1  /* e_asinhl.c -- long double version of e_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  /* __ieee754_sinhl(x)
      20   * Method :
      21   * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
      22   *	1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
      23   *	2.
      24   *						     E + E/(E+1)
      25   *	    0        <= x <= 25     :  sinhl(x) := --------------, E=expm1l(x)
      26   *							 2
      27   *
      28   *	    25       <= x <= lnovft :  sinhl(x) := expl(x)/2
      29   *	    lnovft   <= x <= ln2ovft:  sinhl(x) := expl(x/2)/2 * expl(x/2)
      30   *	    ln2ovft  <  x	    :  sinhl(x) := x*shuge (overflow)
      31   *
      32   * Special cases:
      33   *	sinhl(x) is |x| if x is +INF, -INF, or NaN.
      34   *	only sinhl(0)=0 is exact for finite x.
      35   */
      36  
      37  #include <float.h>
      38  #include <math.h>
      39  #include <math_private.h>
      40  #include <math-underflow.h>
      41  #include <libm-alias-finite.h>
      42  
      43  static const long double one = 1.0, shuge = 1.0e4931L;
      44  
      45  long double
      46  __ieee754_sinhl(long double x)
      47  {
      48  	long double t,w,h;
      49  	uint32_t jx,ix,i0,i1;
      50  
      51      /* Words of |x|. */
      52  	GET_LDOUBLE_WORDS(jx,i0,i1,x);
      53  	ix = jx&0x7fff;
      54  
      55      /* x is INF or NaN */
      56  	if(__builtin_expect(ix==0x7fff, 0)) return x+x;
      57  
      58  	h = 0.5;
      59  	if (jx & 0x8000) h = -h;
      60      /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
      61  	if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */
      62  	    if (ix<0x3fdf) {		/* |x|<2**-32 */
      63  		math_check_force_underflow (x);
      64  		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
      65  	    }
      66  	    t = __expm1l(fabsl(x));
      67  	    if(ix<0x3fff) return h*(2.0*t-t*t/(t+one));
      68  	    return h*(t+t/(t+one));
      69  	}
      70  
      71      /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
      72  	if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
      73  		return h*__ieee754_expl(fabsl(x));
      74  
      75      /* |x| in [log(maxdouble), overflowthreshold] */
      76  	if (ix<0x400c || (ix == 0x400c && (i0 < 0xb174ddc0
      77  					   || (i0 == 0xb174ddc0
      78  					       && i1 <= 0x31aec0ea)))) {
      79  	    w = __ieee754_expl(0.5*fabsl(x));
      80  	    t = h*w;
      81  	    return t*w;
      82  	}
      83  
      84      /* |x| > overflowthreshold, sinhl(x) overflow */
      85  	return x*shuge;
      86  }
      87  libm_alias_finite (__ieee754_sinhl, __sinhl)