mulll.h

#line 2 "../src/kernel/none/mulll.h"
/* Copyright (C) 2000  The PARI group.

This file is part of the PARI/GP package.

PARI/GP is free software; you can redistribute it and/or modify it under the
terms of the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later
version. It is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY WHATSOEVER.

Check the License for details. You should have received a copy of it, along
with the package; see the file 'COPYING'. If not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */

#undef  LOCAL_HIREMAINDER
#define LOCAL_HIREMAINDER
extern ulong hiremainder;

/* Version Peter Montgomery */
/*
 *      Assume (for presentation) that BITS_IN_LONG = 32.
 *      Then 0 <= xhi, xlo, yhi, ylo <= 2^16 - 1.  Hence
 *
 * -2^31 + 2^16 <= (xhi-2^15)*(ylo-2^15) + (xlo-2^15)*(yhi-2^15) <= 2^31.
 *
 *      If xhi*ylo + xlo*yhi = 2^32*overflow + xymid, then
 *
 * -2^32 + 2^16 <= 2^32*overflow + xymid - 2^15*(xhi + ylo + xlo + yhi) <= 0.
 *
 * 2^16*overflow <= (xhi+xlo+yhi+ylo)/2 - xymid/2^16 <= 2^16*overflow + 2^16-1
 *
 *       This inequality was derived using exact (rational) arithmetic;
 *       it remains valid when we truncate the two middle terms.
 */

#if !defined(INLINE)
extern long mulll(ulong x, ulong y);
extern long addmul(ulong x, ulong y);
#else

#if defined(__GNUC__) && !defined(DISABLE_INLINE)
#undef LOCAL_HIREMAINDER
#define LOCAL_HIREMAINDER register ulong hiremainder

#define mulll(x, y) \
__extension__ ({ \
  const ulong __x = (x), __y = (y);\
  const ulong __xlo = LOWWORD(__x), __xhi = HIGHWORD(__x); \
  const ulong __ylo = LOWWORD(__y), __yhi = HIGHWORD(__y); \
  ulong __xylo,__xymid,__xyhi,__xymidhi,__xymidlo; \
  ulong __xhl,__yhl; \
 \
  __xylo = __xlo*__ylo; __xyhi = __xhi*__yhi; \
  __xhl = __xhi+__xlo; __yhl = __yhi+__ylo; \
  __xymid = __xhl*__yhl - (__xyhi+__xylo); \
 \
  __xymidhi = HIGHWORD(__xymid); \
  __xymidlo = __xymid << BITS_IN_HALFULONG; \
 \
  __xylo += __xymidlo; \
  hiremainder = __xyhi + __xymidhi + (__xylo < __xymidlo) \
     + ((((__xhl + __yhl) >> 1) - __xymidhi) & HIGHMASK); \
 \
  __xylo; \
})

#define addmul(x, y) \
__extension__ ({                                           \
  const ulong __x = (x), __y = (y);\
  const ulong __xlo = LOWWORD(__x), __xhi = HIGHWORD(__x); \
  const ulong __ylo = LOWWORD(__y), __yhi = HIGHWORD(__y); \
  ulong __xylo,__xymid,__xyhi,__xymidhi,__xymidlo; \
  ulong __xhl,__yhl; \
 \
  __xylo = __xlo*__ylo; __xyhi = __xhi*__yhi; \
  __xhl = __xhi+__xlo; __yhl = __yhi+__ylo; \
  __xymid = __xhl*__yhl - (__xyhi+__xylo); \
 \
  __xylo += hiremainder; __xyhi += (__xylo < hiremainder); \
 \
  __xymidhi = HIGHWORD(__xymid); \
  __xymidlo = __xymid << BITS_IN_HALFULONG; \
 \
  __xylo += __xymidlo; \
  hiremainder = __xyhi + __xymidhi + (__xylo < __xymidlo) \
     + ((((__xhl + __yhl) >> 1) - __xymidhi) & HIGHMASK); \
 \
  __xylo; \
})

#else

INLINE long
mulll(ulong x, ulong y)
{
  const ulong xlo = LOWWORD(x), xhi = HIGHWORD(x);
  const ulong ylo = LOWWORD(y), yhi = HIGHWORD(y);
  ulong xylo,xymid,xyhi,xymidhi,xymidlo;
  ulong xhl,yhl;

  xylo = xlo*ylo; xyhi = xhi*yhi;
  xhl = xhi+xlo; yhl = yhi+ylo;
  xymid = xhl*yhl - (xyhi+xylo);

  xymidhi = HIGHWORD(xymid);
  xymidlo = xymid << BITS_IN_HALFULONG;

  xylo += xymidlo;
  hiremainder = xyhi + xymidhi + (xylo < xymidlo)
     + ((((xhl + yhl) >> 1) - xymidhi) & HIGHMASK);

  return xylo;
}

INLINE long
addmul(ulong x, ulong y)
{
  const ulong xlo = LOWWORD(x), xhi = HIGHWORD(x);
  const ulong ylo = LOWWORD(y), yhi = HIGHWORD(y);
  ulong xylo,xymid,xyhi,xymidhi,xymidlo;
  ulong xhl,yhl;

  xylo = xlo*ylo; xyhi = xhi*yhi;
  xhl = xhi+xlo; yhl = yhi+ylo;
  xymid = xhl*yhl - (xyhi+xylo);

  xylo += hiremainder; xyhi += (xylo < hiremainder);

  xymidhi = HIGHWORD(xymid);
  xymidlo = xymid << BITS_IN_HALFULONG;

  xylo += xymidlo;
  hiremainder = xyhi + xymidhi + (xylo < xymidlo)
     + ((((xhl + yhl) >> 1) - xymidhi) & HIGHMASK);

  return xylo;
}
#endif

#endif