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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 | FUNCTION |
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15 | < |
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16 | |||
17 | |||
18 | asinh |
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19 | INDEX |
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20 | asinhf |
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21 | |||
22 | |||
23 | #include |
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24 | double asinh(double <[x]>); |
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25 | float asinhf(float <[x]>); |
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26 | |||
27 | |||
28 | #include |
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29 | double asinh(<[x]>) |
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30 | double <[x]>; |
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31 | |||
32 | |||
33 | float <[x]>; |
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34 | |||
35 | |||
36 | < |
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37 | < |
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38 | @ifnottex |
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39 | . sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>)) |
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40 | @end ifnottex |
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41 | @tex |
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42 | $$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$ |
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43 | @end tex |
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44 | |||
45 | |||
46 | |||
47 | |||
48 | < |
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49 | |||
50 | |||
51 | Neither < |
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52 | |||
53 | |||
54 | |||
55 | |||
56 | * Method : |
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57 | * Based on |
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58 | * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
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59 | * we have |
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60 | * asinh(x) := x if 1+x*x=1, |
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61 | * := sign(x)*(log(x)+ln2)) for large |x|, else |
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62 | * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else |
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63 | * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) |
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64 | */ |
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65 | |||
66 | |||
67 | |||
68 | |||
69 | |||
70 | |||
71 | static const double |
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72 | #else |
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73 | static double |
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74 | #endif |
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75 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
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76 | ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
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77 | huge= 1.00000000000000000000e+300; |
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78 | |||
79 | |||
80 | double asinh(double x) |
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81 | #else |
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82 | double asinh(x) |
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83 | double x; |
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84 | #endif |
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85 | { |
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86 | double t,w; |
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87 | __int32_t hx,ix; |
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88 | GET_HIGH_WORD(hx,x); |
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89 | ix = hx&0x7fffffff; |
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90 | if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ |
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91 | if(ix< 0x3e300000) { /* |x|<2**-28 */ |
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92 | if(huge+x>one) return x; /* return x inexact except 0 */ |
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93 | } |
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94 | if(ix>0x41b00000) { /* |x| > 2**28 */ |
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95 | w = __ieee754_log(fabs(x))+ln2; |
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96 | } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ |
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97 | t = fabs(x); |
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98 | w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); |
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99 | } else { /* 2.0 > |x| > 2**-28 */ |
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100 | t = x*x; |
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101 | w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); |
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102 | } |
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103 | if(hx>0) return w; else return -w; |
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104 | } |
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105 | |||
106 | |||
107 |