Line data    Source code

       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             : //__FBSDID("$FreeBSD$");
      15             : 
      16             : /* asinh(x)
      17             :  * Method :
      18             :  *      Based on
      19             :  *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
      20             :  *      we have
      21             :  *      asinh(x) := x  if  1+x*x=1,
      22             :  *               := sign(x)*(log(x)+ln2)) for large |x|, else
      23             :  *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
      24             :  *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
      25             :  */
      26             : 
      27             : #include <float.h>
      28             : 
      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           0 : asinh(double x)
      38             : {
      39             :         double t,w;
      40             :         int32_t hx,ix;
      41           0 :         GET_HIGH_WORD(hx,x);
      42           0 :         ix = hx&0x7fffffff;
      43           0 :         if(ix>=0x7ff00000) return x+x;       /* x is inf or NaN */
      44           0 :         if(ix< 0x3e300000) { /* |x|<2**-28 */
      45           0 :             if(huge+x>one) return x; /* return x inexact except 0 */
      46             :         }
      47           0 :         if(ix>0x41b00000) {  /* |x| > 2**28 */
      48           0 :             w = __ieee754_log(fabs(x))+ln2;
      49           0 :         } else if (ix>0x40000000) {  /* 2**28 > |x| > 2.0 */
      50           0 :             t = fabs(x);
      51           0 :             w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
      52             :         } else {                /* 2.0 > |x| > 2**-28 */
      53           0 :             t = x*x;
      54           0 :             w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
      55             :         }
      56           0 :         if(hx>0) return w; else return -w;
      57             : }