Current File : //proc/self/root/usr/include/xsimd/math/xsimd_logarithm.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_LOGARITHM_HPP
#define XSIMD_LOGARITHM_HPP
#include "xsimd_numerical_constant.hpp"
namespace xsimd
{
/**
* Computes the natural logarithm of the batch \c x.
* @param x batch of floating point values.
* @return the natural logarithm of \c x.
*/
template <class B>
batch_type_t<B> log(const simd_base<B>& x);
/**
* Computes the base 2 logarithm of the batch \c x.
* @param x batch of floating point values.
* @return the base 2 logarithm of \c x.
*/
template <class B>
batch_type_t<B> log2(const simd_base<B>& x);
/**
* Computes the base 10 logarithm of the batch \c x.
* @param x batch of floating point values.
* @return the base 10 logarithm of \c x.
*/
template <class B>
batch_type_t<B> log10(const simd_base<B>& x);
/**
* Computes the natural logarithm of one plus the batch \c x.
* @param x batch of floating point values.
* @return the natural logarithm of one plus \c x.
*/
template <class B>
batch_type_t<B> log1p(const simd_base<B>& x);
/**********************
* log implementation *
**********************/
namespace detail
{
template <class B, class T = typename B::value_type>
struct log_kernel;
template <class B>
struct log_kernel<B, float>
{
/* origin: boost/simd/arch/common/simd/function/log.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 i_type = as_integer_t<B>;
B x = a;
i_type k(0);
auto isnez = (a != B(0.));
#ifndef XSIMD_NO_DENORMALS
auto test = (a < smallestposval<B>()) && isnez;
if (any(test))
{
k = select(bool_cast(test), k - i_type(23), k);
x = select(test, x * B(8388608ul), x);
}
#endif
i_type ix = bitwise_cast<i_type>(x);
ix += 0x3f800000 - 0x3f3504f3;
k += (ix >> 23) - 0x7f;
ix = (ix & i_type(0x007fffff)) + 0x3f3504f3;
x = bitwise_cast<B>(ix);
B f = --x;
B s = f / (B(2.) + f);
B z = s * s;
B w = z * z;
B t1 = w * horner<B, 0x3eccce13, 0x3e789e26>(w);
B t2 = z * horner<B, 0x3f2aaaaa, 0x3e91e9ee>(w);
B R = t2 + t1;
B hfsq = B(0.5) * f * f;
B dk = to_float(k);
B r = fma(dk, log_2hi<B>(), fma(s, (hfsq + R), dk * log_2lo<B>()) - hfsq + f);
#ifndef XSIMD_NO_INFINITIES
B zz = select(isnez, select(a == infinity<B>(), infinity<B>(), r), minusinfinity<B>());
#else
B zz = select(isnez, r, minusinfinity<B>());
#endif
return select(!(a >= B(0.)), nan<B>(), zz);
}
};
template <class B>
struct log_kernel<B, double>
{
/* origin: boost/simd/arch/common/simd/function/log.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 i_type = as_integer_t<B>;
B x = a;
i_type hx = bitwise_cast<i_type>(x) >> 32;
i_type k = zero<i_type>();
auto isnez = (a != B(0.));
#ifndef XSIMD_NO_DENORMALS
auto test = (a < smallestposval<B>()) && isnez;
if (any(test))
{
k = select(bool_cast(test), k - i_type(54), k);
x = select(test, x * B(18014398509481984ull), x);
}
#endif
hx += 0x3ff00000 - 0x3fe6a09e;
k += (hx >> 20) - 0x3ff;
B dk = to_float(k);
hx = (hx & i_type(0x000fffff)) + 0x3fe6a09e;
x = bitwise_cast<B>(hx << 32 | (i_type(0xffffffff) & bitwise_cast<i_type>(x)));
B f = --x;
B hfsq = B(0.5) * f * f;
B s = f / (B(2.) + f);
B z = s * s;
B w = z * z;
B t1 = w * horner<B,
0x3fd999999997fa04ll,
0x3fcc71c51d8e78afll,
0x3fc39a09d078c69fll>(w);
B t2 = z * horner<B,
0x3fe5555555555593ll,
0x3fd2492494229359ll,
0x3fc7466496cb03dell,
0x3fc2f112df3e5244ll>(w);
B R = t2 + t1;
B r = fma(dk, log_2hi<B>(), fma(s, (hfsq + R), dk * log_2lo<B>()) - hfsq + f);
#ifndef XSIMD_NO_INFINITIES
B zz = select(isnez, select(a == infinity<B>(), infinity<B>(), r), minusinfinity<B>());
#else
B zz = select(isnez, r, minusinfinity<B>());
#endif
return select(!(a >= B(0.)), nan<B>(), zz);
}
};
}
template <class B>
inline batch_type_t<B> log(const simd_base<B>& x)
{
return detail::log_kernel<batch_type_t<B>>::compute(x());
}
/***********************
* log2 implementation *
***********************/
namespace detail
{
template <class B, class T = typename B::value_type>
struct log2_kernel;
template <class B>
struct log2_kernel<B, float>
{
/* origin: FreeBSD /usr/src/lib/msun/src/e_log2f.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
static inline B compute(const B& a)
{
using i_type = as_integer_t<B>;
B x = a;
i_type k(0);
auto isnez = (a != B(0.));
#ifndef XSIMD_NO_DENORMALS
auto test = (a < smallestposval<B>()) && isnez;
if (any(test))
{
k = select(bool_cast(test), k - i_type(25), k);
x = select(test, x * B(33554432ul), x);
}
#endif
i_type ix = bitwise_cast<i_type>(x);
ix += 0x3f800000 - 0x3f3504f3;
k += (ix >> 23) - 0x7f;
ix = (ix & i_type(0x007fffff)) + 0x3f3504f3;
x = bitwise_cast<B>(ix);
B f = --x;
B s = f / (B(2.) + f);
B z = s * s;
B w = z * z;
B t1 = w * horner<B, 0x3eccce13, 0x3e789e26>(w);
B t2 = z * horner<B, 0x3f2aaaaa, 0x3e91e9ee>(w);
B R = t1 + t2;
B hfsq = B(0.5) * f * f;
B dk = to_float(k);
B r = fma(fms(s, hfsq + R, hfsq) + f, invlog_2<B>(), dk);
#ifndef XSIMD_NO_INFINITIES
B zz = select(isnez, select(a == infinity<B>(), infinity<B>(), r), minusinfinity<B>());
#else
B zz = select(isnez, r, minusinfinity<B>());
#endif
return select(!(a >= B(0.)), nan<B>(), zz);
}
};
template <class B>
struct log2_kernel<B, double>
{
/* origin: FreeBSD /usr/src/lib/msun/src/e_log2f.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
static inline B compute(const B& a)
{
using i_type = as_integer_t<B>;
B x = a;
i_type hx = bitwise_cast<i_type>(x) >> 32;
i_type k = zero<i_type>();
auto isnez = (a != B(0.));
#ifndef XSIMD_NO_DENORMALS
auto test = (a < smallestposval<B>()) && isnez;
if (any(test))
{
k = select(bool_cast(test), k - i_type(54), k);
x = select(test, x * B(18014398509481984ull), x);
}
#endif
hx += 0x3ff00000 - 0x3fe6a09e;
k += (hx >> 20) - 0x3ff;
hx = (hx & i_type(0x000fffff)) + 0x3fe6a09e;
x = bitwise_cast<B>(hx << 32 | (i_type(0xffffffff) & bitwise_cast<i_type>(x)));
B f = --x;
B s = f / (B(2.) + f);
B z = s * s;
B w = z * z;
B t1 = w * horner<B,
0x3fd999999997fa04ll,
0x3fcc71c51d8e78afll,
0x3fc39a09d078c69fll>(w);
B t2 = z * horner<B,
0x3fe5555555555593ll,
0x3fd2492494229359ll,
0x3fc7466496cb03dell,
0x3fc2f112df3e5244ll>(w);
B R = t2 + t1;
B hfsq = B(0.5) * f * f;
B hi = f - hfsq;
hi = hi & bitwise_cast<B>((allbits<i_type>() << 32));
B lo = fma(s, hfsq + R, f - hi - hfsq);
B val_hi = hi * invlog_2hi<B>();
B val_lo = fma(lo + hi, invlog_2lo<B>(), lo * invlog_2hi<B>());
B dk = to_float(k);
B w1 = dk + val_hi;
val_lo += (dk - w1) + val_hi;
val_hi = w1;
B r = val_lo + val_hi;
#ifndef XSIMD_NO_INFINITIES
B zz = select(isnez, select(a == infinity<B>(), infinity<B>(), r), minusinfinity<B>());
#else
B zz = select(isnez, r, minusinfinity<B>());
#endif
return select(!(a >= B(0.)), nan<B>(), zz);
}
};
}
template <class B>
inline batch_type_t<B> log2(const simd_base<B>& x)
{
return detail::log2_kernel<batch_type_t<B>>::compute(x());
}
/************************
* log10 implementation *
************************/
namespace detail
{
template <class B, class T = typename B::value_type>
struct log10_kernel;
template <class B>
struct log10_kernel<B, float>
{
/* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
static inline B compute(const B& a)
{
const B
ivln10hi(4.3432617188e-01f),
ivln10lo(-3.1689971365e-05f),
log10_2hi(3.0102920532e-01f),
log10_2lo(7.9034151668e-07f);
using i_type = as_integer_t<B>;
B x = a;
i_type k(0);
auto isnez = (a != B(0.));
#ifndef XSIMD_NO_DENORMALS
auto test = (a < smallestposval<B>()) && isnez;
if (any(test))
{
k = select(bool_cast(test), k - i_type(25), k);
x = select(test, x * B(33554432ul), x);
}
#endif
i_type ix = bitwise_cast<i_type>(x);
ix += 0x3f800000 - 0x3f3504f3;
k += (ix >> 23) - 0x7f;
ix = (ix & i_type(0x007fffff)) + 0x3f3504f3;
x = bitwise_cast<B>(ix);
B f = --x;
B s = f / (B(2.) + f);
B z = s * s;
B w = z * z;
B t1 = w * horner<B, 0x3eccce13, 0x3e789e26>(w);
B t2 = z * horner<B, 0x3f2aaaaa, 0x3e91e9ee>(w);
B R = t2 + t1;
B dk = to_float(k);
B hfsq = B(0.5) * f * f;
B hibits = f - hfsq;
hibits &= bitwise_cast<B>(i_type(0xfffff000));
B lobits = fma(s, hfsq + R, f - hibits - hfsq);
B r = fma(dk, log10_2hi,
fma(hibits, ivln10hi,
fma(lobits, ivln10hi,
fma(lobits + hibits, ivln10lo, dk * log10_2lo))));
#ifndef XSIMD_NO_INFINITIES
B zz = select(isnez, select(a == infinity<B>(), infinity<B>(), r), minusinfinity<B>());
#else
B zz = select(isnez, r, minusinfinity<B>());
#endif
return select(!(a >= B(0.)), nan<B>(), zz);
}
};
template <class B>
struct log10_kernel<B, double>
{
/* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
static inline B compute(const B& a)
{
const B
ivln10hi(4.34294481878168880939e-01),
ivln10lo(2.50829467116452752298e-11),
log10_2hi(3.01029995663611771306e-01),
log10_2lo(3.69423907715893078616e-13);
using i_type = as_integer_t<B>;
B x = a;
i_type hx = bitwise_cast<i_type>(x) >> 32;
i_type k = zero<i_type>();
auto isnez = (a != B(0.));
#ifndef XSIMD_NO_DENORMALS
auto test = (a < smallestposval<B>()) && isnez;
if (any(test))
{
k = select(bool_cast(test), k - i_type(54), k);
x = select(test, x * B(18014398509481984ull), x);
}
#endif
hx += 0x3ff00000 - 0x3fe6a09e;
k += (hx >> 20) - 0x3ff;
hx = (hx & i_type(0x000fffff)) + 0x3fe6a09e;
x = bitwise_cast<B>(hx << 32 | (i_type(0xffffffff) & bitwise_cast<i_type>(x)));
B f = --x;
B dk = to_float(k);
B s = f / (B(2.) + f);
B z = s * s;
B w = z * z;
B t1 = w * horner<B,
0x3fd999999997fa04ll,
0x3fcc71c51d8e78afll,
0x3fc39a09d078c69fll>(w);
B t2 = z * horner<B,
0x3fe5555555555593ll,
0x3fd2492494229359ll,
0x3fc7466496cb03dell,
0x3fc2f112df3e5244ll>(w);
B R = t2 + t1;
B hfsq = B(0.5) * f * f;
B hi = f - hfsq;
hi = hi & bitwise_cast<B>(allbits<i_type>() << 32);
B lo = f - hi - hfsq + s * (hfsq + R);
B val_hi = hi * ivln10hi;
B y = dk * log10_2hi;
B val_lo = dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi;
B w1 = y + val_hi;
val_lo += (y - w1) + val_hi;
val_hi = w1;
B r = val_lo + val_hi;
#ifndef XSIMD_NO_INFINITIES
B zz = select(isnez, select(a == infinity<B>(), infinity<B>(), r), minusinfinity<B>());
#else
B zz = select(isnez, r, minusinfinity<B>());
#endif
return select(!(a >= B(0.)), nan<B>(), zz);
}
};
}
template <class B>
inline batch_type_t<B> log10(const simd_base<B>& x)
{
return detail::log10_kernel<batch_type_t<B>>::compute(x());
}
/************************
* log1p implementation *
************************/
namespace detail
{
template <class B, class T = typename B::value_type>
struct log1p_kernel;
template <class B>
struct log1p_kernel<B, float>
{
/* origin: boost/simd/arch/common/simd/function/log1p.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 i_type = as_integer_t<B>;
const B uf = a + B(1.);
auto isnez = (uf != B(0.));
i_type iu = bitwise_cast<i_type>(uf);
iu += 0x3f800000 - 0x3f3504f3;
i_type k = (iu >> 23) - 0x7f;
iu = (iu & i_type(0x007fffff)) + 0x3f3504f3;
B f = --(bitwise_cast<B>(iu));
B s = f / (B(2.) + f);
B z = s * s;
B w = z * z;
B t1 = w * horner<B, 0x3eccce13, 0x3e789e26>(w);
B t2 = z * horner<B, 0x3f2aaaaa, 0x3e91e9ee>(w);
B R = t2 + t1;
B hfsq = B(0.5) * f * f;
B dk = to_float(k);
/* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
B c = select(bool_cast(k >= i_type(2)), B(1.) - (uf - a), a - (uf - B(1.))) / uf;
B r = fma(dk, log_2hi<B>(), fma(s, (hfsq + R), dk * log_2lo<B>() + c) - hfsq + f);
#ifndef XSIMD_NO_INFINITIES
B zz = select(isnez, select(a == infinity<B>(), infinity<B>(), r), minusinfinity<B>());
#else
B zz = select(isnez, r, minusinfinity<B>());
#endif
return select(!(uf >= B(0.)), nan<B>(), zz);
}
};
template <class B>
struct log1p_kernel<B, double>
{
/* origin: boost/simd/arch/common/simd/function/log1p.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 i_type = as_integer_t<B>;
const B uf = a + B(1.);
auto isnez = (uf != B(0.));
i_type hu = bitwise_cast<i_type>(uf) >> 32;
hu += 0x3ff00000 - 0x3fe6a09e;
i_type k = (hu >> 20) - 0x3ff;
/* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
B c = select(bool_cast(k >= i_type(2)), B(1.) - (uf - a), a - (uf - B(1.))) / uf;
hu = (hu & i_type(0x000fffff)) + 0x3fe6a09e;
B f = bitwise_cast<B>((hu << 32) | (i_type(0xffffffff) & bitwise_cast<i_type>(uf)));
f = --f;
B hfsq = B(0.5) * f * f;
B s = f / (B(2.) + f);
B z = s * s;
B w = z * z;
B t1 = w * horner<B,
0x3fd999999997fa04ll,
0x3fcc71c51d8e78afll,
0x3fc39a09d078c69fll>(w);
B t2 = z * horner<B,
0x3fe5555555555593ll,
0x3fd2492494229359ll,
0x3fc7466496cb03dell,
0x3fc2f112df3e5244ll>(w);
B R = t2 + t1;
B dk = to_float(k);
B r = fma(dk, log_2hi<B>(), fma(s, hfsq + R, dk * log_2lo<B>() + c) - hfsq + f);
#ifndef XSIMD_NO_INFINITIES
B zz = select(isnez, select(a == infinity<B>(), infinity<B>(), r), minusinfinity<B>());
#else
B zz = select(isnez, r, minusinfinity<B>());
#endif
return select(!(uf >= B(0.)), nan<B>(), zz);
}
};
}
template <class B>
inline batch_type_t<B> log1p(const simd_base<B>& x)
{
return detail::log1p_kernel<batch_type_t<B>>::compute(x());
}
}
#endif
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