| /* e_acoshl.c -- long double version of e_acosh.c. |
| * Conversion to long double by Ulrich Drepper, |
| * Cygnus Support, drepper@cygnus.com. |
| */ |
| |
| /* |
| * ==================================================== |
| * 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. |
| * ==================================================== |
| */ |
| |
| #if defined(LIBM_SCCS) && !defined(lint) |
| static char rcsid[] = "$NetBSD: $"; |
| #endif |
| |
| /* __ieee754_acoshl(x) |
| * Method : |
| * Based on |
| * acoshl(x) = logl [ x + sqrtl(x*x-1) ] |
| * we have |
| * acoshl(x) := logl(x)+ln2, if x is large; else |
| * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else |
| * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1. |
| * |
| * Special cases: |
| * acoshl(x) is NaN with signal if x<1. |
| * acoshl(NaN) is NaN without signal. |
| */ |
| |
| #include "math.h" |
| #include "math_private.h" |
| |
| #ifdef __STDC__ |
| static const long double |
| #else |
| static long double |
| #endif |
| one = 1.0, |
| ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ |
| |
| #ifdef __STDC__ |
| long double __ieee754_acoshl(long double x) |
| #else |
| long double __ieee754_acoshl(x) |
| long double x; |
| #endif |
| { |
| long double t; |
| u_int32_t se,i0,i1; |
| GET_LDOUBLE_WORDS(se,i0,i1,x); |
| if(se<0x3fff || se & 0x8000) { /* x < 1 */ |
| return (x-x)/(x-x); |
| } else if(se >=0x401d) { /* x > 2**30 */ |
| if(se >=0x7fff) { /* x is inf of NaN */ |
| return x+x; |
| } else |
| return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */ |
| } else if(((se-0x3fff)|i0|i1)==0) { |
| return 0.0; /* acosh(1) = 0 */ |
| } else if (se > 0x4000) { /* 2**28 > x > 2 */ |
| t=x*x; |
| return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one))); |
| } else { /* 1<x<2 */ |
| t = x-one; |
| return __log1pl(t+__sqrtl(2.0*t+t*t)); |
| } |
| } |
