move vector math out of libui
created a new header-only static libmath lib
Test: built & ran
Bug: n/a
Change-Id: Ic63ef5f54d9a0de07a9ab9e4d67be01ab6169fc0
diff --git a/libs/math/Android.bp b/libs/math/Android.bp
new file mode 100644
index 0000000..3ef8b4a
--- /dev/null
+++ b/libs/math/Android.bp
@@ -0,0 +1,21 @@
+// Copyright (C) 2017 The Android Open Source Project
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+cc_library_static {
+ name: "libmath",
+ host_supported: true,
+ export_include_dirs: ["include"],
+}
+
+subdirs = ["tests"]
diff --git a/libs/math/MODULE_LICENSE_APACHE2 b/libs/math/MODULE_LICENSE_APACHE2
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/libs/math/MODULE_LICENSE_APACHE2
diff --git a/libs/math/NOTICE b/libs/math/NOTICE
new file mode 100644
index 0000000..c5b1efa
--- /dev/null
+++ b/libs/math/NOTICE
@@ -0,0 +1,190 @@
+
+ Copyright (c) 2005-2008, The Android Open Source Project
+
+ Licensed under the Apache License, Version 2.0 (the "License");
+ you may not use this file except in compliance with the License.
+
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
+
+
+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
+ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+ 1. Definitions.
+
+ "License" shall mean the terms and conditions for use, reproduction,
+ and distribution as defined by Sections 1 through 9 of this document.
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+ copyright notice that is included in or attached to the work
+ (an example is provided in the Appendix below).
+
+ "Derivative Works" shall mean any work, whether in Source or Object
+ form, that is based on (or derived from) the Work and for which the
+ editorial revisions, annotations, elaborations, or other modifications
+ represent, as a whole, an original work of authorship. For the purposes
+ of this License, Derivative Works shall not include works that remain
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+ the Work and Derivative Works thereof.
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+ "Contribution" shall mean any work of authorship, including
+ the original version of the Work and any modifications or additions
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+ "Contributor" shall mean Licensor and any individual or Legal Entity
+ on behalf of whom a Contribution has been received by Licensor and
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+ 2. Grant of Copyright License. Subject to the terms and conditions of
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+ 3. Grant of Patent License. Subject to the terms and conditions of
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+ (except as stated in this section) patent license to make, have made,
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+ where such license applies only to those patent claims licensable
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+ Contribution(s) alone or by combination of their Contribution(s)
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+ institute patent litigation against any entity (including a
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+ or a Contribution incorporated within the Work constitutes direct
+ or contributory patent infringement, then any patent licenses
+ granted to You under this License for that Work shall terminate
+ as of the date such litigation is filed.
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+ 4. Redistribution. You may reproduce and distribute copies of the
+ Work or Derivative Works thereof in any medium, with or without
+ modifications, and in Source or Object form, provided that You
+ meet the following conditions:
+
+ (a) You must give any other recipients of the Work or
+ Derivative Works a copy of this License; and
+
+ (b) You must cause any modified files to carry prominent notices
+ stating that You changed the files; and
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+ (c) You must retain, in the Source form of any Derivative Works
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+ do not modify the License. You may add Your own attribution
+ notices within Derivative Works that You distribute, alongside
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+ You may add Your own copyright statement to Your modifications and
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+ reproduction, and distribution of the Work otherwise complies with
+ the conditions stated in this License.
+
+ 5. Submission of Contributions. Unless You explicitly state otherwise,
+ any Contribution intentionally submitted for inclusion in the Work
+ by You to the Licensor shall be under the terms and conditions of
+ this License, without any additional terms or conditions.
+ Notwithstanding the above, nothing herein shall supersede or modify
+ the terms of any separate license agreement you may have executed
+ with Licensor regarding such Contributions.
+
+ 6. Trademarks. This License does not grant permission to use the trade
+ names, trademarks, service marks, or product names of the Licensor,
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+ 7. Disclaimer of Warranty. Unless required by applicable law or
+ agreed to in writing, Licensor provides the Work (and each
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+ 8. Limitation of Liability. In no event and under no legal theory,
+ whether in tort (including negligence), contract, or otherwise,
+ unless required by applicable law (such as deliberate and grossly
+ negligent acts) or agreed to in writing, shall any Contributor be
+ liable to You for damages, including any direct, indirect, special,
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+ 9. Accepting Warranty or Additional Liability. While redistributing
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+ defend, and hold each Contributor harmless for any liability
+ incurred by, or claims asserted against, such Contributor by reason
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+
+ END OF TERMS AND CONDITIONS
+
diff --git a/libs/math/include/math/TMatHelpers.h b/libs/math/include/math/TMatHelpers.h
new file mode 100644
index 0000000..478e702
--- /dev/null
+++ b/libs/math/include/math/TMatHelpers.h
@@ -0,0 +1,637 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#pragma once
+
+#include <math.h>
+#include <stdint.h>
+#include <sys/types.h>
+
+#include <cmath>
+#include <exception>
+#include <iomanip>
+#include <stdexcept>
+
+#include <math/quat.h>
+#include <math/TVecHelpers.h>
+
+#include <utils/String8.h>
+
+#ifdef __cplusplus
+# define LIKELY( exp ) (__builtin_expect( !!(exp), true ))
+# define UNLIKELY( exp ) (__builtin_expect( !!(exp), false ))
+#else
+# define LIKELY( exp ) (__builtin_expect( !!(exp), 1 ))
+# define UNLIKELY( exp ) (__builtin_expect( !!(exp), 0 ))
+#endif
+
+#define PURE __attribute__((pure))
+
+#if __cplusplus >= 201402L
+#define CONSTEXPR constexpr
+#else
+#define CONSTEXPR
+#endif
+
+namespace android {
+namespace details {
+// -------------------------------------------------------------------------------------
+
+/*
+ * No user serviceable parts here.
+ *
+ * Don't use this file directly, instead include ui/mat*.h
+ */
+
+
+/*
+ * Matrix utilities
+ */
+
+namespace matrix {
+
+inline constexpr int transpose(int v) { return v; }
+inline constexpr float transpose(float v) { return v; }
+inline constexpr double transpose(double v) { return v; }
+
+inline constexpr int trace(int v) { return v; }
+inline constexpr float trace(float v) { return v; }
+inline constexpr double trace(double v) { return v; }
+
+/*
+ * Matrix inversion
+ */
+template<typename MATRIX>
+MATRIX PURE gaussJordanInverse(const MATRIX& src) {
+ typedef typename MATRIX::value_type T;
+ static constexpr unsigned int N = MATRIX::NUM_ROWS;
+ MATRIX tmp(src);
+ MATRIX inverted(1);
+
+ for (size_t i = 0; i < N; ++i) {
+ // look for largest element in i'th column
+ size_t swap = i;
+ T t = std::abs(tmp[i][i]);
+ for (size_t j = i + 1; j < N; ++j) {
+ const T t2 = std::abs(tmp[j][i]);
+ if (t2 > t) {
+ swap = j;
+ t = t2;
+ }
+ }
+
+ if (swap != i) {
+ // swap columns.
+ std::swap(tmp[i], tmp[swap]);
+ std::swap(inverted[i], inverted[swap]);
+ }
+
+ const T denom(tmp[i][i]);
+ for (size_t k = 0; k < N; ++k) {
+ tmp[i][k] /= denom;
+ inverted[i][k] /= denom;
+ }
+
+ // Factor out the lower triangle
+ for (size_t j = 0; j < N; ++j) {
+ if (j != i) {
+ const T d = tmp[j][i];
+ for (size_t k = 0; k < N; ++k) {
+ tmp[j][k] -= tmp[i][k] * d;
+ inverted[j][k] -= inverted[i][k] * d;
+ }
+ }
+ }
+ }
+
+ return inverted;
+}
+
+
+//------------------------------------------------------------------------------
+// 2x2 matrix inverse is easy.
+template <typename MATRIX>
+CONSTEXPR MATRIX PURE fastInverse2(const MATRIX& x) {
+ typedef typename MATRIX::value_type T;
+
+ // Assuming the input matrix is:
+ // | a b |
+ // | c d |
+ //
+ // The analytic inverse is
+ // | d -b |
+ // | -c a | / (a d - b c)
+ //
+ // Importantly, our matrices are column-major!
+
+ MATRIX inverted(MATRIX::NO_INIT);
+
+ const T a = x[0][0];
+ const T c = x[0][1];
+ const T b = x[1][0];
+ const T d = x[1][1];
+
+ const T det((a * d) - (b * c));
+ inverted[0][0] = d / det;
+ inverted[0][1] = -c / det;
+ inverted[1][0] = -b / det;
+ inverted[1][1] = a / det;
+ return inverted;
+}
+
+
+//------------------------------------------------------------------------------
+// From the Wikipedia article on matrix inversion's section on fast 3x3
+// matrix inversion:
+// http://en.wikipedia.org/wiki/Invertible_matrix#Inversion_of_3.C3.973_matrices
+template <typename MATRIX>
+CONSTEXPR MATRIX PURE fastInverse3(const MATRIX& x) {
+ typedef typename MATRIX::value_type T;
+
+ // Assuming the input matrix is:
+ // | a b c |
+ // | d e f |
+ // | g h i |
+ //
+ // The analytic inverse is
+ // | A B C |^T
+ // | D E F |
+ // | G H I | / determinant
+ //
+ // Which is
+ // | A D G |
+ // | B E H |
+ // | C F I | / determinant
+ //
+ // Where:
+ // A = (ei - fh), B = (fg - di), C = (dh - eg)
+ // D = (ch - bi), E = (ai - cg), F = (bg - ah)
+ // G = (bf - ce), H = (cd - af), I = (ae - bd)
+ //
+ // and the determinant is a*A + b*B + c*C (The rule of Sarrus)
+ //
+ // Importantly, our matrices are column-major!
+
+ MATRIX inverted(MATRIX::NO_INIT);
+
+ const T a = x[0][0];
+ const T b = x[1][0];
+ const T c = x[2][0];
+ const T d = x[0][1];
+ const T e = x[1][1];
+ const T f = x[2][1];
+ const T g = x[0][2];
+ const T h = x[1][2];
+ const T i = x[2][2];
+
+ // Do the full analytic inverse
+ const T A = e * i - f * h;
+ const T B = f * g - d * i;
+ const T C = d * h - e * g;
+ inverted[0][0] = A; // A
+ inverted[0][1] = B; // B
+ inverted[0][2] = C; // C
+ inverted[1][0] = c * h - b * i; // D
+ inverted[1][1] = a * i - c * g; // E
+ inverted[1][2] = b * g - a * h; // F
+ inverted[2][0] = b * f - c * e; // G
+ inverted[2][1] = c * d - a * f; // H
+ inverted[2][2] = a * e - b * d; // I
+
+ const T det(a * A + b * B + c * C);
+ for (size_t col = 0; col < 3; ++col) {
+ for (size_t row = 0; row < 3; ++row) {
+ inverted[col][row] /= det;
+ }
+ }
+
+ return inverted;
+}
+
+/**
+ * Inversion function which switches on the matrix size.
+ * @warning This function assumes the matrix is invertible. The result is
+ * undefined if it is not. It is the responsibility of the caller to
+ * make sure the matrix is not singular.
+ */
+template <typename MATRIX>
+inline constexpr MATRIX PURE inverse(const MATRIX& matrix) {
+ static_assert(MATRIX::NUM_ROWS == MATRIX::NUM_COLS, "only square matrices can be inverted");
+ return (MATRIX::NUM_ROWS == 2) ? fastInverse2<MATRIX>(matrix) :
+ ((MATRIX::NUM_ROWS == 3) ? fastInverse3<MATRIX>(matrix) :
+ gaussJordanInverse<MATRIX>(matrix));
+}
+
+template<typename MATRIX_R, typename MATRIX_A, typename MATRIX_B>
+CONSTEXPR MATRIX_R PURE multiply(const MATRIX_A& lhs, const MATRIX_B& rhs) {
+ // pre-requisite:
+ // lhs : D columns, R rows
+ // rhs : C columns, D rows
+ // res : C columns, R rows
+
+ static_assert(MATRIX_A::NUM_COLS == MATRIX_B::NUM_ROWS,
+ "matrices can't be multiplied. invalid dimensions.");
+ static_assert(MATRIX_R::NUM_COLS == MATRIX_B::NUM_COLS,
+ "invalid dimension of matrix multiply result.");
+ static_assert(MATRIX_R::NUM_ROWS == MATRIX_A::NUM_ROWS,
+ "invalid dimension of matrix multiply result.");
+
+ MATRIX_R res(MATRIX_R::NO_INIT);
+ for (size_t col = 0; col < MATRIX_R::NUM_COLS; ++col) {
+ res[col] = lhs * rhs[col];
+ }
+ return res;
+}
+
+// transpose. this handles matrices of matrices
+template <typename MATRIX>
+CONSTEXPR MATRIX PURE transpose(const MATRIX& m) {
+ // for now we only handle square matrix transpose
+ static_assert(MATRIX::NUM_COLS == MATRIX::NUM_ROWS, "transpose only supports square matrices");
+ MATRIX result(MATRIX::NO_INIT);
+ for (size_t col = 0; col < MATRIX::NUM_COLS; ++col) {
+ for (size_t row = 0; row < MATRIX::NUM_ROWS; ++row) {
+ result[col][row] = transpose(m[row][col]);
+ }
+ }
+ return result;
+}
+
+// trace. this handles matrices of matrices
+template <typename MATRIX>
+CONSTEXPR typename MATRIX::value_type PURE trace(const MATRIX& m) {
+ static_assert(MATRIX::NUM_COLS == MATRIX::NUM_ROWS, "trace only defined for square matrices");
+ typename MATRIX::value_type result(0);
+ for (size_t col = 0; col < MATRIX::NUM_COLS; ++col) {
+ result += trace(m[col][col]);
+ }
+ return result;
+}
+
+// diag. this handles matrices of matrices
+template <typename MATRIX>
+CONSTEXPR typename MATRIX::col_type PURE diag(const MATRIX& m) {
+ static_assert(MATRIX::NUM_COLS == MATRIX::NUM_ROWS, "diag only defined for square matrices");
+ typename MATRIX::col_type result(MATRIX::col_type::NO_INIT);
+ for (size_t col = 0; col < MATRIX::NUM_COLS; ++col) {
+ result[col] = m[col][col];
+ }
+ return result;
+}
+
+//------------------------------------------------------------------------------
+// This is taken from the Imath MatrixAlgo code, and is identical to Eigen.
+template <typename MATRIX>
+TQuaternion<typename MATRIX::value_type> extractQuat(const MATRIX& mat) {
+ typedef typename MATRIX::value_type T;
+
+ TQuaternion<T> quat(TQuaternion<T>::NO_INIT);
+
+ // Compute the trace to see if it is positive or not.
+ const T trace = mat[0][0] + mat[1][1] + mat[2][2];
+
+ // check the sign of the trace
+ if (LIKELY(trace > 0)) {
+ // trace is positive
+ T s = std::sqrt(trace + 1);
+ quat.w = T(0.5) * s;
+ s = T(0.5) / s;
+ quat.x = (mat[1][2] - mat[2][1]) * s;
+ quat.y = (mat[2][0] - mat[0][2]) * s;
+ quat.z = (mat[0][1] - mat[1][0]) * s;
+ } else {
+ // trace is negative
+
+ // Find the index of the greatest diagonal
+ size_t i = 0;
+ if (mat[1][1] > mat[0][0]) { i = 1; }
+ if (mat[2][2] > mat[i][i]) { i = 2; }
+
+ // Get the next indices: (n+1)%3
+ static constexpr size_t next_ijk[3] = { 1, 2, 0 };
+ size_t j = next_ijk[i];
+ size_t k = next_ijk[j];
+ T s = std::sqrt((mat[i][i] - (mat[j][j] + mat[k][k])) + 1);
+ quat[i] = T(0.5) * s;
+ if (s != 0) {
+ s = T(0.5) / s;
+ }
+ quat.w = (mat[j][k] - mat[k][j]) * s;
+ quat[j] = (mat[i][j] + mat[j][i]) * s;
+ quat[k] = (mat[i][k] + mat[k][i]) * s;
+ }
+ return quat;
+}
+
+template <typename MATRIX>
+String8 asString(const MATRIX& m) {
+ String8 s;
+ for (size_t c = 0; c < MATRIX::col_size(); c++) {
+ s.append("| ");
+ for (size_t r = 0; r < MATRIX::row_size(); r++) {
+ s.appendFormat("%7.2f ", m[r][c]);
+ }
+ s.append("|\n");
+ }
+ return s;
+}
+
+} // namespace matrix
+
+// -------------------------------------------------------------------------------------
+
+/*
+ * TMatProductOperators implements basic arithmetic and basic compound assignments
+ * operators on a vector of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TMatProductOperators<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+
+template <template<typename T> class BASE, typename T>
+class TMatProductOperators {
+public:
+ // multiply by a scalar
+ BASE<T>& operator *= (T v) {
+ BASE<T>& lhs(static_cast< BASE<T>& >(*this));
+ for (size_t col = 0; col < BASE<T>::NUM_COLS; ++col) {
+ lhs[col] *= v;
+ }
+ return lhs;
+ }
+
+ // matrix *= matrix
+ template<typename U>
+ const BASE<T>& operator *= (const BASE<U>& rhs) {
+ BASE<T>& lhs(static_cast< BASE<T>& >(*this));
+ lhs = matrix::multiply<BASE<T> >(lhs, rhs);
+ return lhs;
+ }
+
+ // divide by a scalar
+ BASE<T>& operator /= (T v) {
+ BASE<T>& lhs(static_cast< BASE<T>& >(*this));
+ for (size_t col = 0; col < BASE<T>::NUM_COLS; ++col) {
+ lhs[col] /= v;
+ }
+ return lhs;
+ }
+
+ // matrix * matrix, result is a matrix of the same type than the lhs matrix
+ template<typename U>
+ friend CONSTEXPR BASE<T> PURE operator *(const BASE<T>& lhs, const BASE<U>& rhs) {
+ return matrix::multiply<BASE<T> >(lhs, rhs);
+ }
+};
+
+/*
+ * TMatSquareFunctions implements functions on a matrix of type BASE<T>.
+ *
+ * BASE only needs to implement:
+ * - operator[]
+ * - col_type
+ * - row_type
+ * - COL_SIZE
+ * - ROW_SIZE
+ *
+ * By simply inheriting from TMatSquareFunctions<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+
+template<template<typename U> class BASE, typename T>
+class TMatSquareFunctions {
+public:
+
+ /*
+ * NOTE: the functions below ARE NOT member methods. They are friend functions
+ * with they definition inlined with their declaration. This makes these
+ * template functions available to the compiler when (and only when) this class
+ * is instantiated, at which point they're only templated on the 2nd parameter
+ * (the first one, BASE<T> being known).
+ */
+ friend inline CONSTEXPR BASE<T> PURE inverse(const BASE<T>& matrix) {
+ return matrix::inverse(matrix);
+ }
+ friend inline constexpr BASE<T> PURE transpose(const BASE<T>& m) {
+ return matrix::transpose(m);
+ }
+ friend inline constexpr T PURE trace(const BASE<T>& m) {
+ return matrix::trace(m);
+ }
+};
+
+template<template<typename U> class BASE, typename T>
+class TMatHelpers {
+public:
+ constexpr inline size_t getColumnSize() const { return BASE<T>::COL_SIZE; }
+ constexpr inline size_t getRowSize() const { return BASE<T>::ROW_SIZE; }
+ constexpr inline size_t getColumnCount() const { return BASE<T>::NUM_COLS; }
+ constexpr inline size_t getRowCount() const { return BASE<T>::NUM_ROWS; }
+ constexpr inline size_t size() const { return BASE<T>::ROW_SIZE; } // for TVec*<>
+
+ // array access
+ constexpr T const* asArray() const {
+ return &static_cast<BASE<T> const &>(*this)[0][0];
+ }
+
+ // element access
+ inline constexpr T const& operator()(size_t row, size_t col) const {
+ return static_cast<BASE<T> const &>(*this)[col][row];
+ }
+
+ inline T& operator()(size_t row, size_t col) {
+ return static_cast<BASE<T>&>(*this)[col][row];
+ }
+
+ template <typename VEC>
+ static CONSTEXPR BASE<T> translate(const VEC& t) {
+ BASE<T> r;
+ r[BASE<T>::NUM_COLS-1] = t;
+ return r;
+ }
+
+ template <typename VEC>
+ static constexpr BASE<T> scale(const VEC& s) {
+ return BASE<T>(s);
+ }
+
+ friend inline CONSTEXPR BASE<T> PURE abs(BASE<T> m) {
+ for (size_t col = 0; col < BASE<T>::NUM_COLS; ++col) {
+ m[col] = abs(m[col]);
+ }
+ return m;
+ }
+};
+
+// functions for 3x3 and 4x4 matrices
+template<template<typename U> class BASE, typename T>
+class TMatTransform {
+public:
+ inline constexpr TMatTransform() {
+ static_assert(BASE<T>::NUM_ROWS == 3 || BASE<T>::NUM_ROWS == 4, "3x3 or 4x4 matrices only");
+ }
+
+ template <typename A, typename VEC>
+ static CONSTEXPR BASE<T> rotate(A radian, const VEC& about) {
+ BASE<T> r;
+ T c = std::cos(radian);
+ T s = std::sin(radian);
+ if (about.x == 1 && about.y == 0 && about.z == 0) {
+ r[1][1] = c; r[2][2] = c;
+ r[1][2] = s; r[2][1] = -s;
+ } else if (about.x == 0 && about.y == 1 && about.z == 0) {
+ r[0][0] = c; r[2][2] = c;
+ r[2][0] = s; r[0][2] = -s;
+ } else if (about.x == 0 && about.y == 0 && about.z == 1) {
+ r[0][0] = c; r[1][1] = c;
+ r[0][1] = s; r[1][0] = -s;
+ } else {
+ VEC nabout = normalize(about);
+ typename VEC::value_type x = nabout.x;
+ typename VEC::value_type y = nabout.y;
+ typename VEC::value_type z = nabout.z;
+ T nc = 1 - c;
+ T xy = x * y;
+ T yz = y * z;
+ T zx = z * x;
+ T xs = x * s;
+ T ys = y * s;
+ T zs = z * s;
+ r[0][0] = x*x*nc + c; r[1][0] = xy*nc - zs; r[2][0] = zx*nc + ys;
+ r[0][1] = xy*nc + zs; r[1][1] = y*y*nc + c; r[2][1] = yz*nc - xs;
+ r[0][2] = zx*nc - ys; r[1][2] = yz*nc + xs; r[2][2] = z*z*nc + c;
+
+ // Clamp results to -1, 1.
+ for (size_t col = 0; col < 3; ++col) {
+ for (size_t row = 0; row < 3; ++row) {
+ r[col][row] = std::min(std::max(r[col][row], T(-1)), T(1));
+ }
+ }
+ }
+ return r;
+ }
+
+ /**
+ * Create a matrix from euler angles using YPR around YXZ respectively
+ * @param yaw about Y axis
+ * @param pitch about X axis
+ * @param roll about Z axis
+ */
+ template <
+ typename Y, typename P, typename R,
+ typename = typename std::enable_if<std::is_arithmetic<Y>::value >::type,
+ typename = typename std::enable_if<std::is_arithmetic<P>::value >::type,
+ typename = typename std::enable_if<std::is_arithmetic<R>::value >::type
+ >
+ static CONSTEXPR BASE<T> eulerYXZ(Y yaw, P pitch, R roll) {
+ return eulerZYX(roll, pitch, yaw);
+ }
+
+ /**
+ * Create a matrix from euler angles using YPR around ZYX respectively
+ * @param roll about X axis
+ * @param pitch about Y axis
+ * @param yaw about Z axis
+ *
+ * The euler angles are applied in ZYX order. i.e: a vector is first rotated
+ * about X (roll) then Y (pitch) and then Z (yaw).
+ */
+ template <
+ typename Y, typename P, typename R,
+ typename = typename std::enable_if<std::is_arithmetic<Y>::value >::type,
+ typename = typename std::enable_if<std::is_arithmetic<P>::value >::type,
+ typename = typename std::enable_if<std::is_arithmetic<R>::value >::type
+ >
+ static CONSTEXPR BASE<T> eulerZYX(Y yaw, P pitch, R roll) {
+ BASE<T> r;
+ T cy = std::cos(yaw);
+ T sy = std::sin(yaw);
+ T cp = std::cos(pitch);
+ T sp = std::sin(pitch);
+ T cr = std::cos(roll);
+ T sr = std::sin(roll);
+ T cc = cr * cy;
+ T cs = cr * sy;
+ T sc = sr * cy;
+ T ss = sr * sy;
+ r[0][0] = cp * cy;
+ r[0][1] = cp * sy;
+ r[0][2] = -sp;
+ r[1][0] = sp * sc - cs;
+ r[1][1] = sp * ss + cc;
+ r[1][2] = cp * sr;
+ r[2][0] = sp * cc + ss;
+ r[2][1] = sp * cs - sc;
+ r[2][2] = cp * cr;
+
+ // Clamp results to -1, 1.
+ for (size_t col = 0; col < 3; ++col) {
+ for (size_t row = 0; row < 3; ++row) {
+ r[col][row] = std::min(std::max(r[col][row], T(-1)), T(1));
+ }
+ }
+ return r;
+ }
+
+ TQuaternion<T> toQuaternion() const {
+ return matrix::extractQuat(static_cast<const BASE<T>&>(*this));
+ }
+};
+
+
+template <template<typename T> class BASE, typename T>
+class TMatDebug {
+public:
+ friend std::ostream& operator<<(std::ostream& stream, const BASE<T>& m) {
+ for (size_t row = 0; row < BASE<T>::NUM_ROWS; ++row) {
+ if (row != 0) {
+ stream << std::endl;
+ }
+ if (row == 0) {
+ stream << "/ ";
+ } else if (row == BASE<T>::NUM_ROWS-1) {
+ stream << "\\ ";
+ } else {
+ stream << "| ";
+ }
+ for (size_t col = 0; col < BASE<T>::NUM_COLS; ++col) {
+ stream << std::setw(10) << std::to_string(m[col][row]);
+ }
+ if (row == 0) {
+ stream << " \\";
+ } else if (row == BASE<T>::NUM_ROWS-1) {
+ stream << " /";
+ } else {
+ stream << " |";
+ }
+ }
+ return stream;
+ }
+
+ String8 asString() const {
+ return matrix::asString(static_cast<const BASE<T>&>(*this));
+ }
+};
+
+// -------------------------------------------------------------------------------------
+} // namespace details
+} // namespace android
+
+#undef LIKELY
+#undef UNLIKELY
+#undef PURE
+#undef CONSTEXPR
diff --git a/libs/math/include/math/TQuatHelpers.h b/libs/math/include/math/TQuatHelpers.h
new file mode 100644
index 0000000..f0a71ae
--- /dev/null
+++ b/libs/math/include/math/TQuatHelpers.h
@@ -0,0 +1,300 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+
+#pragma once
+
+#include <math.h>
+#include <stdint.h>
+#include <sys/types.h>
+
+#include <iostream>
+
+#include <math/vec3.h>
+
+#define PURE __attribute__((pure))
+
+namespace android {
+namespace details {
+// -------------------------------------------------------------------------------------
+
+/*
+ * No user serviceable parts here.
+ *
+ * Don't use this file directly, instead include ui/quat.h
+ */
+
+
+/*
+ * TQuatProductOperators implements basic arithmetic and basic compound assignment
+ * operators on a quaternion of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TQuatProductOperators<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+
+template <template<typename T> class QUATERNION, typename T>
+class TQuatProductOperators {
+public:
+ /* compound assignment from a another quaternion of the same size but different
+ * element type.
+ */
+ template <typename OTHER>
+ QUATERNION<T>& operator *= (const QUATERNION<OTHER>& r) {
+ QUATERNION<T>& q = static_cast<QUATERNION<T>&>(*this);
+ q = q * r;
+ return q;
+ }
+
+ /* compound assignment products by a scalar
+ */
+ QUATERNION<T>& operator *= (T v) {
+ QUATERNION<T>& lhs = static_cast<QUATERNION<T>&>(*this);
+ for (size_t i = 0; i < QUATERNION<T>::size(); i++) {
+ lhs[i] *= v;
+ }
+ return lhs;
+ }
+ QUATERNION<T>& operator /= (T v) {
+ QUATERNION<T>& lhs = static_cast<QUATERNION<T>&>(*this);
+ for (size_t i = 0; i < QUATERNION<T>::size(); i++) {
+ lhs[i] /= v;
+ }
+ return lhs;
+ }
+
+ /*
+ * NOTE: the functions below ARE NOT member methods. They are friend functions
+ * with they definition inlined with their declaration. This makes these
+ * template functions available to the compiler when (and only when) this class
+ * is instantiated, at which point they're only templated on the 2nd parameter
+ * (the first one, BASE<T> being known).
+ */
+
+ /* The operators below handle operation between quaternion of the same size
+ * but of a different element type.
+ */
+ template<typename RT>
+ friend inline
+ constexpr QUATERNION<T> PURE operator *(const QUATERNION<T>& q, const QUATERNION<RT>& r) {
+ // could be written as:
+ // return QUATERNION<T>(
+ // q.w*r.w - dot(q.xyz, r.xyz),
+ // q.w*r.xyz + r.w*q.xyz + cross(q.xyz, r.xyz));
+
+ return QUATERNION<T>(
+ q.w*r.w - q.x*r.x - q.y*r.y - q.z*r.z,
+ q.w*r.x + q.x*r.w + q.y*r.z - q.z*r.y,
+ q.w*r.y - q.x*r.z + q.y*r.w + q.z*r.x,
+ q.w*r.z + q.x*r.y - q.y*r.x + q.z*r.w);
+ }
+
+ template<typename RT>
+ friend inline
+ constexpr TVec3<T> PURE operator *(const QUATERNION<T>& q, const TVec3<RT>& v) {
+ // note: if q is known to be a unit quaternion, then this simplifies to:
+ // TVec3<T> t = 2 * cross(q.xyz, v)
+ // return v + (q.w * t) + cross(q.xyz, t)
+ return imaginary(q * QUATERNION<T>(v, 0) * inverse(q));
+ }
+
+
+ /* For quaternions, we use explicit "by a scalar" products because it's much faster
+ * than going (implicitly) through the quaternion multiplication.
+ * For reference: we could use the code below instead, but it would be a lot slower.
+ * friend inline
+ * constexpr BASE<T> PURE operator *(const BASE<T>& q, const BASE<T>& r) {
+ * return BASE<T>(
+ * q.w*r.w - q.x*r.x - q.y*r.y - q.z*r.z,
+ * q.w*r.x + q.x*r.w + q.y*r.z - q.z*r.y,
+ * q.w*r.y - q.x*r.z + q.y*r.w + q.z*r.x,
+ * q.w*r.z + q.x*r.y - q.y*r.x + q.z*r.w);
+ *
+ */
+ friend inline
+ constexpr QUATERNION<T> PURE operator *(QUATERNION<T> q, T scalar) {
+ // don't pass q by reference because we need a copy anyways
+ return q *= scalar;
+ }
+ friend inline
+ constexpr QUATERNION<T> PURE operator *(T scalar, QUATERNION<T> q) {
+ // don't pass q by reference because we need a copy anyways
+ return q *= scalar;
+ }
+
+ friend inline
+ constexpr QUATERNION<T> PURE operator /(QUATERNION<T> q, T scalar) {
+ // don't pass q by reference because we need a copy anyways
+ return q /= scalar;
+ }
+};
+
+
+/*
+ * TQuatFunctions implements functions on a quaternion of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TQuatFunctions<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+template <template<typename T> class QUATERNION, typename T>
+class TQuatFunctions {
+public:
+ /*
+ * NOTE: the functions below ARE NOT member methods. They are friend functions
+ * with they definition inlined with their declaration. This makes these
+ * template functions available to the compiler when (and only when) this class
+ * is instantiated, at which point they're only templated on the 2nd parameter
+ * (the first one, BASE<T> being known).
+ */
+
+ template<typename RT>
+ friend inline
+ constexpr T PURE dot(const QUATERNION<T>& p, const QUATERNION<RT>& q) {
+ return p.x * q.x +
+ p.y * q.y +
+ p.z * q.z +
+ p.w * q.w;
+ }
+
+ friend inline
+ constexpr T PURE norm(const QUATERNION<T>& q) {
+ return std::sqrt( dot(q, q) );
+ }
+
+ friend inline
+ constexpr T PURE length(const QUATERNION<T>& q) {
+ return norm(q);
+ }
+
+ friend inline
+ constexpr T PURE length2(const QUATERNION<T>& q) {
+ return dot(q, q);
+ }
+
+ friend inline
+ constexpr QUATERNION<T> PURE normalize(const QUATERNION<T>& q) {
+ return length(q) ? q / length(q) : QUATERNION<T>(1);
+ }
+
+ friend inline
+ constexpr QUATERNION<T> PURE conj(const QUATERNION<T>& q) {
+ return QUATERNION<T>(q.w, -q.x, -q.y, -q.z);
+ }
+
+ friend inline
+ constexpr QUATERNION<T> PURE inverse(const QUATERNION<T>& q) {
+ return conj(q) * (1 / dot(q, q));
+ }
+
+ friend inline
+ constexpr T PURE real(const QUATERNION<T>& q) {
+ return q.w;
+ }
+
+ friend inline
+ constexpr TVec3<T> PURE imaginary(const QUATERNION<T>& q) {
+ return q.xyz;
+ }
+
+ friend inline
+ constexpr QUATERNION<T> PURE unreal(const QUATERNION<T>& q) {
+ return QUATERNION<T>(q.xyz, 0);
+ }
+
+ friend inline
+ constexpr QUATERNION<T> PURE cross(const QUATERNION<T>& p, const QUATERNION<T>& q) {
+ return unreal(p*q);
+ }
+
+ friend inline
+ QUATERNION<T> PURE exp(const QUATERNION<T>& q) {
+ const T nq(norm(q.xyz));
+ return std::exp(q.w)*QUATERNION<T>((sin(nq)/nq)*q.xyz, cos(nq));
+ }
+
+ friend inline
+ QUATERNION<T> PURE log(const QUATERNION<T>& q) {
+ const T nq(norm(q));
+ return QUATERNION<T>((std::acos(q.w/nq)/norm(q.xyz))*q.xyz, log(nq));
+ }
+
+ friend inline
+ QUATERNION<T> PURE pow(const QUATERNION<T>& q, T a) {
+ // could also be computed as: exp(a*log(q));
+ const T nq(norm(q));
+ const T theta(a*std::acos(q.w / nq));
+ return std::pow(nq, a) * QUATERNION<T>(normalize(q.xyz) * std::sin(theta), std::cos(theta));
+ }
+
+ friend inline
+ QUATERNION<T> PURE slerp(const QUATERNION<T>& p, const QUATERNION<T>& q, T t) {
+ // could also be computed as: pow(q * inverse(p), t) * p;
+ const T d = dot(p, q);
+ const T npq = sqrt(dot(p, p) * dot(q, q)); // ||p|| * ||q||
+ const T a = std::acos(std::abs(d) / npq);
+ const T a0 = a * (1 - t);
+ const T a1 = a * t;
+ const T isina = 1 / sin(a);
+ const T s0 = std::sin(a0) * isina;
+ const T s1 = std::sin(a1) * isina;
+ // ensure we're taking the "short" side
+ return normalize(s0 * p + ((d < 0) ? (-s1) : (s1)) * q);
+ }
+
+ friend inline
+ constexpr QUATERNION<T> PURE lerp(const QUATERNION<T>& p, const QUATERNION<T>& q, T t) {
+ return ((1 - t) * p) + (t * q);
+ }
+
+ friend inline
+ constexpr QUATERNION<T> PURE nlerp(const QUATERNION<T>& p, const QUATERNION<T>& q, T t) {
+ return normalize(lerp(p, q, t));
+ }
+
+ friend inline
+ constexpr QUATERNION<T> PURE positive(const QUATERNION<T>& q) {
+ return q.w < 0 ? -q : q;
+ }
+};
+
+/*
+ * TQuatDebug implements functions on a vector of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TQuatDebug<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+template <template<typename T> class QUATERNION, typename T>
+class TQuatDebug {
+public:
+ /*
+ * NOTE: the functions below ARE NOT member methods. They are friend functions
+ * with they definition inlined with their declaration. This makes these
+ * template functions available to the compiler when (and only when) this class
+ * is instantiated, at which point they're only templated on the 2nd parameter
+ * (the first one, BASE<T> being known).
+ */
+ friend std::ostream& operator<< (std::ostream& stream, const QUATERNION<T>& q) {
+ return stream << "< " << q.w << " + " << q.x << "i + " << q.y << "j + " << q.z << "k >";
+ }
+};
+#undef PURE
+
+// -------------------------------------------------------------------------------------
+} // namespace details
+} // namespace android
diff --git a/libs/math/include/math/TVecHelpers.h b/libs/math/include/math/TVecHelpers.h
new file mode 100644
index 0000000..20f852f
--- /dev/null
+++ b/libs/math/include/math/TVecHelpers.h
@@ -0,0 +1,608 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+
+#pragma once
+
+#include <math.h>
+#include <stdint.h>
+#include <sys/types.h>
+
+#include <cmath>
+#include <limits>
+#include <iostream>
+
+#define PURE __attribute__((pure))
+
+#if __cplusplus >= 201402L
+#define CONSTEXPR constexpr
+#else
+#define CONSTEXPR
+#endif
+
+namespace android {
+namespace details {
+// -------------------------------------------------------------------------------------
+
+/*
+ * No user serviceable parts here.
+ *
+ * Don't use this file directly, instead include ui/vec{2|3|4}.h
+ */
+
+/*
+ * TVec{Add|Product}Operators implements basic arithmetic and basic compound assignments
+ * operators on a vector of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TVec{Add|Product}Operators<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+
+template <template<typename T> class VECTOR, typename T>
+class TVecAddOperators {
+public:
+ /* compound assignment from a another vector of the same size but different
+ * element type.
+ */
+ template<typename OTHER>
+ VECTOR<T>& operator +=(const VECTOR<OTHER>& v) {
+ VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
+ for (size_t i = 0; i < lhs.size(); i++) {
+ lhs[i] += v[i];
+ }
+ return lhs;
+ }
+ template<typename OTHER>
+ VECTOR<T>& operator -=(const VECTOR<OTHER>& v) {
+ VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
+ for (size_t i = 0; i < lhs.size(); i++) {
+ lhs[i] -= v[i];
+ }
+ return lhs;
+ }
+
+ /* compound assignment from a another vector of the same type.
+ * These operators can be used for implicit conversion and handle operations
+ * like "vector *= scalar" by letting the compiler implicitly convert a scalar
+ * to a vector (assuming the BASE<T> allows it).
+ */
+ VECTOR<T>& operator +=(const VECTOR<T>& v) {
+ VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
+ for (size_t i = 0; i < lhs.size(); i++) {
+ lhs[i] += v[i];
+ }
+ return lhs;
+ }
+ VECTOR<T>& operator -=(const VECTOR<T>& v) {
+ VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
+ for (size_t i = 0; i < lhs.size(); i++) {
+ lhs[i] -= v[i];
+ }
+ return lhs;
+ }
+
+ /*
+ * NOTE: the functions below ARE NOT member methods. They are friend functions
+ * with they definition inlined with their declaration. This makes these
+ * template functions available to the compiler when (and only when) this class
+ * is instantiated, at which point they're only templated on the 2nd parameter
+ * (the first one, BASE<T> being known).
+ */
+
+ /* The operators below handle operation between vectors of the same size
+ * but of a different element type.
+ */
+ template<typename RT>
+ friend inline constexpr VECTOR<T> PURE operator +(VECTOR<T> lv, const VECTOR<RT>& rv) {
+ // don't pass lv by reference because we need a copy anyways
+ return lv += rv;
+ }
+ template<typename RT>
+ friend inline constexpr VECTOR<T> PURE operator -(VECTOR<T> lv, const VECTOR<RT>& rv) {
+ // don't pass lv by reference because we need a copy anyways
+ return lv -= rv;
+ }
+
+ /* The operators below (which are not templates once this class is instanced,
+ * i.e.: BASE<T> is known) can be used for implicit conversion on both sides.
+ * These handle operations like "vector + scalar" and "scalar + vector" by
+ * letting the compiler implicitly convert a scalar to a vector (assuming
+ * the BASE<T> allows it).
+ */
+ friend inline constexpr VECTOR<T> PURE operator +(VECTOR<T> lv, const VECTOR<T>& rv) {
+ // don't pass lv by reference because we need a copy anyways
+ return lv += rv;
+ }
+ friend inline constexpr VECTOR<T> PURE operator -(VECTOR<T> lv, const VECTOR<T>& rv) {
+ // don't pass lv by reference because we need a copy anyways
+ return lv -= rv;
+ }
+};
+
+template<template<typename T> class VECTOR, typename T>
+class TVecProductOperators {
+public:
+ /* compound assignment from a another vector of the same size but different
+ * element type.
+ */
+ template<typename OTHER>
+ VECTOR<T>& operator *=(const VECTOR<OTHER>& v) {
+ VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
+ for (size_t i = 0; i < lhs.size(); i++) {
+ lhs[i] *= v[i];
+ }
+ return lhs;
+ }
+ template<typename OTHER>
+ VECTOR<T>& operator /=(const VECTOR<OTHER>& v) {
+ VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
+ for (size_t i = 0; i < lhs.size(); i++) {
+ lhs[i] /= v[i];
+ }
+ return lhs;
+ }
+
+ /* compound assignment from a another vector of the same type.
+ * These operators can be used for implicit conversion and handle operations
+ * like "vector *= scalar" by letting the compiler implicitly convert a scalar
+ * to a vector (assuming the BASE<T> allows it).
+ */
+ VECTOR<T>& operator *=(const VECTOR<T>& v) {
+ VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
+ for (size_t i = 0; i < lhs.size(); i++) {
+ lhs[i] *= v[i];
+ }
+ return lhs;
+ }
+ VECTOR<T>& operator /=(const VECTOR<T>& v) {
+ VECTOR<T>& lhs = static_cast<VECTOR<T>&>(*this);
+ for (size_t i = 0; i < lhs.size(); i++) {
+ lhs[i] /= v[i];
+ }
+ return lhs;
+ }
+
+ /*
+ * NOTE: the functions below ARE NOT member methods. They are friend functions
+ * with they definition inlined with their declaration. This makes these
+ * template functions available to the compiler when (and only when) this class
+ * is instantiated, at which point they're only templated on the 2nd parameter
+ * (the first one, BASE<T> being known).
+ */
+
+ /* The operators below handle operation between vectors of the same size
+ * but of a different element type.
+ */
+ template<typename RT>
+ friend inline constexpr VECTOR<T> PURE operator *(VECTOR<T> lv, const VECTOR<RT>& rv) {
+ // don't pass lv by reference because we need a copy anyways
+ return lv *= rv;
+ }
+ template<typename RT>
+ friend inline constexpr VECTOR<T> PURE operator /(VECTOR<T> lv, const VECTOR<RT>& rv) {
+ // don't pass lv by reference because we need a copy anyways
+ return lv /= rv;
+ }
+
+ /* The operators below (which are not templates once this class is instanced,
+ * i.e.: BASE<T> is known) can be used for implicit conversion on both sides.
+ * These handle operations like "vector * scalar" and "scalar * vector" by
+ * letting the compiler implicitly convert a scalar to a vector (assuming
+ * the BASE<T> allows it).
+ */
+ friend inline constexpr VECTOR<T> PURE operator *(VECTOR<T> lv, const VECTOR<T>& rv) {
+ // don't pass lv by reference because we need a copy anyways
+ return lv *= rv;
+ }
+ friend inline constexpr VECTOR<T> PURE operator /(VECTOR<T> lv, const VECTOR<T>& rv) {
+ // don't pass lv by reference because we need a copy anyways
+ return lv /= rv;
+ }
+};
+
+/*
+ * TVecUnaryOperators implements unary operators on a vector of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TVecUnaryOperators<BASE, T> BASE will automatically
+ * get all the functionality here.
+ *
+ * These operators are implemented as friend functions of TVecUnaryOperators<BASE, T>
+ */
+template<template<typename T> class VECTOR, typename T>
+class TVecUnaryOperators {
+public:
+ VECTOR<T>& operator ++() {
+ VECTOR<T>& rhs = static_cast<VECTOR<T>&>(*this);
+ for (size_t i = 0; i < rhs.size(); i++) {
+ ++rhs[i];
+ }
+ return rhs;
+ }
+
+ VECTOR<T>& operator --() {
+ VECTOR<T>& rhs = static_cast<VECTOR<T>&>(*this);
+ for (size_t i = 0; i < rhs.size(); i++) {
+ --rhs[i];
+ }
+ return rhs;
+ }
+
+ CONSTEXPR VECTOR<T> operator -() const {
+ VECTOR<T> r(VECTOR<T>::NO_INIT);
+ VECTOR<T> const& rv(static_cast<VECTOR<T> const&>(*this));
+ for (size_t i = 0; i < r.size(); i++) {
+ r[i] = -rv[i];
+ }
+ return r;
+ }
+};
+
+/*
+ * TVecComparisonOperators implements relational/comparison operators
+ * on a vector of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TVecComparisonOperators<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+template<template<typename T> class VECTOR, typename T>
+class TVecComparisonOperators {
+public:
+ /*
+ * NOTE: the functions below ARE NOT member methods. They are friend functions
+ * with they definition inlined with their declaration. This makes these
+ * template functions available to the compiler when (and only when) this class
+ * is instantiated, at which point they're only templated on the 2nd parameter
+ * (the first one, BASE<T> being known).
+ */
+ template<typename RT>
+ friend inline
+ bool PURE operator ==(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ for (size_t i = 0; i < lv.size(); i++)
+ if (lv[i] != rv[i])
+ return false;
+ return true;
+ }
+
+ template<typename RT>
+ friend inline
+ bool PURE operator !=(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ return !operator ==(lv, rv);
+ }
+
+ template<typename RT>
+ friend inline
+ bool PURE operator >(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ for (size_t i = 0; i < lv.size(); i++) {
+ if (lv[i] == rv[i]) {
+ continue;
+ }
+ return lv[i] > rv[i];
+ }
+ return false;
+ }
+
+ template<typename RT>
+ friend inline
+ constexpr bool PURE operator <=(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ return !(lv > rv);
+ }
+
+ template<typename RT>
+ friend inline
+ bool PURE operator <(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ for (size_t i = 0; i < lv.size(); i++) {
+ if (lv[i] == rv[i]) {
+ continue;
+ }
+ return lv[i] < rv[i];
+ }
+ return false;
+ }
+
+ template<typename RT>
+ friend inline
+ constexpr bool PURE operator >=(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ return !(lv < rv);
+ }
+
+ template<typename RT>
+ friend inline
+ CONSTEXPR VECTOR<bool> PURE equal(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ VECTOR<bool> r;
+ for (size_t i = 0; i < lv.size(); i++) {
+ r[i] = lv[i] == rv[i];
+ }
+ return r;
+ }
+
+ template<typename RT>
+ friend inline
+ CONSTEXPR VECTOR<bool> PURE notEqual(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ VECTOR<bool> r;
+ for (size_t i = 0; i < lv.size(); i++) {
+ r[i] = lv[i] != rv[i];
+ }
+ return r;
+ }
+
+ template<typename RT>
+ friend inline
+ CONSTEXPR VECTOR<bool> PURE lessThan(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ VECTOR<bool> r;
+ for (size_t i = 0; i < lv.size(); i++) {
+ r[i] = lv[i] < rv[i];
+ }
+ return r;
+ }
+
+ template<typename RT>
+ friend inline
+ CONSTEXPR VECTOR<bool> PURE lessThanEqual(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ VECTOR<bool> r;
+ for (size_t i = 0; i < lv.size(); i++) {
+ r[i] = lv[i] <= rv[i];
+ }
+ return r;
+ }
+
+ template<typename RT>
+ friend inline
+ CONSTEXPR VECTOR<bool> PURE greaterThan(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ VECTOR<bool> r;
+ for (size_t i = 0; i < lv.size(); i++) {
+ r[i] = lv[i] > rv[i];
+ }
+ return r;
+ }
+
+ template<typename RT>
+ friend inline
+ CONSTEXPR VECTOR<bool> PURE greaterThanEqual(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ VECTOR<bool> r;
+ for (size_t i = 0; i < lv.size(); i++) {
+ r[i] = lv[i] >= rv[i];
+ }
+ return r;
+ }
+};
+
+/*
+ * TVecFunctions implements functions on a vector of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TVecFunctions<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+template<template<typename T> class VECTOR, typename T>
+class TVecFunctions {
+public:
+ /*
+ * NOTE: the functions below ARE NOT member methods. They are friend functions
+ * with they definition inlined with their declaration. This makes these
+ * template functions available to the compiler when (and only when) this class
+ * is instantiated, at which point they're only templated on the 2nd parameter
+ * (the first one, BASE<T> being known).
+ */
+ template<typename RT>
+ friend inline CONSTEXPR T PURE dot(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ T r(0);
+ for (size_t i = 0; i < lv.size(); i++) {
+ //r = std::fma(lv[i], rv[i], r);
+ r += lv[i] * rv[i];
+ }
+ return r;
+ }
+
+ friend inline constexpr T PURE norm(const VECTOR<T>& lv) {
+ return std::sqrt(dot(lv, lv));
+ }
+
+ friend inline constexpr T PURE length(const VECTOR<T>& lv) {
+ return norm(lv);
+ }
+
+ friend inline constexpr T PURE norm2(const VECTOR<T>& lv) {
+ return dot(lv, lv);
+ }
+
+ friend inline constexpr T PURE length2(const VECTOR<T>& lv) {
+ return norm2(lv);
+ }
+
+ template<typename RT>
+ friend inline constexpr T PURE distance(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ return length(rv - lv);
+ }
+
+ template<typename RT>
+ friend inline constexpr T PURE distance2(const VECTOR<T>& lv, const VECTOR<RT>& rv) {
+ return length2(rv - lv);
+ }
+
+ friend inline constexpr VECTOR<T> PURE normalize(const VECTOR<T>& lv) {
+ return lv * (T(1) / length(lv));
+ }
+
+ friend inline constexpr VECTOR<T> PURE rcp(VECTOR<T> v) {
+ return T(1) / v;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE abs(VECTOR<T> v) {
+ for (size_t i = 0; i < v.size(); i++) {
+ v[i] = std::abs(v[i]);
+ }
+ return v;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE floor(VECTOR<T> v) {
+ for (size_t i = 0; i < v.size(); i++) {
+ v[i] = std::floor(v[i]);
+ }
+ return v;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE ceil(VECTOR<T> v) {
+ for (size_t i = 0; i < v.size(); i++) {
+ v[i] = std::ceil(v[i]);
+ }
+ return v;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE round(VECTOR<T> v) {
+ for (size_t i = 0; i < v.size(); i++) {
+ v[i] = std::round(v[i]);
+ }
+ return v;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE inversesqrt(VECTOR<T> v) {
+ for (size_t i = 0; i < v.size(); i++) {
+ v[i] = T(1) / std::sqrt(v[i]);
+ }
+ return v;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE sqrt(VECTOR<T> v) {
+ for (size_t i = 0; i < v.size(); i++) {
+ v[i] = std::sqrt(v[i]);
+ }
+ return v;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE pow(VECTOR<T> v, T p) {
+ for (size_t i = 0; i < v.size(); i++) {
+ v[i] = std::pow(v[i], p);
+ }
+ return v;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE saturate(const VECTOR<T>& lv) {
+ return clamp(lv, T(0), T(1));
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE clamp(VECTOR<T> v, T min, T max) {
+ for (size_t i = 0; i< v.size(); i++) {
+ v[i] = std::min(max, std::max(min, v[i]));
+ }
+ return v;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE fma(const VECTOR<T>& lv, const VECTOR<T>& rv, VECTOR<T> a) {
+ for (size_t i = 0; i<lv.size(); i++) {
+ //a[i] = std::fma(lv[i], rv[i], a[i]);
+ a[i] += (lv[i] * rv[i]);
+ }
+ return a;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE min(const VECTOR<T>& u, VECTOR<T> v) {
+ for (size_t i = 0; i < v.size(); i++) {
+ v[i] = std::min(u[i], v[i]);
+ }
+ return v;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE max(const VECTOR<T>& u, VECTOR<T> v) {
+ for (size_t i = 0; i < v.size(); i++) {
+ v[i] = std::max(u[i], v[i]);
+ }
+ return v;
+ }
+
+ friend inline CONSTEXPR T PURE max(const VECTOR<T>& v) {
+ T r(std::numeric_limits<T>::lowest());
+ for (size_t i = 0; i < v.size(); i++) {
+ r = std::max(r, v[i]);
+ }
+ return r;
+ }
+
+ friend inline CONSTEXPR T PURE min(const VECTOR<T>& v) {
+ T r(std::numeric_limits<T>::max());
+ for (size_t i = 0; i < v.size(); i++) {
+ r = std::min(r, v[i]);
+ }
+ return r;
+ }
+
+ friend inline CONSTEXPR VECTOR<T> PURE apply(VECTOR<T> v, const std::function<T(T)>& f) {
+ for (size_t i = 0; i < v.size(); i++) {
+ v[i] = f(v[i]);
+ }
+ return v;
+ }
+
+ friend inline CONSTEXPR bool PURE any(const VECTOR<T>& v) {
+ for (size_t i = 0; i < v.size(); i++) {
+ if (v[i] != T(0)) return true;
+ }
+ return false;
+ }
+
+ friend inline CONSTEXPR bool PURE all(const VECTOR<T>& v) {
+ bool result = true;
+ for (size_t i = 0; i < v.size(); i++) {
+ result &= (v[i] != T(0));
+ }
+ return result;
+ }
+
+ template<typename R>
+ friend inline CONSTEXPR VECTOR<R> PURE map(VECTOR<T> v, const std::function<R(T)>& f) {
+ VECTOR<R> result;
+ for (size_t i = 0; i < v.size(); i++) {
+ result[i] = f(v[i]);
+ }
+ return result;
+ }
+};
+
+/*
+ * TVecDebug implements functions on a vector of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TVecDebug<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+template<template<typename T> class VECTOR, typename T>
+class TVecDebug {
+public:
+ /*
+ * NOTE: the functions below ARE NOT member methods. They are friend functions
+ * with they definition inlined with their declaration. This makes these
+ * template functions available to the compiler when (and only when) this class
+ * is instantiated, at which point they're only templated on the 2nd parameter
+ * (the first one, BASE<T> being known).
+ */
+ friend std::ostream& operator<<(std::ostream& stream, const VECTOR<T>& v) {
+ stream << "< ";
+ for (size_t i = 0; i < v.size() - 1; i++) {
+ stream << T(v[i]) << ", ";
+ }
+ stream << T(v[v.size() - 1]) << " >";
+ return stream;
+ }
+};
+
+#undef CONSTEXPR
+#undef PURE
+
+// -------------------------------------------------------------------------------------
+} // namespace details
+} // namespace android
diff --git a/libs/math/include/math/half.h b/libs/math/include/math/half.h
new file mode 100644
index 0000000..3ca8bd1
--- /dev/null
+++ b/libs/math/include/math/half.h
@@ -0,0 +1,205 @@
+/*
+ * Copyright (C) 2016 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#pragma once
+
+#include <stdint.h>
+#include <iosfwd>
+#include <limits>
+#include <type_traits>
+
+#ifdef __cplusplus
+# define LIKELY( exp ) (__builtin_expect( !!(exp), true ))
+# define UNLIKELY( exp ) (__builtin_expect( !!(exp), false ))
+#else
+# define LIKELY( exp ) (__builtin_expect( !!(exp), 1 ))
+# define UNLIKELY( exp ) (__builtin_expect( !!(exp), 0 ))
+#endif
+
+#if __cplusplus >= 201402L
+#define CONSTEXPR constexpr
+#else
+#define CONSTEXPR
+#endif
+
+namespace android {
+
+/*
+ * half-float
+ *
+ * 1 5 10
+ * +-+------+------------+
+ * |s|eee.ee|mm.mmmm.mmmm|
+ * +-+------+------------+
+ *
+ * minimum (denormal) value: 2^-24 = 5.96e-8
+ * minimum (normal) value: 2^-14 = 6.10e-5
+ * maximum value: 2-2^-10 = 65504
+ *
+ * Integers between 0 and 2048 can be represented exactly
+ */
+class half {
+ struct fp16 {
+ uint16_t bits = 0;
+ fp16() noexcept = default;
+ explicit constexpr fp16(uint16_t b) noexcept : bits(b) { }
+ void setS(unsigned int s) noexcept { bits = uint16_t((bits & 0x7FFF) | (s<<15)); }
+ void setE(unsigned int s) noexcept { bits = uint16_t((bits & 0xE3FF) | (s<<10)); }
+ void setM(unsigned int s) noexcept { bits = uint16_t((bits & 0xFC00) | (s<< 0)); }
+ constexpr unsigned int getS() const noexcept { return bits >> 15u; }
+ constexpr unsigned int getE() const noexcept { return (bits >> 10u) & 0x1Fu; }
+ constexpr unsigned int getM() const noexcept { return bits & 0x3FFu; }
+ };
+ struct fp32 {
+ union {
+ uint32_t bits = 0;
+ float fp;
+ };
+ fp32() noexcept = default;
+ explicit constexpr fp32(float f) : fp(f) { }
+ void setS(unsigned int s) noexcept { bits = uint32_t((bits & 0x7FFFFFFF) | (s<<31)); }
+ void setE(unsigned int s) noexcept { bits = uint32_t((bits & 0x807FFFFF) | (s<<23)); }
+ void setM(unsigned int s) noexcept { bits = uint32_t((bits & 0xFF800000) | (s<< 0)); }
+ constexpr unsigned int getS() const noexcept { return bits >> 31u; }
+ constexpr unsigned int getE() const noexcept { return (bits >> 23u) & 0xFFu; }
+ constexpr unsigned int getM() const noexcept { return bits & 0x7FFFFFu; }
+ };
+
+public:
+ CONSTEXPR half(float v) noexcept : mBits(ftoh(v)) { }
+ CONSTEXPR operator float() const noexcept { return htof(mBits); }
+
+ uint16_t getBits() const noexcept { return mBits.bits; }
+ unsigned int getExponent() const noexcept { return mBits.getE(); }
+ unsigned int getMantissa() const noexcept { return mBits.getM(); }
+
+private:
+ friend class std::numeric_limits<half>;
+ friend CONSTEXPR half operator"" _hf(long double v);
+
+ enum Binary { binary };
+ explicit constexpr half(Binary, uint16_t bits) noexcept : mBits(bits) { }
+ static CONSTEXPR fp16 ftoh(float v) noexcept;
+ static CONSTEXPR float htof(fp16 v) noexcept;
+ fp16 mBits;
+};
+
+inline CONSTEXPR half::fp16 half::ftoh(float v) noexcept {
+ fp16 out;
+ fp32 in(v);
+ if (UNLIKELY(in.getE() == 0xFF)) { // inf or nan
+ out.setE(0x1F);
+ out.setM(in.getM() ? 0x200 : 0);
+ } else {
+ int e = static_cast<int>(in.getE()) - 127 + 15;
+ if (e >= 0x1F) {
+ // overflow
+ out.setE(0x31); // +/- inf
+ } else if (e <= 0) {
+ // underflow
+ // flush to +/- 0
+ } else {
+ unsigned int m = in.getM();
+ out.setE(uint16_t(e));
+ out.setM(m >> 13);
+ if (m & 0x1000) {
+ // rounding
+ out.bits++;
+ }
+ }
+ }
+ out.setS(in.getS());
+ return out;
+}
+
+inline CONSTEXPR float half::htof(half::fp16 in) noexcept {
+ fp32 out;
+ if (UNLIKELY(in.getE() == 0x1F)) { // inf or nan
+ out.setE(0xFF);
+ out.setM(in.getM() ? 0x400000 : 0);
+ } else {
+ if (in.getE() == 0) {
+ if (in.getM()) {
+ // TODO: denormal half float, treat as zero for now
+ // (it's stupid because they can be represented as regular float)
+ }
+ } else {
+ int e = static_cast<int>(in.getE()) - 15 + 127;
+ unsigned int m = in.getM();
+ out.setE(uint32_t(e));
+ out.setM(m << 13);
+ }
+ }
+ out.setS(in.getS());
+ return out.fp;
+}
+
+inline CONSTEXPR android::half operator"" _hf(long double v) {
+ return android::half(android::half::binary, android::half::ftoh(static_cast<float>(v)).bits);
+}
+
+} // namespace android
+
+namespace std {
+
+template<> struct is_floating_point<android::half> : public std::true_type {};
+
+template<>
+class numeric_limits<android::half> {
+public:
+ typedef android::half type;
+
+ static constexpr const bool is_specialized = true;
+ static constexpr const bool is_signed = true;
+ static constexpr const bool is_integer = false;
+ static constexpr const bool is_exact = false;
+ static constexpr const bool has_infinity = true;
+ static constexpr const bool has_quiet_NaN = true;
+ static constexpr const bool has_signaling_NaN = false;
+ static constexpr const float_denorm_style has_denorm = denorm_absent;
+ static constexpr const bool has_denorm_loss = true;
+ static constexpr const bool is_iec559 = false;
+ static constexpr const bool is_bounded = true;
+ static constexpr const bool is_modulo = false;
+ static constexpr const bool traps = false;
+ static constexpr const bool tinyness_before = false;
+ static constexpr const float_round_style round_style = round_indeterminate;
+
+ static constexpr const int digits = 11;
+ static constexpr const int digits10 = 3;
+ static constexpr const int max_digits10 = 5;
+ static constexpr const int radix = 2;
+ static constexpr const int min_exponent = -13;
+ static constexpr const int min_exponent10 = -4;
+ static constexpr const int max_exponent = 16;
+ static constexpr const int max_exponent10 = 4;
+
+ inline static constexpr type round_error() noexcept { return android::half(android::half::binary, 0x3800); }
+ inline static constexpr type min() noexcept { return android::half(android::half::binary, 0x0400); }
+ inline static constexpr type max() noexcept { return android::half(android::half::binary, 0x7bff); }
+ inline static constexpr type lowest() noexcept { return android::half(android::half::binary, 0xfbff); }
+ inline static constexpr type epsilon() noexcept { return android::half(android::half::binary, 0x1400); }
+ inline static constexpr type infinity() noexcept { return android::half(android::half::binary, 0x7c00); }
+ inline static constexpr type quiet_NaN() noexcept { return android::half(android::half::binary, 0x7fff); }
+ inline static constexpr type denorm_min() noexcept { return android::half(android::half::binary, 0x0001); }
+ inline static constexpr type signaling_NaN() noexcept { return android::half(android::half::binary, 0x7dff); }
+};
+
+} // namespace std
+
+#undef LIKELY
+#undef UNLIKELY
+#undef CONSTEXPR
diff --git a/libs/math/include/math/mat2.h b/libs/math/include/math/mat2.h
new file mode 100644
index 0000000..3e6cd4c
--- /dev/null
+++ b/libs/math/include/math/mat2.h
@@ -0,0 +1,377 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#pragma once
+
+#include <math/TMatHelpers.h>
+#include <math/vec2.h>
+#include <stdint.h>
+#include <sys/types.h>
+
+#define PURE __attribute__((pure))
+
+#if __cplusplus >= 201402L
+#define CONSTEXPR constexpr
+#else
+#define CONSTEXPR
+#endif
+
+namespace android {
+// -------------------------------------------------------------------------------------
+namespace details {
+
+/**
+ * A 2x2 column-major matrix class.
+ *
+ * Conceptually a 2x2 matrix is a an array of 2 column vec2:
+ *
+ * mat2 m =
+ * \f$
+ * \left(
+ * \begin{array}{cc}
+ * m[0] & m[1] \\
+ * \end{array}
+ * \right)
+ * \f$
+ * =
+ * \f$
+ * \left(
+ * \begin{array}{cc}
+ * m[0][0] & m[1][0] \\
+ * m[0][1] & m[1][1] \\
+ * \end{array}
+ * \right)
+ * \f$
+ * =
+ * \f$
+ * \left(
+ * \begin{array}{cc}
+ * m(0,0) & m(0,1) \\
+ * m(1,0) & m(1,1) \\
+ * \end{array}
+ * \right)
+ * \f$
+ *
+ * m[n] is the \f$ n^{th} \f$ column of the matrix and is a vec2.
+ *
+ */
+template <typename T>
+class TMat22 : public TVecUnaryOperators<TMat22, T>,
+ public TVecComparisonOperators<TMat22, T>,
+ public TVecAddOperators<TMat22, T>,
+ public TMatProductOperators<TMat22, T>,
+ public TMatSquareFunctions<TMat22, T>,
+ public TMatHelpers<TMat22, T>,
+ public TMatDebug<TMat22, T> {
+public:
+ enum no_init { NO_INIT };
+ typedef T value_type;
+ typedef T& reference;
+ typedef T const& const_reference;
+ typedef size_t size_type;
+ typedef TVec2<T> col_type;
+ typedef TVec2<T> row_type;
+
+ static constexpr size_t COL_SIZE = col_type::SIZE; // size of a column (i.e.: number of rows)
+ static constexpr size_t ROW_SIZE = row_type::SIZE; // size of a row (i.e.: number of columns)
+ static constexpr size_t NUM_ROWS = COL_SIZE;
+ static constexpr size_t NUM_COLS = ROW_SIZE;
+
+private:
+ /*
+ * <-- N columns -->
+ *
+ * a[0][0] a[1][0] a[2][0] ... a[N][0] ^
+ * a[0][1] a[1][1] a[2][1] ... a[N][1] |
+ * a[0][2] a[1][2] a[2][2] ... a[N][2] M rows
+ * ... |
+ * a[0][M] a[1][M] a[2][M] ... a[N][M] v
+ *
+ * COL_SIZE = M
+ * ROW_SIZE = N
+ * m[0] = [ a[0][0] a[0][1] a[0][2] ... a[0][M] ]
+ */
+
+ col_type m_value[NUM_COLS];
+
+public:
+ // array access
+ inline constexpr col_type const& operator[](size_t column) const {
+#if __cplusplus >= 201402L
+ // only possible in C++0x14 with constexpr
+ assert(column < NUM_COLS);
+#endif
+ return m_value[column];
+ }
+
+ inline col_type& operator[](size_t column) {
+ assert(column < NUM_COLS);
+ return m_value[column];
+ }
+
+ // -----------------------------------------------------------------------
+ // we want the compiler generated versions for these...
+ TMat22(const TMat22&) = default;
+ ~TMat22() = default;
+ TMat22& operator = (const TMat22&) = default;
+
+ /**
+ * constructors
+ */
+
+ /**
+ * leaves object uninitialized. use with caution.
+ */
+ explicit constexpr TMat22(no_init)
+ : m_value{ col_type(col_type::NO_INIT),
+ col_type(col_type::NO_INIT) } {}
+
+
+ /**
+ * initialize to identity.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{cc}
+ * 1 & 0 \\
+ * 0 & 1 \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ CONSTEXPR TMat22();
+
+ /**
+ * initialize to Identity*scalar.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{cc}
+ * v & 0 \\
+ * 0 & v \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template<typename U>
+ explicit CONSTEXPR TMat22(U v);
+
+ /**
+ * sets the diagonal to a vector.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{cc}
+ * v[0] & 0 \\
+ * 0 & v[1] \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <typename U>
+ explicit CONSTEXPR TMat22(const TVec2<U>& v);
+
+ /**
+ * construct from another matrix of the same size
+ */
+ template <typename U>
+ explicit CONSTEXPR TMat22(const TMat22<U>& rhs);
+
+ /**
+ * construct from 2 column vectors.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{cc}
+ * v0 & v1 \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <typename A, typename B>
+ CONSTEXPR TMat22(const TVec2<A>& v0, const TVec2<B>& v1);
+
+ /** construct from 4 elements in column-major form.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{cc}
+ * m[0][0] & m[1][0] \\
+ * m[0][1] & m[1][1] \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <
+ typename A, typename B,
+ typename C, typename D>
+ CONSTEXPR TMat22(A m00, B m01, C m10, D m11);
+
+ /**
+ * construct from a C array in column major form.
+ */
+ template <typename U>
+ explicit CONSTEXPR TMat22(U const* rawArray);
+
+ /**
+ * Rotate by radians in the 2D plane
+ */
+ static CONSTEXPR TMat22<T> rotate(T radian) {
+ TMat22<T> r(TMat22<T>::NO_INIT);
+ T c = std::cos(radian);
+ T s = std::sin(radian);
+ r[0][0] = c; r[1][1] = c;
+ r[0][1] = s; r[1][0] = -s;
+ return r;
+ }
+};
+
+// ----------------------------------------------------------------------------------------
+// Constructors
+// ----------------------------------------------------------------------------------------
+
+// Since the matrix code could become pretty big quickly, we don't inline most
+// operations.
+
+template <typename T>
+CONSTEXPR TMat22<T>::TMat22() {
+ m_value[0] = col_type(1, 0);
+ m_value[1] = col_type(0, 1);
+}
+
+template <typename T>
+template <typename U>
+CONSTEXPR TMat22<T>::TMat22(U v) {
+ m_value[0] = col_type(v, 0);
+ m_value[1] = col_type(0, v);
+}
+
+template<typename T>
+template<typename U>
+CONSTEXPR TMat22<T>::TMat22(const TVec2<U>& v) {
+ m_value[0] = col_type(v.x, 0);
+ m_value[1] = col_type(0, v.y);
+}
+
+// construct from 4 scalars. Note that the arrangement
+// of values in the constructor is the transpose of the matrix
+// notation.
+template<typename T>
+template <
+ typename A, typename B,
+ typename C, typename D>
+CONSTEXPR TMat22<T>::TMat22( A m00, B m01, C m10, D m11) {
+ m_value[0] = col_type(m00, m01);
+ m_value[1] = col_type(m10, m11);
+}
+
+template <typename T>
+template <typename U>
+CONSTEXPR TMat22<T>::TMat22(const TMat22<U>& rhs) {
+ for (size_t col = 0; col < NUM_COLS; ++col) {
+ m_value[col] = col_type(rhs[col]);
+ }
+}
+
+// Construct from 2 column vectors.
+template <typename T>
+template <typename A, typename B>
+CONSTEXPR TMat22<T>::TMat22(const TVec2<A>& v0, const TVec2<B>& v1) {
+ m_value[0] = v0;
+ m_value[1] = v1;
+}
+
+// Construct from raw array, in column-major form.
+template <typename T>
+template <typename U>
+CONSTEXPR TMat22<T>::TMat22(U const* rawArray) {
+ for (size_t col = 0; col < NUM_COLS; ++col) {
+ for (size_t row = 0; row < NUM_ROWS; ++row) {
+ m_value[col][row] = *rawArray++;
+ }
+ }
+}
+
+// ----------------------------------------------------------------------------------------
+// Arithmetic operators outside of class
+// ----------------------------------------------------------------------------------------
+
+/* We use non-friend functions here to prevent the compiler from using
+ * implicit conversions, for instance of a scalar to a vector. The result would
+ * not be what the caller expects.
+ *
+ * Also note that the order of the arguments in the inner loop is important since
+ * it determines the output type (only relevant when T != U).
+ */
+
+// matrix * column-vector, result is a vector of the same type than the input vector
+template <typename T, typename U>
+CONSTEXPR typename TMat22<U>::col_type PURE operator *(const TMat22<T>& lhs, const TVec2<U>& rhs) {
+ // Result is initialized to zero.
+ typename TMat22<U>::col_type result;
+ for (size_t col = 0; col < TMat22<T>::NUM_COLS; ++col) {
+ result += lhs[col] * rhs[col];
+ }
+ return result;
+}
+
+// row-vector * matrix, result is a vector of the same type than the input vector
+template <typename T, typename U>
+CONSTEXPR typename TMat22<U>::row_type PURE operator *(const TVec2<U>& lhs, const TMat22<T>& rhs) {
+ typename TMat22<U>::row_type result(TMat22<U>::row_type::NO_INIT);
+ for (size_t col = 0; col < TMat22<T>::NUM_COLS; ++col) {
+ result[col] = dot(lhs, rhs[col]);
+ }
+ return result;
+}
+
+// matrix * scalar, result is a matrix of the same type than the input matrix
+template<typename T, typename U>
+constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat22<T>>::type PURE
+operator*(TMat22<T> lhs, U rhs) {
+ return lhs *= rhs;
+}
+
+// scalar * matrix, result is a matrix of the same type than the input matrix
+template<typename T, typename U>
+constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat22<T>>::type PURE
+operator*(U lhs, const TMat22<T>& rhs) {
+ return rhs * lhs;
+}
+
+// ----------------------------------------------------------------------------------------
+
+/* FIXME: this should go into TMatSquareFunctions<> but for some reason
+ * BASE<T>::col_type is not accessible from there (???)
+ */
+template<typename T>
+CONSTEXPR typename TMat22<T>::col_type PURE diag(const TMat22<T>& m) {
+ return matrix::diag(m);
+}
+
+} // namespace details
+
+// ----------------------------------------------------------------------------------------
+
+typedef details::TMat22<double> mat2d;
+typedef details::TMat22<float> mat2;
+typedef details::TMat22<float> mat2f;
+
+// ----------------------------------------------------------------------------------------
+} // namespace android
+
+#undef PURE
+#undef CONSTEXPR
diff --git a/libs/math/include/math/mat3.h b/libs/math/include/math/mat3.h
new file mode 100644
index 0000000..5c8a9b2
--- /dev/null
+++ b/libs/math/include/math/mat3.h
@@ -0,0 +1,440 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#pragma once
+
+#include <math/quat.h>
+#include <math/TMatHelpers.h>
+#include <math/vec3.h>
+#include <stdint.h>
+#include <sys/types.h>
+
+#define PURE __attribute__((pure))
+
+#if __cplusplus >= 201402L
+#define CONSTEXPR constexpr
+#else
+#define CONSTEXPR
+#endif
+
+namespace android {
+// -------------------------------------------------------------------------------------
+namespace details {
+
+template<typename T>
+class TQuaternion;
+
+/**
+ * A 3x3 column-major matrix class.
+ *
+ * Conceptually a 3x3 matrix is a an array of 3 column vec3:
+ *
+ * mat3 m =
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * m[0] & m[1] & m[2] \\
+ * \end{array}
+ * \right)
+ * \f$
+ * =
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * m[0][0] & m[1][0] & m[2][0] \\
+ * m[0][1] & m[1][1] & m[2][1] \\
+ * m[0][2] & m[1][2] & m[2][2] \\
+ * \end{array}
+ * \right)
+ * \f$
+ * =
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * m(0,0) & m(0,1) & m(0,2) \\
+ * m(1,0) & m(1,1) & m(1,2) \\
+ * m(2,0) & m(2,1) & m(2,2) \\
+ * \end{array}
+ * \right)
+ * \f$
+ *
+ * m[n] is the \f$ n^{th} \f$ column of the matrix and is a vec3.
+ *
+ */
+template <typename T>
+class TMat33 : public TVecUnaryOperators<TMat33, T>,
+ public TVecComparisonOperators<TMat33, T>,
+ public TVecAddOperators<TMat33, T>,
+ public TMatProductOperators<TMat33, T>,
+ public TMatSquareFunctions<TMat33, T>,
+ public TMatTransform<TMat33, T>,
+ public TMatHelpers<TMat33, T>,
+ public TMatDebug<TMat33, T> {
+public:
+ enum no_init { NO_INIT };
+ typedef T value_type;
+ typedef T& reference;
+ typedef T const& const_reference;
+ typedef size_t size_type;
+ typedef TVec3<T> col_type;
+ typedef TVec3<T> row_type;
+
+ static constexpr size_t COL_SIZE = col_type::SIZE; // size of a column (i.e.: number of rows)
+ static constexpr size_t ROW_SIZE = row_type::SIZE; // size of a row (i.e.: number of columns)
+ static constexpr size_t NUM_ROWS = COL_SIZE;
+ static constexpr size_t NUM_COLS = ROW_SIZE;
+
+private:
+ /*
+ * <-- N columns -->
+ *
+ * a[0][0] a[1][0] a[2][0] ... a[N][0] ^
+ * a[0][1] a[1][1] a[2][1] ... a[N][1] |
+ * a[0][2] a[1][2] a[2][2] ... a[N][2] M rows
+ * ... |
+ * a[0][M] a[1][M] a[2][M] ... a[N][M] v
+ *
+ * COL_SIZE = M
+ * ROW_SIZE = N
+ * m[0] = [ a[0][0] a[0][1] a[0][2] ... a[0][M] ]
+ */
+
+ col_type m_value[NUM_COLS];
+
+public:
+ // array access
+ inline constexpr col_type const& operator[](size_t column) const {
+#if __cplusplus >= 201402L
+ // only possible in C++0x14 with constexpr
+ assert(column < NUM_COLS);
+#endif
+ return m_value[column];
+ }
+
+ inline col_type& operator[](size_t column) {
+ assert(column < NUM_COLS);
+ return m_value[column];
+ }
+
+ // -----------------------------------------------------------------------
+ // we want the compiler generated versions for these...
+ TMat33(const TMat33&) = default;
+ ~TMat33() = default;
+ TMat33& operator = (const TMat33&) = default;
+
+ /**
+ * constructors
+ */
+
+ /**
+ * leaves object uninitialized. use with caution.
+ */
+ explicit constexpr TMat33(no_init)
+ : m_value{ col_type(col_type::NO_INIT),
+ col_type(col_type::NO_INIT),
+ col_type(col_type::NO_INIT) } {}
+
+
+ /**
+ * initialize to identity.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * 1 & 0 & 0 \\
+ * 0 & 1 & 0 \\
+ * 0 & 0 & 1 \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ CONSTEXPR TMat33();
+
+ /**
+ * initialize to Identity*scalar.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * v & 0 & 0 \\
+ * 0 & v & 0 \\
+ * 0 & 0 & v \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template<typename U>
+ explicit CONSTEXPR TMat33(U v);
+
+ /**
+ * sets the diagonal to a vector.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * v[0] & 0 & 0 \\
+ * 0 & v[1] & 0 \\
+ * 0 & 0 & v[2] \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <typename U>
+ explicit CONSTEXPR TMat33(const TVec3<U>& v);
+
+ /**
+ * construct from another matrix of the same size
+ */
+ template <typename U>
+ explicit CONSTEXPR TMat33(const TMat33<U>& rhs);
+
+ /**
+ * construct from 3 column vectors.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * v0 & v1 & v2 \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <typename A, typename B, typename C>
+ CONSTEXPR TMat33(const TVec3<A>& v0, const TVec3<B>& v1, const TVec3<C>& v2);
+
+ /** construct from 9 elements in column-major form.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * m[0][0] & m[1][0] & m[2][0] \\
+ * m[0][1] & m[1][1] & m[2][1] \\
+ * m[0][2] & m[1][2] & m[2][2] \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <
+ typename A, typename B, typename C,
+ typename D, typename E, typename F,
+ typename G, typename H, typename I>
+ CONSTEXPR TMat33(
+ A m00, B m01, C m02,
+ D m10, E m11, F m12,
+ G m20, H m21, I m22);
+
+ /**
+ * construct from a quaternion
+ */
+ template <typename U>
+ explicit CONSTEXPR TMat33(const TQuaternion<U>& q);
+
+ /**
+ * construct from a C array in column major form.
+ */
+ template <typename U>
+ explicit CONSTEXPR TMat33(U const* rawArray);
+
+ /**
+ * orthogonalize only works on matrices of size 3x3
+ */
+ friend inline
+ CONSTEXPR TMat33 orthogonalize(const TMat33& m) {
+ TMat33 ret(TMat33::NO_INIT);
+ ret[0] = normalize(m[0]);
+ ret[2] = normalize(cross(ret[0], m[1]));
+ ret[1] = normalize(cross(ret[2], ret[0]));
+ return ret;
+ }
+};
+
+// ----------------------------------------------------------------------------------------
+// Constructors
+// ----------------------------------------------------------------------------------------
+
+// Since the matrix code could become pretty big quickly, we don't inline most
+// operations.
+
+template <typename T>
+CONSTEXPR TMat33<T>::TMat33() {
+ m_value[0] = col_type(1, 0, 0);
+ m_value[1] = col_type(0, 1, 0);
+ m_value[2] = col_type(0, 0, 1);
+}
+
+template <typename T>
+template <typename U>
+CONSTEXPR TMat33<T>::TMat33(U v) {
+ m_value[0] = col_type(v, 0, 0);
+ m_value[1] = col_type(0, v, 0);
+ m_value[2] = col_type(0, 0, v);
+}
+
+template<typename T>
+template<typename U>
+CONSTEXPR TMat33<T>::TMat33(const TVec3<U>& v) {
+ m_value[0] = col_type(v.x, 0, 0);
+ m_value[1] = col_type(0, v.y, 0);
+ m_value[2] = col_type(0, 0, v.z);
+}
+
+// construct from 9 scalars. Note that the arrangement
+// of values in the constructor is the transpose of the matrix
+// notation.
+template<typename T>
+template <
+ typename A, typename B, typename C,
+ typename D, typename E, typename F,
+ typename G, typename H, typename I>
+CONSTEXPR TMat33<T>::TMat33(
+ A m00, B m01, C m02,
+ D m10, E m11, F m12,
+ G m20, H m21, I m22) {
+ m_value[0] = col_type(m00, m01, m02);
+ m_value[1] = col_type(m10, m11, m12);
+ m_value[2] = col_type(m20, m21, m22);
+}
+
+template <typename T>
+template <typename U>
+CONSTEXPR TMat33<T>::TMat33(const TMat33<U>& rhs) {
+ for (size_t col = 0; col < NUM_COLS; ++col) {
+ m_value[col] = col_type(rhs[col]);
+ }
+}
+
+// Construct from 3 column vectors.
+template <typename T>
+template <typename A, typename B, typename C>
+CONSTEXPR TMat33<T>::TMat33(const TVec3<A>& v0, const TVec3<B>& v1, const TVec3<C>& v2) {
+ m_value[0] = v0;
+ m_value[1] = v1;
+ m_value[2] = v2;
+}
+
+// Construct from raw array, in column-major form.
+template <typename T>
+template <typename U>
+CONSTEXPR TMat33<T>::TMat33(U const* rawArray) {
+ for (size_t col = 0; col < NUM_COLS; ++col) {
+ for (size_t row = 0; row < NUM_ROWS; ++row) {
+ m_value[col][row] = *rawArray++;
+ }
+ }
+}
+
+template <typename T>
+template <typename U>
+CONSTEXPR TMat33<T>::TMat33(const TQuaternion<U>& q) {
+ const U n = q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w;
+ const U s = n > 0 ? 2/n : 0;
+ const U x = s*q.x;
+ const U y = s*q.y;
+ const U z = s*q.z;
+ const U xx = x*q.x;
+ const U xy = x*q.y;
+ const U xz = x*q.z;
+ const U xw = x*q.w;
+ const U yy = y*q.y;
+ const U yz = y*q.z;
+ const U yw = y*q.w;
+ const U zz = z*q.z;
+ const U zw = z*q.w;
+ m_value[0] = col_type(1-yy-zz, xy+zw, xz-yw); // NOLINT
+ m_value[1] = col_type( xy-zw, 1-xx-zz, yz+xw); // NOLINT
+ m_value[2] = col_type( xz+yw, yz-xw, 1-xx-yy); // NOLINT
+}
+
+// ----------------------------------------------------------------------------------------
+// Arithmetic operators outside of class
+// ----------------------------------------------------------------------------------------
+
+/* We use non-friend functions here to prevent the compiler from using
+ * implicit conversions, for instance of a scalar to a vector. The result would
+ * not be what the caller expects.
+ *
+ * Also note that the order of the arguments in the inner loop is important since
+ * it determines the output type (only relevant when T != U).
+ */
+
+// matrix * column-vector, result is a vector of the same type than the input vector
+template <typename T, typename U>
+CONSTEXPR typename TMat33<U>::col_type PURE operator *(const TMat33<T>& lhs, const TVec3<U>& rhs) {
+ // Result is initialized to zero.
+ typename TMat33<U>::col_type result;
+ for (size_t col = 0; col < TMat33<T>::NUM_COLS; ++col) {
+ result += lhs[col] * rhs[col];
+ }
+ return result;
+}
+
+// row-vector * matrix, result is a vector of the same type than the input vector
+template <typename T, typename U>
+CONSTEXPR typename TMat33<U>::row_type PURE operator *(const TVec3<U>& lhs, const TMat33<T>& rhs) {
+ typename TMat33<U>::row_type result(TMat33<U>::row_type::NO_INIT);
+ for (size_t col = 0; col < TMat33<T>::NUM_COLS; ++col) {
+ result[col] = dot(lhs, rhs[col]);
+ }
+ return result;
+}
+
+// matrix * scalar, result is a matrix of the same type than the input matrix
+template<typename T, typename U>
+constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat33<T>>::type PURE
+operator*(TMat33<T> lhs, U rhs) {
+ return lhs *= rhs;
+}
+
+// scalar * matrix, result is a matrix of the same type than the input matrix
+template<typename T, typename U>
+constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat33<T>>::type PURE
+operator*(U lhs, const TMat33<T>& rhs) {
+ return rhs * lhs;
+}
+
+//------------------------------------------------------------------------------
+template <typename T>
+CONSTEXPR TMat33<T> orthogonalize(const TMat33<T>& m) {
+ TMat33<T> ret(TMat33<T>::NO_INIT);
+ ret[0] = normalize(m[0]);
+ ret[2] = normalize(cross(ret[0], m[1]));
+ ret[1] = normalize(cross(ret[2], ret[0]));
+ return ret;
+}
+
+// ----------------------------------------------------------------------------------------
+
+/* FIXME: this should go into TMatSquareFunctions<> but for some reason
+ * BASE<T>::col_type is not accessible from there (???)
+ */
+template<typename T>
+CONSTEXPR typename TMat33<T>::col_type PURE diag(const TMat33<T>& m) {
+ return matrix::diag(m);
+}
+
+} // namespace details
+
+// ----------------------------------------------------------------------------------------
+
+typedef details::TMat33<double> mat3d;
+typedef details::TMat33<float> mat3;
+typedef details::TMat33<float> mat3f;
+
+// ----------------------------------------------------------------------------------------
+} // namespace android
+
+#undef PURE
+#undef CONSTEXPR
diff --git a/libs/math/include/math/mat4.h b/libs/math/include/math/mat4.h
new file mode 100644
index 0000000..6119ba7
--- /dev/null
+++ b/libs/math/include/math/mat4.h
@@ -0,0 +1,586 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#pragma once
+
+#include <math/mat3.h>
+#include <math/quat.h>
+#include <math/TMatHelpers.h>
+#include <math/vec3.h>
+#include <math/vec4.h>
+
+#include <stdint.h>
+#include <sys/types.h>
+#include <limits>
+
+#define PURE __attribute__((pure))
+
+#if __cplusplus >= 201402L
+#define CONSTEXPR constexpr
+#else
+#define CONSTEXPR
+#endif
+
+namespace android {
+// -------------------------------------------------------------------------------------
+namespace details {
+
+template<typename T>
+class TQuaternion;
+
+/**
+ * A 4x4 column-major matrix class.
+ *
+ * Conceptually a 4x4 matrix is a an array of 4 column double4:
+ *
+ * mat4 m =
+ * \f$
+ * \left(
+ * \begin{array}{cccc}
+ * m[0] & m[1] & m[2] & m[3] \\
+ * \end{array}
+ * \right)
+ * \f$
+ * =
+ * \f$
+ * \left(
+ * \begin{array}{cccc}
+ * m[0][0] & m[1][0] & m[2][0] & m[3][0] \\
+ * m[0][1] & m[1][1] & m[2][1] & m[3][1] \\
+ * m[0][2] & m[1][2] & m[2][2] & m[3][2] \\
+ * m[0][3] & m[1][3] & m[2][3] & m[3][3] \\
+ * \end{array}
+ * \right)
+ * \f$
+ * =
+ * \f$
+ * \left(
+ * \begin{array}{cccc}
+ * m(0,0) & m(0,1) & m(0,2) & m(0,3) \\
+ * m(1,0) & m(1,1) & m(1,2) & m(1,3) \\
+ * m(2,0) & m(2,1) & m(2,2) & m(2,3) \\
+ * m(3,0) & m(3,1) & m(3,2) & m(3,3) \\
+ * \end{array}
+ * \right)
+ * \f$
+ *
+ * m[n] is the \f$ n^{th} \f$ column of the matrix and is a double4.
+ *
+ */
+template <typename T>
+class TMat44 : public TVecUnaryOperators<TMat44, T>,
+ public TVecComparisonOperators<TMat44, T>,
+ public TVecAddOperators<TMat44, T>,
+ public TMatProductOperators<TMat44, T>,
+ public TMatSquareFunctions<TMat44, T>,
+ public TMatTransform<TMat44, T>,
+ public TMatHelpers<TMat44, T>,
+ public TMatDebug<TMat44, T> {
+public:
+ enum no_init { NO_INIT };
+ typedef T value_type;
+ typedef T& reference;
+ typedef T const& const_reference;
+ typedef size_t size_type;
+ typedef TVec4<T> col_type;
+ typedef TVec4<T> row_type;
+
+ static constexpr size_t COL_SIZE = col_type::SIZE; // size of a column (i.e.: number of rows)
+ static constexpr size_t ROW_SIZE = row_type::SIZE; // size of a row (i.e.: number of columns)
+ static constexpr size_t NUM_ROWS = COL_SIZE;
+ static constexpr size_t NUM_COLS = ROW_SIZE;
+
+private:
+ /*
+ * <-- N columns -->
+ *
+ * a[0][0] a[1][0] a[2][0] ... a[N][0] ^
+ * a[0][1] a[1][1] a[2][1] ... a[N][1] |
+ * a[0][2] a[1][2] a[2][2] ... a[N][2] M rows
+ * ... |
+ * a[0][M] a[1][M] a[2][M] ... a[N][M] v
+ *
+ * COL_SIZE = M
+ * ROW_SIZE = N
+ * m[0] = [ a[0][0] a[0][1] a[0][2] ... a[0][M] ]
+ */
+
+ col_type m_value[NUM_COLS];
+
+public:
+ // array access
+ inline constexpr col_type const& operator[](size_t column) const {
+#if __cplusplus >= 201402L
+ // only possible in C++0x14 with constexpr
+ assert(column < NUM_COLS);
+#endif
+ return m_value[column];
+ }
+
+ inline col_type& operator[](size_t column) {
+ assert(column < NUM_COLS);
+ return m_value[column];
+ }
+
+ // -----------------------------------------------------------------------
+ // we want the compiler generated versions for these...
+ TMat44(const TMat44&) = default;
+ ~TMat44() = default;
+ TMat44& operator = (const TMat44&) = default;
+
+ /*
+ * constructors
+ */
+
+ // leaves object uninitialized. use with caution.
+ explicit constexpr TMat44(no_init)
+ : m_value{ col_type(col_type::NO_INIT),
+ col_type(col_type::NO_INIT),
+ col_type(col_type::NO_INIT),
+ col_type(col_type::NO_INIT) } {}
+
+ /** initialize to identity.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{cccc}
+ * 1 & 0 & 0 & 0 \\
+ * 0 & 1 & 0 & 0 \\
+ * 0 & 0 & 1 & 0 \\
+ * 0 & 0 & 0 & 1 \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ CONSTEXPR TMat44();
+
+ /** initialize to Identity*scalar.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{cccc}
+ * v & 0 & 0 & 0 \\
+ * 0 & v & 0 & 0 \\
+ * 0 & 0 & v & 0 \\
+ * 0 & 0 & 0 & v \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template<typename U>
+ explicit CONSTEXPR TMat44(U v);
+
+ /** sets the diagonal to a vector.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{cccc}
+ * v[0] & 0 & 0 & 0 \\
+ * 0 & v[1] & 0 & 0 \\
+ * 0 & 0 & v[2] & 0 \\
+ * 0 & 0 & 0 & v[3] \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <typename U>
+ explicit CONSTEXPR TMat44(const TVec4<U>& v);
+
+ // construct from another matrix of the same size
+ template <typename U>
+ explicit CONSTEXPR TMat44(const TMat44<U>& rhs);
+
+ /** construct from 4 column vectors.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{cccc}
+ * v0 & v1 & v2 & v3 \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <typename A, typename B, typename C, typename D>
+ CONSTEXPR TMat44(const TVec4<A>& v0, const TVec4<B>& v1, const TVec4<C>& v2, const TVec4<D>& v3);
+
+ /** construct from 16 elements in column-major form.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{cccc}
+ * m[0][0] & m[1][0] & m[2][0] & m[3][0] \\
+ * m[0][1] & m[1][1] & m[2][1] & m[3][1] \\
+ * m[0][2] & m[1][2] & m[2][2] & m[3][2] \\
+ * m[0][3] & m[1][3] & m[2][3] & m[3][3] \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <
+ typename A, typename B, typename C, typename D,
+ typename E, typename F, typename G, typename H,
+ typename I, typename J, typename K, typename L,
+ typename M, typename N, typename O, typename P>
+ CONSTEXPR TMat44(
+ A m00, B m01, C m02, D m03,
+ E m10, F m11, G m12, H m13,
+ I m20, J m21, K m22, L m23,
+ M m30, N m31, O m32, P m33);
+
+ /**
+ * construct from a quaternion
+ */
+ template <typename U>
+ explicit CONSTEXPR TMat44(const TQuaternion<U>& q);
+
+ /**
+ * construct from a C array in column major form.
+ */
+ template <typename U>
+ explicit CONSTEXPR TMat44(U const* rawArray);
+
+ /**
+ * construct from a 3x3 matrix
+ */
+ template <typename U>
+ explicit CONSTEXPR TMat44(const TMat33<U>& matrix);
+
+ /**
+ * construct from a 3x3 matrix and 3d translation
+ */
+ template <typename U, typename V>
+ CONSTEXPR TMat44(const TMat33<U>& matrix, const TVec3<V>& translation);
+
+ /**
+ * construct from a 3x3 matrix and 4d last column.
+ */
+ template <typename U, typename V>
+ CONSTEXPR TMat44(const TMat33<U>& matrix, const TVec4<V>& column3);
+
+ /*
+ * helpers
+ */
+
+ static CONSTEXPR TMat44 ortho(T left, T right, T bottom, T top, T near, T far);
+
+ static CONSTEXPR TMat44 frustum(T left, T right, T bottom, T top, T near, T far);
+
+ enum class Fov {
+ HORIZONTAL,
+ VERTICAL
+ };
+ static CONSTEXPR TMat44 perspective(T fov, T aspect, T near, T far, Fov direction = Fov::VERTICAL);
+
+ template <typename A, typename B, typename C>
+ static CONSTEXPR TMat44 lookAt(const TVec3<A>& eye, const TVec3<B>& center, const TVec3<C>& up);
+
+ template <typename A>
+ static CONSTEXPR TVec3<A> project(const TMat44& projectionMatrix, TVec3<A> vertice) {
+ TVec4<A> r = projectionMatrix * TVec4<A>{ vertice, 1 };
+ return r.xyz / r.w;
+ }
+
+ template <typename A>
+ static CONSTEXPR TVec4<A> project(const TMat44& projectionMatrix, TVec4<A> vertice) {
+ vertice = projectionMatrix * vertice;
+ return { vertice.xyz / vertice.w, 1 };
+ }
+
+ /**
+ * Constructs a 3x3 matrix from the upper-left corner of this 4x4 matrix
+ */
+ inline constexpr TMat33<T> upperLeft() const {
+ return TMat33<T>(m_value[0].xyz, m_value[1].xyz, m_value[2].xyz);
+ }
+};
+
+// ----------------------------------------------------------------------------------------
+// Constructors
+// ----------------------------------------------------------------------------------------
+
+// Since the matrix code could become pretty big quickly, we don't inline most
+// operations.
+
+template <typename T>
+CONSTEXPR TMat44<T>::TMat44() {
+ m_value[0] = col_type(1, 0, 0, 0);
+ m_value[1] = col_type(0, 1, 0, 0);
+ m_value[2] = col_type(0, 0, 1, 0);
+ m_value[3] = col_type(0, 0, 0, 1);
+}
+
+template <typename T>
+template <typename U>
+CONSTEXPR TMat44<T>::TMat44(U v) {
+ m_value[0] = col_type(v, 0, 0, 0);
+ m_value[1] = col_type(0, v, 0, 0);
+ m_value[2] = col_type(0, 0, v, 0);
+ m_value[3] = col_type(0, 0, 0, v);
+}
+
+template<typename T>
+template<typename U>
+CONSTEXPR TMat44<T>::TMat44(const TVec4<U>& v) {
+ m_value[0] = col_type(v.x, 0, 0, 0);
+ m_value[1] = col_type(0, v.y, 0, 0);
+ m_value[2] = col_type(0, 0, v.z, 0);
+ m_value[3] = col_type(0, 0, 0, v.w);
+}
+
+// construct from 16 scalars
+template<typename T>
+template <
+ typename A, typename B, typename C, typename D,
+ typename E, typename F, typename G, typename H,
+ typename I, typename J, typename K, typename L,
+ typename M, typename N, typename O, typename P>
+CONSTEXPR TMat44<T>::TMat44(
+ A m00, B m01, C m02, D m03,
+ E m10, F m11, G m12, H m13,
+ I m20, J m21, K m22, L m23,
+ M m30, N m31, O m32, P m33) {
+ m_value[0] = col_type(m00, m01, m02, m03);
+ m_value[1] = col_type(m10, m11, m12, m13);
+ m_value[2] = col_type(m20, m21, m22, m23);
+ m_value[3] = col_type(m30, m31, m32, m33);
+}
+
+template <typename T>
+template <typename U>
+CONSTEXPR TMat44<T>::TMat44(const TMat44<U>& rhs) {
+ for (size_t col = 0; col < NUM_COLS; ++col) {
+ m_value[col] = col_type(rhs[col]);
+ }
+}
+
+// Construct from 4 column vectors.
+template <typename T>
+template <typename A, typename B, typename C, typename D>
+CONSTEXPR TMat44<T>::TMat44(
+ const TVec4<A>& v0, const TVec4<B>& v1,
+ const TVec4<C>& v2, const TVec4<D>& v3) {
+ m_value[0] = col_type(v0);
+ m_value[1] = col_type(v1);
+ m_value[2] = col_type(v2);
+ m_value[3] = col_type(v3);
+}
+
+// Construct from raw array, in column-major form.
+template <typename T>
+template <typename U>
+CONSTEXPR TMat44<T>::TMat44(U const* rawArray) {
+ for (size_t col = 0; col < NUM_COLS; ++col) {
+ for (size_t row = 0; row < NUM_ROWS; ++row) {
+ m_value[col][row] = *rawArray++;
+ }
+ }
+}
+
+template <typename T>
+template <typename U>
+CONSTEXPR TMat44<T>::TMat44(const TQuaternion<U>& q) {
+ const U n = q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w;
+ const U s = n > 0 ? 2/n : 0;
+ const U x = s*q.x;
+ const U y = s*q.y;
+ const U z = s*q.z;
+ const U xx = x*q.x;
+ const U xy = x*q.y;
+ const U xz = x*q.z;
+ const U xw = x*q.w;
+ const U yy = y*q.y;
+ const U yz = y*q.z;
+ const U yw = y*q.w;
+ const U zz = z*q.z;
+ const U zw = z*q.w;
+ m_value[0] = col_type(1-yy-zz, xy+zw, xz-yw, 0);
+ m_value[1] = col_type( xy-zw, 1-xx-zz, yz+xw, 0); // NOLINT
+ m_value[2] = col_type( xz+yw, yz-xw, 1-xx-yy, 0); // NOLINT
+ m_value[3] = col_type( 0, 0, 0, 1); // NOLINT
+}
+
+template <typename T>
+template <typename U>
+CONSTEXPR TMat44<T>::TMat44(const TMat33<U>& m) {
+ m_value[0] = col_type(m[0][0], m[0][1], m[0][2], 0);
+ m_value[1] = col_type(m[1][0], m[1][1], m[1][2], 0);
+ m_value[2] = col_type(m[2][0], m[2][1], m[2][2], 0);
+ m_value[3] = col_type( 0, 0, 0, 1); // NOLINT
+}
+
+template <typename T>
+template <typename U, typename V>
+CONSTEXPR TMat44<T>::TMat44(const TMat33<U>& m, const TVec3<V>& v) {
+ m_value[0] = col_type(m[0][0], m[0][1], m[0][2], 0);
+ m_value[1] = col_type(m[1][0], m[1][1], m[1][2], 0);
+ m_value[2] = col_type(m[2][0], m[2][1], m[2][2], 0);
+ m_value[3] = col_type( v[0], v[1], v[2], 1); // NOLINT
+}
+
+template <typename T>
+template <typename U, typename V>
+CONSTEXPR TMat44<T>::TMat44(const TMat33<U>& m, const TVec4<V>& v) {
+ m_value[0] = col_type(m[0][0], m[0][1], m[0][2], 0); // NOLINT
+ m_value[1] = col_type(m[1][0], m[1][1], m[1][2], 0); // NOLINT
+ m_value[2] = col_type(m[2][0], m[2][1], m[2][2], 0); // NOLINT
+ m_value[3] = col_type( v[0], v[1], v[2], v[3]); // NOLINT
+}
+
+// ----------------------------------------------------------------------------------------
+// Helpers
+// ----------------------------------------------------------------------------------------
+
+template <typename T>
+CONSTEXPR TMat44<T> TMat44<T>::ortho(T left, T right, T bottom, T top, T near, T far) {
+ TMat44<T> m;
+ m[0][0] = 2 / (right - left);
+ m[1][1] = 2 / (top - bottom);
+ m[2][2] = -2 / (far - near);
+ m[3][0] = -(right + left) / (right - left);
+ m[3][1] = -(top + bottom) / (top - bottom);
+ m[3][2] = -(far + near) / (far - near);
+ return m;
+}
+
+template <typename T>
+CONSTEXPR TMat44<T> TMat44<T>::frustum(T left, T right, T bottom, T top, T near, T far) {
+ TMat44<T> m;
+ m[0][0] = (2 * near) / (right - left);
+ m[1][1] = (2 * near) / (top - bottom);
+ m[2][0] = (right + left) / (right - left);
+ m[2][1] = (top + bottom) / (top - bottom);
+ m[2][2] = -(far + near) / (far - near);
+ m[2][3] = -1;
+ m[3][2] = -(2 * far * near) / (far - near);
+ m[3][3] = 0;
+ return m;
+}
+
+template <typename T>
+CONSTEXPR TMat44<T> TMat44<T>::perspective(T fov, T aspect, T near, T far, TMat44::Fov direction) {
+ T h;
+ T w;
+
+ if (direction == TMat44::Fov::VERTICAL) {
+ h = std::tan(fov * M_PI / 360.0f) * near;
+ w = h * aspect;
+ } else {
+ w = std::tan(fov * M_PI / 360.0f) * near;
+ h = w / aspect;
+ }
+ return frustum(-w, w, -h, h, near, far);
+}
+
+/*
+ * Returns a matrix representing the pose of a virtual camera looking towards -Z in its
+ * local Y-up coordinate system. "eye" is where the camera is located, "center" is the points its
+ * looking at and "up" defines where the Y axis of the camera's local coordinate system is.
+ */
+template <typename T>
+template <typename A, typename B, typename C>
+CONSTEXPR TMat44<T> TMat44<T>::lookAt(const TVec3<A>& eye, const TVec3<B>& center, const TVec3<C>& up) {
+ TVec3<T> z_axis(normalize(center - eye));
+ TVec3<T> norm_up(normalize(up));
+ if (std::abs(dot(z_axis, norm_up)) > 0.999) {
+ // Fix up vector if we're degenerate (looking straight up, basically)
+ norm_up = { norm_up.z, norm_up.x, norm_up.y };
+ }
+ TVec3<T> x_axis(normalize(cross(z_axis, norm_up)));
+ TVec3<T> y_axis(cross(x_axis, z_axis));
+ return TMat44<T>(
+ TVec4<T>(x_axis, 0),
+ TVec4<T>(y_axis, 0),
+ TVec4<T>(-z_axis, 0),
+ TVec4<T>(eye, 1));
+}
+
+// ----------------------------------------------------------------------------------------
+// Arithmetic operators outside of class
+// ----------------------------------------------------------------------------------------
+
+/* We use non-friend functions here to prevent the compiler from using
+ * implicit conversions, for instance of a scalar to a vector. The result would
+ * not be what the caller expects.
+ *
+ * Also note that the order of the arguments in the inner loop is important since
+ * it determines the output type (only relevant when T != U).
+ */
+
+// matrix * column-vector, result is a vector of the same type than the input vector
+template <typename T, typename U>
+CONSTEXPR typename TMat44<T>::col_type PURE operator *(const TMat44<T>& lhs, const TVec4<U>& rhs) {
+ // Result is initialized to zero.
+ typename TMat44<T>::col_type result;
+ for (size_t col = 0; col < TMat44<T>::NUM_COLS; ++col) {
+ result += lhs[col] * rhs[col];
+ }
+ return result;
+}
+
+// mat44 * vec3, result is vec3( mat44 * {vec3, 1} )
+template <typename T, typename U>
+CONSTEXPR typename TMat44<T>::col_type PURE operator *(const TMat44<T>& lhs, const TVec3<U>& rhs) {
+ return lhs * TVec4<U>{ rhs, 1 };
+}
+
+
+// row-vector * matrix, result is a vector of the same type than the input vector
+template <typename T, typename U>
+CONSTEXPR typename TMat44<U>::row_type PURE operator *(const TVec4<U>& lhs, const TMat44<T>& rhs) {
+ typename TMat44<U>::row_type result(TMat44<U>::row_type::NO_INIT);
+ for (size_t col = 0; col < TMat44<T>::NUM_COLS; ++col) {
+ result[col] = dot(lhs, rhs[col]);
+ }
+ return result;
+}
+
+// matrix * scalar, result is a matrix of the same type than the input matrix
+template <typename T, typename U>
+constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat44<T>>::type PURE
+operator *(TMat44<T> lhs, U rhs) {
+ return lhs *= rhs;
+}
+
+// scalar * matrix, result is a matrix of the same type than the input matrix
+template <typename T, typename U>
+constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat44<T>>::type PURE
+operator *(U lhs, const TMat44<T>& rhs) {
+ return rhs * lhs;
+}
+
+// ----------------------------------------------------------------------------------------
+
+/* FIXME: this should go into TMatSquareFunctions<> but for some reason
+ * BASE<T>::col_type is not accessible from there (???)
+ */
+template<typename T>
+typename TMat44<T>::col_type PURE diag(const TMat44<T>& m) {
+ return matrix::diag(m);
+}
+
+} // namespace details
+
+// ----------------------------------------------------------------------------------------
+
+typedef details::TMat44<double> mat4d;
+typedef details::TMat44<float> mat4;
+typedef details::TMat44<float> mat4f;
+
+// ----------------------------------------------------------------------------------------
+} // namespace android
+
+#undef PURE
+#undef CONSTEXPR
diff --git a/libs/math/include/math/quat.h b/libs/math/include/math/quat.h
new file mode 100644
index 0000000..1936a2b
--- /dev/null
+++ b/libs/math/include/math/quat.h
@@ -0,0 +1,192 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#pragma once
+
+#include <math/half.h>
+#include <math/TQuatHelpers.h>
+#include <math/vec3.h>
+#include <math/vec4.h>
+
+#include <stdint.h>
+#include <sys/types.h>
+
+#ifndef PURE
+#define PURE __attribute__((pure))
+#endif
+
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wgnu-anonymous-struct"
+#pragma clang diagnostic ignored "-Wnested-anon-types"
+
+namespace android {
+// -------------------------------------------------------------------------------------
+
+namespace details {
+
+template <typename T>
+class TQuaternion : public TVecAddOperators<TQuaternion, T>,
+ public TVecUnaryOperators<TQuaternion, T>,
+ public TVecComparisonOperators<TQuaternion, T>,
+ public TQuatProductOperators<TQuaternion, T>,
+ public TQuatFunctions<TQuaternion, T>,
+ public TQuatDebug<TQuaternion, T> {
+public:
+ enum no_init { NO_INIT };
+ typedef T value_type;
+ typedef T& reference;
+ typedef T const& const_reference;
+ typedef size_t size_type;
+
+ /*
+ * quaternion internals stored as:
+ *
+ * q = w + xi + yj + zk
+ *
+ * q[0] = x;
+ * q[1] = y;
+ * q[2] = z;
+ * q[3] = w;
+ *
+ */
+ union {
+ struct { T x, y, z, w; };
+ TVec4<T> xyzw;
+ TVec3<T> xyz;
+ TVec2<T> xy;
+ };
+
+ enum { SIZE = 4 };
+ inline constexpr static size_type size() { return SIZE; }
+
+ // array access
+ inline constexpr T const& operator[](size_t i) const {
+#if __cplusplus >= 201402L
+ // only possible in C++0x14 with constexpr
+ assert(i < SIZE);
+#endif
+ return (&x)[i];
+ }
+
+ inline T& operator[](size_t i) {
+ assert(i < SIZE);
+ return (&x)[i];
+ }
+
+ // -----------------------------------------------------------------------
+ // we want the compiler generated versions for these...
+ TQuaternion(const TQuaternion&) = default;
+ ~TQuaternion() = default;
+ TQuaternion& operator = (const TQuaternion&) = default;
+
+ // constructors
+
+ // leaves object uninitialized. use with caution.
+ explicit
+ constexpr TQuaternion(no_init) : xyzw(TVec4<T>::NO_INIT) {}
+
+ // default constructor. sets all values to zero.
+ constexpr TQuaternion() : x(0), y(0), z(0), w(0) { }
+
+ // handles implicit conversion to a tvec4. must not be explicit.
+ template<typename A>
+ constexpr TQuaternion(A w) : x(0), y(0), z(0), w(w) {
+ static_assert(std::is_arithmetic<A>::value, "requires arithmetic type");
+ }
+
+ // initialize from 4 values to w + xi + yj + zk
+ template<typename A, typename B, typename C, typename D>
+ constexpr TQuaternion(A w, B x, C y, D z) : x(x), y(y), z(z), w(w) { }
+
+ // initialize from a vec3 + a value to : v.xi + v.yj + v.zk + w
+ template<typename A, typename B>
+ constexpr TQuaternion(const TVec3<A>& v, B w) : x(v.x), y(v.y), z(v.z), w(w) { }
+
+ // initialize from a double4
+ template<typename A>
+ constexpr explicit TQuaternion(const TVec4<A>& v) : x(v.x), y(v.y), z(v.z), w(v.w) { }
+
+ // initialize from a quaternion of a different type
+ template<typename A>
+ constexpr explicit TQuaternion(const TQuaternion<A>& v) : x(v.x), y(v.y), z(v.z), w(v.w) { }
+
+ // conjugate operator
+ constexpr TQuaternion operator~() const {
+ return conj(*this);
+ }
+
+ // constructs a quaternion from an axis and angle
+ template <typename A, typename B>
+ constexpr static TQuaternion PURE fromAxisAngle(const TVec3<A>& axis, B angle) {
+ return TQuaternion(std::sin(angle*0.5) * normalize(axis), std::cos(angle*0.5));
+ }
+};
+
+} // namespace details
+
+// ----------------------------------------------------------------------------------------
+
+typedef details::TQuaternion<double> quatd;
+typedef details::TQuaternion<float> quat;
+typedef details::TQuaternion<float> quatf;
+typedef details::TQuaternion<half> quath;
+
+constexpr inline quat operator"" _i(long double v) {
+ return quat(0, static_cast<float>(v), 0, 0);
+}
+constexpr inline quat operator"" _j(long double v) {
+ return quat(0, 0, static_cast<float>(v), 0);
+}
+constexpr inline quat operator"" _k(long double v) {
+ return quat(0, 0, 0, static_cast<float>(v));
+}
+
+constexpr inline quat operator"" _i(unsigned long long v) { // NOLINT
+ return quat(0, static_cast<float>(v), 0, 0);
+}
+constexpr inline quat operator"" _j(unsigned long long v) { // NOLINT
+ return quat(0, 0, static_cast<float>(v), 0);
+}
+constexpr inline quat operator"" _k(unsigned long long v) { // NOLINT
+ return quat(0, 0, 0, static_cast<float>(v));
+}
+
+constexpr inline quatd operator"" _id(long double v) {
+ return quatd(0, static_cast<double>(v), 0, 0);
+}
+constexpr inline quatd operator"" _jd(long double v) {
+ return quatd(0, 0, static_cast<double>(v), 0);
+}
+constexpr inline quatd operator"" _kd(long double v) {
+ return quatd(0, 0, 0, static_cast<double>(v));
+}
+
+constexpr inline quatd operator"" _id(unsigned long long v) { // NOLINT
+ return quatd(0, static_cast<double>(v), 0, 0);
+}
+constexpr inline quatd operator"" _jd(unsigned long long v) { // NOLINT
+ return quatd(0, 0, static_cast<double>(v), 0);
+}
+constexpr inline quatd operator"" _kd(unsigned long long v) { // NOLINT
+ return quatd(0, 0, 0, static_cast<double>(v));
+}
+
+// ----------------------------------------------------------------------------------------
+} // namespace android
+
+#pragma clang diagnostic pop
+
+#undef PURE
diff --git a/libs/math/include/math/scalar.h b/libs/math/include/math/scalar.h
new file mode 100644
index 0000000..2eced92
--- /dev/null
+++ b/libs/math/include/math/scalar.h
@@ -0,0 +1,44 @@
+/*
+ * Copyright (C) 2016 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#pragma once
+
+#include <algorithm>
+#include <cmath>
+
+namespace android {
+
+template<typename T>
+static constexpr T saturate(T v) noexcept {
+ return T(std::min(T(1), std::max(T(0), v)));
+}
+
+template<typename T>
+static constexpr T clamp(T v, T min, T max) noexcept {
+ return T(std::min(max, std::max(min, v)));
+}
+
+template<typename T>
+static constexpr T mix(T x, T y, T a) noexcept {
+ return x * (T(1) - a) + y * a;
+}
+
+template<typename T>
+static constexpr T lerp(T x, T y, T a) noexcept {
+ return mix(x, y, a);
+}
+
+} // namespace std
diff --git a/libs/math/include/math/vec2.h b/libs/math/include/math/vec2.h
new file mode 100644
index 0000000..a347633
--- /dev/null
+++ b/libs/math/include/math/vec2.h
@@ -0,0 +1,125 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#pragma once
+
+#include <math/TVecHelpers.h>
+#include <math/half.h>
+#include <assert.h>
+#include <stdint.h>
+#include <sys/types.h>
+#include <type_traits>
+
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wgnu-anonymous-struct"
+#pragma clang diagnostic ignored "-Wnested-anon-types"
+
+namespace android {
+// -------------------------------------------------------------------------------------
+
+namespace details {
+
+template <typename T>
+class TVec2 : public TVecProductOperators<TVec2, T>,
+ public TVecAddOperators<TVec2, T>,
+ public TVecUnaryOperators<TVec2, T>,
+ public TVecComparisonOperators<TVec2, T>,
+ public TVecFunctions<TVec2, T>,
+ public TVecDebug<TVec2, T> {
+public:
+ enum no_init { NO_INIT };
+ typedef T value_type;
+ typedef T& reference;
+ typedef T const& const_reference;
+ typedef size_t size_type;
+
+ union {
+ struct { T x, y; };
+ struct { T s, t; };
+ struct { T r, g; };
+ };
+
+ static constexpr size_t SIZE = 2;
+ inline constexpr size_type size() const { return SIZE; }
+
+ // array access
+ inline constexpr T const& operator[](size_t i) const {
+#if __cplusplus >= 201402L
+ // only possible in C++0x14 with constexpr
+ assert(i < SIZE);
+#endif
+ return (&x)[i];
+ }
+
+ inline T& operator[](size_t i) {
+ assert(i < SIZE);
+ return (&x)[i];
+ }
+
+ // -----------------------------------------------------------------------
+ // we want the compiler generated versions for these...
+ TVec2(const TVec2&) = default;
+ ~TVec2() = default;
+ TVec2& operator = (const TVec2&) = default;
+
+ // constructors
+
+ // leaves object uninitialized. use with caution.
+ explicit
+ constexpr TVec2(no_init) { }
+
+ // default constructor
+ constexpr TVec2() : x(0), y(0) { }
+
+ // handles implicit conversion to a tvec4. must not be explicit.
+ template<typename A, typename = typename std::enable_if<std::is_arithmetic<A>::value >::type>
+ constexpr TVec2(A v) : x(v), y(v) { }
+
+ template<typename A, typename B>
+ constexpr TVec2(A x, B y) : x(x), y(y) { }
+
+ template<typename A>
+ explicit
+ constexpr TVec2(const TVec2<A>& v) : x(v.x), y(v.y) { }
+
+ // cross product works only on vectors of size 2 or 3
+ template<typename RT>
+ friend inline
+ constexpr value_type cross(const TVec2& u, const TVec2<RT>& v) {
+ return value_type(u.x*v.y - u.y*v.x);
+ }
+};
+
+} // namespace details
+
+// ----------------------------------------------------------------------------------------
+
+typedef details::TVec2<double> double2;
+typedef details::TVec2<float> float2;
+typedef details::TVec2<float> vec2;
+typedef details::TVec2<half> half2;
+typedef details::TVec2<int32_t> int2;
+typedef details::TVec2<uint32_t> uint2;
+typedef details::TVec2<int16_t> short2;
+typedef details::TVec2<uint16_t> ushort2;
+typedef details::TVec2<int8_t> byte2;
+typedef details::TVec2<uint8_t> ubyte2;
+typedef details::TVec2<bool> bool2;
+
+// ----------------------------------------------------------------------------------------
+} // namespace android
+
+#pragma clang diagnostic pop
diff --git a/libs/math/include/math/vec3.h b/libs/math/include/math/vec3.h
new file mode 100644
index 0000000..009fd84
--- /dev/null
+++ b/libs/math/include/math/vec3.h
@@ -0,0 +1,131 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#pragma once
+
+#include <math/vec2.h>
+#include <math/half.h>
+#include <stdint.h>
+#include <sys/types.h>
+
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wgnu-anonymous-struct"
+#pragma clang diagnostic ignored "-Wnested-anon-types"
+
+namespace android {
+// -------------------------------------------------------------------------------------
+
+namespace details {
+
+template <typename T>
+class TVec3 : public TVecProductOperators<TVec3, T>,
+ public TVecAddOperators<TVec3, T>,
+ public TVecUnaryOperators<TVec3, T>,
+ public TVecComparisonOperators<TVec3, T>,
+ public TVecFunctions<TVec3, T>,
+ public TVecDebug<TVec3, T> {
+public:
+ enum no_init { NO_INIT };
+ typedef T value_type;
+ typedef T& reference;
+ typedef T const& const_reference;
+ typedef size_t size_type;
+
+ union {
+ struct { T x, y, z; };
+ struct { T s, t, p; };
+ struct { T r, g, b; };
+ TVec2<T> xy;
+ TVec2<T> st;
+ TVec2<T> rg;
+ };
+
+ static constexpr size_t SIZE = 3;
+ inline constexpr size_type size() const { return SIZE; }
+
+ // array access
+ inline constexpr T const& operator[](size_t i) const {
+#if __cplusplus >= 201402L
+ // only possible in C++0x14 with constexpr
+ assert(i < SIZE);
+#endif
+ return (&x)[i];
+ }
+
+ inline T& operator[](size_t i) {
+ assert(i < SIZE);
+ return (&x)[i];
+ }
+
+ // -----------------------------------------------------------------------
+ // we want the compiler generated versions for these...
+ TVec3(const TVec3&) = default;
+ ~TVec3() = default;
+ TVec3& operator = (const TVec3&) = default;
+
+ // constructors
+ // leaves object uninitialized. use with caution.
+ explicit
+ constexpr TVec3(no_init) { }
+
+ // default constructor
+ constexpr TVec3() : x(0), y(0), z(0) { }
+
+ // handles implicit conversion to a tvec4. must not be explicit.
+ template<typename A, typename = typename std::enable_if<std::is_arithmetic<A>::value >::type>
+ constexpr TVec3(A v) : x(v), y(v), z(v) { }
+
+ template<typename A, typename B, typename C>
+ constexpr TVec3(A x, B y, C z) : x(x), y(y), z(z) { }
+
+ template<typename A, typename B>
+ constexpr TVec3(const TVec2<A>& v, B z) : x(v.x), y(v.y), z(z) { }
+
+ template<typename A>
+ explicit
+ constexpr TVec3(const TVec3<A>& v) : x(v.x), y(v.y), z(v.z) { }
+
+ // cross product works only on vectors of size 3
+ template <typename RT>
+ friend inline
+ constexpr TVec3 cross(const TVec3& u, const TVec3<RT>& v) {
+ return TVec3(
+ u.y*v.z - u.z*v.y,
+ u.z*v.x - u.x*v.z,
+ u.x*v.y - u.y*v.x);
+ }
+};
+
+} // namespace details
+
+// ----------------------------------------------------------------------------------------
+
+typedef details::TVec3<double> double3;
+typedef details::TVec3<float> float3;
+typedef details::TVec3<float> vec3;
+typedef details::TVec3<half> half3;
+typedef details::TVec3<int32_t> int3;
+typedef details::TVec3<uint32_t> uint3;
+typedef details::TVec3<int16_t> short3;
+typedef details::TVec3<uint16_t> ushort3;
+typedef details::TVec3<int8_t> byte3;
+typedef details::TVec3<uint8_t> ubyte3;
+typedef details::TVec3<bool> bool3;
+
+// ----------------------------------------------------------------------------------------
+} // namespace android
+
+#pragma clang diagnostic pop
diff --git a/libs/math/include/math/vec4.h b/libs/math/include/math/vec4.h
new file mode 100644
index 0000000..1e279fe
--- /dev/null
+++ b/libs/math/include/math/vec4.h
@@ -0,0 +1,128 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#pragma once
+
+#include <math/vec3.h>
+#include <math/half.h>
+#include <stdint.h>
+#include <sys/types.h>
+
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wgnu-anonymous-struct"
+#pragma clang diagnostic ignored "-Wnested-anon-types"
+
+namespace android {
+// -------------------------------------------------------------------------------------
+
+namespace details {
+
+template <typename T>
+class TVec4 : public TVecProductOperators<TVec4, T>,
+ public TVecAddOperators<TVec4, T>,
+ public TVecUnaryOperators<TVec4, T>,
+ public TVecComparisonOperators<TVec4, T>,
+ public TVecFunctions<TVec4, T>,
+ public TVecDebug<TVec4, T> {
+public:
+ enum no_init { NO_INIT };
+ typedef T value_type;
+ typedef T& reference;
+ typedef T const& const_reference;
+ typedef size_t size_type;
+
+ union {
+ struct { T x, y, z, w; };
+ struct { T s, t, p, q; };
+ struct { T r, g, b, a; };
+ TVec2<T> xy;
+ TVec2<T> st;
+ TVec2<T> rg;
+ TVec3<T> xyz;
+ TVec3<T> stp;
+ TVec3<T> rgb;
+ };
+
+ static constexpr size_t SIZE = 4;
+ inline constexpr size_type size() const { return SIZE; }
+
+ // array access
+ inline constexpr T const& operator[](size_t i) const {
+#if __cplusplus >= 201402L
+ // only possible in C++0x14 with constexpr
+ assert(i < SIZE);
+#endif
+ return (&x)[i];
+ }
+
+ inline T& operator[](size_t i) {
+ assert(i < SIZE);
+ return (&x)[i];
+ }
+
+ // -----------------------------------------------------------------------
+ // we want the compiler generated versions for these...
+ TVec4(const TVec4&) = default;
+ ~TVec4() = default;
+ TVec4& operator = (const TVec4&) = default;
+
+ // constructors
+
+ // leaves object uninitialized. use with caution.
+ explicit
+ constexpr TVec4(no_init) { }
+
+ // default constructor
+ constexpr TVec4() : x(0), y(0), z(0), w(0) { }
+
+ // handles implicit conversion to a tvec4. must not be explicit.
+ template<typename A, typename = typename std::enable_if<std::is_arithmetic<A>::value >::type>
+ constexpr TVec4(A v) : x(v), y(v), z(v), w(v) { }
+
+ template<typename A, typename B, typename C, typename D>
+ constexpr TVec4(A x, B y, C z, D w) : x(x), y(y), z(z), w(w) { }
+
+ template<typename A, typename B, typename C>
+ constexpr TVec4(const TVec2<A>& v, B z, C w) : x(v.x), y(v.y), z(z), w(w) { }
+
+ template<typename A, typename B>
+ constexpr TVec4(const TVec3<A>& v, B w) : x(v.x), y(v.y), z(v.z), w(w) { }
+
+ template<typename A>
+ explicit
+ constexpr TVec4(const TVec4<A>& v) : x(v.x), y(v.y), z(v.z), w(v.w) { }
+};
+
+} // namespace details
+
+// ----------------------------------------------------------------------------------------
+
+typedef details::TVec4<double> double4;
+typedef details::TVec4<float> float4;
+typedef details::TVec4<float> vec4;
+typedef details::TVec4<half> half4;
+typedef details::TVec4<int32_t> int4;
+typedef details::TVec4<uint32_t> uint4;
+typedef details::TVec4<int16_t> short4;
+typedef details::TVec4<uint16_t> ushort4;
+typedef details::TVec4<int8_t> byte4;
+typedef details::TVec4<uint8_t> ubyte4;
+typedef details::TVec4<bool> bool4;
+
+// ----------------------------------------------------------------------------------------
+} // namespace android
+
+#pragma clang diagnostic pop
diff --git a/libs/math/tests/Android.bp b/libs/math/tests/Android.bp
new file mode 100644
index 0000000..0ed24a2
--- /dev/null
+++ b/libs/math/tests/Android.bp
@@ -0,0 +1,39 @@
+//
+// Copyright (C) 2014 The Android Open Source Project
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+//
+
+cc_test {
+ name: "vec_test",
+ srcs: ["vec_test.cpp"],
+ static_libs: ["libmath"],
+}
+
+cc_test {
+ name: "mat_test",
+ srcs: ["mat_test.cpp"],
+ static_libs: ["libmath"],
+}
+
+cc_test {
+ name: "half_test",
+ srcs: ["half_test.cpp"],
+ static_libs: ["libmath"],
+}
+
+cc_test {
+ name: "quat_test",
+ srcs: ["quat_test.cpp"],
+ static_libs: ["libmath"],
+}
diff --git a/libs/math/tests/half_test.cpp b/libs/math/tests/half_test.cpp
new file mode 100644
index 0000000..496a7ef
--- /dev/null
+++ b/libs/math/tests/half_test.cpp
@@ -0,0 +1,96 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#define LOG_TAG "HalfTest"
+
+#include <math.h>
+#include <stdlib.h>
+
+#include <math/half.h>
+#include <math/vec4.h>
+
+#include <gtest/gtest.h>
+
+namespace android {
+
+class HalfTest : public testing::Test {
+protected:
+};
+
+TEST_F(HalfTest, Basics) {
+
+ EXPECT_EQ(2UL, sizeof(half));
+
+ // test +/- zero
+ EXPECT_EQ(0x0000, half( 0.0f).getBits());
+ EXPECT_EQ(0x8000, half(-0.0f).getBits());
+
+ // test nan
+ EXPECT_EQ(0x7e00, half(NAN).getBits());
+
+ // test +/- infinity
+ EXPECT_EQ(0x7C00, half( std::numeric_limits<float>::infinity()).getBits());
+ EXPECT_EQ(0xFC00, half(-std::numeric_limits<float>::infinity()).getBits());
+
+ // test a few known values
+ EXPECT_EQ(0x3C01, half(1.0009765625).getBits());
+ EXPECT_EQ(0xC000, half(-2).getBits());
+ EXPECT_EQ(0x0400, half(6.10352e-5).getBits());
+ EXPECT_EQ(0x7BFF, half(65504).getBits());
+ EXPECT_EQ(0x3555, half(1.0f/3).getBits());
+
+ // numeric limits
+ EXPECT_EQ(0x7C00, std::numeric_limits<half>::infinity().getBits());
+ EXPECT_EQ(0x0400, std::numeric_limits<half>::min().getBits());
+ EXPECT_EQ(0x7BFF, std::numeric_limits<half>::max().getBits());
+ EXPECT_EQ(0xFBFF, std::numeric_limits<half>::lowest().getBits());
+
+ // denormals (flushed to zero)
+ EXPECT_EQ(0x0000, half( 6.09756e-5).getBits()); // if handled, should be: 0x03FF
+ EXPECT_EQ(0x0000, half( 5.96046e-8).getBits()); // if handled, should be: 0x0001
+ EXPECT_EQ(0x8000, half(-6.09756e-5).getBits()); // if handled, should be: 0x83FF
+ EXPECT_EQ(0x8000, half(-5.96046e-8).getBits()); // if handled, should be: 0x8001
+
+ // test all exactly representable integers
+ for (int i=-2048 ; i<= 2048 ; ++i) {
+ half h = i;
+ EXPECT_EQ(i, float(h));
+ }
+}
+
+TEST_F(HalfTest, Literals) {
+ half one = 1.0_hf;
+ half pi = 3.1415926_hf;
+ half minusTwo = -2.0_hf;
+
+ EXPECT_EQ(half(1.0f), one);
+ EXPECT_EQ(half(3.1415926), pi);
+ EXPECT_EQ(half(-2.0f), minusTwo);
+}
+
+
+TEST_F(HalfTest, Vec) {
+ float4 f4(1,2,3,4);
+ half4 h4(f4);
+ half3 h3(f4.xyz);
+ half2 h2(f4.xy);
+
+ EXPECT_EQ(f4, h4);
+ EXPECT_EQ(f4.xyz, h3);
+ EXPECT_EQ(f4.xy, h2);
+}
+
+}; // namespace android
diff --git a/libs/math/tests/mat_test.cpp b/libs/math/tests/mat_test.cpp
new file mode 100644
index 0000000..c365366
--- /dev/null
+++ b/libs/math/tests/mat_test.cpp
@@ -0,0 +1,692 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#define LOG_TAG "MatTest"
+
+#include <stdlib.h>
+
+#include <limits>
+#include <random>
+#include <functional>
+
+#include <gtest/gtest.h>
+
+#include <math/mat2.h>
+#include <math/mat4.h>
+
+namespace android {
+
+class MatTest : public testing::Test {
+protected:
+};
+
+TEST_F(MatTest, Basics) {
+ mat4 m0;
+ EXPECT_EQ(sizeof(mat4), sizeof(float)*16);
+}
+
+TEST_F(MatTest, ComparisonOps) {
+ mat4 m0;
+ mat4 m1(2);
+
+ EXPECT_TRUE(m0 == m0);
+ EXPECT_TRUE(m0 != m1);
+ EXPECT_FALSE(m0 != m0);
+ EXPECT_FALSE(m0 == m1);
+}
+
+TEST_F(MatTest, Constructors) {
+ mat4 m0;
+ ASSERT_EQ(m0[0].x, 1);
+ ASSERT_EQ(m0[0].y, 0);
+ ASSERT_EQ(m0[0].z, 0);
+ ASSERT_EQ(m0[0].w, 0);
+ ASSERT_EQ(m0[1].x, 0);
+ ASSERT_EQ(m0[1].y, 1);
+ ASSERT_EQ(m0[1].z, 0);
+ ASSERT_EQ(m0[1].w, 0);
+ ASSERT_EQ(m0[2].x, 0);
+ ASSERT_EQ(m0[2].y, 0);
+ ASSERT_EQ(m0[2].z, 1);
+ ASSERT_EQ(m0[2].w, 0);
+ ASSERT_EQ(m0[3].x, 0);
+ ASSERT_EQ(m0[3].y, 0);
+ ASSERT_EQ(m0[3].z, 0);
+ ASSERT_EQ(m0[3].w, 1);
+
+ mat4 m1(2);
+ mat4 m2(vec4(2));
+ mat4 m3(m2);
+
+ EXPECT_EQ(m1, m2);
+ EXPECT_EQ(m2, m3);
+ EXPECT_EQ(m3, m1);
+
+ mat4 m4(vec4(1), vec4(2), vec4(3), vec4(4));
+}
+
+TEST_F(MatTest, ArithmeticOps) {
+ mat4 m0;
+ mat4 m1(2);
+ mat4 m2(vec4(2));
+
+ m1 += m2;
+ EXPECT_EQ(mat4(4), m1);
+
+ m2 -= m1;
+ EXPECT_EQ(mat4(-2), m2);
+
+ m1 *= 2;
+ EXPECT_EQ(mat4(8), m1);
+
+ m1 /= 2;
+ EXPECT_EQ(mat4(4), m1);
+
+ m0 = -m0;
+ EXPECT_EQ(mat4(-1), m0);
+}
+
+TEST_F(MatTest, UnaryOps) {
+ const mat4 identity;
+ mat4 m0;
+
+ m0 = -m0;
+ EXPECT_EQ(mat4(vec4(-1, 0, 0, 0),
+ vec4(0, -1, 0, 0),
+ vec4(0, 0, -1, 0),
+ vec4(0, 0, 0, -1)), m0);
+
+ m0 = -m0;
+ EXPECT_EQ(identity, m0);
+}
+
+TEST_F(MatTest, MiscOps) {
+ const mat4 identity;
+ mat4 m0;
+ EXPECT_EQ(4, trace(m0));
+
+ mat4 m1(vec4(1, 2, 3, 4), vec4(5, 6, 7, 8), vec4(9, 10, 11, 12), vec4(13, 14, 15, 16));
+ mat4 m2(vec4(1, 5, 9, 13), vec4(2, 6, 10, 14), vec4(3, 7, 11, 15), vec4(4, 8, 12, 16));
+ EXPECT_EQ(m1, transpose(m2));
+ EXPECT_EQ(m2, transpose(m1));
+ EXPECT_EQ(vec4(1, 6, 11, 16), diag(m1));
+
+ EXPECT_EQ(identity, inverse(identity));
+
+ mat4 m3(vec4(4, 3, 0, 0), vec4(3, 2, 0, 0), vec4(0, 0, 1, 0), vec4(0, 0, 0, 1));
+ mat4 m3i(inverse(m3));
+ EXPECT_FLOAT_EQ(-2, m3i[0][0]);
+ EXPECT_FLOAT_EQ(3, m3i[0][1]);
+ EXPECT_FLOAT_EQ(3, m3i[1][0]);
+ EXPECT_FLOAT_EQ(-4, m3i[1][1]);
+
+ mat4 m3ii(inverse(m3i));
+ EXPECT_FLOAT_EQ(m3[0][0], m3ii[0][0]);
+ EXPECT_FLOAT_EQ(m3[0][1], m3ii[0][1]);
+ EXPECT_FLOAT_EQ(m3[1][0], m3ii[1][0]);
+ EXPECT_FLOAT_EQ(m3[1][1], m3ii[1][1]);
+
+ EXPECT_EQ(m1, m1*identity);
+
+
+ for (size_t c=0 ; c<4 ; c++) {
+ for (size_t r=0 ; r<4 ; r++) {
+ EXPECT_FLOAT_EQ(m1[c][r], m1(r, c));
+ }
+ }
+}
+
+TEST_F(MatTest, ElementAccess) {
+ mat4 m(vec4(1, 2, 3, 4), vec4(5, 6, 7, 8), vec4(9, 10, 11, 12), vec4(13, 14, 15, 16));
+ for (size_t c=0 ; c<4 ; c++) {
+ for (size_t r=0 ; r<4 ; r++) {
+ EXPECT_FLOAT_EQ(m[c][r], m(r, c));
+ }
+ }
+
+ m(3,2) = 100;
+ EXPECT_FLOAT_EQ(m[2][3], 100);
+ EXPECT_FLOAT_EQ(m(3, 2), 100);
+}
+
+//------------------------------------------------------------------------------
+// MAT 3
+//------------------------------------------------------------------------------
+
+class Mat3Test : public testing::Test {
+protected:
+};
+
+TEST_F(Mat3Test, Basics) {
+ mat3 m0;
+ EXPECT_EQ(sizeof(mat3), sizeof(float)*9);
+}
+
+TEST_F(Mat3Test, ComparisonOps) {
+ mat3 m0;
+ mat3 m1(2);
+
+ EXPECT_TRUE(m0 == m0);
+ EXPECT_TRUE(m0 != m1);
+ EXPECT_FALSE(m0 != m0);
+ EXPECT_FALSE(m0 == m1);
+}
+
+TEST_F(Mat3Test, Constructors) {
+ mat3 m0;
+ ASSERT_EQ(m0[0].x, 1);
+ ASSERT_EQ(m0[0].y, 0);
+ ASSERT_EQ(m0[0].z, 0);
+ ASSERT_EQ(m0[1].x, 0);
+ ASSERT_EQ(m0[1].y, 1);
+ ASSERT_EQ(m0[1].z, 0);
+ ASSERT_EQ(m0[2].x, 0);
+ ASSERT_EQ(m0[2].y, 0);
+ ASSERT_EQ(m0[2].z, 1);
+
+ mat3 m1(2);
+ mat3 m2(vec3(2));
+ mat3 m3(m2);
+
+ EXPECT_EQ(m1, m2);
+ EXPECT_EQ(m2, m3);
+ EXPECT_EQ(m3, m1);
+}
+
+TEST_F(Mat3Test, ArithmeticOps) {
+ mat3 m0;
+ mat3 m1(2);
+ mat3 m2(vec3(2));
+
+ m1 += m2;
+ EXPECT_EQ(mat3(4), m1);
+
+ m2 -= m1;
+ EXPECT_EQ(mat3(-2), m2);
+
+ m1 *= 2;
+ EXPECT_EQ(mat3(8), m1);
+
+ m1 /= 2;
+ EXPECT_EQ(mat3(4), m1);
+
+ m0 = -m0;
+ EXPECT_EQ(mat3(-1), m0);
+}
+
+TEST_F(Mat3Test, UnaryOps) {
+ const mat3 identity;
+ mat3 m0;
+
+ m0 = -m0;
+ EXPECT_EQ(mat3(vec3(-1, 0, 0),
+ vec3(0, -1, 0),
+ vec3(0, 0, -1)), m0);
+
+ m0 = -m0;
+ EXPECT_EQ(identity, m0);
+}
+
+TEST_F(Mat3Test, MiscOps) {
+ const mat3 identity;
+ mat3 m0;
+ EXPECT_EQ(3, trace(m0));
+
+ mat3 m1(vec3(1, 2, 3), vec3(4, 5, 6), vec3(7, 8, 9));
+ mat3 m2(vec3(1, 4, 7), vec3(2, 5, 8), vec3(3, 6, 9));
+ EXPECT_EQ(m1, transpose(m2));
+ EXPECT_EQ(m2, transpose(m1));
+ EXPECT_EQ(vec3(1, 5, 9), diag(m1));
+
+ EXPECT_EQ(identity, inverse(identity));
+
+ mat3 m3(vec3(4, 3, 0), vec3(3, 2, 0), vec3(0, 0, 1));
+ mat3 m3i(inverse(m3));
+ EXPECT_FLOAT_EQ(-2, m3i[0][0]);
+ EXPECT_FLOAT_EQ(3, m3i[0][1]);
+ EXPECT_FLOAT_EQ(3, m3i[1][0]);
+ EXPECT_FLOAT_EQ(-4, m3i[1][1]);
+
+ mat3 m3ii(inverse(m3i));
+ EXPECT_FLOAT_EQ(m3[0][0], m3ii[0][0]);
+ EXPECT_FLOAT_EQ(m3[0][1], m3ii[0][1]);
+ EXPECT_FLOAT_EQ(m3[1][0], m3ii[1][0]);
+ EXPECT_FLOAT_EQ(m3[1][1], m3ii[1][1]);
+
+ EXPECT_EQ(m1, m1*identity);
+}
+
+//------------------------------------------------------------------------------
+// MAT 2
+//------------------------------------------------------------------------------
+
+class Mat2Test : public testing::Test {
+protected:
+};
+
+TEST_F(Mat2Test, Basics) {
+ mat2 m0;
+ EXPECT_EQ(sizeof(mat2), sizeof(float)*4);
+}
+
+TEST_F(Mat2Test, ComparisonOps) {
+ mat2 m0;
+ mat2 m1(2);
+
+ EXPECT_TRUE(m0 == m0);
+ EXPECT_TRUE(m0 != m1);
+ EXPECT_FALSE(m0 != m0);
+ EXPECT_FALSE(m0 == m1);
+}
+
+TEST_F(Mat2Test, Constructors) {
+ mat2 m0;
+ ASSERT_EQ(m0[0].x, 1);
+ ASSERT_EQ(m0[0].y, 0);
+ ASSERT_EQ(m0[1].x, 0);
+ ASSERT_EQ(m0[1].y, 1);
+
+ mat2 m1(2);
+ mat2 m2(vec2(2));
+ mat2 m3(m2);
+
+ EXPECT_EQ(m1, m2);
+ EXPECT_EQ(m2, m3);
+ EXPECT_EQ(m3, m1);
+}
+
+TEST_F(Mat2Test, ArithmeticOps) {
+ mat2 m0;
+ mat2 m1(2);
+ mat2 m2(vec2(2));
+
+ m1 += m2;
+ EXPECT_EQ(mat2(4), m1);
+
+ m2 -= m1;
+ EXPECT_EQ(mat2(-2), m2);
+
+ m1 *= 2;
+ EXPECT_EQ(mat2(8), m1);
+
+ m1 /= 2;
+ EXPECT_EQ(mat2(4), m1);
+
+ m0 = -m0;
+ EXPECT_EQ(mat2(-1), m0);
+}
+
+TEST_F(Mat2Test, UnaryOps) {
+ const mat2 identity;
+ mat2 m0;
+
+ m0 = -m0;
+ EXPECT_EQ(mat2(vec2(-1, 0),
+ vec2(0, -1)), m0);
+
+ m0 = -m0;
+ EXPECT_EQ(identity, m0);
+}
+
+TEST_F(Mat2Test, MiscOps) {
+ const mat2 identity;
+ mat2 m0;
+ EXPECT_EQ(2, trace(m0));
+
+ mat2 m1(vec2(1, 2), vec2(3, 4));
+ mat2 m2(vec2(1, 3), vec2(2, 4));
+ EXPECT_EQ(m1, transpose(m2));
+ EXPECT_EQ(m2, transpose(m1));
+ EXPECT_EQ(vec2(1, 4), diag(m1));
+
+ EXPECT_EQ(identity, inverse(identity));
+
+ EXPECT_EQ(m1, m1*identity);
+}
+
+//------------------------------------------------------------------------------
+// MORE MATRIX TESTS
+//------------------------------------------------------------------------------
+
+template <typename T>
+class MatTestT : public ::testing::Test {
+public:
+};
+
+typedef ::testing::Types<float,float> TestMatrixValueTypes;
+
+TYPED_TEST_CASE(MatTestT, TestMatrixValueTypes);
+
+#define TEST_MATRIX_INVERSE(MATRIX, EPSILON) \
+{ \
+ typedef decltype(MATRIX) MatrixType; \
+ MatrixType inv1 = inverse(MATRIX); \
+ MatrixType ident1 = MATRIX * inv1; \
+ static const MatrixType IDENTITY; \
+ for (size_t row = 0; row < MatrixType::ROW_SIZE; ++row) { \
+ for (size_t col = 0; col < MatrixType::COL_SIZE; ++col) { \
+ EXPECT_NEAR(ident1[row][col], IDENTITY[row][col], EPSILON); \
+ } \
+ } \
+}
+
+TYPED_TEST(MatTestT, Inverse4) {
+ typedef ::android::details::TMat44<TypeParam> M44T;
+
+ M44T m1(1, 0, 0, 0,
+ 0, 1, 0, 0,
+ 0, 0, 1, 0,
+ 0, 0, 0, 1);
+
+ M44T m2(0, -1, 0, 0,
+ 1, 0, 0, 0,
+ 0, 0, 1, 0,
+ 0, 0, 0, 1);
+
+ M44T m3(1, 0, 0, 0,
+ 0, 2, 0, 0,
+ 0, 0, 0, 1,
+ 0, 0, -1, 0);
+
+ M44T m4(
+ 4.683281e-01, 1.251189e-02, -8.834660e-01, -4.726541e+00,
+ -8.749647e-01, 1.456563e-01, -4.617587e-01, 3.044795e+00,
+ 1.229049e-01, 9.892561e-01, 7.916244e-02, -6.737138e+00,
+ 0.000000e+00, 0.000000e+00, 0.000000e+00, 1.000000e+00);
+
+ M44T m5(
+ 4.683281e-01, 1.251189e-02, -8.834660e-01, -4.726541e+00,
+ -8.749647e-01, 1.456563e-01, -4.617587e-01, 3.044795e+00,
+ 1.229049e-01, 9.892561e-01, 7.916244e-02, -6.737138e+00,
+ 1.000000e+00, 2.000000e+00, 3.000000e+00, 4.000000e+00);
+
+ TEST_MATRIX_INVERSE(m1, 0);
+ TEST_MATRIX_INVERSE(m2, 0);
+ TEST_MATRIX_INVERSE(m3, 0);
+ TEST_MATRIX_INVERSE(m4, 20.0 * std::numeric_limits<TypeParam>::epsilon());
+ TEST_MATRIX_INVERSE(m5, 20.0 * std::numeric_limits<TypeParam>::epsilon());
+}
+
+//------------------------------------------------------------------------------
+TYPED_TEST(MatTestT, Inverse3) {
+ typedef ::android::details::TMat33<TypeParam> M33T;
+
+ M33T m1(1, 0, 0,
+ 0, 1, 0,
+ 0, 0, 1);
+
+ M33T m2(0, -1, 0,
+ 1, 0, 0,
+ 0, 0, 1);
+
+ M33T m3(2, 0, 0,
+ 0, 0, 1,
+ 0, -1, 0);
+
+ M33T m4(
+ 4.683281e-01, 1.251189e-02, 0.000000e+00,
+ -8.749647e-01, 1.456563e-01, 0.000000e+00,
+ 0.000000e+00, 0.000000e+00, 1.000000e+00);
+
+ M33T m5(
+ 4.683281e-01, 1.251189e-02, -8.834660e-01,
+ -8.749647e-01, 1.456563e-01, -4.617587e-01,
+ 1.229049e-01, 9.892561e-01, 7.916244e-02);
+
+ TEST_MATRIX_INVERSE(m1, 0);
+ TEST_MATRIX_INVERSE(m2, 0);
+ TEST_MATRIX_INVERSE(m3, 0);
+ TEST_MATRIX_INVERSE(m4, 20.0 * std::numeric_limits<TypeParam>::epsilon());
+ TEST_MATRIX_INVERSE(m5, 20.0 * std::numeric_limits<TypeParam>::epsilon());
+}
+
+//------------------------------------------------------------------------------
+TYPED_TEST(MatTestT, Inverse2) {
+ typedef ::android::details::TMat22<TypeParam> M22T;
+
+ M22T m1(1, 0,
+ 0, 1);
+
+ M22T m2(0, -1,
+ 1, 0);
+
+ M22T m3(
+ 4.683281e-01, 1.251189e-02,
+ -8.749647e-01, 1.456563e-01);
+
+ M22T m4(
+ 4.683281e-01, 1.251189e-02,
+ -8.749647e-01, 1.456563e-01);
+
+ TEST_MATRIX_INVERSE(m1, 0);
+ TEST_MATRIX_INVERSE(m2, 0);
+ TEST_MATRIX_INVERSE(m3, 20.0 * std::numeric_limits<TypeParam>::epsilon());
+ TEST_MATRIX_INVERSE(m4, 20.0 * std::numeric_limits<TypeParam>::epsilon());
+}
+
+//------------------------------------------------------------------------------
+// A macro to help with vector comparisons within floating point range.
+#define EXPECT_VEC_EQ(VEC1, VEC2) \
+do { \
+ const decltype(VEC1) v1 = VEC1; \
+ const decltype(VEC2) v2 = VEC2; \
+ if (std::is_same<TypeParam,float>::value) { \
+ for (size_t i = 0; i < v1.size(); ++i) { \
+ EXPECT_FLOAT_EQ(v1[i], v2[i]); \
+ } \
+ } else if (std::is_same<TypeParam,float>::value) { \
+ for (size_t i = 0; i < v1.size(); ++i) { \
+ EXPECT_DOUBLE_EQ(v1[i], v2[i]); \
+ } \
+ } else { \
+ for (size_t i = 0; i < v1.size(); ++i) { \
+ EXPECT_EQ(v1[i], v2[i]); \
+ } \
+ } \
+} while(0)
+
+//------------------------------------------------------------------------------
+// A macro to help with type comparisons within floating point range.
+#define ASSERT_TYPE_EQ(T1, T2) \
+do { \
+ const decltype(T1) t1 = T1; \
+ const decltype(T2) t2 = T2; \
+ if (std::is_same<TypeParam,float>::value) { \
+ ASSERT_FLOAT_EQ(t1, t2); \
+ } else if (std::is_same<TypeParam,float>::value) { \
+ ASSERT_DOUBLE_EQ(t1, t2); \
+ } else { \
+ ASSERT_EQ(t1, t2); \
+ } \
+} while(0)
+
+//------------------------------------------------------------------------------
+// Test some translation stuff.
+TYPED_TEST(MatTestT, Translation4) {
+ typedef ::android::details::TMat44<TypeParam> M44T;
+ typedef ::android::details::TVec4<TypeParam> V4T;
+
+ V4T translateBy(-7.3, 1.1, 14.4, 0.0);
+ V4T translation(translateBy[0], translateBy[1], translateBy[2], 1.0);
+ M44T translation_matrix = M44T::translate(translation);
+
+ V4T p1(9.9, 3.1, 41.1, 1.0);
+ V4T p2(-18.0, 0.0, 1.77, 1.0);
+ V4T p3(0, 0, 0, 1);
+ V4T p4(-1000, -1000, 1000, 1.0);
+
+ EXPECT_VEC_EQ(translation_matrix * p1, translateBy + p1);
+ EXPECT_VEC_EQ(translation_matrix * p2, translateBy + p2);
+ EXPECT_VEC_EQ(translation_matrix * p3, translateBy + p3);
+ EXPECT_VEC_EQ(translation_matrix * p4, translateBy + p4);
+}
+
+//------------------------------------------------------------------------------
+template <typename MATRIX>
+static void verifyOrthonormal(const MATRIX& A) {
+ typedef typename MATRIX::value_type T;
+
+ static constexpr T value_eps = T(100) * std::numeric_limits<T>::epsilon();
+
+ const MATRIX prod = A * transpose(A);
+ for (size_t i = 0; i < MATRIX::NUM_COLS; ++i) {
+ for (size_t j = 0; j < MATRIX::NUM_ROWS; ++j) {
+ if (i == j) {
+ ASSERT_NEAR(prod[i][j], T(1), value_eps);
+ } else {
+ ASSERT_NEAR(prod[i][j], T(0), value_eps);
+ }
+ }
+ }
+}
+
+//------------------------------------------------------------------------------
+// Test euler code.
+TYPED_TEST(MatTestT, EulerZYX_44) {
+ typedef ::android::details::TMat44<TypeParam> M44T;
+
+ std::default_random_engine generator(82828);
+ std::uniform_real_distribution<float> distribution(-6.0 * 2.0*M_PI, 6.0 * 2.0*M_PI);
+ auto rand_gen = std::bind(distribution, generator);
+
+ for (size_t i = 0; i < 100; ++i) {
+ M44T m = M44T::eulerZYX(rand_gen(), rand_gen(), rand_gen());
+ verifyOrthonormal(m);
+ }
+
+ M44T m = M44T::eulerZYX(1, 2, 3);
+ verifyOrthonormal(m);
+}
+
+//------------------------------------------------------------------------------
+// Test euler code.
+TYPED_TEST(MatTestT, EulerZYX_33) {
+
+ typedef ::android::details::TMat33<TypeParam> M33T;
+
+ std::default_random_engine generator(112233);
+ std::uniform_real_distribution<float> distribution(-6.0 * 2.0*M_PI, 6.0 * 2.0*M_PI);
+ auto rand_gen = std::bind(distribution, generator);
+
+ for (size_t i = 0; i < 100; ++i) {
+ M33T m = M33T::eulerZYX(rand_gen(), rand_gen(), rand_gen());
+ verifyOrthonormal(m);
+ }
+
+ M33T m = M33T::eulerZYX(1, 2, 3);
+ verifyOrthonormal(m);
+}
+
+//------------------------------------------------------------------------------
+// Test to quaternion with post translation.
+TYPED_TEST(MatTestT, ToQuaternionPostTranslation) {
+
+ typedef ::android::details::TMat44<TypeParam> M44T;
+ typedef ::android::details::TVec4<TypeParam> V4T;
+ typedef ::android::details::TQuaternion<TypeParam> QuatT;
+
+ std::default_random_engine generator(112233);
+ std::uniform_real_distribution<float> distribution(-6.0 * 2.0*M_PI, 6.0 * 2.0*M_PI);
+ auto rand_gen = std::bind(distribution, generator);
+
+ for (size_t i = 0; i < 100; ++i) {
+ M44T r = M44T::eulerZYX(rand_gen(), rand_gen(), rand_gen());
+ M44T t = M44T::translate(V4T(rand_gen(), rand_gen(), rand_gen(), 1));
+ QuatT qr = r.toQuaternion();
+ M44T tr = t * r;
+ QuatT qtr = tr.toQuaternion();
+
+ ASSERT_TYPE_EQ(qr.x, qtr.x);
+ ASSERT_TYPE_EQ(qr.y, qtr.y);
+ ASSERT_TYPE_EQ(qr.z, qtr.z);
+ ASSERT_TYPE_EQ(qr.w, qtr.w);
+ }
+
+ M44T r = M44T::eulerZYX(1, 2, 3);
+ M44T t = M44T::translate(V4T(20, -15, 2, 1));
+ QuatT qr = r.toQuaternion();
+ M44T tr = t * r;
+ QuatT qtr = tr.toQuaternion();
+
+ ASSERT_TYPE_EQ(qr.x, qtr.x);
+ ASSERT_TYPE_EQ(qr.y, qtr.y);
+ ASSERT_TYPE_EQ(qr.z, qtr.z);
+ ASSERT_TYPE_EQ(qr.w, qtr.w);
+}
+
+//------------------------------------------------------------------------------
+// Test to quaternion with post translation.
+TYPED_TEST(MatTestT, ToQuaternionPointTransformation33) {
+ static constexpr TypeParam value_eps =
+ TypeParam(1000) * std::numeric_limits<TypeParam>::epsilon();
+
+ typedef ::android::details::TMat33<TypeParam> M33T;
+ typedef ::android::details::TVec3<TypeParam> V3T;
+ typedef ::android::details::TQuaternion<TypeParam> QuatT;
+
+ std::default_random_engine generator(112233);
+ std::uniform_real_distribution<float> distribution(-100.0, 100.0);
+ auto rand_gen = std::bind(distribution, generator);
+
+ for (size_t i = 0; i < 100; ++i) {
+ M33T r = M33T::eulerZYX(rand_gen(), rand_gen(), rand_gen());
+ QuatT qr = r.toQuaternion();
+ V3T p(rand_gen(), rand_gen(), rand_gen());
+
+ V3T pr = r * p;
+ V3T pq = qr * p;
+
+ ASSERT_NEAR(pr.x, pq.x, value_eps);
+ ASSERT_NEAR(pr.y, pq.y, value_eps);
+ ASSERT_NEAR(pr.z, pq.z, value_eps);
+ }
+}
+
+//------------------------------------------------------------------------------
+// Test to quaternion with post translation.
+TYPED_TEST(MatTestT, ToQuaternionPointTransformation44) {
+ static constexpr TypeParam value_eps =
+ TypeParam(1000) * std::numeric_limits<TypeParam>::epsilon();
+
+ typedef ::android::details::TMat44<TypeParam> M44T;
+ typedef ::android::details::TVec4<TypeParam> V4T;
+ typedef ::android::details::TVec3<TypeParam> V3T;
+ typedef ::android::details::TQuaternion<TypeParam> QuatT;
+
+ std::default_random_engine generator(992626);
+ std::uniform_real_distribution<float> distribution(-100.0, 100.0);
+ auto rand_gen = std::bind(distribution, generator);
+
+ for (size_t i = 0; i < 100; ++i) {
+ M44T r = M44T::eulerZYX(rand_gen(), rand_gen(), rand_gen());
+ QuatT qr = r.toQuaternion();
+ V3T p(rand_gen(), rand_gen(), rand_gen());
+
+ V4T pr = r * V4T(p.x, p.y, p.z, 1);
+ pr.x /= pr.w;
+ pr.y /= pr.w;
+ pr.z /= pr.w;
+ V3T pq = qr * p;
+
+ ASSERT_NEAR(pr.x, pq.x, value_eps);
+ ASSERT_NEAR(pr.y, pq.y, value_eps);
+ ASSERT_NEAR(pr.z, pq.z, value_eps);
+ }
+}
+
+#undef TEST_MATRIX_INVERSE
+
+}; // namespace android
diff --git a/libs/math/tests/quat_test.cpp b/libs/math/tests/quat_test.cpp
new file mode 100644
index 0000000..c20771e
--- /dev/null
+++ b/libs/math/tests/quat_test.cpp
@@ -0,0 +1,301 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#define LOG_TAG "QuatTest"
+
+#include <math.h>
+#include <stdlib.h>
+
+#include <random>
+#include <functional>
+
+#include <math/quat.h>
+#include <math/mat4.h>
+#include <math/vec3.h>
+#include <math/vec4.h>
+
+#include <gtest/gtest.h>
+
+namespace android {
+
+class QuatTest : public testing::Test {
+protected:
+};
+
+TEST_F(QuatTest, Basics) {
+ quatd q;
+ double4& v(q.xyzw);
+
+ EXPECT_EQ(sizeof(quatd), sizeof(double)*4);
+ EXPECT_EQ(reinterpret_cast<void*>(&q), reinterpret_cast<void*>(&v));
+}
+
+TEST_F(QuatTest, Constructors) {
+ quatd q0;
+ EXPECT_EQ(q0.x, 0);
+ EXPECT_EQ(q0.y, 0);
+ EXPECT_EQ(q0.z, 0);
+ EXPECT_EQ(q0.w, 0);
+
+ quatd q1(1);
+ EXPECT_EQ(q1.x, 0);
+ EXPECT_EQ(q1.y, 0);
+ EXPECT_EQ(q1.z, 0);
+ EXPECT_EQ(q1.w, 1);
+
+ quatd q2(1, 2, 3, 4);
+ EXPECT_EQ(q2.x, 2);
+ EXPECT_EQ(q2.y, 3);
+ EXPECT_EQ(q2.z, 4);
+ EXPECT_EQ(q2.w, 1);
+
+ quatd q3(q2);
+ EXPECT_EQ(q3.x, 2);
+ EXPECT_EQ(q3.y, 3);
+ EXPECT_EQ(q3.z, 4);
+ EXPECT_EQ(q3.w, 1);
+
+ quatd q4(q3.xyz, 42);
+ EXPECT_EQ(q4.x, 2);
+ EXPECT_EQ(q4.y, 3);
+ EXPECT_EQ(q4.z, 4);
+ EXPECT_EQ(q4.w, 42);
+
+ quatd q5(double3(q2.xy, 42), 24);
+ EXPECT_EQ(q5.x, 2);
+ EXPECT_EQ(q5.y, 3);
+ EXPECT_EQ(q5.z, 42);
+ EXPECT_EQ(q5.w, 24);
+
+ quatd q6;
+ q6 = 12;
+ EXPECT_EQ(q6.x, 0);
+ EXPECT_EQ(q6.y, 0);
+ EXPECT_EQ(q6.z, 0);
+ EXPECT_EQ(q6.w, 12);
+
+ quatd q7 = 1 + 2_id + 3_jd + 4_kd;
+ EXPECT_EQ(q7.x, 2);
+ EXPECT_EQ(q7.y, 3);
+ EXPECT_EQ(q7.z, 4);
+ EXPECT_EQ(q7.w, 1);
+
+ quatf qf(2);
+ EXPECT_EQ(qf.x, 0);
+ EXPECT_EQ(qf.y, 0);
+ EXPECT_EQ(qf.z, 0);
+ EXPECT_EQ(qf.w, 2);
+}
+
+TEST_F(QuatTest, Access) {
+ quatd q0(1, 2, 3, 4);
+ q0.x = 10;
+ q0.y = 20;
+ q0.z = 30;
+ q0.w = 40;
+ EXPECT_EQ(q0.x, 10);
+ EXPECT_EQ(q0.y, 20);
+ EXPECT_EQ(q0.z, 30);
+ EXPECT_EQ(q0.w, 40);
+
+ q0[0] = 100;
+ q0[1] = 200;
+ q0[2] = 300;
+ q0[3] = 400;
+ EXPECT_EQ(q0.x, 100);
+ EXPECT_EQ(q0.y, 200);
+ EXPECT_EQ(q0.z, 300);
+ EXPECT_EQ(q0.w, 400);
+
+ q0.xyz = double3(1, 2, 3);
+ EXPECT_EQ(q0.x, 1);
+ EXPECT_EQ(q0.y, 2);
+ EXPECT_EQ(q0.z, 3);
+ EXPECT_EQ(q0.w, 400);
+}
+
+TEST_F(QuatTest, UnaryOps) {
+ quatd q0(1, 2, 3, 4);
+
+ q0 += 1;
+ EXPECT_EQ(q0.x, 2);
+ EXPECT_EQ(q0.y, 3);
+ EXPECT_EQ(q0.z, 4);
+ EXPECT_EQ(q0.w, 2);
+
+ q0 -= 1;
+ EXPECT_EQ(q0.x, 2);
+ EXPECT_EQ(q0.y, 3);
+ EXPECT_EQ(q0.z, 4);
+ EXPECT_EQ(q0.w, 1);
+
+ q0 *= 2;
+ EXPECT_EQ(q0.x, 4);
+ EXPECT_EQ(q0.y, 6);
+ EXPECT_EQ(q0.z, 8);
+ EXPECT_EQ(q0.w, 2);
+
+ q0 /= 2;
+ EXPECT_EQ(q0.x, 2);
+ EXPECT_EQ(q0.y, 3);
+ EXPECT_EQ(q0.z, 4);
+ EXPECT_EQ(q0.w, 1);
+
+ quatd q1(10, 20, 30, 40);
+
+ q0 += q1;
+ EXPECT_EQ(q0.x, 22);
+ EXPECT_EQ(q0.y, 33);
+ EXPECT_EQ(q0.z, 44);
+ EXPECT_EQ(q0.w, 11);
+
+ q0 -= q1;
+ EXPECT_EQ(q0.x, 2);
+ EXPECT_EQ(q0.y, 3);
+ EXPECT_EQ(q0.z, 4);
+ EXPECT_EQ(q0.w, 1);
+
+ q1 = -q1;
+ EXPECT_EQ(q1.x, -20);
+ EXPECT_EQ(q1.y, -30);
+ EXPECT_EQ(q1.z, -40);
+ EXPECT_EQ(q1.w, -10);
+
+ // TODO(mathias): multiplies
+}
+
+TEST_F(QuatTest, ComparisonOps) {
+ quatd q0(1, 2, 3, 4);
+ quatd q1(10, 20, 30, 40);
+
+ EXPECT_TRUE(q0 == q0);
+ EXPECT_TRUE(q0 != q1);
+ EXPECT_FALSE(q0 != q0);
+ EXPECT_FALSE(q0 == q1);
+}
+
+TEST_F(QuatTest, ArithmeticOps) {
+ quatd q0(1, 2, 3, 4);
+ quatd q1(10, 20, 30, 40);
+
+ quatd q2(q0 + q1);
+ EXPECT_EQ(q2.x, 22);
+ EXPECT_EQ(q2.y, 33);
+ EXPECT_EQ(q2.z, 44);
+ EXPECT_EQ(q2.w, 11);
+
+ q0 = q1 * 2;
+ EXPECT_EQ(q0.x, 40);
+ EXPECT_EQ(q0.y, 60);
+ EXPECT_EQ(q0.z, 80);
+ EXPECT_EQ(q0.w, 20);
+
+ q0 = 2 * q1;
+ EXPECT_EQ(q0.x, 40);
+ EXPECT_EQ(q0.y, 60);
+ EXPECT_EQ(q0.z, 80);
+ EXPECT_EQ(q0.w, 20);
+
+ quatf qf(2);
+ q0 = q1 * qf;
+ EXPECT_EQ(q0.x, 40);
+ EXPECT_EQ(q0.y, 60);
+ EXPECT_EQ(q0.z, 80);
+ EXPECT_EQ(q0.w, 20);
+
+ EXPECT_EQ(1_id * 1_id, quat(-1));
+ EXPECT_EQ(1_jd * 1_jd, quat(-1));
+ EXPECT_EQ(1_kd * 1_kd, quat(-1));
+ EXPECT_EQ(1_id * 1_jd * 1_kd, quat(-1));
+}
+
+TEST_F(QuatTest, ArithmeticFunc) {
+ quatd q(1, 2, 3, 4);
+ quatd qc(conj(q));
+ __attribute__((unused)) quatd qi(inverse(q));
+ quatd qn(normalize(q));
+
+ EXPECT_EQ(qc.x, -2);
+ EXPECT_EQ(qc.y, -3);
+ EXPECT_EQ(qc.z, -4);
+ EXPECT_EQ(qc.w, 1);
+
+ EXPECT_EQ(~q, qc);
+ EXPECT_EQ(length(q), length(qc));
+ EXPECT_EQ(sqrt(30), length(q));
+ EXPECT_FLOAT_EQ(1, length(qn));
+ EXPECT_FLOAT_EQ(1, dot(qn, qn));
+
+ quatd qr = quatd::fromAxisAngle(double3(0, 0, 1), M_PI / 2);
+ EXPECT_EQ(mat4d(qr).toQuaternion(), qr);
+ EXPECT_EQ(1_id, mat4d(1_id).toQuaternion());
+ EXPECT_EQ(1_jd, mat4d(1_jd).toQuaternion());
+ EXPECT_EQ(1_kd, mat4d(1_kd).toQuaternion());
+
+
+ EXPECT_EQ(qr, log(exp(qr)));
+
+ quatd qq = qr * qr;
+ quatd q2 = pow(qr, 2);
+ EXPECT_NEAR(qq.x, q2.x, 1e-15);
+ EXPECT_NEAR(qq.y, q2.y, 1e-15);
+ EXPECT_NEAR(qq.z, q2.z, 1e-15);
+ EXPECT_NEAR(qq.w, q2.w, 1e-15);
+
+ quatd qa = quatd::fromAxisAngle(double3(0, 0, 1), 0);
+ quatd qb = quatd::fromAxisAngle(double3(0, 0, 1), M_PI / 2);
+ quatd qs = slerp(qa, qb, 0.5);
+ qr = quatd::fromAxisAngle(double3(0, 0, 1), M_PI / 4);
+ EXPECT_FLOAT_EQ(qr.x, qs.x);
+ EXPECT_FLOAT_EQ(qr.y, qs.y);
+ EXPECT_FLOAT_EQ(qr.z, qs.z);
+ EXPECT_FLOAT_EQ(qr.w, qs.w);
+
+ qs = nlerp(qa, qb, 0.5);
+ EXPECT_FLOAT_EQ(qr.x, qs.x);
+ EXPECT_FLOAT_EQ(qr.y, qs.y);
+ EXPECT_FLOAT_EQ(qr.z, qs.z);
+ EXPECT_FLOAT_EQ(qr.w, qs.w);
+}
+
+TEST_F(QuatTest, MultiplicationExhaustive) {
+ static constexpr double value_eps = double(1000) * std::numeric_limits<double>::epsilon();
+
+ std::default_random_engine generator(171717);
+ std::uniform_real_distribution<double> distribution(-10.0, 10.0);
+ auto rand_gen = std::bind(distribution, generator);
+
+ for (size_t i = 0; i < (1024 * 1024); ++i) {
+ double3 axis_a = normalize(double3(rand_gen(), rand_gen(), rand_gen()));
+ double angle_a = rand_gen();
+ quatd a = quatd::fromAxisAngle(axis_a, angle_a);
+
+ double3 axis_b = normalize(double3(rand_gen(), rand_gen(), rand_gen()));
+ double angle_b = rand_gen();
+ quatd b = quatd::fromAxisAngle(axis_b, angle_b);
+
+ quatd ab = a * b;
+ quatd ab_other(a.w * b.xyz + b.w * a.xyz + cross(a.xyz, b.xyz),
+ (a.w * b.w) - dot(a.xyz, b.xyz));
+
+ ASSERT_NEAR(ab.x, ab_other.x, value_eps);
+ ASSERT_NEAR(ab.y, ab_other.y, value_eps);
+ ASSERT_NEAR(ab.z, ab_other.z, value_eps);
+ ASSERT_NEAR(ab.w, ab_other.w, value_eps);
+ }
+}
+
+}; // namespace android
diff --git a/libs/math/tests/vec_test.cpp b/libs/math/tests/vec_test.cpp
new file mode 100644
index 0000000..79ae2e4
--- /dev/null
+++ b/libs/math/tests/vec_test.cpp
@@ -0,0 +1,270 @@
+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#define LOG_TAG "VecTest"
+
+#include <math.h>
+#include <stdlib.h>
+
+#include <math/vec4.h>
+
+#include <gtest/gtest.h>
+
+namespace android {
+
+class VecTest : public testing::Test {
+};
+
+TEST_F(VecTest, Basics) {
+ vec4 v4;
+ vec3& v3(v4.xyz);
+
+ EXPECT_EQ(sizeof(vec4), sizeof(float)*4);
+ EXPECT_EQ(sizeof(vec3), sizeof(float)*3);
+ EXPECT_EQ(sizeof(vec2), sizeof(float)*2);
+ EXPECT_EQ(reinterpret_cast<void*>(&v3), reinterpret_cast<void*>(&v4));
+}
+
+TEST_F(VecTest, Constructors) {
+ vec4 v0;
+ EXPECT_EQ(v0.x, 0);
+ EXPECT_EQ(v0.y, 0);
+ EXPECT_EQ(v0.z, 0);
+ EXPECT_EQ(v0.w, 0);
+
+ vec4 v1(1);
+ EXPECT_EQ(v1.x, 1);
+ EXPECT_EQ(v1.y, 1);
+ EXPECT_EQ(v1.z, 1);
+ EXPECT_EQ(v1.w, 1);
+
+ vec4 v2(1, 2, 3, 4);
+ EXPECT_EQ(v2.x, 1);
+ EXPECT_EQ(v2.y, 2);
+ EXPECT_EQ(v2.z, 3);
+ EXPECT_EQ(v2.w, 4);
+
+ vec4 v3(v2);
+ EXPECT_EQ(v3.x, 1);
+ EXPECT_EQ(v3.y, 2);
+ EXPECT_EQ(v3.z, 3);
+ EXPECT_EQ(v3.w, 4);
+
+ vec4 v4(v3.xyz, 42);
+ EXPECT_EQ(v4.x, 1);
+ EXPECT_EQ(v4.y, 2);
+ EXPECT_EQ(v4.z, 3);
+ EXPECT_EQ(v4.w, 42);
+
+ vec4 v5(vec3(v2.xy, 42), 24);
+ EXPECT_EQ(v5.x, 1);
+ EXPECT_EQ(v5.y, 2);
+ EXPECT_EQ(v5.z, 42);
+ EXPECT_EQ(v5.w, 24);
+
+ float4 vf(2);
+ EXPECT_EQ(vf.x, 2);
+ EXPECT_EQ(vf.y, 2);
+ EXPECT_EQ(vf.z, 2);
+ EXPECT_EQ(vf.w, 2);
+}
+
+TEST_F(VecTest, Access) {
+ vec4 v0(1, 2, 3, 4);
+
+ v0.x = 10;
+ v0.y = 20;
+ v0.z = 30;
+ v0.w = 40;
+ EXPECT_EQ(v0.x, 10);
+ EXPECT_EQ(v0.y, 20);
+ EXPECT_EQ(v0.z, 30);
+ EXPECT_EQ(v0.w, 40);
+
+ v0[0] = 100;
+ v0[1] = 200;
+ v0[2] = 300;
+ v0[3] = 400;
+ EXPECT_EQ(v0.x, 100);
+ EXPECT_EQ(v0.y, 200);
+ EXPECT_EQ(v0.z, 300);
+ EXPECT_EQ(v0.w, 400);
+
+ v0.xyz = vec3(1, 2, 3);
+ EXPECT_EQ(v0.x, 1);
+ EXPECT_EQ(v0.y, 2);
+ EXPECT_EQ(v0.z, 3);
+ EXPECT_EQ(v0.w, 400);
+}
+
+TEST_F(VecTest, UnaryOps) {
+ vec4 v0(1, 2, 3, 4);
+
+ v0 += 1;
+ EXPECT_EQ(v0.x, 2);
+ EXPECT_EQ(v0.y, 3);
+ EXPECT_EQ(v0.z, 4);
+ EXPECT_EQ(v0.w, 5);
+
+ v0 -= 1;
+ EXPECT_EQ(v0.x, 1);
+ EXPECT_EQ(v0.y, 2);
+ EXPECT_EQ(v0.z, 3);
+ EXPECT_EQ(v0.w, 4);
+
+ v0 *= 2;
+ EXPECT_EQ(v0.x, 2);
+ EXPECT_EQ(v0.y, 4);
+ EXPECT_EQ(v0.z, 6);
+ EXPECT_EQ(v0.w, 8);
+
+ v0 /= 2;
+ EXPECT_EQ(v0.x, 1);
+ EXPECT_EQ(v0.y, 2);
+ EXPECT_EQ(v0.z, 3);
+ EXPECT_EQ(v0.w, 4);
+
+ vec4 v1(10, 20, 30, 40);
+
+ v0 += v1;
+ EXPECT_EQ(v0.x, 11);
+ EXPECT_EQ(v0.y, 22);
+ EXPECT_EQ(v0.z, 33);
+ EXPECT_EQ(v0.w, 44);
+
+ v0 -= v1;
+ EXPECT_EQ(v0.x, 1);
+ EXPECT_EQ(v0.y, 2);
+ EXPECT_EQ(v0.z, 3);
+ EXPECT_EQ(v0.w, 4);
+
+ v0 *= v1;
+ EXPECT_EQ(v0.x, 10);
+ EXPECT_EQ(v0.y, 40);
+ EXPECT_EQ(v0.z, 90);
+ EXPECT_EQ(v0.w, 160);
+
+ v0 /= v1;
+ EXPECT_EQ(v0.x, 1);
+ EXPECT_EQ(v0.y, 2);
+ EXPECT_EQ(v0.z, 3);
+ EXPECT_EQ(v0.w, 4);
+
+ v1 = -v1;
+ EXPECT_EQ(v1.x, -10);
+ EXPECT_EQ(v1.y, -20);
+ EXPECT_EQ(v1.z, -30);
+ EXPECT_EQ(v1.w, -40);
+
+ float4 fv(1, 2, 3, 4);
+ v1 += fv;
+ EXPECT_EQ(v1.x, -9);
+ EXPECT_EQ(v1.y, -18);
+ EXPECT_EQ(v1.z, -27);
+ EXPECT_EQ(v1.w, -36);
+}
+
+TEST_F(VecTest, ComparisonOps) {
+ vec4 v0(1, 2, 3, 4);
+ vec4 v1(10, 20, 30, 40);
+
+ EXPECT_TRUE(v0 == v0);
+ EXPECT_TRUE(v0 != v1);
+ EXPECT_FALSE(v0 != v0);
+ EXPECT_FALSE(v0 == v1);
+}
+
+TEST_F(VecTest, ComparisonFunctions) {
+ vec4 v0(1, 2, 3, 4);
+ vec4 v1(10, 20, 30, 40);
+
+ EXPECT_TRUE(all(equal(v0, v0)));
+ EXPECT_TRUE(all(notEqual(v0, v1)));
+ EXPECT_FALSE(any(notEqual(v0, v0)));
+ EXPECT_FALSE(any(equal(v0, v1)));
+
+ EXPECT_FALSE(all(lessThan(v0, v0)));
+ EXPECT_TRUE(all(lessThanEqual(v0, v0)));
+ EXPECT_FALSE(all(greaterThan(v0, v0)));
+ EXPECT_TRUE(all(greaterThanEqual(v0, v0)));
+ EXPECT_TRUE(all(lessThan(v0, v1)));
+ EXPECT_TRUE(all(greaterThan(v1, v0)));
+}
+
+TEST_F(VecTest, ArithmeticOps) {
+ vec4 v0(1, 2, 3, 4);
+ vec4 v1(10, 20, 30, 40);
+
+ vec4 v2(v0 + v1);
+ EXPECT_EQ(v2.x, 11);
+ EXPECT_EQ(v2.y, 22);
+ EXPECT_EQ(v2.z, 33);
+ EXPECT_EQ(v2.w, 44);
+
+ v0 = v1 * 2;
+ EXPECT_EQ(v0.x, 20);
+ EXPECT_EQ(v0.y, 40);
+ EXPECT_EQ(v0.z, 60);
+ EXPECT_EQ(v0.w, 80);
+
+ v0 = 2 * v1;
+ EXPECT_EQ(v0.x, 20);
+ EXPECT_EQ(v0.y, 40);
+ EXPECT_EQ(v0.z, 60);
+ EXPECT_EQ(v0.w, 80);
+
+ float4 vf(2);
+ v0 = v1 * vf;
+ EXPECT_EQ(v0.x, 20);
+ EXPECT_EQ(v0.y, 40);
+ EXPECT_EQ(v0.z, 60);
+ EXPECT_EQ(v0.w, 80);
+}
+
+TEST_F(VecTest, ArithmeticFunc) {
+ vec3 east(1, 0, 0);
+ vec3 north(0, 1, 0);
+ vec3 up(cross(east, north));
+ EXPECT_EQ(up, vec3(0, 0, 1));
+ EXPECT_EQ(dot(east, north), 0);
+ EXPECT_EQ(length(east), 1);
+ EXPECT_EQ(distance(east, north), sqrtf(2));
+
+ vec3 v0(1, 2, 3);
+ vec3 vn(normalize(v0));
+ EXPECT_FLOAT_EQ(1, length(vn));
+ EXPECT_FLOAT_EQ(length(v0), dot(v0, vn));
+
+ float3 vf(east);
+ EXPECT_EQ(length(vf), 1);
+
+ EXPECT_TRUE(any(vec3(0, 0, 1)));
+ EXPECT_FALSE(any(vec3(0, 0, 0)));
+
+ EXPECT_TRUE(all(vec3(1, 1, 1)));
+ EXPECT_FALSE(all(vec3(0, 0, 1)));
+
+ EXPECT_TRUE(any(bool3(false, false, true)));
+ EXPECT_FALSE(any(bool3(false)));
+
+ EXPECT_TRUE(all(bool3(true)));
+ EXPECT_FALSE(all(bool3(false, false, true)));
+
+ std::function<bool(float)> p = [](auto v) -> bool { return v > 0.0f; };
+ EXPECT_TRUE(all(map(vec3(1, 2, 3), p)));
+}
+
+}; // namespace android