libm/s_asinh.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 /* asinh(x)
  13  * Method :
  14  *      Based on
  15  *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
  16  *      we have
  17  *      asinh(x) := x  if  1+x*x=1,
  18  *               := sign(x)*(log(x)+ln2)) for large |x|, else
  19  *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
  20  *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
  21  */
  22
  23 #include "math.h"
  24 #include "math_private.h"
  25
  26 static const double
  27 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  28 ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
  29 huge=  1.00000000000000000000e+300;
  30
  31 double asinh(double x)
  32 {
  33         double t,w;
  34         int32_t hx,ix;
  35         GET_HIGH_WORD(hx,x);
  36         ix = hx&0x7fffffff;
  37         if(ix>=0x7ff00000) return x+x;  /* x is inf or NaN */
  38         if(ix< 0x3e300000) {    /* |x|<2**-28 */
  39             if(huge+x>one) return x;    /* return x inexact except 0 */
  40         }
  41         if(ix>0x41b00000) {     /* |x| > 2**28 */
  42             w = __ieee754_log(fabs(x))+ln2;
  43         } else if (ix>0x40000000) {     /* 2**28 > |x| > 2.0 */
  44             t = fabs(x);
  45             w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
  46         } else {                /* 2.0 > |x| > 2**-28 */
  47             t = x*x;
  48             w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
  49         }
  50         if(hx>0) return w; else return -w;
  51 }
  52 libm_hidden_def(asinh)