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