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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 | /* |
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| 16 | FUNCTION |
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| 17 | <<atanh>>, <<atanhf>>---inverse hyperbolic tangent |
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| 18 | |
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| 19 | INDEX |
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| 20 | atanh |
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| 21 | INDEX |
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| 22 | atanhf |
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| 23 | |
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| 24 | SYNOPSIS |
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| 25 | #include <math.h> |
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| 26 | double atanh(double <[x]>); |
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| 27 | float atanhf(float <[x]>); |
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| 28 | |
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| 29 | DESCRIPTION |
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| 30 | <<atanh>> calculates the inverse hyperbolic tangent of <[x]>. |
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| 31 | |
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| 32 | <<atanhf>> is identical, other than taking and returning |
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| 33 | <<float>> values. |
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| 34 | |
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| 35 | RETURNS |
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| 36 | <<atanh>> and <<atanhf>> return the calculated value. |
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| 37 | |
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| 38 | If |
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| 39 | @ifnottex |
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| 40 | |<[x]>| |
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| 41 | @end ifnottex |
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| 42 | @tex |
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| 43 | $|x|$ |
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| 44 | @end tex |
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| 45 | is greater than 1, the global <<errno>> is set to <<EDOM>> and |
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| 46 | the result is a NaN. A <<DOMAIN error>> is reported. |
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| 47 | |
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| 48 | If |
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| 49 | @ifnottex |
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| 50 | |<[x]>| |
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| 51 | @end ifnottex |
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| 52 | @tex |
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| 53 | $|x|$ |
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| 54 | @end tex |
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| 55 | is 1, the global <<errno>> is set to <<EDOM>>; and the result is |
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| 56 | infinity with the same sign as <<x>>. A <<SING error>> is reported. |
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| 57 | |
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| 58 | You can modify the error handling for these routines using |
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| 59 | <<matherr>>. |
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| 60 | |
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| 61 | PORTABILITY |
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| 62 | Neither <<atanh>> nor <<atanhf>> are ANSI C. |
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| 63 | |
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| 64 | QUICKREF |
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| 65 | atanh - pure |
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| 66 | atanhf - pure |
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| 67 | |
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| 68 | |
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| 69 | */ |
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| 70 | |
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| 71 | /* atanh(x) |
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| 72 | * Method : |
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| 73 | * 1.Reduced x to positive by atanh(-x) = -atanh(x) |
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| 74 | * 2.For x>=0.5 |
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| 75 | * 1 2x x |
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| 76 | * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) |
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| 77 | * 2 1 - x 1 - x |
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| 78 | * |
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| 79 | * For x<0.5 |
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| 80 | * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) |
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| 81 | * |
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| 82 | * Special cases: |
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| 83 | * atanh(x) is NaN if |x| > 1 with signal; |
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| 84 | * atanh(NaN) is that NaN with no signal; |
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| 85 | * atanh(+-1) is +-INF with signal. |
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| 86 | * |
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| 87 | */ |
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| 88 | |
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| 89 | #include "fdlibm.h" |
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| 90 | |
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| 91 | #ifndef _DOUBLE_IS_32BITS |
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| 92 | |
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| 93 | #ifdef __STDC__ |
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| 94 | static const double one = 1.0, huge = 1e300; |
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| 95 | #else |
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| 96 | static double one = 1.0, huge = 1e300; |
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| 97 | #endif |
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| 98 | |
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| 99 | #ifdef __STDC__ |
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| 100 | static const double zero = 0.0; |
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| 101 | #else |
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| 102 | static double zero = 0.0; |
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| 103 | #endif |
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| 104 | |
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| 105 | #ifdef __STDC__ |
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| 106 | double atanh(double x) |
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| 107 | #else |
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| 108 | double atanh(x) |
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| 109 | double x; |
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| 110 | #endif |
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| 111 | { |
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| 112 | double t; |
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| 113 | __int32_t hx,ix; |
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| 114 | __uint32_t lx; |
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| 115 | EXTRACT_WORDS(hx,lx,x); |
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| 116 | ix = hx&0x7fffffff; |
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| 117 | if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ |
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| 118 | return (x-x)/(x-x); |
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| 119 | if(ix==0x3ff00000) |
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| 120 | return x/zero; |
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| 121 | if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ |
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| 122 | SET_HIGH_WORD(x,ix); |
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| 123 | if(ix<0x3fe00000) { /* x < 0.5 */ |
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| 124 | t = x+x; |
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| 125 | t = 0.5*log1p(t+t*x/(one-x)); |
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| 126 | } else |
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| 127 | t = 0.5*log1p((x+x)/(one-x)); |
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| 128 | if(hx>=0) return t; else return -t; |
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| 129 | } |
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| 130 | |
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| 131 | #endif /* defined(_DOUBLE_IS_32BITS) */ |
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