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Diffstat (limited to 'third_party/highway/hwy/contrib/math/math-inl.h')
| -rw-r--r-- | third_party/highway/hwy/contrib/math/math-inl.h | 1242 |
1 files changed, 1242 insertions, 0 deletions
diff --git a/third_party/highway/hwy/contrib/math/math-inl.h b/third_party/highway/hwy/contrib/math/math-inl.h new file mode 100644 index 0000000000..b4cbb5d119 --- /dev/null +++ b/third_party/highway/hwy/contrib/math/math-inl.h @@ -0,0 +1,1242 @@ +// Copyright 2020 Google LLC +// SPDX-License-Identifier: Apache-2.0 +// +// 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. + +// Include guard (still compiled once per target) +#if defined(HIGHWAY_HWY_CONTRIB_MATH_MATH_INL_H_) == \ + defined(HWY_TARGET_TOGGLE) +#ifdef HIGHWAY_HWY_CONTRIB_MATH_MATH_INL_H_ +#undef HIGHWAY_HWY_CONTRIB_MATH_MATH_INL_H_ +#else +#define HIGHWAY_HWY_CONTRIB_MATH_MATH_INL_H_ +#endif + +#include "hwy/highway.h" + +HWY_BEFORE_NAMESPACE(); +namespace hwy { +namespace HWY_NAMESPACE { + +/** + * Highway SIMD version of std::acos(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 2 + * Valid Range: [-1, +1] + * @return arc cosine of 'x' + */ +template <class D, class V> +HWY_INLINE V Acos(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallAcos(const D d, VecArg<V> x) { + return Acos(d, x); +} + +/** + * Highway SIMD version of std::acosh(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 3 + * Valid Range: float32[1, +FLT_MAX], float64[1, +DBL_MAX] + * @return hyperbolic arc cosine of 'x' + */ +template <class D, class V> +HWY_INLINE V Acosh(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallAcosh(const D d, VecArg<V> x) { + return Acosh(d, x); +} + +/** + * Highway SIMD version of std::asin(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 2 + * Valid Range: [-1, +1] + * @return arc sine of 'x' + */ +template <class D, class V> +HWY_INLINE V Asin(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallAsin(const D d, VecArg<V> x) { + return Asin(d, x); +} + +/** + * Highway SIMD version of std::asinh(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 3 + * Valid Range: float32[-FLT_MAX, +FLT_MAX], float64[-DBL_MAX, +DBL_MAX] + * @return hyperbolic arc sine of 'x' + */ +template <class D, class V> +HWY_INLINE V Asinh(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallAsinh(const D d, VecArg<V> x) { + return Asinh(d, x); +} + +/** + * Highway SIMD version of std::atan(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 3 + * Valid Range: float32[-FLT_MAX, +FLT_MAX], float64[-DBL_MAX, +DBL_MAX] + * @return arc tangent of 'x' + */ +template <class D, class V> +HWY_INLINE V Atan(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallAtan(const D d, VecArg<V> x) { + return Atan(d, x); +} + +/** + * Highway SIMD version of std::atanh(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 3 + * Valid Range: (-1, +1) + * @return hyperbolic arc tangent of 'x' + */ +template <class D, class V> +HWY_INLINE V Atanh(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallAtanh(const D d, VecArg<V> x) { + return Atanh(d, x); +} + +/** + * Highway SIMD version of std::cos(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 3 + * Valid Range: [-39000, +39000] + * @return cosine of 'x' + */ +template <class D, class V> +HWY_INLINE V Cos(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallCos(const D d, VecArg<V> x) { + return Cos(d, x); +} + +/** + * Highway SIMD version of std::exp(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 1 + * Valid Range: float32[-FLT_MAX, +104], float64[-DBL_MAX, +706] + * @return e^x + */ +template <class D, class V> +HWY_INLINE V Exp(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallExp(const D d, VecArg<V> x) { + return Exp(d, x); +} + +/** + * Highway SIMD version of std::expm1(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 4 + * Valid Range: float32[-FLT_MAX, +104], float64[-DBL_MAX, +706] + * @return e^x - 1 + */ +template <class D, class V> +HWY_INLINE V Expm1(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallExpm1(const D d, VecArg<V> x) { + return Expm1(d, x); +} + +/** + * Highway SIMD version of std::log(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 4 + * Valid Range: float32(0, +FLT_MAX], float64(0, +DBL_MAX] + * @return natural logarithm of 'x' + */ +template <class D, class V> +HWY_INLINE V Log(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallLog(const D d, VecArg<V> x) { + return Log(d, x); +} + +/** + * Highway SIMD version of std::log10(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 2 + * Valid Range: float32(0, +FLT_MAX], float64(0, +DBL_MAX] + * @return base 10 logarithm of 'x' + */ +template <class D, class V> +HWY_INLINE V Log10(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallLog10(const D d, VecArg<V> x) { + return Log10(d, x); +} + +/** + * Highway SIMD version of std::log1p(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 2 + * Valid Range: float32[0, +FLT_MAX], float64[0, +DBL_MAX] + * @return log(1 + x) + */ +template <class D, class V> +HWY_INLINE V Log1p(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallLog1p(const D d, VecArg<V> x) { + return Log1p(d, x); +} + +/** + * Highway SIMD version of std::log2(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 2 + * Valid Range: float32(0, +FLT_MAX], float64(0, +DBL_MAX] + * @return base 2 logarithm of 'x' + */ +template <class D, class V> +HWY_INLINE V Log2(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallLog2(const D d, VecArg<V> x) { + return Log2(d, x); +} + +/** + * Highway SIMD version of std::sin(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 3 + * Valid Range: [-39000, +39000] + * @return sine of 'x' + */ +template <class D, class V> +HWY_INLINE V Sin(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallSin(const D d, VecArg<V> x) { + return Sin(d, x); +} + +/** + * Highway SIMD version of std::sinh(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 4 + * Valid Range: float32[-88.7228, +88.7228], float64[-709, +709] + * @return hyperbolic sine of 'x' + */ +template <class D, class V> +HWY_INLINE V Sinh(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallSinh(const D d, VecArg<V> x) { + return Sinh(d, x); +} + +/** + * Highway SIMD version of std::tanh(x). + * + * Valid Lane Types: float32, float64 + * Max Error: ULP = 4 + * Valid Range: float32[-FLT_MAX, +FLT_MAX], float64[-DBL_MAX, +DBL_MAX] + * @return hyperbolic tangent of 'x' + */ +template <class D, class V> +HWY_INLINE V Tanh(const D d, V x); +template <class D, class V> +HWY_NOINLINE V CallTanh(const D d, VecArg<V> x) { + return Tanh(d, x); +} + +//////////////////////////////////////////////////////////////////////////////// +// Implementation +//////////////////////////////////////////////////////////////////////////////// +namespace impl { + +// Estrin's Scheme is a faster method for evaluating large polynomials on +// super scalar architectures. It works by factoring the Horner's Method +// polynomial into power of two sub-trees that can be evaluated in parallel. +// Wikipedia Link: https://en.wikipedia.org/wiki/Estrin%27s_scheme +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1) { + return MulAdd(c1, x, c0); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2) { + T x2 = Mul(x, x); + return MulAdd(x2, c2, MulAdd(c1, x, c0)); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3) { + T x2 = Mul(x, x); + return MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0)); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + return MulAdd(x4, c4, MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + return MulAdd(x4, MulAdd(c5, x, c4), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + return MulAdd(x4, MulAdd(x2, c6, MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + return MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7, T c8) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + T x8 = Mul(x4, x4); + return MulAdd(x8, c8, + MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0)))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7, T c8, T c9) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + T x8 = Mul(x4, x4); + return MulAdd(x8, MulAdd(c9, x, c8), + MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0)))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7, T c8, T c9, T c10) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + T x8 = Mul(x4, x4); + return MulAdd(x8, MulAdd(x2, c10, MulAdd(c9, x, c8)), + MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0)))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7, T c8, T c9, T c10, T c11) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + T x8 = Mul(x4, x4); + return MulAdd(x8, MulAdd(x2, MulAdd(c11, x, c10), MulAdd(c9, x, c8)), + MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0)))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7, T c8, T c9, T c10, T c11, + T c12) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + T x8 = Mul(x4, x4); + return MulAdd( + x8, MulAdd(x4, c12, MulAdd(x2, MulAdd(c11, x, c10), MulAdd(c9, x, c8))), + MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0)))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7, T c8, T c9, T c10, T c11, + T c12, T c13) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + T x8 = Mul(x4, x4); + return MulAdd(x8, + MulAdd(x4, MulAdd(c13, x, c12), + MulAdd(x2, MulAdd(c11, x, c10), MulAdd(c9, x, c8))), + MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0)))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7, T c8, T c9, T c10, T c11, + T c12, T c13, T c14) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + T x8 = Mul(x4, x4); + return MulAdd(x8, + MulAdd(x4, MulAdd(x2, c14, MulAdd(c13, x, c12)), + MulAdd(x2, MulAdd(c11, x, c10), MulAdd(c9, x, c8))), + MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0)))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7, T c8, T c9, T c10, T c11, + T c12, T c13, T c14, T c15) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + T x8 = Mul(x4, x4); + return MulAdd(x8, + MulAdd(x4, MulAdd(x2, MulAdd(c15, x, c14), MulAdd(c13, x, c12)), + MulAdd(x2, MulAdd(c11, x, c10), MulAdd(c9, x, c8))), + MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0)))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7, T c8, T c9, T c10, T c11, + T c12, T c13, T c14, T c15, T c16) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + T x8 = Mul(x4, x4); + T x16 = Mul(x8, x8); + return MulAdd( + x16, c16, + MulAdd(x8, + MulAdd(x4, MulAdd(x2, MulAdd(c15, x, c14), MulAdd(c13, x, c12)), + MulAdd(x2, MulAdd(c11, x, c10), MulAdd(c9, x, c8))), + MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0))))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7, T c8, T c9, T c10, T c11, + T c12, T c13, T c14, T c15, T c16, T c17) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + T x8 = Mul(x4, x4); + T x16 = Mul(x8, x8); + return MulAdd( + x16, MulAdd(c17, x, c16), + MulAdd(x8, + MulAdd(x4, MulAdd(x2, MulAdd(c15, x, c14), MulAdd(c13, x, c12)), + MulAdd(x2, MulAdd(c11, x, c10), MulAdd(c9, x, c8))), + MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0))))); +} +template <class T> +HWY_INLINE HWY_MAYBE_UNUSED T Estrin(T x, T c0, T c1, T c2, T c3, T c4, T c5, + T c6, T c7, T c8, T c9, T c10, T c11, + T c12, T c13, T c14, T c15, T c16, T c17, + T c18) { + T x2 = Mul(x, x); + T x4 = Mul(x2, x2); + T x8 = Mul(x4, x4); + T x16 = Mul(x8, x8); + return MulAdd( + x16, MulAdd(x2, c18, MulAdd(c17, x, c16)), + MulAdd(x8, + MulAdd(x4, MulAdd(x2, MulAdd(c15, x, c14), MulAdd(c13, x, c12)), + MulAdd(x2, MulAdd(c11, x, c10), MulAdd(c9, x, c8))), + MulAdd(x4, MulAdd(x2, MulAdd(c7, x, c6), MulAdd(c5, x, c4)), + MulAdd(x2, MulAdd(c3, x, c2), MulAdd(c1, x, c0))))); +} + +template <class FloatOrDouble> +struct AsinImpl {}; +template <class FloatOrDouble> +struct AtanImpl {}; +template <class FloatOrDouble> +struct CosSinImpl {}; +template <class FloatOrDouble> +struct ExpImpl {}; +template <class FloatOrDouble> +struct LogImpl {}; + +template <> +struct AsinImpl<float> { + // Polynomial approximation for asin(x) over the range [0, 0.5). + template <class D, class V> + HWY_INLINE V AsinPoly(D d, V x2, V /*x*/) { + const auto k0 = Set(d, +0.1666677296f); + const auto k1 = Set(d, +0.07495029271f); + const auto k2 = Set(d, +0.04547423869f); + const auto k3 = Set(d, +0.02424046025f); + const auto k4 = Set(d, +0.04197454825f); + + return Estrin(x2, k0, k1, k2, k3, k4); + } +}; + +#if HWY_HAVE_FLOAT64 && HWY_HAVE_INTEGER64 + +template <> +struct AsinImpl<double> { + // Polynomial approximation for asin(x) over the range [0, 0.5). + template <class D, class V> + HWY_INLINE V AsinPoly(D d, V x2, V /*x*/) { + const auto k0 = Set(d, +0.1666666666666497543); + const auto k1 = Set(d, +0.07500000000378581611); + const auto k2 = Set(d, +0.04464285681377102438); + const auto k3 = Set(d, +0.03038195928038132237); + const auto k4 = Set(d, +0.02237176181932048341); + const auto k5 = Set(d, +0.01735956991223614604); + const auto k6 = Set(d, +0.01388715184501609218); + const auto k7 = Set(d, +0.01215360525577377331); + const auto k8 = Set(d, +0.006606077476277170610); + const auto k9 = Set(d, +0.01929045477267910674); + const auto k10 = Set(d, -0.01581918243329996643); + const auto k11 = Set(d, +0.03161587650653934628); + + return Estrin(x2, k0, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11); + } +}; + +#endif + +template <> +struct AtanImpl<float> { + // Polynomial approximation for atan(x) over the range [0, 1.0). + template <class D, class V> + HWY_INLINE V AtanPoly(D d, V x) { + const auto k0 = Set(d, -0.333331018686294555664062f); + const auto k1 = Set(d, +0.199926957488059997558594f); + const auto k2 = Set(d, -0.142027363181114196777344f); + const auto k3 = Set(d, +0.106347933411598205566406f); + const auto k4 = Set(d, -0.0748900920152664184570312f); + const auto k5 = Set(d, +0.0425049886107444763183594f); + const auto k6 = Set(d, -0.0159569028764963150024414f); + const auto k7 = Set(d, +0.00282363896258175373077393f); + + const auto y = Mul(x, x); + return MulAdd(Estrin(y, k0, k1, k2, k3, k4, k5, k6, k7), Mul(y, x), x); + } +}; + +#if HWY_HAVE_FLOAT64 && HWY_HAVE_INTEGER64 + +template <> +struct AtanImpl<double> { + // Polynomial approximation for atan(x) over the range [0, 1.0). + template <class D, class V> + HWY_INLINE V AtanPoly(D d, V x) { + const auto k0 = Set(d, -0.333333333333311110369124); + const auto k1 = Set(d, +0.199999999996591265594148); + const auto k2 = Set(d, -0.14285714266771329383765); + const auto k3 = Set(d, +0.111111105648261418443745); + const auto k4 = Set(d, -0.090908995008245008229153); + const auto k5 = Set(d, +0.0769219538311769618355029); + const auto k6 = Set(d, -0.0666573579361080525984562); + const auto k7 = Set(d, +0.0587666392926673580854313); + const auto k8 = Set(d, -0.0523674852303482457616113); + const auto k9 = Set(d, +0.0466667150077840625632675); + const auto k10 = Set(d, -0.0407629191276836500001934); + const auto k11 = Set(d, +0.0337852580001353069993897); + const auto k12 = Set(d, -0.0254517624932312641616861); + const auto k13 = Set(d, +0.016599329773529201970117); + const auto k14 = Set(d, -0.00889896195887655491740809); + const auto k15 = Set(d, +0.00370026744188713119232403); + const auto k16 = Set(d, -0.00110611831486672482563471); + const auto k17 = Set(d, +0.000209850076645816976906797); + const auto k18 = Set(d, -1.88796008463073496563746e-5); + + const auto y = Mul(x, x); + return MulAdd(Estrin(y, k0, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10, k11, + k12, k13, k14, k15, k16, k17, k18), + Mul(y, x), x); + } +}; + +#endif + +template <> +struct CosSinImpl<float> { + // Rounds float toward zero and returns as int32_t. + template <class D, class V> + HWY_INLINE Vec<Rebind<int32_t, D>> ToInt32(D /*unused*/, V x) { + return ConvertTo(Rebind<int32_t, D>(), x); + } + + template <class D, class V> + HWY_INLINE V Poly(D d, V x) { + const auto k0 = Set(d, -1.66666597127914428710938e-1f); + const auto k1 = Set(d, +8.33307858556509017944336e-3f); + const auto k2 = Set(d, -1.981069071916863322258e-4f); + const auto k3 = Set(d, +2.6083159809786593541503e-6f); + + const auto y = Mul(x, x); + return MulAdd(Estrin(y, k0, k1, k2, k3), Mul(y, x), x); + } + + template <class D, class V, class VI32> + HWY_INLINE V CosReduce(D d, V x, VI32 q) { + // kHalfPiPart0f + kHalfPiPart1f + kHalfPiPart2f + kHalfPiPart3f ~= -pi/2 + const V kHalfPiPart0f = Set(d, -0.5f * 3.140625f); + const V kHalfPiPart1f = Set(d, -0.5f * 0.0009670257568359375f); + const V kHalfPiPart2f = Set(d, -0.5f * 6.2771141529083251953e-7f); + const V kHalfPiPart3f = Set(d, -0.5f * 1.2154201256553420762e-10f); + + // Extended precision modular arithmetic. + const V qf = ConvertTo(d, q); + x = MulAdd(qf, kHalfPiPart0f, x); + x = MulAdd(qf, kHalfPiPart1f, x); + x = MulAdd(qf, kHalfPiPart2f, x); + x = MulAdd(qf, kHalfPiPart3f, x); + return x; + } + + template <class D, class V, class VI32> + HWY_INLINE V SinReduce(D d, V x, VI32 q) { + // kPiPart0f + kPiPart1f + kPiPart2f + kPiPart3f ~= -pi + const V kPiPart0f = Set(d, -3.140625f); + const V kPiPart1f = Set(d, -0.0009670257568359375f); + const V kPiPart2f = Set(d, -6.2771141529083251953e-7f); + const V kPiPart3f = Set(d, -1.2154201256553420762e-10f); + + // Extended precision modular arithmetic. + const V qf = ConvertTo(d, q); + x = MulAdd(qf, kPiPart0f, x); + x = MulAdd(qf, kPiPart1f, x); + x = MulAdd(qf, kPiPart2f, x); + x = MulAdd(qf, kPiPart3f, x); + return x; + } + + // (q & 2) == 0 ? -0.0 : +0.0 + template <class D, class VI32> + HWY_INLINE Vec<Rebind<float, D>> CosSignFromQuadrant(D d, VI32 q) { + const VI32 kTwo = Set(Rebind<int32_t, D>(), 2); + return BitCast(d, ShiftLeft<30>(AndNot(q, kTwo))); + } + + // ((q & 1) ? -0.0 : +0.0) + template <class D, class VI32> + HWY_INLINE Vec<Rebind<float, D>> SinSignFromQuadrant(D d, VI32 q) { + const VI32 kOne = Set(Rebind<int32_t, D>(), 1); + return BitCast(d, ShiftLeft<31>(And(q, kOne))); + } +}; + +#if HWY_HAVE_FLOAT64 && HWY_HAVE_INTEGER64 + +template <> +struct CosSinImpl<double> { + // Rounds double toward zero and returns as int32_t. + template <class D, class V> + HWY_INLINE Vec<Rebind<int32_t, D>> ToInt32(D /*unused*/, V x) { + return DemoteTo(Rebind<int32_t, D>(), x); + } + + template <class D, class V> + HWY_INLINE V Poly(D d, V x) { + const auto k0 = Set(d, -0.166666666666666657414808); + const auto k1 = Set(d, +0.00833333333333332974823815); + const auto k2 = Set(d, -0.000198412698412696162806809); + const auto k3 = Set(d, +2.75573192239198747630416e-6); + const auto k4 = Set(d, -2.50521083763502045810755e-8); + const auto k5 = Set(d, +1.60590430605664501629054e-10); + const auto k6 = Set(d, -7.64712219118158833288484e-13); + const auto k7 = Set(d, +2.81009972710863200091251e-15); + const auto k8 = Set(d, -7.97255955009037868891952e-18); + + const auto y = Mul(x, x); + return MulAdd(Estrin(y, k0, k1, k2, k3, k4, k5, k6, k7, k8), Mul(y, x), x); + } + + template <class D, class V, class VI32> + HWY_INLINE V CosReduce(D d, V x, VI32 q) { + // kHalfPiPart0d + kHalfPiPart1d + kHalfPiPart2d + kHalfPiPart3d ~= -pi/2 + const V kHalfPiPart0d = Set(d, -0.5 * 3.1415926218032836914); + const V kHalfPiPart1d = Set(d, -0.5 * 3.1786509424591713469e-8); + const V kHalfPiPart2d = Set(d, -0.5 * 1.2246467864107188502e-16); + const V kHalfPiPart3d = Set(d, -0.5 * 1.2736634327021899816e-24); + + // Extended precision modular arithmetic. + const V qf = PromoteTo(d, q); + x = MulAdd(qf, kHalfPiPart0d, x); + x = MulAdd(qf, kHalfPiPart1d, x); + x = MulAdd(qf, kHalfPiPart2d, x); + x = MulAdd(qf, kHalfPiPart3d, x); + return x; + } + + template <class D, class V, class VI32> + HWY_INLINE V SinReduce(D d, V x, VI32 q) { + // kPiPart0d + kPiPart1d + kPiPart2d + kPiPart3d ~= -pi + const V kPiPart0d = Set(d, -3.1415926218032836914); + const V kPiPart1d = Set(d, -3.1786509424591713469e-8); + const V kPiPart2d = Set(d, -1.2246467864107188502e-16); + const V kPiPart3d = Set(d, -1.2736634327021899816e-24); + + // Extended precision modular arithmetic. + const V qf = PromoteTo(d, q); + x = MulAdd(qf, kPiPart0d, x); + x = MulAdd(qf, kPiPart1d, x); + x = MulAdd(qf, kPiPart2d, x); + x = MulAdd(qf, kPiPart3d, x); + return x; + } + + // (q & 2) == 0 ? -0.0 : +0.0 + template <class D, class VI32> + HWY_INLINE Vec<Rebind<double, D>> CosSignFromQuadrant(D d, VI32 q) { + const VI32 kTwo = Set(Rebind<int32_t, D>(), 2); + return BitCast( + d, ShiftLeft<62>(PromoteTo(Rebind<int64_t, D>(), AndNot(q, kTwo)))); + } + + // ((q & 1) ? -0.0 : +0.0) + template <class D, class VI32> + HWY_INLINE Vec<Rebind<double, D>> SinSignFromQuadrant(D d, VI32 q) { + const VI32 kOne = Set(Rebind<int32_t, D>(), 1); + return BitCast( + d, ShiftLeft<63>(PromoteTo(Rebind<int64_t, D>(), And(q, kOne)))); + } +}; + +#endif + +template <> +struct ExpImpl<float> { + // Rounds float toward zero and returns as int32_t. + template <class D, class V> + HWY_INLINE Vec<Rebind<int32_t, D>> ToInt32(D /*unused*/, V x) { + return ConvertTo(Rebind<int32_t, D>(), x); + } + + template <class D, class V> + HWY_INLINE V ExpPoly(D d, V x) { + const auto k0 = Set(d, +0.5f); + const auto k1 = Set(d, +0.166666671633720397949219f); + const auto k2 = Set(d, +0.0416664853692054748535156f); + const auto k3 = Set(d, +0.00833336077630519866943359f); + const auto k4 = Set(d, +0.00139304355252534151077271f); + const auto k5 = Set(d, +0.000198527617612853646278381f); + + return MulAdd(Estrin(x, k0, k1, k2, k3, k4, k5), Mul(x, x), x); + } + + // Computes 2^x, where x is an integer. + template <class D, class VI32> + HWY_INLINE Vec<D> Pow2I(D d, VI32 x) { + const Rebind<int32_t, D> di32; + const VI32 kOffset = Set(di32, 0x7F); + return BitCast(d, ShiftLeft<23>(Add(x, kOffset))); + } + + // Sets the exponent of 'x' to 2^e. + template <class D, class V, class VI32> + HWY_INLINE V LoadExpShortRange(D d, V x, VI32 e) { + const VI32 y = ShiftRight<1>(e); + return Mul(Mul(x, Pow2I(d, y)), Pow2I(d, Sub(e, y))); + } + + template <class D, class V, class VI32> + HWY_INLINE V ExpReduce(D d, V x, VI32 q) { + // kLn2Part0f + kLn2Part1f ~= -ln(2) + const V kLn2Part0f = Set(d, -0.693145751953125f); + const V kLn2Part1f = Set(d, -1.428606765330187045e-6f); + + // Extended precision modular arithmetic. + const V qf = ConvertTo(d, q); + x = MulAdd(qf, kLn2Part0f, x); + x = MulAdd(qf, kLn2Part1f, x); + return x; + } +}; + +template <> +struct LogImpl<float> { + template <class D, class V> + HWY_INLINE Vec<Rebind<int32_t, D>> Log2p1NoSubnormal(D /*d*/, V x) { + const Rebind<int32_t, D> di32; + const Rebind<uint32_t, D> du32; + const auto kBias = Set(di32, 0x7F); + return Sub(BitCast(di32, ShiftRight<23>(BitCast(du32, x))), kBias); + } + + // Approximates Log(x) over the range [sqrt(2) / 2, sqrt(2)]. + template <class D, class V> + HWY_INLINE V LogPoly(D d, V x) { + const V k0 = Set(d, 0.66666662693f); + const V k1 = Set(d, 0.40000972152f); + const V k2 = Set(d, 0.28498786688f); + const V k3 = Set(d, 0.24279078841f); + + const V x2 = Mul(x, x); + const V x4 = Mul(x2, x2); + return MulAdd(MulAdd(k2, x4, k0), x2, Mul(MulAdd(k3, x4, k1), x4)); + } +}; + +#if HWY_HAVE_FLOAT64 && HWY_HAVE_INTEGER64 +template <> +struct ExpImpl<double> { + // Rounds double toward zero and returns as int32_t. + template <class D, class V> + HWY_INLINE Vec<Rebind<int32_t, D>> ToInt32(D /*unused*/, V x) { + return DemoteTo(Rebind<int32_t, D>(), x); + } + + template <class D, class V> + HWY_INLINE V ExpPoly(D d, V x) { + const auto k0 = Set(d, +0.5); + const auto k1 = Set(d, +0.166666666666666851703837); + const auto k2 = Set(d, +0.0416666666666665047591422); + const auto k3 = Set(d, +0.00833333333331652721664984); + const auto k4 = Set(d, +0.00138888888889774492207962); + const auto k5 = Set(d, +0.000198412698960509205564975); + const auto k6 = Set(d, +2.4801587159235472998791e-5); + const auto k7 = Set(d, +2.75572362911928827629423e-6); + const auto k8 = Set(d, +2.75573911234900471893338e-7); + const auto k9 = Set(d, +2.51112930892876518610661e-8); + const auto k10 = Set(d, +2.08860621107283687536341e-9); + + return MulAdd(Estrin(x, k0, k1, k2, k3, k4, k5, k6, k7, k8, k9, k10), + Mul(x, x), x); + } + + // Computes 2^x, where x is an integer. + template <class D, class VI32> + HWY_INLINE Vec<D> Pow2I(D d, VI32 x) { + const Rebind<int32_t, D> di32; + const Rebind<int64_t, D> di64; + const VI32 kOffset = Set(di32, 0x3FF); + return BitCast(d, ShiftLeft<52>(PromoteTo(di64, Add(x, kOffset)))); + } + + // Sets the exponent of 'x' to 2^e. + template <class D, class V, class VI32> + HWY_INLINE V LoadExpShortRange(D d, V x, VI32 e) { + const VI32 y = ShiftRight<1>(e); + return Mul(Mul(x, Pow2I(d, y)), Pow2I(d, Sub(e, y))); + } + + template <class D, class V, class VI32> + HWY_INLINE V ExpReduce(D d, V x, VI32 q) { + // kLn2Part0d + kLn2Part1d ~= -ln(2) + const V kLn2Part0d = Set(d, -0.6931471805596629565116018); + const V kLn2Part1d = Set(d, -0.28235290563031577122588448175e-12); + + // Extended precision modular arithmetic. + const V qf = PromoteTo(d, q); + x = MulAdd(qf, kLn2Part0d, x); + x = MulAdd(qf, kLn2Part1d, x); + return x; + } +}; + +template <> +struct LogImpl<double> { + template <class D, class V> + HWY_INLINE Vec<Rebind<int64_t, D>> Log2p1NoSubnormal(D /*d*/, V x) { + const Rebind<int64_t, D> di64; + const Rebind<uint64_t, D> du64; + return Sub(BitCast(di64, ShiftRight<52>(BitCast(du64, x))), + Set(di64, 0x3FF)); + } + + // Approximates Log(x) over the range [sqrt(2) / 2, sqrt(2)]. + template <class D, class V> + HWY_INLINE V LogPoly(D d, V x) { + const V k0 = Set(d, 0.6666666666666735130); + const V k1 = Set(d, 0.3999999999940941908); + const V k2 = Set(d, 0.2857142874366239149); + const V k3 = Set(d, 0.2222219843214978396); + const V k4 = Set(d, 0.1818357216161805012); + const V k5 = Set(d, 0.1531383769920937332); + const V k6 = Set(d, 0.1479819860511658591); + + const V x2 = Mul(x, x); + const V x4 = Mul(x2, x2); + return MulAdd(MulAdd(MulAdd(MulAdd(k6, x4, k4), x4, k2), x4, k0), x2, + (Mul(MulAdd(MulAdd(k5, x4, k3), x4, k1), x4))); + } +}; + +#endif + +template <class D, class V, bool kAllowSubnormals = true> +HWY_INLINE V Log(const D d, V x) { + // http://git.musl-libc.org/cgit/musl/tree/src/math/log.c for more info. + using T = TFromD<D>; + impl::LogImpl<T> impl; + + constexpr bool kIsF32 = (sizeof(T) == 4); + + // Float Constants + const V kLn2Hi = Set(d, kIsF32 ? static_cast<T>(0.69313812256f) + : static_cast<T>(0.693147180369123816490)); + const V kLn2Lo = Set(d, kIsF32 ? static_cast<T>(9.0580006145e-6f) + : static_cast<T>(1.90821492927058770002e-10)); + const V kOne = Set(d, static_cast<T>(+1.0)); + const V kMinNormal = Set(d, kIsF32 ? static_cast<T>(1.175494351e-38f) + : static_cast<T>(2.2250738585072014e-308)); + const V kScale = Set(d, kIsF32 ? static_cast<T>(3.355443200e+7f) + : static_cast<T>(1.8014398509481984e+16)); + + // Integer Constants + using TI = MakeSigned<T>; + const Rebind<TI, D> di; + using VI = decltype(Zero(di)); + const VI kLowerBits = Set(di, kIsF32 ? static_cast<TI>(0x00000000L) + : static_cast<TI>(0xFFFFFFFFLL)); + const VI kMagic = Set(di, kIsF32 ? static_cast<TI>(0x3F3504F3L) + : static_cast<TI>(0x3FE6A09E00000000LL)); + const VI kExpMask = Set(di, kIsF32 ? static_cast<TI>(0x3F800000L) + : static_cast<TI>(0x3FF0000000000000LL)); + const VI kExpScale = + Set(di, kIsF32 ? static_cast<TI>(-25) : static_cast<TI>(-54)); + const VI kManMask = Set(di, kIsF32 ? static_cast<TI>(0x7FFFFFL) + : static_cast<TI>(0xFFFFF00000000LL)); + + // Scale up 'x' so that it is no longer denormalized. + VI exp_bits; + V exp; + if (kAllowSubnormals == true) { + const auto is_denormal = Lt(x, kMinNormal); + x = IfThenElse(is_denormal, Mul(x, kScale), x); + + // Compute the new exponent. + exp_bits = Add(BitCast(di, x), Sub(kExpMask, kMagic)); + const VI exp_scale = + BitCast(di, IfThenElseZero(is_denormal, BitCast(d, kExpScale))); + exp = ConvertTo( + d, Add(exp_scale, impl.Log2p1NoSubnormal(d, BitCast(d, exp_bits)))); + } else { + // Compute the new exponent. + exp_bits = Add(BitCast(di, x), Sub(kExpMask, kMagic)); + exp = ConvertTo(d, impl.Log2p1NoSubnormal(d, BitCast(d, exp_bits))); + } + + // Renormalize. + const V y = Or(And(x, BitCast(d, kLowerBits)), + BitCast(d, Add(And(exp_bits, kManMask), kMagic))); + + // Approximate and reconstruct. + const V ym1 = Sub(y, kOne); + const V z = Div(ym1, Add(y, kOne)); + + return MulSub( + exp, kLn2Hi, + Sub(MulSub(z, Sub(ym1, impl.LogPoly(d, z)), Mul(exp, kLn2Lo)), ym1)); +} + +} // namespace impl + +template <class D, class V> +HWY_INLINE V Acos(const D d, V x) { + using T = TFromD<D>; + + const V kZero = Zero(d); + const V kHalf = Set(d, static_cast<T>(+0.5)); + const V kPi = Set(d, static_cast<T>(+3.14159265358979323846264)); + const V kPiOverTwo = Set(d, static_cast<T>(+1.57079632679489661923132169)); + + const V sign_x = And(SignBit(d), x); + const V abs_x = Xor(x, sign_x); + const auto mask = Lt(abs_x, kHalf); + const V yy = + IfThenElse(mask, Mul(abs_x, abs_x), NegMulAdd(abs_x, kHalf, kHalf)); + const V y = IfThenElse(mask, abs_x, Sqrt(yy)); + + impl::AsinImpl<T> impl; + const V t = Mul(impl.AsinPoly(d, yy, y), Mul(y, yy)); + + const V t_plus_y = Add(t, y); + const V z = + IfThenElse(mask, Sub(kPiOverTwo, Add(Xor(y, sign_x), Xor(t, sign_x))), + Add(t_plus_y, t_plus_y)); + return IfThenElse(Or(mask, Ge(x, kZero)), z, Sub(kPi, z)); +} + +template <class D, class V> +HWY_INLINE V Acosh(const D d, V x) { + using T = TFromD<D>; + + const V kLarge = Set(d, static_cast<T>(268435456.0)); + const V kLog2 = Set(d, static_cast<T>(0.693147180559945286227)); + const V kOne = Set(d, static_cast<T>(+1.0)); + const V kTwo = Set(d, static_cast<T>(+2.0)); + + const auto is_x_large = Gt(x, kLarge); + const auto is_x_gt_2 = Gt(x, kTwo); + + const V x_minus_1 = Sub(x, kOne); + const V y0 = MulSub(kTwo, x, Div(kOne, Add(Sqrt(MulSub(x, x, kOne)), x))); + const V y1 = + Add(Sqrt(MulAdd(x_minus_1, kTwo, Mul(x_minus_1, x_minus_1))), x_minus_1); + const V y2 = + IfThenElse(is_x_gt_2, IfThenElse(is_x_large, x, y0), Add(y1, kOne)); + const V z = impl::Log<D, V, /*kAllowSubnormals=*/false>(d, y2); + + const auto is_pole = Eq(y2, kOne); + const auto divisor = Sub(IfThenZeroElse(is_pole, y2), kOne); + return Add(IfThenElse(is_x_gt_2, z, + IfThenElse(is_pole, y1, Div(Mul(z, y1), divisor))), + IfThenElseZero(is_x_large, kLog2)); +} + +template <class D, class V> +HWY_INLINE V Asin(const D d, V x) { + using T = TFromD<D>; + + const V kHalf = Set(d, static_cast<T>(+0.5)); + const V kTwo = Set(d, static_cast<T>(+2.0)); + const V kPiOverTwo = Set(d, static_cast<T>(+1.57079632679489661923132169)); + + const V sign_x = And(SignBit(d), x); + const V abs_x = Xor(x, sign_x); + const auto mask = Lt(abs_x, kHalf); + const V yy = + IfThenElse(mask, Mul(abs_x, abs_x), NegMulAdd(abs_x, kHalf, kHalf)); + const V y = IfThenElse(mask, abs_x, Sqrt(yy)); + + impl::AsinImpl<T> impl; + const V z0 = MulAdd(impl.AsinPoly(d, yy, y), Mul(yy, y), y); + const V z1 = NegMulAdd(z0, kTwo, kPiOverTwo); + return Or(IfThenElse(mask, z0, z1), sign_x); +} + +template <class D, class V> +HWY_INLINE V Asinh(const D d, V x) { + using T = TFromD<D>; + + const V kSmall = Set(d, static_cast<T>(1.0 / 268435456.0)); + const V kLarge = Set(d, static_cast<T>(268435456.0)); + const V kLog2 = Set(d, static_cast<T>(0.693147180559945286227)); + const V kOne = Set(d, static_cast<T>(+1.0)); + const V kTwo = Set(d, static_cast<T>(+2.0)); + + const V sign_x = And(SignBit(d), x); // Extract the sign bit + const V abs_x = Xor(x, sign_x); + + const auto is_x_large = Gt(abs_x, kLarge); + const auto is_x_lt_2 = Lt(abs_x, kTwo); + + const V x2 = Mul(x, x); + const V sqrt_x2_plus_1 = Sqrt(Add(x2, kOne)); + + const V y0 = MulAdd(abs_x, kTwo, Div(kOne, Add(sqrt_x2_plus_1, abs_x))); + const V y1 = Add(Div(x2, Add(sqrt_x2_plus_1, kOne)), abs_x); + const V y2 = + IfThenElse(is_x_lt_2, Add(y1, kOne), IfThenElse(is_x_large, abs_x, y0)); + const V z = impl::Log<D, V, /*kAllowSubnormals=*/false>(d, y2); + + const auto is_pole = Eq(y2, kOne); + const auto divisor = Sub(IfThenZeroElse(is_pole, y2), kOne); + const auto large = IfThenElse(is_pole, y1, Div(Mul(z, y1), divisor)); + const V y = IfThenElse(Lt(abs_x, kSmall), x, large); + return Or(Add(IfThenElse(is_x_lt_2, y, z), IfThenElseZero(is_x_large, kLog2)), + sign_x); +} + +template <class D, class V> +HWY_INLINE V Atan(const D d, V x) { + using T = TFromD<D>; + + const V kOne = Set(d, static_cast<T>(+1.0)); + const V kPiOverTwo = Set(d, static_cast<T>(+1.57079632679489661923132169)); + + const V sign = And(SignBit(d), x); + const V abs_x = Xor(x, sign); + const auto mask = Gt(abs_x, kOne); + + impl::AtanImpl<T> impl; + const auto divisor = IfThenElse(mask, abs_x, kOne); + const V y = impl.AtanPoly(d, IfThenElse(mask, Div(kOne, divisor), abs_x)); + return Or(IfThenElse(mask, Sub(kPiOverTwo, y), y), sign); +} + +template <class D, class V> +HWY_INLINE V Atanh(const D d, V x) { + using T = TFromD<D>; + + const V kHalf = Set(d, static_cast<T>(+0.5)); + const V kOne = Set(d, static_cast<T>(+1.0)); + + const V sign = And(SignBit(d), x); // Extract the sign bit + const V abs_x = Xor(x, sign); + return Mul(Log1p(d, Div(Add(abs_x, abs_x), Sub(kOne, abs_x))), + Xor(kHalf, sign)); +} + +template <class D, class V> +HWY_INLINE V Cos(const D d, V x) { + using T = TFromD<D>; + impl::CosSinImpl<T> impl; + + // Float Constants + const V kOneOverPi = Set(d, static_cast<T>(0.31830988618379067153)); + + // Integer Constants + const Rebind<int32_t, D> di32; + using VI32 = decltype(Zero(di32)); + const VI32 kOne = Set(di32, 1); + + const V y = Abs(x); // cos(x) == cos(|x|) + + // Compute the quadrant, q = int(|x| / pi) * 2 + 1 + const VI32 q = Add(ShiftLeft<1>(impl.ToInt32(d, Mul(y, kOneOverPi))), kOne); + + // Reduce range, apply sign, and approximate. + return impl.Poly( + d, Xor(impl.CosReduce(d, y, q), impl.CosSignFromQuadrant(d, q))); +} + +template <class D, class V> +HWY_INLINE V Exp(const D d, V x) { + using T = TFromD<D>; + + const V kHalf = Set(d, static_cast<T>(+0.5)); + const V kLowerBound = + Set(d, static_cast<T>((sizeof(T) == 4 ? -104.0 : -1000.0))); + const V kNegZero = Set(d, static_cast<T>(-0.0)); + const V kOne = Set(d, static_cast<T>(+1.0)); + const V kOneOverLog2 = Set(d, static_cast<T>(+1.442695040888963407359924681)); + + impl::ExpImpl<T> impl; + + // q = static_cast<int32>((x / log(2)) + ((x < 0) ? -0.5 : +0.5)) + const auto q = + impl.ToInt32(d, MulAdd(x, kOneOverLog2, Or(kHalf, And(x, kNegZero)))); + + // Reduce, approximate, and then reconstruct. + const V y = impl.LoadExpShortRange( + d, Add(impl.ExpPoly(d, impl.ExpReduce(d, x, q)), kOne), q); + return IfThenElseZero(Ge(x, kLowerBound), y); +} + +template <class D, class V> +HWY_INLINE V Expm1(const D d, V x) { + using T = TFromD<D>; + + const V kHalf = Set(d, static_cast<T>(+0.5)); + const V kLowerBound = + Set(d, static_cast<T>((sizeof(T) == 4 ? -104.0 : -1000.0))); + const V kLn2Over2 = Set(d, static_cast<T>(+0.346573590279972654708616)); + const V kNegOne = Set(d, static_cast<T>(-1.0)); + const V kNegZero = Set(d, static_cast<T>(-0.0)); + const V kOne = Set(d, static_cast<T>(+1.0)); + const V kOneOverLog2 = Set(d, static_cast<T>(+1.442695040888963407359924681)); + + impl::ExpImpl<T> impl; + + // q = static_cast<int32>((x / log(2)) + ((x < 0) ? -0.5 : +0.5)) + const auto q = + impl.ToInt32(d, MulAdd(x, kOneOverLog2, Or(kHalf, And(x, kNegZero)))); + + // Reduce, approximate, and then reconstruct. + const V y = impl.ExpPoly(d, impl.ExpReduce(d, x, q)); + const V z = IfThenElse(Lt(Abs(x), kLn2Over2), y, + Sub(impl.LoadExpShortRange(d, Add(y, kOne), q), kOne)); + return IfThenElse(Lt(x, kLowerBound), kNegOne, z); +} + +template <class D, class V> +HWY_INLINE V Log(const D d, V x) { + return impl::Log<D, V, /*kAllowSubnormals=*/true>(d, x); +} + +template <class D, class V> +HWY_INLINE V Log10(const D d, V x) { + using T = TFromD<D>; + return Mul(Log(d, x), Set(d, static_cast<T>(0.4342944819032518276511))); +} + +template <class D, class V> +HWY_INLINE V Log1p(const D d, V x) { + using T = TFromD<D>; + const V kOne = Set(d, static_cast<T>(+1.0)); + + const V y = Add(x, kOne); + const auto is_pole = Eq(y, kOne); + const auto divisor = Sub(IfThenZeroElse(is_pole, y), kOne); + const auto non_pole = + Mul(impl::Log<D, V, /*kAllowSubnormals=*/false>(d, y), Div(x, divisor)); + return IfThenElse(is_pole, x, non_pole); +} + +template <class D, class V> +HWY_INLINE V Log2(const D d, V x) { + using T = TFromD<D>; + return Mul(Log(d, x), Set(d, static_cast<T>(1.44269504088896340735992))); +} + +template <class D, class V> +HWY_INLINE V Sin(const D d, V x) { + using T = TFromD<D>; + impl::CosSinImpl<T> impl; + + // Float Constants + const V kOneOverPi = Set(d, static_cast<T>(0.31830988618379067153)); + const V kHalf = Set(d, static_cast<T>(0.5)); + + // Integer Constants + const Rebind<int32_t, D> di32; + using VI32 = decltype(Zero(di32)); + + const V abs_x = Abs(x); + const V sign_x = Xor(abs_x, x); + + // Compute the quadrant, q = int((|x| / pi) + 0.5) + const VI32 q = impl.ToInt32(d, MulAdd(abs_x, kOneOverPi, kHalf)); + + // Reduce range, apply sign, and approximate. + return impl.Poly(d, Xor(impl.SinReduce(d, abs_x, q), + Xor(impl.SinSignFromQuadrant(d, q), sign_x))); +} + +template <class D, class V> +HWY_INLINE V Sinh(const D d, V x) { + using T = TFromD<D>; + const V kHalf = Set(d, static_cast<T>(+0.5)); + const V kOne = Set(d, static_cast<T>(+1.0)); + const V kTwo = Set(d, static_cast<T>(+2.0)); + + const V sign = And(SignBit(d), x); // Extract the sign bit + const V abs_x = Xor(x, sign); + const V y = Expm1(d, abs_x); + const V z = Mul(Div(Add(y, kTwo), Add(y, kOne)), Mul(y, kHalf)); + return Xor(z, sign); // Reapply the sign bit +} + +template <class D, class V> +HWY_INLINE V Tanh(const D d, V x) { + using T = TFromD<D>; + const V kLimit = Set(d, static_cast<T>(18.714973875)); + const V kOne = Set(d, static_cast<T>(+1.0)); + const V kTwo = Set(d, static_cast<T>(+2.0)); + + const V sign = And(SignBit(d), x); // Extract the sign bit + const V abs_x = Xor(x, sign); + const V y = Expm1(d, Mul(abs_x, kTwo)); + const V z = IfThenElse(Gt(abs_x, kLimit), kOne, Div(y, Add(y, kTwo))); + return Xor(z, sign); // Reapply the sign bit +} + +// NOLINTNEXTLINE(google-readability-namespace-comments) +} // namespace HWY_NAMESPACE +} // namespace hwy +HWY_AFTER_NAMESPACE(); + +#endif // HIGHWAY_HWY_CONTRIB_MATH_MATH_INL_H_ |