335 lines
9.8 KiB
C
335 lines
9.8 KiB
C
/*
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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 "mpir.h"
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#include "gmp-impl.h"
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void mpir_fft_butterfly_twiddle(mp_ptr u, mp_ptr v,
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mp_ptr s, mp_ptr t, mp_size_t limbs, mp_bitcnt_t b1, mp_bitcnt_t b2)
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{
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mp_limb_t nw = limbs*GMP_LIMB_BITS;
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mp_size_t x, y;
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int negate1 = 0;
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int negate2 = 0;
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if (b1 >= nw)
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{
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negate2 = 1;
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b1 -= nw;
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}
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x = b1/GMP_LIMB_BITS;
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b1 = b1%GMP_LIMB_BITS;
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if (b2 >= nw)
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{
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negate1 = 1;
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b2 -= nw;
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}
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y = b2/GMP_LIMB_BITS;
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b2 = b2%GMP_LIMB_BITS;
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mpir_butterfly_lshB(u, v, s, t, limbs, x, y);
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mpn_mul_2expmod_2expp1(u, u, limbs, b1);
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if (negate2) mpn_neg_n(u, u, limbs + 1);
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mpn_mul_2expmod_2expp1(v, v, limbs, b2);
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if (negate1) mpn_neg_n(v, v, limbs + 1);
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}
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void mpir_fft_radix2_twiddle(mp_ptr * ii, mp_size_t is,
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mp_size_t n, mp_bitcnt_t w, mp_ptr * t1, mp_ptr * t2,
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mp_size_t ws, mp_size_t r, mp_size_t c, mp_size_t rs)
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{
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mp_size_t i;
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mp_size_t limbs;
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start:
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limbs = (w*n)/GMP_LIMB_BITS;
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if (n == 1)
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{
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mp_size_t tw1 = r*c;
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mp_size_t tw2 = tw1 + rs*c;
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mpir_fft_butterfly_twiddle(*t1, *t2, ii[0], ii[is], limbs, tw1*ws, tw2*ws);
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MP_PTR_SWAP(ii[0], *t1);
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MP_PTR_SWAP(ii[is], *t2);
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return;
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}
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for (i = 0; i < n; i++)
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{
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mpir_fft_butterfly(*t1, *t2, ii[i*is], ii[(n+i)*is], i, limbs, w);
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MP_PTR_SWAP(ii[i*is], *t1);
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MP_PTR_SWAP(ii[(n+i)*is], *t2);
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}
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mpir_fft_radix2_twiddle(ii, is, n/2, 2*w, t1, t2, ws, r, c, 2*rs);
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#if 0
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ii += n * is;
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n /= 2;
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w += w;
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r += rs;
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rs += rs;
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goto start;
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#else
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mpir_fft_radix2_twiddle(ii+n*is, is, n/2, 2*w, t1, t2, ws, r + rs, c, 2*rs);
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#endif
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}
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void mpir_fft_trunc1_twiddle(mp_ptr * ii, mp_size_t is,
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mp_size_t n, mp_bitcnt_t w, mp_ptr * t1, mp_ptr * t2,
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mp_size_t ws, mp_size_t r, mp_size_t c, mp_size_t rs, mp_size_t trunc)
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{
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mp_size_t i;
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mp_size_t limbs = (w*n)/GMP_LIMB_BITS;
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if (trunc == 2*n)
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mpir_fft_radix2_twiddle(ii, is, n, w, t1, t2, ws, r, c, rs);
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else if (trunc <= n)
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{
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for (i = 0; i < n; i++)
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mpn_add_n(ii[i*is], ii[i*is], ii[(i+n)*is], limbs + 1);
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mpir_fft_trunc1_twiddle(ii, is, n/2, 2*w, t1, t2, ws, r, c, 2*rs, trunc);
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} else
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{
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for (i = 0; i < n; i++)
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{
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mpir_fft_butterfly(*t1, *t2, ii[i*is], ii[(n+i)*is], i, limbs, w);
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MP_PTR_SWAP(ii[i*is], *t1);
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MP_PTR_SWAP(ii[(n+i)*is], *t2);
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}
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mpir_fft_radix2_twiddle(ii, is, n/2, 2*w, t1, t2, ws, r, c, 2*rs);
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mpir_fft_trunc1_twiddle(ii + n*is, is, n/2, 2*w,
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t1, t2, ws, r + rs, c, 2*rs, trunc - n);
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}
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}
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void mpir_fft_mfa_trunc_sqrt2(mp_ptr * ii, mp_size_t n,
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mp_bitcnt_t w, mp_ptr * t1, mp_ptr * t2,
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mp_ptr * temp, mp_size_t n1, mp_size_t trunc)
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{
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mp_size_t i, j, s;
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mp_size_t n2 = (2*n)/n1;
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mp_size_t trunc2 = (trunc - 2*n)/n1;
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mp_size_t limbs = (n*w)/GMP_LIMB_BITS;
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mp_bitcnt_t depth = 0;
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mp_bitcnt_t depth2 = 0;
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while ((((mp_size_t)1)<<depth) < n2) depth++;
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while ((((mp_size_t)1)<<depth2) < n1) depth2++;
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/* first half matrix fourier FFT : n2 rows, n1 cols */
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/* FFTs on columns */
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for (i = 0; i < n1; i++)
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{
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/* relevant part of first layer of full sqrt2 FFT */
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if (w & 1)
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{
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for (j = i; j < trunc - 2*n; j+=n1)
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{
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if (j & 1)
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mpir_fft_butterfly_sqrt2(*t1, *t2, ii[j], ii[2*n+j], j, limbs, w, *temp);
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else
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mpir_fft_butterfly(*t1, *t2, ii[j], ii[2*n+j], j/2, limbs, w);
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MP_PTR_SWAP(ii[j], *t1);
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MP_PTR_SWAP(ii[2*n+j], *t2);
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}
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for ( ; j < 2*n; j+=n1)
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{
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if (i & 1)
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mpir_fft_adjust_sqrt2(ii[j + 2*n], ii[j], j, limbs, w, *temp);
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else
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mpir_fft_adjust(ii[j + 2*n], ii[j], j/2, limbs, w);
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}
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} else
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{
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for (j = i; j < trunc - 2*n; j+=n1)
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{
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mpir_fft_butterfly(*t1, *t2, ii[j], ii[2*n+j], j, limbs, w/2);
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MP_PTR_SWAP(ii[j], *t1);
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MP_PTR_SWAP(ii[2*n+j], *t2);
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}
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for ( ; j < 2*n; j+=n1)
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mpir_fft_adjust(ii[j + 2*n], ii[j], j, limbs, w/2);
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}
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/*
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FFT of length n2 on column i, applying z^{r*i} for rows going up in steps
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of 1 starting at row 0, where z => w bits
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*/
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mpir_fft_radix2_twiddle(ii + i, n1, n2/2, w*n1, t1, t2, w, 0, i, 1);
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for (j = 0; j < n2; j++)
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{
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mp_size_t s = mpir_revbin(j, depth);
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if (j < s) MP_PTR_SWAP(ii[i+j*n1], ii[i+s*n1]);
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}
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}
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/* FFTs on rows */
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for (i = 0; i < n2; i++)
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{
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mpir_fft_radix2(ii + i*n1, n1/2, w*n2, t1, t2);
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for (j = 0; j < n1; j++)
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{
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mp_size_t t = mpir_revbin(j, depth2);
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if (j < t) MP_PTR_SWAP(ii[i*n1+j], ii[i*n1+t]);
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}
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}
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/* second half matrix fourier FFT : n2 rows, n1 cols */
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ii += 2*n;
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/* FFTs on columns */
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for (i = 0; i < n1; i++)
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{
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/*
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FFT of length n2 on column i, applying z^{r*i} for rows going up in steps
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of 1 starting at row 0, where z => w bits
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*/
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mpir_fft_trunc1_twiddle(ii + i, n1, n2/2, w*n1, t1, t2, w, 0, i, 1, trunc2);
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for (j = 0; j < n2; j++)
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{
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mp_size_t s = mpir_revbin(j, depth);
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if (j < s) MP_PTR_SWAP(ii[i+j*n1], ii[i+s*n1]);
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}
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}
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/* FFTs on relevant rows */
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for (s = 0; s < trunc2; s++)
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{
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i = mpir_revbin(s, depth);
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mpir_fft_radix2(ii + i*n1, n1/2, w*n2, t1, t2);
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for (j = 0; j < n1; j++)
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{
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mp_size_t t = mpir_revbin(j, depth2);
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if (j < t) MP_PTR_SWAP(ii[i*n1+j], ii[i*n1+t]);
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}
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}
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}
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void mpir_fft_mfa_trunc_sqrt2_outer(mp_ptr * ii, mp_size_t n,
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mp_bitcnt_t w, mp_ptr * t1, mp_ptr * t2,
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mp_ptr * temp, mp_size_t n1, mp_size_t trunc)
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{
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mp_size_t i, j;
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mp_size_t n2 = (2*n)/n1;
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mp_size_t trunc2 = (trunc - 2*n)/n1;
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mp_size_t limbs = (n*w)/GMP_LIMB_BITS;
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mp_bitcnt_t depth = 0;
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mp_bitcnt_t depth2 = 0;
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while ((((mp_size_t)1)<<depth) < n2) depth++;
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while ((((mp_size_t)1)<<depth2) < n1) depth2++;
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/* first half matrix fourier FFT : n2 rows, n1 cols */
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/* FFTs on columns */
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for (i = 0; i < n1; i++)
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{
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/* relevant part of first layer of full sqrt2 FFT */
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if (w & 1)
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{
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for (j = i; j < trunc - 2*n; j+=n1)
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{
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if (j & 1)
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mpir_fft_butterfly_sqrt2(*t1, *t2, ii[j], ii[2*n+j], j, limbs, w, *temp);
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else
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mpir_fft_butterfly(*t1, *t2, ii[j], ii[2*n+j], j/2, limbs, w);
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MP_PTR_SWAP(ii[j], *t1);
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MP_PTR_SWAP(ii[2*n+j], *t2);
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}
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for ( ; j < 2*n; j+=n1)
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{
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if (i & 1)
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mpir_fft_adjust_sqrt2(ii[j + 2*n], ii[j], j, limbs, w, *temp);
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else
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mpir_fft_adjust(ii[j + 2*n], ii[j], j/2, limbs, w);
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}
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} else
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{
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for (j = i; j < trunc - 2*n; j+=n1)
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{
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mpir_fft_butterfly(*t1, *t2, ii[j], ii[2*n+j], j, limbs, w/2);
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MP_PTR_SWAP(ii[j], *t1);
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MP_PTR_SWAP(ii[2*n+j], *t2);
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}
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for ( ; j < 2*n; j+=n1)
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mpir_fft_adjust(ii[j + 2*n], ii[j], j, limbs, w/2);
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}
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/*
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FFT of length n2 on column i, applying z^{r*i} for rows going up in steps
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of 1 starting at row 0, where z => w bits
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*/
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mpir_fft_radix2_twiddle(ii + i, n1, n2/2, w*n1, t1, t2, w, 0, i, 1);
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for (j = 0; j < n2; j++)
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{
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mp_size_t s = mpir_revbin(j, depth);
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if (j < s) MP_PTR_SWAP(ii[i+j*n1], ii[i+s*n1]);
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}
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}
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/* second half matrix fourier FFT : n2 rows, n1 cols */
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ii += 2*n;
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/* FFTs on columns */
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for (i = 0; i < n1; i++)
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{
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/*
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FFT of length n2 on column i, applying z^{r*i} for rows going up in steps
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of 1 starting at row 0, where z => w bits
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*/
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mpir_fft_trunc1_twiddle(ii + i, n1, n2/2, w*n1, t1, t2, w, 0, i, 1, trunc2);
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for (j = 0; j < n2; j++)
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{
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mp_size_t s = mpir_revbin(j, depth);
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if (j < s) MP_PTR_SWAP(ii[i+j*n1], ii[i+s*n1]);
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}
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}
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}
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