projects / thirdparty / glibc.git / blame
| Commit | Line | Data |
|---|---|---|
| f964490f RM |
1 | /* @(#)e_acosh.c 5.1 93/09/24 */ |
| 2 | /* | |
| 3 | * ==================================================== | |
| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
| 5 | * | |
| 6 | * Developed at SunPro, 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 | ||
| f964490f RM |
13 | /* __ieee754_acosh(x) |
| 14 | * Method : | |
| 15 | * Based on | |
| 16 | * acosh(x) = log [ x + sqrt(x*x-1) ] | |
| 17 | * we have | |
| 18 | * acosh(x) := log(x)+ln2, if x is large; else | |
| 19 | * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else | |
| 20 | * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. | |
| 21 | * | |
| 22 | * Special cases: | |
| 23 | * acosh(x) is NaN with signal if x<1. | |
| 24 | * acosh(NaN) is NaN without signal. | |
| 25 | */ | |
| 26 | ||
| 1ed0291c RH |
27 | #include <math.h> |
| 28 | #include <math_private.h> | |
| f964490f | 29 | |
| f964490f | 30 | static const long double |
| f964490f | 31 | one = 1.0L, |
| 396e3ecf | 32 | ln2 = M_LN2l; |
| f964490f | 33 | |
| 0ac5ae23 UD |
34 | long double |
| 35 | __ieee754_acoshl(long double x) | |
| f964490f RM |
36 | { |
| 37 | long double t; | |
| 38 | int64_t hx; | |
| 4ebd120c AM |
39 | uint64_t lx; |
| 40 | double xhi, xlo; | |
| 41 | ||
| 42 | ldbl_unpack (x, &xhi, &xlo); | |
| 43 | EXTRACT_WORDS64 (hx, xhi); | |
| 44 | EXTRACT_WORDS64 (lx, xlo); | |
| f964490f RM |
45 | if(hx<0x3ff0000000000000LL) { /* x < 1 */ |
| 46 | return (x-x)/(x-x); | |
| 440169d6 | 47 | } else if(hx >=0x4370000000000000LL) { /* x >= 2**56 */ |
| f964490f | 48 | if(hx >=0x7ff0000000000000LL) { /* x is inf of NaN */ |
| 0ac5ae23 | 49 | return x+x; |
| f964490f RM |
50 | } else |
| 51 | return __ieee754_logl(x)+ln2; /* acosh(huge)=log(2x) */ | |
| 52 | } else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) { | |
| 53 | return 0.0; /* acosh(1) = 0 */ | |
| 440169d6 | 54 | } else if (hx > 0x4000000000000000LL) { /* 2**56 > x > 2 */ |
| f964490f RM |
55 | t=x*x; |
| 56 | return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one))); | |
| 57 | } else { /* 1<x<2 */ | |
| 58 | t = x-one; | |
| 396e3ecf | 59 | return __log1pl(t+__ieee754_sqrtl(2.0*t+t*t)); |
| f964490f RM |
60 | } |
| 61 | } | |
| 0ac5ae23 | 62 | strong_alias (__ieee754_acoshl, __acoshl_finite) |