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/* mulmod_bnm1.c -- multiplication mod B^n-1.
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5c3484 |
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Contributed to the GNU project by Niels Möller, Torbjorn Granlund and
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5c3484 |
Marco Bodrato.
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5c3484 |
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THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
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SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
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5c3484 |
GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
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5c3484 |
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Copyright 2009, 2010, 2012, 2013 Free Software Foundation, Inc.
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5c3484 |
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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5c3484 |
it under the terms of either:
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5c3484 |
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5c3484 |
* the GNU Lesser General Public License as published by the Free
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5c3484 |
Software Foundation; either version 3 of the License, or (at your
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5c3484 |
option) any later version.
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5c3484 |
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5c3484 |
or
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5c3484 |
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* the GNU General Public License as published by the Free Software
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5c3484 |
Foundation; either version 2 of the License, or (at your option) any
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5c3484 |
later version.
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5c3484 |
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or both in parallel, as here.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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5c3484 |
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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5c3484 |
for more details.
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5c3484 |
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library. If not,
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see https://www.gnu.org/licenses/. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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/* Inputs are {ap,rn} and {bp,rn}; output is {rp,rn}, computation is
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mod B^rn - 1, and values are semi-normalised; zero is represented
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as either 0 or B^n - 1. Needs a scratch of 2rn limbs at tp.
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tp==rp is allowed. */
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void
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mpn_bc_mulmod_bnm1 (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t rn,
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mp_ptr tp)
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{
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mp_limb_t cy;
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ASSERT (0 < rn);
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mpn_mul_n (tp, ap, bp, rn);
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cy = mpn_add_n (rp, tp, tp + rn, rn);
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/* If cy == 1, then the value of rp is at most B^rn - 2, so there can
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* be no overflow when adding in the carry. */
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MPN_INCR_U (rp, rn, cy);
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}
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5c3484 |
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/* Inputs are {ap,rn+1} and {bp,rn+1}; output is {rp,rn+1}, in
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semi-normalised representation, computation is mod B^rn + 1. Needs
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a scratch area of 2rn + 2 limbs at tp; tp == rp is allowed.
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Output is normalised. */
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static void
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mpn_bc_mulmod_bnp1 (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t rn,
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5c3484 |
mp_ptr tp)
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{
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5c3484 |
mp_limb_t cy;
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5c3484 |
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ASSERT (0 < rn);
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5c3484 |
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mpn_mul_n (tp, ap, bp, rn + 1);
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ASSERT (tp[2*rn+1] == 0);
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ASSERT (tp[2*rn] < GMP_NUMB_MAX);
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cy = tp[2*rn] + mpn_sub_n (rp, tp, tp+rn, rn);
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rp[rn] = 0;
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MPN_INCR_U (rp, rn+1, cy );
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}
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/* Computes {rp,MIN(rn,an+bn)} <- {ap,an}*{bp,bn} Mod(B^rn-1)
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*
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* The result is expected to be ZERO if and only if one of the operand
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* already is. Otherwise the class [0] Mod(B^rn-1) is represented by
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* B^rn-1. This should not be a problem if mulmod_bnm1 is used to
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* combine results and obtain a natural number when one knows in
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* advance that the final value is less than (B^rn-1).
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* Moreover it should not be a problem if mulmod_bnm1 is used to
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* compute the full product with an+bn <= rn, because this condition
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* implies (B^an-1)(B^bn-1) < (B^rn-1) .
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*
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* Requires 0 < bn <= an <= rn and an + bn > rn/2
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* Scratch need: rn + (need for recursive call OR rn + 4). This gives
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*
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* S(n) <= rn + MAX (rn + 4, S(n/2)) <= 2rn + 4
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*/
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void
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mpn_mulmod_bnm1 (mp_ptr rp, mp_size_t rn, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn, mp_ptr tp)
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5c3484 |
{
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ASSERT (0 < bn);
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ASSERT (bn <= an);
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ASSERT (an <= rn);
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5c3484 |
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if ((rn & 1) != 0 || BELOW_THRESHOLD (rn, MULMOD_BNM1_THRESHOLD))
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{
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if (UNLIKELY (bn < rn))
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5c3484 |
{
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5c3484 |
if (UNLIKELY (an + bn <= rn))
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{
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5c3484 |
mpn_mul (rp, ap, an, bp, bn);
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}
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else
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{
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5c3484 |
mp_limb_t cy;
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5c3484 |
mpn_mul (tp, ap, an, bp, bn);
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cy = mpn_add (rp, tp, rn, tp + rn, an + bn - rn);
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MPN_INCR_U (rp, rn, cy);
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}
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}
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else
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mpn_bc_mulmod_bnm1 (rp, ap, bp, rn, tp);
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}
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else
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{
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5c3484 |
mp_size_t n;
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5c3484 |
mp_limb_t cy;
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5c3484 |
mp_limb_t hi;
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5c3484 |
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n = rn >> 1;
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5c3484 |
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/* We need at least an + bn >= n, to be able to fit one of the
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5c3484 |
recursive products at rp. Requiring strict inequality makes
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the code slightly simpler. If desired, we could avoid this
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restriction by initially halving rn as long as rn is even and
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an + bn <= rn/2. */
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5c3484 |
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ASSERT (an + bn > n);
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5c3484 |
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/* Compute xm = a*b mod (B^n - 1), xp = a*b mod (B^n + 1)
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5c3484 |
and crt together as
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5c3484 |
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x = -xp * B^n + (B^n + 1) * [ (xp + xm)/2 mod (B^n-1)]
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*/
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#define a0 ap
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#define a1 (ap + n)
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#define b0 bp
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#define b1 (bp + n)
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5c3484 |
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#define xp tp /* 2n + 2 */
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5c3484 |
/* am1 maybe in {xp, n} */
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5c3484 |
/* bm1 maybe in {xp + n, n} */
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5c3484 |
#define sp1 (tp + 2*n + 2)
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5c3484 |
/* ap1 maybe in {sp1, n + 1} */
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5c3484 |
/* bp1 maybe in {sp1 + n + 1, n + 1} */
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5c3484 |
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{
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5c3484 |
mp_srcptr am1, bm1;
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5c3484 |
mp_size_t anm, bnm;
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5c3484 |
mp_ptr so;
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5c3484 |
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5c3484 |
bm1 = b0;
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5c3484 |
bnm = bn;
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5c3484 |
if (LIKELY (an > n))
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5c3484 |
{
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5c3484 |
am1 = xp;
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5c3484 |
cy = mpn_add (xp, a0, n, a1, an - n);
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5c3484 |
MPN_INCR_U (xp, n, cy);
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anm = n;
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5c3484 |
so = xp + n;
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5c3484 |
if (LIKELY (bn > n))
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5c3484 |
{
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5c3484 |
bm1 = so;
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5c3484 |
cy = mpn_add (so, b0, n, b1, bn - n);
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5c3484 |
MPN_INCR_U (so, n, cy);
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bnm = n;
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5c3484 |
so += n;
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5c3484 |
}
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5c3484 |
}
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5c3484 |
else
|
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5c3484 |
{
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5c3484 |
so = xp;
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5c3484 |
am1 = a0;
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5c3484 |
anm = an;
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5c3484 |
}
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5c3484 |
|
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mpn_mulmod_bnm1 (rp, n, am1, anm, bm1, bnm, so);
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5c3484 |
}
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5c3484 |
|
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5c3484 |
{
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5c3484 |
int k;
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5c3484 |
mp_srcptr ap1, bp1;
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5c3484 |
mp_size_t anp, bnp;
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5c3484 |
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5c3484 |
bp1 = b0;
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5c3484 |
bnp = bn;
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5c3484 |
if (LIKELY (an > n)) {
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5c3484 |
ap1 = sp1;
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5c3484 |
cy = mpn_sub (sp1, a0, n, a1, an - n);
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5c3484 |
sp1[n] = 0;
|
|
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5c3484 |
MPN_INCR_U (sp1, n + 1, cy);
|
|
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5c3484 |
anp = n + ap1[n];
|
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5c3484 |
if (LIKELY (bn > n)) {
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|
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5c3484 |
bp1 = sp1 + n + 1;
|
|
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5c3484 |
cy = mpn_sub (sp1 + n + 1, b0, n, b1, bn - n);
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|
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5c3484 |
sp1[2*n+1] = 0;
|
|
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5c3484 |
MPN_INCR_U (sp1 + n + 1, n + 1, cy);
|
|
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5c3484 |
bnp = n + bp1[n];
|
|
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5c3484 |
}
|
|
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5c3484 |
} else {
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|
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5c3484 |
ap1 = a0;
|
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5c3484 |
anp = an;
|
|
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5c3484 |
}
|
|
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5c3484 |
|
|
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5c3484 |
if (BELOW_THRESHOLD (n, MUL_FFT_MODF_THRESHOLD))
|
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5c3484 |
k=0;
|
|
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5c3484 |
else
|
|
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5c3484 |
{
|
|
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5c3484 |
int mask;
|
|
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5c3484 |
k = mpn_fft_best_k (n, 0);
|
|
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5c3484 |
mask = (1<
|
|
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5c3484 |
while (n & mask) {k--; mask >>=1;};
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|
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5c3484 |
}
|
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5c3484 |
if (k >= FFT_FIRST_K)
|
|
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5c3484 |
xp[n] = mpn_mul_fft (xp, n, ap1, anp, bp1, bnp, k);
|
|
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5c3484 |
else if (UNLIKELY (bp1 == b0))
|
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5c3484 |
{
|
|
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5c3484 |
ASSERT (anp + bnp <= 2*n+1);
|
|
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5c3484 |
ASSERT (anp + bnp > n);
|
|
Packit |
5c3484 |
ASSERT (anp >= bnp);
|
|
Packit |
5c3484 |
mpn_mul (xp, ap1, anp, bp1, bnp);
|
|
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5c3484 |
anp = anp + bnp - n;
|
|
Packit |
5c3484 |
ASSERT (anp <= n || xp[2*n]==0);
|
|
Packit |
5c3484 |
anp-= anp > n;
|
|
Packit |
5c3484 |
cy = mpn_sub (xp, xp, n, xp + n, anp);
|
|
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5c3484 |
xp[n] = 0;
|
|
Packit |
5c3484 |
MPN_INCR_U (xp, n+1, cy);
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
else
|
|
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5c3484 |
mpn_bc_mulmod_bnp1 (xp, ap1, bp1, n, xp);
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
/* Here the CRT recomposition begins.
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
xm <- (xp + xm)/2 = (xp + xm)B^n/2 mod (B^n-1)
|
|
Packit |
5c3484 |
Division by 2 is a bitwise rotation.
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
Assumes xp normalised mod (B^n+1).
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
The residue class [0] is represented by [B^n-1]; except when
|
|
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5c3484 |
both input are ZERO.
|
|
Packit |
5c3484 |
*/
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
#if HAVE_NATIVE_mpn_rsh1add_n || HAVE_NATIVE_mpn_rsh1add_nc
|
|
Packit |
5c3484 |
#if HAVE_NATIVE_mpn_rsh1add_nc
|
|
Packit |
5c3484 |
cy = mpn_rsh1add_nc(rp, rp, xp, n, xp[n]); /* B^n = 1 */
|
|
Packit |
5c3484 |
hi = cy << (GMP_NUMB_BITS - 1);
|
|
Packit |
5c3484 |
cy = 0;
|
|
Packit |
5c3484 |
/* next update of rp[n-1] will set cy = 1 only if rp[n-1]+=hi
|
|
Packit |
5c3484 |
overflows, i.e. a further increment will not overflow again. */
|
|
Packit |
5c3484 |
#else /* ! _nc */
|
|
Packit |
5c3484 |
cy = xp[n] + mpn_rsh1add_n(rp, rp, xp, n); /* B^n = 1 */
|
|
Packit |
5c3484 |
hi = (cy<<(GMP_NUMB_BITS-1))&GMP_NUMB_MASK; /* (cy&1) << ... */
|
|
Packit |
5c3484 |
cy >>= 1;
|
|
Packit |
5c3484 |
/* cy = 1 only if xp[n] = 1 i.e. {xp,n} = ZERO, this implies that
|
|
Packit |
5c3484 |
the rsh1add was a simple rshift: the top bit is 0. cy=1 => hi=0. */
|
|
Packit |
5c3484 |
#endif
|
|
Packit |
5c3484 |
#if GMP_NAIL_BITS == 0
|
|
Packit |
5c3484 |
add_ssaaaa(cy, rp[n-1], cy, rp[n-1], 0, hi);
|
|
Packit |
5c3484 |
#else
|
|
Packit |
5c3484 |
cy += (hi & rp[n-1]) >> (GMP_NUMB_BITS-1);
|
|
Packit |
5c3484 |
rp[n-1] ^= hi;
|
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Packit |
5c3484 |
#endif
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Packit |
5c3484 |
#else /* ! HAVE_NATIVE_mpn_rsh1add_n */
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Packit |
5c3484 |
#if HAVE_NATIVE_mpn_add_nc
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Packit |
5c3484 |
cy = mpn_add_nc(rp, rp, xp, n, xp[n]);
|
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Packit |
5c3484 |
#else /* ! _nc */
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Packit |
5c3484 |
cy = xp[n] + mpn_add_n(rp, rp, xp, n); /* xp[n] == 1 implies {xp,n} == ZERO */
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Packit |
5c3484 |
#endif
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Packit |
5c3484 |
cy += (rp[0]&1;;
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Packit |
5c3484 |
mpn_rshift(rp, rp, n, 1);
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Packit |
5c3484 |
ASSERT (cy <= 2);
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Packit |
5c3484 |
hi = (cy<<(GMP_NUMB_BITS-1))&GMP_NUMB_MASK; /* (cy&1) << ... */
|
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Packit |
5c3484 |
cy >>= 1;
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5c3484 |
/* We can have cy != 0 only if hi = 0... */
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Packit |
5c3484 |
ASSERT ((rp[n-1] & GMP_NUMB_HIGHBIT) == 0);
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Packit |
5c3484 |
rp[n-1] |= hi;
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Packit |
5c3484 |
/* ... rp[n-1] + cy can not overflow, the following INCR is correct. */
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|
Packit |
5c3484 |
#endif
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|
Packit |
5c3484 |
ASSERT (cy <= 1);
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Packit |
5c3484 |
/* Next increment can not overflow, read the previous comments about cy. */
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Packit |
5c3484 |
ASSERT ((cy == 0) || ((rp[n-1] & GMP_NUMB_HIGHBIT) == 0));
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|
Packit |
5c3484 |
MPN_INCR_U(rp, n, cy);
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|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
/* Compute the highest half:
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|
Packit |
5c3484 |
([(xp + xm)/2 mod (B^n-1)] - xp ) * B^n
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|
Packit |
5c3484 |
*/
|
|
Packit |
5c3484 |
if (UNLIKELY (an + bn < rn))
|
|
Packit |
5c3484 |
{
|
|
Packit |
5c3484 |
/* Note that in this case, the only way the result can equal
|
|
Packit |
5c3484 |
zero mod B^{rn} - 1 is if one of the inputs is zero, and
|
|
Packit |
5c3484 |
then the output of both the recursive calls and this CRT
|
|
Packit |
5c3484 |
reconstruction is zero, not B^{rn} - 1. Which is good,
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|
Packit |
5c3484 |
since the latter representation doesn't fit in the output
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|
Packit |
5c3484 |
area.*/
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|
Packit |
5c3484 |
cy = mpn_sub_n (rp + n, rp, xp, an + bn - n);
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Packit |
5c3484 |
|
|
Packit |
5c3484 |
/* FIXME: This subtraction of the high parts is not really
|
|
Packit |
5c3484 |
necessary, we do it to get the carry out, and for sanity
|
|
Packit |
5c3484 |
checking. */
|
|
Packit |
5c3484 |
cy = xp[n] + mpn_sub_nc (xp + an + bn - n, rp + an + bn - n,
|
|
Packit |
5c3484 |
xp + an + bn - n, rn - (an + bn), cy);
|
|
Packit |
5c3484 |
ASSERT (an + bn == rn - 1 ||
|
|
Packit |
5c3484 |
mpn_zero_p (xp + an + bn - n + 1, rn - 1 - (an + bn)));
|
|
Packit |
5c3484 |
cy = mpn_sub_1 (rp, rp, an + bn, cy);
|
|
Packit |
5c3484 |
ASSERT (cy == (xp + an + bn - n)[0]);
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
else
|
|
Packit |
5c3484 |
{
|
|
Packit |
5c3484 |
cy = xp[n] + mpn_sub_n (rp + n, rp, xp, n);
|
|
Packit |
5c3484 |
/* cy = 1 only if {xp,n+1} is not ZERO, i.e. {rp,n} is not ZERO.
|
|
Packit |
5c3484 |
DECR will affect _at most_ the lowest n limbs. */
|
|
Packit |
5c3484 |
MPN_DECR_U (rp, 2*n, cy);
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
#undef a0
|
|
Packit |
5c3484 |
#undef a1
|
|
Packit |
5c3484 |
#undef b0
|
|
Packit |
5c3484 |
#undef b1
|
|
Packit |
5c3484 |
#undef xp
|
|
Packit |
5c3484 |
#undef sp1
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
}
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
mp_size_t
|
|
Packit |
5c3484 |
mpn_mulmod_bnm1_next_size (mp_size_t n)
|
|
Packit |
5c3484 |
{
|
|
Packit |
5c3484 |
mp_size_t nh;
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
if (BELOW_THRESHOLD (n, MULMOD_BNM1_THRESHOLD))
|
|
Packit |
5c3484 |
return n;
|
|
Packit |
5c3484 |
if (BELOW_THRESHOLD (n, 4 * (MULMOD_BNM1_THRESHOLD - 1) + 1))
|
|
Packit |
5c3484 |
return (n + (2-1)) & (-2);
|
|
Packit |
5c3484 |
if (BELOW_THRESHOLD (n, 8 * (MULMOD_BNM1_THRESHOLD - 1) + 1))
|
|
Packit |
5c3484 |
return (n + (4-1)) & (-4);
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
nh = (n + 1) >> 1;
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
if (BELOW_THRESHOLD (nh, MUL_FFT_MODF_THRESHOLD))
|
|
Packit |
5c3484 |
return (n + (8-1)) & (-8);
|
|
Packit |
5c3484 |
|
|
Packit |
5c3484 |
return 2 * mpn_fft_next_size (nh, mpn_fft_best_k (nh, 0));
|
|
Packit |
5c3484 |
}
|