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| 2 | /* @(#)e_atanh.c 5.1 93/09/24 */ |
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| 3 | /* |
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| 4 | * ==================================================== |
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 6 | * |
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 8 | * Permission to use, copy, modify, and distribute this |
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| 9 | * software is freely granted, provided that this notice |
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| 10 | * is preserved. |
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| 11 | * ==================================================== |
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| 12 | * |
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| 13 | */ |
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| 14 | |
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| 15 | /* __ieee754_atanh(x) |
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| 16 | * Method : |
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| 17 | * 1.Reduced x to positive by atanh(-x) = -atanh(x) |
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| 18 | * 2.For x>=0.5 |
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| 19 | * 1 2x x |
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| 20 | * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) |
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| 21 | * 2 1 - x 1 - x |
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| 22 | * |
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| 23 | * For x<0.5 |
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| 24 | * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) |
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| 25 | * |
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| 26 | * Special cases: |
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| 27 | * atanh(x) is NaN if |x| > 1 with signal; |
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| 28 | * atanh(NaN) is that NaN with no signal; |
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| 29 | * atanh(+-1) is +-INF with signal. |
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| 30 | * |
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| 31 | */ |
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| 32 | |
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| 33 | #include <libm/fdlibm.h> |
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| 34 | |
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| 35 | #ifdef __STDC__ |
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| 36 | static const double one = 1.0, huge = 1e300; |
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| 37 | #else |
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| 38 | static double one = 1.0, huge = 1e300; |
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| 39 | #endif |
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| 40 | |
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| 41 | static double zero = 0.0; |
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| 42 | |
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| 43 | #ifdef __STDC__ |
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| 44 | double __ieee754_atanh(double x) |
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| 45 | #else |
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| 46 | double __ieee754_atanh(x) |
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| 47 | double x; |
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| 48 | #endif |
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| 49 | { |
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| 50 | double t; |
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| 51 | int hx,n0,ix; |
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| 52 | unsigned lx; |
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| 53 | n0 = ((*(int*)&one)>>29)^1; |
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| 54 | hx = *(n0+(int*)&x); /* high word */ |
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| 55 | lx = *(1-n0+(int*)&x); /* low word */ |
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| 56 | ix = hx&0x7fffffff; |
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| 57 | if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ |
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| 58 | return (x-x)/(x-x); |
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| 59 | if(ix==0x3ff00000) |
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| 60 | return x/zero; |
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| 61 | if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ |
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| 62 | *(n0+(int*)&x) = ix; /* x <- |x| */ |
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| 63 | if(ix<0x3fe00000) { /* x < 0.5 */ |
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| 64 | t = x+x; |
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| 65 | t = 0.5*log1p(t+t*x/(one-x)); |
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| 66 | } else |
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| 67 | t = 0.5*log1p((x+x)/(one-x)); |
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| 68 | if(hx>=0) return t; else return -t; |
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| 69 | } |
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