1 | |
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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 "fdlibm.h" |
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34 | |
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35 | #ifndef _DOUBLE_IS_32BITS |
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36 | |
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37 | #ifdef __STDC__ |
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38 | static const double one = 1.0, huge = 1e300; |
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39 | #else |
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40 | static double one = 1.0, huge = 1e300; |
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41 | #endif |
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42 | |
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43 | #ifdef __STDC__ |
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44 | static const double zero = 0.0; |
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45 | #else |
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46 | static double zero = 0.0; |
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47 | #endif |
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48 | |
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49 | #ifdef __STDC__ |
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50 | double __ieee754_atanh(double x) |
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51 | #else |
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52 | double __ieee754_atanh(x) |
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53 | double x; |
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54 | #endif |
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55 | { |
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56 | double t; |
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57 | __int32_t hx,ix; |
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58 | __uint32_t lx; |
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59 | EXTRACT_WORDS(hx,lx,x); |
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60 | ix = hx&0x7fffffff; |
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61 | if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ |
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62 | return (x-x)/(x-x); |
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63 | if(ix==0x3ff00000) |
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64 | return x/zero; |
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65 | if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ |
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66 | SET_HIGH_WORD(x,ix); |
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67 | if(ix<0x3fe00000) { /* x < 0.5 */ |
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68 | t = x+x; |
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69 | t = 0.5*log1p(t+t*x/(one-x)); |
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70 | } else |
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71 | t = 0.5*log1p((x+x)/(one-x)); |
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72 | if(hx>=0) return t; else return -t; |
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73 | } |
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74 | |
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75 | #endif /* defined(_DOUBLE_IS_32BITS) */ |
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