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/***************************************************************************
* 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