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       ---
       s_asinh.c (1671B)
       ---
            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
            8  * software is freely granted, provided that this notice
            9  * is preserved.
           10  * ====================================================
           11  */
           12 
           13 #ifndef lint
           14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_asinh.c,v 1.8 2002/05/28 18:15:04 alfred Exp $";
           15 #endif
           16 
           17 /* asinh(x)
           18  * Method :
           19  *        Based on
           20  *                asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
           21  *        we have
           22  *        asinh(x) := x  if  1+x*x=1,
           23  *                 := sign(x)*(log(x)+ln2)) for large |x|, else
           24  *                 := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
           25  *                 := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
           26  */
           27 
           28 #include "math.h"
           29 #include "math_private.h"
           30 
           31 static const double
           32 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
           33 ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
           34 huge=  1.00000000000000000000e+300;
           35 
           36 double
           37 asinh(double x)
           38 {
           39         double t,w;
           40         int32_t hx,ix;
           41         GET_HIGH_WORD(hx,x);
           42         ix = hx&0x7fffffff;
           43         if(ix>=0x7ff00000) return x+x;        /* x is inf or NaN */
           44         if(ix< 0x3e300000) {        /* |x|<2**-28 */
           45             if(huge+x>one) return x;        /* return x inexact except 0 */
           46         }
           47         if(ix>0x41b00000) {        /* |x| > 2**28 */
           48             w = __ieee754_log(fabs(x))+ln2;
           49         } else if (ix>0x40000000) {        /* 2**28 > |x| > 2.0 */
           50             t = fabs(x);
           51             w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
           52         } else {                /* 2.0 > |x| > 2**-28 */
           53             t = x*x;
           54             w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
           55         }
           56         if(hx>0) return w; else return -w;
           57 }