diff options
Diffstat (limited to 'src/math/coshl.c')
| -rw-r--r-- | src/math/coshl.c | 69 |
1 files changed, 14 insertions, 55 deletions
diff --git a/src/math/coshl.c b/src/math/coshl.c index 3ea56e00..d09070bb 100644 --- a/src/math/coshl.c +++ b/src/math/coshl.c @@ -1,35 +1,3 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_coshl.c */ -/* - * ==================================================== - * 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. - * ==================================================== - */ -/* coshl(x) - * Method : - * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 - * 1. Replace x by |x| (coshl(x) = coshl(-x)). - * 2. - * [ exp(x) - 1 ]^2 - * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- - * 2*exp(x) - * - * exp(x) + 1/exp(x) - * ln2/2 <= x <= 22 : coshl(x) := ------------------- - * 2 - * 22 <= x <= lnovft : coshl(x) := expl(x)/2 - * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) - * ln2ovft < x : coshl(x) := inf (overflow) - * - * Special cases: - * coshl(x) is |x| if x is +INF, -INF, or NaN. - * only coshl(0)=1 is exact for finite x. - */ - #include "libm.h" #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 @@ -45,41 +13,32 @@ long double coshl(long double x) struct{uint64_t m; uint16_t se; uint16_t pad;} i; } u = {.f = x}; unsigned ex = u.i.se & 0x7fff; + uint32_t w; long double t; - uint32_t mx,lx; /* |x| */ u.i.se = ex; x = u.f; - mx = u.i.m >> 32; - lx = u.i.m; + w = u.i.m >> 32; - /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ - if (ex < 0x3fff-2 || (ex == 0x3fff-2 && mx < 0xb17217f7)) { - t = expm1l(x); - if (ex < 0x3fff-64) + /* |x| < log(2) */ + if (ex < 0x3fff-1 || (ex == 0x3fff-1 && w < 0xb17217f7)) { + if (ex < 0x3fff-32) { + FORCE_EVAL(x + 0x1p120f); return 1; + } + t = expm1l(x); return 1 + t*t/(2*(1+t)); } - /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ - if (ex < 0x3fff+4 || (ex == 0x3fff+4 && mx < 0xb0000000)) { + /* |x| < log(LDBL_MAX) */ + if (ex < 0x3fff+13 || (ex == 0x3fff+13 && w < 0xb17217f7)) { t = expl(x); - return 0.5*t + 0.5/t; - } - - /* |x| in [22, ln(maxdouble)] return 0.5*exp(|x|) */ - if (ex < 0x3fff+13 || (ex == 0x3fff+13 && mx < 0xb1700000)) - return 0.5*expl(x); - - /* |x| in [log(maxdouble), log(2*maxdouble)) */ - if (ex == 0x3fff+13 && (mx < 0xb174ddc0 || - (mx == 0xb174ddc0 && lx < 0x31aec0eb))) { - t = expl(0.5*x); - return 0.5*t*t; + return 0.5*(t + 1/t); } - /* |x| >= log(2*maxdouble) or nan */ - return x*0x1p16383L; + /* |x| > log(LDBL_MAX) or nan */ + t = expl(0.5*x); + return 0.5*t*t; } #endif |