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| 2 | /* @(#)s_asinh.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 | /* asinh(x) |
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| 15 | * Method : |
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| 16 | * Based on |
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| 17 | * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
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| 18 | * we have |
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| 19 | * asinh(x) := x if 1+x*x=1, |
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| 20 | * := sign(x)*(log(x)+ln2)) for large |x|, else |
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| 21 | * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else |
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| 22 | * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) |
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| 23 | */ |
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| 24 | |
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| 25 | #include <libm/fdlibm.h> |
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| 26 | |
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| 27 | #ifdef __STDC__ |
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| 28 | static const double |
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| 29 | #else |
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| 30 | static double |
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| 31 | #endif |
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| 32 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
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| 33 | ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
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| 34 | huge= 1.00000000000000000000e+300; |
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| 35 | |
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| 36 | #ifdef __STDC__ |
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| 37 | double asinh(double x) |
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| 38 | #else |
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| 39 | double asinh(x) |
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| 40 | double x; |
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| 41 | #endif |
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| 42 | { |
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| 43 | double t,w; |
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| 44 | int n0,hx,ix; |
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| 45 | n0 = ((*(int*)&one)>>29)^1; |
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| 46 | hx = *(n0+(int*)&x); |
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| 47 | ix = hx&0x7fffffff; |
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| 48 | if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ |
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| 49 | if(ix< 0x3e300000) { /* |x|<2**-28 */ |
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| 50 | if(huge+x>one) return x; /* return x inexact except 0 */ |
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| 51 | } |
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| 52 | if(ix>0x41b00000) { /* |x| > 2**28 */ |
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| 53 | w = __ieee754_log(fabs(x))+ln2; |
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| 54 | } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ |
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| 55 | t = fabs(x); |
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| 56 | w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t)); |
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| 57 | } else { /* 2.0 > |x| > 2**-28 */ |
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| 58 | t = x*x; |
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| 59 | w =log1p(fabs(x)+t/(one+sqrt(one+t))); |
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| 60 | } |
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| 61 | if(hx>0) return w; else return -w; |
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| 62 | } |
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