/*
* In-place transposition of a 2^n x 2^n or a 2^n x (2*2^n)
* or a (2*2^n) x 2^n matrix.
*/
int
transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols)
{
mpd_size_t size = mul_size_t(rows, cols);
assert(ispower2(rows));
assert(ispower2(cols));
if (cols == rows) {
squaretrans_pow2(matrix, rows);
}
else if (cols == mul_size_t(2, rows)) {
if (!swap_halfrows_pow2(matrix, rows, cols, FORWARD_CYCLE)) {
return 0;
}
squaretrans_pow2(matrix, rows);
squaretrans_pow2(matrix+(size/2), rows);
}
else if (rows == mul_size_t(2, cols)) {
squaretrans_pow2(matrix, cols);
squaretrans_pow2(matrix+(size/2), cols);
if (!swap_halfrows_pow2(matrix, cols, rows, BACKWARD_CYCLE)) {
return 0;
}
}
else {
abort(); /* GCOV_NOT_REACHED */
}
return 1;
}
/*
* In-place transposition of a 2^n x 2^n or a 2^n x (2*2^n)
* or a (2*2^n) x 2^n matrix.
*/
static int
transpose_pow2_c(uint8_t *matrix, mpd_size_t rows, mpd_size_t cols)
{
mpd_size_t size = mul_size_t(rows, cols);
assert(ispower2(rows));
assert(ispower2(cols));
if (cols == rows) {
squaretrans_pow2_c(matrix, rows);
}
else if (cols == mul_size_t(2, rows)) {
if (!swap_halfrows_pow2_c(matrix, rows, cols, FORWARD_CYCLE)) {
return 0;
}
squaretrans_pow2_c(matrix, rows);
squaretrans_pow2_c(matrix+(size/2), rows);
}
else if (rows == mul_size_t(2, cols)) {
squaretrans_pow2_c(matrix, cols);
squaretrans_pow2_c(matrix+(size/2), cols);
if (!swap_halfrows_pow2_c(matrix, cols, rows, BACKWARD_CYCLE)) {
return 0;
}
}
else {
mpd_err_fatal("transpose_pow2_c: illegal matrix size");
}
return 1;
}
/* initialize transform parameters */
struct fnt_params *
_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum)
{
struct fnt_params *tparams;
mpd_uint_t umod;
#ifdef PPRO
double dmod;
uint32_t dinvmod[3];
#endif
mpd_uint_t kernel, imag, w;
mpd_uint_t i;
mpd_size_t nhalf;
assert(ispower2(n));
assert(sign == -1 || sign == 1);
assert(P1 <= modnum && modnum <= P3);
nhalf = n/2;
tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t));
if (tparams == NULL) {
return NULL;
}
SETMODULUS(modnum);
kernel = _mpd_getkernel(n, sign, modnum);
imag = _mpd_getkernel(4, -sign, modnum);
tparams->modnum = modnum;
tparams->modulus = umod;
tparams->imag = imag;
tparams->kernel = kernel;
w = 1;
for (i = 0; i < nhalf; i++) {
tparams->wtable[i] = w;
w = MULMOD(w, kernel);
}
return tparams;
}
/* 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;
}
/* 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);
}
/* reverse transform, sign = 1 */
int
std_inv_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
{
struct fnt_params *tparams;
assert(ispower2(n));
assert(n >= 4);
assert(n <= 3*MPD_MAXTRANSFORM_2N);
if ((tparams = _mpd_init_fnt_params(n, 1, modnum)) == NULL) {
return 0;
}
fnt_dif2(a, n, tparams);
mpd_free(tparams);
return 1;
}
