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| Current File : //usr/include/xsimd/math/xsimd_exp_reduction.hpp |
/***************************************************************************
* 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_EXP_REDUCTION_HPP
#define XSIMD_EXP_REDUCTION_HPP
#include "xsimd_horner.hpp"
#include "xsimd_numerical_constant.hpp"
#include "xsimd_rounding.hpp"
namespace xsimd
{
struct exp_tag
{
};
struct exp2_tag
{
};
struct exp10_tag
{
};
namespace detail
{
/**********************
* exp_reduction_base *
**********************/
template <class B, class Tag>
struct exp_reduction_base;
template <class B>
struct exp_reduction_base<B, exp_tag>
{
static constexpr B maxlog() noexcept
{
return xsimd::maxlog<B>();
}
static constexpr B minlog() noexcept
{
return xsimd::minlog<B>();
}
};
template <class B>
struct exp_reduction_base<B, exp2_tag>
{
static constexpr B maxlog() noexcept
{
return xsimd::maxlog2<B>();
}
static constexpr B minlog() noexcept
{
return xsimd::minlog2<B>();
}
};
template <class B>
struct exp_reduction_base<B, exp10_tag>
{
static constexpr B maxlog() noexcept
{
return xsimd::maxlog10<B>();
}
static constexpr B minlog() noexcept
{
return xsimd::minlog10<B>();
}
};
/*****************
* exp_reduction *
*****************/
template <class B, class Tag, class T = typename B::value_type>
struct exp_reduction;
/* origin: boost/simd/arch/common/detail/generic/f_expo_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)
* ====================================================
*/
template <class B>
struct exp_reduction<B, exp_tag, float> : exp_reduction_base<B, exp_tag>
{
static inline B approx(const B& x)
{
B y = horner<B,
0x3f000000, // 5.0000000e-01
0x3e2aa9a5, // 1.6666277e-01
0x3d2aa957, // 4.1665401e-02
0x3c098d8b, // 8.3955629e-03
0x3ab778cf // 1.3997796e-03
>(x);
return ++fma(y, x * x, x);
}
static inline B reduce(const B& a, B& x)
{
B k = nearbyint(invlog_2<B>() * a);
x = fnma(k, log_2hi<B>(), a);
x = fnma(k, log_2lo<B>(), x);
return k;
}
};
template <class B>
struct exp_reduction<B, exp2_tag, float> : exp_reduction_base<B, exp2_tag>
{
static inline B approx(const B& x)
{
B y = horner<B,
0x3e75fdf1, // 2.4022652e-01
0x3d6356eb, // 5.5502813e-02
0x3c1d9422, // 9.6178371e-03
0x3ab01218, // 1.3433127e-03
0x3922c8c4 // 1.5524315e-04
>(x);
return ++fma(y, x * x, x * log_2<B>());
}
static inline B reduce(const B& a, B& x)
{
B k = nearbyint(a);
x = (a - k);
return k;
}
};
template <class B>
struct exp_reduction<B, exp10_tag, float> : exp_reduction_base<B, exp10_tag>
{
static inline B approx(const B& x)
{
return ++(horner<B,
0x40135d8e, // 2.3025851e+00
0x4029a926, // 2.6509490e+00
0x400237da, // 2.0346589e+00
0x3f95eb4c, // 1.1712432e+00
0x3f0aacef, // 5.4170126e-01
0x3e54dff1 // 2.0788552e-01
>(x) *
x);
}
static inline B reduce(const B& a, B& x)
{
B k = nearbyint(invlog10_2<B>() * a);
x = fnma(k, log10_2hi<B>(), a);
x -= k * log10_2lo<B>();
return k;
}
};
/* origin: boost/simd/arch/common/detail/generic/d_expo_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)
* ====================================================
*/
template <class B>
struct exp_reduction<B, exp_tag, double> : exp_reduction_base<B, exp_tag>
{
static inline B approx(const B& x)
{
B t = x * x;
return fnma(t,
horner<B,
0x3fc555555555553eull,
0xbf66c16c16bebd93ull,
0x3f11566aaf25de2cull,
0xbebbbd41c5d26bf1ull,
0x3e66376972bea4d0ull>(t),
x);
}
static inline B reduce(const B& a, B& hi, B& lo, B& x)
{
B k = nearbyint(invlog_2<B>() * a);
hi = fnma(k, log_2hi<B>(), a);
lo = k * log_2lo<B>();
x = hi - lo;
return k;
}
static inline B finalize(const B& x, const B& c, const B& hi, const B& lo)
{
return B(1.) - (((lo - (x * c) / (B(2.) - c)) - hi));
}
};
template <class B>
struct exp_reduction<B, exp2_tag, double> : exp_reduction_base<B, exp2_tag>
{
static inline B approx(const B& x)
{
B t = x * x;
return fnma(t,
horner<B,
0x3fc555555555553eull,
0xbf66c16c16bebd93ull,
0x3f11566aaf25de2cull,
0xbebbbd41c5d26bf1ull,
0x3e66376972bea4d0ull>(t),
x);
}
static inline B reduce(const B& a, B&, B&, B& x)
{
B k = nearbyint(a);
x = (a - k) * log_2<B>();
return k;
}
static inline B finalize(const B& x, const B& c, const B&, const B&)
{
return B(1.) + x + x * c / (B(2.) - c);
}
};
template <class B>
struct exp_reduction<B, exp10_tag, double> : exp_reduction_base<B, exp10_tag>
{
static inline B approx(const B& x)
{
B xx = x * x;
B px = x * horner<B,
0x40a2b4798e134a01ull,
0x40796b7a050349e4ull,
0x40277d9474c55934ull,
0x3fa4fd75f3062dd4ull>(xx);
B x2 = px / (horner1<B,
0x40a03f37650df6e2ull,
0x4093e05eefd67782ull,
0x405545fdce51ca08ull>(xx) -
px);
return ++(x2 + x2);
}
static inline B reduce(const B& a, B&, B&, B& x)
{
B k = nearbyint(invlog10_2<B>() * a);
x = fnma(k, log10_2hi<B>(), a);
x = fnma(k, log10_2lo<B>(), x);
return k;
}
static inline B finalize(const B&, const B& c, const B&, const B&)
{
return c;
}
};
}
}
#endif
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