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/***************************************************************************
* Copyright (c) Johan Mabille, Sylvain Corlay, Wolf Vollprecht and *
* Martin Renou *
* Copyright (c) QuantStack *
* *
* Distributed under the terms of the BSD 3-Clause License. *
* *
* The full license is in the file LICENSE, distributed with this software. *
****************************************************************************/
#ifndef XSIMD_INVTRIGO_HPP
#define XSIMD_INVTRIGO_HPP
#include "xsimd_fp_sign.hpp"
#include "xsimd_horner.hpp"
#include "xsimd_numerical_constant.hpp"
namespace xsimd
{
namespace detail
{
template <class B, class T = typename B::value_type>
struct invtrigo_kernel_impl;
/* origin: boost/simd/arch/common/detail/simd/f_invtrig.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 invtrigo_kernel_impl<B, float>
{
static inline B asin(const B& a)
{
B x = abs(a);
B sign = bitofsign(a);
auto x_larger_05 = x > B(0.5);
B z = select(x_larger_05, B(0.5) * (B(1.) - x), x * x);
x = select(x_larger_05, sqrt(z), x);
B z1 = horner<B,
0x3e2aaae4,
0x3d9980f6,
0x3d3a3ec7,
0x3cc617e3,
0x3d2cb352>(z);
z1 = fma(z1, z * x, x);
z = select(x_larger_05, pio2<B>() - (z1 + z1), z1);
return z ^ sign;
}
static inline B kernel_atan(const B& x, const B& recx)
{
const auto flag1 = x < tan3pio8<B>();
const auto flag2 = (x >= B(detail::caster32_t(0x3ed413cd).f)) && flag1;
B yy = select(flag1, B(0.), pio2<B>());
yy = select(flag2, pio4<B>(), yy);
B xx = select(flag1, x, -recx);
xx = select(flag2, (x - B(1.)) / (x + B(1.)), xx);
const B z = xx * xx;
B z1 = horner<B,
0xbeaaaa2aul,
0x3e4c925ful,
0xbe0e1b85ul,
0x3da4f0d1ul>(z);
z1 = fma(xx, z1 * z, xx);
z1 = select(flag2, z1 + pio_4lo<B>(), z1);
z1 = select(!flag1, z1 + pio_2lo<B>(), z1);
return yy + z1;
}
};
/* origin: boost/simd/arch/common/detail/simd/d_invtrig.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 invtrigo_kernel_impl<B, double>
{
static inline B asin(const B& a)
{
B x = abs(a);
auto small_cond = x < sqrteps<B>();
B ct1 = B(detail::caster64_t(int64_t(0x3fe4000000000000)).f);
B zz1 = B(1.) - x;
B vp = zz1 * horner<B,
0x403c896240f3081dull,
0xc03991aaac01ab68ull,
0x401bdff5baf33e6aull,
0xbfe2079259f9290full,
0x3f684fc3988e9f08ull>(zz1) /
horner1<B,
0x40756709b0b644beull,
0xc077fe08959063eeull,
0x40626219af6a7f42ull,
0xc035f2a2b6bf5d8cull>(zz1);
zz1 = sqrt(zz1 + zz1);
B z = pio4<B>() - zz1;
zz1 = fms(zz1, vp, pio_2lo<B>());
z = z - zz1;
zz1 = z + pio4<B>();
B zz2 = a * a;
z = zz2 * horner<B,
0xc020656c06ceafd5ull,
0x40339007da779259ull,
0xc0304331de27907bull,
0x4015c74b178a2dd9ull,
0xbfe34341333e5c16ull,
0x3f716b9b0bd48ad3ull>(zz2) /
horner1<B,
0xc04898220a3607acull,
0x4061705684ffbf9dull,
0xc06265bb6d3576d7ull,
0x40519fc025fe9054ull,
0xc02d7b590b5e0eabull>(zz2);
zz2 = fma(x, z, x);
return select(x > B(1.), nan<B>(),
select(small_cond, x,
select(x > ct1, zz1, zz2)) ^
bitofsign(a));
}
static inline B kernel_atan(const B& x, const B& recx)
{
const auto flag1 = x < tan3pio8<B>();
const auto flag2 = (x >= tanpio8<B>()) && flag1;
B yy = select(flag1, B(0.), pio2<B>());
yy = select(flag2, pio4<B>(), yy);
B xx = select(flag1, x, -recx);
xx = select(flag2, (x - B(1.)) / (x + B(1.)), xx);
B z = xx * xx;
z *= horner<B,
0xc0503669fd28ec8eull,
0xc05eb8bf2d05ba25ull,
0xc052c08c36880273ull,
0xc03028545b6b807aull,
0xbfec007fa1f72594ull>(z) /
horner1<B,
0x4068519efbbd62ecull,
0x407e563f13b049eaull,
0x407b0e18d2e2be3bull,
0x4064a0dd43b8fa25ull,
0x4038dbc45b14603cull>(z);
z = fma(xx, z, xx);
z = select(flag2, z + pio_4lo<B>(), z);
z = z + select(flag1, B(0.), pio_2lo<B>());
return yy + z;
}
};
template <class B>
struct invtrigo_kernel
{
static inline B asin(const B& a)
{
return invtrigo_kernel_impl<B>::asin(a);
}
static inline B acos(const B& a)
{
B x = abs(a);
auto x_larger_05 = x > B(0.5);
x = select(x_larger_05, sqrt(fma(B(-0.5), x, B(0.5))), a);
x = asin(x);
x = select(x_larger_05, x + x, x);
x = select(a < B(-0.5), pi<B>() - x, x);
return select(x_larger_05, x, pio2<B>() - x);
}
static inline B atan(const B& a)
{
const B absa = abs(a);
const B x = kernel_atan(absa, B(1.) / absa);
return x ^ bitofsign(a);
}
static inline B acot(const B& a)
{
const B absa = abs(a);
const B x = kernel_atan(B(1.) / absa, absa);
return x ^ bitofsign(a);
}
static inline B atan2(const B& y, const B& x)
{
const B q = abs(y / x);
const B z = kernel_atan(q, B(1.) / q);
return select(x > B(0.), z, pi<B>() - z) * signnz(y);
}
static inline B kernel_atan(const B& x, const B& recx)
{
return invtrigo_kernel_impl<B>::kernel_atan(x, recx);
}
};
}
}
#endif
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