| |
| /* @(#)e_atanh.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_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 "math.h" |
| #include "math_private.h" |
| |
| static const double one = 1.0, huge = 1e300; |
| static const double zero = 0.0; |
| |
| double |
| __ieee754_atanh(double x) |
| { |
| double t; |
| int32_t hx,ix; |
| u_int32_t lx; |
| EXTRACT_WORDS(hx,lx,x); |
| ix = hx&0x7fffffff; |
| if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ |
| return (x-x)/(x-x); |
| if(ix==0x3ff00000) |
| return x/zero; |
| if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ |
| SET_HIGH_WORD(x,ix); |
| if(ix<0x3fe00000) { /* x < 0.5 */ |
| t = x+x; |
| t = 0.5*log1p(t+t*x/(one-x)); |
| } else |
| t = 0.5*log1p((x+x)/(one-x)); |
| if(hx>=0) return t; else return -t; |
| } |
