1 /* @(#)e_acosh.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 /* acosh(x) 14 * Method : 15 * Based on 16 * acosh(x) = log [ x + sqrt(x*x-1) ] 17 * we have 18 * acosh(x) := log(x)+ln2, if x is large; else 19 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else 20 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. 21 * 22 * Special cases: 23 * acosh(x) is NaN with signal if x<1. 24 * acosh(NaN) is NaN without signal. 25 */ 26 27 #include <float.h> 28 #include <math.h> 29 30 #include "math_private.h" 31 32 static const double 33 one = 1.0, 34 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 35 36 double 37 acosh(double x) 38 { 39 double t; 40 int32_t hx; 41 u_int32_t lx; 42 EXTRACT_WORDS(hx,lx,x); 43 if(hx<0x3ff00000) { /* x < 1 */ 44 return (x-x)/(x-x); 45 } else if(hx >=0x41b00000) { /* x > 2**28 */ 46 if(hx >=0x7ff00000) { /* x is inf of NaN */ 47 return x+x; 48 } else 49 return log(x)+ln2; /* acosh(huge)=log(2x) */ 50 } else if(((hx-0x3ff00000)|lx)==0) { 51 return 0.0; /* acosh(1) = 0 */ 52 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 53 t=x*x; 54 return log(2.0*x-one/(x+sqrt(t-one))); 55 } else { /* 1<x<2 */ 56 t = x-one; 57 return log1p(t+sqrt(2.0*t+t*t)); 58 } 59 } 60 61 #if LDBL_MANT_DIG == DBL_MANT_DIG 62 __strong_alias(acoshl, acosh); 63 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 64