/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│ │vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│ ╚──────────────────────────────────────────────────────────────────────────────╝ │ │ │ Musl Libc │ │ Copyright © 2005-2014 Rich Felker, et al. │ │ │ │ Permission is hereby granted, free of charge, to any person obtaining │ │ a copy of this software and associated documentation files (the │ │ "Software"), to deal in the Software without restriction, including │ │ without limitation the rights to use, copy, modify, merge, publish, │ │ distribute, sublicense, and/or sell copies of the Software, and to │ │ permit persons to whom the Software is furnished to do so, subject to │ │ the following conditions: │ │ │ │ The above copyright notice and this permission notice shall be │ │ included in all copies or substantial portions of the Software. │ │ │ │ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ │ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ │ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ │ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ │ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ │ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ │ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ │ │ ╚─────────────────────────────────────────────────────────────────────────────*/ #include "libc/math.h" #include "libc/tinymath/internal.h" asm(".ident\t\"\\n\\n\ OpenBSD libm (MIT License)\\n\ Copyright (c) 2008 Stephen L. Moshier \""); asm(".ident\t\"\\n\\n\ Musl libc (MIT License)\\n\ Copyright 2005-2014 Rich Felker, et. al.\""); asm(".include \"libc/disclaimer.inc\""); // clang-format off /* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expm1l.c */ /* * Copyright (c) 2008 Stephen L. Moshier * * Permission to use, copy, modify, and distribute this software for any * purpose with or without fee is hereby granted, provided that the above * copyright notice and this permission notice appear in all copies. * * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ /* * Exponential function, minus 1 * Long double precision * * * SYNOPSIS: * * long double x, y, expm1l(); * * y = expm1l( x ); * * * DESCRIPTION: * * Returns e (2.71828...) raised to the x power, minus 1. * * Range reduction is accomplished by separating the argument * into an integer k and fraction f such that * * x k f * e = 2 e. * * An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1 * in the basic range [-0.5 ln 2, 0.5 ln 2]. * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * IEEE -45,+maxarg 200,000 1.2e-19 2.5e-20 */ #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 long double expm1l(long double x) { return expm1(x); } #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 /* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x) -.5 ln 2 < x < .5 ln 2 Theoretical peak relative error = 3.4e-22 */ static const long double P0 = -1.586135578666346600772998894928250240826E4L, P1 = 2.642771505685952966904660652518429479531E3L, P2 = -3.423199068835684263987132888286791620673E2L, P3 = 1.800826371455042224581246202420972737840E1L, P4 = -5.238523121205561042771939008061958820811E-1L, Q0 = -9.516813471998079611319047060563358064497E4L, Q1 = 3.964866271411091674556850458227710004570E4L, Q2 = -7.207678383830091850230366618190187434796E3L, Q3 = 7.206038318724600171970199625081491823079E2L, Q4 = -4.002027679107076077238836622982900945173E1L, /* Q5 = 1.000000000000000000000000000000000000000E0 */ /* C1 + C2 = ln 2 */ C1 = 6.93145751953125E-1L, C2 = 1.428606820309417232121458176568075500134E-6L, /* ln 2^-65 */ minarg = -4.5054566736396445112120088E1L, /* ln 2^16384 */ maxarg = 1.1356523406294143949492E4L; long double expm1l(long double x) { long double px, qx, xx; int k; if (isnan(x)) return x; if (x > maxarg) return x*0x1p16383L; /* overflow, unless x==inf */ if (x == 0.0) return x; if (x < minarg) return -1.0; xx = C1 + C2; /* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */ px = floorl(0.5 + x / xx); k = px; /* remainder times ln 2 */ x -= px * C1; x -= px * C2; /* Approximate exp(remainder ln 2).*/ px = (((( P4 * x + P3) * x + P2) * x + P1) * x + P0) * x; qx = (((( x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0; xx = x * x; qx = x + (0.5 * xx + xx * px / qx); /* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2). We have qx = exp(remainder ln 2) - 1, so exp(x) - 1 = 2^k (qx + 1) - 1 = 2^k qx + 2^k - 1. */ px = scalbnl(1.0, k); x = px * qx + (px - 1.0); return x; } #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 // TODO: broken implementation to make things compile long double expm1l(long double x) { return expm1(x); } #else #error "architecture unsupported" #endif