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

/*
 * ====================================================
 * 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.
 * ====================================================
 */

/*
 * __ieee754_fmod(x,y)
 * Return x mod y in exact arithmetic
 * Method: shift and subtract
 */

#include <math.h>
#include <math_private.h>
#include <libm-alias-finite.h>

static const double one = 1.0, Zero[] = { 0.0, -0.0, };

double
__ieee754_fmod (double x, double y)
{
  int32_t n, hx, hy, hz, ix, iy, sx, i;
  uint32_t lx, ly, lz;

  EXTRACT_WORDS (hx, lx, x);
  EXTRACT_WORDS (hy, ly, y);
  sx = hx & 0x80000000;                 /* sign of x */
  hx ^= sx;                     /* |x| */
  hy &= 0x7fffffff;             /* |y| */

  /* purge off exception values */
  if ((hy | ly) == 0 || (hx >= 0x7ff00000) ||   /* y=0,or x not finite */
      ((hy | ((ly | -ly) >> 31)) > 0x7ff00000)) /* or y is NaN */
    return (x * y) / (x * y);
  if (hx <= hy)
    {
      if ((hx < hy) || (lx < ly))
	return x;                               /* |x|<|y| return x */
      if (lx == ly)
	return Zero[(uint32_t) sx >> 31];      /* |x|=|y| return x*0*/
    }

  /* determine ix = ilogb(x) */
  if (__glibc_unlikely (hx < 0x00100000))                  /* subnormal x */
    {
      if (hx == 0)
	{
	  for (ix = -1043, i = lx; i > 0; i <<= 1)
	    ix -= 1;
	}
      else
	{
	  for (ix = -1022, i = (hx << 11); i > 0; i <<= 1)
	    ix -= 1;
	}
    }
  else
    ix = (hx >> 20) - 1023;

  /* determine iy = ilogb(y) */
  if (__glibc_unlikely (hy < 0x00100000))                  /* subnormal y */
    {
      if (hy == 0)
	{
	  for (iy = -1043, i = ly; i > 0; i <<= 1)
	    iy -= 1;
	}
      else
	{
	  for (iy = -1022, i = (hy << 11); i > 0; i <<= 1)
	    iy -= 1;
	}
    }
  else
    iy = (hy >> 20) - 1023;

  /* set up {hx,lx}, {hy,ly} and align y to x */
  if (__glibc_likely (ix >= -1022))
    hx = 0x00100000 | (0x000fffff & hx);
  else                  /* subnormal x, shift x to normal */
    {
      n = -1022 - ix;
      if (n <= 31)
	{
	  hx = (hx << n) | (lx >> (32 - n));
	  lx <<= n;
	}
      else
	{
	  hx = lx << (n - 32);
	  lx = 0;
	}
    }
  if (__glibc_likely (iy >= -1022))
    hy = 0x00100000 | (0x000fffff & hy);
  else                  /* subnormal y, shift y to normal */
    {
      n = -1022 - iy;
      if (n <= 31)
	{
	  hy = (hy << n) | (ly >> (32 - n));
	  ly <<= n;
	}
      else
	{
	  hy = ly << (n - 32);
	  ly = 0;
	}
    }

  /* fix point fmod */
  n = ix - iy;
  while (n--)
    {
      hz = hx - hy; lz = lx - ly; if (lx < ly)
	hz -= 1;
      if (hz < 0)
	{
	  hx = hx + hx + (lx >> 31); lx = lx + lx;
	}
      else
	{
	  if ((hz | lz) == 0)           /* return sign(x)*0 */
	    return Zero[(uint32_t) sx >> 31];
	  hx = hz + hz + (lz >> 31); lx = lz + lz;
	}
    }
  hz = hx - hy; lz = lx - ly; if (lx < ly)
    hz -= 1;
  if (hz >= 0)
    {
      hx = hz; lx = lz;
    }

  /* convert back to floating value and restore the sign */
  if ((hx | lx) == 0)                   /* return sign(x)*0 */
    return Zero[(uint32_t) sx >> 31];
  while (hx < 0x00100000)               /* normalize x */
    {
      hx = hx + hx + (lx >> 31); lx = lx + lx;
      iy -= 1;
    }
  if (__glibc_likely (iy >= -1022))              /* normalize output */
    {
      hx = ((hx - 0x00100000) | ((iy + 1023) << 20));
      INSERT_WORDS (x, hx | sx, lx);
    }
  else                          /* subnormal output */
    {
      n = -1022 - iy;
      if (n <= 20)
	{
	  lx = (lx >> n) | ((uint32_t) hx << (32 - n));
	  hx >>= n;
	}
      else if (n <= 31)
	{
	  lx = (hx << (32 - n)) | (lx >> n); hx = sx;
	}
      else
	{
	  lx = hx >> (n - 32); hx = sx;
	}
      INSERT_WORDS (x, hx | sx, lx);
      x *= one;                 /* create necessary signal */
    }
  return x;                     /* exact output */
}
libm_alias_finite (__ieee754_fmod, __fmod)