1  /* s_asinhl.c -- long double version of s_asinh.c.
       2   */
       3  
       4  /*
       5   * ====================================================
       6   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       7   *
       8   * Developed at SunPro, a Sun Microsystems, Inc. business.
       9   * Permission to use, copy, modify, and distribute this
      10   * software is freely granted, provided that this notice
      11   * is preserved.
      12   * ====================================================
      13   */
      14  
      15  #if defined(LIBM_SCCS) && !defined(lint)
      16  static char rcsid[] = "$NetBSD: $";
      17  #endif
      18  
      19  /* asinhl(x)
      20   * Method :
      21   *	Based on
      22   *		asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
      23   *	we have
      24   *	asinhl(x) := x  if  1+x*x=1,
      25   *		  := signl(x)*(logl(x)+ln2)) for large |x|, else
      26   *		  := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
      27   *		  := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
      28   */
      29  
      30  #include <float.h>
      31  #include <math.h>
      32  #include <math_private.h>
      33  #include <math-underflow.h>
      34  #include <libm-alias-ldouble.h>
      35  
      36  static const long double
      37  one =  1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */
      38  ln2 =  6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
      39  huge=  1.000000000000000000e+4900L;
      40  
      41  long double __asinhl(long double x)
      42  {
      43  	long double t,w;
      44  	int32_t hx,ix;
      45  	GET_LDOUBLE_EXP(hx,x);
      46  	ix = hx&0x7fff;
      47  	if(__builtin_expect(ix< 0x3fde, 0)) {	/* |x|<2**-34 */
      48  	    math_check_force_underflow (x);
      49  	    if(huge+x>one) return x;	/* return x inexact except 0 */
      50  	}
      51  	if(__builtin_expect(ix>0x4020,0)) {		/* |x| > 2**34 */
      52  	    if(ix==0x7fff) return x+x;	/* x is inf or NaN */
      53  	    w = __ieee754_logl(fabsl(x))+ln2;
      54  	} else {
      55  	    long double xa = fabsl(x);
      56  	    if (ix>0x4000) {	/* 2**34 > |x| > 2.0 */
      57  		w = __ieee754_logl(2.0*xa+one/(sqrtl(xa*xa+one)+xa));
      58  	    } else {		/* 2.0 > |x| > 2**-28 */
      59  		t = xa*xa;
      60  		w =__log1pl(xa+t/(one+sqrtl(one+t)));
      61  	    }
      62  	}
      63  	return copysignl(w, x);
      64  }
      65  libm_alias_ldouble (__asinh, asinh)