255 lines
7.5 KiB
C
255 lines
7.5 KiB
C
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/*
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Copyright 2009, 2011 William Hart. All rights reserved.
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Redistribution and use in source and binary forms, with or without modification, are
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permitted provided that the following conditions are met:
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1. Redistributions of source code must retain the above copyright notice, this list of
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conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright notice, this list
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of conditions and the following disclaimer in the documentation and/or other materials
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provided with the distribution.
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THIS SOFTWARE IS PROVIDED BY William Hart ``AS IS'' AND ANY EXPRESS OR IMPLIED
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WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
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FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL William Hart OR
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CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
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ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
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ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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The views and conclusions contained in the software and documentation are those of the
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authors and should not be interpreted as representing official policies, either expressed
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or implied, of William Hart.
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*/
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#include "gmp.h"
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#include "flint.h"
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#include "fft.h"
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#include "longlong.h"
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#include "ulong_extras.h"
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#include "fft_tuning.h"
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#include "mpn_extras.h"
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static mp_size_t mulmod_2expp1_table_n[FFT_N_NUM] = MULMOD_TAB;
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void fft_naive_convolution_1(mp_limb_t * r, mp_limb_t * ii, mp_limb_t * jj, mp_size_t m)
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{
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mp_size_t i, j;
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for (i = 0; i < m; i++)
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r[i] = ii[0]*jj[i];
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for (i = 1; i < m; i++)
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{
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for (j = 0; j < m - i; j++)
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r[i+j] += ii[i]*jj[j];
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for ( ; j < m; j++)
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r[i+j-m] -=ii[i]*jj[j];
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}
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}
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void _fft_mulmod_2expp1(mp_limb_t * r1, mp_limb_t * i1, mp_limb_t * i2,
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mp_size_t r_limbs, mp_bitcnt_t depth, mp_bitcnt_t w)
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{
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mp_size_t n = (UWORD(1)<<depth);
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mp_bitcnt_t bits1 = (r_limbs*FLINT_BITS)/(2*n);
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mp_size_t limb_add, limbs = (n*w)/FLINT_BITS;
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mp_size_t size = limbs + 1;
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mp_size_t i, j, ll;
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mp_limb_t * ptr;
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mp_limb_t ** ii, ** jj, *tt, *t1, *t2, *s1, *r, *ii0, *jj0;
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mp_limb_t c;
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ii = flint_malloc((2*(n + n*size) + 4*n + 5*size)*sizeof(mp_limb_t));
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for (i = 0, ptr = (mp_limb_t *) ii + 2*n; i < 2*n; i++, ptr += size)
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{
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ii[i] = ptr;
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}
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ii0 = ptr;
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t1 = ii0 + 2*n;
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t2 = t1 + size;
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s1 = t2 + size;
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r = s1 + size;
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tt = r + 2*n;
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if (i1 != i2)
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{
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jj = flint_malloc((2*(n + n*size) + 2*n)*sizeof(mp_limb_t));
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for (i = 0, ptr = (mp_limb_t *) jj + 2*n; i < 2*n; i++, ptr += size)
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{
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jj[i] = ptr;
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}
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jj0 = ptr;
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} else
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{
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jj = ii;
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jj0 = ii0;
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}
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j = fft_split_bits(ii, i1, r_limbs, bits1, limbs);
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for ( ; j < 2*n; j++)
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flint_mpn_zero(ii[j], limbs + 1);
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for (i = 0; i < 2*n; i++)
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ii0[i] = ii[i][0];
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fft_negacyclic(ii, n, w, &t1, &t2, &s1);
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for (j = 0; j < 2*n; j++)
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mpn_normmod_2expp1(ii[j], limbs);
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if (i1 != i2)
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{
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j = fft_split_bits(jj, i2, r_limbs, bits1, limbs);
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for ( ; j < 2*n; j++)
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flint_mpn_zero(jj[j], limbs + 1);
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for (i = 0; i < 2*n; i++)
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jj0[i] = jj[i][0];
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fft_negacyclic(jj, n, w, &t1, &t2, &s1);
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}
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for (j = 0; j < 2*n; j++)
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{
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if (i1 != i2) mpn_normmod_2expp1(jj[j], limbs);
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c = 2*ii[j][limbs] + jj[j][limbs];
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ii[j][limbs] = flint_mpn_mulmod_2expp1_basecase(ii[j], ii[j], jj[j], c, n*w, tt);
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}
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ifft_negacyclic(ii, n, w, &t1, &t2, &s1);
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fft_naive_convolution_1(r, ii0, jj0, 2*n);
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for (j = 0; j < 2*n; j++)
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{
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mp_limb_t t, cy2;
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mpn_div_2expmod_2expp1(ii[j], ii[j], limbs, depth + 1);
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mpn_normmod_2expp1(ii[j], limbs);
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t = ii[j][limbs];
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ii[j][limbs] = r[j] - ii[j][0];
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cy2 = mpn_add_1(ii[j], ii[j], limbs + 1, ii[j][limbs]);
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add_ssaaaa(r[j], ii[j][limbs], 0, ii[j][limbs], 0, t);
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if (cy2) r[j]++;
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}
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flint_mpn_zero(r1, r_limbs + 1);
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fft_combine_bits(r1, ii, 2*n - 1, bits1, limbs + 1, r_limbs + 1);
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/*
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as the negacyclic convolution has effectively done subtractions
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some of the coefficients will be negative, so need to subtract p
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*/
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ll = 0;
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limb_add = bits1/FLINT_BITS;
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for (j = 0; j < 2*n - 2; j++)
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{
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if (r[j])
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mpn_sub_1(r1 + ll + 1, r1 + ll + 1, r_limbs - ll, 1);
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else if ((mp_limb_signed_t) ii[j][limbs] < 0) /* coefficient was -ve */
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{
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mpn_sub_1(r1 + ll + 1, r1 + ll + 1, r_limbs - ll, 1);
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mpn_sub_1(r1 + ll + limbs + 1, r1 + ll + limbs + 1, r_limbs - limbs - ll, 1);
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}
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ll += limb_add;
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}
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/* penultimate coefficient, top bit was already ignored */
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if (r[j] || (mp_limb_signed_t) ii[j][limbs] < 0) /* coefficient was -ve */
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mpn_sub_1(r1 + ll + 1, r1 + ll + 1, r_limbs - ll, 1);
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/* final coefficient wraps around */
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if (limb_add)
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r1[r_limbs] += mpn_add_n(r1 + r_limbs - limb_add, r1 + r_limbs - limb_add, ii[2*n - 1], limb_add);
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c = mpn_sub_n(r1, r1, ii[2*n - 1] + limb_add, limbs + 1 - limb_add);
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mpn_addmod_2expp1_1(r1 + limbs + 1 - limb_add, r_limbs - limbs - 1 + limb_add, -c);
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mpn_normmod_2expp1(r1, r_limbs);
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flint_free(ii);
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if (i1 != i2) flint_free(jj);
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}
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void fft_mulmod_2expp1(mp_limb_t * r, mp_limb_t * i1, mp_limb_t * i2,
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mp_size_t n, mp_size_t w, mp_limb_t * tt)
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{
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mp_size_t bits = n*w;
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mp_size_t limbs = bits/FLINT_BITS;
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mp_bitcnt_t depth1, depth = 1;
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mp_size_t w1, off;
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mp_limb_t c = 2*i1[limbs] + i2[limbs];
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if (c & 1)
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{
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mpn_neg_n(r, i1, limbs + 1);
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mpn_normmod_2expp1(r, limbs);
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return;
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} else if (c & 2)
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{
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mpn_neg_n(r, i2, limbs + 1);
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mpn_normmod_2expp1(r, limbs);
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return;
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}
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if (limbs <= FFT_MULMOD_2EXPP1_CUTOFF)
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{
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r[limbs] = flint_mpn_mulmod_2expp1_basecase(r, i1, i2, c, bits, tt);
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return;
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}
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while ((UWORD(1)<<depth) < bits) depth++;
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if (depth < 12) off = mulmod_2expp1_table_n[0];
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else off = mulmod_2expp1_table_n[FLINT_MIN(depth, FFT_N_NUM + 11) - 12];
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depth1 = depth/2 - off;
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w1 = bits/(UWORD(1)<<(2*depth1));
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_fft_mulmod_2expp1(r, i1, i2, limbs, depth1, w1);
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}
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slong fft_adjust_limbs(mp_size_t limbs)
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{
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mp_size_t bits1 = limbs*FLINT_BITS, bits2;
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mp_size_t depth = 1, limbs2, depth1 = 1, depth2 = 1, adj;
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mp_size_t off1, off2;
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if (limbs <= FFT_MULMOD_2EXPP1_CUTOFF) return limbs;
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depth = FLINT_CLOG2(limbs);
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limbs2 = (WORD(1)<<depth); /* within a factor of 2 of limbs */
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bits2 = limbs2*FLINT_BITS;
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depth1 = FLINT_CLOG2(bits1);
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if (depth1 < 12) off1 = mulmod_2expp1_table_n[0];
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else off1 = mulmod_2expp1_table_n[FLINT_MIN(depth1, FFT_N_NUM + 11) - 12];
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depth1 = depth1/2 - off1;
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depth2 = FLINT_CLOG2(bits2);
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if (depth2 < 12) off2 = mulmod_2expp1_table_n[0];
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else off2 = mulmod_2expp1_table_n[FLINT_MIN(depth2, FFT_N_NUM + 11) - 12];
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depth2 = depth2/2 - off2;
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depth1 = FLINT_MAX(depth1, depth2);
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adj = (WORD(1)<<(depth1 + 1));
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limbs2 = adj*((limbs + adj - 1)/adj); /* round up number of limbs */
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bits1 = limbs2*FLINT_BITS;
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bits2 = (WORD(1)<<(depth1*2));
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bits1 = bits2*((bits1 + bits2 - 1)/bits2); /* round up bits */
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limbs = bits1/FLINT_BITS;
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return limbs;
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}
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