mpir/fft/mulmod_2expp1.c

/* 

Copyright 2009, 2011 William Hart. All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are
permitted provided that the following conditions are met:

   1. Redistributions of source code must retain the above copyright notice, this list of
      conditions and the following disclaimer.

   2. Redistributions in binary form must reproduce the above copyright notice, this list
      of conditions and the following disclaimer in the documentation and/or other materials
      provided with the distribution.

THIS SOFTWARE IS PROVIDED BY William Hart ``AS IS'' AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL William Hart OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

The views and conclusions contained in the software and documentation are those of the
authors and should not be interpreted as representing official policies, either expressed
or implied, of William Hart.

*/

#include "mpir.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "fft_tuning.h"

static mp_size_t mulmod_2expp1_table_n[FFT_N_NUM] = MULMOD_TAB;

void fft_naive_convolution_1(mp_ptr r, mp_srcptr ii, mp_srcptr jj, mp_size_t m)
{
   mp_size_t i, j;

   for (i = 0; i < m; i++)
      r[i] = ii[0]*jj[i];

   for (i = 1; i < m; i++)
   {
      for (j = 0; j < m - i; j++)
         r[i+j] += ii[i]*jj[j];

      for ( ; j < m; j++)
         r[i+j-m] -=ii[i]*jj[j];
   }
}

void fft_mulmod_2expp1(mp_ptr r1, mp_srcptr i1, mp_srcptr i2, 
                 mp_size_t r_limbs, mp_bitcnt_t depth, mp_bitcnt_t w)
{
   mp_size_t n = (((mp_size_t)1)<<depth);
   mp_bitcnt_t bits1 = (r_limbs*GMP_LIMB_BITS)/(2*n);
   
   mp_size_t limb_add, limbs = (n*w)/GMP_LIMB_BITS;
   mp_size_t size = limbs + 1;
   mp_size_t i, j, ll;

   mp_limb_t * ptr;
   mp_limb_t ** ii, ** jj, *tt, *t1, *t2, *s1, *r, *ii0, *jj0;
   mp_limb_t c;
   TMP_DECL;

   TMP_MARK;
   ii = TMP_BALLOC_MP_PTRS(2*(n + n*size) + 4*n + 5*size);
   for (i = 0, ptr = (mp_ptr) ii + 2*n; i < 2*n; i++, ptr += size) 
   {
      ii[i] = ptr;
   }
   ii0 = ptr;
   t1 = ii0 + 2*n;
   t2 = t1 + size;
   s1 = t2 + size;
   r = s1 + size;
   tt = r + 2*n;
   
   if (i1 != i2)
   {
      jj = TMP_BALLOC_MP_PTRS(2*(n + n*size) + 2*n);
      for (i = 0, ptr = (mp_ptr) jj + 2*n; i < 2*n; i++, ptr += size) 
      {
         jj[i] = ptr;
      }
      jj0 = ptr;
   } else
   {
      jj = ii;
      jj0 = ii0;
   }

   j = fft_split_bits(ii, i1, r_limbs, bits1, limbs);
   for ( ; j < 2*n; j++)
      mpn_zero(ii[j], limbs + 1);

   for (i = 0; i < 2*n; i++)
      ii0[i] = ii[i][0];
 
   fft_negacyclic(ii, n, w, &t1, &t2, &s1);
   for (j = 0; j < 2*n; j++)
      mpn_normmod_2expp1(ii[j], limbs);

   if (i1 != i2)
   {
      j = fft_split_bits(jj, i2, r_limbs, bits1, limbs);
      for ( ; j < 2*n; j++)
          mpn_zero(jj[j], limbs + 1);

      for (i = 0; i < 2*n; i++)
         jj0[i] = jj[i][0];

      fft_negacyclic(jj, n, w, &t1, &t2, &s1);
   }
      
   for (j = 0; j < 2*n; j++)
   {
      if (i1 != i2) mpn_normmod_2expp1(jj[j], limbs);
      c = 2*ii[j][limbs] + jj[j][limbs];

      ii[j][limbs] = mpn_mulmod_2expp1_basecase(ii[j], ii[j], jj[j], c, n*w, tt);
   }
   
   ifft_negacyclic(ii, n, w, &t1, &t2, &s1);
   
   fft_naive_convolution_1(r, ii0, jj0, 2*n);

   for (j = 0; j < 2*n; j++)
   {
      mp_limb_t t, cy2;
      
      mpn_div_2expmod_2expp1(ii[j], ii[j], limbs, depth + 1);
      mpn_normmod_2expp1(ii[j], limbs);

      t = ii[j][limbs];
      ii[j][limbs] = r[j] - ii[j][0];
      cy2 = mpn_add_1(ii[j], ii[j], limbs + 1, ii[j][limbs]);
      add_ssaaaa(r[j], ii[j][limbs], 0, ii[j][limbs], 0, t);
      if (cy2) r[j]++;
   }
   
   mpn_zero(r1, r_limbs + 1);
   fft_combine_bits(r1, ii, 2*n - 1, bits1, limbs + 1, r_limbs + 1);
   
   /* 
      as the negacyclic convolution has effectively done subtractions
      some of the coefficients will be negative, so need to subtract p
   */
   ll = 0;
   limb_add = bits1/GMP_LIMB_BITS;
   
   for (j = 0; j < 2*n - 2; j++)
   {   
      if (r[j]) 
         mpn_sub_1(r1 + ll + 1, r1 + ll + 1, r_limbs - ll, 1);
      else if ((mp_limb_signed_t) ii[j][limbs] < 0) /* coefficient was -ve */
      {
         mpn_sub_1(r1 + ll + 1, r1 + ll + 1, r_limbs - ll, 1);
         mpn_sub_1(r1 + ll + limbs + 1, r1 + ll + limbs + 1, r_limbs - limbs - ll, 1);
      }

      ll += limb_add;
   }
   /* penultimate coefficient, top bit was already ignored */
   if (r[j] || (mp_limb_signed_t) ii[j][limbs] < 0) /* coefficient was -ve */
      mpn_sub_1(r1 + ll + 1, r1 + ll + 1, r_limbs - ll, 1);
   
   /* final coefficient wraps around */
   r1[r_limbs] += mpn_add_n(r1 + r_limbs - limb_add, r1 + r_limbs - limb_add, ii[2*n - 1], limb_add);
   c = mpn_sub_n(r1, r1, ii[2*n - 1] + limb_add, limbs + 1 - limb_add);
   mpn_addmod_2expp1_1(r1 + limbs + 1 - limb_add, r_limbs - limbs - 1 + limb_add, -c);
   mpn_normmod_2expp1(r1, r_limbs);
   
   TMP_FREE;
}

mpir_si fft_adjust_limbs(mp_size_t limbs)
{
   mp_size_t bits1 = limbs*GMP_LIMB_BITS, bits2;
   mp_size_t depth = 1, limbs2, depth1 = 1, depth2 = 1, adj;
   mp_size_t off1, off2;

   if (limbs <= FFT_MULMOD_2EXPP1_CUTOFF) return limbs;
         
   while ((((mpir_ui)1)<<depth)<limbs) depth++;
   limbs2 = (((mpir_si)1)<<depth); /* within a factor of 2 of limbs */
   bits2 = limbs2*GMP_LIMB_BITS;

   while ((((mpir_ui)1)<<depth1) < bits1) depth1++;
   if (depth1 < 12) off1 = mulmod_2expp1_table_n[0];
   else off1 = mulmod_2expp1_table_n[MIN(depth1, FFT_N_NUM + 11) - 12];
   depth1 = depth1/2 - off1;
   
   while ((((mpir_ui)1)<<depth2) < bits2) depth2++;
   if (depth2 < 12) off2 = mulmod_2expp1_table_n[0];
   else off2 = mulmod_2expp1_table_n[MIN(depth2, FFT_N_NUM + 11) - 12];
   depth2 = depth2/2 - off2;
   
   depth1 = MAX(depth1, depth2);
   adj = (((mpir_si)1)<<(depth1 + 1));
   limbs2 = adj*((limbs + adj - 1)/adj); /* round up number of limbs */
   bits1 = limbs2*GMP_LIMB_BITS;
   bits2 = (((mpir_si)1)<<(depth1*2));
   bits1 = bits2*((bits1 + bits2 - 1)/bits2); /* round up bits */
   limbs = bits1/GMP_LIMB_BITS;

   return limbs;
}

int
mpn_mulmod_Bexpp1_fft (mp_ptr op, mp_size_t pl,
	     mp_srcptr n, mp_size_t nl,
	     mp_srcptr m, mp_size_t ml)
{
   mp_ptr a, b, tt;
   mp_limb_t cy;

   TMP_DECL;
   TMP_MARK;

   /* temporary space */
   tt = TMP_ALLOC_LIMBS(2*pl);
   
   /* make copies of inputs, padded out to pl limbs */
   a = TMP_ALLOC_LIMBS(pl + 1);
   mpn_copyi(a, n, nl);
   MPN_ZERO(a + nl, pl + 1 - nl);
   
   b = TMP_ALLOC_LIMBS(pl + 1);
   mpn_copyi(b, m, ml);
   MPN_ZERO(b + ml, pl + 1 - ml);
   
   /* this function only cares about the product, limbs = pl*GMP_LIMB_BITS */
   cy = mpn_mulmod_Bexpp1(op, a, b, pl, tt);
   
   TMP_FREE;

   return cy;
}