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4349 | Serge | 1 | |
2 | /* |
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3 | * ==================================================== |
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4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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5 | * |
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6 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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7 | * Permission to use, copy, modify, and distribute this |
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8 | * software is freely granted, provided that this notice |
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9 | * is preserved. |
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10 | * ==================================================== |
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11 | */ |
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12 | |||
13 | |||
14 | * Method : |
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15 | * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 |
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16 | * 1. Replace x by |x| (cosh(x) = cosh(-x)). |
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17 | * 2. |
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18 | * [ exp(x) - 1 ]^2 |
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19 | * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- |
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20 | * 2*exp(x) |
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21 | * |
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22 | * exp(x) + 1/exp(x) |
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23 | * ln2/2 <= x <= 22 : cosh(x) := ------------------- |
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24 | * 2 |
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25 | * 22 <= x <= lnovft : cosh(x) := exp(x)/2 |
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26 | * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) |
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27 | * ln2ovft < x : cosh(x) := huge*huge (overflow) |
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28 | * |
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29 | * Special cases: |
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30 | * cosh(x) is |x| if x is +INF, -INF, or NaN. |
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31 | * only cosh(0)=1 is exact for finite x. |
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32 | */ |
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33 | |||
34 | |||
35 | |||
36 | |||
37 | |||
38 | |||
39 | static const double one = 1.0, half=0.5, huge = 1.0e300; |
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40 | #else |
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41 | static double one = 1.0, half=0.5, huge = 1.0e300; |
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42 | #endif |
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43 | |||
44 | |||
45 | double __ieee754_cosh(double x) |
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46 | #else |
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47 | double __ieee754_cosh(x) |
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48 | double x; |
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49 | #endif |
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50 | { |
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51 | double t,w; |
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52 | __int32_t ix; |
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53 | __uint32_t lx; |
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54 | |||
55 | |||
56 | GET_HIGH_WORD(ix,x); |
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57 | ix &= 0x7fffffff; |
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58 | |||
59 | |||
60 | if(ix>=0x7ff00000) return x*x; |
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61 | |||
62 | |||
63 | if(ix<0x3fd62e43) { |
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64 | t = expm1(fabs(x)); |
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65 | w = one+t; |
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66 | if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ |
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67 | return one+(t*t)/(w+w); |
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68 | } |
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69 | |||
70 | |||
71 | if (ix < 0x40360000) { |
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72 | t = __ieee754_exp(fabs(x)); |
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73 | return half*t+half/t; |
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74 | } |
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75 | |||
76 | |||
77 | if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); |
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78 | |||
79 | |||
80 | GET_LOW_WORD(lx,x); |
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81 | if (ix<0x408633CE || |
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82 | (ix==0x408633ce && lx<=(__uint32_t)0x8fb9f87d)) { |
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83 | w = __ieee754_exp(half*fabs(x)); |
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84 | t = half*w; |
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85 | return t*w; |
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86 | } |
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87 | |||
88 | |||
89 | return huge*huge; |
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90 | } |
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91 | |||
92 | |||
93 |