glibc/sysdeps/ieee754/dbl-64/e_remainder.c

/*
 * IBM Accurate Mathematical Library
 * written by International Business Machines Corp.
 * Copyright (C) 2001-2024 Free Software Foundation, Inc.
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published by
 * the Free Software Foundation; either version 2.1 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program; if not, see <https://www.gnu.org/licenses/>.
 */
/**************************************************************************/
/*  MODULE_NAME urem.c                                                    */
/*                                                                        */
/*  FUNCTION: uremainder                                                  */
/*                                                                        */
/* An ultimate remainder routine. Given two IEEE double machine numbers x */
/* ,y   it computes the correctly rounded (to nearest) value of remainder */
/* of dividing x by y.                                                    */
/* Assumption: Machine arithmetic operations are performed in             */
/* round to nearest mode of IEEE 754 standard.                            */
/*                                                                        */
/* ************************************************************************/

#include "endian.h"
#include "mydefs.h"
#include "urem.h"
#include <math.h>
#include <math_private.h>
#include <fenv_private.h>
#include <libm-alias-finite.h>

/**************************************************************************/
/* An ultimate remainder routine. Given two IEEE double machine numbers x */
/* ,y   it computes the correctly rounded (to nearest) value of remainder */
/**************************************************************************/
double
__ieee754_remainder (double x, double y)
{
  double z, d, xx;
  int4 kx, ky, n, nn, n1, m1, l;
  mynumber u, t, w = { { 0, 0 } }, v = { { 0, 0 } }, ww = { { 0, 0 } }, r;
  u.x = x;
  t.x = y;
  kx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign  for x*/
  t.i[HIGH_HALF] &= 0x7fffffff;   /*no sign for y */
  ky = t.i[HIGH_HALF];
  /*------ |x| < 2^1023  and   2^-970 < |y| < 2^1024 ------------------*/
  if (kx < 0x7fe00000 && ky < 0x7ff00000 && ky >= 0x03500000)
    {
      SET_RESTORE_ROUND_NOEX (FE_TONEAREST);
      if (kx + 0x00100000 < ky)
	return x;
      if ((kx - 0x01500000) < ky)
	{
	  z = x / t.x;
	  v.i[HIGH_HALF] = t.i[HIGH_HALF];
	  d = (z + big.x) - big.x;
	  xx = (x - d * v.x) - d * (t.x - v.x);
	  if (d - z != 0.5 && d - z != -0.5)
	    return (xx != 0) ? xx : ((x > 0) ? ZERO.x : nZERO.x);
	  else
	    {
	      if (fabs (xx) > 0.5 * t.x)
		return (z > d) ? xx - t.x : xx + t.x;
	      else
		return xx;
	    }
	} /*    (kx<(ky+0x01500000))         */
      else
	{
	  r.x = 1.0 / t.x;
	  n = t.i[HIGH_HALF];
	  nn = (n & 0x7ff00000) + 0x01400000;
	  w.i[HIGH_HALF] = n;
	  ww.x = t.x - w.x;
	  l = (kx - nn) & 0xfff00000;
	  n1 = ww.i[HIGH_HALF];
	  m1 = r.i[HIGH_HALF];
	  while (l > 0)
	    {
	      r.i[HIGH_HALF] = m1 - l;
	      z = u.x * r.x;
	      w.i[HIGH_HALF] = n + l;
	      ww.i[HIGH_HALF] = (n1) ? n1 + l : n1;
	      d = (z + big.x) - big.x;
	      u.x = (u.x - d * w.x) - d * ww.x;
	      l = (u.i[HIGH_HALF] & 0x7ff00000) - nn;
	    }
	  r.i[HIGH_HALF] = m1;
	  w.i[HIGH_HALF] = n;
	  ww.i[HIGH_HALF] = n1;
	  z = u.x * r.x;
	  d = (z + big.x) - big.x;
	  u.x = (u.x - d * w.x) - d * ww.x;
	  if (fabs (u.x) < 0.5 * t.x)
	    return (u.x != 0) ? u.x : ((x > 0) ? ZERO.x : nZERO.x);
	  else
	  if (fabs (u.x) > 0.5 * t.x)
	    return (d > z) ? u.x + t.x : u.x - t.x;
	  else
	    {
	      z = u.x / t.x; d = (z + big.x) - big.x;
              return ((u.x - d * w.x) - d * ww.x);
	    }
	}
    } /*   (kx<0x7fe00000&&ky<0x7ff00000&&ky>=0x03500000)     */
  else
    {
      if (kx < 0x7fe00000 && ky < 0x7ff00000 && (ky > 0 || t.i[LOW_HALF] != 0))
	{
	  y = fabs (y) * t128.x;
	  z = __ieee754_remainder (x, y) * t128.x;
	  z = __ieee754_remainder (z, y) * tm128.x;
	  return z;
	}
      else
	{
	  if ((kx & 0x7ff00000) == 0x7fe00000 && ky < 0x7ff00000 &&
              (ky > 0 || t.i[LOW_HALF] != 0))
	    {
	      y = fabs (y);
	      z = 2.0 * __ieee754_remainder (0.5 * x, y);
	      d = fabs (z);
	      if (d <= fabs (d - y))
		return z;
	      else if (d == y)
		return 0.0 * x;
	      else
		return (z > 0) ? z - y : z + y;
	    }
	  else /* if x is too big */
	    {
	      if (ky == 0 && t.i[LOW_HALF] == 0) /* y = 0 */
		return (x * y) / (x * y);
	      else if (kx >= 0x7ff00000         /* x not finite */
		       || (ky > 0x7ff00000      /* y is NaN */
			   || (ky == 0x7ff00000 && t.i[LOW_HALF] != 0)))
		return (x * y) / (x * y);
	      else
		return x;
	    }
	}
    }
}
libm_alias_finite (__ieee754_remainder, __remainder)