/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│ │ vi: set noet ft=c ts=8 sw=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/kernel.internal.h" asm(".ident\t\"\\n\\n\ FreeBSD libm (BSD-2 License)\\n\ Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\""); asm(".ident\t\"\\n\\n\ fdlibm (fdlibm license)\\n\ Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\""); 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: FreeBSD /usr/src/lib/msun/ld80/k_cosl.c */ /* origin: FreeBSD /usr/src/lib/msun/ld128/k_cosl.c */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 #if LDBL_MANT_DIG == 64 /* * ld80 version of __cos.c. See __cos.c for most comments. */ /* * Domain [-0.7854, 0.7854], range ~[-2.43e-23, 2.425e-23]: * |cos(x) - c(x)| < 2**-75.1 * * The coefficients of c(x) were generated by a pari-gp script using * a Remez algorithm that searches for the best higher coefficients * after rounding leading coefficients to a specified precision. * * Simpler methods like Chebyshev or basic Remez barely suffice for * cos() in 64-bit precision, because we want the coefficient of x^2 * to be precisely -0.5 so that multiplying by it is exact, and plain * rounding of the coefficients of a good polynomial approximation only * gives this up to about 64-bit precision. Plain rounding also gives * a mediocre approximation for the coefficient of x^4, but a rounding * error of 0.5 ulps for this coefficient would only contribute ~0.01 * ulps to the final error, so this is unimportant. Rounding errors in * higher coefficients are even less important. * * In fact, coefficients above the x^4 one only need to have 53-bit * precision, and this is more efficient. We get this optimization * almost for free from the complications needed to search for the best * higher coefficients. */ static const long double C1 = 0.0416666666666666666136L; /* 0xaaaaaaaaaaaaaa9b.0p-68 */ static const double C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */ C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */ C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */ C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */ C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */ C7 = 4.7383039476436467e-14; /* 0x1aac9d9af5c43e.0p-97 */ #define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7))))))) #elif LDBL_MANT_DIG == 113 /* * ld128 version of __cos.c. See __cos.c for most comments. */ /* * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]: * |cos(x) - c(x))| < 2**-122.0 * * 113-bit precision requires more care than 64-bit precision, since * simple methods give a minimax polynomial with coefficient for x^2 * that is 1 ulp below 0.5, but we want it to be precisely 0.5. See * above for more details. */ static const long double C1 = 0.04166666666666666666666666666666658424671L, C2 = -0.001388888888888888888888888888863490893732L, C3 = 0.00002480158730158730158730158600795304914210L, C4 = -0.2755731922398589065255474947078934284324e-6L, C5 = 0.2087675698786809897659225313136400793948e-8L, C6 = -0.1147074559772972315817149986812031204775e-10L, C7 = 0.4779477332386808976875457937252120293400e-13L; static const double C8 = -0.1561920696721507929516718307820958119868e-15, C9 = 0.4110317413744594971475941557607804508039e-18, C10 = -0.8896592467191938803288521958313920156409e-21, C11 = 0.1601061435794535138244346256065192782581e-23; #define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+ \ z*(C8+z*(C9+z*(C10+z*C11))))))))))) #endif long double __cosl(long double x, long double y) { long double hz,z,r,w; z = x*x; r = POLY(z); hz = 0.5*z; w = 1.0-hz; return w + (((1.0-w)-hz) + (z*r-x*y)); } #endif