1 2 /* @(#)e_acosh.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, 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 + ieee_sqrt(x*x-1) ] 19 * we have 20 * acosh(x) := ieee_log(x)+ln2, if x is large; else 21 * acosh(x) := ieee_log(2x-1/(ieee_sqrt(x*x-1)+x)) if x>2; else 22 * acosh(x) := ieee_log1p(t+ieee_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 #ifdef __STDC__ 32 static const double 33 #else 34 static double 35 #endif 36 one = 1.0, 37 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 38 39 #ifdef __STDC__ 40 double __ieee754_acosh(double x) 41 #else 42 double __ieee754_acosh(x) 43 double x; 44 #endif 45 { 46 double t; 47 int hx; 48 hx = __HI(x); 49 if(hx<0x3ff00000) { /* x < 1 */ 50 return (x-x)/(x-x); 51 } else if(hx >=0x41b00000) { /* x > 2**28 */ 52 if(hx >=0x7ff00000) { /* x is inf of NaN */ 53 return x+x; 54 } else 55 return __ieee754_log(x)+ln2; /* acosh(huge)=ieee_log(2x) */ 56 } else if(((hx-0x3ff00000)|__LO(x))==0) { 57 return 0.0; /* acosh(1) = 0 */ 58 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 59 t=x*x; 60 return __ieee754_log(2.0*x-one/(x+ieee_sqrt(t-one))); 61 } else { /* 1<x<2 */ 62 t = x-one; 63 return ieee_log1p(t+ieee_sqrt(2.0*t+t*t)); 64 } 65 } 66
