| The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 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 | #ifndef lint |
| 16 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_acosh.c,v 1.8 2005/02/04 18:26:05 das Exp $"; |
| 17 | #endif |
| 18 | |
| 19 | /* __ieee754_acosh(x) |
| 20 | * Method : |
| 21 | * Based on |
| 22 | * acosh(x) = log [ x + sqrt(x*x-1) ] |
| 23 | * we have |
| 24 | * acosh(x) := log(x)+ln2, if x is large; else |
| 25 | * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else |
| 26 | * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. |
| 27 | * |
| 28 | * Special cases: |
| 29 | * acosh(x) is NaN with signal if x<1. |
| 30 | * acosh(NaN) is NaN without signal. |
| 31 | */ |
| 32 | |
| 33 | #include "math.h" |
| 34 | #include "math_private.h" |
| 35 | |
| 36 | static const double |
| 37 | one = 1.0, |
| 38 | ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ |
| 39 | |
| 40 | double |
| 41 | __ieee754_acosh(double x) |
| 42 | { |
| 43 | double t; |
| 44 | int32_t hx; |
| 45 | u_int32_t lx; |
| 46 | EXTRACT_WORDS(hx,lx,x); |
| 47 | if(hx<0x3ff00000) { /* x < 1 */ |
| 48 | return (x-x)/(x-x); |
| 49 | } else if(hx >=0x41b00000) { /* x > 2**28 */ |
| 50 | if(hx >=0x7ff00000) { /* x is inf of NaN */ |
| 51 | return x+x; |
| 52 | } else |
| 53 | return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ |
| 54 | } else if(((hx-0x3ff00000)|lx)==0) { |
| 55 | return 0.0; /* acosh(1) = 0 */ |
| 56 | } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ |
| 57 | t=x*x; |
| 58 | return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); |
| 59 | } else { /* 1<x<2 */ |
| 60 | t = x-one; |
| 61 | return log1p(t+sqrt(2.0*t+t*t)); |
| 62 | } |
| 63 | } |