1/* e_acoshl.c -- long double version of e_acosh.c. 2 * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz. 3 */ 4 5/* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16/* acoshq(x) 17 * Method : 18 * Based on 19 * acoshl(x) = logq [ x + sqrtq(x*x-1) ] 20 * we have 21 * acoshl(x) := logq(x)+ln2, if x is large; else 22 * acoshl(x) := logq(2x-1/(sqrtq(x*x-1)+x)) if x>2; else 23 * acoshl(x) := log1pq(t+sqrtq(2.0*t+t*t)); where t=x-1. 24 * 25 * Special cases: 26 * acoshl(x) is NaN with signal if x<1. 27 * acoshl(NaN) is NaN without signal. 28 */ 29 30#include "quadmath-imp.h" 31 32static const __float128 33one = 1.0, 34ln2 = 0.6931471805599453094172321214581766Q; 35 36__float128 37acoshq(__float128 x) 38{ 39 __float128 t; 40 uint64_t lx; 41 int64_t hx; 42 GET_FLT128_WORDS64(hx,lx,x); 43 if(hx<0x3fff000000000000LL) { /* x < 1 */ 44 return (x-x)/(x-x); 45 } else if(hx >=0x4035000000000000LL) { /* x > 2**54 */ 46 if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */ 47 return x+x; 48 } else 49 return logq(x)+ln2; /* acoshl(huge)=logq(2x) */ 50 } else if(((hx-0x3fff000000000000LL)|lx)==0) { 51 return 0; /* acosh(1) = 0 */ 52 } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */ 53 t=x*x; 54 return logq(2*x-one/(x+sqrtq(t-one))); 55 } else { /* 1<x<2 */ 56 t = x-one; 57 return log1pq(t+sqrtq(2*t+t*t)); 58 } 59} 60