| /* @(#)e_acosh.c 5.1 93/09/24 */ |
| /* |
| * ==================================================== |
| * 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. |
| * ==================================================== |
| */ |
| |
| /* __ieee754_acosh(x) |
| * Method : |
| * Based on |
| * acosh(x) = log [ x + sqrt(x*x-1) ] |
| * we have |
| * acosh(x) := log(x)+ln2, if x is large; else |
| * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else |
| * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. |
| * |
| * Special cases: |
| * acosh(x) is NaN with signal if x<1. |
| * acosh(NaN) is NaN without signal. |
| */ |
| |
| #include <math.h> |
| #include <math_private.h> |
| |
| static const long double |
| one = 1.0L, |
| ln2 = M_LN2l; |
| |
| long double |
| __ieee754_acoshl(long double x) |
| { |
| long double t; |
| int64_t hx; |
| uint64_t lx; |
| double xhi, xlo; |
| |
| ldbl_unpack (x, &xhi, &xlo); |
| EXTRACT_WORDS64 (hx, xhi); |
| EXTRACT_WORDS64 (lx, xlo); |
| if(hx<0x3ff0000000000000LL) { /* x < 1 */ |
| return (x-x)/(x-x); |
| } else if(hx >=0x41b0000000000000LL) { /* x > 2**28 */ |
| if(hx >=0x7ff0000000000000LL) { /* x is inf of NaN */ |
| return x+x; |
| } else |
| return __ieee754_logl(x)+ln2; /* acosh(huge)=log(2x) */ |
| } else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) { |
| return 0.0; /* acosh(1) = 0 */ |
| } else if (hx > 0x4000000000000000LL) { /* 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+__ieee754_sqrtl(2.0*t+t*t)); |
| } |
| } |
| strong_alias (__ieee754_acoshl, __acoshl_finite) |
