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Diffstat (limited to 'third_party/xsimd/include/xsimd/arch/generic/xsimd_generic_trigo.hpp')
| -rw-r--r-- | third_party/xsimd/include/xsimd/arch/generic/xsimd_generic_trigo.hpp | 969 |
1 files changed, 969 insertions, 0 deletions
diff --git a/third_party/xsimd/include/xsimd/arch/generic/xsimd_generic_trigo.hpp b/third_party/xsimd/include/xsimd/arch/generic/xsimd_generic_trigo.hpp new file mode 100644 index 0000000000..2568a7253f --- /dev/null +++ b/third_party/xsimd/include/xsimd/arch/generic/xsimd_generic_trigo.hpp @@ -0,0 +1,969 @@ +/*************************************************************************** + * Copyright (c) Johan Mabille, Sylvain Corlay, Wolf Vollprecht and * + * Martin Renou * + * Copyright (c) QuantStack * + * Copyright (c) Serge Guelton * + * * + * Distributed under the terms of the BSD 3-Clause License. * + * * + * The full license is in the file LICENSE, distributed with this software. * + ****************************************************************************/ + +#ifndef XSIMD_GENERIC_TRIGO_HPP +#define XSIMD_GENERIC_TRIGO_HPP + +#include "./xsimd_generic_details.hpp" + +#include <array> + +namespace xsimd +{ + + namespace kernel + { + /* origin: boost/simd/arch/common/detail/simd/trig_base.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + + using namespace types; + + // acos + template <class A, class T> + inline batch<T, A> acos(batch<T, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<T, A>; + batch_type x = abs(self); + auto x_larger_05 = x > batch_type(0.5); + x = select(x_larger_05, sqrt(fma(batch_type(-0.5), x, batch_type(0.5))), self); + x = asin(x); + x = select(x_larger_05, x + x, x); + x = select(self < batch_type(-0.5), constants::pi<batch_type>() - x, x); + return select(x_larger_05, x, constants::pio2<batch_type>() - x); + } + template <class A, class T> + inline batch<std::complex<T>, A> acos(const batch<std::complex<T>, A>& z, requires_arch<generic>) noexcept + { + using batch_type = batch<std::complex<T>, A>; + using real_batch = typename batch_type::real_batch; + batch_type tmp = asin(z); + return { constants::pio2<real_batch>() - tmp.real(), -tmp.imag() }; + } + + // acosh + /* origin: boost/simd/arch/common/simd/function/acosh.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + template <class A, class T> + inline batch<T, A> acosh(batch<T, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<T, A>; + batch_type x = self - batch_type(1.); + auto test = x > constants::oneotwoeps<batch_type>(); + batch_type z = select(test, self, x + sqrt(x + x + x * x)); + batch_type l1pz = log1p(z); + return select(test, l1pz + constants::log_2<batch_type>(), l1pz); + } + template <class A, class T> + inline batch<std::complex<T>, A> acosh(const batch<std::complex<T>, A>& z, requires_arch<generic>) noexcept + { + using batch_type = batch<std::complex<T>, A>; + batch_type w = acos(z); + w = batch_type(-w.imag(), w.real()); + return w; + } + + // asin + template <class A> + inline batch<float, A> asin(batch<float, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<float, A>; + batch_type x = abs(self); + batch_type sign = bitofsign(self); + auto x_larger_05 = x > batch_type(0.5); + batch_type z = select(x_larger_05, batch_type(0.5) * (batch_type(1.) - x), x * x); + x = select(x_larger_05, sqrt(z), x); + batch_type z1 = detail::horner<batch_type, + 0x3e2aaae4, + 0x3d9980f6, + 0x3d3a3ec7, + 0x3cc617e3, + 0x3d2cb352>(z); + z1 = fma(z1, z * x, x); + z = select(x_larger_05, constants::pio2<batch_type>() - (z1 + z1), z1); + return z ^ sign; + } + template <class A> + inline batch<double, A> asin(batch<double, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<double, A>; + batch_type x = abs(self); + auto small_cond = x < constants::sqrteps<batch_type>(); + batch_type ct1 = batch_type(bit_cast<double>(int64_t(0x3fe4000000000000))); + batch_type zz1 = batch_type(1.) - x; + batch_type vp = zz1 * detail::horner<batch_type, 0x403c896240f3081dull, 0xc03991aaac01ab68ull, 0x401bdff5baf33e6aull, 0xbfe2079259f9290full, 0x3f684fc3988e9f08ull>(zz1) / detail::horner1<batch_type, 0x40756709b0b644beull, 0xc077fe08959063eeull, 0x40626219af6a7f42ull, 0xc035f2a2b6bf5d8cull>(zz1); + zz1 = sqrt(zz1 + zz1); + batch_type z = constants::pio4<batch_type>() - zz1; + zz1 = fms(zz1, vp, constants::pio_2lo<batch_type>()); + z = z - zz1; + zz1 = z + constants::pio4<batch_type>(); + batch_type zz2 = self * self; + z = zz2 * detail::horner<batch_type, 0xc020656c06ceafd5ull, 0x40339007da779259ull, 0xc0304331de27907bull, 0x4015c74b178a2dd9ull, 0xbfe34341333e5c16ull, 0x3f716b9b0bd48ad3ull>(zz2) / detail::horner1<batch_type, 0xc04898220a3607acull, 0x4061705684ffbf9dull, 0xc06265bb6d3576d7ull, 0x40519fc025fe9054ull, 0xc02d7b590b5e0eabull>(zz2); + zz2 = fma(x, z, x); + return select(x > batch_type(1.), constants::nan<batch_type>(), + select(small_cond, x, + select(x > ct1, zz1, zz2)) + ^ bitofsign(self)); + } + template <class A, class T> + inline batch<std::complex<T>, A> asin(const batch<std::complex<T>, A>& z, requires_arch<generic>) noexcept + { + using batch_type = batch<std::complex<T>, A>; + using real_batch = typename batch_type::real_batch; + real_batch x = z.real(); + real_batch y = z.imag(); + + batch_type ct(-y, x); + batch_type zz(real_batch(1.) - (x - y) * (x + y), -2 * x * y); + zz = log(ct + sqrt(zz)); + batch_type resg(zz.imag(), -zz.real()); + + return select(y == real_batch(0.), + select(fabs(x) > real_batch(1.), + batch_type(constants::pio2<real_batch>(), real_batch(0.)), + batch_type(asin(x), real_batch(0.))), + resg); + } + + // asinh + /* origin: boost/simd/arch/common/simd/function/asinh.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + namespace detail + { + template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type> + inline batch<T, A> + average(const batch<T, A>& x1, const batch<T, A>& x2) noexcept + { + return (x1 & x2) + ((x1 ^ x2) >> 1); + } + + template <class A, class T> + inline batch<T, A> + averagef(const batch<T, A>& x1, const batch<T, A>& x2) noexcept + { + using batch_type = batch<T, A>; + return fma(x1, batch_type(0.5), x2 * batch_type(0.5)); + } + template <class A> + inline batch<float, A> average(batch<float, A> const& x1, batch<float, A> const& x2) noexcept + { + return averagef(x1, x2); + } + template <class A> + inline batch<double, A> average(batch<double, A> const& x1, batch<double, A> const& x2) noexcept + { + return averagef(x1, x2); + } + } + template <class A> + inline batch<float, A> asinh(batch<float, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<float, A>; + batch_type x = abs(self); + auto lthalf = x < batch_type(0.5); + batch_type x2 = x * x; + batch_type bts = bitofsign(self); + batch_type z(0.); + if (any(lthalf)) + { + z = detail::horner<batch_type, + 0x3f800000, + 0xbe2aa9ad, + 0x3d9949b1, + 0xbd2ee581, + 0x3ca4d6e6>(x2) + * x; + if (all(lthalf)) + return z ^ bts; + } + batch_type tmp = select(x > constants::oneosqrteps<batch_type>(), x, detail::average(x, hypot(batch_type(1.), x))); +#ifndef XSIMD_NO_NANS + return select(isnan(self), constants::nan<batch_type>(), select(lthalf, z, log(tmp) + constants::log_2<batch_type>()) ^ bts); +#else + return select(lthalf, z, log(tmp) + constants::log_2<batch_type>()) ^ bts; +#endif + } + template <class A> + inline batch<double, A> asinh(batch<double, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<double, A>; + batch_type x = abs(self); + auto test = x > constants::oneosqrteps<batch_type>(); + batch_type z = select(test, x - batch_type(1.), x + x * x / (batch_type(1.) + hypot(batch_type(1.), x))); +#ifndef XSIMD_NO_INFINITIES + z = select(x == constants::infinity<batch_type>(), x, z); +#endif + batch_type l1pz = log1p(z); + z = select(test, l1pz + constants::log_2<batch_type>(), l1pz); + return bitofsign(self) ^ z; + } + template <class A, class T> + inline batch<std::complex<T>, A> asinh(const batch<std::complex<T>, A>& z, requires_arch<generic>) noexcept + { + using batch_type = batch<std::complex<T>, A>; + batch_type w = asin(batch_type(-z.imag(), z.real())); + w = batch_type(w.imag(), -w.real()); + return w; + } + + // atan + namespace detail + { + template <class A> + static inline batch<float, A> kernel_atan(const batch<float, A>& x, const batch<float, A>& recx) noexcept + { + using batch_type = batch<float, A>; + const auto flag1 = x < constants::tan3pio8<batch_type>(); + const auto flag2 = (x >= batch_type(bit_cast<float>((uint32_t)0x3ed413cd))) && flag1; + batch_type yy = select(flag1, batch_type(0.), constants::pio2<batch_type>()); + yy = select(flag2, constants::pio4<batch_type>(), yy); + batch_type xx = select(flag1, x, -recx); + xx = select(flag2, (x - batch_type(1.)) / (x + batch_type(1.)), xx); + const batch_type z = xx * xx; + batch_type z1 = detail::horner<batch_type, + 0xbeaaaa2aul, + 0x3e4c925ful, + 0xbe0e1b85ul, + 0x3da4f0d1ul>(z); + z1 = fma(xx, z1 * z, xx); + z1 = select(flag2, z1 + constants::pio_4lo<batch_type>(), z1); + z1 = select(!flag1, z1 + constants::pio_2lo<batch_type>(), z1); + return yy + z1; + } + template <class A> + static inline batch<double, A> kernel_atan(const batch<double, A>& x, const batch<double, A>& recx) noexcept + { + using batch_type = batch<double, A>; + const auto flag1 = x < constants::tan3pio8<batch_type>(); + const auto flag2 = (x >= constants::tanpio8<batch_type>()) && flag1; + batch_type yy = select(flag1, batch_type(0.), constants::pio2<batch_type>()); + yy = select(flag2, constants::pio4<batch_type>(), yy); + batch_type xx = select(flag1, x, -recx); + xx = select(flag2, (x - batch_type(1.)) / (x + batch_type(1.)), xx); + batch_type z = xx * xx; + z *= detail::horner<batch_type, + 0xc0503669fd28ec8eull, + 0xc05eb8bf2d05ba25ull, + 0xc052c08c36880273ull, + 0xc03028545b6b807aull, + 0xbfec007fa1f72594ull>(z) + / detail::horner1<batch_type, + 0x4068519efbbd62ecull, + 0x407e563f13b049eaull, + 0x407b0e18d2e2be3bull, + 0x4064a0dd43b8fa25ull, + 0x4038dbc45b14603cull>(z); + z = fma(xx, z, xx); + z = select(flag2, z + constants::pio_4lo<batch_type>(), z); + z = z + select(flag1, batch_type(0.), constants::pio_2lo<batch_type>()); + return yy + z; + } + } + template <class A, class T> + inline batch<T, A> atan(batch<T, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<T, A>; + const batch_type absa = abs(self); + const batch_type x = detail::kernel_atan(absa, batch_type(1.) / absa); + return x ^ bitofsign(self); + } + template <class A, class T> + inline batch<std::complex<T>, A> atan(const batch<std::complex<T>, A>& z, requires_arch<generic>) noexcept + { + using batch_type = batch<std::complex<T>, A>; + using real_batch = typename batch_type::real_batch; + real_batch x = z.real(); + real_batch y = z.imag(); + real_batch x2 = x * x; + real_batch one(1.); + real_batch a = one - x2 - (y * y); + real_batch w = 0.5 * atan2(2. * x, a); + real_batch num = y + one; + num = x2 + num * num; + real_batch den = y - one; + den = x2 + den * den; + batch_type res = select((x == real_batch(0.)) && (y == real_batch(1.)), + batch_type(real_batch(0.), constants::infinity<real_batch>()), + batch_type(w, 0.25 * log(num / den))); + return res; + } + + // atanh + /* origin: boost/simd/arch/common/simd/function/acosh.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + template <class A, class T> + inline batch<T, A> atanh(batch<T, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<T, A>; + batch_type x = abs(self); + batch_type t = x + x; + batch_type z = batch_type(1.) - x; + auto test = x < batch_type(0.5); + batch_type tmp = select(test, x, t) / z; + return bitofsign(self) ^ (batch_type(0.5) * log1p(select(test, fma(t, tmp, t), tmp))); + } + template <class A, class T> + inline batch<std::complex<T>, A> atanh(const batch<std::complex<T>, A>& z, requires_arch<generic>) noexcept + { + using batch_type = batch<std::complex<T>, A>; + batch_type w = atan(batch_type(-z.imag(), z.real())); + w = batch_type(w.imag(), -w.real()); + return w; + } + + // atan2 + template <class A, class T> + inline batch<T, A> atan2(batch<T, A> const& self, batch<T, A> const& other, requires_arch<generic>) noexcept + { + using batch_type = batch<T, A>; + const batch_type q = abs(self / other); + const batch_type z = detail::kernel_atan(q, batch_type(1.) / q); + return select(other > batch_type(0.), z, constants::pi<batch_type>() - z) * signnz(self); + } + + // cos + namespace detail + { + template <class T, class A> + inline batch<T, A> quadrant(const batch<T, A>& x) noexcept + { + return x & batch<T, A>(3); + } + + template <class A> + inline batch<float, A> quadrant(const batch<float, A>& x) noexcept + { + return to_float(quadrant(to_int(x))); + } + + template <class A> + inline batch<double, A> quadrant(const batch<double, A>& x) noexcept + { + using batch_type = batch<double, A>; + batch_type a = x * batch_type(0.25); + return (a - floor(a)) * batch_type(4.); + } + /* origin: boost/simd/arch/common/detail/simd/f_trig_evaluation.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + + template <class A> + inline batch<float, A> cos_eval(const batch<float, A>& z) noexcept + { + using batch_type = batch<float, A>; + batch_type y = detail::horner<batch_type, + 0x3d2aaaa5, + 0xbab60619, + 0x37ccf5ce>(z); + return batch_type(1.) + fma(z, batch_type(-0.5), y * z * z); + } + + template <class A> + inline batch<float, A> sin_eval(const batch<float, A>& z, const batch<float, A>& x) noexcept + { + using batch_type = batch<float, A>; + batch_type y = detail::horner<batch_type, + 0xbe2aaaa2, + 0x3c08839d, + 0xb94ca1f9>(z); + return fma(y * z, x, x); + } + + template <class A> + static inline batch<float, A> base_tancot_eval(const batch<float, A>& z) noexcept + { + using batch_type = batch<float, A>; + batch_type zz = z * z; + batch_type y = detail::horner<batch_type, + 0x3eaaaa6f, + 0x3e0896dd, + 0x3d5ac5c9, + 0x3cc821b5, + 0x3b4c779c, + 0x3c19c53b>(zz); + return fma(y, zz * z, z); + } + + template <class A, class BB> + static inline batch<float, A> tan_eval(const batch<float, A>& z, const BB& test) noexcept + { + using batch_type = batch<float, A>; + batch_type y = base_tancot_eval(z); + return select(test, y, -batch_type(1.) / y); + } + + template <class A, class BB> + static inline batch<float, A> cot_eval(const batch<float, A>& z, const BB& test) noexcept + { + using batch_type = batch<float, A>; + batch_type y = base_tancot_eval(z); + return select(test, batch_type(1.) / y, -y); + } + + /* origin: boost/simd/arch/common/detail/simd/d_trig_evaluation.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + template <class A> + static inline batch<double, A> cos_eval(const batch<double, A>& z) noexcept + { + using batch_type = batch<double, A>; + batch_type y = detail::horner<batch_type, + 0x3fe0000000000000ull, + 0xbfa5555555555551ull, + 0x3f56c16c16c15d47ull, + 0xbefa01a019ddbcd9ull, + 0x3e927e4f8e06d9a5ull, + 0xbe21eea7c1e514d4ull, + 0x3da8ff831ad9b219ull>(z); + return batch_type(1.) - y * z; + } + + template <class A> + static inline batch<double, A> sin_eval(const batch<double, A>& z, const batch<double, A>& x) noexcept + { + using batch_type = batch<double, A>; + batch_type y = detail::horner<batch_type, + 0xbfc5555555555548ull, + 0x3f8111111110f7d0ull, + 0xbf2a01a019bfdf03ull, + 0x3ec71de3567d4896ull, + 0xbe5ae5e5a9291691ull, + 0x3de5d8fd1fcf0ec1ull>(z); + return fma(y * z, x, x); + } + + template <class A> + static inline batch<double, A> base_tancot_eval(const batch<double, A>& z) noexcept + { + using batch_type = batch<double, A>; + batch_type zz = z * z; + batch_type num = detail::horner<batch_type, + 0xc1711fead3299176ull, + 0x413199eca5fc9dddull, + 0xc0c992d8d24f3f38ull>(zz); + batch_type den = detail::horner1<batch_type, + 0xc189afe03cbe5a31ull, + 0x4177d98fc2ead8efull, + 0xc13427bc582abc96ull, + 0x40cab8a5eeb36572ull>(zz); + return fma(z, (zz * (num / den)), z); + } + + template <class A, class BB> + static inline batch<double, A> tan_eval(const batch<double, A>& z, const BB& test) noexcept + { + using batch_type = batch<double, A>; + batch_type y = base_tancot_eval(z); + return select(test, y, -batch_type(1.) / y); + } + + template <class A, class BB> + static inline batch<double, A> cot_eval(const batch<double, A>& z, const BB& test) noexcept + { + using batch_type = batch<double, A>; + batch_type y = base_tancot_eval(z); + return select(test, batch_type(1.) / y, -y); + } + /* origin: boost/simd/arch/common/detail/simd/trig_reduction.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + + struct trigo_radian_tag + { + }; + struct trigo_pi_tag + { + }; + + template <class B, class Tag = trigo_radian_tag> + struct trigo_reducer + { + static inline B reduce(const B& x, B& xr) noexcept + { + if (all(x <= constants::pio4<B>())) + { + xr = x; + return B(0.); + } + else if (all(x <= constants::pio2<B>())) + { + auto test = x > constants::pio4<B>(); + xr = x - constants::pio2_1<B>(); + xr -= constants::pio2_2<B>(); + xr -= constants::pio2_3<B>(); + xr = select(test, xr, x); + return select(test, B(1.), B(0.)); + } + else if (all(x <= constants::twentypi<B>())) + { + B xi = nearbyint(x * constants::twoopi<B>()); + xr = fnma(xi, constants::pio2_1<B>(), x); + xr -= xi * constants::pio2_2<B>(); + xr -= xi * constants::pio2_3<B>(); + return quadrant(xi); + } + else if (all(x <= constants::mediumpi<B>())) + { + B fn = nearbyint(x * constants::twoopi<B>()); + B r = x - fn * constants::pio2_1<B>(); + B w = fn * constants::pio2_1t<B>(); + B t = r; + w = fn * constants::pio2_2<B>(); + r = t - w; + w = fn * constants::pio2_2t<B>() - ((t - r) - w); + t = r; + w = fn * constants::pio2_3<B>(); + r = t - w; + w = fn * constants::pio2_3t<B>() - ((t - r) - w); + xr = r - w; + return quadrant(fn); + } + else + { + static constexpr std::size_t size = B::size; + using value_type = typename B::value_type; + alignas(B) std::array<value_type, size> tmp; + alignas(B) std::array<value_type, size> txr; + alignas(B) std::array<value_type, size> args; + x.store_aligned(args.data()); + + for (std::size_t i = 0; i < size; ++i) + { + double arg = args[i]; + if (arg == std::numeric_limits<value_type>::infinity()) + { + tmp[i] = 0.; + txr[i] = std::numeric_limits<value_type>::quiet_NaN(); + } + else + { + double y[2]; + std::int32_t n = ::xsimd::detail::__ieee754_rem_pio2(arg, y); + tmp[i] = value_type(n & 3); + txr[i] = value_type(y[0]); + } + } + xr = B::load_aligned(&txr[0]); + B res = B::load_aligned(&tmp[0]); + return res; + } + } + }; + + template <class B> + struct trigo_reducer<B, trigo_pi_tag> + { + static inline B reduce(const B& x, B& xr) noexcept + { + B xi = nearbyint(x * B(2.)); + B x2 = x - xi * B(0.5); + xr = x2 * constants::pi<B>(); + return quadrant(xi); + } + }; + + } + template <class A, class T> + inline batch<T, A> cos(batch<T, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<T, A>; + const batch_type x = abs(self); + batch_type xr = constants::nan<batch_type>(); + const batch_type n = detail::trigo_reducer<batch_type>::reduce(x, xr); + auto tmp = select(n >= batch_type(2.), batch_type(1.), batch_type(0.)); + auto swap_bit = fma(batch_type(-2.), tmp, n); + auto sign_bit = select((swap_bit ^ tmp) != batch_type(0.), constants::signmask<batch_type>(), batch_type(0.)); + const batch_type z = xr * xr; + const batch_type se = detail::sin_eval(z, xr); + const batch_type ce = detail::cos_eval(z); + const batch_type z1 = select(swap_bit != batch_type(0.), se, ce); + return z1 ^ sign_bit; + } + + template <class A, class T> + inline batch<std::complex<T>, A> cos(batch<std::complex<T>, A> const& z, requires_arch<generic>) noexcept + { + return { cos(z.real()) * cosh(z.imag()), -sin(z.real()) * sinh(z.imag()) }; + } + + // cosh + + /* origin: boost/simd/arch/common/simd/function/cosh.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + + template <class A, class T> + inline batch<T, A> cosh(batch<T, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<T, A>; + batch_type x = abs(self); + auto test1 = x > (constants::maxlog<batch_type>() - constants::log_2<batch_type>()); + batch_type fac = select(test1, batch_type(0.5), batch_type(1.)); + batch_type tmp = exp(x * fac); + batch_type tmp1 = batch_type(0.5) * tmp; + return select(test1, tmp1 * tmp, detail::average(tmp, batch_type(1.) / tmp)); + } + template <class A, class T> + inline batch<std::complex<T>, A> cosh(const batch<std::complex<T>, A>& z, requires_arch<generic>) noexcept + { + auto x = z.real(); + auto y = z.imag(); + return { cosh(x) * cos(y), sinh(x) * sin(y) }; + } + + // sin + namespace detail + { + template <class A, class T, class Tag = trigo_radian_tag> + inline batch<T, A> sin(batch<T, A> const& self, Tag = Tag()) noexcept + { + using batch_type = batch<T, A>; + const batch_type x = abs(self); + batch_type xr = constants::nan<batch_type>(); + const batch_type n = detail::trigo_reducer<batch_type, Tag>::reduce(x, xr); + auto tmp = select(n >= batch_type(2.), batch_type(1.), batch_type(0.)); + auto swap_bit = fma(batch_type(-2.), tmp, n); + auto sign_bit = bitofsign(self) ^ select(tmp != batch_type(0.), constants::signmask<batch_type>(), batch_type(0.)); + const batch_type z = xr * xr; + const batch_type se = detail::sin_eval(z, xr); + const batch_type ce = detail::cos_eval(z); + const batch_type z1 = select(swap_bit == batch_type(0.), se, ce); + return z1 ^ sign_bit; + } + } + + template <class A, class T> + inline batch<T, A> sin(batch<T, A> const& self, requires_arch<generic>) noexcept + { + return detail::sin(self); + } + + template <class A, class T> + inline batch<std::complex<T>, A> sin(batch<std::complex<T>, A> const& z, requires_arch<generic>) noexcept + { + return { sin(z.real()) * cosh(z.imag()), cos(z.real()) * sinh(z.imag()) }; + } + + // sincos + template <class A, class T> + inline std::pair<batch<T, A>, batch<T, A>> sincos(batch<T, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<T, A>; + const batch_type x = abs(self); + batch_type xr = constants::nan<batch_type>(); + const batch_type n = detail::trigo_reducer<batch_type>::reduce(x, xr); + auto tmp = select(n >= batch_type(2.), batch_type(1.), batch_type(0.)); + auto swap_bit = fma(batch_type(-2.), tmp, n); + const batch_type z = xr * xr; + const batch_type se = detail::sin_eval(z, xr); + const batch_type ce = detail::cos_eval(z); + auto sin_sign_bit = bitofsign(self) ^ select(tmp != batch_type(0.), constants::signmask<batch_type>(), batch_type(0.)); + const batch_type sin_z1 = select(swap_bit == batch_type(0.), se, ce); + auto cos_sign_bit = select((swap_bit ^ tmp) != batch_type(0.), constants::signmask<batch_type>(), batch_type(0.)); + const batch_type cos_z1 = select(swap_bit != batch_type(0.), se, ce); + return std::make_pair(sin_z1 ^ sin_sign_bit, cos_z1 ^ cos_sign_bit); + } + + template <class A, class T> + inline std::pair<batch<std::complex<T>, A>, batch<std::complex<T>, A>> + sincos(batch<std::complex<T>, A> const& z, requires_arch<generic>) noexcept + { + using batch_type = batch<std::complex<T>, A>; + using real_batch = typename batch_type::real_batch; + real_batch rcos = cos(z.real()); + real_batch rsin = sin(z.real()); + real_batch icosh = cosh(z.imag()); + real_batch isinh = sinh(z.imag()); + return std::make_pair(batch_type(rsin * icosh, rcos * isinh), batch_type(rcos * icosh, -rsin * isinh)); + } + + // sinh + namespace detail + { + /* origin: boost/simd/arch/common/detail/generic/sinh_kernel.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + template <class A> + inline batch<float, A> sinh_kernel(batch<float, A> const& self) noexcept + { + using batch_type = batch<float, A>; + batch_type sqr_self = self * self; + return detail::horner<batch_type, + 0x3f800000, // 1.0f + 0x3e2aaacc, // 1.66667160211E-1f + 0x3c087bbe, // 8.33028376239E-3f + 0x39559e2f // 2.03721912945E-4f + >(sqr_self) + * self; + } + + template <class A> + inline batch<double, A> sinh_kernel(batch<double, A> const& self) noexcept + { + using batch_type = batch<double, A>; + batch_type sqrself = self * self; + return fma(self, (detail::horner<batch_type, + 0xc115782bdbf6ab05ull, // -3.51754964808151394800E5 + 0xc0c694b8c71d6182ull, // -1.15614435765005216044E4, + 0xc064773a398ff4feull, // -1.63725857525983828727E2, + 0xbfe9435fe8bb3cd6ull // -7.89474443963537015605E-1 + >(sqrself) + / detail::horner1<batch_type, + 0xc1401a20e4f90044ull, // -2.11052978884890840399E6 + 0x40e1a7ba7ed72245ull, // 3.61578279834431989373E4, + 0xc0715b6096e96484ull // -2.77711081420602794433E2, + >(sqrself)) + * sqrself, + self); + } + } + /* origin: boost/simd/arch/common/simd/function/sinh.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + template <class A, class T> + inline batch<T, A> sinh(batch<T, A> const& a, requires_arch<generic>) noexcept + { + using batch_type = batch<T, A>; + batch_type half(0.5); + batch_type x = abs(a); + auto lt1 = x < batch_type(1.); + batch_type bts = bitofsign(a); + batch_type z(0.); + if (any(lt1)) + { + z = detail::sinh_kernel(x); + if (all(lt1)) + return z ^ bts; + } + auto test1 = x > (constants::maxlog<batch_type>() - constants::log_2<batch_type>()); + batch_type fac = select(test1, half, batch_type(1.)); + batch_type tmp = exp(x * fac); + batch_type tmp1 = half * tmp; + batch_type r = select(test1, tmp1 * tmp, tmp1 - half / tmp); + return select(lt1, z, r) ^ bts; + } + template <class A, class T> + inline batch<std::complex<T>, A> sinh(const batch<std::complex<T>, A>& z, requires_arch<generic>) noexcept + { + auto x = z.real(); + auto y = z.imag(); + return { sinh(x) * cos(y), cosh(x) * sin(y) }; + } + + // tan + template <class A, class T> + inline batch<T, A> tan(batch<T, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<T, A>; + const batch_type x = abs(self); + batch_type xr = constants::nan<batch_type>(); + const batch_type n = detail::trigo_reducer<batch_type>::reduce(x, xr); + auto tmp = select(n >= batch_type(2.), batch_type(1.), batch_type(0.)); + auto swap_bit = fma(batch_type(-2.), tmp, n); + auto test = (swap_bit == batch_type(0.)); + const batch_type y = detail::tan_eval(xr, test); + return y ^ bitofsign(self); + } + template <class A, class T> + inline batch<std::complex<T>, A> tan(batch<std::complex<T>, A> const& z, requires_arch<generic>) noexcept + { + using batch_type = batch<std::complex<T>, A>; + using real_batch = typename batch_type::real_batch; + real_batch d = cos(2 * z.real()) + cosh(2 * z.imag()); + batch_type winf(constants::infinity<real_batch>(), constants::infinity<real_batch>()); + real_batch wreal = sin(2 * z.real()) / d; + real_batch wimag = sinh(2 * z.imag()); + batch_type wres = select(isinf(wimag), batch_type(wreal, real_batch(1.)), batch_type(wreal, wimag / d)); + return select(d == real_batch(0.), winf, wres); + } + + // tanh + namespace detail + { + /* origin: boost/simd/arch/common/detail/generic/tanh_kernel.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + template <class B> + struct tanh_kernel; + + template <class A> + struct tanh_kernel<batch<float, A>> + { + using batch_type = batch<float, A>; + static inline batch_type tanh(const batch_type& x) noexcept + { + batch_type sqrx = x * x; + return fma(detail::horner<batch_type, + 0xbeaaaa99, // -3.33332819422E-1F + 0x3e088393, // +1.33314422036E-1F + 0xbd5c1e2d, // -5.37397155531E-2F + 0x3ca9134e, // +2.06390887954E-2F + 0xbbbaf0ea // -5.70498872745E-3F + >(sqrx) + * sqrx, + x, x); + } + + static inline batch_type cotanh(const batch_type& x) noexcept + { + return batch_type(1.) / tanh(x); + } + }; + + template <class A> + struct tanh_kernel<batch<double, A>> + { + using batch_type = batch<double, A>; + static inline batch_type tanh(const batch_type& x) noexcept + { + batch_type sqrx = x * x; + return fma(sqrx * p(sqrx) / q(sqrx), x, x); + } + + static inline batch_type cotanh(const batch_type& x) noexcept + { + batch_type sqrx = x * x; + batch_type qval = q(sqrx); + return qval / (x * fma(p(sqrx), sqrx, qval)); + } + + static inline batch_type p(const batch_type& x) noexcept + { + return detail::horner<batch_type, + 0xc0993ac030580563, // -1.61468768441708447952E3 + 0xc058d26a0e26682d, // -9.92877231001918586564E1, + 0xbfeedc5baafd6f4b // -9.64399179425052238628E-1 + >(x); + } + + static inline batch_type q(const batch_type& x) noexcept + { + return detail::horner1<batch_type, + 0x40b2ec102442040c, // 4.84406305325125486048E3 + 0x40a176fa0e5535fa, // 2.23548839060100448583E3, + 0x405c33f28a581B86 // 1.12811678491632931402E2, + >(x); + } + }; + + } + /* origin: boost/simd/arch/common/simd/function/tanh.hpp */ + /* + * ==================================================== + * copyright 2016 NumScale SAS + * + * Distributed under the Boost Software License, Version 1.0. + * (See copy at http://boost.org/LICENSE_1_0.txt) + * ==================================================== + */ + template <class A, class T> + inline batch<T, A> tanh(batch<T, A> const& self, requires_arch<generic>) noexcept + { + using batch_type = batch<T, A>; + batch_type one(1.); + batch_type x = abs(self); + auto test = x < (batch_type(5.) / batch_type(8.)); + batch_type bts = bitofsign(self); + batch_type z = one; + if (any(test)) + { + z = detail::tanh_kernel<batch_type>::tanh(x); + if (all(test)) + return z ^ bts; + } + batch_type r = fma(batch_type(-2.), one / (one + exp(x + x)), one); + return select(test, z, r) ^ bts; + } + template <class A, class T> + inline batch<std::complex<T>, A> tanh(const batch<std::complex<T>, A>& z, requires_arch<generic>) noexcept + { + using real_batch = typename batch<std::complex<T>, A>::real_batch; + auto x = z.real(); + auto y = z.imag(); + real_batch two(2); + auto d = cosh(two * x) + cos(two * y); + return { sinh(two * x) / d, sin(two * y) / d }; + } + + } + +} + +#endif |