difradix2.c

/*
 * Copyright (c) 2008-2020 Stefan Krah. 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 THE AUTHOR AND CONTRIBUTORS "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 THE AUTHOR 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.
 */


#include "mpdecimal.h"

#include <assert.h>

#include "bits.h"
#include "constants.h"
#include "difradix2.h"
#include "numbertheory.h"
#include "umodarith.h"


/* Bignum: The actual transform routine (decimation in frequency). */


/*
 * Generate index pairs (x, bitreverse(x)) and carry out the permutation.
 * n must be a power of two.
 * Algorithm due to Brent/Lehmann, see Joerg Arndt, "Matters Computational",
 * Chapter 1.14.4. [http://www.jjj.de/fxt/]
 */
static inline void
bitreverse_permute(mpd_uint_t a[], mpd_size_t n)
{
    mpd_size_t x = 0;
    mpd_size_t r = 0;
    mpd_uint_t t;

    do { /* Invariant: r = bitreverse(x) */
        if (r > x) {
            t = a[x];
            a[x] = a[r];
            a[r] = t;
        }
        /* Flip trailing consecutive 1 bits and the first zero bit
         * that absorbs a possible carry. */
        x += 1;
        /* Mirror the operation on r: Flip n_trailing_zeros(x)+1
           high bits of r. */
        r ^= (n - (n >> (mpd_bsf(x)+1)));
        /* The loop invariant is preserved. */
    } while (x < n);
}


/* Fast Number Theoretic Transform, decimation in frequency. */
void
fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams)
{
    mpd_uint_t *wtable = tparams->wtable;
    mpd_uint_t umod;
#ifdef PPRO
    double dmod;
    uint32_t dinvmod[3];
#endif
    mpd_uint_t u0, u1, v0, v1;
    mpd_uint_t w, w0, w1, wstep;
    mpd_size_t m, mhalf;
    mpd_size_t j, r;


    assert(ispower2(n));
    assert(n >= 4);

    SETMODULUS(tparams->modnum);

    /* m == n */
    mhalf = n / 2;
    for (j = 0; j < mhalf; j += 2) {

        w0 = wtable[j];
        w1 = wtable[j+1];

        u0 = a[j];
        v0 = a[j+mhalf];

        u1 = a[j+1];
        v1 = a[j+1+mhalf];

        a[j] = addmod(u0, v0, umod);
        v0 = submod(u0, v0, umod);

        a[j+1] = addmod(u1, v1, umod);
        v1 = submod(u1, v1, umod);

        MULMOD2(&v0, w0, &v1, w1);

        a[j+mhalf] = v0;
        a[j+1+mhalf] = v1;

    }

    wstep = 2;
    for (m = n/2; m >= 2; m>>=1, wstep<<=1) {

        mhalf = m / 2;

        /* j == 0 */
        for (r = 0; r < n; r += 2*m) {

            u0 = a[r];
            v0 = a[r+mhalf];

            u1 = a[m+r];
            v1 = a[m+r+mhalf];

            a[r] = addmod(u0, v0, umod);
            v0 = submod(u0, v0, umod);

            a[m+r] = addmod(u1, v1, umod);
            v1 = submod(u1, v1, umod);

            a[r+mhalf] = v0;
            a[m+r+mhalf] = v1;
        }

        for (j = 1; j < mhalf; j++) {

            w = wtable[j*wstep];

            for (r = 0; r < n; r += 2*m) {

                u0 = a[r+j];
                v0 = a[r+j+mhalf];

                u1 = a[m+r+j];
                v1 = a[m+r+j+mhalf];

                a[r+j] = addmod(u0, v0, umod);
                v0 = submod(u0, v0, umod);

                a[m+r+j] = addmod(u1, v1, umod);
                v1 = submod(u1, v1, umod);

                MULMOD2C(&v0, &v1, w);

                a[r+j+mhalf] = v0;
                a[m+r+j+mhalf] = v1;
            }

        }

    }

    bitreverse_permute(a, n);
}