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 #include <sys/cdefs.h> 15 /* 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 <float.h> 30 31 #include "math.h" 32 #include "math_private.h" 33 34 static const double 35 one = 1.0, 36 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 37 38 double 39 acosh(double x) 40 { 41 double t; 42 int32_t hx; 43 u_int32_t lx; 44 EXTRACT_WORDS(hx,lx,x); 45 if(hx<0x3ff00000) { /* x < 1 */ 46 return (x-x)/(x-x); 47 } else if(hx >=0x41b00000) { /* x > 2**28 */ 48 if(hx >=0x7ff00000) { /* x is inf of NaN */ 49 return x+x; 50 } else 51 return log(x)+ln2; /* acosh(huge)=log(2x) */ 52 } else if(((hx-0x3ff00000)|lx)==0) { 53 return 0.0; /* acosh(1) = 0 */ 54 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 55 t=x*x; 56 return log(2.0*x-one/(x+sqrt(t-one))); 57 } else { /* 1<x<2 */ 58 t = x-one; 59 return log1p(t+sqrt(2.0*t+t*t)); 60 } 61 } 62 63 #if LDBL_MANT_DIG == 53 64 __weak_reference(acosh, acoshl); 65 #endif 66