pqc/external/flint-2.4.3/fmpz_factor/factor_pp1.c

/*=============================================================================

    This file is part of FLINT.

    FLINT is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    FLINT 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 General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with FLINT; if not, write to the Free Software
    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301 USA

=============================================================================*/
/******************************************************************************

    Copyright (C) 2012 William Hart

******************************************************************************/

#define ulong ulongxx /* interferes with system includes */
#include <string.h>
#undef ulong
#define ulong mp_limb_t
#include <gmp.h>
#include "flint.h"
#include "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_mod_poly.h"
#include "mpn_extras.h"
#include "ulong_extras.h"

#define DEBUG 0 /* turn on some trace information */

#define pp1_mulmod(rxx, axx, bxx, nnn, nxx, ninv, norm)             \
   flint_mpn_mulmod_preinvn(rxx, axx, bxx, nnn, nxx, ninv, norm)

#ifdef FLINT64
static
ulong pp1_primorial[15] =
{
   UWORD(2), UWORD(6), UWORD(30), UWORD(210), UWORD(2310), UWORD(30030), UWORD(510510), UWORD(9699690),
   UWORD(223092870), UWORD(6469693230), UWORD(200560490130), UWORD(7420738134810),
   UWORD(304250263527210), UWORD(13082761331670030), UWORD(614889782588491410)
};
#define num_primorials 15
#else
static
ulong pp1_primorial[9] = 
{
   UWORD(2), UWORD(6), UWORD(30), UWORD(210), UWORD(2310), UWORD(30030), UWORD(510510), UWORD(9699690),
   UWORD(223092870)
};
#define num_primorials 9
#endif

void pp1_set(mp_ptr x1, mp_ptr y1, 
              mp_srcptr x2, mp_srcptr y2, mp_size_t nn)
{
   mpn_copyi(x1, x2, nn);
   mpn_copyi(y1, y2, nn);
}

void pp1_set_ui(mp_ptr x, mp_size_t nn, ulong norm, ulong c)
{
   mpn_zero(x, nn);
   x[0] = (c << norm);
   if (nn > 1 && norm)
      x[1] = (c >> (FLINT_BITS - norm));
}

void pp1_print(mp_srcptr x, mp_srcptr y, mp_size_t nn, ulong norm)
{
   mp_ptr tx = flint_malloc(nn*sizeof(mp_limb_t));
   mp_ptr ty = flint_malloc(nn*sizeof(mp_limb_t));

   if (norm)
   {
      mpn_rshift(tx, x, nn, norm);
      mpn_rshift(ty, y, nn, norm);
   } else
   {
       mpn_copyi(tx, x, nn);
       mpn_copyi(ty, y, nn);
   }

   flint_printf("["), gmp_printf("%Nd", tx, nn), flint_printf(", "), gmp_printf("%Nd", ty, nn), flint_printf("]");

   flint_free(tx);
   flint_free(ty);
}

void pp1_2k(mp_ptr x, mp_ptr y, mp_size_t nn, mp_srcptr n, 
            mp_srcptr ninv, mp_srcptr x0, ulong norm)
{
   pp1_mulmod(y, y, x, nn, n, ninv, norm);
   if (mpn_sub_n(y, y, x0, nn))
      mpn_add_n(y, y, n, nn);

   pp1_mulmod(x, x, x, nn, n, ninv, norm);
   if (mpn_sub_1(x, x, nn, UWORD(2) << norm))
      mpn_add_n(x, x, n, nn);
}

void pp1_2kp1(mp_ptr x, mp_ptr y, mp_size_t nn, mp_srcptr n, 
              mp_srcptr ninv, mp_srcptr x0, ulong norm)
{
   pp1_mulmod(x, x, y, nn, n, ninv, norm);
   if (mpn_sub_n(x, x, x0, nn))
      mpn_add_n(x, x, n, nn);

   pp1_mulmod(y, y, y, nn, n, ninv, norm);
   if (mpn_sub_1(y, y, nn, UWORD(2) << norm))
      mpn_add_n(y, y, n, nn);
}

void pp1_pow_ui(mp_ptr x, mp_ptr y, mp_size_t nn, 
                ulong exp, mp_srcptr n, mp_srcptr ninv, ulong norm)
{
   mp_limb_t t[30];
   mp_ptr x0 = t;
   ulong bit = ((UWORD(1) << FLINT_BIT_COUNT(exp)) >> 2);

   if (nn > 30)
      x0 = flint_malloc(nn*sizeof(mp_limb_t));
   mpn_copyi(x0, x, nn);

   pp1_mulmod(y, x, x, nn, n, ninv, norm);
   if (mpn_sub_1(y, y, nn, UWORD(2) << norm))
      mpn_add_n(y, y, n, nn);

   while (bit)
   {
      if (exp & bit)
         pp1_2kp1(x, y, nn, n, ninv, x0, norm);
      else
         pp1_2k(x, y, nn, n, ninv, x0, norm);

      bit >>= 1;
   }

   if (nn > 30)
      flint_free(x0);
}

mp_size_t pp1_factor(mp_ptr factor, mp_srcptr n,
                     mp_srcptr x, mp_size_t nn, ulong norm)
{
   mp_size_t ret = 0, xn = nn;
   
   mp_ptr n2 = flint_malloc(nn*sizeof(mp_limb_t));
   mp_ptr x2 = flint_malloc(nn*sizeof(mp_limb_t));

   if (norm)
      mpn_rshift(n2, n, nn, norm);
   else
      mpn_copyi(n2, n, nn);

   if (norm)
      mpn_rshift(x2, x, nn, norm);
   else
      mpn_copyi(x2, x, nn);
   
   if (mpn_sub_1(x2, x2, nn, 2))
      mpn_add_n(x2, x2, n2, nn);

   MPN_NORM(x2, xn);

   if (xn == 0)
      goto cleanup;
   
   ret = flint_mpn_gcd_full(factor, n2, nn, x2, xn);

cleanup:

   flint_free(n2);
   flint_free(x2);

   return ret;
}

mp_size_t pp1_find_power(mp_ptr factor, mp_ptr x, mp_ptr y, mp_size_t nn, 
                          ulong p, mp_srcptr n, mp_srcptr ninv, ulong norm)
{
   mp_size_t ret;
   
   do
   {
      pp1_pow_ui(x, y, nn, p, n, ninv, norm);
      ret = pp1_factor(factor, n, x, nn, norm);
   } while (ret == 1 && factor[0] == 1);

   return ret;
}

int fmpz_factor_pp1(fmpz_t fac, const fmpz_t n_in, ulong B1, ulong B2sqrt, ulong c)
{
   slong i, j;
   int ret = 0;
   mp_size_t nn = fmpz_size(n_in), r;
   mp_ptr x, y, oldx, oldy, n, ninv, factor, ptr_0, ptr_1, ptr_2, ptr_k;
   ulong pr, oldpr, sqrt, bits0, norm;
   n_primes_t iter;

   if (fmpz_is_even(n_in))
   {
      fmpz_set_ui(fac, 2);
      return 1;
   }

#if DEBUG
   flint_printf("starting stage 1\n");
#endif

   n_primes_init(iter);

   sqrt = n_sqrt(B1);
   bits0 = FLINT_BIT_COUNT(B1);

   x      = flint_malloc(nn*sizeof(mp_limb_t));
   y      = flint_malloc(nn*sizeof(mp_limb_t));
   oldx   = flint_malloc(nn*sizeof(mp_limb_t));
   oldy   = flint_malloc(nn*sizeof(mp_limb_t));
   n      = flint_malloc(nn*sizeof(mp_limb_t));
   ninv   = flint_malloc(nn*sizeof(mp_limb_t));
   factor = flint_malloc(nn*sizeof(mp_limb_t));
      
   if (nn == 1)
   {
      n[0] = fmpz_get_ui(n_in);
      count_leading_zeros(norm, n[0]);
      n[0] <<= norm;
   } else
   {
      mp_ptr np = COEFF_TO_PTR(*n_in)->_mp_d;
      count_leading_zeros(norm, np[nn - 1]);
      if (norm)
         mpn_lshift(n, np, nn, norm);
      else
         mpn_copyi(n, np, nn);
   }

   flint_mpn_preinvn(ninv, n, nn);
   
   pp1_set_ui(x, nn, norm, c);
   
   /* mul by various prime powers */
   pr = 0;
   oldpr = 0;

   for (i = 0; pr < B1; )
   {
      j = i + 1024;
      oldpr = pr;
      pp1_set(oldx, oldy, x, y, nn);
      for ( ; i < j; i++)
      {
         pr = n_primes_next(iter);
         if (pr < sqrt)
         {
            ulong bits = FLINT_BIT_COUNT(pr);
            ulong exp = bits0 / bits;
            pp1_pow_ui(x, y, nn, n_pow(pr, exp), n, ninv, norm);
         } else
            pp1_pow_ui(x, y, nn, pr, n, ninv, norm);
      }
      
      r = pp1_factor(factor, n, x, nn, norm);
      if (r == 0)
         break;
      if (r != 1 || factor[0] != 1)
      {
         ret = 1;
         goto cleanup;
      }
   }

   if (pr < B1) /* factor = 0 */
   {
      n_primes_jump_after(iter, oldpr);
      pp1_set(x, y, oldx, oldy, nn);
         
      do
      {
         pr = n_primes_next(iter);
         pp1_set(oldx, oldy, x, y, nn);
         if (pr < sqrt)
         {
            ulong bits = FLINT_BIT_COUNT(pr);
            ulong exp = bits0 / bits;
            pp1_pow_ui(x, y, nn, n_pow(pr, exp), n, ninv, norm);
         } else
            pp1_pow_ui(x, y, nn, pr, n, ninv, norm);

         r = pp1_factor(factor, n, x, nn, norm);
         if (r == 0)
            break;
         if (r != 1 || factor[0] != 1)
         {
            ret = 1;
            goto cleanup;
         }
      } while (1);

      /* factor is still 0 */
      ret = pp1_find_power(factor, oldx, oldy, nn, pr, n, ninv, norm);
   } else /* stage 2 */
   {
      double quot;
      int num;
      char * sieve = flint_malloc(32768);
      slong * sieve_index = flint_malloc(32768*sizeof(slong));
      mp_ptr diff = flint_malloc(16384*nn*sizeof(mp_limb_t));
      ulong offset[15], num_roots;
      slong k, index = 0, s;
      fmpz * roots, * roots2, * evals;
      fmpz_poly_struct ** tree, ** tree2;

#if DEBUG
      ulong primorial;
      flint_printf("starting stage 2\n");
#endif

      /* find primorial <= B2sqrt ... */
      for (num = 1; num < num_primorials; num++)
      {
         if (pp1_primorial[num] > B2sqrt)
            break;
      }
      num--;
 
      /* ... but not too big */
      quot = (double) B2sqrt / (double) pp1_primorial[num];
      if (quot < 1.1 && num > 0)
         num--;

#if DEBUG
      primorial = pp1_primorial[num];
      flint_printf("found primorial %wu\n", primorial);
#endif

      /* adjust B2sqrt to multiple of primorial */
      B2sqrt = (((B2sqrt - 1)/ pp1_primorial[num]) + 1) * pp1_primorial[num];

#if DEBUG
      flint_printf("adjusted B2sqrt %wu\n", B2sqrt);
#endif

      /* compute num roots */
      num++; /* number of primes is 1 more than primorial index */
      pr = 2;
      num_roots = B2sqrt;
      for (i = 0; i < num; i++)
      {
         num_roots = (num_roots*(pr - 1))/pr;
         pr = n_nextprime(pr, 0);
      }

#if DEBUG
      flint_printf("computed num_roots %wu\n", num_roots);
      flint_printf("B2 = %wu\n", num_roots * B2sqrt);
#endif

      /* construct roots */
      roots = _fmpz_vec_init(num_roots);
      for (i = 0; i < num_roots; i++)
      {
         __mpz_struct * m = _fmpz_promote(roots + i);
         mpz_realloc(m, nn);
      }

      roots2 = _fmpz_vec_init(num_roots);
      for (i = 0; i < num_roots; i++)
      {
         __mpz_struct * m = _fmpz_promote(roots2 + i);
         mpz_realloc(m, nn);
      }

      evals = _fmpz_vec_init(num_roots);

#if DEBUG
      flint_printf("constructed roots\n");
#endif

      /* compute differences table v0, ... */
      mpn_zero(diff, nn);
      diff[0] = (UWORD(2) << norm);

      /* ... v2, ... */
      pp1_mulmod(diff + nn, x, x, nn, n, ninv, norm);
      if (mpn_sub_1(diff + nn, diff + nn, nn, UWORD(2) << norm))
         mpn_add_n(diff + nn, diff + nn, n, nn);

      /* ... the rest ... v_{k+2} = v_k v_2 - v_{k-2} */
      k = 2*nn;
      for (i = 2; i < 16384; i++, k += nn)
      {
         pp1_mulmod(diff + k, diff + k - nn, diff + nn, nn, n, ninv, norm);
         if (mpn_sub_n(diff + k, diff + k, diff + k - 2*nn, nn))
            mpn_add_n(diff + k, diff + k, n, nn);
      }

#if DEBUG
      flint_printf("conputed differences table\n");
#endif

      /* initial positions */
      pr = 2;
      for (i = 0; i < num; i++)
      {
         offset[i] = pr/2;
         pr = n_nextprime(pr, 0);
      }

      s = 0;
      while (2*s + 1 < B2sqrt)
      {
         /* sieve */
         memset(sieve, 1, 32768);
         pr = 3;
         for (i = 1; i < num; i++)
         {
            j = offset[i];
            while (j < 32768)
               sieve[j] = 0, j += pr;

            /* store offset for start of next sieve run */
            offset[i] = j - 32768;
            pr = n_nextprime(pr, 0);
         }

         /* compute roots */
         for (i = 0; i < 32768 && 2*(s + i) + 1 < B2sqrt; i++)
         {
            if (sieve[i])
            {
               ptr_2 = COEFF_TO_PTR(roots[index])->_mp_d;
               k = (i + 1)/2;
               for (j = i - 1; j >= k; j--)
               {
                  if (sieve[j] && sieve[2*j - i])
                  {
                     /* V_{n+k} = V_n V_k - V_{n-k} */
                     ptr_0 = COEFF_TO_PTR(roots[sieve_index[2*j - i]])->_mp_d;
                     ptr_1 = COEFF_TO_PTR(roots[sieve_index[j]])->_mp_d;
                     ptr_k = diff + (i - j)*nn;
                     pp1_mulmod(ptr_2, ptr_1, ptr_k, nn, n, ninv, norm);
                     if (mpn_sub_n(ptr_2, ptr_2, ptr_0, nn))
                        mpn_add_n(ptr_2, ptr_2, n, nn);
                     break;
                  }
               }

               if (j < k) /* pair not found, compute using pow_ui */
               {
                  mpn_copyi(ptr_2, x, nn);
                  pp1_pow_ui(ptr_2, y, nn, 2*(s + i) + 1, n, ninv, norm);
               }
             
               sieve_index[i] = index;
               index++;
            }
         }

         s += 32768;
      }

#if DEBUG
      flint_printf("roots computed %wd\n", index);
#endif

      /* v_1 */
      mpn_copyi(oldx, x, nn);
      pp1_pow_ui(oldx, y, nn, B2sqrt, n, ninv, norm);
      ptr_0 = COEFF_TO_PTR(roots2[0])->_mp_d;
      mpn_copyi(ptr_0, oldx, nn);

      /* v_2 */
      ptr_1 = COEFF_TO_PTR(roots2[1])->_mp_d;
      pp1_mulmod(ptr_1, ptr_0, ptr_0, nn, n, ninv, norm);
      if (mpn_sub_1(ptr_1, ptr_1, nn, UWORD(2) << norm))
         mpn_add_n(ptr_1, ptr_1, n, nn);
     
      for (i = 2; i < num_roots; i++)
      {
         /* V_{k+n} = V_k V_n - V_{k-n} */
         ptr_2 = COEFF_TO_PTR(roots2[i])->_mp_d;
      
         pp1_mulmod(ptr_2, ptr_1, oldx, nn, n, ninv, norm);
         if (mpn_sub_n(ptr_2, ptr_2, ptr_0, nn))
             mpn_add_n(ptr_2, ptr_2, n, nn);
                     
         ptr_0 = ptr_1;
         ptr_1 = ptr_2;
      }

#if DEBUG
      flint_printf("roots2 computed %wu\n", num_roots);
#endif

      for (i = 0; i < num_roots; i++)
      {
         mp_size_t sn;
         __mpz_struct * m1 = COEFF_TO_PTR(roots[i]);
         __mpz_struct * m2 = COEFF_TO_PTR(roots2[i]);
         
         ptr_1 = m1->_mp_d;
         ptr_2 = m2->_mp_d;
      
         mpn_rshift(ptr_1, ptr_1, nn, norm);
         mpn_rshift(ptr_2, ptr_2, nn, norm);

         sn = nn;
         MPN_NORM(ptr_1, sn);
         m1->_mp_size = sn;

         sn = nn;
         MPN_NORM(ptr_2, sn);
         m2->_mp_size = sn;

         _fmpz_demote_val(roots + i);
         _fmpz_demote_val(roots2 + i);
      }

#if DEBUG
      flint_printf("normalised roots\n");
#endif

      tree = _fmpz_mod_poly_tree_alloc(num_roots);
      _fmpz_mod_poly_tree_build(tree, roots, num_roots, n_in);

      tree2 = _fmpz_mod_poly_tree_alloc(num_roots);
      _fmpz_mod_poly_tree_build(tree2, roots2, num_roots, n_in);

      fmpz_poly_mul(tree2[FLINT_CLOG2(num_roots)], tree2[FLINT_CLOG2(num_roots)-1], tree2[FLINT_CLOG2(num_roots)-1]+1);
     
#if DEBUG
      flint_printf("built trees\n");
#endif

      _fmpz_mod_poly_evaluate_fmpz_vec_fast_precomp(evals, tree2[FLINT_CLOG2(num_roots)]->coeffs, tree2[FLINT_CLOG2(num_roots)]->length, tree, num_roots, n_in);
      _fmpz_mod_poly_tree_free(tree, num_roots);
      _fmpz_mod_poly_tree_free(tree2, num_roots);
      
#if DEBUG
      flint_printf("evaluated at roots\n");
#endif

      for (i = 0; i < num_roots; i++)
      {
         fmpz_gcd(fac, n_in, evals + i);
         if (!fmpz_is_zero(fac) && !fmpz_is_one(fac))
         {
            ret = 1;
            break;
         }
      }

      _fmpz_vec_clear(evals, num_roots);
      _fmpz_vec_clear(roots, num_roots);
      _fmpz_vec_clear(roots2, num_roots);
      flint_free(sieve);
      flint_free(diff);


      if (i < num_roots)
         goto cleanup2;
   }

#if DEBUG
   flint_printf("done stage2\n");
#endif

cleanup:

   if (ret)
   {
      __mpz_struct * fm = _fmpz_promote(fac);
      mpz_realloc(fm, r);
      mpn_copyi(fm->_mp_d, factor, r);
      fm->_mp_size = r;
      _fmpz_demote_val(fac);
   }

cleanup2:

   flint_free(x);
   flint_free(y);
   flint_free(oldx);
   flint_free(oldy);
   flint_free(n);
   flint_free(ninv);
   
   n_primes_clear(iter);

   return ret;
}