1 /* from: FreeBSD: head/lib/msun/src/e_coshl.c XXX */ 2 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunPro, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 #include <sys/cdefs.h> 15 /* 16 * See e_cosh.c for complete comments. 17 * 18 * Converted to long double by Bruce D. Evans. 19 */ 20 21 #include "namespace.h" 22 #include <float.h> 23 24 __weak_alias(coshl, _coshl) 25 26 #ifdef __HAVE_LONG_DOUBLE 27 #error SHOULD STOP HERE!!! 28 29 #ifdef __i386__ 30 #include <ieeefp.h> 31 #endif 32 33 #include "math.h" 34 #include "math_private.h" 35 #if LDBL_MANT_DIG == 64 36 #include "../ld80/k_expl.h" 37 #elif LDBL_MANT_DIG == 113 38 #include "../ld128/k_expl.h" 39 #else 40 #error "Unsupported long double format" 41 #endif 42 43 #if LDBL_MAX_EXP != 0x4000 44 /* We also require the usual expsign encoding. */ 45 #error "Unsupported long double format" 46 #endif 47 48 #define BIAS (LDBL_MAX_EXP - 1) 49 50 static const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L; 51 #if LDBL_MANT_DIG == 64 52 /* 53 * Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]: 54 * |cosh(x) - c(x)| < 2**-68.8 55 */ 56 static const union ieee_ext_u 57 C4u = LD80C(0xaaaaaaaaaaaaac78, -5, 4.16666666666666682297e-2L); 58 #define C4 C4u.extu_ld 59 static const double 60 C2 = 0.5, 61 C6 = 1.3888888888888616e-3, /* 0x16c16c16c16b99.0p-62 */ 62 C8 = 2.4801587301767953e-5, /* 0x1a01a01a027061.0p-68 */ 63 C10 = 2.7557319163300398e-7, /* 0x127e4fb6c9b55f.0p-74 */ 64 C12 = 2.0876768371393075e-9, /* 0x11eed99406a3f4.0p-81 */ 65 C14 = 1.1469537039374480e-11, /* 0x1938c67cd18c48.0p-89 */ 66 C16 = 4.8473490896852041e-14; /* 0x1b49c429701e45.0p-97 */ 67 #elif LDBL_MANT_DIG == 113 68 /* 69 * Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]: 70 * |cosh(x) - c(x)| < 2**-121.69 71 */ 72 static const long double 73 C4 = 4.16666666666666666666666666666666225e-2L, /* 0x1555555555555555555555555554e.0p-117L */ 74 C6 = 1.38888888888888888888888888889434831e-3L, /* 0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */ 75 C8 = 2.48015873015873015873015871870962089e-5L, /* 0x1a01a01a01a01a01a01a017af2756.0p-128L */ 76 C10 = 2.75573192239858906525574318600800201e-7L, /* 0x127e4fb7789f5c72ef01c8a040640.0p-134L */ 77 C12 = 2.08767569878680989791444691755468269e-9L, /* 0x11eed8eff8d897b543d0679607399.0p-141L */ 78 C14= 1.14707455977297247387801189650495351e-11L, /* 0x193974a8c07c9d24ae169a7fa9b54.0p-149L */ 79 C16 = 4.77947733238737883626416876486279985e-14L; /* 0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */ 80 static const double 81 C2 = 0.5, 82 C18 = 1.5619206968597871e-16, /* 0x16827863b9900b.0p-105 */ 83 C20 = 4.1103176218528049e-19, /* 0x1e542ba3d3c269.0p-114 */ 84 C22 = 8.8967926401641701e-22, /* 0x10ce399542a014.0p-122 */ 85 C24 = 1.6116681626523904e-24, /* 0x1f2c981d1f0cb7.0p-132 */ 86 C26 = 2.5022374732804632e-27; /* 0x18c7ecf8b2c4a0.0p-141 */ 87 #else 88 #error "Unsupported long double format" 89 #endif /* LDBL_MANT_DIG == 64 */ 90 91 /* log(2**16385 - 0.5) rounded up: */ 92 static const float 93 o_threshold = 1.13572168e4; /* 0xb174de.0p-10 */ 94 95 long double 96 coshl(long double x) 97 { 98 long double hi,lo,x2; 99 #if LDBL_MANT_DIG == 113 100 double dx2; 101 #endif 102 uint16_t ix; 103 104 GET_LDBL_EXPSIGN(ix,x); 105 ix &= 0x7fff; 106 107 /* x is INF or NaN */ 108 if(ix>=0x7fff) return x*x; 109 110 ENTERI(); 111 112 /* |x| < 1, return 1 or c(x) */ 113 if(ix<0x3fff) { 114 if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x| < TINY */ 115 RETURNI(1+tiny); /* cosh(tiny) = 1(+) with inexact */ 116 x2 = x*x; 117 #if LDBL_MANT_DIG == 64 118 long double x4 = x2*x2; 119 RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) + 120 ((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1); 121 #elif LDBL_MANT_DIG == 113 122 dx2 = x2; 123 RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 + 124 C20)*x2 + C18)*x2 + 125 C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 + 126 C4)*(x2*x2) + C2*x2 + 1); 127 #endif 128 } 129 130 /* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */ 131 if (ix < 0x4005) { 132 k_hexpl(fabsl(x), &hi, &lo); 133 RETURNI(lo + 0.25/(hi + lo) + hi); 134 } 135 136 /* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */ 137 if (fabsl(x) <= o_threshold) 138 RETURNI(hexpl(fabsl(x))); 139 140 /* |x| > o_threshold, cosh(x) overflow */ 141 RETURNI(huge*huge); 142 } 143 #else 144 #include "math.h" 145 146 long double 147 coshl(long double x) 148 { 149 return cosh(x); 150 } 151 152 #endif 153