diff options
Diffstat (limited to 'lib/msun/src/e_coshl.c')
| -rw-r--r-- | lib/msun/src/e_coshl.c | 130 |
1 files changed, 130 insertions, 0 deletions
diff --git a/lib/msun/src/e_coshl.c b/lib/msun/src/e_coshl.c new file mode 100644 index 0000000..0a21277 --- /dev/null +++ b/lib/msun/src/e_coshl.c @@ -0,0 +1,130 @@ +/* from: FreeBSD: head/lib/msun/src/e_coshl.c XXX */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +/* + * See e_cosh.c for complete comments. + * + * Converted to long double by Bruce D. Evans. + */ + +#include <float.h> +#ifdef __i386__ +#include <ieeefp.h> +#endif + +#include "fpmath.h" +#include "math.h" +#include "math_private.h" +#include "k_expl.h" + +#if LDBL_MAX_EXP != 0x4000 +/* We also require the usual expsign encoding. */ +#error "Unsupported long double format" +#endif + +#define BIAS (LDBL_MAX_EXP - 1) + +static const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L; +#if LDBL_MANT_DIG == 64 +/* + * Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]: + * |cosh(x) - c(x)| < 2**-68.8 + */ +static const union IEEEl2bits +C4u = LD80C(0xaaaaaaaaaaaaac78, -5, 4.16666666666666682297e-2L); +#define C4 C4u.e +static const double +C2 = 0.5, +C6 = 1.3888888888888616e-3, /* 0x16c16c16c16b99.0p-62 */ +C8 = 2.4801587301767953e-5, /* 0x1a01a01a027061.0p-68 */ +C10 = 2.7557319163300398e-7, /* 0x127e4fb6c9b55f.0p-74 */ +C12 = 2.0876768371393075e-9, /* 0x11eed99406a3f4.0p-81 */ +C14 = 1.1469537039374480e-11, /* 0x1938c67cd18c48.0p-89 */ +C16 = 4.8473490896852041e-14; /* 0x1b49c429701e45.0p-97 */ +#elif LDBL_MANT_DIG == 113 +/* + * Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]: + * |cosh(x) - c(x)| < 2**-121.69 + */ +static const long double +C4 = 4.16666666666666666666666666666666225e-2L, /* 0x1555555555555555555555555554e.0p-117L */ +C6 = 1.38888888888888888888888888889434831e-3L, /* 0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */ +C8 = 2.48015873015873015873015871870962089e-5L, /* 0x1a01a01a01a01a01a01a017af2756.0p-128L */ +C10 = 2.75573192239858906525574318600800201e-7L, /* 0x127e4fb7789f5c72ef01c8a040640.0p-134L */ +C12 = 2.08767569878680989791444691755468269e-9L, /* 0x11eed8eff8d897b543d0679607399.0p-141L */ +C14= 1.14707455977297247387801189650495351e-11L, /* 0x193974a8c07c9d24ae169a7fa9b54.0p-149L */ +C16 = 4.77947733238737883626416876486279985e-14L; /* 0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */ +static const double +C2 = 0.5, +C18 = 1.5619206968597871e-16, /* 0x16827863b9900b.0p-105 */ +C20 = 4.1103176218528049e-19, /* 0x1e542ba3d3c269.0p-114 */ +C22 = 8.8967926401641701e-22, /* 0x10ce399542a014.0p-122 */ +C24 = 1.6116681626523904e-24, /* 0x1f2c981d1f0cb7.0p-132 */ +C26 = 2.5022374732804632e-27; /* 0x18c7ecf8b2c4a0.0p-141 */ +#else +#error "Unsupported long double format" +#endif /* LDBL_MANT_DIG == 64 */ + +/* log(2**16385 - 0.5) rounded up: */ +static const float +o_threshold = 1.13572168e4; /* 0xb174de.0p-10 */ + +long double +coshl(long double x) +{ + long double hi,lo,x2,x4; + double dx2; + uint16_t ix; + + GET_LDBL_EXPSIGN(ix,x); + ix &= 0x7fff; + + /* x is INF or NaN */ + if(ix>=0x7fff) return x*x; + + ENTERI(); + + /* |x| < 1, return 1 or c(x) */ + if(ix<0x3fff) { + if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x| < TINY */ + RETURNI(1+tiny); /* cosh(tiny) = 1(+) with inexact */ + x2 = x*x; +#if LDBL_MANT_DIG == 64 + x4 = x2*x2; + RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) + + ((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1); +#elif LDBL_MANT_DIG == 113 + dx2 = x2; + RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 + + C20)*x2 + C18)*x2 + + C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 + + C4)*(x2*x2) + C2*x2 + 1); +#endif + } + + /* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */ + if (ix < 0x4005) { + k_hexpl(fabsl(x), &hi, &lo); + RETURNI(lo + 0.25/(hi + lo) + hi); + } + + /* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */ + if (fabsl(x) <= o_threshold) + RETURNI(hexpl(fabsl(x))); + + /* |x| > o_threshold, cosh(x) overflow */ + RETURNI(huge*huge); +} |
