| /* e_acoshl.c -- long double version of e_acosh.c. | |
| * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. | |
| */ | |
| /* | |
| * ==================================================== | |
| * 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. | |
| * ==================================================== | |
| */ | |
| /* acoshq(x) | |
| * Method : | |
| * Based on | |
| * acoshl(x) = logq [ x + sqrtq(x*x-1) ] | |
| * we have | |
| * acoshl(x) := logq(x)+ln2, if x is large; else | |
| * acoshl(x) := logq(2x-1/(sqrtq(x*x-1)+x)) if x>2; else | |
| * acoshl(x) := log1pq(t+sqrtq(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 "quadmath-imp.h" | |
| static const __float128 | |
| one = 1.0, | |
| ln2 = 0.6931471805599453094172321214581766Q; | |
| __float128 | |
| acoshq(__float128 x) | |
| { | |
| __float128 t; | |
| uint64_t lx; | |
| int64_t hx; | |
| GET_FLT128_WORDS64(hx,lx,x); | |
| if(hx<0x3fff000000000000LL) { /* x < 1 */ | |
| return (x-x)/(x-x); | |
| } else if(hx >=0x4035000000000000LL) { /* x > 2**54 */ | |
| if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */ | |
| return x+x; | |
| } else | |
| return logq(x)+ln2; /* acoshl(huge)=logq(2x) */ | |
| } else if(((hx-0x3fff000000000000LL)|lx)==0) { | |
| return 0; /* acosh(1) = 0 */ | |
| } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */ | |
| t=x*x; | |
| return logq(2*x-one/(x+sqrtq(t-one))); | |
| } else { /* 1<x<2 */ | |
| t = x-one; | |
| return log1pq(t+sqrtq(2*t+t*t)); | |
| } | |
| } |