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| Rev | Author | Line No. | Line |
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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 |