/*

 * Copyright (c) 2008-2024 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 <assert.h>

#include <stdio.h>

#include "bits.h"

#include "constants.h"

#include "difradix2.h"

#include "numbertheory.h"

#include "mpdecimal.h"

#include "sixstep.h"

#include "transpose.h"

#include "umodarith.h"

/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the

   form 2**n (See literature/six-step.txt). */

/* forward transform with sign = -1 */

int

six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)

{

    struct fnt_params *tparams;

    mpd_size_t log2n, C, R;

    mpd_uint_t kernel;

    mpd_uint_t umod;

#ifdef PPRO

    double dmod;

    uint32_t dinvmod[3];

#endif

    mpd_uint_t *x, w0, w1, wstep;

    mpd_size_t i, k;

    assert(ispower2(n));

    assert(n >= 16);

    assert(n <= MPD_MAXTRANSFORM_2N);

    log2n = mpd_bsr(n);

    C = ((mpd_size_t)1) << (log2n / 2);  /* number of columns */

    R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */

    /* Transpose the matrix. */

    if (!transpose_pow2(a, R, C)) {

        return 0;

    }

    /* Length R transform on the rows. */

    if ((tparams = _mpd_init_fnt_params(R, -1, modnum)) == NULL) {

        return 0;

    }

    for (x = a; x < a+n; x += R) {

        fnt_dif2(x, R, tparams);

    }

    /* Transpose the matrix. */

    if (!transpose_pow2(a, C, R)) {

        mpd_free(tparams);

        return 0;

    }

    /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */

    SETMODULUS(modnum);

    kernel = _mpd_getkernel(n, -1, modnum);

    for (i = 1; i < R; i++) {

        w0 = 1;                  /* r**(i*0): initial value for k=0 */

        w1 = POWMOD(kernel, i);  /* r**(i*1): initial value for k=1 */

        wstep = MULMOD(w1, w1);  /* r**(2*i) */

        for (k = 0; k < C; k += 2) {

            mpd_uint_t x0 = a[i*C+k];

            mpd_uint_t x1 = a[i*C+k+1];

            MULMOD2(&x0, w0, &x1, w1);

            MULMOD2C(&w0, &w1, wstep);  /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */

            a[i*C+k] = x0;

            a[i*C+k+1] = x1;

        }

    }

    /* Length C transform on the rows. */

    if (C != R) {

        mpd_free(tparams);

        if ((tparams = _mpd_init_fnt_params(C, -1, modnum)) == NULL) {

            return 0;

        }

    }

    for (x = a; x < a+n; x += C) {

        fnt_dif2(x, C, tparams);

    }

    mpd_free(tparams);

#if 0

    /* An unordered transform is sufficient for convolution. */

    /* Transpose the matrix. */

    if (!transpose_pow2(a, R, C)) {

        return 0;

    }

#endif

    return 1;

}

/* reverse transform, sign = 1 */

int

inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)

{

    struct fnt_params *tparams;

    mpd_size_t log2n, C, R;

    mpd_uint_t kernel;

    mpd_uint_t umod;

#ifdef PPRO

    double dmod;

    uint32_t dinvmod[3];

#endif

    mpd_uint_t *x, w0, w1, wstep;

    mpd_size_t i, k;

    assert(ispower2(n));

    assert(n >= 16);

    assert(n <= MPD_MAXTRANSFORM_2N);

    log2n = mpd_bsr(n);

    C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */

    R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */

#if 0

    /* An unordered transform is sufficient for convolution. */

    /* Transpose the matrix, producing an R*C matrix. */

    if (!transpose_pow2(a, C, R)) {

        return 0;

    }

#endif

    /* Length C transform on the rows. */

    if ((tparams = _mpd_init_fnt_params(C, 1, modnum)) == NULL) {

        return 0;

    }

    for (x = a; x < a+n; x += C) {

        fnt_dif2(x, C, tparams);

    }

    /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */

    SETMODULUS(modnum);

    kernel = _mpd_getkernel(n, 1, modnum);

    for (i = 1; i < R; i++) {

        w0 = 1;

        w1 = POWMOD(kernel, i);

        wstep = MULMOD(w1, w1);

        for (k = 0; k < C; k += 2) {

            mpd_uint_t x0 = a[i*C+k];

            mpd_uint_t x1 = a[i*C+k+1];

            MULMOD2(&x0, w0, &x1, w1);

            MULMOD2C(&w0, &w1, wstep);

            a[i*C+k] = x0;

            a[i*C+k+1] = x1;

        }

    }

    /* Transpose the matrix. */

    if (!transpose_pow2(a, R, C)) {

        mpd_free(tparams);

        return 0;

    }

    /* Length R transform on the rows. */

    if (R != C) {

        mpd_free(tparams);

        if ((tparams = _mpd_init_fnt_params(R, 1, modnum)) == NULL) {

            return 0;

        }

    }

    for (x = a; x < a+n; x += R) {

        fnt_dif2(x, R, tparams);

    }

    mpd_free(tparams);

    /* Transpose the matrix. */

    if (!transpose_pow2(a, C, R)) {

        return 0;

    }

    return 1;

}