Home | History | Annotate | Line # | Download | only in src 
      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 #include <sys/cdefs.h>
     14 #if defined(LIBM_SCCS) && !defined(lint)
     15 __RCSID("$NetBSD: s_asinh.c,v 1.12 2002/05/26 22:01:54 wiz Exp $");
     16 #endif
     17 
     18 /* asinh(x)
     19  * Method :
     20  *	Based on
     21  *		asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
     22  *	we have
     23  *	asinh(x) := x  if  1+x*x=1,
     24  *		 := sign(x)*(log(x)+ln2)) for large |x|, else
     25  *		 := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
     26  *		 := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
     27  */
     28 
     29 #include "math.h"
     30 #include "math_private.h"
     31 
     32 static const double
     33 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
     34 ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
     35 huge=  1.00000000000000000000e+300;
     36 
     37 double
     38 asinh(double x)
     39 {
     40 	double t,w;
     41 	int32_t hx,ix;
     42 	GET_HIGH_WORD(hx,x);
     43 	ix = hx&0x7fffffff;
     44 	if(ix>=0x7ff00000) return x+x;	/* x is inf or NaN */
     45 	if(ix< 0x3e300000) {	/* |x|<2**-28 */
     46 	    if(huge+x>one) return x;	/* return x inexact except 0 */
     47 	}
     48 	if(ix>0x41b00000) {	/* |x| > 2**28 */
     49 	    w = __ieee754_log(fabs(x))+ln2;
     50 	} else if (ix>0x40000000) {	/* 2**28 > |x| > 2.0 */
     51 	    t = fabs(x);
     52 	    w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
     53 	} else {		/* 2.0 > |x| > 2**-28 */
     54 	    t = x*x;
     55 	    w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
     56 	}
     57 	if(hx>0) return w; else return -w;
     58 }
     59