| /* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */ |
| |
| /* @(#)e_acosh.c 1.3 95/01/18 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunSoft, 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_acosh.c for complete comments. |
| * |
| * Converted to long double by David Schultz <das@FreeBSD.ORG> and |
| * Bruce D. Evans. |
| */ |
| |
| #include <float.h> |
| #ifdef __i386__ |
| #include <ieeefp.h> |
| #endif |
| |
| #include "fpmath.h" |
| #include "math.h" |
| #include "math_private.h" |
| |
| /* EXP_LARGE is the threshold above which we use acosh(x) ~= log(2x). */ |
| #if LDBL_MANT_DIG == 64 |
| #define EXP_LARGE 34 |
| #elif LDBL_MANT_DIG == 113 |
| #define EXP_LARGE 58 |
| #else |
| #error "Unsupported long double format" |
| #endif |
| |
| #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 double |
| one = 1.0; |
| |
| #if LDBL_MANT_DIG == 64 |
| static const union IEEEl2bits |
| u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L); |
| #define ln2 u_ln2.e |
| #elif LDBL_MANT_DIG == 113 |
| static const long double |
| ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */ |
| #else |
| #error "Unsupported long double format" |
| #endif |
| |
| long double |
| acoshl(long double x) |
| { |
| long double t; |
| int16_t hx; |
| |
| ENTERI(); |
| GET_LDBL_EXPSIGN(hx, x); |
| if (hx < 0x3fff) { /* x < 1, or misnormal */ |
| RETURNI((x-x)/(x-x)); |
| } else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */ |
| if (hx >= 0x7fff) { /* x is inf, NaN or misnormal */ |
| RETURNI(x+x); |
| } else |
| RETURNI(logl(x)+ln2); /* acosh(huge)=log(2x), or misnormal */ |
| } else if (hx == 0x3fff && x == 1) { |
| RETURNI(0.0); /* acosh(1) = 0 */ |
| } else if (hx >= 0x4000) { /* LARGE > x >= 2, or misnormal */ |
| t=x*x; |
| RETURNI(logl(2.0*x-one/(x+sqrtl(t-one)))); |
| } else { /* 1<x<2 */ |
| t = x-one; |
| RETURNI(log1pl(t+sqrtl(2.0*t+t*t))); |
| } |
| } |