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  #if defined(LIBM_SCCS) && !defined(lint)
      14  static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc 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 <float.h>
      29  #include <math.h>
      30  #include <math_private.h>
      31  #include <math-underflow.h>
      32  #include <math_ldbl_opt.h>
      33  
      34  static const long double
      35  one =  1.00000000000000000000e+00L, /* 0x3ff0000000000000, 0 */
      36  ln2 =  0.6931471805599453094172321214581766L, /* 0x3fe62e42fefa39ef, 0x3c7abc9e3b398040 */
      37  huge=  1.00000000000000000000e+300L;
      38  
      39  long double __asinhl(long double x)
      40  {
      41  	long double t,w;
      42  	int64_t hx,ix;
      43  	double xhi;
      44  
      45  	xhi = ldbl_high (x);
      46  	EXTRACT_WORDS64 (hx, xhi);
      47  	ix = hx&0x7fffffffffffffffLL;
      48  	if(ix>=0x7ff0000000000000LL) return x+x;	/* x is inf or NaN */
      49  	if(ix< 0x3c70000000000000LL) {	/* |x|<2**-56 */
      50  	    math_check_force_underflow (x);
      51  	    if(huge+x>one) return x;	/* return x inexact except 0 */
      52  	}
      53  	if(ix>0x4370000000000000LL) {	/* |x| > 2**56 */
      54  	    w = __ieee754_logl(fabsl(x))+ln2;
      55  	} else if (ix>0x4000000000000000LL) {	/* 2**56 >= |x| > 2.0 */
      56  	    t = fabs(x);
      57  	    w = __ieee754_logl(2.0*t+one/(sqrtl(x*x+one)+t));
      58  	} else {		/* 2.0 >= |x| >= 2**-56 */
      59  	    t = x*x;
      60  	    w =__log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
      61  	}
      62  	if(hx>0) return w; else return -w;
      63  }
      64  long_double_symbol (libm, __asinhl, asinhl);