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path: root/src/math/atanh.c
blob: dbe241d168300810846f80625d8027ccb1948a8b (plain)
 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 ``` ``````/* origin: FreeBSD /usr/src/lib/msun/src/e_atanh.c */ /* * ==================================================== * 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. * ==================================================== * */ /* 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 "libm.h" static const double huge = 1e300; double atanh(double x) { double t; int32_t hx,ix; uint32_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/0.0; if (ix < 0x3e300000 && (huge+x) > 0.0) /* x < 2**-28 */ return x; SET_HIGH_WORD(x, ix); if (ix < 0x3fe00000) { /* x < 0.5 */ t = x+x; t = 0.5*log1p(t + t*x/(1.0-x)); } else t = 0.5*log1p((x+x)/(1.0-x)); if (hx >= 0) return t; return -t; } ``````