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/* @(#)s_asinh.c 5.1 93/09/24 */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunPro, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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/* asinh(x) |
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* Method : |
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* Based on |
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* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
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* we have |
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* asinh(x) := x if 1+x*x=1, |
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* := sign(x)*(log(x)+ln2)) for large |x|, else |
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* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else |
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* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) |
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*/ |
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#include <float.h> |
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#include <math.h> |
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#include "math_private.h" |
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static const double |
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
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ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
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huge= 1.00000000000000000000e+300; |
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double |
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asinh(double x) |
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{ |
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double t,w; |
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int32_t hx,ix; |
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GET_HIGH_WORD(hx,x); |
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ix = hx&0x7fffffff; |
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✗✓ |
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if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ |
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✓✓ |
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if(ix< 0x3e300000) { /* |x|<2**-28 */ |
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✓✗ |
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if(huge+x>one) return x; /* return x inexact except 0 */ |
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} |
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✗✓ |
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if(ix>0x41b00000) { /* |x| > 2**28 */ |
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w = log(fabs(x))+ln2; |
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✓✓ |
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} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ |
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t = fabs(x); |
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w = log(2.0*t+one/(sqrt(x*x+one)+t)); |
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} else { /* 2.0 > |x| > 2**-28 */ |
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t = x*x; |
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w =log1p(fabs(x)+t/(one+sqrt(one+t))); |
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} |
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✓✓ |
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if(hx>0) return w; else return -w; |
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} |
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DEF_STD(asinh); |
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LDBL_MAYBE_CLONE(asinh); |