kc3-lang/libquadmath/math/tanhq.c

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• Hash : 4f659ab9
  Author : Thomas de Grivel
  Date : 2025-11-02T19:33:45
  

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• math/tanhq.c

• /* s_tanhl.c -- long double version of s_tanh.c.
   * Conversion to long double by Ulrich Drepper,
   * Cygnus Support, drepper@cygnus.com.
   */
  
  /*
   * ====================================================
   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   *
   * Developed at SunPro, a Sun Microsystems, Inc. business.
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice
   * is preserved.
   * ====================================================
   */
  
  /* Changes for 128-bit long double contributed by
     Stephen L. Moshier <moshier@na-net.ornl.gov> */
  
  /* tanhq(x)
   * Return the Hyperbolic Tangent of x
   *
   * Method :
   *                                      x    -x
   *                                     e  - e
   *      0. tanhq(x) is defined to be -----------
   *                                      x    -x
   *                                     e  + e
   *      1. reduce x to non-negative by tanhq(-x) = -tanhq(x).
   *      2.  0      <= x <= 2**-57 : tanhq(x) := x*(one+x)
   *                                               -t
   *          2**-57 <  x <=  1     : tanhq(x) := -----; t = expm1q(-2x)
   *                                              t + 2
   *                                                    2
   *          1      <= x <=  40.0  : tanhq(x) := 1-  ----- ; t=expm1q(2x)
   *                                                  t + 2
   *          40.0   <  x <= INF    : tanhq(x) := 1.
   *
   * Special cases:
   *      tanhq(NaN) is NaN;
   *      only tanhq(0)=0 is exact for finite argument.
   */
  
  #include "quadmath-imp.h"
  
  static const __float128 one = 1.0, two = 2.0, tiny = 1.0e-4900Q;
  
  __float128
  tanhq (__float128 x)
  {
    __float128 t, z;
    uint32_t jx, ix;
    ieee854_float128 u;
  
    /* Words of |x|. */
    u.value = x;
    jx = u.words32.w0;
    ix = jx & 0x7fffffff;
    /* x is INF or NaN */
    if (ix >= 0x7fff0000)
      {
        /* for NaN it's not important which branch: tanhq(NaN) = NaN */
        if (jx & 0x80000000)
  	return one / x - one;	/* tanhq(-inf)= -1; */
        else
  	return one / x + one;	/* tanhq(+inf)=+1 */
      }
  
    /* |x| < 40 */
    if (ix < 0x40044000)
      {
        if (u.value == 0)
  	return x;		/* x == +- 0 */
        if (ix < 0x3fc60000)	/* |x| < 2^-57 */
  	{
  	  math_check_force_underflow (x);
  	  return x * (one + tiny); /* tanh(small) = small */
  	}
        u.words32.w0 = ix;	/* Absolute value of x.  */
        if (ix >= 0x3fff0000)
  	{			/* |x| >= 1  */
  	  t = expm1q (two * u.value);
  	  z = one - two / (t + two);
  	}
        else
  	{
  	  t = expm1q (-two * u.value);
  	  z = -t / (t + two);
  	}
        /* |x| > 40, return +-1 */
      }
    else
      {
        z = one - tiny;		/* raised inexact flag */
      }
    return (jx & 0x80000000) ? -z : z;
  }
  

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