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// Copyright 2020 Google LLC
//
// This source code is licensed under the BSD-style license found in the
// LICENSE file in the root directory of this source tree.
#include <assert.h>
#include <stddef.h>
#include <wasm_simd128.h>
#include <xnnpack/common.h>
#include <xnnpack/math-stubs.h>
// Table of exp2(k / 16) values decremented (as integer) by (k << 19), k = 0..15
extern XNN_INTERNAL const float xnn_table_exp2minus_k_over_16[16];
void xnn_math_f32_expm1minus__wasmsimd_rr2_lut16_p3_andnot(
size_t n,
const float* input,
float* output)
{
assert(n % (4 * sizeof(float)) == 0);
// Large number such that ulp(magic bias) == exp2(-4)
const v128_t vmagic_bias = wasm_f32x4_splat(0x1.800000p19f);
const v128_t vlog2e = wasm_f32x4_splat(0x1.715476p+0f);
// Mask for the lowest 4 bits
const v128_t vindex_mask = wasm_i32x4_splat(0xF);
// The largest x for which expm1f(x) is saturated at -1.0f.
const v128_t vsat_cutoff = wasm_f32x4_splat(-0x1.154246p+4f);
// Last 9 bits are zeroes
const v128_t vminus_ln2_hi = wasm_f32x4_splat(-0x1.62E400p-1f);
const v128_t vminus_ln2_lo = wasm_f32x4_splat(-0x1.7F7D1Cp-20f);
// Coefficient of polynomial approximation
// exp(t) - 1 ~ t * (1 + t * (c2 + t * c3))
// on [-log(2)/32, log(2)/32]
const v128_t vc3 = wasm_f32x4_splat(0x1.55561Cp-3f);
const v128_t vc2 = wasm_f32x4_splat(0x1.0001ECp-1f);
const v128_t vone = wasm_f32x4_splat(1.0f);
for (; n != 0; n -= 4 * sizeof(float)) {
v128_t vx = wasm_v128_load(input);
// Compute reduced argument n := round(x / log(2), 4).
// We do it by adding a large number (magic bias), which cause rounding of the result to 4 fractional bits, then
// subtracing the large number back. The trick with adding large number is valid only within certain bounds
// (|x / log(2)| <= 2**18, i.e. |x| <= 0x1.62E43p+17 = 181704.375), but that is acceptable, because inputs x are
// restricted to [-17.328680, 0].
// Note that addition-subtraction of the large number doesn't cause overflow for inputs in this range.
v128_t vn = wasm_f32x4_add(wasm_f32x4_mul(vx, vlog2e), vmagic_bias);
// Create a floating-point number s (scale) such that s := 2**n for valid inputs, i.e. -17.328680 <= x <= 0.0. As n
// has 4 fractional bits, we split s == 2**n = 2**int(n) * 2**frac(n). We create s in two steps:
// 1. Fetch 2**frac(n) from the table using the 4 low bits of n, as integer. Note that the fetched values are in
// the [1.0, 2.0) range, i.e. their floating-point exponent is 0.
// 2. Adjust fecthed value by addition of int(n) to its floating-point exponent. The result is always a normalized
// number, because for -17.328680 <= x <= 0.0 we have -25 <= int(n) <= 0, and thus the adjusted exponent is not
// lower than -25.
//
// Shift bits 4:12 into 23:31 (position of floating-point exponent).
const v128_t ven = wasm_i32x4_shl(vn, 19);
// Use bits 0:4 bits of n, as integer, as an index for table lookup of l := 2**frac(n).
const v128_t vidx = wasm_i32x4_shl(wasm_v128_and(vn, vindex_mask), 2);
const uint64_t vidx_lo = wasm_i64x2_extract_lane(vidx, 0);
const uint64_t vidx_hi = wasm_i64x2_extract_lane(vidx, 1);
const float vl0 = *((const float*) ((uintptr_t) xnn_table_exp2minus_k_over_16 + (uint32_t) vidx_lo));
const float vl1 = *((const float*) ((uintptr_t) xnn_table_exp2minus_k_over_16 + (uint32_t) (vidx_lo >> 32)));
const float vl2 = *((const float*) ((uintptr_t) xnn_table_exp2minus_k_over_16 + (uint32_t) vidx_hi));
const float vl3 = *((const float*) ((uintptr_t) xnn_table_exp2minus_k_over_16 + (uint32_t) (vidx_hi >> 32)));
const v128_t vl = wasm_f32x4_make(vl0, vl1, vl2, vl3);
// Adjust exponent of the value l fetched from the table to get the final s value.
v128_t vs = wasm_i32x4_add(vl, ven);
// Subtract the large number back to get final n := round(x / log(2), 4).
vn = wasm_f32x4_sub(vn, vmagic_bias);
// Compute reduced argument t := x - n * log(2).
// Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
v128_t vt = wasm_f32x4_add(wasm_f32x4_mul(vn, vminus_ln2_hi), vx);
vt = wasm_f32x4_add(wasm_f32x4_mul(vn, vminus_ln2_lo), vt);
// The function saturates at -1 for large negative inputs: expm1f(x) == -1.0f for x <= sat_cutoff ~= -17.328680.
// To guarantee this behaviour, we zero out s (scale) and t (reduced argument) for x <= sat_cutoff.
const v128_t vm = wasm_f32x4_le(vx, vsat_cutoff);
vs = wasm_v128_andnot(vs, vm);
vt = wasm_v128_andnot(vt, vm);
// Compute degree-3 polynomial approximation for exp(t) - 1 on [-log(2)/32, log(2)/32].
// P(t) = t * (1 + t * (c2 + t * c3)) = t + t * (t * (c2 + t * c3)) = t + t * p
v128_t vp = wasm_f32x4_add(wasm_f32x4_mul(vc3, vt), vc2);
vp = wasm_f32x4_mul(vp, vt);
// Reconstruct the exp(x) - 1 value:
// exp(x) - 1 = s * (1 + t * (1 + t * (c2 + t * c3))) - 1
// = (s - 1) + s * (t + t * p)
// = ((t * s) + (t * s) * p) + (s - 1)
vt = wasm_f32x4_mul(vt, vs);
const v128_t vsm1 = wasm_f32x4_sub(vs, vone);
vp = wasm_f32x4_add(wasm_f32x4_mul(vp, vt), vt);
const v128_t vf = wasm_f32x4_add(vp, vsm1);
wasm_v128_store(output, vf);
input += 4;
output += 4;
}
}