| /* @(#)e_atanh.c 5.1 93/09/24 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| /* __ieee754_atanh(x) |
| * Method : |
| * 1.Reduced x to positive by atanh(-x) = -atanh(x) |
| * 2.For x>=0.5 |
| * 1 2x x |
| * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) |
| * 2 1 - x 1 - x |
| * |
| * For x<0.5 |
| * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) |
| * |
| * Special cases: |
| * atanh(x) is NaN if |x| > 1 with signal; |
| * atanh(NaN) is that NaN with no signal; |
| * atanh(+-1) is +-INF with signal. |
| * |
| */ |
| |
| #include <float.h> |
| #include <math.h> |
| #include <math_private.h> |
| |
| static const long double one = 1.0L, huge = 1e300L; |
| |
| static const long double zero = 0.0L; |
| |
| long double |
| __ieee754_atanhl(long double x) |
| { |
| long double t; |
| int64_t hx,ix; |
| double xhi; |
| |
| xhi = ldbl_high (x); |
| EXTRACT_WORDS64 (hx, xhi); |
| ix = hx&0x7fffffffffffffffLL; |
| if (ix >= 0x3ff0000000000000LL) { /* |x|>=1 */ |
| if (ix > 0x3ff0000000000000LL) |
| return (x-x)/(x-x); |
| t = fabsl (x); |
| if (t > one) |
| return (x-x)/(x-x); |
| if (t == one) |
| return x/zero; |
| } |
| if(ix<0x3c70000000000000LL&&(huge+x)>zero) /* x<2**-56 */ |
| { |
| math_check_force_underflow (x); |
| return x; |
| } |
| x = fabsl (x); |
| if(ix<0x3fe0000000000000LL) { /* x < 0.5 */ |
| t = x+x; |
| t = 0.5*__log1pl(t+t*x/(one-x)); |
| } else |
| t = 0.5*__log1pl((x+x)/(one-x)); |
| if(hx>=0) return t; else return -t; |
| } |
| strong_alias (__ieee754_atanhl, __atanhl_finite) |
