/* forward transform, sign = -1; transform length = 3 * 2^n */
int
four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
{
mpd_size_t R = 3; /* number of rows */
mpd_size_t C = n / 3; /* number of columns */
mpd_uint_t w3table[3];
mpd_uint_t kernel, w0, w1, wstep;
mpd_uint_t *s, *p0, *p1, *p2;
mpd_uint_t umod;
#ifdef PPRO
double dmod;
uint32_t dinvmod[3];
#endif
mpd_size_t i, k;
assert(n >= 48);
assert(n <= 3*MPD_MAXTRANSFORM_2N);
SETMODULUS(modnum);
_mpd_init_w3table(w3table, -1, modnum);
/* size three ntt on the columns */
for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
SIZE3_NTT(p0, p1, p2, w3table);
}
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-1; 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;
}
}
/* transform rows */
for (s = a; s < a+n; s += C) {
if (!six_step_fnt(s, C, modnum)) {
return 0;
}
}
#if 0
/* An unordered transform is sufficient for convolution. */
if (ordered) {
transpose_3xpow2(a, R, C);
}
#endif
return 1;
}
/* backward transform, sign = 1; transform length = 3 * 2**n */
int
inv_four_step_fnt(const mpd_context_t *ctx, mpd_uint_t *a, mpd_size_t n, int modnum)
{
mpd_size_t R = 3; /* number of rows */
mpd_size_t C = n / 3; /* number of columns */
mpd_uint_t w3table[3];
mpd_uint_t kernel, w0, w1, wstep;
mpd_uint_t *s, *p0, *p1, *p2;
mpd_uint_t umod;
#ifdef PPRO
double dmod;
uint32_t dinvmod[3];
#endif
mpd_size_t i, k;
assert(n >= 48);
assert(n <= 3*MPD_MAXTRANSFORM_2N);
#if 0
/* An unordered transform is sufficient for convolution. */
/* Transpose the matrix, producing an R*C matrix. */
transpose_3xpow2(a, C, R);
#endif
/* Length C transform on the rows. */
for (s = a; s < a+n; s += C) {
if (!inv_six_step_fnt(ctx, s, C, modnum)) {
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;
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;
}
}
/* Length R transform on the columns. */
_mpd_init_w3table(w3table, 1, modnum);
for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {
SIZE3_NTT(p0, p1, p2, w3table);
}
return 1;
}