1260067Skargl/* from: FreeBSD: head/lib/msun/src/e_coshl.c XXX */ 2260067Skargl 3260067Skargl/* 4260067Skargl * ==================================================== 5260067Skargl * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6260067Skargl * 7260067Skargl * Developed at SunPro, a Sun Microsystems, Inc. business. 8260067Skargl * Permission to use, copy, modify, and distribute this 9260067Skargl * software is freely granted, provided that this notice 10260067Skargl * is preserved. 11260067Skargl * ==================================================== 12260067Skargl */ 13260067Skargl 14260067Skargl#include <sys/cdefs.h> 15260067Skargl__FBSDID("$FreeBSD$"); 16260067Skargl 17260067Skargl/* 18260067Skargl * See e_cosh.c for complete comments. 19260067Skargl * 20260067Skargl * Converted to long double by Bruce D. Evans. 21260067Skargl */ 22260067Skargl 23260067Skargl#include <float.h> 24260067Skargl#ifdef __i386__ 25260067Skargl#include <ieeefp.h> 26260067Skargl#endif 27260067Skargl 28260067Skargl#include "fpmath.h" 29260067Skargl#include "math.h" 30260067Skargl#include "math_private.h" 31260067Skargl#include "k_expl.h" 32260067Skargl 33260067Skargl#if LDBL_MAX_EXP != 0x4000 34260067Skargl/* We also require the usual expsign encoding. */ 35260067Skargl#error "Unsupported long double format" 36260067Skargl#endif 37260067Skargl 38260067Skargl#define BIAS (LDBL_MAX_EXP - 1) 39260067Skargl 40260067Skarglstatic const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L; 41260067Skargl#if LDBL_MANT_DIG == 64 42260067Skargl/* 43260067Skargl * Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]: 44260067Skargl * |cosh(x) - c(x)| < 2**-68.8 45260067Skargl */ 46260067Skarglstatic const union IEEEl2bits 47260067SkarglC4u = LD80C(0xaaaaaaaaaaaaac78, -5, 4.16666666666666682297e-2L); 48260067Skargl#define C4 C4u.e 49260067Skarglstatic const double 50260067SkarglC2 = 0.5, 51260067SkarglC6 = 1.3888888888888616e-3, /* 0x16c16c16c16b99.0p-62 */ 52260067SkarglC8 = 2.4801587301767953e-5, /* 0x1a01a01a027061.0p-68 */ 53260067SkarglC10 = 2.7557319163300398e-7, /* 0x127e4fb6c9b55f.0p-74 */ 54260067SkarglC12 = 2.0876768371393075e-9, /* 0x11eed99406a3f4.0p-81 */ 55260067SkarglC14 = 1.1469537039374480e-11, /* 0x1938c67cd18c48.0p-89 */ 56260067SkarglC16 = 4.8473490896852041e-14; /* 0x1b49c429701e45.0p-97 */ 57260067Skargl#elif LDBL_MANT_DIG == 113 58260067Skargl/* 59260067Skargl * Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]: 60260067Skargl * |cosh(x) - c(x)| < 2**-121.69 61260067Skargl */ 62260067Skarglstatic const long double 63260067SkarglC4 = 4.16666666666666666666666666666666225e-2L, /* 0x1555555555555555555555555554e.0p-117L */ 64260067SkarglC6 = 1.38888888888888888888888888889434831e-3L, /* 0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */ 65260067SkarglC8 = 2.48015873015873015873015871870962089e-5L, /* 0x1a01a01a01a01a01a01a017af2756.0p-128L */ 66260067SkarglC10 = 2.75573192239858906525574318600800201e-7L, /* 0x127e4fb7789f5c72ef01c8a040640.0p-134L */ 67260067SkarglC12 = 2.08767569878680989791444691755468269e-9L, /* 0x11eed8eff8d897b543d0679607399.0p-141L */ 68260067SkarglC14= 1.14707455977297247387801189650495351e-11L, /* 0x193974a8c07c9d24ae169a7fa9b54.0p-149L */ 69260067SkarglC16 = 4.77947733238737883626416876486279985e-14L; /* 0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */ 70260067Skarglstatic const double 71260067SkarglC2 = 0.5, 72260067SkarglC18 = 1.5619206968597871e-16, /* 0x16827863b9900b.0p-105 */ 73260067SkarglC20 = 4.1103176218528049e-19, /* 0x1e542ba3d3c269.0p-114 */ 74260067SkarglC22 = 8.8967926401641701e-22, /* 0x10ce399542a014.0p-122 */ 75260067SkarglC24 = 1.6116681626523904e-24, /* 0x1f2c981d1f0cb7.0p-132 */ 76260067SkarglC26 = 2.5022374732804632e-27; /* 0x18c7ecf8b2c4a0.0p-141 */ 77260067Skargl#else 78260067Skargl#error "Unsupported long double format" 79260067Skargl#endif /* LDBL_MANT_DIG == 64 */ 80260067Skargl 81271779Stijl/* log(2**16385 - 0.5) rounded up: */ 82260067Skarglstatic const float 83260067Skarglo_threshold = 1.13572168e4; /* 0xb174de.0p-10 */ 84260067Skargl 85260067Skargllong double 86260067Skarglcoshl(long double x) 87260067Skargl{ 88260067Skargl long double hi,lo,x2,x4; 89260067Skargl double dx2; 90260067Skargl uint16_t ix; 91260067Skargl 92260067Skargl GET_LDBL_EXPSIGN(ix,x); 93260067Skargl ix &= 0x7fff; 94260067Skargl 95260067Skargl /* x is INF or NaN */ 96260067Skargl if(ix>=0x7fff) return x*x; 97260067Skargl 98260067Skargl ENTERI(); 99260067Skargl 100260067Skargl /* |x| < 1, return 1 or c(x) */ 101260067Skargl if(ix<0x3fff) { 102260067Skargl if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x| < TINY */ 103260067Skargl RETURNI(1+tiny); /* cosh(tiny) = 1(+) with inexact */ 104260067Skargl x2 = x*x; 105260067Skargl#if LDBL_MANT_DIG == 64 106260067Skargl x4 = x2*x2; 107260067Skargl RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) + 108260067Skargl ((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1); 109260067Skargl#elif LDBL_MANT_DIG == 113 110260067Skargl dx2 = x2; 111260067Skargl RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 + 112260067Skargl C20)*x2 + C18)*x2 + 113260067Skargl C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 + 114260067Skargl C4)*(x2*x2) + C2*x2 + 1); 115260067Skargl#endif 116260067Skargl } 117260067Skargl 118260067Skargl /* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */ 119260067Skargl if (ix < 0x4005) { 120260067Skargl k_hexpl(fabsl(x), &hi, &lo); 121260067Skargl RETURNI(lo + 0.25/(hi + lo) + hi); 122260067Skargl } 123260067Skargl 124260067Skargl /* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */ 125260067Skargl if (fabsl(x) <= o_threshold) 126260067Skargl RETURNI(hexpl(fabsl(x))); 127260067Skargl 128260067Skargl /* |x| > o_threshold, cosh(x) overflow */ 129260067Skargl RETURNI(huge*huge); 130260067Skargl} 131