207 lines
6.3 KiB
C
207 lines
6.3 KiB
C
/* mpn_mul -- Multiply two natural numbers.
|
|
|
|
THE HELPER FUNCTIONS IN THIS FILE (meaning everything except mpn_mul)
|
|
ARE INTERNAL FUNCTIONS WITH MUTABLE INTERFACES. IT IS ONLY SAFE TO REACH
|
|
THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST GUARANTEED
|
|
THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
|
|
|
|
|
|
Copyright 1991, 1993, 1994, 1996, 1997, 1999, 2000, 2001, 2002, 2003, 2005
|
|
Free Software Foundation, Inc.
|
|
|
|
This file is part of the GNU MP Library.
|
|
|
|
The GNU MP Library 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.
|
|
|
|
The GNU MP Library 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 the GNU MP Library; see the file COPYING.LIB. If not, write to
|
|
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
|
|
MA 02110-1301, USA. */
|
|
|
|
#include "gmp.h"
|
|
#include "gmp-impl.h"
|
|
|
|
|
|
#ifndef MUL_BASECASE_MAX_UN
|
|
#define MUL_BASECASE_MAX_UN 500
|
|
#endif
|
|
|
|
/* Multiply the natural numbers u (pointed to by UP, with UN limbs) and v
|
|
(pointed to by VP, with VN limbs), and store the result at PRODP. The
|
|
result is UN + VN limbs. Return the most significant limb of the result.
|
|
|
|
NOTE: The space pointed to by PRODP is overwritten before finished with U
|
|
and V, so overlap is an error.
|
|
|
|
Argument constraints:
|
|
1. UN >= VN.
|
|
2. PRODP != UP and PRODP != VP, i.e. the destination must be distinct from
|
|
the multiplier and the multiplicand. */
|
|
|
|
mp_limb_t
|
|
mpn_mul (mp_ptr prodp,
|
|
mp_srcptr up, mp_size_t un,
|
|
mp_srcptr vp, mp_size_t vn)
|
|
{
|
|
mp_size_t l;
|
|
mp_limb_t c;
|
|
|
|
ASSERT (un >= vn);
|
|
ASSERT (vn >= 1);
|
|
ASSERT (! MPN_OVERLAP_P (prodp, un+vn, up, un));
|
|
ASSERT (! MPN_OVERLAP_P (prodp, un+vn, vp, vn));
|
|
|
|
if (up == vp && un == vn)
|
|
{
|
|
mpn_sqr_n (prodp, up, un);
|
|
return prodp[2 * un - 1];
|
|
}
|
|
|
|
if (vn < MUL_KARATSUBA_THRESHOLD)
|
|
{ /* plain schoolbook multiplication */
|
|
if (un <= MUL_BASECASE_MAX_UN)
|
|
mpn_mul_basecase (prodp, up, un, vp, vn);
|
|
else
|
|
{
|
|
/* We have un >> MUL_BASECASE_MAX_UN > vn. For better memory
|
|
locality, split up[] into MUL_BASECASE_MAX_UN pieces and multiply
|
|
these pieces with the vp[] operand. After each such partial
|
|
multiplication (but the last) we copy the most significant vn
|
|
limbs into a temporary buffer since that part would otherwise be
|
|
overwritten by the next multiplication. After the next
|
|
multiplication, we add it back. This illustrates the situation:
|
|
|
|
-->vn<--
|
|
| |<------- un ------->|
|
|
_____________________|
|
|
X /|
|
|
/XX__________________/ |
|
|
_____________________ |
|
|
X / |
|
|
/XX__________________/ |
|
|
_____________________ |
|
|
/ / |
|
|
/____________________/ |
|
|
==================================================================
|
|
|
|
The parts marked with X are the parts whose sums are copied into
|
|
the temporary buffer. */
|
|
|
|
mp_limb_t tp[MUL_KARATSUBA_THRESHOLD_LIMIT];
|
|
mp_limb_t cy;
|
|
ASSERT (MUL_KARATSUBA_THRESHOLD <= MUL_KARATSUBA_THRESHOLD_LIMIT);
|
|
|
|
mpn_mul_basecase (prodp, up, MUL_BASECASE_MAX_UN, vp, vn);
|
|
prodp += MUL_BASECASE_MAX_UN;
|
|
MPN_COPY (tp, prodp, vn); /* preserve high triangle */
|
|
up += MUL_BASECASE_MAX_UN;
|
|
un -= MUL_BASECASE_MAX_UN;
|
|
while (un > MUL_BASECASE_MAX_UN)
|
|
{
|
|
mpn_mul_basecase (prodp, up, MUL_BASECASE_MAX_UN, vp, vn);
|
|
cy = mpn_add_n (prodp, prodp, tp, vn); /* add back preserved triangle */
|
|
mpn_incr_u (prodp + vn, cy); /* safe? */
|
|
prodp += MUL_BASECASE_MAX_UN;
|
|
MPN_COPY (tp, prodp, vn); /* preserve high triangle */
|
|
up += MUL_BASECASE_MAX_UN;
|
|
un -= MUL_BASECASE_MAX_UN;
|
|
}
|
|
if (un > vn)
|
|
{
|
|
mpn_mul_basecase (prodp, up, un, vp, vn);
|
|
}
|
|
else
|
|
{
|
|
ASSERT_ALWAYS (un > 0);
|
|
mpn_mul_basecase (prodp, vp, vn, up, un);
|
|
}
|
|
cy = mpn_add_n (prodp, prodp, tp, vn); /* add back preserved triangle */
|
|
mpn_incr_u (prodp + vn, cy); /* safe? */
|
|
}
|
|
return prodp[un + vn - 1];
|
|
}
|
|
|
|
if (ABOVE_THRESHOLD (vn, MUL_FFT_THRESHOLD))
|
|
{
|
|
mpn_mul_fft_full (prodp, up, un, vp, vn);
|
|
return prodp[un + vn - 1];
|
|
}
|
|
|
|
mpn_mul_n (prodp, up, vp, vn);
|
|
if (un != vn)
|
|
{ mp_limb_t t;
|
|
mp_ptr ws;
|
|
TMP_DECL;
|
|
TMP_MARK;
|
|
|
|
prodp += vn;
|
|
l = vn;
|
|
up += vn;
|
|
un -= vn;
|
|
|
|
if (un < vn)
|
|
{
|
|
/* Swap u's and v's. */
|
|
MPN_SRCPTR_SWAP (up,un, vp,vn);
|
|
}
|
|
|
|
ws = TMP_ALLOC_LIMBS ((vn >= MUL_KARATSUBA_THRESHOLD ? vn : un) + vn);
|
|
|
|
t = 0;
|
|
while (vn >= MUL_KARATSUBA_THRESHOLD)
|
|
{
|
|
mpn_mul_n (ws, up, vp, vn);
|
|
if (l <= 2*vn)
|
|
{
|
|
t += mpn_add_n (prodp, prodp, ws, l);
|
|
if (l != 2*vn)
|
|
{
|
|
t = mpn_add_1 (prodp + l, ws + l, 2*vn - l, t);
|
|
l = 2*vn;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
c = mpn_add_n (prodp, prodp, ws, 2*vn);
|
|
t += mpn_add_1 (prodp + 2*vn, prodp + 2*vn, l - 2*vn, c);
|
|
}
|
|
prodp += vn;
|
|
l -= vn;
|
|
up += vn;
|
|
un -= vn;
|
|
if (un < vn)
|
|
{
|
|
/* Swap u's and v's. */
|
|
MPN_SRCPTR_SWAP (up,un, vp,vn);
|
|
}
|
|
}
|
|
|
|
if (vn != 0)
|
|
{
|
|
mpn_mul_basecase (ws, up, un, vp, vn);
|
|
if (l <= un + vn)
|
|
{
|
|
t += mpn_add_n (prodp, prodp, ws, l);
|
|
if (l != un + vn)
|
|
t = mpn_add_1 (prodp + l, ws + l, un + vn - l, t);
|
|
}
|
|
else
|
|
{
|
|
c = mpn_add_n (prodp, prodp, ws, un + vn);
|
|
t += mpn_add_1 (prodp + un + vn, prodp + un + vn, l - un - vn, c);
|
|
}
|
|
}
|
|
|
|
TMP_FREE;
|
|
}
|
|
return prodp[un + vn - 1];
|
|
}
|