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208 lines
7 KiB
C
208 lines
7 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2014 Rich Felker, et al. │
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│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
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│ a copy of this software and associated documentation files (the │
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│ "Software"), to deal in the Software without restriction, including │
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│ without limitation the rights to use, copy, modify, merge, publish, │
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│ distribute, sublicense, and/or sell copies of the Software, and to │
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│ permit persons to whom the Software is furnished to do so, subject to │
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│ the following conditions: │
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│ │
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│ The above copyright notice and this permission notice shall be │
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│ included in all copies or substantial portions of the Software. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
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│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
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│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
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│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
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│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
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│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
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│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/complex.h"
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#include "libc/math.h"
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#include "libc/tinymath/complex.internal.h"
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#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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asm(".ident\t\"\\n\\n\
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OpenBSD libm (ISC License)\\n\
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Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>\"");
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asm(".ident\t\"\\n\\n\
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Musl libc (MIT License)\\n\
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Copyright 2005-2014 Rich Felker, et. al.\"");
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asm(".include \"libc/disclaimer.inc\"");
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// clang-format off
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/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_log1pl.c */
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/*
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* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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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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* Relative error logarithm
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* Natural logarithm of 1+x, 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, log1pl();
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*
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* y = log1pl( 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 1+x.
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*
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* The argument 1+x 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) = 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 -1.0, 9.0 100000 8.2e-20 2.5e-20
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*/
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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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/**
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* Returns log(𝟷+𝑥).
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*/
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long double log1pl(long double xm1)
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{
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long double x, y, z;
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int e;
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if (isnan(xm1))
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return xm1;
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if (xm1 == INFINITY)
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return xm1;
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if (xm1 == 0.0)
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return xm1;
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x = xm1 + 1.0;
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/* Test for domain errors. */
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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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Use frexp so that denormal numbers will be handled properly. */
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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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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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if (e != 0)
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x = 2.0 * x - 1.0;
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else
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x = xm1;
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} else {
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if (e != 0)
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x = x - 1.0;
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else
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x = xm1;
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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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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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#endif /* ieee80 */
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