Current File : //usr/include/xsimd/math/xsimd_exponential.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_EXPONENTIAL_HPP
#define XSIMD_EXPONENTIAL_HPP
#include "xsimd_exp_reduction.hpp"
#include "xsimd_fp_manipulation.hpp"
namespace xsimd
{
/**
* Computes the natural exponential of the batch \c x.
* @param x batch of floating point values.
* @return the natural exponential of \c x.
*/
template <class B>
batch_type_t<B> exp(const simd_base<B>& x);
/**
* Computes the base 2 exponential of the batch \c x.
* @param x batch of floating point values.
* @return the base 2 exponential of \c x.
*/
template <class B>
batch_type_t<B> exp2(const simd_base<B>& x);
/**
* Computes the base 10 exponential of the batch \c x.
* @param x batch of floating point values.
* @return the base 10 exponential of \c x.
*/
template <class B>
batch_type_t<B> exp10(const simd_base<B>& x);
/**
* Computes the natural exponential of the batch \c x, minus one.
* @param x batch of floating point values.
* @return the natural exponential of \c x, minus one.
*/
template <class B>
batch_type_t<B> expm1(const simd_base<B>& x);
/******************************
* exponential implementation *
******************************/
namespace detail
{
template <class B, class Tag, class T = typename B::value_type>
struct exp_kernel;
template <class B, class Tag>
struct exp_kernel<B, Tag, float>
{
/* origin: boost/simd/arch/common/detail/simd/expo_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)
* ====================================================
*/
static inline B compute(const B& a)
{
using reducer_t = exp_reduction<B, Tag>;
B x;
B k = reducer_t::reduce(a, x);
x = reducer_t::approx(x);
x = select(a <= reducer_t::minlog(), B(0.), ldexp(x, to_int(k)));
x = select(a >= reducer_t::maxlog(), infinity<B>(), x);
return x;
}
};
template <class B, class Tag>
struct exp_kernel<B, Tag, double>
{
/* origin: boost/simd/arch/common/detail/simd/expo_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)
* ====================================================
*/
static inline B compute(const B& a)
{
using reducer_t = exp_reduction<B, Tag>;
B hi, lo, x;
B k = reducer_t::reduce(a, hi, lo, x);
B c = reducer_t::approx(x);
c = reducer_t::finalize(x, c, hi, lo);
c = select(a <= reducer_t::minlog(), B(0.), ldexp(c, to_int(k)));
c = select(a >= reducer_t::maxlog(), infinity<B>(), c);
return c;
}
};
}
template <class B>
inline batch_type_t<B> exp(const simd_base<B>& x)
{
return detail::exp_kernel<batch_type_t<B>, exp_tag>::compute(x());
}
template <class B>
inline batch_type_t<B> exp2(const simd_base<B>& x)
{
return detail::exp_kernel<batch_type_t<B>, exp2_tag>::compute(x());
}
template <class B>
inline batch_type_t<B> exp10(const simd_base<B>& x)
{
return detail::exp_kernel<batch_type_t<B>, exp10_tag>::compute(x());
}
/************************
* expm1 implementation *
************************/
namespace detail
{
template <class B, class T = typename B::value_type>
struct expm1_kernel;
template <class B>
inline B expm1_real_impl(const B& x)
{
return select(x < logeps<B>(),
B(-1.),
select(x > maxlog<B>(),
infinity<B>(),
expm1_kernel<B>::compute_impl(x)));
}
template <class B>
struct expm1_kernel<B, float>
{
/* origin: boost/simd/arch/common/detail/generic/expm1_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)
* ====================================================
*/
static inline B compute_impl(const B& a)
{
B k = nearbyint(invlog_2<B>() * a);
B x = fnma(k, log_2hi<B>(), a);
x = fnma(k, log_2lo<B>(), x);
B hx = x * B(0.5);
B hxs = x * hx;
B r = horner<B,
0X3F800000UL, // 1
0XBD08887FUL, // -3.3333298E-02
0X3ACF6DB4UL // 1.582554
>(hxs);
B t = fnma(r, hx, B(3.));
B e = hxs * ((r - t) / (B(6.) - x * t));
e = fms(x, e, hxs);
using i_type = as_integer_t<B>;
i_type ik = to_int(k);
B two2mk = bitwise_cast<B>((maxexponent<B>() - ik) << nmb<B>());
B y = B(1.) - two2mk - (e - x);
return ldexp(y, ik);
}
static inline B compute(const B& a)
{
return expm1_real_impl(a);
}
};
template <class B>
struct expm1_kernel<B, double>
{
/* origin: boost/simd/arch/common/detail/generic/expm1_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)
* ====================================================
*/
static inline B compute_impl(const B& a)
{
B k = nearbyint(invlog_2<B>() * a);
B hi = fnma(k, log_2hi<B>(), a);
B lo = k * log_2lo<B>();
B x = hi - lo;
B hxs = x * x * B(0.5);
B r = horner<B,
0X3FF0000000000000ULL,
0XBFA11111111110F4ULL,
0X3F5A01A019FE5585ULL,
0XBF14CE199EAADBB7ULL,
0X3ED0CFCA86E65239ULL,
0XBE8AFDB76E09C32DULL>(hxs);
B t = B(3.) - r * B(0.5) * x;
B e = hxs * ((r - t) / (B(6) - x * t));
B c = (hi - x) - lo;
e = (x * (e - c) - c) - hxs;
using i_type = as_integer_t<B>;
i_type ik = to_int(k);
B two2mk = bitwise_cast<B>((maxexponent<B>() - ik) << nmb<B>());
B ct1 = B(1.) - two2mk - (e - x);
B ct2 = ++(x - (e + two2mk));
B y = select(k < B(20.), ct1, ct2);
return ldexp(y, ik);
}
static inline B compute(const B& a)
{
return expm1_real_impl(a);
}
};
}
template <class B>
inline batch_type_t<B> expm1(const simd_base<B>& x)
{
return detail::expm1_kernel<batch_type_t<B>>::compute(x());
}
}
#endif
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