Szabolcs NagyandRich Felker
f4e4632abf
This is in preparation for the aarch64 port only to have the long double math symbols available on ld128 platforms. The implementations should be fixed up later once we have proper tests for these functions. Added bigendian handling for ld128 bit manipulations too.
176 lines
4.5 KiB
C
176 lines
4.5 KiB
C
/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_logl.c */
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/*
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* Copyright (c) 2008 Stephen L. Moshier <[email protected]>
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*/
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/*
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* Natural logarithm, long double precision
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*
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*
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* SYNOPSIS:
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*
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* long double x, y, logl();
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*
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* y = logl( x );
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*
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*
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* DESCRIPTION:
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*
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* Returns the base e (2.718...) logarithm of x.
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*
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* The argument is separated into its exponent and fractional
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* parts. If the exponent is between -1 and +1, the logarithm
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* of the fraction is approximated by
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*
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* log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
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*
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* Otherwise, setting z = 2(x-1)/(x+1),
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*
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* log(x) = log(1+z/2) - log(1-z/2) = z + z**3 P(z)/Q(z).
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE 0.5, 2.0 150000 8.71e-20 2.75e-20
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* IEEE exp(+-10000) 100000 5.39e-20 2.34e-20
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*
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* In the tests over the interval exp(+-10000), the logarithms
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* of the random arguments were uniformly distributed over
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* [-10000, +10000].
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*/
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#include "libm.h"
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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long double logl(long double x)
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{
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return log(x);
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}
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#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
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* 1/sqrt(2) <= x < sqrt(2)
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* Theoretical peak relative error = 2.32e-20
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*/
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static const long double P[] = {
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4.5270000862445199635215E-5L,
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4.9854102823193375972212E-1L,
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6.5787325942061044846969E0L,
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2.9911919328553073277375E1L,
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6.0949667980987787057556E1L,
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5.7112963590585538103336E1L,
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2.0039553499201281259648E1L,
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};
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static const long double Q[] = {
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/* 1.0000000000000000000000E0,*/
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1.5062909083469192043167E1L,
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8.3047565967967209469434E1L,
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2.2176239823732856465394E2L,
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3.0909872225312059774938E2L,
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2.1642788614495947685003E2L,
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6.0118660497603843919306E1L,
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};
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/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
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* where z = 2(x-1)/(x+1)
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* 1/sqrt(2) <= x < sqrt(2)
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* Theoretical peak relative error = 6.16e-22
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*/
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static const long double R[4] = {
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1.9757429581415468984296E-3L,
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-7.1990767473014147232598E-1L,
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1.0777257190312272158094E1L,
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-3.5717684488096787370998E1L,
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};
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static const long double S[4] = {
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/* 1.00000000000000000000E0L,*/
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-2.6201045551331104417768E1L,
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1.9361891836232102174846E2L,
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-4.2861221385716144629696E2L,
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};
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static const long double C1 = 6.9314575195312500000000E-1L;
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static const long double C2 = 1.4286068203094172321215E-6L;
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#define SQRTH 0.70710678118654752440L
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long double logl(long double x)
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{
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long double y, z;
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int e;
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if (isnan(x))
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return x;
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if (x == INFINITY)
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return x;
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if (x <= 0.0) {
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if (x == 0.0)
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return -1/(x*x); /* -inf with divbyzero */
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return 0/0.0f; /* nan with invalid */
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}
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/* separate mantissa from exponent */
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/* Note, frexp is used so that denormal numbers
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* will be handled properly.
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*/
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x = frexpl(x, &e);
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/* logarithm using log(x) = z + z**3 P(z)/Q(z),
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* where z = 2(x-1)/(x+1)
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*/
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if (e > 2 || e < -2) {
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if (x < SQRTH) { /* 2(2x-1)/(2x+1) */
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e -= 1;
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z = x - 0.5;
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y = 0.5 * z + 0.5;
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} else { /* 2 (x-1)/(x+1) */
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z = x - 0.5;
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z -= 0.5;
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y = 0.5 * x + 0.5;
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}
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x = z / y;
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z = x*x;
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z = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3));
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z = z + e * C2;
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z = z + x;
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z = z + e * C1;
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return z;
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}
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/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
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if (x < SQRTH) {
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e -= 1;
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x = 2.0*x - 1.0;
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} else {
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x = x - 1.0;
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}
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z = x*x;
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y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6));
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y = y + e * C2;
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z = y - 0.5*z;
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/* Note, the sum of above terms does not exceed x/4,
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* so it contributes at most about 1/4 lsb to the error.
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*/
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z = z + x;
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z = z + e * C1; /* This sum has an error of 1/2 lsb. */
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return z;
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}
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#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
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// TODO: broken implementation to make things compile
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long double logl(long double x)
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{
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return log(x);
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}
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#endif
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