1 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, 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 14 /* acosh(x) 15 * Method : 16 * Based on 17 * acosh(x) = log [ x + sqrt(x*x-1) ] 18 * we have 19 * acosh(x) := log(x)+ln2, if x is large; else 20 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else 21 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. 22 * 23 * Special cases: 24 * acosh(x) is NaN with signal if x<1. 25 * acosh(NaN) is NaN without signal. 26 */ 27 28 #include <float.h> 29 30 #include "math.h" 31 #include "math_private.h" 32 33 static const double 34 one = 1.0, 35 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 36 37 double 38 acosh(double x) 39 { 40 double t; 41 int32_t hx; 42 u_int32_t lx; 43 EXTRACT_WORDS(hx,lx,x); 44 if(hx<0x3ff00000) { /* x < 1 */ 45 return (x-x)/(x-x); 46 } else if(hx >=0x41b00000) { /* x > 2**28 */ 47 if(hx >=0x7ff00000) { /* x is inf of NaN */ 48 return x+x; 49 } else 50 return log(x)+ln2; /* acosh(huge)=log(2x) */ 51 } else if(((hx-0x3ff00000)|lx)==0) { 52 return 0.0; /* acosh(1) = 0 */ 53 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 54 t=x*x; 55 return log(2.0*x-one/(x+sqrt(t-one))); 56 } else { /* 1<x<2 */ 57 t = x-one; 58 return log1p(t+sqrt(2.0*t+t*t)); 59 } 60 } 61 62 #if LDBL_MANT_DIG == 53 63 __weak_reference(acosh, acoshl); 64 #endif 65