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1 | /* @(#)s_asinh.c 5.1 93/09/24 */ |
2 | /* | |
3 | * ==================================================== | |
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
5 | * | |
6 | * Developed at SunPro, a Sun Microsystems, Inc. business. | |
7 | * Permission to use, copy, modify, and distribute this | |
cccda09f | 8 | * software is freely granted, provided that this notice |
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9 | * is preserved. |
10 | * ==================================================== | |
11 | */ | |
12 | ||
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13 | /* asinh(x) |
14 | * Method : | |
cccda09f | 15 | * Based on |
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16 | * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
17 | * we have | |
18 | * asinh(x) := x if 1+x*x=1, | |
19 | * := sign(x)*(log(x)+ln2)) for large |x|, else | |
20 | * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else | |
21 | * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) | |
22 | */ | |
23 | ||
24 | #include "math.h" | |
25 | #include "math_private.h" | |
26 | ||
f7eac6eb | 27 | static const double |
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28 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
29 | ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ | |
30 | huge= 1.00000000000000000000e+300; | |
31 | ||
0ac5ae23 UD |
32 | double |
33 | __asinh(double x) | |
f7eac6eb | 34 | { |
0ac5ae23 | 35 | double w; |
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36 | int32_t hx,ix; |
37 | GET_HIGH_WORD(hx,x); | |
38 | ix = hx&0x7fffffff; | |
0ac5ae23 | 39 | if(__builtin_expect(ix< 0x3e300000, 0)) { /* |x|<2**-28 */ |
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40 | if(huge+x>one) return x; /* return x inexact except 0 */ |
41 | } | |
0ac5ae23 UD |
42 | if(__builtin_expect(ix>0x41b00000, 0)) { /* |x| > 2**28 */ |
43 | if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ | |
f7eac6eb | 44 | w = __ieee754_log(fabs(x))+ln2; |
0ac5ae23 UD |
45 | } else { |
46 | double xa = fabs(x); | |
47 | if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ | |
48 | w = __ieee754_log(2.0*xa+one/(__ieee754_sqrt(xa*xa+one)+xa)); | |
49 | } else { /* 2.0 > |x| > 2**-28 */ | |
50 | double t = xa*xa; | |
51 | w =__log1p(xa+t/(one+__ieee754_sqrt(one+t))); | |
52 | } | |
f7eac6eb | 53 | } |
0ac5ae23 | 54 | return __copysign(w, x); |
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55 | } |
56 | weak_alias (__asinh, asinh) | |
57 | #ifdef NO_LONG_DOUBLE | |
58 | strong_alias (__asinh, __asinhl) | |
59 | weak_alias (__asinh, asinhl) | |
60 | #endif |