| /* 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)); |
| } |
| } |
