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 #include <sys/cdefs.h> 16 __FBSDID("$FreeBSD$"); 17 18 /* __ieee754_acosh(x) 19 * Method : 20 * Based on 21 * acosh(x) = log [ x + sqrt(x*x-1) ] 22 * we have 23 * acosh(x) := log(x)+ln2, if x is large; else 24 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else 25 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. 26 * 27 * Special cases: 28 * acosh(x) is NaN with signal if x<1. 29 * acosh(NaN) is NaN without signal. 30 */ 31 32 #include <float.h> 33 34 #include "math.h" 35 #include "math_private.h" 36 37 static const double 38 one = 1.0, 39 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ 40 41 double 42 __ieee754_acosh(double x) 43 { 44 double t; 45 int32_t hx; 46 u_int32_t lx; 47 EXTRACT_WORDS(hx,lx,x); 48 if(hx<0x3ff00000) { /* x < 1 */ 49 return (x-x)/(x-x); 50 } else if(hx >=0x41b00000) { /* x > 2**28 */ 51 if(hx >=0x7ff00000) { /* x is inf of NaN */ 52 return x+x; 53 } else 54 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ 55 } else if(((hx-0x3ff00000)|lx)==0) { 56 return 0.0; /* acosh(1) = 0 */ 57 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 58 t=x*x; 59 return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); 60 } else { /* 1<x<2 */ 61 t = x-one; 62 return log1p(t+sqrt(2.0*t+t*t)); 63 } 64 } 65 66 #if LDBL_MANT_DIG == 53 67 __weak_reference(acosh, acoshl); 68 #endif 69