1 2 /* @(#)e_acosh.c 5.1 93/09/24 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunPro, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 * 13 */ 14 15 /* __ieee754_acosh(x) 16 * Method : 17 * Based on 18 * acosh(x) = log [ x + sqrt(x*x-1) ] 19 * we have 20 * acosh(x) := log(x)+ln2, if x is large; else 21 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else 22 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. 23 * 24 * Special cases: 25 * acosh(x) is NaN with signal if x<1. 26 * acosh(NaN) is NaN without signal. 27 */ 28 29 #include "fdlibm.h" 30 31 #ifndef _DOUBLE_IS_32BITS 32 33 #ifdef __STDC__ 34 static const double 35 #else 36 static double 37 #endif 38 one = 1.0, 39 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 40 41 #ifdef __STDC__ __ieee754_acosh(double x)42 double __ieee754_acosh(double x) 43 #else 44 double __ieee754_acosh(x) 45 double x; 46 #endif 47 { 48 double t; 49 __int32_t hx; 50 __uint32_t lx; 51 EXTRACT_WORDS(hx,lx,x); 52 if(hx<0x3ff00000) { /* x < 1 */ 53 return (x-x)/(x-x); 54 } else if(hx >=0x41b00000) { /* x > 2**28 */ 55 if(hx >=0x7ff00000) { /* x is inf of NaN */ 56 return x+x; 57 } else 58 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ 59 } else if(((hx-0x3ff00000)|lx)==0) { 60 return 0.0; /* acosh(1) = 0 */ 61 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 62 t=x*x; 63 return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one))); 64 } else { /* 1<x<2 */ 65 t = x-one; 66 return log1p(t+__ieee754_sqrt(2.0*t+t*t)); 67 } 68 } 69 70 #endif /* defined(_DOUBLE_IS_32BITS) */ 71