /* 0xBFC2E427, 0x8DC6C509 */
+const T2: f64 = 6.46249402391333854778e-02; /* 0x3FB08B42, 0x94D5419B */
+const T3: f64 = -3.27885410759859649565e-02; /* 0xBFA0C9A8, 0xDF35B713 */
+const T4: f64 = 1.79706750811820387126e-02; /* 0x3F9266E7, 0x970AF9EC */
+const T5: f64 = -1.03142241298341437450e-02; /* 0xBF851F9F, 0xBA91EC6A */
+const T6: f64 = 6.10053870246291332635e-03; /* 0x3F78FCE0, 0xE370E344 */
+const T7: f64 = -3.68452016781138256760e-03; /* 0xBF6E2EFF, 0xB3E914D7 */
+const T8: f64 = 2.25964780900612472250e-03; /* 0x3F6282D3, 0x2E15C915 */
+const T9: f64 = -1.40346469989232843813e-03; /* 0xBF56FE8E, 0xBF2D1AF1 */
+const T10: f64 = 8.81081882437654011382e-04; /* 0x3F4CDF0C, 0xEF61A8E9 */
+const T11: f64 = -5.38595305356740546715e-04; /* 0xBF41A610, 0x9C73E0EC */
+const T12: f64 = 3.15632070903625950361e-04; /* 0x3F34AF6D, 0x6C0EBBF7 */
+const T13: f64 = -3.12754168375120860518e-04; /* 0xBF347F24, 0xECC38C38 */
+const T14: f64 = 3.35529192635519073543e-04; /* 0x3F35FD3E, 0xE8C2D3F4 */
+const U0: f64 = -7.72156649015328655494e-02; /* 0xBFB3C467, 0xE37DB0C8 */
+const U1: f64 = 6.32827064025093366517e-01; /* 0x3FE4401E, 0x8B005DFF */
+const U2: f64 = 1.45492250137234768737e+00; /* 0x3FF7475C, 0xD119BD6F */
+const U3: f64 = 9.77717527963372745603e-01; /* 0x3FEF4976, 0x44EA8450 */
+const U4: f64 = 2.28963728064692451092e-01; /* 0x3FCD4EAE, 0xF6010924 */
+const U5: f64 = 1.33810918536787660377e-02; /* 0x3F8B678B, 0xBF2BAB09 */
+const V1: f64 = 2.45597793713041134822e+00; /* 0x4003A5D7, 0xC2BD619C */
+const V2: f64 = 2.12848976379893395361e+00; /* 0x40010725, 0xA42B18F5 */
+const V3: f64 = 7.69285150456672783825e-01; /* 0x3FE89DFB, 0xE45050AF */
+const V4: f64 = 1.04222645593369134254e-01; /* 0x3FBAAE55, 0xD6537C88 */
+const V5: f64 = 3.21709242282423911810e-03; /* 0x3F6A5ABB, 0x57D0CF61 */
+const S0: f64 = -7.72156649015328655494e-02; /* 0xBFB3C467, 0xE37DB0C8 */
+const S1: f64 = 2.14982415960608852501e-01; /* 0x3FCB848B, 0x36E20878 */
+const S2: f64 = 3.25778796408930981787e-01; /* 0x3FD4D98F, 0x4F139F59 */
+const S3: f64 = 1.46350472652464452805e-01; /* 0x3FC2BB9C, 0xBEE5F2F7 */
+const S4: f64 = 2.66422703033638609560e-02; /* 0x3F9B481C, 0x7E939961 */
+const S5: f64 = 1.84028451407337715652e-03; /* 0x3F5E26B6, 0x7368F239 */
+const S6: f64 = 3.19475326584100867617e-05; /* 0x3F00BFEC, 0xDD17E945 */
+const R1: f64 = 1.39200533467621045958e+00; /* 0x3FF645A7, 0x62C4AB74 */
+const R2: f64 = 7.21935547567138069525e-01; /* 0x3FE71A18, 0x93D3DCDC */
+const R3: f64 = 1.71933865632803078993e-01; /* 0x3FC601ED, 0xCCFBDF27 */
+const R4: f64 = 1.86459191715652901344e-02; /* 0x3F9317EA, 0x742ED475 */
+const R5: f64 = 7.77942496381893596434e-04; /* 0x3F497DDA, 0xCA41A95B */
+const R6: f64 = 7.32668430744625636189e-06; /* 0x3EDEBAF7, 0xA5B38140 */
+const W0: f64 = 4.18938533204672725052e-01; /* 0x3FDACFE3, 0x90C97D69 */
+const W1: f64 = 8.33333333333329678849e-02; /* 0x3FB55555, 0x5555553B */
+const W2: f64 = -2.77777777728775536470e-03; /* 0xBF66C16C, 0x16B02E5C */
+const W3: f64 = 7.93650558643019558500e-04; /* 0x3F4A019F, 0x98CF38B6 */
+const W4: f64 = -5.95187557450339963135e-04; /* 0xBF4380CB, 0x8C0FE741 */
+const W5: f64 = 8.36339918996282139126e-04; /* 0x3F4B67BA, 0x4CDAD5D1 */
+const W6: f64 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
+
+/* sin(PI*x) assuming x > 2^-100, if sin(PI*x)==0 the sign is arbitrary */
+fn sin_pi(mut x: f64) -> f64 {
+ let mut n: i32;
+
+ /* spurious inexact if odd int */
+ x = 2.0 * (x * 0.5 - floor(x * 0.5)); /* x mod 2.0 */
+
+ n = (x * 4.0) as i32;
+ n = (n + 1) / 2;
+ x -= (n as f64) * 0.5;
+ x *= PI;
+
+ match n {
+ 1 => k_cos(x, 0.0),
+ 2 => k_sin(-x, 0.0, 0),
+ 3 => -k_cos(x, 0.0),
+ 0 | _ => k_sin(x, 0.0, 0),
+ }
+}
+
+pub fn lgamma_r(mut x: f64) -> (f64, i32) {
+ let u: u64 = x.to_bits();
+ let mut t: f64;
+ let y: f64;
+ let mut z: f64;
+ let nadj: f64;
+ let p: f64;
+ let p1: f64;
+ let p2: f64;
+ let p3: f64;
+ let q: f64;
+ let mut r: f64;
+ let w: f64;
+ let ix: u32;
+ let sign: bool;
+ let i: i32;
+ let mut signgam: i32;
+
+ /* purge off +-inf, NaN, +-0, tiny and negative arguments */
+ signgam = 1;
+ sign = (u >> 63) != 0;
+ ix = ((u >> 32) as u32) & 0x7fffffff;
+ if ix >= 0x7ff00000 {
+ return (x * x, signgam);
+ }
+ if ix < (0x3ff - 70) << 20 {
+ /* |x|<2**-70, return -log(|x|) */
+ if sign {
+ x = -x;
+ signgam = -1;
+ }
+ return (-log(x), signgam);
+ }
+ if sign {
+ x = -x;
+ t = sin_pi(x);
+ if t == 0.0 {
+ /* -integer */
+ return (1.0 / (x - x), signgam);
+ }
+ if t > 0.0 {
+ signgam = -1;
+ } else {
+ t = -t;
+ }
+ nadj = log(PI / (t * x));
+ } else {
+ nadj = 0.0;
+ }
+
+ /* purge off 1 and 2 */
+ if (ix == 0x3ff00000 || ix == 0x40000000) && (u & 0xffffffff) == 0 {
+ r = 0.0;
+ }
+ /* for x < 2.0 */
+ else if ix < 0x40000000 {
+ if ix <= 0x3feccccc {
+ /* lgamma(x) = lgamma(x+1)-log(x) */
+ r = -log(x);
+ if ix >= 0x3FE76944 {
+ y = 1.0 - x;
+ i = 0;
+ } else if ix >= 0x3FCDA661 {
+ y = x - (TC - 1.0);
+ i = 1;
+ } else {
+ y = x;
+ i = 2;
+ }
+ } else {
+ r = 0.0;
+ if ix >= 0x3FFBB4C3 {
+ /* [1.7316,2] */
+ y = 2.0 - x;
+ i = 0;
+ } else if ix >= 0x3FF3B4C4 {
+ /* [1.23,1.73] */
+ y = x - TC;
+ i = 1;
+ } else {
+ y = x - 1.0;
+ i = 2;
+ }
+ }
+ match i {
+ 0 => {
+ z = y * y;
+ p1 = A0 + z * (A2 + z * (A4 + z * (A6 + z * (A8 + z * A10))));
+ p2 = z * (A1 + z * (A3 + z * (A5 + z * (A7 + z * (A9 + z * A11)))));
+ p = y * p1 + p2;
+ r += p - 0.5 * y;
+ }
+ 1 => {
+ z = y * y;
+ w = z * y;
+ p1 = T0 + w * (T3 + w * (T6 + w * (T9 + w * T12))); /* parallel comp */
+ p2 = T1 + w * (T4 + w * (T7 + w * (T10 + w * T13)));
+ p3 = T2 + w * (T5 + w * (T8 + w * (T11 + w * T14)));
+ p = z * p1 - (TT - w * (p2 + y * p3));
+ r += TF + p;
+ }
+ 2 => {
+ p1 = y * (U0 + y * (U1 + y * (U2 + y * (U3 + y * (U4 + y * U5)))));
+ p2 = 1.0 + y * (V1 + y * (V2 + y * (V3 + y * (V4 + y * V5))));
+ r += -0.5 * y + p1 / p2;
+ }
+ #[cfg(debug_assertions)]
+ _ => unreachable!(),
+ #[cfg(not(debug_assertions))]
+ _ => {}
+ }
+ } else if ix < 0x40200000 {
+ /* x < 8.0 */
+ i = x as i32;
+ y = x - (i as f64);
+ p = y * (S0 + y * (S1 + y * (S2 + y * (S3 + y * (S4 + y * (S5 + y * S6))))));
+ q = 1.0 + y * (R1 + y * (R2 + y * (R3 + y * (R4 + y * (R5 + y * R6)))));
+ r = 0.5 * y + p / q;
+ z = 1.0; /* lgamma(1+s) = log(s) + lgamma(s) */
+ // TODO: In C, this was implemented using switch jumps with fallthrough.
+ // Does this implementation have performance problems?
+ if i >= 7 {
+ z *= y + 6.0;
+ }
+ if i >= 6 {
+ z *= y + 5.0;
+ }
+ if i >= 5 {
+ z *= y + 4.0;
+ }
+ if i >= 4 {
+ z *= y + 3.0;
+ }
+ if i >= 3 {
+ z *= y + 2.0;
+ r += log(z);
+ }
+ } else if ix < 0x43900000 {
+ /* 8.0 <= x < 2**58 */
+ t = log(x);
+ z = 1.0 / x;
+ y = z * z;
+ w = W0 + z * (W1 + y * (W2 + y * (W3 + y * (W4 + y * (W5 + y * W6)))));
+ r = (x - 0.5) * (t - 1.0) + w;
+ } else {
+ /* 2**58 <= x <= inf */
+ r = x * (log(x) - 1.0);
+ }
+ if sign {
+ r = nadj - r;
+ }
+ return (r, signgam);
+}
diff --git a/src/math/lgammaf.rs b/src/math/lgammaf.rs
new file mode 100644
index 0000000..dfdc87f
--- /dev/null
+++ b/src/math/lgammaf.rs
@@ -0,0 +1,5 @@
+use super::lgammaf_r;
+
+pub fn lgammaf(x: f32) -> f32 {
+ lgammaf_r(x).0
+}
diff --git a/src/math/lgammaf_r.rs b/src/math/lgammaf_r.rs
new file mode 100644
index 0000000..c5e559f
--- /dev/null
+++ b/src/math/lgammaf_r.rs
@@ -0,0 +1,254 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{floorf, k_cosf, k_sinf, logf};
+
+const PI: f32 = 3.1415927410e+00; /* 0x40490fdb */
+const A0: f32 = 7.7215664089e-02; /* 0x3d9e233f */
+const A1: f32 = 3.2246702909e-01; /* 0x3ea51a66 */
+const A2: f32 = 6.7352302372e-02; /* 0x3d89f001 */
+const A3: f32 = 2.0580807701e-02; /* 0x3ca89915 */
+const A4: f32 = 7.3855509982e-03; /* 0x3bf2027e */
+const A5: f32 = 2.8905137442e-03; /* 0x3b3d6ec6 */
+const A6: f32 = 1.1927076848e-03; /* 0x3a9c54a1 */
+const A7: f32 = 5.1006977446e-04; /* 0x3a05b634 */
+const A8: f32 = 2.2086278477e-04; /* 0x39679767 */
+const A9: f32 = 1.0801156895e-04; /* 0x38e28445 */
+const A10: f32 = 2.5214456400e-05; /* 0x37d383a2 */
+const A11: f32 = 4.4864096708e-05; /* 0x383c2c75 */
+const TC: f32 = 1.4616321325e+00; /* 0x3fbb16c3 */
+const TF: f32 = -1.2148628384e-01; /* 0xbdf8cdcd */
+/* TT = -(tail of TF) */
+const TT: f32 = 6.6971006518e-09; /* 0x31e61c52 */
+const T0: f32 = 4.8383611441e-01; /* 0x3ef7b95e */
+const T1: f32 = -1.4758771658e-01; /* 0xbe17213c */
+const T2: f32 = 6.4624942839e-02; /* 0x3d845a15 */
+const T3: f32 = -3.2788541168e-02; /* 0xbd064d47 */
+const T4: f32 = 1.7970675603e-02; /* 0x3c93373d */
+const T5: f32 = -1.0314224288e-02; /* 0xbc28fcfe */
+const T6: f32 = 6.1005386524e-03; /* 0x3bc7e707 */
+const T7: f32 = -3.6845202558e-03; /* 0xbb7177fe */
+const T8: f32 = 2.2596477065e-03; /* 0x3b141699 */
+const T9: f32 = -1.4034647029e-03; /* 0xbab7f476 */
+const T10: f32 = 8.8108185446e-04; /* 0x3a66f867 */
+const T11: f32 = -5.3859531181e-04; /* 0xba0d3085 */
+const T12: f32 = 3.1563205994e-04; /* 0x39a57b6b */
+const T13: f32 = -3.1275415677e-04; /* 0xb9a3f927 */
+const T14: f32 = 3.3552918467e-04; /* 0x39afe9f7 */
+const U0: f32 = -7.7215664089e-02; /* 0xbd9e233f */
+const U1: f32 = 6.3282704353e-01; /* 0x3f2200f4 */
+const U2: f32 = 1.4549225569e+00; /* 0x3fba3ae7 */
+const U3: f32 = 9.7771751881e-01; /* 0x3f7a4bb2 */
+const U4: f32 = 2.2896373272e-01; /* 0x3e6a7578 */
+const U5: f32 = 1.3381091878e-02; /* 0x3c5b3c5e */
+const V1: f32 = 2.4559779167e+00; /* 0x401d2ebe */
+const V2: f32 = 2.1284897327e+00; /* 0x4008392d */
+const V3: f32 = 7.6928514242e-01; /* 0x3f44efdf */
+const V4: f32 = 1.0422264785e-01; /* 0x3dd572af */
+const V5: f32 = 3.2170924824e-03; /* 0x3b52d5db */
+const S0: f32 = -7.7215664089e-02; /* 0xbd9e233f */
+const S1: f32 = 2.1498242021e-01; /* 0x3e5c245a */
+const S2: f32 = 3.2577878237e-01; /* 0x3ea6cc7a */
+const S3: f32 = 1.4635047317e-01; /* 0x3e15dce6 */
+const S4: f32 = 2.6642270386e-02; /* 0x3cda40e4 */
+const S5: f32 = 1.8402845599e-03; /* 0x3af135b4 */
+const S6: f32 = 3.1947532989e-05; /* 0x3805ff67 */
+const R1: f32 = 1.3920053244e+00; /* 0x3fb22d3b */
+const R2: f32 = 7.2193557024e-01; /* 0x3f38d0c5 */
+const R3: f32 = 1.7193385959e-01; /* 0x3e300f6e */
+const R4: f32 = 1.8645919859e-02; /* 0x3c98bf54 */
+const R5: f32 = 7.7794247773e-04; /* 0x3a4beed6 */
+const R6: f32 = 7.3266842264e-06; /* 0x36f5d7bd */
+const W0: f32 = 4.1893854737e-01; /* 0x3ed67f1d */
+const W1: f32 = 8.3333335817e-02; /* 0x3daaaaab */
+const W2: f32 = -2.7777778450e-03; /* 0xbb360b61 */
+const W3: f32 = 7.9365057172e-04; /* 0x3a500cfd */
+const W4: f32 = -5.9518753551e-04; /* 0xba1c065c */
+const W5: f32 = 8.3633989561e-04; /* 0x3a5b3dd2 */
+const W6: f32 = -1.6309292987e-03; /* 0xbad5c4e8 */
+
+/* sin(PI*x) assuming x > 2^-100, if sin(PI*x)==0 the sign is arbitrary */
+fn sin_pi(mut x: f32) -> f32 {
+ let mut y: f64;
+ let mut n: isize;
+
+ /* spurious inexact if odd int */
+ x = 2.0 * (x * 0.5 - floorf(x * 0.5)); /* x mod 2.0 */
+
+ n = (x * 4.0) as isize;
+ n = (n + 1) / 2;
+ y = (x as f64) - (n as f64) * 0.5;
+ y *= 3.14159265358979323846;
+ match n {
+ 1 => k_cosf(y),
+ 2 => k_sinf(-y),
+ 3 => -k_cosf(y),
+ 0 | _ => k_sinf(y),
+ }
+}
+
+pub fn lgammaf_r(mut x: f32) -> (f32, i32) {
+ let u = x.to_bits();
+ let mut t: f32;
+ let y: f32;
+ let mut z: f32;
+ let nadj: f32;
+ let p: f32;
+ let p1: f32;
+ let p2: f32;
+ let p3: f32;
+ let q: f32;
+ let mut r: f32;
+ let w: f32;
+ let ix: u32;
+ let i: i32;
+ let sign: bool;
+ let mut signgam: i32;
+
+ /* purge off +-inf, NaN, +-0, tiny and negative arguments */
+ signgam = 1;
+ sign = (u >> 31) != 0;
+ ix = u & 0x7fffffff;
+ if ix >= 0x7f800000 {
+ return (x * x, signgam);
+ }
+ if ix < 0x35000000 {
+ /* |x| < 2**-21, return -log(|x|) */
+ if sign {
+ signgam = -1;
+ x = -x;
+ }
+ return (-logf(x), signgam);
+ }
+ if sign {
+ x = -x;
+ t = sin_pi(x);
+ if t == 0.0 {
+ /* -integer */
+ return (1.0 / (x - x), signgam);
+ }
+ if t > 0.0 {
+ signgam = -1;
+ } else {
+ t = -t;
+ }
+ nadj = logf(PI / (t * x));
+ } else {
+ nadj = 0.0;
+ }
+
+ /* purge off 1 and 2 */
+ if ix == 0x3f800000 || ix == 0x40000000 {
+ r = 0.0;
+ }
+ /* for x < 2.0 */
+ else if ix < 0x40000000 {
+ if ix <= 0x3f666666 {
+ /* lgamma(x) = lgamma(x+1)-log(x) */
+ r = -logf(x);
+ if ix >= 0x3f3b4a20 {
+ y = 1.0 - x;
+ i = 0;
+ } else if ix >= 0x3e6d3308 {
+ y = x - (TC - 1.0);
+ i = 1;
+ } else {
+ y = x;
+ i = 2;
+ }
+ } else {
+ r = 0.0;
+ if ix >= 0x3fdda618 {
+ /* [1.7316,2] */
+ y = 2.0 - x;
+ i = 0;
+ } else if ix >= 0x3F9da620 {
+ /* [1.23,1.73] */
+ y = x - TC;
+ i = 1;
+ } else {
+ y = x - 1.0;
+ i = 2;
+ }
+ }
+ match i {
+ 0 => {
+ z = y * y;
+ p1 = A0 + z * (A2 + z * (A4 + z * (A6 + z * (A8 + z * A10))));
+ p2 = z * (A1 + z * (A3 + z * (A5 + z * (A7 + z * (A9 + z * A11)))));
+ p = y * p1 + p2;
+ r += p - 0.5 * y;
+ }
+ 1 => {
+ z = y * y;
+ w = z * y;
+ p1 = T0 + w * (T3 + w * (T6 + w * (T9 + w * T12))); /* parallel comp */
+ p2 = T1 + w * (T4 + w * (T7 + w * (T10 + w * T13)));
+ p3 = T2 + w * (T5 + w * (T8 + w * (T11 + w * T14)));
+ p = z * p1 - (TT - w * (p2 + y * p3));
+ r += TF + p;
+ }
+ 2 => {
+ p1 = y * (U0 + y * (U1 + y * (U2 + y * (U3 + y * (U4 + y * U5)))));
+ p2 = 1.0 + y * (V1 + y * (V2 + y * (V3 + y * (V4 + y * V5))));
+ r += -0.5 * y + p1 / p2;
+ }
+ #[cfg(debug_assertions)]
+ _ => unreachable!(),
+ #[cfg(not(debug_assertions))]
+ _ => {}
+ }
+ } else if ix < 0x41000000 {
+ /* x < 8.0 */
+ i = x as i32;
+ y = x - (i as f32);
+ p = y * (S0 + y * (S1 + y * (S2 + y * (S3 + y * (S4 + y * (S5 + y * S6))))));
+ q = 1.0 + y * (R1 + y * (R2 + y * (R3 + y * (R4 + y * (R5 + y * R6)))));
+ r = 0.5 * y + p / q;
+ z = 1.0; /* lgamma(1+s) = log(s) + lgamma(s) */
+ // TODO: In C, this was implemented using switch jumps with fallthrough.
+ // Does this implementation have performance problems?
+ if i >= 7 {
+ z *= y + 6.0;
+ }
+ if i >= 6 {
+ z *= y + 5.0;
+ }
+ if i >= 5 {
+ z *= y + 4.0;
+ }
+ if i >= 4 {
+ z *= y + 3.0;
+ }
+ if i >= 3 {
+ z *= y + 2.0;
+ r += logf(z);
+ }
+ } else if ix < 0x5c800000 {
+ /* 8.0 <= x < 2**58 */
+ t = logf(x);
+ z = 1.0 / x;
+ y = z * z;
+ w = W0 + z * (W1 + y * (W2 + y * (W3 + y * (W4 + y * (W5 + y * W6)))));
+ r = (x - 0.5) * (t - 1.0) + w;
+ } else {
+ /* 2**58 <= x <= inf */
+ r = x * (logf(x) - 1.0);
+ }
+ if sign {
+ r = nadj - r;
+ }
+ return (r, signgam);
+}
diff --git a/src/math/log.rs b/src/math/log.rs
new file mode 100644
index 0000000..27a26da
--- /dev/null
+++ b/src/math/log.rs
@@ -0,0 +1,117 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_log.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* log(x)
+ * Return the logarithm of x
+ *
+ * Method :
+ * 1. Argument Reduction: find k and f such that
+ * x = 2^k * (1+f),
+ * where sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ * 2. Approximation of log(1+f).
+ * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+ * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+ * = 2s + s*R
+ * We use a special Remez algorithm on [0,0.1716] to generate
+ * a polynomial of degree 14 to approximate R The maximum error
+ * of this polynomial approximation is bounded by 2**-58.45. In
+ * other words,
+ * 2 4 6 8 10 12 14
+ * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
+ * (the values of Lg1 to Lg7 are listed in the program)
+ * and
+ * | 2 14 | -58.45
+ * | Lg1*s +...+Lg7*s - R(z) | <= 2
+ * | |
+ * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+ * In order to guarantee error in log below 1ulp, we compute log
+ * by
+ * log(1+f) = f - s*(f - R) (if f is not too large)
+ * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
+ *
+ * 3. Finally, log(x) = k*ln2 + log(1+f).
+ * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
+ * Here ln2 is split into two floating point number:
+ * ln2_hi + ln2_lo,
+ * where n*ln2_hi is always exact for |n| < 2000.
+ *
+ * Special cases:
+ * log(x) is NaN with signal if x < 0 (including -INF) ;
+ * log(+INF) is +INF; log(0) is -INF with signal;
+ * log(NaN) is that NaN with no signal.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+const LN2_HI: f64 = 6.93147180369123816490e-01; /* 3fe62e42 fee00000 */
+const LN2_LO: f64 = 1.90821492927058770002e-10; /* 3dea39ef 35793c76 */
+const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
+const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
+const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
+const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
+const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
+const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
+const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn log(mut x: f64) -> f64 {
+ let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54
+
+ let mut ui = x.to_bits();
+ let mut hx: u32 = (ui >> 32) as u32;
+ let mut k: i32 = 0;
+
+ if (hx < 0x00100000) || ((hx >> 31) != 0) {
+ /* x < 2**-126 */
+ if ui << 1 == 0 {
+ return -1. / (x * x); /* log(+-0)=-inf */
+ }
+ if hx >> 31 != 0 {
+ return (x - x) / 0.0; /* log(-#) = NaN */
+ }
+ /* subnormal number, scale x up */
+ k -= 54;
+ x *= x1p54;
+ ui = x.to_bits();
+ hx = (ui >> 32) as u32;
+ } else if hx >= 0x7ff00000 {
+ return x;
+ } else if hx == 0x3ff00000 && ui << 32 == 0 {
+ return 0.;
+ }
+
+ /* reduce x into [sqrt(2)/2, sqrt(2)] */
+ hx += 0x3ff00000 - 0x3fe6a09e;
+ k += ((hx >> 20) as i32) - 0x3ff;
+ hx = (hx & 0x000fffff) + 0x3fe6a09e;
+ ui = ((hx as u64) << 32) | (ui & 0xffffffff);
+ x = f64::from_bits(ui);
+
+ let f: f64 = x - 1.0;
+ let hfsq: f64 = 0.5 * f * f;
+ let s: f64 = f / (2.0 + f);
+ let z: f64 = s * s;
+ let w: f64 = z * z;
+ let t1: f64 = w * (LG2 + w * (LG4 + w * LG6));
+ let t2: f64 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
+ let r: f64 = t2 + t1;
+ let dk: f64 = k as f64;
+ s * (hfsq + r) + dk * LN2_LO - hfsq + f + dk * LN2_HI
+}
diff --git a/src/math/log10.rs b/src/math/log10.rs
new file mode 100644
index 0000000..40dacf2
--- /dev/null
+++ b/src/math/log10.rs
@@ -0,0 +1,117 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/*
+ * Return the base 10 logarithm of x. See log.c for most comments.
+ *
+ * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
+ * as in log.c, then combine and scale in extra precision:
+ * log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
+ */
+
+use core::f64;
+
+const IVLN10HI: f64 = 4.34294481878168880939e-01; /* 0x3fdbcb7b, 0x15200000 */
+const IVLN10LO: f64 = 2.50829467116452752298e-11; /* 0x3dbb9438, 0xca9aadd5 */
+const LOG10_2HI: f64 = 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */
+const LOG10_2LO: f64 = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
+const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
+const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
+const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
+const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
+const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
+const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
+const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn log10(mut x: f64) -> f64 {
+ let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54
+
+ let mut ui: u64 = x.to_bits();
+ let hfsq: f64;
+ let f: f64;
+ let s: f64;
+ let z: f64;
+ let r: f64;
+ let mut w: f64;
+ let t1: f64;
+ let t2: f64;
+ let dk: f64;
+ let y: f64;
+ let mut hi: f64;
+ let lo: f64;
+ let mut val_hi: f64;
+ let mut val_lo: f64;
+ let mut hx: u32;
+ let mut k: i32;
+
+ hx = (ui >> 32) as u32;
+ k = 0;
+ if hx < 0x00100000 || (hx >> 31) > 0 {
+ if ui << 1 == 0 {
+ return -1. / (x * x); /* log(+-0)=-inf */
+ }
+ if (hx >> 31) > 0 {
+ return (x - x) / 0.0; /* log(-#) = NaN */
+ }
+ /* subnormal number, scale x up */
+ k -= 54;
+ x *= x1p54;
+ ui = x.to_bits();
+ hx = (ui >> 32) as u32;
+ } else if hx >= 0x7ff00000 {
+ return x;
+ } else if hx == 0x3ff00000 && ui << 32 == 0 {
+ return 0.;
+ }
+
+ /* reduce x into [sqrt(2)/2, sqrt(2)] */
+ hx += 0x3ff00000 - 0x3fe6a09e;
+ k += (hx >> 20) as i32 - 0x3ff;
+ hx = (hx & 0x000fffff) + 0x3fe6a09e;
+ ui = (hx as u64) << 32 | (ui & 0xffffffff);
+ x = f64::from_bits(ui);
+
+ f = x - 1.0;
+ hfsq = 0.5 * f * f;
+ s = f / (2.0 + f);
+ z = s * s;
+ w = z * z;
+ t1 = w * (LG2 + w * (LG4 + w * LG6));
+ t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
+ r = t2 + t1;
+
+ /* See log2.c for details. */
+ /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
+ hi = f - hfsq;
+ ui = hi.to_bits();
+ ui &= (-1i64 as u64) << 32;
+ hi = f64::from_bits(ui);
+ lo = f - hi - hfsq + s * (hfsq + r);
+
+ /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
+ val_hi = hi * IVLN10HI;
+ dk = k as f64;
+ y = dk * LOG10_2HI;
+ val_lo = dk * LOG10_2LO + (lo + hi) * IVLN10LO + lo * IVLN10HI;
+
+ /*
+ * Extra precision in for adding y is not strictly needed
+ * since there is no very large cancellation near x = sqrt(2) or
+ * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
+ * with some parallelism and it reduces the error for many args.
+ */
+ w = y + val_hi;
+ val_lo += (y - w) + val_hi;
+ val_hi = w;
+
+ val_lo + val_hi
+}
diff --git a/src/math/log10f.rs b/src/math/log10f.rs
new file mode 100644
index 0000000..108dfa8
--- /dev/null
+++ b/src/math/log10f.rs
@@ -0,0 +1,91 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/*
+ * See comments in log10.c.
+ */
+
+use core::f32;
+
+const IVLN10HI: f32 = 4.3432617188e-01; /* 0x3ede6000 */
+const IVLN10LO: f32 = -3.1689971365e-05; /* 0xb804ead9 */
+const LOG10_2HI: f32 = 3.0102920532e-01; /* 0x3e9a2080 */
+const LOG10_2LO: f32 = 7.9034151668e-07; /* 0x355427db */
+/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
+const LG1: f32 = 0.66666662693; /* 0xaaaaaa.0p-24 */
+const LG2: f32 = 0.40000972152; /* 0xccce13.0p-25 */
+const LG3: f32 = 0.28498786688; /* 0x91e9ee.0p-25 */
+const LG4: f32 = 0.24279078841; /* 0xf89e26.0p-26 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn log10f(mut x: f32) -> f32 {
+ let x1p25f = f32::from_bits(0x4c000000); // 0x1p25f === 2 ^ 25
+
+ let mut ui: u32 = x.to_bits();
+ let hfsq: f32;
+ let f: f32;
+ let s: f32;
+ let z: f32;
+ let r: f32;
+ let w: f32;
+ let t1: f32;
+ let t2: f32;
+ let dk: f32;
+ let mut hi: f32;
+ let lo: f32;
+ let mut ix: u32;
+ let mut k: i32;
+
+ ix = ui;
+ k = 0;
+ if ix < 0x00800000 || (ix >> 31) > 0 {
+ /* x < 2**-126 */
+ if ix << 1 == 0 {
+ return -1. / (x * x); /* log(+-0)=-inf */
+ }
+ if (ix >> 31) > 0 {
+ return (x - x) / 0.0; /* log(-#) = NaN */
+ }
+ /* subnormal number, scale up x */
+ k -= 25;
+ x *= x1p25f;
+ ui = x.to_bits();
+ ix = ui;
+ } else if ix >= 0x7f800000 {
+ return x;
+ } else if ix == 0x3f800000 {
+ return 0.;
+ }
+
+ /* reduce x into [sqrt(2)/2, sqrt(2)] */
+ ix += 0x3f800000 - 0x3f3504f3;
+ k += (ix >> 23) as i32 - 0x7f;
+ ix = (ix & 0x007fffff) + 0x3f3504f3;
+ ui = ix;
+ x = f32::from_bits(ui);
+
+ f = x - 1.0;
+ s = f / (2.0 + f);
+ z = s * s;
+ w = z * z;
+ t1 = w * (LG2 + w * LG4);
+ t2 = z * (LG1 + w * LG3);
+ r = t2 + t1;
+ hfsq = 0.5 * f * f;
+
+ hi = f - hfsq;
+ ui = hi.to_bits();
+ ui &= 0xfffff000;
+ hi = f32::from_bits(ui);
+ lo = f - hi - hfsq + s * (hfsq + r);
+ dk = k as f32;
+ dk * LOG10_2LO + (lo + hi) * IVLN10LO + lo * IVLN10HI + hi * IVLN10HI + dk * LOG10_2HI
+}
diff --git a/src/math/log1p.rs b/src/math/log1p.rs
new file mode 100644
index 0000000..4fd1c73
--- /dev/null
+++ b/src/math/log1p.rs
@@ -0,0 +1,143 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* double log1p(double x)
+ * Return the natural logarithm of 1+x.
+ *
+ * Method :
+ * 1. Argument Reduction: find k and f such that
+ * 1+x = 2^k * (1+f),
+ * where sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ * Note. If k=0, then f=x is exact. However, if k!=0, then f
+ * may not be representable exactly. In that case, a correction
+ * term is need. Let u=1+x rounded. Let c = (1+x)-u, then
+ * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
+ * and add back the correction term c/u.
+ * (Note: when x > 2**53, one can simply return log(x))
+ *
+ * 2. Approximation of log(1+f): See log.c
+ *
+ * 3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c
+ *
+ * Special cases:
+ * log1p(x) is NaN with signal if x < -1 (including -INF) ;
+ * log1p(+INF) is +INF; log1p(-1) is -INF with signal;
+ * log1p(NaN) is that NaN with no signal.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ *
+ * Note: Assuming log() return accurate answer, the following
+ * algorithm can be used to compute log1p(x) to within a few ULP:
+ *
+ * u = 1+x;
+ * if(u==1.0) return x ; else
+ * return log(u)*(x/(u-1.0));
+ *
+ * See HP-15C Advanced Functions Handbook, p.193.
+ */
+
+use core::f64;
+
+const LN2_HI: f64 = 6.93147180369123816490e-01; /* 3fe62e42 fee00000 */
+const LN2_LO: f64 = 1.90821492927058770002e-10; /* 3dea39ef 35793c76 */
+const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
+const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
+const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
+const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
+const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
+const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
+const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn log1p(x: f64) -> f64 {
+ let mut ui: u64 = x.to_bits();
+ let hfsq: f64;
+ let mut f: f64 = 0.;
+ let mut c: f64 = 0.;
+ let s: f64;
+ let z: f64;
+ let r: f64;
+ let w: f64;
+ let t1: f64;
+ let t2: f64;
+ let dk: f64;
+ let hx: u32;
+ let mut hu: u32;
+ let mut k: i32;
+
+ hx = (ui >> 32) as u32;
+ k = 1;
+ if hx < 0x3fda827a || (hx >> 31) > 0 {
+ /* 1+x < sqrt(2)+ */
+ if hx >= 0xbff00000 {
+ /* x <= -1.0 */
+ if x == -1. {
+ return x / 0.0; /* log1p(-1) = -inf */
+ }
+ return (x - x) / 0.0; /* log1p(x<-1) = NaN */
+ }
+ if hx << 1 < 0x3ca00000 << 1 {
+ /* |x| < 2**-53 */
+ /* underflow if subnormal */
+ if (hx & 0x7ff00000) == 0 {
+ force_eval!(x as f32);
+ }
+ return x;
+ }
+ if hx <= 0xbfd2bec4 {
+ /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
+ k = 0;
+ c = 0.;
+ f = x;
+ }
+ } else if hx >= 0x7ff00000 {
+ return x;
+ }
+ if k > 0 {
+ ui = (1. + x).to_bits();
+ hu = (ui >> 32) as u32;
+ hu += 0x3ff00000 - 0x3fe6a09e;
+ k = (hu >> 20) as i32 - 0x3ff;
+ /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
+ if k < 54 {
+ c = if k >= 2 {
+ 1. - (f64::from_bits(ui) - x)
+ } else {
+ x - (f64::from_bits(ui) - 1.)
+ };
+ c /= f64::from_bits(ui);
+ } else {
+ c = 0.;
+ }
+ /* reduce u into [sqrt(2)/2, sqrt(2)] */
+ hu = (hu & 0x000fffff) + 0x3fe6a09e;
+ ui = (hu as u64) << 32 | (ui & 0xffffffff);
+ f = f64::from_bits(ui) - 1.;
+ }
+ hfsq = 0.5 * f * f;
+ s = f / (2.0 + f);
+ z = s * s;
+ w = z * z;
+ t1 = w * (LG2 + w * (LG4 + w * LG6));
+ t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
+ r = t2 + t1;
+ dk = k as f64;
+ s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI
+}
diff --git a/src/math/log1pf.rs b/src/math/log1pf.rs
new file mode 100644
index 0000000..500e8ee
--- /dev/null
+++ b/src/math/log1pf.rs
@@ -0,0 +1,98 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use core::f32;
+
+const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */
+const LN2_LO: f32 = 9.0580006145e-06; /* 0x3717f7d1 */
+/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
+const LG1: f32 = 0.66666662693; /* 0xaaaaaa.0p-24 */
+const LG2: f32 = 0.40000972152; /* 0xccce13.0p-25 */
+const LG3: f32 = 0.28498786688; /* 0x91e9ee.0p-25 */
+const LG4: f32 = 0.24279078841; /* 0xf89e26.0p-26 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn log1pf(x: f32) -> f32 {
+ let mut ui: u32 = x.to_bits();
+ let hfsq: f32;
+ let mut f: f32 = 0.;
+ let mut c: f32 = 0.;
+ let s: f32;
+ let z: f32;
+ let r: f32;
+ let w: f32;
+ let t1: f32;
+ let t2: f32;
+ let dk: f32;
+ let ix: u32;
+ let mut iu: u32;
+ let mut k: i32;
+
+ ix = ui;
+ k = 1;
+ if ix < 0x3ed413d0 || (ix >> 31) > 0 {
+ /* 1+x < sqrt(2)+ */
+ if ix >= 0xbf800000 {
+ /* x <= -1.0 */
+ if x == -1. {
+ return x / 0.0; /* log1p(-1)=+inf */
+ }
+ return (x - x) / 0.0; /* log1p(x<-1)=NaN */
+ }
+ if ix << 1 < 0x33800000 << 1 {
+ /* |x| < 2**-24 */
+ /* underflow if subnormal */
+ if (ix & 0x7f800000) == 0 {
+ force_eval!(x * x);
+ }
+ return x;
+ }
+ if ix <= 0xbe95f619 {
+ /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
+ k = 0;
+ c = 0.;
+ f = x;
+ }
+ } else if ix >= 0x7f800000 {
+ return x;
+ }
+ if k > 0 {
+ ui = (1. + x).to_bits();
+ iu = ui;
+ iu += 0x3f800000 - 0x3f3504f3;
+ k = (iu >> 23) as i32 - 0x7f;
+ /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
+ if k < 25 {
+ c = if k >= 2 {
+ 1. - (f32::from_bits(ui) - x)
+ } else {
+ x - (f32::from_bits(ui) - 1.)
+ };
+ c /= f32::from_bits(ui);
+ } else {
+ c = 0.;
+ }
+ /* reduce u into [sqrt(2)/2, sqrt(2)] */
+ iu = (iu & 0x007fffff) + 0x3f3504f3;
+ ui = iu;
+ f = f32::from_bits(ui) - 1.;
+ }
+ s = f / (2.0 + f);
+ z = s * s;
+ w = z * z;
+ t1 = w * (LG2 + w * LG4);
+ t2 = z * (LG1 + w * LG3);
+ r = t2 + t1;
+ hfsq = 0.5 * f * f;
+ dk = k as f32;
+ s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI
+}
diff --git a/src/math/log2.rs b/src/math/log2.rs
new file mode 100644
index 0000000..83da3a1
--- /dev/null
+++ b/src/math/log2.rs
@@ -0,0 +1,106 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_log2.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/*
+ * Return the base 2 logarithm of x. See log.c for most comments.
+ *
+ * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
+ * as in log.c, then combine and scale in extra precision:
+ * log2(x) = (f - f*f/2 + r)/log(2) + k
+ */
+
+use core::f64;
+
+const IVLN2HI: f64 = 1.44269504072144627571e+00; /* 0x3ff71547, 0x65200000 */
+const IVLN2LO: f64 = 1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */
+const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */
+const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */
+const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */
+const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */
+const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */
+const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */
+const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn log2(mut x: f64) -> f64 {
+ let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54
+
+ let mut ui: u64 = x.to_bits();
+ let hfsq: f64;
+ let f: f64;
+ let s: f64;
+ let z: f64;
+ let r: f64;
+ let mut w: f64;
+ let t1: f64;
+ let t2: f64;
+ let y: f64;
+ let mut hi: f64;
+ let lo: f64;
+ let mut val_hi: f64;
+ let mut val_lo: f64;
+ let mut hx: u32;
+ let mut k: i32;
+
+ hx = (ui >> 32) as u32;
+ k = 0;
+ if hx < 0x00100000 || (hx >> 31) > 0 {
+ if ui << 1 == 0 {
+ return -1. / (x * x); /* log(+-0)=-inf */
+ }
+ if (hx >> 31) > 0 {
+ return (x - x) / 0.0; /* log(-#) = NaN */
+ }
+ /* subnormal number, scale x up */
+ k -= 54;
+ x *= x1p54;
+ ui = x.to_bits();
+ hx = (ui >> 32) as u32;
+ } else if hx >= 0x7ff00000 {
+ return x;
+ } else if hx == 0x3ff00000 && ui << 32 == 0 {
+ return 0.;
+ }
+
+ /* reduce x into [sqrt(2)/2, sqrt(2)] */
+ hx += 0x3ff00000 - 0x3fe6a09e;
+ k += (hx >> 20) as i32 - 0x3ff;
+ hx = (hx & 0x000fffff) + 0x3fe6a09e;
+ ui = (hx as u64) << 32 | (ui & 0xffffffff);
+ x = f64::from_bits(ui);
+
+ f = x - 1.0;
+ hfsq = 0.5 * f * f;
+ s = f / (2.0 + f);
+ z = s * s;
+ w = z * z;
+ t1 = w * (LG2 + w * (LG4 + w * LG6));
+ t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
+ r = t2 + t1;
+
+ /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
+ hi = f - hfsq;
+ ui = hi.to_bits();
+ ui &= (-1i64 as u64) << 32;
+ hi = f64::from_bits(ui);
+ lo = f - hi - hfsq + s * (hfsq + r);
+
+ val_hi = hi * IVLN2HI;
+ val_lo = (lo + hi) * IVLN2LO + lo * IVLN2HI;
+
+ /* spadd(val_hi, val_lo, y), except for not using double_t: */
+ y = k.into();
+ w = y + val_hi;
+ val_lo += (y - w) + val_hi;
+ val_hi = w;
+
+ val_lo + val_hi
+}
diff --git a/src/math/log2f.rs b/src/math/log2f.rs
new file mode 100644
index 0000000..3a20fb1
--- /dev/null
+++ b/src/math/log2f.rs
@@ -0,0 +1,87 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_log2f.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/*
+ * See comments in log2.c.
+ */
+
+use core::f32;
+
+const IVLN2HI: f32 = 1.4428710938e+00; /* 0x3fb8b000 */
+const IVLN2LO: f32 = -1.7605285393e-04; /* 0xb9389ad4 */
+/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
+const LG1: f32 = 0.66666662693; /* 0xaaaaaa.0p-24 */
+const LG2: f32 = 0.40000972152; /* 0xccce13.0p-25 */
+const LG3: f32 = 0.28498786688; /* 0x91e9ee.0p-25 */
+const LG4: f32 = 0.24279078841; /* 0xf89e26.0p-26 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn log2f(mut x: f32) -> f32 {
+ let x1p25f = f32::from_bits(0x4c000000); // 0x1p25f === 2 ^ 25
+
+ let mut ui: u32 = x.to_bits();
+ let hfsq: f32;
+ let f: f32;
+ let s: f32;
+ let z: f32;
+ let r: f32;
+ let w: f32;
+ let t1: f32;
+ let t2: f32;
+ let mut hi: f32;
+ let lo: f32;
+ let mut ix: u32;
+ let mut k: i32;
+
+ ix = ui;
+ k = 0;
+ if ix < 0x00800000 || (ix >> 31) > 0 {
+ /* x < 2**-126 */
+ if ix << 1 == 0 {
+ return -1. / (x * x); /* log(+-0)=-inf */
+ }
+ if (ix >> 31) > 0 {
+ return (x - x) / 0.0; /* log(-#) = NaN */
+ }
+ /* subnormal number, scale up x */
+ k -= 25;
+ x *= x1p25f;
+ ui = x.to_bits();
+ ix = ui;
+ } else if ix >= 0x7f800000 {
+ return x;
+ } else if ix == 0x3f800000 {
+ return 0.;
+ }
+
+ /* reduce x into [sqrt(2)/2, sqrt(2)] */
+ ix += 0x3f800000 - 0x3f3504f3;
+ k += (ix >> 23) as i32 - 0x7f;
+ ix = (ix & 0x007fffff) + 0x3f3504f3;
+ ui = ix;
+ x = f32::from_bits(ui);
+
+ f = x - 1.0;
+ s = f / (2.0 + f);
+ z = s * s;
+ w = z * z;
+ t1 = w * (LG2 + w * LG4);
+ t2 = z * (LG1 + w * LG3);
+ r = t2 + t1;
+ hfsq = 0.5 * f * f;
+
+ hi = f - hfsq;
+ ui = hi.to_bits();
+ ui &= 0xfffff000;
+ hi = f32::from_bits(ui);
+ lo = f - hi - hfsq + s * (hfsq + r);
+ (lo + hi) * IVLN2LO + lo * IVLN2HI + hi * IVLN2HI + k as f32
+}
diff --git a/src/math/logf.rs b/src/math/logf.rs
new file mode 100644
index 0000000..2b57b93
--- /dev/null
+++ b/src/math/logf.rs
@@ -0,0 +1,65 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_logf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */
+const LN2_LO: f32 = 9.0580006145e-06; /* 0x3717f7d1 */
+/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
+const LG1: f32 = 0.66666662693; /* 0xaaaaaa.0p-24*/
+const LG2: f32 = 0.40000972152; /* 0xccce13.0p-25 */
+const LG3: f32 = 0.28498786688; /* 0x91e9ee.0p-25 */
+const LG4: f32 = 0.24279078841; /* 0xf89e26.0p-26 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn logf(mut x: f32) -> f32 {
+ let x1p25 = f32::from_bits(0x4c000000); // 0x1p25f === 2 ^ 25
+
+ let mut ix = x.to_bits();
+ let mut k = 0i32;
+
+ if (ix < 0x00800000) || ((ix >> 31) != 0) {
+ /* x < 2**-126 */
+ if ix << 1 == 0 {
+ return -1. / (x * x); /* log(+-0)=-inf */
+ }
+ if (ix >> 31) != 0 {
+ return (x - x) / 0.; /* log(-#) = NaN */
+ }
+ /* subnormal number, scale up x */
+ k -= 25;
+ x *= x1p25;
+ ix = x.to_bits();
+ } else if ix >= 0x7f800000 {
+ return x;
+ } else if ix == 0x3f800000 {
+ return 0.;
+ }
+
+ /* reduce x into [sqrt(2)/2, sqrt(2)] */
+ ix += 0x3f800000 - 0x3f3504f3;
+ k += ((ix >> 23) as i32) - 0x7f;
+ ix = (ix & 0x007fffff) + 0x3f3504f3;
+ x = f32::from_bits(ix);
+
+ let f = x - 1.;
+ let s = f / (2. + f);
+ let z = s * s;
+ let w = z * z;
+ let t1 = w * (LG2 + w * LG4);
+ let t2 = z * (LG1 + w * LG3);
+ let r = t2 + t1;
+ let hfsq = 0.5 * f * f;
+ let dk = k as f32;
+ s * (hfsq + r) + dk * LN2_LO - hfsq + f + dk * LN2_HI
+}
diff --git a/src/math/mod.rs b/src/math/mod.rs
new file mode 100644
index 0000000..c8d7bd8
--- /dev/null
+++ b/src/math/mod.rs
@@ -0,0 +1,350 @@
+macro_rules! force_eval {
+ ($e:expr) => {
+ unsafe {
+ ::core::ptr::read_volatile(&$e);
+ }
+ };
+}
+
+#[cfg(not(debug_assertions))]
+macro_rules! i {
+ ($array:expr, $index:expr) => {
+ unsafe { *$array.get_unchecked($index) }
+ };
+ ($array:expr, $index:expr, = , $rhs:expr) => {
+ unsafe {
+ *$array.get_unchecked_mut($index) = $rhs;
+ }
+ };
+ ($array:expr, $index:expr, += , $rhs:expr) => {
+ unsafe {
+ *$array.get_unchecked_mut($index) += $rhs;
+ }
+ };
+ ($array:expr, $index:expr, -= , $rhs:expr) => {
+ unsafe {
+ *$array.get_unchecked_mut($index) -= $rhs;
+ }
+ };
+ ($array:expr, $index:expr, &= , $rhs:expr) => {
+ unsafe {
+ *$array.get_unchecked_mut($index) &= $rhs;
+ }
+ };
+ ($array:expr, $index:expr, == , $rhs:expr) => {
+ unsafe { *$array.get_unchecked_mut($index) == $rhs }
+ };
+}
+
+#[cfg(debug_assertions)]
+macro_rules! i {
+ ($array:expr, $index:expr) => {
+ *$array.get($index).unwrap()
+ };
+ ($array:expr, $index:expr, = , $rhs:expr) => {
+ *$array.get_mut($index).unwrap() = $rhs;
+ };
+ ($array:expr, $index:expr, -= , $rhs:expr) => {
+ *$array.get_mut($index).unwrap() -= $rhs;
+ };
+ ($array:expr, $index:expr, += , $rhs:expr) => {
+ *$array.get_mut($index).unwrap() += $rhs;
+ };
+ ($array:expr, $index:expr, &= , $rhs:expr) => {
+ *$array.get_mut($index).unwrap() &= $rhs;
+ };
+ ($array:expr, $index:expr, == , $rhs:expr) => {
+ *$array.get_mut($index).unwrap() == $rhs
+ };
+}
+
+macro_rules! llvm_intrinsically_optimized {
+ (#[cfg($($clause:tt)*)] $e:expr) => {
+ #[cfg(all(feature = "unstable", $($clause)*))]
+ {
+ if true { // thwart the dead code lint
+ $e
+ }
+ }
+ };
+}
+
+// Public modules
+mod acos;
+mod acosf;
+mod acosh;
+mod acoshf;
+mod asin;
+mod asinf;
+mod asinh;
+mod asinhf;
+mod atan;
+mod atan2;
+mod atan2f;
+mod atanf;
+mod atanh;
+mod atanhf;
+mod cbrt;
+mod cbrtf;
+mod ceil;
+mod ceilf;
+mod copysign;
+mod copysignf;
+mod cos;
+mod cosf;
+mod cosh;
+mod coshf;
+mod erf;
+mod erff;
+mod exp;
+mod exp10;
+mod exp10f;
+mod exp2;
+mod exp2f;
+mod expf;
+mod expm1;
+mod expm1f;
+mod fabs;
+mod fabsf;
+mod fdim;
+mod fdimf;
+mod floor;
+mod floorf;
+mod fma;
+mod fmaf;
+mod fmax;
+mod fmaxf;
+mod fmin;
+mod fminf;
+mod fmod;
+mod fmodf;
+mod frexp;
+mod frexpf;
+mod hypot;
+mod hypotf;
+mod ilogb;
+mod ilogbf;
+mod j0;
+mod j0f;
+mod j1;
+mod j1f;
+mod jn;
+mod jnf;
+mod ldexp;
+mod ldexpf;
+mod lgamma;
+mod lgamma_r;
+mod lgammaf;
+mod lgammaf_r;
+mod log;
+mod log10;
+mod log10f;
+mod log1p;
+mod log1pf;
+mod log2;
+mod log2f;
+mod logf;
+mod modf;
+mod modff;
+mod nextafter;
+mod nextafterf;
+mod pow;
+mod powf;
+mod remainder;
+mod remainderf;
+mod remquo;
+mod remquof;
+mod round;
+mod roundf;
+mod scalbn;
+mod scalbnf;
+mod sin;
+mod sincos;
+mod sincosf;
+mod sinf;
+mod sinh;
+mod sinhf;
+mod sqrt;
+mod sqrtf;
+mod tan;
+mod tanf;
+mod tanh;
+mod tanhf;
+mod tgamma;
+mod tgammaf;
+mod trunc;
+mod truncf;
+
+// Use separated imports instead of {}-grouped imports for easier merging.
+pub use self::acos::acos;
+pub use self::acosf::acosf;
+pub use self::acosh::acosh;
+pub use self::acoshf::acoshf;
+pub use self::asin::asin;
+pub use self::asinf::asinf;
+pub use self::asinh::asinh;
+pub use self::asinhf::asinhf;
+pub use self::atan::atan;
+pub use self::atan2::atan2;
+pub use self::atan2f::atan2f;
+pub use self::atanf::atanf;
+pub use self::atanh::atanh;
+pub use self::atanhf::atanhf;
+pub use self::cbrt::cbrt;
+pub use self::cbrtf::cbrtf;
+pub use self::ceil::ceil;
+pub use self::ceilf::ceilf;
+pub use self::copysign::copysign;
+pub use self::copysignf::copysignf;
+pub use self::cos::cos;
+pub use self::cosf::cosf;
+pub use self::cosh::cosh;
+pub use self::coshf::coshf;
+pub use self::erf::erf;
+pub use self::erf::erfc;
+pub use self::erff::erfcf;
+pub use self::erff::erff;
+pub use self::exp::exp;
+pub use self::exp10::exp10;
+pub use self::exp10f::exp10f;
+pub use self::exp2::exp2;
+pub use self::exp2f::exp2f;
+pub use self::expf::expf;
+pub use self::expm1::expm1;
+pub use self::expm1f::expm1f;
+pub use self::fabs::fabs;
+pub use self::fabsf::fabsf;
+pub use self::fdim::fdim;
+pub use self::fdimf::fdimf;
+pub use self::floor::floor;
+pub use self::floorf::floorf;
+pub use self::fma::fma;
+pub use self::fmaf::fmaf;
+pub use self::fmax::fmax;
+pub use self::fmaxf::fmaxf;
+pub use self::fmin::fmin;
+pub use self::fminf::fminf;
+pub use self::fmod::fmod;
+pub use self::fmodf::fmodf;
+pub use self::frexp::frexp;
+pub use self::frexpf::frexpf;
+pub use self::hypot::hypot;
+pub use self::hypotf::hypotf;
+pub use self::ilogb::ilogb;
+pub use self::ilogbf::ilogbf;
+pub use self::j0::j0;
+pub use self::j0::y0;
+pub use self::j0f::j0f;
+pub use self::j0f::y0f;
+pub use self::j1::j1;
+pub use self::j1::y1;
+pub use self::j1f::j1f;
+pub use self::j1f::y1f;
+pub use self::jn::jn;
+pub use self::jn::yn;
+pub use self::jnf::jnf;
+pub use self::jnf::ynf;
+pub use self::ldexp::ldexp;
+pub use self::ldexpf::ldexpf;
+pub use self::lgamma::lgamma;
+pub use self::lgamma_r::lgamma_r;
+pub use self::lgammaf::lgammaf;
+pub use self::lgammaf_r::lgammaf_r;
+pub use self::log::log;
+pub use self::log10::log10;
+pub use self::log10f::log10f;
+pub use self::log1p::log1p;
+pub use self::log1pf::log1pf;
+pub use self::log2::log2;
+pub use self::log2f::log2f;
+pub use self::logf::logf;
+pub use self::modf::modf;
+pub use self::modff::modff;
+pub use self::nextafter::nextafter;
+pub use self::nextafterf::nextafterf;
+pub use self::pow::pow;
+pub use self::powf::powf;
+pub use self::remainder::remainder;
+pub use self::remainderf::remainderf;
+pub use self::remquo::remquo;
+pub use self::remquof::remquof;
+pub use self::round::round;
+pub use self::roundf::roundf;
+pub use self::scalbn::scalbn;
+pub use self::scalbnf::scalbnf;
+pub use self::sin::sin;
+pub use self::sincos::sincos;
+pub use self::sincosf::sincosf;
+pub use self::sinf::sinf;
+pub use self::sinh::sinh;
+pub use self::sinhf::sinhf;
+pub use self::sqrt::sqrt;
+pub use self::sqrtf::sqrtf;
+pub use self::tan::tan;
+pub use self::tanf::tanf;
+pub use self::tanh::tanh;
+pub use self::tanhf::tanhf;
+pub use self::tgamma::tgamma;
+pub use self::tgammaf::tgammaf;
+pub use self::trunc::trunc;
+pub use self::truncf::truncf;
+
+// Private modules
+mod expo2;
+mod fenv;
+mod k_cos;
+mod k_cosf;
+mod k_expo2;
+mod k_expo2f;
+mod k_sin;
+mod k_sinf;
+mod k_tan;
+mod k_tanf;
+mod rem_pio2;
+mod rem_pio2_large;
+mod rem_pio2f;
+
+// Private re-imports
+use self::expo2::expo2;
+use self::k_cos::k_cos;
+use self::k_cosf::k_cosf;
+use self::k_expo2::k_expo2;
+use self::k_expo2f::k_expo2f;
+use self::k_sin::k_sin;
+use self::k_sinf::k_sinf;
+use self::k_tan::k_tan;
+use self::k_tanf::k_tanf;
+use self::rem_pio2::rem_pio2;
+use self::rem_pio2_large::rem_pio2_large;
+use self::rem_pio2f::rem_pio2f;
+
+#[inline]
+fn get_high_word(x: f64) -> u32 {
+ (x.to_bits() >> 32) as u32
+}
+
+#[inline]
+fn get_low_word(x: f64) -> u32 {
+ x.to_bits() as u32
+}
+
+#[inline]
+fn with_set_high_word(f: f64, hi: u32) -> f64 {
+ let mut tmp = f.to_bits();
+ tmp &= 0x00000000_ffffffff;
+ tmp |= (hi as u64) << 32;
+ f64::from_bits(tmp)
+}
+
+#[inline]
+fn with_set_low_word(f: f64, lo: u32) -> f64 {
+ let mut tmp = f.to_bits();
+ tmp &= 0xffffffff_00000000;
+ tmp |= lo as u64;
+ f64::from_bits(tmp)
+}
+
+#[inline]
+fn combine_words(hi: u32, lo: u32) -> f64 {
+ f64::from_bits((hi as u64) << 32 | lo as u64)
+}
diff --git a/src/math/modf.rs b/src/math/modf.rs
new file mode 100644
index 0000000..bcab33a
--- /dev/null
+++ b/src/math/modf.rs
@@ -0,0 +1,34 @@
+pub fn modf(x: f64) -> (f64, f64) {
+ let rv2: f64;
+ let mut u = x.to_bits();
+ let mask: u64;
+ let e = ((u >> 52 & 0x7ff) as i32) - 0x3ff;
+
+ /* no fractional part */
+ if e >= 52 {
+ rv2 = x;
+ if e == 0x400 && (u << 12) != 0 {
+ /* nan */
+ return (x, rv2);
+ }
+ u &= 1 << 63;
+ return (f64::from_bits(u), rv2);
+ }
+
+ /* no integral part*/
+ if e < 0 {
+ u &= 1 << 63;
+ rv2 = f64::from_bits(u);
+ return (x, rv2);
+ }
+
+ mask = ((!0) >> 12) >> e;
+ if (u & mask) == 0 {
+ rv2 = x;
+ u &= 1 << 63;
+ return (f64::from_bits(u), rv2);
+ }
+ u &= !mask;
+ rv2 = f64::from_bits(u);
+ return (x - rv2, rv2);
+}
diff --git a/src/math/modff.rs b/src/math/modff.rs
new file mode 100644
index 0000000..56ece12
--- /dev/null
+++ b/src/math/modff.rs
@@ -0,0 +1,33 @@
+pub fn modff(x: f32) -> (f32, f32) {
+ let rv2: f32;
+ let mut u: u32 = x.to_bits();
+ let mask: u32;
+ let e = ((u >> 23 & 0xff) as i32) - 0x7f;
+
+ /* no fractional part */
+ if e >= 23 {
+ rv2 = x;
+ if e == 0x80 && (u << 9) != 0 {
+ /* nan */
+ return (x, rv2);
+ }
+ u &= 0x80000000;
+ return (f32::from_bits(u), rv2);
+ }
+ /* no integral part */
+ if e < 0 {
+ u &= 0x80000000;
+ rv2 = f32::from_bits(u);
+ return (x, rv2);
+ }
+
+ mask = 0x007fffff >> e;
+ if (u & mask) == 0 {
+ rv2 = x;
+ u &= 0x80000000;
+ return (f32::from_bits(u), rv2);
+ }
+ u &= !mask;
+ rv2 = f32::from_bits(u);
+ return (x - rv2, rv2);
+}
diff --git a/src/math/nextafter.rs b/src/math/nextafter.rs
new file mode 100644
index 0000000..13094a1
--- /dev/null
+++ b/src/math/nextafter.rs
@@ -0,0 +1,37 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn nextafter(x: f64, y: f64) -> f64 {
+ if x.is_nan() || y.is_nan() {
+ return x + y;
+ }
+
+ let mut ux_i = x.to_bits();
+ let uy_i = y.to_bits();
+ if ux_i == uy_i {
+ return y;
+ }
+
+ let ax = ux_i & !1_u64 / 2;
+ let ay = uy_i & !1_u64 / 2;
+ if ax == 0 {
+ if ay == 0 {
+ return y;
+ }
+ ux_i = (uy_i & 1_u64 << 63) | 1;
+ } else if ax > ay || ((ux_i ^ uy_i) & 1_u64 << 63) != 0 {
+ ux_i -= 1;
+ } else {
+ ux_i += 1;
+ }
+
+ let e = ux_i.wrapping_shr(52 & 0x7ff);
+ // raise overflow if ux.f is infinite and x is finite
+ if e == 0x7ff {
+ force_eval!(x + x);
+ }
+ let ux_f = f64::from_bits(ux_i);
+ // raise underflow if ux.f is subnormal or zero
+ if e == 0 {
+ force_eval!(x * x + ux_f * ux_f);
+ }
+ ux_f
+}
diff --git a/src/math/nextafterf.rs b/src/math/nextafterf.rs
new file mode 100644
index 0000000..df9b108
--- /dev/null
+++ b/src/math/nextafterf.rs
@@ -0,0 +1,37 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn nextafterf(x: f32, y: f32) -> f32 {
+ if x.is_nan() || y.is_nan() {
+ return x + y;
+ }
+
+ let mut ux_i = x.to_bits();
+ let uy_i = y.to_bits();
+ if ux_i == uy_i {
+ return y;
+ }
+
+ let ax = ux_i & 0x7fff_ffff_u32;
+ let ay = uy_i & 0x7fff_ffff_u32;
+ if ax == 0 {
+ if ay == 0 {
+ return y;
+ }
+ ux_i = (uy_i & 0x8000_0000_u32) | 1;
+ } else if ax > ay || ((ux_i ^ uy_i) & 0x8000_0000_u32) != 0 {
+ ux_i -= 1;
+ } else {
+ ux_i += 1;
+ }
+
+ let e = ux_i.wrapping_shr(0x7f80_0000_u32);
+ // raise overflow if ux_f is infinite and x is finite
+ if e == 0x7f80_0000_u32 {
+ force_eval!(x + x);
+ }
+ let ux_f = f32::from_bits(ux_i);
+ // raise underflow if ux_f is subnormal or zero
+ if e == 0 {
+ force_eval!(x * x + ux_f * ux_f);
+ }
+ ux_f
+}
diff --git a/src/math/pow.rs b/src/math/pow.rs
new file mode 100644
index 0000000..ce8e83e
--- /dev/null
+++ b/src/math/pow.rs
@@ -0,0 +1,633 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_pow.c */
+/*
+ * ====================================================
+ * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+// pow(x,y) return x**y
+//
+// n
+// Method: Let x = 2 * (1+f)
+// 1. Compute and return log2(x) in two pieces:
+// log2(x) = w1 + w2,
+// where w1 has 53-24 = 29 bit trailing zeros.
+// 2. Perform y*log2(x) = n+y' by simulating muti-precision
+// arithmetic, where |y'|<=0.5.
+// 3. Return x**y = 2**n*exp(y'*log2)
+//
+// Special cases:
+// 1. (anything) ** 0 is 1
+// 2. 1 ** (anything) is 1
+// 3. (anything except 1) ** NAN is NAN
+// 4. NAN ** (anything except 0) is NAN
+// 5. +-(|x| > 1) ** +INF is +INF
+// 6. +-(|x| > 1) ** -INF is +0
+// 7. +-(|x| < 1) ** +INF is +0
+// 8. +-(|x| < 1) ** -INF is +INF
+// 9. -1 ** +-INF is 1
+// 10. +0 ** (+anything except 0, NAN) is +0
+// 11. -0 ** (+anything except 0, NAN, odd integer) is +0
+// 12. +0 ** (-anything except 0, NAN) is +INF, raise divbyzero
+// 13. -0 ** (-anything except 0, NAN, odd integer) is +INF, raise divbyzero
+// 14. -0 ** (+odd integer) is -0
+// 15. -0 ** (-odd integer) is -INF, raise divbyzero
+// 16. +INF ** (+anything except 0,NAN) is +INF
+// 17. +INF ** (-anything except 0,NAN) is +0
+// 18. -INF ** (+odd integer) is -INF
+// 19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer)
+// 20. (anything) ** 1 is (anything)
+// 21. (anything) ** -1 is 1/(anything)
+// 22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
+// 23. (-anything except 0 and inf) ** (non-integer) is NAN
+//
+// Accuracy:
+// pow(x,y) returns x**y nearly rounded. In particular
+// pow(integer,integer)
+// always returns the correct integer provided it is
+// representable.
+//
+// Constants :
+// The hexadecimal values are the intended ones for the following
+// constants. The decimal values may be used, provided that the
+// compiler will convert from decimal to binary accurately enough
+// to produce the hexadecimal values shown.
+//
+use super::{fabs, get_high_word, scalbn, sqrt, with_set_high_word, with_set_low_word};
+
+const BP: [f64; 2] = [1.0, 1.5];
+const DP_H: [f64; 2] = [0.0, 5.84962487220764160156e-01]; /* 0x3fe2b803_40000000 */
+const DP_L: [f64; 2] = [0.0, 1.35003920212974897128e-08]; /* 0x3E4CFDEB, 0x43CFD006 */
+const TWO53: f64 = 9007199254740992.0; /* 0x43400000_00000000 */
+const HUGE: f64 = 1.0e300;
+const TINY: f64 = 1.0e-300;
+
+// poly coefs for (3/2)*(log(x)-2s-2/3*s**3:
+const L1: f64 = 5.99999999999994648725e-01; /* 0x3fe33333_33333303 */
+const L2: f64 = 4.28571428578550184252e-01; /* 0x3fdb6db6_db6fabff */
+const L3: f64 = 3.33333329818377432918e-01; /* 0x3fd55555_518f264d */
+const L4: f64 = 2.72728123808534006489e-01; /* 0x3fd17460_a91d4101 */
+const L5: f64 = 2.30660745775561754067e-01; /* 0x3fcd864a_93c9db65 */
+const L6: f64 = 2.06975017800338417784e-01; /* 0x3fca7e28_4a454eef */
+const P1: f64 = 1.66666666666666019037e-01; /* 0x3fc55555_5555553e */
+const P2: f64 = -2.77777777770155933842e-03; /* 0xbf66c16c_16bebd93 */
+const P3: f64 = 6.61375632143793436117e-05; /* 0x3f11566a_af25de2c */
+const P4: f64 = -1.65339022054652515390e-06; /* 0xbebbbd41_c5d26bf1 */
+const P5: f64 = 4.13813679705723846039e-08; /* 0x3e663769_72bea4d0 */
+const LG2: f64 = 6.93147180559945286227e-01; /* 0x3fe62e42_fefa39ef */
+const LG2_H: f64 = 6.93147182464599609375e-01; /* 0x3fe62e43_00000000 */
+const LG2_L: f64 = -1.90465429995776804525e-09; /* 0xbe205c61_0ca86c39 */
+const OVT: f64 = 8.0085662595372944372e-017; /* -(1024-log2(ovfl+.5ulp)) */
+const CP: f64 = 9.61796693925975554329e-01; /* 0x3feec709_dc3a03fd =2/(3ln2) */
+const CP_H: f64 = 9.61796700954437255859e-01; /* 0x3feec709_e0000000 =(float)cp */
+const CP_L: f64 = -7.02846165095275826516e-09; /* 0xbe3e2fe0_145b01f5 =tail of cp_h*/
+const IVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547_652b82fe =1/ln2 */
+const IVLN2_H: f64 = 1.44269502162933349609e+00; /* 0x3ff71547_60000000 =24b 1/ln2*/
+const IVLN2_L: f64 = 1.92596299112661746887e-08; /* 0x3e54ae0b_f85ddf44 =1/ln2 tail*/
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn pow(x: f64, y: f64) -> f64 {
+ let t1: f64;
+ let t2: f64;
+
+ let (hx, lx): (i32, u32) = ((x.to_bits() >> 32) as i32, x.to_bits() as u32);
+ let (hy, ly): (i32, u32) = ((y.to_bits() >> 32) as i32, y.to_bits() as u32);
+
+ let mut ix: i32 = (hx & 0x7fffffff) as i32;
+ let iy: i32 = (hy & 0x7fffffff) as i32;
+
+ /* x**0 = 1, even if x is NaN */
+ if ((iy as u32) | ly) == 0 {
+ return 1.0;
+ }
+
+ /* 1**y = 1, even if y is NaN */
+ if hx == 0x3ff00000 && lx == 0 {
+ return 1.0;
+ }
+
+ /* NaN if either arg is NaN */
+ if ix > 0x7ff00000
+ || (ix == 0x7ff00000 && lx != 0)
+ || iy > 0x7ff00000
+ || (iy == 0x7ff00000 && ly != 0)
+ {
+ return x + y;
+ }
+
+ /* determine if y is an odd int when x < 0
+ * yisint = 0 ... y is not an integer
+ * yisint = 1 ... y is an odd int
+ * yisint = 2 ... y is an even int
+ */
+ let mut yisint: i32 = 0;
+ let mut k: i32;
+ let mut j: i32;
+ if hx < 0 {
+ if iy >= 0x43400000 {
+ yisint = 2; /* even integer y */
+ } else if iy >= 0x3ff00000 {
+ k = (iy >> 20) - 0x3ff; /* exponent */
+
+ if k > 20 {
+ j = (ly >> (52 - k)) as i32;
+
+ if (j << (52 - k)) == (ly as i32) {
+ yisint = 2 - (j & 1);
+ }
+ } else if ly == 0 {
+ j = iy >> (20 - k);
+
+ if (j << (20 - k)) == iy {
+ yisint = 2 - (j & 1);
+ }
+ }
+ }
+ }
+
+ if ly == 0 {
+ /* special value of y */
+ if iy == 0x7ff00000 {
+ /* y is +-inf */
+
+ return if ((ix - 0x3ff00000) | (lx as i32)) == 0 {
+ /* (-1)**+-inf is 1 */
+ 1.0
+ } else if ix >= 0x3ff00000 {
+ /* (|x|>1)**+-inf = inf,0 */
+ if hy >= 0 {
+ y
+ } else {
+ 0.0
+ }
+ } else {
+ /* (|x|<1)**+-inf = 0,inf */
+ if hy >= 0 {
+ 0.0
+ } else {
+ -y
+ }
+ };
+ }
+
+ if iy == 0x3ff00000 {
+ /* y is +-1 */
+ return if hy >= 0 { x } else { 1.0 / x };
+ }
+
+ if hy == 0x40000000 {
+ /* y is 2 */
+ return x * x;
+ }
+
+ if hy == 0x3fe00000 {
+ /* y is 0.5 */
+ if hx >= 0 {
+ /* x >= +0 */
+ return sqrt(x);
+ }
+ }
+ }
+
+ let mut ax: f64 = fabs(x);
+ if lx == 0 {
+ /* special value of x */
+ if ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000 {
+ /* x is +-0,+-inf,+-1 */
+ let mut z: f64 = ax;
+
+ if hy < 0 {
+ /* z = (1/|x|) */
+ z = 1.0 / z;
+ }
+
+ if hx < 0 {
+ if ((ix - 0x3ff00000) | yisint) == 0 {
+ z = (z - z) / (z - z); /* (-1)**non-int is NaN */
+ } else if yisint == 1 {
+ z = -z; /* (x<0)**odd = -(|x|**odd) */
+ }
+ }
+
+ return z;
+ }
+ }
+
+ let mut s: f64 = 1.0; /* sign of result */
+ if hx < 0 {
+ if yisint == 0 {
+ /* (x<0)**(non-int) is NaN */
+ return (x - x) / (x - x);
+ }
+
+ if yisint == 1 {
+ /* (x<0)**(odd int) */
+ s = -1.0;
+ }
+ }
+
+ /* |y| is HUGE */
+ if iy > 0x41e00000 {
+ /* if |y| > 2**31 */
+ if iy > 0x43f00000 {
+ /* if |y| > 2**64, must o/uflow */
+ if ix <= 0x3fefffff {
+ return if hy < 0 { HUGE * HUGE } else { TINY * TINY };
+ }
+
+ if ix >= 0x3ff00000 {
+ return if hy > 0 { HUGE * HUGE } else { TINY * TINY };
+ }
+ }
+
+ /* over/underflow if x is not close to one */
+ if ix < 0x3fefffff {
+ return if hy < 0 {
+ s * HUGE * HUGE
+ } else {
+ s * TINY * TINY
+ };
+ }
+ if ix > 0x3ff00000 {
+ return if hy > 0 {
+ s * HUGE * HUGE
+ } else {
+ s * TINY * TINY
+ };
+ }
+
+ /* now |1-x| is TINY <= 2**-20, suffice to compute
+ log(x) by x-x^2/2+x^3/3-x^4/4 */
+ let t: f64 = ax - 1.0; /* t has 20 trailing zeros */
+ let w: f64 = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
+ let u: f64 = IVLN2_H * t; /* ivln2_h has 21 sig. bits */
+ let v: f64 = t * IVLN2_L - w * IVLN2;
+ t1 = with_set_low_word(u + v, 0);
+ t2 = v - (t1 - u);
+ } else {
+ // double ss,s2,s_h,s_l,t_h,t_l;
+ let mut n: i32 = 0;
+
+ if ix < 0x00100000 {
+ /* take care subnormal number */
+ ax *= TWO53;
+ n -= 53;
+ ix = get_high_word(ax) as i32;
+ }
+
+ n += (ix >> 20) - 0x3ff;
+ j = ix & 0x000fffff;
+
+ /* determine interval */
+ let k: i32;
+ ix = j | 0x3ff00000; /* normalize ix */
+ if j <= 0x3988E {
+ /* |x|<sqrt(3/2) */
+ k = 0;
+ } else if j < 0xBB67A {
+ /* |x|<sqrt(3) */
+ k = 1;
+ } else {
+ k = 0;
+ n += 1;
+ ix -= 0x00100000;
+ }
+ ax = with_set_high_word(ax, ix as u32);
+
+ /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+ let u: f64 = ax - BP[k as usize]; /* bp[0]=1.0, bp[1]=1.5 */
+ let v: f64 = 1.0 / (ax + BP[k as usize]);
+ let ss: f64 = u * v;
+ let s_h = with_set_low_word(ss, 0);
+
+ /* t_h=ax+bp[k] High */
+ let t_h: f64 = with_set_high_word(
+ 0.0,
+ ((ix as u32 >> 1) | 0x20000000) + 0x00080000 + ((k as u32) << 18),
+ );
+ let t_l: f64 = ax - (t_h - BP[k as usize]);
+ let s_l: f64 = v * ((u - s_h * t_h) - s_h * t_l);
+
+ /* compute log(ax) */
+ let s2: f64 = ss * ss;
+ let mut r: f64 = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
+ r += s_l * (s_h + ss);
+ let s2: f64 = s_h * s_h;
+ let t_h: f64 = with_set_low_word(3.0 + s2 + r, 0);
+ let t_l: f64 = r - ((t_h - 3.0) - s2);
+
+ /* u+v = ss*(1+...) */
+ let u: f64 = s_h * t_h;
+ let v: f64 = s_l * t_h + t_l * ss;
+
+ /* 2/(3log2)*(ss+...) */
+ let p_h: f64 = with_set_low_word(u + v, 0);
+ let p_l = v - (p_h - u);
+ let z_h: f64 = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */
+ let z_l: f64 = CP_L * p_h + p_l * CP + DP_L[k as usize];
+
+ /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+ let t: f64 = n as f64;
+ t1 = with_set_low_word(((z_h + z_l) + DP_H[k as usize]) + t, 0);
+ t2 = z_l - (((t1 - t) - DP_H[k as usize]) - z_h);
+ }
+
+ /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+ let y1: f64 = with_set_low_word(y, 0);
+ let p_l: f64 = (y - y1) * t1 + y * t2;
+ let mut p_h: f64 = y1 * t1;
+ let z: f64 = p_l + p_h;
+ let mut j: i32 = (z.to_bits() >> 32) as i32;
+ let i: i32 = z.to_bits() as i32;
+ // let (j, i): (i32, i32) = ((z.to_bits() >> 32) as i32, z.to_bits() as i32);
+
+ if j >= 0x40900000 {
+ /* z >= 1024 */
+ if (j - 0x40900000) | i != 0 {
+ /* if z > 1024 */
+ return s * HUGE * HUGE; /* overflow */
+ }
+
+ if p_l + OVT > z - p_h {
+ return s * HUGE * HUGE; /* overflow */
+ }
+ } else if (j & 0x7fffffff) >= 0x4090cc00 {
+ /* z <= -1075 */
+ // FIXME: instead of abs(j) use unsigned j
+
+ if (((j as u32) - 0xc090cc00) | (i as u32)) != 0 {
+ /* z < -1075 */
+ return s * TINY * TINY; /* underflow */
+ }
+
+ if p_l <= z - p_h {
+ return s * TINY * TINY; /* underflow */
+ }
+ }
+
+ /* compute 2**(p_h+p_l) */
+ let i: i32 = j & (0x7fffffff as i32);
+ k = (i >> 20) - 0x3ff;
+ let mut n: i32 = 0;
+
+ if i > 0x3fe00000 {
+ /* if |z| > 0.5, set n = [z+0.5] */
+ n = j + (0x00100000 >> (k + 1));
+ k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
+ let t: f64 = with_set_high_word(0.0, (n & !(0x000fffff >> k)) as u32);
+ n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
+ if j < 0 {
+ n = -n;
+ }
+ p_h -= t;
+ }
+
+ let t: f64 = with_set_low_word(p_l + p_h, 0);
+ let u: f64 = t * LG2_H;
+ let v: f64 = (p_l - (t - p_h)) * LG2 + t * LG2_L;
+ let mut z: f64 = u + v;
+ let w: f64 = v - (z - u);
+ let t: f64 = z * z;
+ let t1: f64 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
+ let r: f64 = (z * t1) / (t1 - 2.0) - (w + z * w);
+ z = 1.0 - (r - z);
+ j = get_high_word(z) as i32;
+ j += n << 20;
+
+ if (j >> 20) <= 0 {
+ /* subnormal output */
+ z = scalbn(z, n);
+ } else {
+ z = with_set_high_word(z, j as u32);
+ }
+
+ s * z
+}
+
+#[cfg(test)]
+mod tests {
+ extern crate core;
+
+ use self::core::f64::consts::{E, PI};
+ use self::core::f64::{EPSILON, INFINITY, MAX, MIN, MIN_POSITIVE, NAN, NEG_INFINITY};
+ use super::pow;
+
+ const POS_ZERO: &[f64] = &[0.0];
+ const NEG_ZERO: &[f64] = &[-0.0];
+ const POS_ONE: &[f64] = &[1.0];
+ const NEG_ONE: &[f64] = &[-1.0];
+ const POS_FLOATS: &[f64] = &[99.0 / 70.0, E, PI];
+ const NEG_FLOATS: &[f64] = &[-99.0 / 70.0, -E, -PI];
+ const POS_SMALL_FLOATS: &[f64] = &[(1.0 / 2.0), MIN_POSITIVE, EPSILON];
+ const NEG_SMALL_FLOATS: &[f64] = &[-(1.0 / 2.0), -MIN_POSITIVE, -EPSILON];
+ const POS_EVENS: &[f64] = &[2.0, 6.0, 8.0, 10.0, 22.0, 100.0, MAX];
+ const NEG_EVENS: &[f64] = &[MIN, -100.0, -22.0, -10.0, -8.0, -6.0, -2.0];
+ const POS_ODDS: &[f64] = &[3.0, 7.0];
+ const NEG_ODDS: &[f64] = &[-7.0, -3.0];
+ const NANS: &[f64] = &[NAN];
+ const POS_INF: &[f64] = &[INFINITY];
+ const NEG_INF: &[f64] = &[NEG_INFINITY];
+
+ const ALL: &[&[f64]] = &[
+ POS_ZERO,
+ NEG_ZERO,
+ NANS,
+ NEG_SMALL_FLOATS,
+ POS_SMALL_FLOATS,
+ NEG_FLOATS,
+ POS_FLOATS,
+ NEG_EVENS,
+ POS_EVENS,
+ NEG_ODDS,
+ POS_ODDS,
+ NEG_INF,
+ POS_INF,
+ NEG_ONE,
+ POS_ONE,
+ ];
+ const POS: &[&[f64]] = &[POS_ZERO, POS_ODDS, POS_ONE, POS_FLOATS, POS_EVENS, POS_INF];
+ const NEG: &[&[f64]] = &[NEG_ZERO, NEG_ODDS, NEG_ONE, NEG_FLOATS, NEG_EVENS, NEG_INF];
+
+ fn pow_test(base: f64, exponent: f64, expected: f64) {
+ let res = pow(base, exponent);
+ assert!(
+ if expected.is_nan() {
+ res.is_nan()
+ } else {
+ pow(base, exponent) == expected
+ },
+ "{} ** {} was {} instead of {}",
+ base,
+ exponent,
+ res,
+ expected
+ );
+ }
+
+ fn test_sets_as_base(sets: &[&[f64]], exponent: f64, expected: f64) {
+ sets.iter()
+ .for_each(|s| s.iter().for_each(|val| pow_test(*val, exponent, expected)));
+ }
+
+ fn test_sets_as_exponent(base: f64, sets: &[&[f64]], expected: f64) {
+ sets.iter()
+ .for_each(|s| s.iter().for_each(|val| pow_test(base, *val, expected)));
+ }
+
+ fn test_sets(sets: &[&[f64]], computed: &dyn Fn(f64) -> f64, expected: &dyn Fn(f64) -> f64) {
+ sets.iter().for_each(|s| {
+ s.iter().for_each(|val| {
+ let exp = expected(*val);
+ let res = computed(*val);
+
+ assert!(
+ if exp.is_nan() {
+ res.is_nan()
+ } else {
+ exp == res
+ },
+ "test for {} was {} instead of {}",
+ val,
+ res,
+ exp
+ );
+ })
+ });
+ }
+
+ #[test]
+ fn zero_as_exponent() {
+ test_sets_as_base(ALL, 0.0, 1.0);
+ test_sets_as_base(ALL, -0.0, 1.0);
+ }
+
+ #[test]
+ fn one_as_base() {
+ test_sets_as_exponent(1.0, ALL, 1.0);
+ }
+
+ #[test]
+ fn nan_inputs() {
+ // NAN as the base:
+ // (NAN ^ anything *but 0* should be NAN)
+ test_sets_as_exponent(NAN, &ALL[2..], NAN);
+
+ // NAN as the exponent:
+ // (anything *but 1* ^ NAN should be NAN)
+ test_sets_as_base(&ALL[..(ALL.len() - 2)], NAN, NAN);
+ }
+
+ #[test]
+ fn infinity_as_base() {
+ // Positive Infinity as the base:
+ // (+Infinity ^ positive anything but 0 and NAN should be +Infinity)
+ test_sets_as_exponent(INFINITY, &POS[1..], INFINITY);
+
+ // (+Infinity ^ negative anything except 0 and NAN should be 0.0)
+ test_sets_as_exponent(INFINITY, &NEG[1..], 0.0);
+
+ // Negative Infinity as the base:
+ // (-Infinity ^ positive odd ints should be -Infinity)
+ test_sets_as_exponent(NEG_INFINITY, &[POS_ODDS], NEG_INFINITY);
+
+ // (-Infinity ^ anything but odd ints should be == -0 ^ (-anything))
+ // We can lump in pos/neg odd ints here because they don't seem to
+ // cause panics (div by zero) in release mode (I think).
+ test_sets(ALL, &|v: f64| pow(NEG_INFINITY, v), &|v: f64| pow(-0.0, -v));
+ }
+
+ #[test]
+ fn infinity_as_exponent() {
+ // Positive/Negative base greater than 1:
+ // (pos/neg > 1 ^ Infinity should be Infinity - note this excludes NAN as the base)
+ test_sets_as_base(&ALL[5..(ALL.len() - 2)], INFINITY, INFINITY);
+
+ // (pos/neg > 1 ^ -Infinity should be 0.0)
+ test_sets_as_base(&ALL[5..ALL.len() - 2], NEG_INFINITY, 0.0);
+
+ // Positive/Negative base less than 1:
+ let base_below_one = &[POS_ZERO, NEG_ZERO, NEG_SMALL_FLOATS, POS_SMALL_FLOATS];
+
+ // (pos/neg < 1 ^ Infinity should be 0.0 - this also excludes NAN as the base)
+ test_sets_as_base(base_below_one, INFINITY, 0.0);
+
+ // (pos/neg < 1 ^ -Infinity should be Infinity)
+ test_sets_as_base(base_below_one, NEG_INFINITY, INFINITY);
+
+ // Positive/Negative 1 as the base:
+ // (pos/neg 1 ^ Infinity should be 1)
+ test_sets_as_base(&[NEG_ONE, POS_ONE], INFINITY, 1.0);
+
+ // (pos/neg 1 ^ -Infinity should be 1)
+ test_sets_as_base(&[NEG_ONE, POS_ONE], NEG_INFINITY, 1.0);
+ }
+
+ #[test]
+ fn zero_as_base() {
+ // Positive Zero as the base:
+ // (+0 ^ anything positive but 0 and NAN should be +0)
+ test_sets_as_exponent(0.0, &POS[1..], 0.0);
+
+ // (+0 ^ anything negative but 0 and NAN should be Infinity)
+ // (this should panic because we're dividing by zero)
+ test_sets_as_exponent(0.0, &NEG[1..], INFINITY);
+
+ // Negative Zero as the base:
+ // (-0 ^ anything positive but 0, NAN, and odd ints should be +0)
+ test_sets_as_exponent(-0.0, &POS[3..], 0.0);
+
+ // (-0 ^ anything negative but 0, NAN, and odd ints should be Infinity)
+ // (should panic because of divide by zero)
+ test_sets_as_exponent(-0.0, &NEG[3..], INFINITY);
+
+ // (-0 ^ positive odd ints should be -0)
+ test_sets_as_exponent(-0.0, &[POS_ODDS], -0.0);
+
+ // (-0 ^ negative odd ints should be -Infinity)
+ // (should panic because of divide by zero)
+ test_sets_as_exponent(-0.0, &[NEG_ODDS], NEG_INFINITY);
+ }
+
+ #[test]
+ fn special_cases() {
+ // One as the exponent:
+ // (anything ^ 1 should be anything - i.e. the base)
+ test_sets(ALL, &|v: f64| pow(v, 1.0), &|v: f64| v);
+
+ // Negative One as the exponent:
+ // (anything ^ -1 should be 1/anything)
+ test_sets(ALL, &|v: f64| pow(v, -1.0), &|v: f64| 1.0 / v);
+
+ // Factoring -1 out:
+ // (negative anything ^ integer should be (-1 ^ integer) * (positive anything ^ integer))
+ &[POS_ZERO, NEG_ZERO, POS_ONE, NEG_ONE, POS_EVENS, NEG_EVENS]
+ .iter()
+ .for_each(|int_set| {
+ int_set.iter().for_each(|int| {
+ test_sets(ALL, &|v: f64| pow(-v, *int), &|v: f64| {
+ pow(-1.0, *int) * pow(v, *int)
+ });
+ })
+ });
+
+ // Negative base (imaginary results):
+ // (-anything except 0 and Infinity ^ non-integer should be NAN)
+ &NEG[1..(NEG.len() - 1)].iter().for_each(|set| {
+ set.iter().for_each(|val| {
+ test_sets(&ALL[3..7], &|v: f64| pow(*val, v), &|_| NAN);
+ })
+ });
+ }
+
+ #[test]
+ fn normal_cases() {
+ assert_eq!(pow(2.0, 20.0), (1 << 20) as f64);
+ assert_eq!(pow(-1.0, 9.0), -1.0);
+ assert!(pow(-1.0, 2.2).is_nan());
+ assert!(pow(-1.0, -1.14).is_nan());
+ }
+}
diff --git a/src/math/powf.rs b/src/math/powf.rs
new file mode 100644
index 0000000..f3cf76f
--- /dev/null
+++ b/src/math/powf.rs
@@ -0,0 +1,342 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_powf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{fabsf, scalbnf, sqrtf};
+
+const BP: [f32; 2] = [1.0, 1.5];
+const DP_H: [f32; 2] = [0.0, 5.84960938e-01]; /* 0x3f15c000 */
+const DP_L: [f32; 2] = [0.0, 1.56322085e-06]; /* 0x35d1cfdc */
+const TWO24: f32 = 16777216.0; /* 0x4b800000 */
+const HUGE: f32 = 1.0e30;
+const TINY: f32 = 1.0e-30;
+const L1: f32 = 6.0000002384e-01; /* 0x3f19999a */
+const L2: f32 = 4.2857143283e-01; /* 0x3edb6db7 */
+const L3: f32 = 3.3333334327e-01; /* 0x3eaaaaab */
+const L4: f32 = 2.7272811532e-01; /* 0x3e8ba305 */
+const L5: f32 = 2.3066075146e-01; /* 0x3e6c3255 */
+const L6: f32 = 2.0697501302e-01; /* 0x3e53f142 */
+const P1: f32 = 1.6666667163e-01; /* 0x3e2aaaab */
+const P2: f32 = -2.7777778450e-03; /* 0xbb360b61 */
+const P3: f32 = 6.6137559770e-05; /* 0x388ab355 */
+const P4: f32 = -1.6533901999e-06; /* 0xb5ddea0e */
+const P5: f32 = 4.1381369442e-08; /* 0x3331bb4c */
+const LG2: f32 = 6.9314718246e-01; /* 0x3f317218 */
+const LG2_H: f32 = 6.93145752e-01; /* 0x3f317200 */
+const LG2_L: f32 = 1.42860654e-06; /* 0x35bfbe8c */
+const OVT: f32 = 4.2995665694e-08; /* -(128-log2(ovfl+.5ulp)) */
+const CP: f32 = 9.6179670095e-01; /* 0x3f76384f =2/(3ln2) */
+const CP_H: f32 = 9.6191406250e-01; /* 0x3f764000 =12b cp */
+const CP_L: f32 = -1.1736857402e-04; /* 0xb8f623c6 =tail of cp_h */
+const IVLN2: f32 = 1.4426950216e+00;
+const IVLN2_H: f32 = 1.4426879883e+00;
+const IVLN2_L: f32 = 7.0526075433e-06;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn powf(x: f32, y: f32) -> f32 {
+ let mut z: f32;
+ let mut ax: f32;
+ let z_h: f32;
+ let z_l: f32;
+ let mut p_h: f32;
+ let mut p_l: f32;
+ let y1: f32;
+ let mut t1: f32;
+ let t2: f32;
+ let mut r: f32;
+ let s: f32;
+ let mut sn: f32;
+ let mut t: f32;
+ let mut u: f32;
+ let mut v: f32;
+ let mut w: f32;
+ let i: i32;
+ let mut j: i32;
+ let mut k: i32;
+ let mut yisint: i32;
+ let mut n: i32;
+ let hx: i32;
+ let hy: i32;
+ let mut ix: i32;
+ let iy: i32;
+ let mut is: i32;
+
+ hx = x.to_bits() as i32;
+ hy = y.to_bits() as i32;
+
+ ix = hx & 0x7fffffff;
+ iy = hy & 0x7fffffff;
+
+ /* x**0 = 1, even if x is NaN */
+ if iy == 0 {
+ return 1.0;
+ }
+
+ /* 1**y = 1, even if y is NaN */
+ if hx == 0x3f800000 {
+ return 1.0;
+ }
+
+ /* NaN if either arg is NaN */
+ if ix > 0x7f800000 || iy > 0x7f800000 {
+ return x + y;
+ }
+
+ /* determine if y is an odd int when x < 0
+ * yisint = 0 ... y is not an integer
+ * yisint = 1 ... y is an odd int
+ * yisint = 2 ... y is an even int
+ */
+ yisint = 0;
+ if hx < 0 {
+ if iy >= 0x4b800000 {
+ yisint = 2; /* even integer y */
+ } else if iy >= 0x3f800000 {
+ k = (iy >> 23) - 0x7f; /* exponent */
+ j = iy >> (23 - k);
+ if (j << (23 - k)) == iy {
+ yisint = 2 - (j & 1);
+ }
+ }
+ }
+
+ /* special value of y */
+ if iy == 0x7f800000 {
+ /* y is +-inf */
+ if ix == 0x3f800000 {
+ /* (-1)**+-inf is 1 */
+ return 1.0;
+ } else if ix > 0x3f800000 {
+ /* (|x|>1)**+-inf = inf,0 */
+ return if hy >= 0 { y } else { 0.0 };
+ } else {
+ /* (|x|<1)**+-inf = 0,inf */
+ return if hy >= 0 { 0.0 } else { -y };
+ }
+ }
+ if iy == 0x3f800000 {
+ /* y is +-1 */
+ return if hy >= 0 { x } else { 1.0 / x };
+ }
+
+ if hy == 0x40000000 {
+ /* y is 2 */
+ return x * x;
+ }
+
+ if hy == 0x3f000000
+ /* y is 0.5 */
+ && hx >= 0
+ {
+ /* x >= +0 */
+ return sqrtf(x);
+ }
+
+ ax = fabsf(x);
+ /* special value of x */
+ if ix == 0x7f800000 || ix == 0 || ix == 0x3f800000 {
+ /* x is +-0,+-inf,+-1 */
+ z = ax;
+ if hy < 0 {
+ /* z = (1/|x|) */
+ z = 1.0 / z;
+ }
+
+ if hx < 0 {
+ if ((ix - 0x3f800000) | yisint) == 0 {
+ z = (z - z) / (z - z); /* (-1)**non-int is NaN */
+ } else if yisint == 1 {
+ z = -z; /* (x<0)**odd = -(|x|**odd) */
+ }
+ }
+ return z;
+ }
+
+ sn = 1.0; /* sign of result */
+ if hx < 0 {
+ if yisint == 0 {
+ /* (x<0)**(non-int) is NaN */
+ return (x - x) / (x - x);
+ }
+
+ if yisint == 1 {
+ /* (x<0)**(odd int) */
+ sn = -1.0;
+ }
+ }
+
+ /* |y| is HUGE */
+ if iy > 0x4d000000 {
+ /* if |y| > 2**27 */
+ /* over/underflow if x is not close to one */
+ if ix < 0x3f7ffff8 {
+ return if hy < 0 {
+ sn * HUGE * HUGE
+ } else {
+ sn * TINY * TINY
+ };
+ }
+
+ if ix > 0x3f800007 {
+ return if hy > 0 {
+ sn * HUGE * HUGE
+ } else {
+ sn * TINY * TINY
+ };
+ }
+
+ /* now |1-x| is TINY <= 2**-20, suffice to compute
+ log(x) by x-x^2/2+x^3/3-x^4/4 */
+ t = ax - 1.; /* t has 20 trailing zeros */
+ w = (t * t) * (0.5 - t * (0.333333333333 - t * 0.25));
+ u = IVLN2_H * t; /* IVLN2_H has 16 sig. bits */
+ v = t * IVLN2_L - w * IVLN2;
+ t1 = u + v;
+ is = t1.to_bits() as i32;
+ t1 = f32::from_bits(is as u32 & 0xfffff000);
+ t2 = v - (t1 - u);
+ } else {
+ let mut s2: f32;
+ let mut s_h: f32;
+ let s_l: f32;
+ let mut t_h: f32;
+ let mut t_l: f32;
+
+ n = 0;
+ /* take care subnormal number */
+ if ix < 0x00800000 {
+ ax *= TWO24;
+ n -= 24;
+ ix = ax.to_bits() as i32;
+ }
+ n += ((ix) >> 23) - 0x7f;
+ j = ix & 0x007fffff;
+ /* determine interval */
+ ix = j | 0x3f800000; /* normalize ix */
+ if j <= 0x1cc471 {
+ /* |x|<sqrt(3/2) */
+ k = 0;
+ } else if j < 0x5db3d7 {
+ /* |x|<sqrt(3) */
+ k = 1;
+ } else {
+ k = 0;
+ n += 1;
+ ix -= 0x00800000;
+ }
+ ax = f32::from_bits(ix as u32);
+
+ /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+ u = ax - BP[k as usize]; /* bp[0]=1.0, bp[1]=1.5 */
+ v = 1.0 / (ax + BP[k as usize]);
+ s = u * v;
+ s_h = s;
+ is = s_h.to_bits() as i32;
+ s_h = f32::from_bits(is as u32 & 0xfffff000);
+ /* t_h=ax+bp[k] High */
+ is = (((ix as u32 >> 1) & 0xfffff000) | 0x20000000) as i32;
+ t_h = f32::from_bits(is as u32 + 0x00400000 + ((k as u32) << 21));
+ t_l = ax - (t_h - BP[k as usize]);
+ s_l = v * ((u - s_h * t_h) - s_h * t_l);
+ /* compute log(ax) */
+ s2 = s * s;
+ r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
+ r += s_l * (s_h + s);
+ s2 = s_h * s_h;
+ t_h = 3.0 + s2 + r;
+ is = t_h.to_bits() as i32;
+ t_h = f32::from_bits(is as u32 & 0xfffff000);
+ t_l = r - ((t_h - 3.0) - s2);
+ /* u+v = s*(1+...) */
+ u = s_h * t_h;
+ v = s_l * t_h + t_l * s;
+ /* 2/(3log2)*(s+...) */
+ p_h = u + v;
+ is = p_h.to_bits() as i32;
+ p_h = f32::from_bits(is as u32 & 0xfffff000);
+ p_l = v - (p_h - u);
+ z_h = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */
+ z_l = CP_L * p_h + p_l * CP + DP_L[k as usize];
+ /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+ t = n as f32;
+ t1 = ((z_h + z_l) + DP_H[k as usize]) + t;
+ is = t1.to_bits() as i32;
+ t1 = f32::from_bits(is as u32 & 0xfffff000);
+ t2 = z_l - (((t1 - t) - DP_H[k as usize]) - z_h);
+ };
+
+ /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+ is = y.to_bits() as i32;
+ y1 = f32::from_bits(is as u32 & 0xfffff000);
+ p_l = (y - y1) * t1 + y * t2;
+ p_h = y1 * t1;
+ z = p_l + p_h;
+ j = z.to_bits() as i32;
+ if j > 0x43000000 {
+ /* if z > 128 */
+ return sn * HUGE * HUGE; /* overflow */
+ } else if j == 0x43000000 {
+ /* if z == 128 */
+ if p_l + OVT > z - p_h {
+ return sn * HUGE * HUGE; /* overflow */
+ }
+ } else if (j & 0x7fffffff) > 0x43160000 {
+ /* z < -150 */
+ // FIXME: check should be (uint32_t)j > 0xc3160000
+ return sn * TINY * TINY; /* underflow */
+ } else if j as u32 == 0xc3160000
+ /* z == -150 */
+ && p_l <= z - p_h
+ {
+ return sn * TINY * TINY; /* underflow */
+ }
+
+ /*
+ * compute 2**(p_h+p_l)
+ */
+ i = j & 0x7fffffff;
+ k = (i >> 23) - 0x7f;
+ n = 0;
+ if i > 0x3f000000 {
+ /* if |z| > 0.5, set n = [z+0.5] */
+ n = j + (0x00800000 >> (k + 1));
+ k = ((n & 0x7fffffff) >> 23) - 0x7f; /* new k for n */
+ t = f32::from_bits(n as u32 & !(0x007fffff >> k));
+ n = ((n & 0x007fffff) | 0x00800000) >> (23 - k);
+ if j < 0 {
+ n = -n;
+ }
+ p_h -= t;
+ }
+ t = p_l + p_h;
+ is = t.to_bits() as i32;
+ t = f32::from_bits(is as u32 & 0xffff8000);
+ u = t * LG2_H;
+ v = (p_l - (t - p_h)) * LG2 + t * LG2_L;
+ z = u + v;
+ w = v - (z - u);
+ t = z * z;
+ t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
+ r = (z * t1) / (t1 - 2.0) - (w + z * w);
+ z = 1.0 - (r - z);
+ j = z.to_bits() as i32;
+ j += n << 23;
+ if (j >> 23) <= 0 {
+ /* subnormal output */
+ z = scalbnf(z, n);
+ } else {
+ z = f32::from_bits(j as u32);
+ }
+ sn * z
+}
diff --git a/src/math/rem_pio2.rs b/src/math/rem_pio2.rs
new file mode 100644
index 0000000..6b7dbd3
--- /dev/null
+++ b/src/math/rem_pio2.rs
@@ -0,0 +1,220 @@
+// origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c
+//
+// ====================================================
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+//
+// Developed at SunPro, a Sun Microsystems, Inc. business.
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+//
+// Optimized by Bruce D. Evans. */
+use super::rem_pio2_large;
+
+// #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
+// #define EPS DBL_EPSILON
+const EPS: f64 = 2.2204460492503131e-16;
+// #elif FLT_EVAL_METHOD==2
+// #define EPS LDBL_EPSILON
+// #endif
+
+// TODO: Support FLT_EVAL_METHOD?
+
+const TO_INT: f64 = 1.5 / EPS;
+/// 53 bits of 2/pi
+const INV_PIO2: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
+/// first 33 bits of pi/2
+const PIO2_1: f64 = 1.57079632673412561417e+00; /* 0x3FF921FB, 0x54400000 */
+/// pi/2 - PIO2_1
+const PIO2_1T: f64 = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
+/// second 33 bits of pi/2
+const PIO2_2: f64 = 6.07710050630396597660e-11; /* 0x3DD0B461, 0x1A600000 */
+/// pi/2 - (PIO2_1+PIO2_2)
+const PIO2_2T: f64 = 2.02226624879595063154e-21; /* 0x3BA3198A, 0x2E037073 */
+/// third 33 bits of pi/2
+const PIO2_3: f64 = 2.02226624871116645580e-21; /* 0x3BA3198A, 0x2E000000 */
+/// pi/2 - (PIO2_1+PIO2_2+PIO2_3)
+const PIO2_3T: f64 = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
+
+// return the remainder of x rem pi/2 in y[0]+y[1]
+// use rem_pio2_large() for large x
+//
+// caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn rem_pio2(x: f64) -> (i32, f64, f64) {
+ let x1p24 = f64::from_bits(0x4170000000000000);
+
+ let sign = (f64::to_bits(x) >> 63) as i32;
+ let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
+
+ fn medium(x: f64, ix: u32) -> (i32, f64, f64) {
+ /* rint(x/(pi/2)), Assume round-to-nearest. */
+ let f_n = x as f64 * INV_PIO2 + TO_INT - TO_INT;
+ let n = f_n as i32;
+ let mut r = x - f_n * PIO2_1;
+ let mut w = f_n * PIO2_1T; /* 1st round, good to 85 bits */
+ let mut y0 = r - w;
+ let ui = f64::to_bits(y0);
+ let ey = (ui >> 52) as i32 & 0x7ff;
+ let ex = (ix >> 20) as i32;
+ if ex - ey > 16 {
+ /* 2nd round, good to 118 bits */
+ let t = r;
+ w = f_n * PIO2_2;
+ r = t - w;
+ w = f_n * PIO2_2T - ((t - r) - w);
+ y0 = r - w;
+ let ey = (f64::to_bits(y0) >> 52) as i32 & 0x7ff;
+ if ex - ey > 49 {
+ /* 3rd round, good to 151 bits, covers all cases */
+ let t = r;
+ w = f_n * PIO2_3;
+ r = t - w;
+ w = f_n * PIO2_3T - ((t - r) - w);
+ y0 = r - w;
+ }
+ }
+ let y1 = (r - y0) - w;
+ (n, y0, y1)
+ }
+
+ if ix <= 0x400f6a7a {
+ /* |x| ~<= 5pi/4 */
+ if (ix & 0xfffff) == 0x921fb {
+ /* |x| ~= pi/2 or 2pi/2 */
+ return medium(x, ix); /* cancellation -- use medium case */
+ }
+ if ix <= 0x4002d97c {
+ /* |x| ~<= 3pi/4 */
+ if sign == 0 {
+ let z = x - PIO2_1; /* one round good to 85 bits */
+ let y0 = z - PIO2_1T;
+ let y1 = (z - y0) - PIO2_1T;
+ return (1, y0, y1);
+ } else {
+ let z = x + PIO2_1;
+ let y0 = z + PIO2_1T;
+ let y1 = (z - y0) + PIO2_1T;
+ return (-1, y0, y1);
+ }
+ } else if sign == 0 {
+ let z = x - 2.0 * PIO2_1;
+ let y0 = z - 2.0 * PIO2_1T;
+ let y1 = (z - y0) - 2.0 * PIO2_1T;
+ return (2, y0, y1);
+ } else {
+ let z = x + 2.0 * PIO2_1;
+ let y0 = z + 2.0 * PIO2_1T;
+ let y1 = (z - y0) + 2.0 * PIO2_1T;
+ return (-2, y0, y1);
+ }
+ }
+ if ix <= 0x401c463b {
+ /* |x| ~<= 9pi/4 */
+ if ix <= 0x4015fdbc {
+ /* |x| ~<= 7pi/4 */
+ if ix == 0x4012d97c {
+ /* |x| ~= 3pi/2 */
+ return medium(x, ix);
+ }
+ if sign == 0 {
+ let z = x - 3.0 * PIO2_1;
+ let y0 = z - 3.0 * PIO2_1T;
+ let y1 = (z - y0) - 3.0 * PIO2_1T;
+ return (3, y0, y1);
+ } else {
+ let z = x + 3.0 * PIO2_1;
+ let y0 = z + 3.0 * PIO2_1T;
+ let y1 = (z - y0) + 3.0 * PIO2_1T;
+ return (-3, y0, y1);
+ }
+ } else {
+ if ix == 0x401921fb {
+ /* |x| ~= 4pi/2 */
+ return medium(x, ix);
+ }
+ if sign == 0 {
+ let z = x - 4.0 * PIO2_1;
+ let y0 = z - 4.0 * PIO2_1T;
+ let y1 = (z - y0) - 4.0 * PIO2_1T;
+ return (4, y0, y1);
+ } else {
+ let z = x + 4.0 * PIO2_1;
+ let y0 = z + 4.0 * PIO2_1T;
+ let y1 = (z - y0) + 4.0 * PIO2_1T;
+ return (-4, y0, y1);
+ }
+ }
+ }
+ if ix < 0x413921fb {
+ /* |x| ~< 2^20*(pi/2), medium size */
+ return medium(x, ix);
+ }
+ /*
+ * all other (large) arguments
+ */
+ if ix >= 0x7ff00000 {
+ /* x is inf or NaN */
+ let y0 = x - x;
+ let y1 = y0;
+ return (0, y0, y1);
+ }
+ /* set z = scalbn(|x|,-ilogb(x)+23) */
+ let mut ui = f64::to_bits(x);
+ ui &= (!1) >> 12;
+ ui |= (0x3ff + 23) << 52;
+ let mut z = f64::from_bits(ui);
+ let mut tx = [0.0; 3];
+ for i in 0..2 {
+ tx[i] = z as i32 as f64;
+ z = (z - tx[i]) * x1p24;
+ }
+ tx[2] = z;
+ /* skip zero terms, first term is non-zero */
+ let mut i = 2;
+ while i != 0 && tx[i] == 0.0 {
+ i -= 1;
+ }
+ let mut ty = [0.0; 3];
+ let n = rem_pio2_large(&tx[..=i], &mut ty, ((ix as i32) >> 20) - (0x3ff + 23), 1);
+ if sign != 0 {
+ return (-n, -ty[0], -ty[1]);
+ }
+ (n, ty[0], ty[1])
+}
+
+#[cfg(test)]
+mod tests {
+ use super::rem_pio2;
+
+ #[test]
+ fn test_near_pi() {
+ assert_eq!(
+ rem_pio2(3.141592025756836),
+ (2, -6.278329573009626e-7, -2.1125998133974653e-23)
+ );
+ assert_eq!(
+ rem_pio2(3.141592033207416),
+ (2, -6.20382377148128e-7, -2.1125998133974653e-23)
+ );
+ assert_eq!(
+ rem_pio2(3.141592144966125),
+ (2, -5.086236681942706e-7, -2.1125998133974653e-23)
+ );
+ assert_eq!(
+ rem_pio2(3.141592979431152),
+ (2, 3.2584135866119817e-7, -2.1125998133974653e-23)
+ );
+ }
+
+ #[test]
+ fn test_overflow_b9b847() {
+ let _ = rem_pio2(-3054214.5490637687);
+ }
+
+ #[test]
+ fn test_overflow_4747b9() {
+ let _ = rem_pio2(917340800458.2274);
+ }
+}
diff --git a/src/math/rem_pio2_large.rs b/src/math/rem_pio2_large.rs
new file mode 100644
index 0000000..002ce2e
--- /dev/null
+++ b/src/math/rem_pio2_large.rs
@@ -0,0 +1,470 @@
+#![allow(unused_unsafe)]
+/* origin: FreeBSD /usr/src/lib/msun/src/k_rem_pio2.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::floor;
+use super::scalbn;
+
+// initial value for jk
+const INIT_JK: [usize; 4] = [3, 4, 4, 6];
+
+// Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
+//
+// integer array, contains the (24*i)-th to (24*i+23)-th
+// bit of 2/pi after binary point. The corresponding
+// floating value is
+//
+// ipio2[i] * 2^(-24(i+1)).
+//
+// NB: This table must have at least (e0-3)/24 + jk terms.
+// For quad precision (e0 <= 16360, jk = 6), this is 686.
+#[cfg(target_pointer_width = "32")]
+const IPIO2: [i32; 66] = [
+ 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, 0x439041, 0xFE5163,
+ 0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
+ 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C,
+ 0x845F8B, 0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
+ 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 0xF17B3D, 0x0739F7, 0x8A5292,
+ 0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
+ 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA,
+ 0x73A8C9, 0x60E27B, 0xC08C6B,
+];
+
+#[cfg(target_pointer_width = "64")]
+const IPIO2: [i32; 690] = [
+ 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, 0x439041, 0xFE5163,
+ 0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
+ 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C,
+ 0x845F8B, 0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
+ 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 0xF17B3D, 0x0739F7, 0x8A5292,
+ 0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
+ 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA,
+ 0x73A8C9, 0x60E27B, 0xC08C6B, 0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6,
+ 0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2, 0xDE4F98, 0x327DBB, 0xC33D26,
+ 0xEF6B1E, 0x5EF89F, 0x3A1F35, 0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30,
+ 0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C, 0x467D86, 0x2D71E3, 0x9AC69B,
+ 0x006233, 0x7CD2B4, 0x97A7B4, 0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770,
+ 0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7, 0xCB2324, 0x778AD6, 0x23545A,
+ 0xB91F00, 0x1B0AF1, 0xDFCE19, 0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522,
+ 0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16, 0xDE3B58, 0x929BDE, 0x2822D2,
+ 0xE88628, 0x4D58E2, 0x32CAC6, 0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E,
+ 0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48, 0xD36710, 0xD8DDAA, 0x425FAE,
+ 0xCE616A, 0xA4280A, 0xB499D3, 0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF,
+ 0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55, 0x36D9CA, 0xD2A828, 0x8D61C2,
+ 0x77C912, 0x142604, 0x9B4612, 0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929,
+ 0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC, 0xC3E7B3, 0x28F8C7, 0x940593,
+ 0x3E71C1, 0xB3092E, 0xF3450B, 0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C,
+ 0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4, 0x9794E8, 0x84E6E2, 0x973199,
+ 0x6BED88, 0x365F5F, 0x0EFDBB, 0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC,
+ 0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C, 0x90AA47, 0x02E774, 0x24D6BD,
+ 0xA67DF7, 0x72486E, 0xEF169F, 0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5,
+ 0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437, 0x10D86D, 0x324832, 0x754C5B,
+ 0xD4714E, 0x6E5445, 0xC1090B, 0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA,
+ 0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD, 0x6AE290, 0x89D988, 0x50722C,
+ 0xBEA404, 0x940777, 0x7030F3, 0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3,
+ 0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717, 0x3BDF08, 0x2B3715, 0xA0805C,
+ 0x93805A, 0x921110, 0xD8E80F, 0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61,
+ 0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB, 0xAA140A, 0x2F2689, 0x768364,
+ 0x333B09, 0x1A940E, 0xAA3A51, 0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0,
+ 0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C, 0x5BC3D8, 0xC492F5, 0x4BADC6,
+ 0xA5CA4E, 0xCD37A7, 0x36A9E6, 0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC,
+ 0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED, 0x306529, 0xBF5657, 0x3AFF47,
+ 0xB9F96A, 0xF3BE75, 0xDF9328, 0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D,
+ 0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0, 0xA8654F, 0xA5C1D2, 0x0F3F0B,
+ 0xCD785B, 0x76F923, 0x048B7B, 0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4,
+ 0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3, 0xDA4886, 0xA05DF7, 0xF480C6,
+ 0x2FF0AC, 0x9AECDD, 0xBC5C3F, 0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD,
+ 0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B, 0x2A1216, 0x2DB7DC, 0xFDE5FA,
+ 0xFEDB89, 0xFDBE89, 0x6C76E4, 0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761,
+ 0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31, 0x48D784, 0x16DF30, 0x432DC7,
+ 0x356125, 0xCE70C9, 0xB8CB30, 0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262,
+ 0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E, 0xC4F133, 0x5F6E13, 0xE4305D,
+ 0xA92E85, 0xC3B21D, 0x3632A1, 0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C,
+ 0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4, 0xCBDA11, 0xD0BE7D, 0xC1DB9B,
+ 0xBD17AB, 0x81A2CA, 0x5C6A08, 0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196,
+ 0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9, 0x4F6A68, 0xA82A4A, 0x5AC44F,
+ 0xBCF82D, 0x985AD7, 0x95C7F4, 0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC,
+ 0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C, 0xD0C0B2, 0x485551, 0x0EFB1E,
+ 0xC37295, 0x3B06A3, 0x3540C0, 0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C,
+ 0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0, 0x3C3ABA, 0x461846, 0x5F7555,
+ 0xF5BDD2, 0xC6926E, 0x5D2EAC, 0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22,
+ 0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893, 0x745D7C, 0xB2AD6B, 0x9D6ECD,
+ 0x7B723E, 0x6A11C6, 0xA9CFF7, 0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5,
+ 0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F, 0xBEFDFD, 0xEF4556, 0x367ED9,
+ 0x13D9EC, 0xB9BA8B, 0xFC97C4, 0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF,
+ 0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B, 0x9C2A3E, 0xCC5F11, 0x4A0BFD,
+ 0xFBF4E1, 0x6D3B8E, 0x2C86E2, 0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138,
+ 0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E, 0xCC2254, 0xDC552A, 0xD6C6C0,
+ 0x96190B, 0xB8701A, 0x649569, 0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34,
+ 0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9, 0x9B5861, 0xBC57E1, 0xC68351,
+ 0x103ED8, 0x4871DD, 0xDD1C2D, 0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F,
+ 0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855, 0x382682, 0x9BE7CA, 0xA40D51,
+ 0xB13399, 0x0ED7A9, 0x480569, 0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B,
+ 0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE, 0x5FD45E, 0xA4677B, 0x7AACBA,
+ 0xA2F655, 0x23882B, 0x55BA41, 0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49,
+ 0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F, 0xAE5ADB, 0x86C547, 0x624385,
+ 0x3B8621, 0x94792C, 0x876110, 0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8,
+ 0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365, 0xB1933D, 0x0B7CBD, 0xDC51A4,
+ 0x63DD27, 0xDDE169, 0x19949A, 0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270,
+ 0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5, 0x4D7E6F, 0x5119A5, 0xABF9B5,
+ 0xD6DF82, 0x61DD96, 0x023616, 0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B,
+ 0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0,
+];
+
+const PIO2: [f64; 8] = [
+ 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
+ 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
+ 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
+ 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
+ 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
+ 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
+ 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
+ 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
+];
+
+// fn rem_pio2_large(x : &[f64], y : &mut [f64], e0 : i32, prec : usize) -> i32
+//
+// Input parameters:
+// x[] The input value (must be positive) is broken into nx
+// pieces of 24-bit integers in double precision format.
+// x[i] will be the i-th 24 bit of x. The scaled exponent
+// of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
+// match x's up to 24 bits.
+//
+// Example of breaking a double positive z into x[0]+x[1]+x[2]:
+// e0 = ilogb(z)-23
+// z = scalbn(z,-e0)
+// for i = 0,1,2
+// x[i] = floor(z)
+// z = (z-x[i])*2**24
+//
+// y[] ouput result in an array of double precision numbers.
+// The dimension of y[] is:
+// 24-bit precision 1
+// 53-bit precision 2
+// 64-bit precision 2
+// 113-bit precision 3
+// The actual value is the sum of them. Thus for 113-bit
+// precison, one may have to do something like:
+//
+// long double t,w,r_head, r_tail;
+// t = (long double)y[2] + (long double)y[1];
+// w = (long double)y[0];
+// r_head = t+w;
+// r_tail = w - (r_head - t);
+//
+// e0 The exponent of x[0]. Must be <= 16360 or you need to
+// expand the ipio2 table.
+//
+// prec an integer indicating the precision:
+// 0 24 bits (single)
+// 1 53 bits (double)
+// 2 64 bits (extended)
+// 3 113 bits (quad)
+//
+// Here is the description of some local variables:
+//
+// jk jk+1 is the initial number of terms of ipio2[] needed
+// in the computation. The minimum and recommended value
+// for jk is 3,4,4,6 for single, double, extended, and quad.
+// jk+1 must be 2 larger than you might expect so that our
+// recomputation test works. (Up to 24 bits in the integer
+// part (the 24 bits of it that we compute) and 23 bits in
+// the fraction part may be lost to cancelation before we
+// recompute.)
+//
+// jz local integer variable indicating the number of
+// terms of ipio2[] used.
+//
+// jx nx - 1
+//
+// jv index for pointing to the suitable ipio2[] for the
+// computation. In general, we want
+// ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
+// is an integer. Thus
+// e0-3-24*jv >= 0 or (e0-3)/24 >= jv
+// Hence jv = max(0,(e0-3)/24).
+//
+// jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
+//
+// q[] double array with integral value, representing the
+// 24-bits chunk of the product of x and 2/pi.
+//
+// q0 the corresponding exponent of q[0]. Note that the
+// exponent for q[i] would be q0-24*i.
+//
+// PIo2[] double precision array, obtained by cutting pi/2
+// into 24 bits chunks.
+//
+// f[] ipio2[] in floating point
+//
+// iq[] integer array by breaking up q[] in 24-bits chunk.
+//
+// fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
+//
+// ih integer. If >0 it indicates q[] is >= 0.5, hence
+// it also indicates the *sign* of the result.
+
+/// Return the last three digits of N with y = x - N*pi/2
+/// so that |y| < pi/2.
+///
+/// The method is to compute the integer (mod 8) and fraction parts of
+/// (2/pi)*x without doing the full multiplication. In general we
+/// skip the part of the product that are known to be a huge integer (
+/// more accurately, = 0 mod 8 ). Thus the number of operations are
+/// independent of the exponent of the input.
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn rem_pio2_large(x: &[f64], y: &mut [f64], e0: i32, prec: usize) -> i32 {
+ let x1p24 = f64::from_bits(0x4170000000000000); // 0x1p24 === 2 ^ 24
+ let x1p_24 = f64::from_bits(0x3e70000000000000); // 0x1p_24 === 2 ^ (-24)
+
+ #[cfg(all(target_pointer_width = "64", feature = "checked"))]
+ assert!(e0 <= 16360);
+
+ let nx = x.len();
+
+ let mut fw: f64;
+ let mut n: i32;
+ let mut ih: i32;
+ let mut z: f64;
+ let mut f: [f64; 20] = [0.; 20];
+ let mut fq: [f64; 20] = [0.; 20];
+ let mut q: [f64; 20] = [0.; 20];
+ let mut iq: [i32; 20] = [0; 20];
+
+ /* initialize jk*/
+ let jk = INIT_JK[prec];
+ let jp = jk;
+
+ /* determine jx,jv,q0, note that 3>q0 */
+ let jx = nx - 1;
+ let mut jv = (e0 - 3) / 24;
+ if jv < 0 {
+ jv = 0;
+ }
+ let mut q0 = e0 - 24 * (jv + 1);
+ let jv = jv as usize;
+
+ /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
+ let mut j = (jv as i32) - (jx as i32);
+ let m = jx + jk;
+ for i in 0..=m {
+ i!(f, i, =, if j < 0 {
+ 0.
+ } else {
+ i!(IPIO2, j as usize) as f64
+ });
+ j += 1;
+ }
+
+ /* compute q[0],q[1],...q[jk] */
+ for i in 0..=jk {
+ fw = 0f64;
+ for j in 0..=jx {
+ fw += i!(x, j) * i!(f, jx + i - j);
+ }
+ i!(q, i, =, fw);
+ }
+
+ let mut jz = jk;
+
+ 'recompute: loop {
+ /* distill q[] into iq[] reversingly */
+ let mut i = 0i32;
+ z = i!(q, jz);
+ for j in (1..=jz).rev() {
+ fw = (x1p_24 * z) as i32 as f64;
+ i!(iq, i as usize, =, (z - x1p24 * fw) as i32);
+ z = i!(q, j - 1) + fw;
+ i += 1;
+ }
+
+ /* compute n */
+ z = scalbn(z, q0); /* actual value of z */
+ z -= 8.0 * floor(z * 0.125); /* trim off integer >= 8 */
+ n = z as i32;
+ z -= n as f64;
+ ih = 0;
+ if q0 > 0 {
+ /* need iq[jz-1] to determine n */
+ i = i!(iq, jz - 1) >> (24 - q0);
+ n += i;
+ i!(iq, jz - 1, -=, i << (24 - q0));
+ ih = i!(iq, jz - 1) >> (23 - q0);
+ } else if q0 == 0 {
+ ih = i!(iq, jz - 1) >> 23;
+ } else if z >= 0.5 {
+ ih = 2;
+ }
+
+ if ih > 0 {
+ /* q > 0.5 */
+ n += 1;
+ let mut carry = 0i32;
+ for i in 0..jz {
+ /* compute 1-q */
+ let j = i!(iq, i);
+ if carry == 0 {
+ if j != 0 {
+ carry = 1;
+ i!(iq, i, =, 0x1000000 - j);
+ }
+ } else {
+ i!(iq, i, =, 0xffffff - j);
+ }
+ }
+ if q0 > 0 {
+ /* rare case: chance is 1 in 12 */
+ match q0 {
+ 1 => {
+ i!(iq, jz - 1, &=, 0x7fffff);
+ }
+ 2 => {
+ i!(iq, jz - 1, &=, 0x3fffff);
+ }
+ _ => {}
+ }
+ }
+ if ih == 2 {
+ z = 1. - z;
+ if carry != 0 {
+ z -= scalbn(1., q0);
+ }
+ }
+ }
+
+ /* check if recomputation is needed */
+ if z == 0. {
+ let mut j = 0;
+ for i in (jk..=jz - 1).rev() {
+ j |= i!(iq, i);
+ }
+ if j == 0 {
+ /* need recomputation */
+ let mut k = 1;
+ while i!(iq, jk - k, ==, 0) {
+ k += 1; /* k = no. of terms needed */
+ }
+
+ for i in (jz + 1)..=(jz + k) {
+ /* add q[jz+1] to q[jz+k] */
+ i!(f, jx + i, =, i!(IPIO2, jv + i) as f64);
+ fw = 0f64;
+ for j in 0..=jx {
+ fw += i!(x, j) * i!(f, jx + i - j);
+ }
+ i!(q, i, =, fw);
+ }
+ jz += k;
+ continue 'recompute;
+ }
+ }
+
+ break;
+ }
+
+ /* chop off zero terms */
+ if z == 0. {
+ jz -= 1;
+ q0 -= 24;
+ while i!(iq, jz) == 0 {
+ jz -= 1;
+ q0 -= 24;
+ }
+ } else {
+ /* break z into 24-bit if necessary */
+ z = scalbn(z, -q0);
+ if z >= x1p24 {
+ fw = (x1p_24 * z) as i32 as f64;
+ i!(iq, jz, =, (z - x1p24 * fw) as i32);
+ jz += 1;
+ q0 += 24;
+ i!(iq, jz, =, fw as i32);
+ } else {
+ i!(iq, jz, =, z as i32);
+ }
+ }
+
+ /* convert integer "bit" chunk to floating-point value */
+ fw = scalbn(1., q0);
+ for i in (0..=jz).rev() {
+ i!(q, i, =, fw * (i!(iq, i) as f64));
+ fw *= x1p_24;
+ }
+
+ /* compute PIo2[0,...,jp]*q[jz,...,0] */
+ for i in (0..=jz).rev() {
+ fw = 0f64;
+ let mut k = 0;
+ while (k <= jp) && (k <= jz - i) {
+ fw += i!(PIO2, k) * i!(q, i + k);
+ k += 1;
+ }
+ i!(fq, jz - i, =, fw);
+ }
+
+ /* compress fq[] into y[] */
+ match prec {
+ 0 => {
+ fw = 0f64;
+ for i in (0..=jz).rev() {
+ fw += i!(fq, i);
+ }
+ i!(y, 0, =, if ih == 0 { fw } else { -fw });
+ }
+ 1 | 2 => {
+ fw = 0f64;
+ for i in (0..=jz).rev() {
+ fw += i!(fq, i);
+ }
+ // TODO: drop excess precision here once double_t is used
+ fw = fw as f64;
+ i!(y, 0, =, if ih == 0 { fw } else { -fw });
+ fw = i!(fq, 0) - fw;
+ for i in 1..=jz {
+ fw += i!(fq, i);
+ }
+ i!(y, 1, =, if ih == 0 { fw } else { -fw });
+ }
+ 3 => {
+ /* painful */
+ for i in (1..=jz).rev() {
+ fw = i!(fq, i - 1) + i!(fq, i);
+ i!(fq, i, +=, i!(fq, i - 1) - fw);
+ i!(fq, i - 1, =, fw);
+ }
+ for i in (2..=jz).rev() {
+ fw = i!(fq, i - 1) + i!(fq, i);
+ i!(fq, i, +=, i!(fq, i - 1) - fw);
+ i!(fq, i - 1, =, fw);
+ }
+ fw = 0f64;
+ for i in (2..=jz).rev() {
+ fw += i!(fq, i);
+ }
+ if ih == 0 {
+ i!(y, 0, =, i!(fq, 0));
+ i!(y, 1, =, i!(fq, 1));
+ i!(y, 2, =, fw);
+ } else {
+ i!(y, 0, =, -i!(fq, 0));
+ i!(y, 1, =, -i!(fq, 1));
+ i!(y, 2, =, -fw);
+ }
+ }
+ #[cfg(debug_assertions)]
+ _ => unreachable!(),
+ #[cfg(not(debug_assertions))]
+ _ => {}
+ }
+ n & 7
+}
diff --git a/src/math/rem_pio2f.rs b/src/math/rem_pio2f.rs
new file mode 100644
index 0000000..5d392ba
--- /dev/null
+++ b/src/math/rem_pio2f.rs
@@ -0,0 +1,62 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Debugged and optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::rem_pio2_large;
+
+use core::f64;
+
+const TOINT: f64 = 1.5 / f64::EPSILON;
+
+/// 53 bits of 2/pi
+const INV_PIO2: f64 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
+/// first 25 bits of pi/2
+const PIO2_1: f64 = 1.57079631090164184570e+00; /* 0x3FF921FB, 0x50000000 */
+/// pi/2 - pio2_1
+const PIO2_1T: f64 = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
+
+/// Return the remainder of x rem pi/2 in *y
+///
+/// use double precision for everything except passing x
+/// use __rem_pio2_large() for large x
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub(crate) fn rem_pio2f(x: f32) -> (i32, f64) {
+ let x64 = x as f64;
+
+ let mut tx: [f64; 1] = [0.];
+ let mut ty: [f64; 1] = [0.];
+
+ let ix = x.to_bits() & 0x7fffffff;
+ /* 25+53 bit pi is good enough for medium size */
+ if ix < 0x4dc90fdb {
+ /* |x| ~< 2^28*(pi/2), medium size */
+ /* Use a specialized rint() to get fn. Assume round-to-nearest. */
+ let f_n = x64 * INV_PIO2 + TOINT - TOINT;
+ return (f_n as i32, x64 - f_n * PIO2_1 - f_n * PIO2_1T);
+ }
+ if ix >= 0x7f800000 {
+ /* x is inf or NaN */
+ return (0, x64 - x64);
+ }
+ /* scale x into [2^23, 2^24-1] */
+ let sign = (x.to_bits() >> 31) != 0;
+ let e0 = ((ix >> 23) - (0x7f + 23)) as i32; /* e0 = ilogb(|x|)-23, positive */
+ tx[0] = f32::from_bits(ix - (e0 << 23) as u32) as f64;
+ let n = rem_pio2_large(&tx, &mut ty, e0, 0);
+ if sign {
+ return (-n, -ty[0]);
+ }
+ (n, ty[0])
+}
diff --git a/src/math/remainder.rs b/src/math/remainder.rs
new file mode 100644
index 0000000..9e966c9
--- /dev/null
+++ b/src/math/remainder.rs
@@ -0,0 +1,5 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn remainder(x: f64, y: f64) -> f64 {
+ let (result, _) = super::remquo(x, y);
+ result
+}
diff --git a/src/math/remainderf.rs b/src/math/remainderf.rs
new file mode 100644
index 0000000..b1407cf
--- /dev/null
+++ b/src/math/remainderf.rs
@@ -0,0 +1,5 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn remainderf(x: f32, y: f32) -> f32 {
+ let (result, _) = super::remquof(x, y);
+ result
+}
diff --git a/src/math/remquo.rs b/src/math/remquo.rs
new file mode 100644
index 0000000..0afd1f7
--- /dev/null
+++ b/src/math/remquo.rs
@@ -0,0 +1,110 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn remquo(mut x: f64, mut y: f64) -> (f64, i32) {
+ let ux: u64 = x.to_bits();
+ let mut uy: u64 = y.to_bits();
+ let mut ex = ((ux >> 52) & 0x7ff) as i32;
+ let mut ey = ((uy >> 52) & 0x7ff) as i32;
+ let sx = (ux >> 63) != 0;
+ let sy = (uy >> 63) != 0;
+ let mut q: u32;
+ let mut i: u64;
+ let mut uxi: u64 = ux;
+
+ if (uy << 1) == 0 || y.is_nan() || ex == 0x7ff {
+ return ((x * y) / (x * y), 0);
+ }
+ if (ux << 1) == 0 {
+ return (x, 0);
+ }
+
+ /* normalize x and y */
+ if ex == 0 {
+ i = uxi << 12;
+ while (i >> 63) == 0 {
+ ex -= 1;
+ i <<= 1;
+ }
+ uxi <<= -ex + 1;
+ } else {
+ uxi &= (!0) >> 12;
+ uxi |= 1 << 52;
+ }
+ if ey == 0 {
+ i = uy << 12;
+ while (i >> 63) == 0 {
+ ey -= 1;
+ i <<= 1;
+ }
+ uy <<= -ey + 1;
+ } else {
+ uy &= (!0) >> 12;
+ uy |= 1 << 52;
+ }
+
+ q = 0;
+
+ if ex + 1 != ey {
+ if ex < ey {
+ return (x, 0);
+ }
+ /* x mod y */
+ while ex > ey {
+ i = uxi.wrapping_sub(uy);
+ if (i >> 63) == 0 {
+ uxi = i;
+ q += 1;
+ }
+ uxi <<= 1;
+ q <<= 1;
+ ex -= 1;
+ }
+ i = uxi.wrapping_sub(uy);
+ if (i >> 63) == 0 {
+ uxi = i;
+ q += 1;
+ }
+ if uxi == 0 {
+ ex = -60;
+ } else {
+ while (uxi >> 52) == 0 {
+ uxi <<= 1;
+ ex -= 1;
+ }
+ }
+ }
+
+ /* scale result and decide between |x| and |x|-|y| */
+ if ex > 0 {
+ uxi -= 1 << 52;
+ uxi |= (ex as u64) << 52;
+ } else {
+ uxi >>= -ex + 1;
+ }
+ x = f64::from_bits(uxi);
+ if sy {
+ y = -y;
+ }
+ if ex == ey || (ex + 1 == ey && (2.0 * x > y || (2.0 * x == y && (q % 2) != 0))) {
+ x -= y;
+ // TODO: this matches musl behavior, but it is incorrect
+ q = q.wrapping_add(1);
+ }
+ q &= 0x7fffffff;
+ let quo = if sx ^ sy { -(q as i32) } else { q as i32 };
+ if sx {
+ (-x, quo)
+ } else {
+ (x, quo)
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::remquo;
+
+ #[test]
+ fn test_q_overflow() {
+ // 0xc000000000000001, 0x04c0000000000004
+ let _ = remquo(-2.0000000000000004, 8.406091369059082e-286);
+ }
+}
diff --git a/src/math/remquof.rs b/src/math/remquof.rs
new file mode 100644
index 0000000..d71bd38
--- /dev/null
+++ b/src/math/remquof.rs
@@ -0,0 +1,97 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn remquof(mut x: f32, mut y: f32) -> (f32, i32) {
+ let ux: u32 = x.to_bits();
+ let mut uy: u32 = y.to_bits();
+ let mut ex = ((ux >> 23) & 0xff) as i32;
+ let mut ey = ((uy >> 23) & 0xff) as i32;
+ let sx = (ux >> 31) != 0;
+ let sy = (uy >> 31) != 0;
+ let mut q: u32;
+ let mut i: u32;
+ let mut uxi: u32 = ux;
+
+ if (uy << 1) == 0 || y.is_nan() || ex == 0xff {
+ return ((x * y) / (x * y), 0);
+ }
+ if (ux << 1) == 0 {
+ return (x, 0);
+ }
+
+ /* normalize x and y */
+ if ex == 0 {
+ i = uxi << 9;
+ while (i >> 31) == 0 {
+ ex -= 1;
+ i <<= 1;
+ }
+ uxi <<= -ex + 1;
+ } else {
+ uxi &= (!0) >> 9;
+ uxi |= 1 << 23;
+ }
+ if ey == 0 {
+ i = uy << 9;
+ while (i >> 31) == 0 {
+ ey -= 1;
+ i <<= 1;
+ }
+ uy <<= -ey + 1;
+ } else {
+ uy &= (!0) >> 9;
+ uy |= 1 << 23;
+ }
+
+ q = 0;
+ if ex + 1 != ey {
+ if ex < ey {
+ return (x, 0);
+ }
+ /* x mod y */
+ while ex > ey {
+ i = uxi.wrapping_sub(uy);
+ if (i >> 31) == 0 {
+ uxi = i;
+ q += 1;
+ }
+ uxi <<= 1;
+ q <<= 1;
+ ex -= 1;
+ }
+ i = uxi.wrapping_sub(uy);
+ if (i >> 31) == 0 {
+ uxi = i;
+ q += 1;
+ }
+ if uxi == 0 {
+ ex = -30;
+ } else {
+ while (uxi >> 23) == 0 {
+ uxi <<= 1;
+ ex -= 1;
+ }
+ }
+ }
+
+ /* scale result and decide between |x| and |x|-|y| */
+ if ex > 0 {
+ uxi -= 1 << 23;
+ uxi |= (ex as u32) << 23;
+ } else {
+ uxi >>= -ex + 1;
+ }
+ x = f32::from_bits(uxi);
+ if sy {
+ y = -y;
+ }
+ if ex == ey || (ex + 1 == ey && (2.0 * x > y || (2.0 * x == y && (q % 2) != 0))) {
+ x -= y;
+ q += 1;
+ }
+ q &= 0x7fffffff;
+ let quo = if sx ^ sy { -(q as i32) } else { q as i32 };
+ if sx {
+ (-x, quo)
+ } else {
+ (x, quo)
+ }
+}
diff --git a/src/math/round.rs b/src/math/round.rs
new file mode 100644
index 0000000..bf72f5b
--- /dev/null
+++ b/src/math/round.rs
@@ -0,0 +1,46 @@
+use core::f64;
+
+const TOINT: f64 = 1.0 / f64::EPSILON;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn round(mut x: f64) -> f64 {
+ let i = x.to_bits();
+ let e: u64 = i >> 52 & 0x7ff;
+ let mut y: f64;
+
+ if e >= 0x3ff + 52 {
+ return x;
+ }
+ if e < 0x3ff - 1 {
+ // raise inexact if x!=0
+ force_eval!(x + TOINT);
+ return 0.0 * x;
+ }
+ if i >> 63 != 0 {
+ x = -x;
+ }
+ y = x + TOINT - TOINT - x;
+ if y > 0.5 {
+ y = y + x - 1.0;
+ } else if y <= -0.5 {
+ y = y + x + 1.0;
+ } else {
+ y = y + x;
+ }
+
+ if i >> 63 != 0 {
+ -y
+ } else {
+ y
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::round;
+
+ #[test]
+ fn negative_zero() {
+ assert_eq!(round(-0.0_f64).to_bits(), (-0.0_f64).to_bits());
+ }
+}
diff --git a/src/math/roundf.rs b/src/math/roundf.rs
new file mode 100644
index 0000000..497e88d
--- /dev/null
+++ b/src/math/roundf.rs
@@ -0,0 +1,44 @@
+use core::f32;
+
+const TOINT: f32 = 1.0 / f32::EPSILON;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn roundf(mut x: f32) -> f32 {
+ let i = x.to_bits();
+ let e: u32 = i >> 23 & 0xff;
+ let mut y: f32;
+
+ if e >= 0x7f + 23 {
+ return x;
+ }
+ if e < 0x7f - 1 {
+ force_eval!(x + TOINT);
+ return 0.0 * x;
+ }
+ if i >> 31 != 0 {
+ x = -x;
+ }
+ y = x + TOINT - TOINT - x;
+ if y > 0.5f32 {
+ y = y + x - 1.0;
+ } else if y <= -0.5f32 {
+ y = y + x + 1.0;
+ } else {
+ y = y + x;
+ }
+ if i >> 31 != 0 {
+ -y
+ } else {
+ y
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::roundf;
+
+ #[test]
+ fn negative_zero() {
+ assert_eq!(roundf(-0.0_f32).to_bits(), (-0.0_f32).to_bits());
+ }
+}
diff --git a/src/math/scalbn.rs b/src/math/scalbn.rs
new file mode 100644
index 0000000..00c455a
--- /dev/null
+++ b/src/math/scalbn.rs
@@ -0,0 +1,33 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn scalbn(x: f64, mut n: i32) -> f64 {
+ let x1p1023 = f64::from_bits(0x7fe0000000000000); // 0x1p1023 === 2 ^ 1023
+ let x1p53 = f64::from_bits(0x4340000000000000); // 0x1p53 === 2 ^ 53
+ let x1p_1022 = f64::from_bits(0x0010000000000000); // 0x1p-1022 === 2 ^ (-1022)
+
+ let mut y = x;
+
+ if n > 1023 {
+ y *= x1p1023;
+ n -= 1023;
+ if n > 1023 {
+ y *= x1p1023;
+ n -= 1023;
+ if n > 1023 {
+ n = 1023;
+ }
+ }
+ } else if n < -1022 {
+ /* make sure final n < -53 to avoid double
+ rounding in the subnormal range */
+ y *= x1p_1022 * x1p53;
+ n += 1022 - 53;
+ if n < -1022 {
+ y *= x1p_1022 * x1p53;
+ n += 1022 - 53;
+ if n < -1022 {
+ n = -1022;
+ }
+ }
+ }
+ y * f64::from_bits(((0x3ff + n) as u64) << 52)
+}
diff --git a/src/math/scalbnf.rs b/src/math/scalbnf.rs
new file mode 100644
index 0000000..73f4bb5
--- /dev/null
+++ b/src/math/scalbnf.rs
@@ -0,0 +1,29 @@
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn scalbnf(mut x: f32, mut n: i32) -> f32 {
+ let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
+ let x1p_126 = f32::from_bits(0x800000); // 0x1p-126f === 2 ^ -126
+ let x1p24 = f32::from_bits(0x4b800000); // 0x1p24f === 2 ^ 24
+
+ if n > 127 {
+ x *= x1p127;
+ n -= 127;
+ if n > 127 {
+ x *= x1p127;
+ n -= 127;
+ if n > 127 {
+ n = 127;
+ }
+ }
+ } else if n < -126 {
+ x *= x1p_126 * x1p24;
+ n += 126 - 24;
+ if n < -126 {
+ x *= x1p_126 * x1p24;
+ n += 126 - 24;
+ if n < -126 {
+ n = -126;
+ }
+ }
+ }
+ x * f32::from_bits(((0x7f + n) as u32) << 23)
+}
diff --git a/src/math/sin.rs b/src/math/sin.rs
new file mode 100644
index 0000000..1329b41
--- /dev/null
+++ b/src/math/sin.rs
@@ -0,0 +1,85 @@
+// origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */
+//
+// ====================================================
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+//
+// Developed at SunPro, a Sun Microsystems, Inc. business.
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+
+use super::{k_cos, k_sin, rem_pio2};
+
+// sin(x)
+// Return sine function of x.
+//
+// kernel function:
+// k_sin ... sine function on [-pi/4,pi/4]
+// k_cos ... cose function on [-pi/4,pi/4]
+// rem_pio2 ... argument reduction routine
+//
+// Method.
+// Let S,C and T denote the sin, cos and tan respectively on
+// [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+// in [-pi/4 , +pi/4], and let n = k mod 4.
+// We have
+//
+// n sin(x) cos(x) tan(x)
+// ----------------------------------------------------------
+// 0 S C T
+// 1 C -S -1/T
+// 2 -S -C T
+// 3 -C S -1/T
+// ----------------------------------------------------------
+//
+// Special cases:
+// Let trig be any of sin, cos, or tan.
+// trig(+-INF) is NaN, with signals;
+// trig(NaN) is that NaN;
+//
+// Accuracy:
+// TRIG(x) returns trig(x) nearly rounded
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn sin(x: f64) -> f64 {
+ let x1p120 = f64::from_bits(0x4770000000000000); // 0x1p120f === 2 ^ 120
+
+ /* High word of x. */
+ let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
+
+ /* |x| ~< pi/4 */
+ if ix <= 0x3fe921fb {
+ if ix < 0x3e500000 {
+ /* |x| < 2**-26 */
+ /* raise inexact if x != 0 and underflow if subnormal*/
+ if ix < 0x00100000 {
+ force_eval!(x / x1p120);
+ } else {
+ force_eval!(x + x1p120);
+ }
+ return x;
+ }
+ return k_sin(x, 0.0, 0);
+ }
+
+ /* sin(Inf or NaN) is NaN */
+ if ix >= 0x7ff00000 {
+ return x - x;
+ }
+
+ /* argument reduction needed */
+ let (n, y0, y1) = rem_pio2(x);
+ match n & 3 {
+ 0 => k_sin(y0, y1, 1),
+ 1 => k_cos(y0, y1),
+ 2 => -k_sin(y0, y1, 1),
+ _ => -k_cos(y0, y1),
+ }
+}
+
+#[test]
+fn test_near_pi() {
+ let x = f64::from_bits(0x400921fb000FD5DD); // 3.141592026217707
+ let sx = f64::from_bits(0x3ea50d15ced1a4a2); // 6.273720864039205e-7
+ assert_eq!(sin(x), sx);
+}
diff --git a/src/math/sincos.rs b/src/math/sincos.rs
new file mode 100644
index 0000000..d49f65c
--- /dev/null
+++ b/src/math/sincos.rs
@@ -0,0 +1,59 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{get_high_word, k_cos, k_sin, rem_pio2};
+
+pub fn sincos(x: f64) -> (f64, f64) {
+ let s: f64;
+ let c: f64;
+ let mut ix: u32;
+
+ ix = get_high_word(x);
+ ix &= 0x7fffffff;
+
+ /* |x| ~< pi/4 */
+ if ix <= 0x3fe921fb {
+ /* if |x| < 2**-27 * sqrt(2) */
+ if ix < 0x3e46a09e {
+ /* raise inexact if x!=0 and underflow if subnormal */
+ let x1p120 = f64::from_bits(0x4770000000000000); // 0x1p120 == 2^120
+ if ix < 0x00100000 {
+ force_eval!(x / x1p120);
+ } else {
+ force_eval!(x + x1p120);
+ }
+ return (x, 1.0);
+ }
+ return (k_sin(x, 0.0, 0), k_cos(x, 0.0));
+ }
+
+ /* sincos(Inf or NaN) is NaN */
+ if ix >= 0x7ff00000 {
+ let rv = x - x;
+ return (rv, rv);
+ }
+
+ /* argument reduction needed */
+ let (n, y0, y1) = rem_pio2(x);
+ s = k_sin(y0, y1, 1);
+ c = k_cos(y0, y1);
+ match n & 3 {
+ 0 => (s, c),
+ 1 => (c, -s),
+ 2 => (-s, -c),
+ 3 => (-c, s),
+ #[cfg(debug_assertions)]
+ _ => unreachable!(),
+ #[cfg(not(debug_assertions))]
+ _ => (0.0, 1.0),
+ }
+}
diff --git a/src/math/sincosf.rs b/src/math/sincosf.rs
new file mode 100644
index 0000000..2725caa
--- /dev/null
+++ b/src/math/sincosf.rs
@@ -0,0 +1,154 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_sinf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{k_cosf, k_sinf, rem_pio2f};
+
+/* Small multiples of pi/2 rounded to double precision. */
+const PI_2: f32 = 0.5 * 3.1415926535897931160E+00;
+const S1PIO2: f32 = 1.0 * PI_2; /* 0x3FF921FB, 0x54442D18 */
+const S2PIO2: f32 = 2.0 * PI_2; /* 0x400921FB, 0x54442D18 */
+const S3PIO2: f32 = 3.0 * PI_2; /* 0x4012D97C, 0x7F3321D2 */
+const S4PIO2: f32 = 4.0 * PI_2; /* 0x401921FB, 0x54442D18 */
+
+pub fn sincosf(x: f32) -> (f32, f32) {
+ let s: f32;
+ let c: f32;
+ let mut ix: u32;
+ let sign: bool;
+
+ ix = x.to_bits();
+ sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+
+ /* |x| ~<= pi/4 */
+ if ix <= 0x3f490fda {
+ /* |x| < 2**-12 */
+ if ix < 0x39800000 {
+ /* raise inexact if x!=0 and underflow if subnormal */
+
+ let x1p120 = f32::from_bits(0x7b800000); // 0x1p120 == 2^120
+ if ix < 0x00100000 {
+ force_eval!(x / x1p120);
+ } else {
+ force_eval!(x + x1p120);
+ }
+ return (x, 1.0);
+ }
+ return (k_sinf(x as f64), k_cosf(x as f64));
+ }
+
+ /* |x| ~<= 5*pi/4 */
+ if ix <= 0x407b53d1 {
+ if ix <= 0x4016cbe3 {
+ /* |x| ~<= 3pi/4 */
+ if sign {
+ s = -k_cosf((x + S1PIO2) as f64);
+ c = k_sinf((x + S1PIO2) as f64);
+ } else {
+ s = k_cosf((S1PIO2 - x) as f64);
+ c = k_sinf((S1PIO2 - x) as f64);
+ }
+ }
+ /* -sin(x+c) is not correct if x+c could be 0: -0 vs +0 */
+ else {
+ if sign {
+ s = -k_sinf((x + S2PIO2) as f64);
+ c = -k_cosf((x + S2PIO2) as f64);
+ } else {
+ s = -k_sinf((x - S2PIO2) as f64);
+ c = -k_cosf((x - S2PIO2) as f64);
+ }
+ }
+
+ return (s, c);
+ }
+
+ /* |x| ~<= 9*pi/4 */
+ if ix <= 0x40e231d5 {
+ if ix <= 0x40afeddf {
+ /* |x| ~<= 7*pi/4 */
+ if sign {
+ s = k_cosf((x + S3PIO2) as f64);
+ c = -k_sinf((x + S3PIO2) as f64);
+ } else {
+ s = -k_cosf((x - S3PIO2) as f64);
+ c = k_sinf((x - S3PIO2) as f64);
+ }
+ } else {
+ if sign {
+ s = k_sinf((x + S4PIO2) as f64);
+ c = k_cosf((x + S4PIO2) as f64);
+ } else {
+ s = k_sinf((x - S4PIO2) as f64);
+ c = k_cosf((x - S4PIO2) as f64);
+ }
+ }
+
+ return (s, c);
+ }
+
+ /* sin(Inf or NaN) is NaN */
+ if ix >= 0x7f800000 {
+ let rv = x - x;
+ return (rv, rv);
+ }
+
+ /* general argument reduction needed */
+ let (n, y) = rem_pio2f(x);
+ s = k_sinf(y);
+ c = k_cosf(y);
+ match n & 3 {
+ 0 => (s, c),
+ 1 => (c, -s),
+ 2 => (-s, -c),
+ 3 => (-c, s),
+ #[cfg(debug_assertions)]
+ _ => unreachable!(),
+ #[cfg(not(debug_assertions))]
+ _ => (0.0, 1.0),
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::sincosf;
+ use crate::_eqf;
+
+ #[test]
+ fn with_pi() {
+ let (s, c) = sincosf(core::f32::consts::PI);
+ _eqf(s.abs(), 0.0).unwrap();
+ _eqf(c, -1.0).unwrap();
+ }
+
+ #[test]
+ fn rotational_symmetry() {
+ use core::f32::consts::PI;
+ const N: usize = 24;
+ for n in 0..N {
+ let theta = 2. * PI * (n as f32) / (N as f32);
+ let (s, c) = sincosf(theta);
+ let (s_plus, c_plus) = sincosf(theta + 2. * PI);
+ let (s_minus, c_minus) = sincosf(theta - 2. * PI);
+
+ const TOLERANCE: f32 = 1e-6;
+ assert!((s - s_plus).abs() < TOLERANCE);
+ assert!((s - s_minus).abs() < TOLERANCE);
+ assert!((c - c_plus).abs() < TOLERANCE);
+ assert!((c - c_minus).abs() < TOLERANCE);
+ }
+ }
+}
diff --git a/src/math/sinf.rs b/src/math/sinf.rs
new file mode 100644
index 0000000..6e20be2
--- /dev/null
+++ b/src/math/sinf.rs
@@ -0,0 +1,93 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_sinf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{k_cosf, k_sinf, rem_pio2f};
+
+use core::f64::consts::FRAC_PI_2;
+
+/* Small multiples of pi/2 rounded to double precision. */
+const S1_PIO2: f64 = 1. * FRAC_PI_2; /* 0x3FF921FB, 0x54442D18 */
+const S2_PIO2: f64 = 2. * FRAC_PI_2; /* 0x400921FB, 0x54442D18 */
+const S3_PIO2: f64 = 3. * FRAC_PI_2; /* 0x4012D97C, 0x7F3321D2 */
+const S4_PIO2: f64 = 4. * FRAC_PI_2; /* 0x401921FB, 0x54442D18 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn sinf(x: f32) -> f32 {
+ let x64 = x as f64;
+
+ let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120
+
+ let mut ix = x.to_bits();
+ let sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+
+ if ix <= 0x3f490fda {
+ /* |x| ~<= pi/4 */
+ if ix < 0x39800000 {
+ /* |x| < 2**-12 */
+ /* raise inexact if x!=0 and underflow if subnormal */
+ force_eval!(if ix < 0x00800000 {
+ x / x1p120
+ } else {
+ x + x1p120
+ });
+ return x;
+ }
+ return k_sinf(x64);
+ }
+ if ix <= 0x407b53d1 {
+ /* |x| ~<= 5*pi/4 */
+ if ix <= 0x4016cbe3 {
+ /* |x| ~<= 3pi/4 */
+ if sign {
+ return -k_cosf(x64 + S1_PIO2);
+ } else {
+ return k_cosf(x64 - S1_PIO2);
+ }
+ }
+ return k_sinf(if sign {
+ -(x64 + S2_PIO2)
+ } else {
+ -(x64 - S2_PIO2)
+ });
+ }
+ if ix <= 0x40e231d5 {
+ /* |x| ~<= 9*pi/4 */
+ if ix <= 0x40afeddf {
+ /* |x| ~<= 7*pi/4 */
+ if sign {
+ return k_cosf(x64 + S3_PIO2);
+ } else {
+ return -k_cosf(x64 - S3_PIO2);
+ }
+ }
+ return k_sinf(if sign { x64 + S4_PIO2 } else { x64 - S4_PIO2 });
+ }
+
+ /* sin(Inf or NaN) is NaN */
+ if ix >= 0x7f800000 {
+ return x - x;
+ }
+
+ /* general argument reduction needed */
+ let (n, y) = rem_pio2f(x);
+ match n & 3 {
+ 0 => k_sinf(y),
+ 1 => k_cosf(y),
+ 2 => k_sinf(-y),
+ _ => -k_cosf(y),
+ }
+}
diff --git a/src/math/sinh.rs b/src/math/sinh.rs
new file mode 100644
index 0000000..fd24fd2
--- /dev/null
+++ b/src/math/sinh.rs
@@ -0,0 +1,49 @@
+use super::{expm1, expo2};
+
+// sinh(x) = (exp(x) - 1/exp(x))/2
+// = (exp(x)-1 + (exp(x)-1)/exp(x))/2
+// = x + x^3/6 + o(x^5)
+//
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn sinh(x: f64) -> f64 {
+ // union {double f; uint64_t i;} u = {.f = x};
+ // uint32_t w;
+ // double t, h, absx;
+
+ let mut uf: f64 = x;
+ let mut ui: u64 = f64::to_bits(uf);
+ let w: u32;
+ let t: f64;
+ let mut h: f64;
+ let absx: f64;
+
+ h = 0.5;
+ if ui >> 63 != 0 {
+ h = -h;
+ }
+ /* |x| */
+ ui &= !1 / 2;
+ uf = f64::from_bits(ui);
+ absx = uf;
+ w = (ui >> 32) as u32;
+
+ /* |x| < log(DBL_MAX) */
+ if w < 0x40862e42 {
+ t = expm1(absx);
+ if w < 0x3ff00000 {
+ if w < 0x3ff00000 - (26 << 20) {
+ /* note: inexact and underflow are raised by expm1 */
+ /* note: this branch avoids spurious underflow */
+ return x;
+ }
+ return h * (2.0 * t - t * t / (t + 1.0));
+ }
+ /* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
+ return h * (t + t / (t + 1.0));
+ }
+
+ /* |x| > log(DBL_MAX) or nan */
+ /* note: the result is stored to handle overflow */
+ t = 2.0 * h * expo2(absx);
+ t
+}
diff --git a/src/math/sinhf.rs b/src/math/sinhf.rs
new file mode 100644
index 0000000..24f863c
--- /dev/null
+++ b/src/math/sinhf.rs
@@ -0,0 +1,30 @@
+use super::expm1f;
+use super::k_expo2f;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn sinhf(x: f32) -> f32 {
+ let mut h = 0.5f32;
+ let mut ix = x.to_bits();
+ if (ix >> 31) != 0 {
+ h = -h;
+ }
+ /* |x| */
+ ix &= 0x7fffffff;
+ let absx = f32::from_bits(ix);
+ let w = ix;
+
+ /* |x| < log(FLT_MAX) */
+ if w < 0x42b17217 {
+ let t = expm1f(absx);
+ if w < 0x3f800000 {
+ if w < (0x3f800000 - (12 << 23)) {
+ return x;
+ }
+ return h * (2. * t - t * t / (t + 1.));
+ }
+ return h * (t + t / (t + 1.));
+ }
+
+ /* |x| > logf(FLT_MAX) or nan */
+ 2. * h * k_expo2f(absx)
+}
diff --git a/src/math/sqrt.rs b/src/math/sqrt.rs
new file mode 100644
index 0000000..f06b209
--- /dev/null
+++ b/src/math/sqrt.rs
@@ -0,0 +1,264 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_sqrt.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* sqrt(x)
+ * Return correctly rounded sqrt.
+ * ------------------------------------------
+ * | Use the hardware sqrt if you have one |
+ * ------------------------------------------
+ * Method:
+ * Bit by bit method using integer arithmetic. (Slow, but portable)
+ * 1. Normalization
+ * Scale x to y in [1,4) with even powers of 2:
+ * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
+ * sqrt(x) = 2^k * sqrt(y)
+ * 2. Bit by bit computation
+ * Let q = sqrt(y) truncated to i bit after binary point (q = 1),
+ * i 0
+ * i+1 2
+ * s = 2*q , and y = 2 * ( y - q ). (1)
+ * i i i i
+ *
+ * To compute q from q , one checks whether
+ * i+1 i
+ *
+ * -(i+1) 2
+ * (q + 2 ) <= y. (2)
+ * i
+ * -(i+1)
+ * If (2) is false, then q = q ; otherwise q = q + 2 .
+ * i+1 i i+1 i
+ *
+ * With some algebraic manipulation, it is not difficult to see
+ * that (2) is equivalent to
+ * -(i+1)
+ * s + 2 <= y (3)
+ * i i
+ *
+ * The advantage of (3) is that s and y can be computed by
+ * i i
+ * the following recurrence formula:
+ * if (3) is false
+ *
+ * s = s , y = y ; (4)
+ * i+1 i i+1 i
+ *
+ * otherwise,
+ * -i -(i+1)
+ * s = s + 2 , y = y - s - 2 (5)
+ * i+1 i i+1 i i
+ *
+ * One may easily use induction to prove (4) and (5).
+ * Note. Since the left hand side of (3) contain only i+2 bits,
+ * it does not necessary to do a full (53-bit) comparison
+ * in (3).
+ * 3. Final rounding
+ * After generating the 53 bits result, we compute one more bit.
+ * Together with the remainder, we can decide whether the
+ * result is exact, bigger than 1/2ulp, or less than 1/2ulp
+ * (it will never equal to 1/2ulp).
+ * The rounding mode can be detected by checking whether
+ * huge + tiny is equal to huge, and whether huge - tiny is
+ * equal to huge for some floating point number "huge" and "tiny".
+ *
+ * Special cases:
+ * sqrt(+-0) = +-0 ... exact
+ * sqrt(inf) = inf
+ * sqrt(-ve) = NaN ... with invalid signal
+ * sqrt(NaN) = NaN ... with invalid signal for signaling NaN
+ */
+
+use core::f64;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn sqrt(x: f64) -> f64 {
+ // On wasm32 we know that LLVM's intrinsic will compile to an optimized
+ // `f64.sqrt` native instruction, so we can leverage this for both code size
+ // and speed.
+ llvm_intrinsically_optimized! {
+ #[cfg(target_arch = "wasm32")] {
+ return if x < 0.0 {
+ f64::NAN
+ } else {
+ unsafe { ::core::intrinsics::sqrtf64(x) }
+ }
+ }
+ }
+ #[cfg(target_feature = "sse2")]
+ {
+ // Note: This path is unlikely since LLVM will usually have already
+ // optimized sqrt calls into hardware instructions if sse2 is available,
+ // but if someone does end up here they'll apprected the speed increase.
+ #[cfg(target_arch = "x86")]
+ use core::arch::x86::*;
+ #[cfg(target_arch = "x86_64")]
+ use core::arch::x86_64::*;
+ unsafe {
+ let m = _mm_set_sd(x);
+ let m_sqrt = _mm_sqrt_pd(m);
+ _mm_cvtsd_f64(m_sqrt)
+ }
+ }
+ #[cfg(not(target_feature = "sse2"))]
+ {
+ use core::num::Wrapping;
+
+ const TINY: f64 = 1.0e-300;
+
+ let mut z: f64;
+ let sign: Wrapping<u32> = Wrapping(0x80000000);
+ let mut ix0: i32;
+ let mut s0: i32;
+ let mut q: i32;
+ let mut m: i32;
+ let mut t: i32;
+ let mut i: i32;
+ let mut r: Wrapping<u32>;
+ let mut t1: Wrapping<u32>;
+ let mut s1: Wrapping<u32>;
+ let mut ix1: Wrapping<u32>;
+ let mut q1: Wrapping<u32>;
+
+ ix0 = (x.to_bits() >> 32) as i32;
+ ix1 = Wrapping(x.to_bits() as u32);
+
+ /* take care of Inf and NaN */
+ if (ix0 & 0x7ff00000) == 0x7ff00000 {
+ return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
+ }
+ /* take care of zero */
+ if ix0 <= 0 {
+ if ((ix0 & !(sign.0 as i32)) | ix1.0 as i32) == 0 {
+ return x; /* sqrt(+-0) = +-0 */
+ }
+ if ix0 < 0 {
+ return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
+ }
+ }
+ /* normalize x */
+ m = ix0 >> 20;
+ if m == 0 {
+ /* subnormal x */
+ while ix0 == 0 {
+ m -= 21;
+ ix0 |= (ix1 >> 11).0 as i32;
+ ix1 <<= 21;
+ }
+ i = 0;
+ while (ix0 & 0x00100000) == 0 {
+ i += 1;
+ ix0 <<= 1;
+ }
+ m -= i - 1;
+ ix0 |= (ix1 >> (32 - i) as usize).0 as i32;
+ ix1 = ix1 << i as usize;
+ }
+ m -= 1023; /* unbias exponent */
+ ix0 = (ix0 & 0x000fffff) | 0x00100000;
+ if (m & 1) == 1 {
+ /* odd m, double x to make it even */
+ ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+ ix1 += ix1;
+ }
+ m >>= 1; /* m = [m/2] */
+
+ /* generate sqrt(x) bit by bit */
+ ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+ ix1 += ix1;
+ q = 0; /* [q,q1] = sqrt(x) */
+ q1 = Wrapping(0);
+ s0 = 0;
+ s1 = Wrapping(0);
+ r = Wrapping(0x00200000); /* r = moving bit from right to left */
+
+ while r != Wrapping(0) {
+ t = s0 + r.0 as i32;
+ if t <= ix0 {
+ s0 = t + r.0 as i32;
+ ix0 -= t;
+ q += r.0 as i32;
+ }
+ ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+ ix1 += ix1;
+ r >>= 1;
+ }
+
+ r = sign;
+ while r != Wrapping(0) {
+ t1 = s1 + r;
+ t = s0;
+ if t < ix0 || (t == ix0 && t1 <= ix1) {
+ s1 = t1 + r;
+ if (t1 & sign) == sign && (s1 & sign) == Wrapping(0) {
+ s0 += 1;
+ }
+ ix0 -= t;
+ if ix1 < t1 {
+ ix0 -= 1;
+ }
+ ix1 -= t1;
+ q1 += r;
+ }
+ ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+ ix1 += ix1;
+ r >>= 1;
+ }
+
+ /* use floating add to find out rounding direction */
+ if (ix0 as u32 | ix1.0) != 0 {
+ z = 1.0 - TINY; /* raise inexact flag */
+ if z >= 1.0 {
+ z = 1.0 + TINY;
+ if q1.0 == 0xffffffff {
+ q1 = Wrapping(0);
+ q += 1;
+ } else if z > 1.0 {
+ if q1.0 == 0xfffffffe {
+ q += 1;
+ }
+ q1 += Wrapping(2);
+ } else {
+ q1 += q1 & Wrapping(1);
+ }
+ }
+ }
+ ix0 = (q >> 1) + 0x3fe00000;
+ ix1 = q1 >> 1;
+ if (q & 1) == 1 {
+ ix1 |= sign;
+ }
+ ix0 += m << 20;
+ f64::from_bits((ix0 as u64) << 32 | ix1.0 as u64)
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use core::f64::*;
+
+ #[test]
+ fn sanity_check() {
+ assert_eq!(sqrt(100.0), 10.0);
+ assert_eq!(sqrt(4.0), 2.0);
+ }
+
+ /// The spec: https://en.cppreference.com/w/cpp/numeric/math/sqrt
+ #[test]
+ fn spec_tests() {
+ // Not Asserted: FE_INVALID exception is raised if argument is negative.
+ assert!(sqrt(-1.0).is_nan());
+ assert!(sqrt(NAN).is_nan());
+ for f in [0.0, -0.0, INFINITY].iter().copied() {
+ assert_eq!(sqrt(f), f);
+ }
+ }
+}
diff --git a/src/math/sqrtf.rs b/src/math/sqrtf.rs
new file mode 100644
index 0000000..ee868c8
--- /dev/null
+++ b/src/math/sqrtf.rs
@@ -0,0 +1,152 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_sqrtf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn sqrtf(x: f32) -> f32 {
+ // On wasm32 we know that LLVM's intrinsic will compile to an optimized
+ // `f32.sqrt` native instruction, so we can leverage this for both code size
+ // and speed.
+ llvm_intrinsically_optimized! {
+ #[cfg(target_arch = "wasm32")] {
+ return if x < 0.0 {
+ ::core::f32::NAN
+ } else {
+ unsafe { ::core::intrinsics::sqrtf32(x) }
+ }
+ }
+ }
+ #[cfg(target_feature = "sse")]
+ {
+ // Note: This path is unlikely since LLVM will usually have already
+ // optimized sqrt calls into hardware instructions if sse is available,
+ // but if someone does end up here they'll apprected the speed increase.
+ #[cfg(target_arch = "x86")]
+ use core::arch::x86::*;
+ #[cfg(target_arch = "x86_64")]
+ use core::arch::x86_64::*;
+ unsafe {
+ let m = _mm_set_ss(x);
+ let m_sqrt = _mm_sqrt_ss(m);
+ _mm_cvtss_f32(m_sqrt)
+ }
+ }
+ #[cfg(not(target_feature = "sse"))]
+ {
+ const TINY: f32 = 1.0e-30;
+
+ let mut z: f32;
+ let sign: i32 = 0x80000000u32 as i32;
+ let mut ix: i32;
+ let mut s: i32;
+ let mut q: i32;
+ let mut m: i32;
+ let mut t: i32;
+ let mut i: i32;
+ let mut r: u32;
+
+ ix = x.to_bits() as i32;
+
+ /* take care of Inf and NaN */
+ if (ix as u32 & 0x7f800000) == 0x7f800000 {
+ return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
+ }
+
+ /* take care of zero */
+ if ix <= 0 {
+ if (ix & !sign) == 0 {
+ return x; /* sqrt(+-0) = +-0 */
+ }
+ if ix < 0 {
+ return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
+ }
+ }
+
+ /* normalize x */
+ m = ix >> 23;
+ if m == 0 {
+ /* subnormal x */
+ i = 0;
+ while ix & 0x00800000 == 0 {
+ ix <<= 1;
+ i = i + 1;
+ }
+ m -= i - 1;
+ }
+ m -= 127; /* unbias exponent */
+ ix = (ix & 0x007fffff) | 0x00800000;
+ if m & 1 == 1 {
+ /* odd m, double x to make it even */
+ ix += ix;
+ }
+ m >>= 1; /* m = [m/2] */
+
+ /* generate sqrt(x) bit by bit */
+ ix += ix;
+ q = 0;
+ s = 0;
+ r = 0x01000000; /* r = moving bit from right to left */
+
+ while r != 0 {
+ t = s + r as i32;
+ if t <= ix {
+ s = t + r as i32;
+ ix -= t;
+ q += r as i32;
+ }
+ ix += ix;
+ r >>= 1;
+ }
+
+ /* use floating add to find out rounding direction */
+ if ix != 0 {
+ z = 1.0 - TINY; /* raise inexact flag */
+ if z >= 1.0 {
+ z = 1.0 + TINY;
+ if z > 1.0 {
+ q += 2;
+ } else {
+ q += q & 1;
+ }
+ }
+ }
+
+ ix = (q >> 1) + 0x3f000000;
+ ix += m << 23;
+ f32::from_bits(ix as u32)
+ }
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use core::f32::*;
+
+ #[test]
+ fn sanity_check() {
+ assert_eq!(sqrtf(100.0), 10.0);
+ assert_eq!(sqrtf(4.0), 2.0);
+ }
+
+ /// The spec: https://en.cppreference.com/w/cpp/numeric/math/sqrt
+ #[test]
+ fn spec_tests() {
+ // Not Asserted: FE_INVALID exception is raised if argument is negative.
+ assert!(sqrtf(-1.0).is_nan());
+ assert!(sqrtf(NAN).is_nan());
+ for f in [0.0, -0.0, INFINITY].iter().copied() {
+ assert_eq!(sqrtf(f), f);
+ }
+ }
+}
diff --git a/src/math/tan.rs b/src/math/tan.rs
new file mode 100644
index 0000000..5a72f68
--- /dev/null
+++ b/src/math/tan.rs
@@ -0,0 +1,70 @@
+// origin: FreeBSD /usr/src/lib/msun/src/s_tan.c */
+//
+// ====================================================
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+//
+// Developed at SunPro, a Sun Microsystems, Inc. business.
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+
+use super::{k_tan, rem_pio2};
+
+// tan(x)
+// Return tangent function of x.
+//
+// kernel function:
+// k_tan ... tangent function on [-pi/4,pi/4]
+// rem_pio2 ... argument reduction routine
+//
+// Method.
+// Let S,C and T denote the sin, cos and tan respectively on
+// [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+// in [-pi/4 , +pi/4], and let n = k mod 4.
+// We have
+//
+// n sin(x) cos(x) tan(x)
+// ----------------------------------------------------------
+// 0 S C T
+// 1 C -S -1/T
+// 2 -S -C T
+// 3 -C S -1/T
+// ----------------------------------------------------------
+//
+// Special cases:
+// Let trig be any of sin, cos, or tan.
+// trig(+-INF) is NaN, with signals;
+// trig(NaN) is that NaN;
+//
+// Accuracy:
+// TRIG(x) returns trig(x) nearly rounded
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn tan(x: f64) -> f64 {
+ let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120
+
+ let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
+ /* |x| ~< pi/4 */
+ if ix <= 0x3fe921fb {
+ if ix < 0x3e400000 {
+ /* |x| < 2**-27 */
+ /* raise inexact if x!=0 and underflow if subnormal */
+ force_eval!(if ix < 0x00100000 {
+ x / x1p120 as f64
+ } else {
+ x + x1p120 as f64
+ });
+ return x;
+ }
+ return k_tan(x, 0.0, 0);
+ }
+
+ /* tan(Inf or NaN) is NaN */
+ if ix >= 0x7ff00000 {
+ return x - x;
+ }
+
+ /* argument reduction */
+ let (n, y0, y1) = rem_pio2(x);
+ k_tan(y0, y1, n & 1)
+}
diff --git a/src/math/tanf.rs b/src/math/tanf.rs
new file mode 100644
index 0000000..10de59c
--- /dev/null
+++ b/src/math/tanf.rs
@@ -0,0 +1,78 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_tanf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+use super::{k_tanf, rem_pio2f};
+
+use core::f64::consts::FRAC_PI_2;
+
+/* Small multiples of pi/2 rounded to double precision. */
+const T1_PIO2: f64 = 1. * FRAC_PI_2; /* 0x3FF921FB, 0x54442D18 */
+const T2_PIO2: f64 = 2. * FRAC_PI_2; /* 0x400921FB, 0x54442D18 */
+const T3_PIO2: f64 = 3. * FRAC_PI_2; /* 0x4012D97C, 0x7F3321D2 */
+const T4_PIO2: f64 = 4. * FRAC_PI_2; /* 0x401921FB, 0x54442D18 */
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn tanf(x: f32) -> f32 {
+ let x64 = x as f64;
+
+ let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120
+
+ let mut ix = x.to_bits();
+ let sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+
+ if ix <= 0x3f490fda {
+ /* |x| ~<= pi/4 */
+ if ix < 0x39800000 {
+ /* |x| < 2**-12 */
+ /* raise inexact if x!=0 and underflow if subnormal */
+ force_eval!(if ix < 0x00800000 {
+ x / x1p120
+ } else {
+ x + x1p120
+ });
+ return x;
+ }
+ return k_tanf(x64, false);
+ }
+ if ix <= 0x407b53d1 {
+ /* |x| ~<= 5*pi/4 */
+ if ix <= 0x4016cbe3 {
+ /* |x| ~<= 3pi/4 */
+ return k_tanf(if sign { x64 + T1_PIO2 } else { x64 - T1_PIO2 }, true);
+ } else {
+ return k_tanf(if sign { x64 + T2_PIO2 } else { x64 - T2_PIO2 }, false);
+ }
+ }
+ if ix <= 0x40e231d5 {
+ /* |x| ~<= 9*pi/4 */
+ if ix <= 0x40afeddf {
+ /* |x| ~<= 7*pi/4 */
+ return k_tanf(if sign { x64 + T3_PIO2 } else { x64 - T3_PIO2 }, true);
+ } else {
+ return k_tanf(if sign { x64 + T4_PIO2 } else { x64 - T4_PIO2 }, false);
+ }
+ }
+
+ /* tan(Inf or NaN) is NaN */
+ if ix >= 0x7f800000 {
+ return x - x;
+ }
+
+ /* argument reduction */
+ let (n, y) = rem_pio2f(x);
+ k_tanf(y, n & 1 != 0)
+}
diff --git a/src/math/tanh.rs b/src/math/tanh.rs
new file mode 100644
index 0000000..980c685
--- /dev/null
+++ b/src/math/tanh.rs
@@ -0,0 +1,53 @@
+use super::expm1;
+
+/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
+ * = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
+ * = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
+ */
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn tanh(mut x: f64) -> f64 {
+ let mut uf: f64 = x;
+ let mut ui: u64 = f64::to_bits(uf);
+
+ let w: u32;
+ let sign: bool;
+ let mut t: f64;
+
+ /* x = |x| */
+ sign = ui >> 63 != 0;
+ ui &= !1 / 2;
+ uf = f64::from_bits(ui);
+ x = uf;
+ w = (ui >> 32) as u32;
+
+ if w > 0x3fe193ea {
+ /* |x| > log(3)/2 ~= 0.5493 or nan */
+ if w > 0x40340000 {
+ /* |x| > 20 or nan */
+ /* note: this branch avoids raising overflow */
+ t = 1.0 - 0.0 / x;
+ } else {
+ t = expm1(2.0 * x);
+ t = 1.0 - 2.0 / (t + 2.0);
+ }
+ } else if w > 0x3fd058ae {
+ /* |x| > log(5/3)/2 ~= 0.2554 */
+ t = expm1(2.0 * x);
+ t = t / (t + 2.0);
+ } else if w >= 0x00100000 {
+ /* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */
+ t = expm1(-2.0 * x);
+ t = -t / (t + 2.0);
+ } else {
+ /* |x| is subnormal */
+ /* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */
+ force_eval!(x as f32);
+ t = x;
+ }
+
+ if sign {
+ -t
+ } else {
+ t
+ }
+}
diff --git a/src/math/tanhf.rs b/src/math/tanhf.rs
new file mode 100644
index 0000000..fc94e3d
--- /dev/null
+++ b/src/math/tanhf.rs
@@ -0,0 +1,39 @@
+use super::expm1f;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn tanhf(mut x: f32) -> f32 {
+ /* x = |x| */
+ let mut ix = x.to_bits();
+ let sign = (ix >> 31) != 0;
+ ix &= 0x7fffffff;
+ x = f32::from_bits(ix);
+ let w = ix;
+
+ let tt = if w > 0x3f0c9f54 {
+ /* |x| > log(3)/2 ~= 0.5493 or nan */
+ if w > 0x41200000 {
+ /* |x| > 10 */
+ 1. + 0. / x
+ } else {
+ let t = expm1f(2. * x);
+ 1. - 2. / (t + 2.)
+ }
+ } else if w > 0x3e82c578 {
+ /* |x| > log(5/3)/2 ~= 0.2554 */
+ let t = expm1f(2. * x);
+ t / (t + 2.)
+ } else if w >= 0x00800000 {
+ /* |x| >= 0x1p-126 */
+ let t = expm1f(-2. * x);
+ -t / (t + 2.)
+ } else {
+ /* |x| is subnormal */
+ force_eval!(x * x);
+ x
+ };
+ if sign {
+ -tt
+ } else {
+ tt
+ }
+}
diff --git a/src/math/tgamma.rs b/src/math/tgamma.rs
new file mode 100644
index 0000000..f8ccf66
--- /dev/null
+++ b/src/math/tgamma.rs
@@ -0,0 +1,207 @@
+/*
+"A Precision Approximation of the Gamma Function" - Cornelius Lanczos (1964)
+"Lanczos Implementation of the Gamma Function" - Paul Godfrey (2001)
+"An Analysis of the Lanczos Gamma Approximation" - Glendon Ralph Pugh (2004)
+
+approximation method:
+
+ (x - 0.5) S(x)
+Gamma(x) = (x + g - 0.5) * ----------------
+ exp(x + g - 0.5)
+
+with
+ a1 a2 a3 aN
+S(x) ~= [ a0 + ----- + ----- + ----- + ... + ----- ]
+ x + 1 x + 2 x + 3 x + N
+
+with a0, a1, a2, a3,.. aN constants which depend on g.
+
+for x < 0 the following reflection formula is used:
+
+Gamma(x)*Gamma(-x) = -pi/(x sin(pi x))
+
+most ideas and constants are from boost and python
+*/
+extern crate core;
+use super::{exp, floor, k_cos, k_sin, pow};
+
+const PI: f64 = 3.141592653589793238462643383279502884;
+
+/* sin(pi x) with x > 0x1p-100, if sin(pi*x)==0 the sign is arbitrary */
+fn sinpi(mut x: f64) -> f64 {
+ let mut n: isize;
+
+ /* argument reduction: x = |x| mod 2 */
+ /* spurious inexact when x is odd int */
+ x = x * 0.5;
+ x = 2.0 * (x - floor(x));
+
+ /* reduce x into [-.25,.25] */
+ n = (4.0 * x) as isize;
+ n = (n + 1) / 2;
+ x -= (n as f64) * 0.5;
+
+ x *= PI;
+ match n {
+ 1 => k_cos(x, 0.0),
+ 2 => k_sin(-x, 0.0, 0),
+ 3 => -k_cos(x, 0.0),
+ 0 | _ => k_sin(x, 0.0, 0),
+ }
+}
+
+const N: usize = 12;
+//static const double g = 6.024680040776729583740234375;
+const GMHALF: f64 = 5.524680040776729583740234375;
+const SNUM: [f64; N + 1] = [
+ 23531376880.410759688572007674451636754734846804940,
+ 42919803642.649098768957899047001988850926355848959,
+ 35711959237.355668049440185451547166705960488635843,
+ 17921034426.037209699919755754458931112671403265390,
+ 6039542586.3520280050642916443072979210699388420708,
+ 1439720407.3117216736632230727949123939715485786772,
+ 248874557.86205415651146038641322942321632125127801,
+ 31426415.585400194380614231628318205362874684987640,
+ 2876370.6289353724412254090516208496135991145378768,
+ 186056.26539522349504029498971604569928220784236328,
+ 8071.6720023658162106380029022722506138218516325024,
+ 210.82427775157934587250973392071336271166969580291,
+ 2.5066282746310002701649081771338373386264310793408,
+];
+const SDEN: [f64; N + 1] = [
+ 0.0,
+ 39916800.0,
+ 120543840.0,
+ 150917976.0,
+ 105258076.0,
+ 45995730.0,
+ 13339535.0,
+ 2637558.0,
+ 357423.0,
+ 32670.0,
+ 1925.0,
+ 66.0,
+ 1.0,
+];
+/* n! for small integer n */
+const FACT: [f64; 23] = [
+ 1.0,
+ 1.0,
+ 2.0,
+ 6.0,
+ 24.0,
+ 120.0,
+ 720.0,
+ 5040.0,
+ 40320.0,
+ 362880.0,
+ 3628800.0,
+ 39916800.0,
+ 479001600.0,
+ 6227020800.0,
+ 87178291200.0,
+ 1307674368000.0,
+ 20922789888000.0,
+ 355687428096000.0,
+ 6402373705728000.0,
+ 121645100408832000.0,
+ 2432902008176640000.0,
+ 51090942171709440000.0,
+ 1124000727777607680000.0,
+];
+
+/* S(x) rational function for positive x */
+fn s(x: f64) -> f64 {
+ let mut num: f64 = 0.0;
+ let mut den: f64 = 0.0;
+
+ /* to avoid overflow handle large x differently */
+ if x < 8.0 {
+ for i in (0..=N).rev() {
+ num = num * x + SNUM[i];
+ den = den * x + SDEN[i];
+ }
+ } else {
+ for i in 0..=N {
+ num = num / x + SNUM[i];
+ den = den / x + SDEN[i];
+ }
+ }
+ return num / den;
+}
+
+pub fn tgamma(mut x: f64) -> f64 {
+ let u: u64 = x.to_bits();
+ let absx: f64;
+ let mut y: f64;
+ let mut dy: f64;
+ let mut z: f64;
+ let mut r: f64;
+ let ix: u32 = ((u >> 32) as u32) & 0x7fffffff;
+ let sign: bool = (u >> 63) != 0;
+
+ /* special cases */
+ if ix >= 0x7ff00000 {
+ /* tgamma(nan)=nan, tgamma(inf)=inf, tgamma(-inf)=nan with invalid */
+ return x + core::f64::INFINITY;
+ }
+ if ix < ((0x3ff - 54) << 20) {
+ /* |x| < 2^-54: tgamma(x) ~ 1/x, +-0 raises div-by-zero */
+ return 1.0 / x;
+ }
+
+ /* integer arguments */
+ /* raise inexact when non-integer */
+ if x == floor(x) {
+ if sign {
+ return 0.0 / 0.0;
+ }
+ if x <= FACT.len() as f64 {
+ return FACT[(x as usize) - 1];
+ }
+ }
+
+ /* x >= 172: tgamma(x)=inf with overflow */
+ /* x =< -184: tgamma(x)=+-0 with underflow */
+ if ix >= 0x40670000 {
+ /* |x| >= 184 */
+ if sign {
+ let x1p_126 = f64::from_bits(0x3810000000000000); // 0x1p-126 == 2^-126
+ force_eval!((x1p_126 / x) as f32);
+ if floor(x) * 0.5 == floor(x * 0.5) {
+ return 0.0;
+ } else {
+ return -0.0;
+ }
+ }
+ let x1p1023 = f64::from_bits(0x7fe0000000000000); // 0x1p1023 == 2^1023
+ x *= x1p1023;
+ return x;
+ }
+
+ absx = if sign { -x } else { x };
+
+ /* handle the error of x + g - 0.5 */
+ y = absx + GMHALF;
+ if absx > GMHALF {
+ dy = y - absx;
+ dy -= GMHALF;
+ } else {
+ dy = y - GMHALF;
+ dy -= absx;
+ }
+
+ z = absx - 0.5;
+ r = s(absx) * exp(-y);
+ if x < 0.0 {
+ /* reflection formula for negative x */
+ /* sinpi(absx) is not 0, integers are already handled */
+ r = -PI / (sinpi(absx) * absx * r);
+ dy = -dy;
+ z = -z;
+ }
+ r += dy * (GMHALF + 0.5) * r / y;
+ z = pow(y, 0.5 * z);
+ y = r * z * z;
+ return y;
+}
diff --git a/src/math/tgammaf.rs b/src/math/tgammaf.rs
new file mode 100644
index 0000000..a8f161f
--- /dev/null
+++ b/src/math/tgammaf.rs
@@ -0,0 +1,5 @@
+use super::tgamma;
+
+pub fn tgammaf(x: f32) -> f32 {
+ tgamma(x as f64) as f32
+}
diff --git a/src/math/trunc.rs b/src/math/trunc.rs
new file mode 100644
index 0000000..f7892a2
--- /dev/null
+++ b/src/math/trunc.rs
@@ -0,0 +1,40 @@
+use core::f64;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn trunc(x: f64) -> f64 {
+ // On wasm32 we know that LLVM's intrinsic will compile to an optimized
+ // `f64.trunc` native instruction, so we can leverage this for both code size
+ // and speed.
+ llvm_intrinsically_optimized! {
+ #[cfg(target_arch = "wasm32")] {
+ return unsafe { ::core::intrinsics::truncf64(x) }
+ }
+ }
+ let x1p120 = f64::from_bits(0x4770000000000000); // 0x1p120f === 2 ^ 120
+
+ let mut i: u64 = x.to_bits();
+ let mut e: i64 = (i >> 52 & 0x7ff) as i64 - 0x3ff + 12;
+ let m: u64;
+
+ if e >= 52 + 12 {
+ return x;
+ }
+ if e < 12 {
+ e = 1;
+ }
+ m = -1i64 as u64 >> e;
+ if (i & m) == 0 {
+ return x;
+ }
+ force_eval!(x + x1p120);
+ i &= !m;
+ f64::from_bits(i)
+}
+
+#[cfg(test)]
+mod tests {
+ #[test]
+ fn sanity_check() {
+ assert_eq!(super::trunc(1.1), 1.0);
+ }
+}
diff --git a/src/math/truncf.rs b/src/math/truncf.rs
new file mode 100644
index 0000000..a4c0016
--- /dev/null
+++ b/src/math/truncf.rs
@@ -0,0 +1,40 @@
+use core::f32;
+
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn truncf(x: f32) -> f32 {
+ // On wasm32 we know that LLVM's intrinsic will compile to an optimized
+ // `f32.trunc` native instruction, so we can leverage this for both code size
+ // and speed.
+ llvm_intrinsically_optimized! {
+ #[cfg(target_arch = "wasm32")] {
+ return unsafe { ::core::intrinsics::truncf32(x) }
+ }
+ }
+ let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120
+
+ let mut i: u32 = x.to_bits();
+ let mut e: i32 = (i >> 23 & 0xff) as i32 - 0x7f + 9;
+ let m: u32;
+
+ if e >= 23 + 9 {
+ return x;
+ }
+ if e < 9 {
+ e = 1;
+ }
+ m = -1i32 as u32 >> e;
+ if (i & m) == 0 {
+ return x;
+ }
+ force_eval!(x + x1p120);
+ i &= !m;
+ f32::from_bits(i)
+}
+
+#[cfg(test)]
+mod tests {
+ #[test]
+ fn sanity_check() {
+ assert_eq!(super::truncf(1.1), 1.0);
+ }
+}