1  /* s_tanhl.c -- long double version of s_tanh.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  /* tanhl(x)
      20   * Return the Hyperbolic Tangent of x
      21   *
      22   * Method :
      23   *				        x    -x
      24   *				       e  - e
      25   *	0. tanhl(x) is defined to be -----------
      26   *				        x    -x
      27   *				       e  + e
      28   *	1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
      29   *	2.  0      <= x <= 2**-55 : tanhl(x) := x*(one+x)
      30   *					         -t
      31   *	    2**-55 <  x <=  1     : tanhl(x) := -----; t = expm1l(-2x)
      32   *					        t + 2
      33   *						      2
      34   *	    1      <= x <=  23.0  : tanhl(x) := 1-  ----- ; t=expm1l(2x)
      35   *						    t + 2
      36   *	    23.0   <  x <= INF    : tanhl(x) := 1.
      37   *
      38   * Special cases:
      39   *	tanhl(NaN) is NaN;
      40   *	only tanhl(0)=0 is exact for finite argument.
      41   */
      42  
      43  #include <float.h>
      44  #include <math.h>
      45  #include <math_private.h>
      46  #include <math-underflow.h>
      47  #include <libm-alias-ldouble.h>
      48  
      49  static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;
      50  
      51  long double __tanhl(long double x)
      52  {
      53  	long double t,z;
      54  	int32_t se;
      55  	uint32_t j0,j1,ix;
      56  
      57      /* High word of |x|. */
      58  	GET_LDOUBLE_WORDS(se,j0,j1,x);
      59  	ix = se&0x7fff;
      60  
      61      /* x is INF or NaN */
      62  	if(ix==0x7fff) {
      63  	    /* for NaN it's not important which branch: tanhl(NaN) = NaN */
      64  	    if (se&0x8000) return one/x-one;	/* tanhl(-inf)= -1; */
      65  	    else           return one/x+one;	/* tanhl(+inf)=+1 */
      66  	}
      67  
      68      /* |x| < 23 */
      69  	if (ix < 0x4003 || (ix == 0x4003 && j0 < 0xb8000000u)) {/* |x|<23 */
      70  	    if ((ix|j0|j1) == 0)
      71  		return x;		/* x == +- 0 */
      72  	    if (ix<0x3fc8)		/* |x|<2**-55 */
      73  	      {
      74  		math_check_force_underflow (x);
      75  		return x*(one+tiny);	/* tanh(small) = small */
      76  	      }
      77  	    if (ix>=0x3fff) {	/* |x|>=1  */
      78  		t = __expm1l(two*fabsl(x));
      79  		z = one - two/(t+two);
      80  	    } else {
      81  	        t = __expm1l(-two*fabsl(x));
      82  	        z= -t/(t+two);
      83  	    }
      84      /* |x| > 23, return +-1 */
      85  	} else {
      86  	    z = one - tiny;		/* raised inexact flag */
      87  	}
      88  	return (se&0x8000)? -z: z;
      89  }
      90  libm_alias_ldouble (__tanh, tanh)