1c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* from: FreeBSD: head/lib/msun/src/e_coshl.c XXX */ 2c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 3c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* 4c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * ==================================================== 5c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * 7c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Developed at SunPro, a Sun Microsystems, Inc. business. 8c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Permission to use, copy, modify, and distribute this 9c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * software is freely granted, provided that this notice 10c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * is preserved. 11c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * ==================================================== 12c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes */ 13c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 14c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include <sys/cdefs.h> 15c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes__FBSDID("$FreeBSD$"); 16c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 17c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* 18c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * See e_cosh.c for complete comments. 19c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * 20c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Converted to long double by Bruce D. Evans. 21c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes */ 22c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 23c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include <float.h> 24c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#ifdef __i386__ 25c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include <ieeefp.h> 26c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#endif 27c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 28c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include "fpmath.h" 29c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include "math.h" 30c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include "math_private.h" 31c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#include "k_expl.h" 32c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 33c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#if LDBL_MAX_EXP != 0x4000 34c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* We also require the usual expsign encoding. */ 35c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#error "Unsupported long double format" 36c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#endif 37c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 38c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#define BIAS (LDBL_MAX_EXP - 1) 39c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 40c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L; 41c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#if LDBL_MANT_DIG == 64 42c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* 43c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]: 44c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * |cosh(x) - c(x)| < 2**-68.8 45c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes */ 46c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const union IEEEl2bits 47c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC4u = LD80C(0xaaaaaaaaaaaaac78, -5, 4.16666666666666682297e-2L); 48c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#define C4 C4u.e 49c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const double 50c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC2 = 0.5, 51c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC6 = 1.3888888888888616e-3, /* 0x16c16c16c16b99.0p-62 */ 52c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC8 = 2.4801587301767953e-5, /* 0x1a01a01a027061.0p-68 */ 53c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC10 = 2.7557319163300398e-7, /* 0x127e4fb6c9b55f.0p-74 */ 54c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC12 = 2.0876768371393075e-9, /* 0x11eed99406a3f4.0p-81 */ 55c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC14 = 1.1469537039374480e-11, /* 0x1938c67cd18c48.0p-89 */ 56c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC16 = 4.8473490896852041e-14; /* 0x1b49c429701e45.0p-97 */ 57c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#elif LDBL_MANT_DIG == 113 58c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* 59c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]: 60c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes * |cosh(x) - c(x)| < 2**-121.69 61c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes */ 62c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const long double 63c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC4 = 4.16666666666666666666666666666666225e-2L, /* 0x1555555555555555555555555554e.0p-117L */ 64c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC6 = 1.38888888888888888888888888889434831e-3L, /* 0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */ 65c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC8 = 2.48015873015873015873015871870962089e-5L, /* 0x1a01a01a01a01a01a01a017af2756.0p-128L */ 66c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC10 = 2.75573192239858906525574318600800201e-7L, /* 0x127e4fb7789f5c72ef01c8a040640.0p-134L */ 67c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC12 = 2.08767569878680989791444691755468269e-9L, /* 0x11eed8eff8d897b543d0679607399.0p-141L */ 68c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC14= 1.14707455977297247387801189650495351e-11L, /* 0x193974a8c07c9d24ae169a7fa9b54.0p-149L */ 69c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC16 = 4.77947733238737883626416876486279985e-14L; /* 0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */ 70c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const double 71c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC2 = 0.5, 72c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC18 = 1.5619206968597871e-16, /* 0x16827863b9900b.0p-105 */ 73c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC20 = 4.1103176218528049e-19, /* 0x1e542ba3d3c269.0p-114 */ 74c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC22 = 8.8967926401641701e-22, /* 0x10ce399542a014.0p-122 */ 75c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC24 = 1.6116681626523904e-24, /* 0x1f2c981d1f0cb7.0p-132 */ 76c729d4f23771a01226c761423c6b35210dbb6ca7Elliott HughesC26 = 2.5022374732804632e-27; /* 0x18c7ecf8b2c4a0.0p-141 */ 77c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#else 78c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#error "Unsupported long double format" 79c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#endif /* LDBL_MANT_DIG == 64 */ 80c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 81c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes/* log(2**16385 - 0.5) rounded up: */ 82c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughesstatic const float 83c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hugheso_threshold = 1.13572168e4; /* 0xb174de.0p-10 */ 84c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 85c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hugheslong double 86c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughescoshl(long double x) 87c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes{ 88c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes long double hi,lo,x2,x4; 89c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes double dx2; 90c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes uint16_t ix; 91c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 92c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes GET_LDBL_EXPSIGN(ix,x); 93c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes ix &= 0x7fff; 94c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 95c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes /* x is INF or NaN */ 96c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if(ix>=0x7fff) return x*x; 97c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 98c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes ENTERI(); 99c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 100c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes /* |x| < 1, return 1 or c(x) */ 101c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if(ix<0x3fff) { 102c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x| < TINY */ 103c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes RETURNI(1+tiny); /* cosh(tiny) = 1(+) with inexact */ 104c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes x2 = x*x; 105c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#if LDBL_MANT_DIG == 64 106c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes x4 = x2*x2; 107c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) + 108c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes ((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1); 109c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#elif LDBL_MANT_DIG == 113 110c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes dx2 = x2; 111c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 + 112c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes C20)*x2 + C18)*x2 + 113c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 + 114c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes C4)*(x2*x2) + C2*x2 + 1); 115c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes#endif 116c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes } 117c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 118c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes /* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */ 119c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if (ix < 0x4005) { 120c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes k_hexpl(fabsl(x), &hi, &lo); 121c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes RETURNI(lo + 0.25/(hi + lo) + hi); 122c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes } 123c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 124c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes /* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */ 125c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes if (fabsl(x) <= o_threshold) 126c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes RETURNI(hexpl(fabsl(x))); 127c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes 128c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes /* |x| > o_threshold, cosh(x) overflow */ 129c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes RETURNI(huge*huge); 130c729d4f23771a01226c761423c6b35210dbb6ca7Elliott Hughes} 131