| |
| /* @(#)e_acosh.c 1.3 95/01/18 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| * |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| /* __ieee754_acosh(x) |
| * Method : |
| * Based on |
| * acosh(x) = log [ x + sqrt(x*x-1) ] |
| * we have |
| * acosh(x) := log(x)+ln2, if x is large; else |
| * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else |
| * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. |
| * |
| * Special cases: |
| * acosh(x) is NaN with signal if x<1. |
| * acosh(NaN) is NaN without signal. |
| */ |
| |
| #include <float.h> |
| |
| #include "math.h" |
| #include "math_private.h" |
| |
| static const double |
| one = 1.0, |
| ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ |
| |
| double |
| __ieee754_acosh(double x) |
| { |
| double t; |
| int32_t hx; |
| u_int32_t lx; |
| EXTRACT_WORDS(hx,lx,x); |
| if(hx<0x3ff00000) { /* x < 1 */ |
| return (x-x)/(x-x); |
| } else if(hx >=0x41b00000) { /* x > 2**28 */ |
| if(hx >=0x7ff00000) { /* x is inf of NaN */ |
| return x+x; |
| } else |
| return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ |
| } else if(((hx-0x3ff00000)|lx)==0) { |
| return 0.0; /* acosh(1) = 0 */ |
| } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ |
| t=x*x; |
| return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); |
| } else { /* 1<x<2 */ |
| t = x-one; |
| return log1p(t+sqrt(2.0*t+t*t)); |
| } |
| } |
| |
| #if LDBL_MANT_DIG == 53 |
| __weak_reference(acosh, acoshl); |
| #endif |
