fft.h

/* mul_fft -- radix 2 fft routines for MPIR.

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.

*/

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

    Copyright (C) 2009, 2011 William Hart
 
******************************************************************************/

#ifndef FFT_H
#define FFT_H

#undef ulong
#define ulong ulongxx /* interferes with system includes */
#include <stdlib.h>
#include <stdio.h>
#undef ulong

#include <gmp.h>
#define ulong mp_limb_t
#include "flint.h"
#include "mpn_extras.h"

#ifdef __cplusplus
 extern "C" {
#endif

#if defined(__MPIR_VERSION)

#if !defined(__MPIR_RELEASE ) || __MPIR_RELEASE < 20600
#define mpn_sumdiff_n __MPN(sumdiff_n)
extern
mp_limb_t mpn_sumdiff_n(mp_ptr, mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
#endif

#else

static __inline__ mp_limb_t
mpn_sumdiff_n(mp_ptr s, mp_ptr d, mp_srcptr x, mp_srcptr y, mp_size_t n)
{
    mp_limb_t ret;
    mp_ptr t;

    if (n == 0)
        return 0;

    if ((s == x && d == y) || (s == y && d == x))
    {
        t = flint_malloc(n * sizeof(mp_limb_t));
        ret = mpn_sub_n(t, x, y, n);
        ret += 2 * mpn_add_n(s, x, y, n);
        flint_mpn_copyi(d, t, n);
        flint_free(t);
        return ret;
    }

    if (s == x || s == y)
    {
        ret = mpn_sub_n(d, x, y, n);
        ret += 2 * mpn_add_n(s, x, y, n);
        return ret;
    }

    ret = 2 * mpn_add_n(s, x, y, n);
    ret += mpn_sub_n(d, x, y, n);
    return ret;
}

#endif

#define fft_sumdiff(t, u, r, s, n) \
   (n == 0 ? 0 : mpn_sumdiff_n(t, u, r, s, n))


#define SWAP_PTRS(xx, yy) \
   do { \
      mp_limb_t * __ptr = xx; \
      xx = yy; \
      yy = __ptr; \
   } while (0)

/* used for generating random values mod p in test code */
#define random_fermat(nn, state, limbs) \
   do { \
      if (n_randint(state, 10) == 0) { \
         flint_mpn_zero(nn, limbs); \
         nn[limbs] = 1; \
      } else { \
         if (n_randint(state, 2) == 0) \
            flint_mpn_rrandom(nn, state->gmp_state, limbs); \
         else \
            flint_mpn_urandomb(nn, state->gmp_state, limbs*FLINT_BITS); \
         nn[limbs] = n_randint(state, 1024); \
      } \
      if (n_randint(state, 2)) \
         nn[limbs] = -nn[limbs]; \
   } while (0)

static __inline__
void mpn_addmod_2expp1_1(mp_limb_t * r, mp_size_t limbs, mp_limb_signed_t c)
{
   mp_limb_t sum = r[0] + c;

   /* check if adding c would cause a carry to propagate */
   if ((mp_limb_signed_t)(sum ^ r[0]) >= 0)
      r[0] = sum;
   else
   {
      if (c >= 0) mpn_add_1(r, r, limbs + 1, c);
      else mpn_sub_1(r, r, limbs + 1, -c);
   }
}

void fft_combine_limbs(mp_limb_t * res, mp_limb_t ** poly, slong length, 
            mp_size_t coeff_limbs, mp_size_t output_limbs, mp_size_t total_limbs);

void fft_combine_bits(mp_limb_t * res, mp_limb_t ** poly, slong length, 
                 mp_bitcnt_t bits, mp_size_t output_limbs, mp_size_t total_limbs);

mp_size_t fft_split_limbs(mp_limb_t ** poly, mp_srcptr limbs, 
            mp_size_t total_limbs, mp_size_t coeff_limbs, mp_size_t output_limbs);

mp_size_t fft_split_bits(mp_limb_t ** poly, mp_srcptr limbs, 
                 mp_size_t total_limbs, mp_bitcnt_t bits, mp_size_t output_limbs);

void fermat_to_mpz(mpz_t m, mp_limb_t * i, mp_size_t limbs);

void mpn_normmod_2expp1(mp_limb_t * t, mp_size_t limbs);

void butterfly_lshB(mp_limb_t * t, mp_limb_t * u, mp_limb_t * i1, 
                       mp_limb_t * i2, mp_size_t limbs, mp_size_t x, mp_size_t y);

void butterfly_rshB(mp_limb_t * t, mp_limb_t * u, mp_limb_t * i1, 
                       mp_limb_t * i2, mp_size_t limbs, mp_size_t x, mp_size_t y);

void mpn_mul_2expmod_2expp1(mp_limb_t * t, 
                                  mp_limb_t * i1, mp_size_t limbs, mp_bitcnt_t d);

void mpn_div_2expmod_2expp1(mp_limb_t * t, 
                                  mp_limb_t * i1, mp_size_t limbs, mp_bitcnt_t d);

void fft_adjust(mp_limb_t * r, mp_limb_t * i1, 
                                     mp_size_t i, mp_size_t limbs, mp_bitcnt_t w);

void fft_butterfly(mp_limb_t * s, mp_limb_t * t, mp_limb_t * i1, 
                     mp_limb_t * i2, mp_size_t i, mp_size_t limbs, mp_bitcnt_t w);

void ifft_butterfly(mp_limb_t * s, mp_limb_t * t, mp_limb_t * i1, 
                     mp_limb_t * i2, mp_size_t i, mp_size_t limbs, mp_bitcnt_t w);

void fft_radix2(mp_limb_t ** ii, 
                    mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2);

void fft_truncate1(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w, 
                               mp_limb_t ** t1, mp_limb_t ** t2, mp_size_t trunc);

void fft_truncate(mp_limb_t ** ii,  mp_size_t n, mp_bitcnt_t w, 
                               mp_limb_t ** t1, mp_limb_t ** t2, mp_size_t trunc);

void ifft_radix2(mp_limb_t ** ii, mp_size_t n, 
                                 mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2);

void ifft_truncate1(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w, 
                               mp_limb_t ** t1, mp_limb_t ** t2, mp_size_t trunc);

void ifft_truncate(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w, 
                               mp_limb_t ** t1, mp_limb_t ** t2, mp_size_t trunc);

void fft_butterfly_sqrt2(mp_limb_t * s, mp_limb_t * t, 
                         mp_limb_t * i1, mp_limb_t * i2, mp_size_t i, 
                                mp_size_t limbs, mp_bitcnt_t w, mp_limb_t * temp);

void ifft_butterfly_sqrt2(mp_limb_t * s, mp_limb_t * t, mp_limb_t * i1, 
   mp_limb_t * i2, mp_size_t i, mp_size_t limbs, mp_bitcnt_t w, mp_limb_t * temp);

void fft_adjust_sqrt2(mp_limb_t * r, mp_limb_t * i1, 
                   mp_size_t i, mp_size_t limbs, mp_bitcnt_t w, mp_limb_t * temp);

void fft_truncate_sqrt2(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w, 
            mp_limb_t ** t1, mp_limb_t ** t2, mp_limb_t ** temp, mp_size_t trunc);

void ifft_truncate_sqrt2(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w, 
            mp_limb_t ** t1, mp_limb_t ** t2, mp_limb_t ** temp, mp_size_t trunc);

void mul_truncate_sqrt2(mp_ptr r1, mp_srcptr i1, mp_size_t n1,
                        mp_srcptr i2, mp_size_t n2, mp_bitcnt_t depth, mp_bitcnt_t w);

void fft_butterfly_twiddle(mp_limb_t * u, mp_limb_t * v, 
   mp_limb_t * s, mp_limb_t * t, mp_size_t limbs, mp_bitcnt_t b1, mp_bitcnt_t b2);

void ifft_butterfly_twiddle(mp_limb_t * u, mp_limb_t * v, 
   mp_limb_t * s, mp_limb_t * t, mp_size_t limbs, mp_bitcnt_t b1, mp_bitcnt_t b2);

void fft_radix2_twiddle(mp_limb_t ** ii, mp_size_t is,
      mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
                            mp_size_t ws, mp_size_t r, mp_size_t c, mp_size_t rs);

void ifft_radix2_twiddle(mp_limb_t ** ii, mp_size_t is,
        mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
                            mp_size_t ws, mp_size_t r, mp_size_t c, mp_size_t rs);

void fft_truncate1_twiddle(mp_limb_t ** ii, mp_size_t is,
        mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
           mp_size_t ws, mp_size_t r, mp_size_t c, mp_size_t rs, mp_size_t trunc);

void ifft_truncate1_twiddle(mp_limb_t ** ii, mp_size_t is,
        mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
           mp_size_t ws, mp_size_t r, mp_size_t c, mp_size_t rs, mp_size_t trunc);

void fft_mfa_truncate_sqrt2(mp_limb_t ** ii, mp_size_t n, 
                       mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2, 
                                mp_limb_t ** temp, mp_size_t n1, mp_size_t trunc);

void ifft_mfa_truncate_sqrt2(mp_limb_t ** ii, mp_size_t n, 
                      mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
                                mp_limb_t ** temp, mp_size_t n1, mp_size_t trunc);

void mul_mfa_truncate_sqrt2(mp_ptr r1, mp_srcptr i1, mp_size_t n1,
                        mp_srcptr i2, mp_size_t n2, mp_bitcnt_t depth, mp_bitcnt_t w);

void fft_mfa_truncate_sqrt2_outer(mp_limb_t ** ii, mp_size_t n, 
                      mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2, 
                                mp_limb_t ** temp, mp_size_t n1, mp_size_t trunc);

void fft_mfa_truncate_sqrt2_inner(mp_limb_t ** ii, mp_limb_t ** jj, 
            mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2, 
                mp_limb_t ** temp, mp_size_t n1, mp_size_t trunc, mp_limb_t * tt);

void ifft_mfa_truncate_sqrt2_outer(mp_limb_t ** ii, mp_size_t n, 
                        mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2, 
                                mp_limb_t ** temp, mp_size_t n1, mp_size_t trunc);

void fft_negacyclic(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w, 
                             mp_limb_t ** t1, mp_limb_t ** t2, mp_limb_t ** temp);

void ifft_negacyclic(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w, 
                             mp_limb_t ** t1, mp_limb_t ** t2, mp_limb_t ** temp);

void fft_naive_convolution_1(mp_limb_t * r, mp_limb_t * ii, 
                                                     mp_limb_t * jj, mp_size_t m);

void _fft_mulmod_2expp1(mp_limb_t * r1, mp_limb_t * i1, mp_limb_t * i2, 
                             mp_size_t r_limbs, mp_bitcnt_t depth, mp_bitcnt_t w);

slong fft_adjust_limbs(mp_size_t limbs);

void fft_mulmod_2expp1(mp_limb_t * r, mp_limb_t * i1, mp_limb_t * i2, 
                                        mp_size_t n, mp_size_t w, mp_limb_t * tt);

void flint_mpn_mul_fft_main(mp_ptr r1, mp_srcptr i1, mp_size_t n1,
                        mp_srcptr i2, mp_size_t n2);

void fft_convolution(mp_limb_t ** ii, mp_limb_t ** jj, slong depth, 
                                 slong limbs, slong trunc, mp_limb_t ** t1, 
                                mp_limb_t ** t2, mp_limb_t ** s1, mp_limb_t * tt);

#ifdef __cplusplus
}
#endif

#endif