projects / thirdparty / glibc.git / blame
| Commit | Line | Data |
|---|---|---|
| f964490f RM |
1 | /* @(#)e_atanh.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_atanh(x) |
| 14 | * Method : | |
| 15 | * 1.Reduced x to positive by atanh(-x) = -atanh(x) | |
| 16 | * 2.For x>=0.5 | |
| 17 | * 1 2x x | |
| 18 | * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) | |
| 19 | * 2 1 - x 1 - x | |
| 20 | * | |
| 0ac5ae23 | 21 | * For x<0.5 |
| f964490f RM |
22 | * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) |
| 23 | * | |
| 24 | * Special cases: | |
| 25 | * atanh(x) is NaN if |x| > 1 with signal; | |
| 26 | * atanh(NaN) is that NaN with no signal; | |
| 27 | * atanh(+-1) is +-INF with signal. | |
| 28 | * | |
| 29 | */ | |
| 30 | ||
| 31 | #include "math.h" | |
| 32 | #include "math_private.h" | |
| 33 | ||
| f964490f | 34 | static const long double one = 1.0L, huge = 1e300L; |
| f964490f | 35 | |
| f964490f | 36 | static const long double zero = 0.0L; |
| f964490f | 37 | |
| 0ac5ae23 UD |
38 | long double |
| 39 | __ieee754_atanhl(long double x) | |
| f964490f RM |
40 | { |
| 41 | long double t; | |
| 42 | int64_t hx,ix; | |
| 43 | u_int64_t lx; | |
| 44 | GET_LDOUBLE_WORDS64(hx,lx,x); | |
| 45 | ix = hx&0x7fffffffffffffffLL; | |
| 46 | if (ix >= 0x3ff0000000000000LL) { /* |x|>=1 */ | |
| 47 | if (ix > 0x3ff0000000000000LL) | |
| 0ac5ae23 | 48 | return (x-x)/(x-x); |
| f964490f RM |
49 | t = fabsl (x); |
| 50 | if (t > one) | |
| 51 | return (x-x)/(x-x); | |
| 52 | if (t == one) | |
| 53 | return x/zero; | |
| 54 | } | |
| 55 | if(ix<0x3e20000000000000LL&&(huge+x)>zero) return x; /* x<2**-29 */ | |
| 56 | x = fabsl (x); | |
| 57 | if(ix<0x3fe0000000000000LL) { /* x < 0.5 */ | |
| 58 | t = x+x; | |
| 59 | t = 0.5*__log1pl(t+t*x/(one-x)); | |
| 60 | } else | |
| 61 | t = 0.5*__log1pl((x+x)/(one-x)); | |
| 62 | if(hx>=0) return t; else return -t; | |
| 63 | } | |
| 0ac5ae23 | 64 | strong_alias (__ieee754_atanhl, __atanhl_finite) |