lib/libm/src/s_asinh.c

   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 }