static fftw_rader_data *create_rader_aux(int p, int flags)
{
fftw_complex *omega, *work;
int g, ginv, gpower;
int i;
FFTW_TRIG_REAL twoPiOverN;
fftw_real scale = 1.0 / (p - 1); /* for convolution */
fftw_plan plan;
fftw_rader_data *d;
if (p < 2)
fftw_die("non-prime order in Rader\n");
flags &= ~FFTW_IN_PLACE;
d = (fftw_rader_data *) fftw_malloc(sizeof(fftw_rader_data));
g = find_generator(p);
ginv = power_mod(g, p - 2, p);
omega = (fftw_complex *) fftw_malloc((p - 1) * sizeof(fftw_complex));
plan = fftw_create_plan(p - 1, FFTW_FORWARD,
flags & ~FFTW_NO_VECTOR_RECURSE);
work = (fftw_complex *) fftw_malloc((p - 1) * sizeof(fftw_complex));
twoPiOverN = FFTW_K2PI / (FFTW_TRIG_REAL) p;
gpower = 1;
for (i = 0; i < p - 1; ++i) {
c_re(work[i]) = scale * FFTW_TRIG_COS(twoPiOverN * gpower);
c_im(work[i]) = FFTW_FORWARD * scale * FFTW_TRIG_SIN(twoPiOverN
* gpower);
gpower = MULMOD(gpower, ginv, p);
}
/* fft permuted roots of unity */
fftw_executor_simple(p - 1, work, omega, plan->root, 1, 1,
plan->recurse_kind);
fftw_free(work);
d->plan = plan;
d->omega = omega;
d->g = g;
d->ginv = ginv;
d->p = p;
d->flags = flags;
d->refcount = 1;
d->next = NULL;
d->cdesc = (fftw_codelet_desc *) fftw_malloc(sizeof(fftw_codelet_desc));
d->cdesc->name = NULL;
d->cdesc->codelet = NULL;
d->cdesc->size = p;
d->cdesc->dir = FFTW_FORWARD;
d->cdesc->type = FFTW_RADER;
d->cdesc->signature = g;
d->cdesc->ntwiddle = 0;
d->cdesc->twiddle_order = NULL;
return d;
}
/*
* Implementation of the FFT tester described in
*
* Funda Ergün. Testing multivariate linear functions: Overcoming the
* generator bottleneck. In Proceedings of the Twenty-Seventh Annual
* ACM Symposium on the Theory of Computing, pages 407-416, Las Vegas,
* Nevada, 29 May--1 June 1995.
*/
void test_ergun(int n, fftw_direction dir, fftw_plan plan)
{
fftw_complex *inA, *inB, *inC, *outA, *outB, *outC;
fftw_complex *tmp;
fftw_complex impulse;
int i;
int rounds = 20;
FFTW_TRIG_REAL twopin = FFTW_K2PI / (FFTW_TRIG_REAL) n;
inA = (fftw_complex *) fftw_malloc(n * sizeof(fftw_complex));
inB = (fftw_complex *) fftw_malloc(n * sizeof(fftw_complex));
inC = (fftw_complex *) fftw_malloc(n * sizeof(fftw_complex));
outA = (fftw_complex *) fftw_malloc(n * sizeof(fftw_complex));
outB = (fftw_complex *) fftw_malloc(n * sizeof(fftw_complex));
outC = (fftw_complex *) fftw_malloc(n * sizeof(fftw_complex));
tmp = (fftw_complex *) fftw_malloc(n * sizeof(fftw_complex));
WHEN_VERBOSE(2,
printf("Validating plan, n = %d, dir = %s\n", n,
dir == FFTW_FORWARD ? "FORWARD" : "BACKWARD"));
/* test 1: check linearity */
for (i = 0; i < rounds; ++i) {
fftw_complex alpha, beta;
c_re(alpha) = DRAND();
c_im(alpha) = DRAND();
c_re(beta) = DRAND();
c_im(beta) = DRAND();
fill_random(inA, n);
fill_random(inB, n);
fftw_out_of_place(plan, n, inA, outA);
fftw_out_of_place(plan, n, inB, outB);
array_scale(outA, alpha, n);
array_scale(outB, beta, n);
array_add(tmp, outA, outB, n);
array_scale(inA, alpha, n);
array_scale(inB, beta, n);
array_add(inC, inA, inB, n);
fftw_out_of_place(plan, n, inC, outC);
array_compare(outC, tmp, n);
}
/* test 2: check that the unit impulse is transformed properly */
c_re(impulse) = 1.0;
c_im(impulse) = 0.0;
for (i = 0; i < n; ++i) {
/* impulse */
c_re(inA[i]) = 0.0;
c_im(inA[i]) = 0.0;
/* transform of the impulse */
outA[i] = impulse;
}
inA[0] = impulse;
for (i = 0; i < rounds; ++i) {
fill_random(inB, n);
array_sub(inC, inA, inB, n);
fftw_out_of_place(plan, n, inB, outB);
fftw_out_of_place(plan, n, inC, outC);
array_add(tmp, outB, outC, n);
array_compare(tmp, outA, n);
}
/* test 3: check the time-shift property */
/* the paper performs more tests, but this code should be fine too */
for (i = 0; i < rounds; ++i) {
int j;
fill_random(inA, n);
array_rol(inB, inA, n, 1, 1);
fftw_out_of_place(plan, n, inA, outA);
fftw_out_of_place(plan, n, inB, outB);
for (j = 0; j < n; ++j) {
FFTW_TRIG_REAL s = dir * FFTW_TRIG_SIN(j * twopin);
FFTW_TRIG_REAL c = FFTW_TRIG_COS(j * twopin);
c_re(tmp[j]) = c_re(outB[j]) * c - c_im(outB[j]) * s;
c_im(tmp[j]) = c_re(outB[j]) * s + c_im(outB[j]) * c;
}
array_compare(tmp, outA, n);
}
WHEN_VERBOSE(2, printf("Validation done\n"));
fftw_free(tmp);
fftw_free(outC);
fftw_free(outB);
fftw_free(outA);
fftw_free(inC);
fftw_free(inB);
fftw_free(inA);
}
/* Same as test_ergun, but for multi-dimensional transforms: */
void testnd_ergun(int rank, int *n, fftw_direction dir, fftwnd_plan plan)
{
fftw_complex *inA, *inB, *inC, *outA, *outB, *outC;
fftw_complex *tmp;
fftw_complex impulse;
int N, n_before, n_after, dim;
int i, which_impulse;
int rounds = 20;
FFTW_TRIG_REAL twopin;
N = 1;
for (dim = 0; dim < rank; ++dim)
N *= n[dim];
inA = (fftw_complex *) fftw_malloc(N * sizeof(fftw_complex));
inB = (fftw_complex *) fftw_malloc(N * sizeof(fftw_complex));
inC = (fftw_complex *) fftw_malloc(N * sizeof(fftw_complex));
outA = (fftw_complex *) fftw_malloc(N * sizeof(fftw_complex));
outB = (fftw_complex *) fftw_malloc(N * sizeof(fftw_complex));
outC = (fftw_complex *) fftw_malloc(N * sizeof(fftw_complex));
tmp = (fftw_complex *) fftw_malloc(N * sizeof(fftw_complex));
WHEN_VERBOSE(2,
printf("Validating plan, N = %d, dir = %s\n", N,
dir == FFTW_FORWARD ? "FORWARD" : "BACKWARD"));
/* test 1: check linearity */
for (i = 0; i < rounds; ++i) {
fftw_complex alpha, beta;
c_re(alpha) = DRAND();
c_im(alpha) = DRAND();
c_re(beta) = DRAND();
c_im(beta) = DRAND();
fill_random(inA, N);
fill_random(inB, N);
fftwnd(plan, 1, inA, 1, N, outA, 1, N);
fftwnd(plan, 1, inB, 1, N, outB, 1, N);
array_scale(outA, alpha, N);
array_scale(outB, beta, N);
array_add(tmp, outA, outB, N);
array_scale(inA, alpha, N);
array_scale(inB, beta, N);
array_add(inC, inA, inB, N);
fftwnd(plan, 1, inC, 1, N, outC, 1, N);
array_compare(outC, tmp, N);
}
/*
* test 2: check that the unit impulse is transformed properly -- we
* need to test both the real and imaginary impulses
*/
for (which_impulse = 0; which_impulse < 2; ++which_impulse) {
if (which_impulse == 0) { /* real impulse */
c_re(impulse) = 1.0;
c_im(impulse) = 0.0;
} else { /* imaginary impulse */
c_re(impulse) = 0.0;
c_im(impulse) = 1.0;
}
for (i = 0; i < N; ++i) {
/* impulse */
c_re(inA[i]) = 0.0;
c_im(inA[i]) = 0.0;
/* transform of the impulse */
outA[i] = impulse;
}
inA[0] = impulse;
for (i = 0; i < rounds; ++i) {
fill_random(inB, N);
array_sub(inC, inA, inB, N);
fftwnd(plan, 1, inB, 1, N, outB, 1, N);
fftwnd(plan, 1, inC, 1, N, outC, 1, N);
array_add(tmp, outB, outC, N);
array_compare(tmp, outA, N);
}
}
/* test 3: check the time-shift property */
/* the paper performs more tests, but this code should be fine too */
/* -- we have to check shifts in each dimension */
n_before = 1;
n_after = N;
for (dim = 0; dim < rank; ++dim) {
int n_cur = n[dim];
n_after /= n_cur;
twopin = FFTW_K2PI / (FFTW_TRIG_REAL) n_cur;
for (i = 0; i < rounds; ++i) {
int j, jb, ja;
fill_random(inA, N);
array_rol(inB, inA, n_cur, n_before, n_after);
fftwnd(plan, 1, inA, 1, N, outA, 1, N);
fftwnd(plan, 1, inB, 1, N, outB, 1, N);
for (jb = 0; jb < n_before; ++jb)
for (j = 0; j < n_cur; ++j) {
FFTW_TRIG_REAL s = dir * FFTW_TRIG_SIN(j * twopin);
FFTW_TRIG_REAL c = FFTW_TRIG_COS(j * twopin);
for (ja = 0; ja < n_after; ++ja) {
c_re(tmp[(jb * n_cur + j) * n_after + ja]) =
c_re(outB[(jb * n_cur + j) * n_after + ja]) * c
- c_im(outB[(jb * n_cur + j) * n_after + ja]) * s;
c_im(tmp[(jb * n_cur + j) * n_after + ja]) =
c_re(outB[(jb * n_cur + j) * n_after + ja]) * s
+ c_im(outB[(jb * n_cur + j) * n_after + ja]) * c;
}
}
array_compare(tmp, outA, N);
}
n_before *= n_cur;
}
WHEN_VERBOSE(2, printf("Validation done\n"));
fftw_free(tmp);
fftw_free(outC);
fftw_free(outB);
fftw_free(outA);
fftw_free(inC);
fftw_free(inB);
fftw_free(inA);
}
/*
* This is a real (as opposed to complex) variation of the FFT tester
* described in
*
* Funda Ergün. Testing multivariate linear functions: Overcoming the
* generator bottleneck. In Proceedings of the Twenty-Seventh Annual
* ACM Symposium on the Theory of Computing, pages 407-416, Las Vegas,
* Nevada, 29 May--1 June 1995.
*/
void test_ergun(int n, fftw_direction dir, fftw_plan plan)
{
fftw_real *inA, *inB, *inC, *outA, *outB, *outC;
fftw_real *inA1, *inB1;
fftw_real *tmp;
int i;
int rounds = 20;
FFTW_TRIG_REAL twopin = FFTW_K2PI / (FFTW_TRIG_REAL) n;
inA = (fftw_real *) fftw_malloc(n * sizeof(fftw_real));
inB = (fftw_real *) fftw_malloc(n * sizeof(fftw_real));
inA1 = (fftw_real *) fftw_malloc(n * sizeof(fftw_real));
inB1 = (fftw_real *) fftw_malloc(n * sizeof(fftw_real));
inC = (fftw_real *) fftw_malloc(n * sizeof(fftw_real));
outA = (fftw_real *) fftw_malloc(n * sizeof(fftw_real));
outB = (fftw_real *) fftw_malloc(n * sizeof(fftw_real));
outC = (fftw_real *) fftw_malloc(n * sizeof(fftw_real));
tmp = (fftw_real *) fftw_malloc(n * sizeof(fftw_real));
WHEN_VERBOSE(2,
printf("Validating plan, n = %d, dir = %s\n", n,
dir == FFTW_REAL_TO_COMPLEX ?
"REAL_TO_COMPLEX" : "COMPLEX_TO_REAL"));
/* test 1: check linearity */
for (i = 0; i < rounds; ++i) {
fftw_real alpha, beta;
alpha = DRAND();
beta = DRAND();
rfill_random(inA, n);
rfill_random(inB, n);
rarray_scale(inA1, inA, alpha, n);
rarray_scale(inB1, inB, beta, n);
rarray_add(inC, inA1, inB1, n);
rfftw_out_of_place(plan, n, inA, outA);
rfftw_out_of_place(plan, n, inB, outB);
rarray_scale(outA, outA, alpha, n);
rarray_scale(outB, outB, beta, n);
rarray_add(tmp, outA, outB, n);
rfftw_out_of_place(plan, n, inC, outC);
rarray_compare(outC, tmp, n);
}
/* test 2: check that the unit impulse is transformed properly */
for (i = 0; i < n; ++i) {
/* impulse */
inA[i] = 0.0;
/* transform of the impulse */
if (2 * i <= n)
outA[i] = 1.0;
else
outA[i] = 0.0;
}
inA[0] = 1.0;
if (dir == FFTW_REAL_TO_COMPLEX) {
for (i = 0; i < rounds; ++i) {
rfill_random(inB, n);
rarray_sub(inC, inA, inB, n);
rfftw_out_of_place(plan, n, inB, outB);
rfftw_out_of_place(plan, n, inC, outC);
rarray_add(tmp, outB, outC, n);
rarray_compare(tmp, outA, n);
}
} else {
for (i = 0; i < rounds; ++i) {
rfill_random(outB, n);
rarray_sub(outC, outA, outB, n);
rfftw_out_of_place(plan, n, outB, inB);
rfftw_out_of_place(plan, n, outC, inC);
rarray_add(tmp, inB, inC, n);
rarray_scale(tmp, tmp, 1.0 / ((double) n), n);
rarray_compare(tmp, inA, n);
}
}
/* test 3: check the time-shift property */
/* the paper performs more tests, but this code should be fine too */
if (dir == FFTW_REAL_TO_COMPLEX) {
for (i = 0; i < rounds; ++i) {
int j;
rfill_random(inA, n);
rarray_rol(inB, inA, n, 1, 1);
rfftw_out_of_place(plan, n, inA, outA);
rfftw_out_of_place(plan, n, inB, outB);
tmp[0] = outB[0];
for (j = 1; 2 * j < n; ++j) {
FFTW_TRIG_REAL s = dir * FFTW_TRIG_SIN(j * twopin);
FFTW_TRIG_REAL c = FFTW_TRIG_COS(j * twopin);
tmp[j] = outB[j] * c - outB[n - j] * s;
tmp[n - j] = outB[j] * s + outB[n - j] * c;
}
if (2 * j == n)
tmp[j] = -outB[j];
rarray_compare(tmp, outA, n);
}
} else {
for (i = 0; i < rounds; ++i) {
int j;
rfill_random(inA, n);
inB[0] = inA[0];
for (j = 1; 2 * j < n; ++j) {
FFTW_TRIG_REAL s = dir * FFTW_TRIG_SIN(j * twopin);
FFTW_TRIG_REAL c = FFTW_TRIG_COS(j * twopin);
inB[j] = inA[j] * c - inA[n - j] * s;
inB[n - j] = inA[j] * s + inA[n - j] * c;
}
if (2 * j == n)
inB[j] = -inA[j];
rfftw_out_of_place(plan, n, inA, outA);
rfftw_out_of_place(plan, n, inB, outB);
rarray_rol(tmp, outA, n, 1, 1);
rarray_compare(tmp, outB, n);
}
}
WHEN_VERBOSE(2, printf("Validation done\n"));
fftw_free(tmp);
fftw_free(outC);
fftw_free(outB);
fftw_free(outA);
fftw_free(inC);
fftw_free(inB1);
fftw_free(inA1);
fftw_free(inB);
fftw_free(inA);
}