mulmod_bnm1.c
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- /* mulmod_bnm1.c -- multiplication mod B^n-1.
- Contributed to the GNU project by Niels M鰈ler, Torbjorn Granlund and
- Marco Bodrato.
- THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
- SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
- GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
- Copyright 2009, 2010 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 3 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. If not, see http://www.gnu.org/licenses/. */
- #include "gmp.h"
- #include "gmp-impl.h"
- #include "longlong.h"
- /* Inputs are {ap,rn} and {bp,rn}; output is {rp,rn}, computation is
- mod B^rn - 1, and values are semi-normalised; zero is represented
- as either 0 or B^n - 1. Needs a scratch of 2rn limbs at tp.
- tp==rp is allowed. */
- void
- mpn_bc_mulmod_bnm1 (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t rn,
- mp_ptr tp)
- {
- mp_limb_t cy;
- ASSERT (0 < rn);
- mpn_mul_n (tp, ap, bp, rn);
- cy = mpn_add_n (rp, tp, tp + rn, rn);
- /* If cy == 1, then the value of rp is at most B^rn - 2, so there can
- * be no overflow when adding in the carry. */
- MPN_INCR_U (rp, rn, cy);
- }
- /* Inputs are {ap,rn+1} and {bp,rn+1}; output is {rp,rn+1}, in
- semi-normalised representation, computation is mod B^rn + 1. Needs
- a scratch area of 2rn + 2 limbs at tp; tp == rp is allowed.
- Output is normalised. */
- static void
- mpn_bc_mulmod_bnp1 (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t rn,
- mp_ptr tp)
- {
- mp_limb_t cy;
- ASSERT (0 < rn);
- mpn_mul_n (tp, ap, bp, rn + 1);
- ASSERT (tp[2*rn+1] == 0);
- ASSERT (tp[2*rn] < GMP_NUMB_MAX);
- cy = tp[2*rn] + mpn_sub_n (rp, tp, tp+rn, rn);
- rp[rn] = 0;
- MPN_INCR_U (rp, rn+1, cy );
- }
- /* Computes {rp,MIN(rn,an+bn)} <- {ap,an}*{bp,bn} Mod(B^rn-1)
- *
- * The result is expected to be ZERO if and only if one of the operand
- * already is. Otherwise the class [0] Mod(B^rn-1) is represented by
- * B^rn-1. This should not be a problem if mulmod_bnm1 is used to
- * combine results and obtain a natural number when one knows in
- * advance that the final value is less than (B^rn-1).
- * Moreover it should not be a problem if mulmod_bnm1 is used to
- * compute the full product with an+bn <= rn, because this condition
- * implies (B^an-1)(B^bn-1) < (B^rn-1) .
- *
- * Requires 0 < bn <= an <= rn and an + bn > rn/2
- * Scratch need: rn + (need for recursive call OR rn + 4). This gives
- *
- * S(n) <= rn + MAX (rn + 4, S(n/2)) <= 2rn + 4
- */
- void
- 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)
- {
- ASSERT (0 < bn);
- ASSERT (bn <= an);
- ASSERT (an <= rn);
- if ((rn & 1) != 0 || BELOW_THRESHOLD (rn, MULMOD_BNM1_THRESHOLD))
- {
- if (UNLIKELY (bn < rn))
- {
- if (UNLIKELY (an + bn <= rn))
- {
- mpn_mul (rp, ap, an, bp, bn);
- }
- else
- {
- mp_limb_t cy;
- mpn_mul (tp, ap, an, bp, bn);
- cy = mpn_add (rp, tp, rn, tp + rn, an + bn - rn);
- MPN_INCR_U (rp, rn, cy);
- }
- }
- else
- mpn_bc_mulmod_bnm1 (rp, ap, bp, rn, tp);
- }
- else
- {
- mp_size_t n;
- mp_limb_t cy;
- mp_limb_t hi;
- n = rn >> 1;
- /* We need at least an + bn >= n, to be able to fit one of the
- recursive products at rp. Requiring strict inequality makes
- the coded slightly simpler. If desired, we could avoid this
- restriction by initially halving rn as long as rn is even and
- an + bn <= rn/2. */
- ASSERT (an + bn > n);
- /* Compute xm = a*b mod (B^n - 1), xp = a*b mod (B^n + 1)
- and crt together as
- x = -xp * B^n + (B^n + 1) * [ (xp + xm)/2 mod (B^n-1)]
- */
- #define a0 ap
- #define a1 (ap + n)
- #define b0 bp
- #define b1 (bp + n)
- #define xp tp /* 2n + 2 */
- /* am1 maybe in {xp, n} */
- /* bm1 maybe in {xp + n, n} */
- #define sp1 (tp + 2*n + 2)
- /* ap1 maybe in {sp1, n + 1} */
- /* bp1 maybe in {sp1 + n + 1, n + 1} */
- {
- mp_srcptr am1, bm1;
- mp_size_t anm, bnm;
- mp_ptr so;
- if (LIKELY (an > n))
- {
- am1 = xp;
- cy = mpn_add (xp, a0, n, a1, an - n);
- MPN_INCR_U (xp, n, cy);
- anm = n;
- if (LIKELY (bn > n))
- {
- bm1 = xp + n;
- cy = mpn_add (xp + n, b0, n, b1, bn - n);
- MPN_INCR_U (xp + n, n, cy);
- bnm = n;
- so = xp + 2*n;
- }
- else
- {
- so = xp + n;
- bm1 = b0;
- bnm = bn;
- }
- }
- else
- {
- so = xp;
- am1 = a0;
- anm = an;
- bm1 = b0;
- bnm = bn;
- }
- mpn_mulmod_bnm1 (rp, n, am1, anm, bm1, bnm, so);
- }
- {
- int k;
- mp_srcptr ap1, bp1;
- mp_size_t anp, bnp;
- if (LIKELY (an > n)) {
- ap1 = sp1;
- cy = mpn_sub (sp1, a0, n, a1, an - n);
- sp1[n] = 0;
- MPN_INCR_U (sp1, n + 1, cy);
- anp = n + ap1[n];
- } else {
- ap1 = a0;
- anp = an;
- }
- if (LIKELY (bn > n)) {
- bp1 = sp1 + n + 1;
- cy = mpn_sub (sp1 + n + 1, b0, n, b1, bn - n);
- sp1[2*n+1] = 0;
- MPN_INCR_U (sp1 + n + 1, n + 1, cy);
- bnp = n + bp1[n];
- } else {
- bp1 = b0;
- bnp = bn;
- }
- if (BELOW_THRESHOLD (n, MUL_FFT_MODF_THRESHOLD))
- k=0;
- else
- {
- int mask;
- k = mpn_fft_best_k (n, 0);
- mask = (1<<k) -1;
- while (n & mask) {k--; mask >>=1;};
- }
- if (k >= FFT_FIRST_K)
- xp[n] = mpn_mul_fft (xp, n, ap1, anp, bp1, bnp, k);
- else if (UNLIKELY (bp1 == b0))
- {
- ASSERT (anp + bnp <= 2*n+1);
- ASSERT (anp + bnp > n);
- ASSERT (anp >= bnp);
- mpn_mul (xp, ap1, anp, bp1, bnp);
- anp = anp + bnp - n;
- ASSERT (anp <= n || xp[2*n]==0);
- anp-= anp > n;
- cy = mpn_sub (xp, xp, n, xp + n, anp);
- xp[n] = 0;
- MPN_INCR_U (xp, n+1, cy);
- }
- else
- mpn_bc_mulmod_bnp1 (xp, ap1, bp1, n, xp);
- }
- /* Here the CRT recomposition begins.
- xm <- (xp + xm)/2 = (xp + xm)B^n/2 mod (B^n-1)
- Division by 2 is a bitwise rotation.
- Assumes xp normalised mod (B^n+1).
- The residue class [0] is represented by [B^n-1]; except when
- both input are ZERO.
- */
- #if HAVE_NATIVE_mpn_rsh1add_n || HAVE_NATIVE_mpn_rsh1add_nc
- #if HAVE_NATIVE_mpn_rsh1add_nc
- cy = mpn_rsh1add_nc(rp, rp, xp, n, xp[n]); /* B^n = 1 */
- hi = cy << (GMP_NUMB_BITS - 1);
- cy = 0;
- /* next update of rp[n-1] will set cy = 1 only if rp[n-1]+=hi
- overflows, i.e. a further increment will not overflow again. */
- #else /* ! _nc */
- cy = xp[n] + mpn_rsh1add_n(rp, rp, xp, n); /* B^n = 1 */
- hi = (cy<<(GMP_NUMB_BITS-1))&GMP_NUMB_MASK; /* (cy&1) << ... */
- cy >>= 1;
- /* cy = 1 only if xp[n] = 1 i.e. {xp,n} = ZERO, this implies that
- the rsh1add was a simple rshift: the top bit is 0. cy=1 => hi=0. */
- #endif
- #if GMP_NAIL_BITS == 0
- add_ssaaaa(cy, rp[n-1], cy, rp[n-1], 0, hi);
- #else
- cy += (hi & rp[n-1]) >> (GMP_NUMB_BITS-1);
- rp[n-1] ^= hi;
- #endif
- #else /* ! HAVE_NATIVE_mpn_rsh1add_n */
- #if HAVE_NATIVE_mpn_add_nc
- cy = mpn_add_nc(rp, rp, xp, n, xp[n]);
- #else /* ! _nc */
- cy = xp[n] + mpn_add_n(rp, rp, xp, n); /* xp[n] == 1 implies {xp,n} == ZERO */
- #endif
- cy += (rp[0]&1);
- mpn_rshift(rp, rp, n, 1);
- ASSERT (cy <= 2);
- hi = (cy<<(GMP_NUMB_BITS-1))&GMP_NUMB_MASK; /* (cy&1) << ... */
- cy >>= 1;
- /* We can have cy != 0 only if hi = 0... */
- ASSERT ((rp[n-1] & GMP_NUMB_HIGHBIT) == 0);
- rp[n-1] |= hi;
- /* ... rp[n-1] + cy can not overflow, the following INCR is correct. */
- #endif
- ASSERT (cy <= 1);
- /* Next increment can not overflow, read the previous comments about cy. */
- ASSERT ((cy == 0) || ((rp[n-1] & GMP_NUMB_HIGHBIT) == 0));
- MPN_INCR_U(rp, n, cy);
- /* Compute the highest half:
- ([(xp + xm)/2 mod (B^n-1)] - xp ) * B^n
- */
- if (UNLIKELY (an + bn < rn))
- {
- /* Note that in this case, the only way the result can equal
- zero mod B^{rn} - 1 is if one of the inputs is zero, and
- then the output of both the recursive calls and this CRT
- reconstruction is zero, not B^{rn} - 1. Which is good,
- since the latter representation doesn't fit in the output
- area.*/
- cy = mpn_sub_n (rp + n, rp, xp, an + bn - n);
- /* FIXME: This subtraction of the high parts is not really
- necessary, we do it to get the carry out, and for sanity
- checking. */
- cy = xp[n] + mpn_sub_nc (xp + an + bn - n, rp + an + bn - n,
- xp + an + bn - n, rn - (an + bn), cy);
- ASSERT (an + bn == rn - 1 ||
- mpn_zero_p (xp + an + bn - n + 1, rn - 1 - (an + bn)));
- cy = mpn_sub_1 (rp, rp, an + bn, cy);
- ASSERT (cy == (xp + an + bn - n)[0]);
- }
- else
- {
- cy = xp[n] + mpn_sub_n (rp + n, rp, xp, n);
- /* cy = 1 only if {xp,n+1} is not ZERO, i.e. {rp,n} is not ZERO.
- DECR will affect _at most_ the lowest n limbs. */
- MPN_DECR_U (rp, 2*n, cy);
- }
- #undef a0
- #undef a1
- #undef b0
- #undef b1
- #undef xp
- #undef sp1
- }
- }
- mp_size_t
- mpn_mulmod_bnm1_next_size (mp_size_t n)
- {
- mp_size_t nh;
- if (BELOW_THRESHOLD (n, MULMOD_BNM1_THRESHOLD))
- return n;
- if (BELOW_THRESHOLD (n, 4 * (MULMOD_BNM1_THRESHOLD - 1) + 1))
- return (n + (2-1)) & (-2);
- if (BELOW_THRESHOLD (n, 8 * (MULMOD_BNM1_THRESHOLD - 1) + 1))
- return (n + (4-1)) & (-4);
- nh = (n + 1) >> 1;
- if (BELOW_THRESHOLD (nh, MUL_FFT_MODF_THRESHOLD))
- return (n + (8-1)) & (-8);
- return 2 * mpn_fft_next_size (nh, mpn_fft_best_k (nh, 0));
- }