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- /* @(#)s_asinh.c 5.1 93/09/24 */
- /*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
- #if defined(LIBM_SCCS) && !defined(lint)
- static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $";
- #endif
- /* asinh(x)
- * Method :
- * Based on
- * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
- * we have
- * asinh(x) := x if 1+x*x=1,
- * := sign(x)*(log(x)+ln2)) for large |x|, else
- * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
- * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
- */
- #include "math.h"
- #include "math_private.h"
- #ifdef __STDC__
- static const double
- #else
- static double
- #endif
- one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
- ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
- huge= 1.00000000000000000000e+300;
- #ifdef __STDC__
- double asinh(double x)
- #else
- double asinh(x)
- double x;
- #endif
- {
- double t,w;
- int32_t hx,ix;
- GET_HIGH_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
- if(ix< 0x3e300000) { /* |x|<2**-28 */
- if(huge+x>one) return x; /* return x inexact except 0 */
- }
- if(ix>0x41b00000) { /* |x| > 2**28 */
- w = __ieee754_log(fabs(x))+ln2;
- } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
- t = fabs(x);
- w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
- } else { /* 2.0 > |x| > 2**-28 */
- t = x*x;
- w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
- }
- if(hx>0) return w; else return -w;
- }
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