void complex_plan_forward (complex_plan plan, double *data)
{
if (plan->bluestein)
bluestein (plan->length, data, plan->work, -1);
else
cfftf (plan->length, data, plan->work);
}
void faad_mdct(mdct_info *mdct, real_t *X_in, real_t *X_out)
{
uint16_t k;
complex_t x;
ALIGN complex_t Z1[512];
complex_t *sincos = mdct->sincos;
uint16_t N = mdct->N;
uint16_t N2 = N >> 1;
uint16_t N4 = N >> 2;
uint16_t N8 = N >> 3;
#ifndef FIXED_POINT
real_t scale = REAL_CONST(N);
#else
real_t scale = REAL_CONST(4.0/N);
#endif
/* pre-FFT complex multiplication */
for (k = 0; k < N8; k++)
{
uint16_t n = k << 1;
RE(x) = X_in[N - N4 - 1 - n] + X_in[N - N4 + n];
IM(x) = X_in[ N4 + n] - X_in[ N4 - 1 - n];
ComplexMult(&RE(Z1[k]), &IM(Z1[k]),
RE(x), IM(x), RE(sincos[k]), IM(sincos[k]));
RE(Z1[k]) = MUL_R(RE(Z1[k]), scale);
IM(Z1[k]) = MUL_R(IM(Z1[k]), scale);
RE(x) = X_in[N2 - 1 - n] - X_in[ n];
IM(x) = X_in[N2 + n] + X_in[N - 1 - n];
ComplexMult(&RE(Z1[k + N8]), &IM(Z1[k + N8]),
RE(x), IM(x), RE(sincos[k + N8]), IM(sincos[k + N8]));
RE(Z1[k + N8]) = MUL_R(RE(Z1[k + N8]), scale);
IM(Z1[k + N8]) = MUL_R(IM(Z1[k + N8]), scale);
}
/* complex FFT, any non-scaling FFT can be used here */
cfftf(mdct->cfft, Z1);
/* post-FFT complex multiplication */
for (k = 0; k < N4; k++)
{
uint16_t n = k << 1;
ComplexMult(&RE(x), &IM(x),
RE(Z1[k]), IM(Z1[k]), RE(sincos[k]), IM(sincos[k]));
X_out[ n] = -RE(x);
X_out[N2 - 1 - n] = IM(x);
X_out[N2 + n] = -IM(x);
X_out[N - 1 - n] = RE(x);
}
}
PyObject *
fftpack_cfftf(PyObject *NPY_UNUSED(self), PyObject *args)
{
PyObject *op1, *op2;
PyArrayObject *data;
PyArray_Descr *descr;
double *wsave, *dptr;
npy_intp nsave;
int npts, nrepeats, i;
if(!PyArg_ParseTuple(args, "OO", &op1, &op2)) {
return NULL;
}
data = (PyArrayObject *)PyArray_CopyFromObject(op1,
NPY_CDOUBLE, 1, 0);
if (data == NULL) {
return NULL;
}
descr = PyArray_DescrFromType(NPY_DOUBLE);
if (PyArray_AsCArray(&op2, (void *)&wsave, &nsave, 1, descr) == -1) {
goto fail;
}
if (data == NULL) {
goto fail;
}
npts = PyArray_DIM(data, PyArray_NDIM(data) - 1);
if (nsave != npts*4 + 15) {
PyErr_SetString(ErrorObject, "invalid work array for fft size");
goto fail;
}
nrepeats = PyArray_SIZE(data)/npts;
dptr = (double *)PyArray_DATA(data);
NPY_SIGINT_ON;
for (i = 0; i < nrepeats; i++) {
cfftf(npts, dptr, wsave);
dptr += npts*2;
}
NPY_SIGINT_OFF;
PyArray_Free(op2, (char *)wsave);
return (PyObject *)data;
fail:
PyArray_Free(op2, (char *)wsave);
Py_DECREF(data);
return NULL;
}
void bluestein_i (size_t n, double **tstorage, size_t *worksize)
{
static const double pi=3.14159265358979323846;
size_t n2=good_size(n*2-1);
size_t m, coeff;
double angle, xn2;
double *bk, *bkf, *work;
double pibyn=pi/n;
*worksize=2+2*n+8*n2+16;
*tstorage = RALLOC(double,2+2*n+8*n2+16);
((size_t *)(*tstorage))[0]=n2;
bk = *tstorage+2;
bkf = *tstorage+2+2*n;
work= *tstorage+2+2*(n+n2);
/* initialize b_k */
bk[0] = 1;
bk[1] = 0;
coeff=0;
for (m=1; m<n; ++m)
{
coeff+=2*m-1;
if (coeff>=2*n) coeff-=2*n;
angle = pibyn*coeff;
bk[2*m] = cos(angle);
bk[2*m+1] = sin(angle);
}
/* initialize the zero-padded, Fourier transformed b_k. Add normalisation. */
xn2 = 1./n2;
bkf[0] = bk[0]*xn2;
bkf[1] = bk[1]*xn2;
for (m=2; m<2*n; m+=2)
{
bkf[m] = bkf[2*n2-m] = bk[m] *xn2;
bkf[m+1] = bkf[2*n2-m+1] = bk[m+1] *xn2;
}
for (m=2*n;m<=(2*n2-2*n+1);++m)
bkf[m]=0.;
cffti (n2,work);
cfftf (n2,bkf,work);
}
void faad_mdct(mdct_info *mdct, real_t *X_in, real_t *X_out)
{
uint16_t k;
complex_t x;
ALIGN complex_t Z1[512];
complex_t *sincos = mdct->sincos;
uint16_t N = mdct->N;
uint16_t N2 = N >> 1;
uint16_t N4 = N >> 2;
uint16_t N8 = N >> 3;
#ifndef FIXED_POINT
real_t scale = REAL_CONST(N);
#else
real_t scale = REAL_CONST(4.0/N);
#endif
#ifdef ALLOW_SMALL_FRAMELENGTH
#ifdef FIXED_POINT
/* detect non-power of 2 */
if (N & (N-1))
{
/* adjust scale for non-power of 2 MDCT */
/* *= sqrt(2048/1920) */
scale = MUL_C(scale, COEF_CONST(1.0327955589886444));
}
#endif
#endif
/* pre-FFT complex multiplication */
for (k = 0; k < N8; k++)
{
uint16_t n = k << 1;
RE(x) = X_in[N - N4 - 1 - n] + X_in[N - N4 + n];
IM(x) = X_in[ N4 + n] - X_in[ N4 - 1 - n];
ComplexMult(&RE(Z1[k]), &IM(Z1[k]),
RE(x), IM(x), RE(sincos[k]), IM(sincos[k]));
RE(Z1[k]) = MUL_R(RE(Z1[k]), scale);
IM(Z1[k]) = MUL_R(IM(Z1[k]), scale);
RE(x) = X_in[N2 - 1 - n] - X_in[ n];
IM(x) = X_in[N2 + n] + X_in[N - 1 - n];
ComplexMult(&RE(Z1[k + N8]), &IM(Z1[k + N8]),
RE(x), IM(x), RE(sincos[k + N8]), IM(sincos[k + N8]));
RE(Z1[k + N8]) = MUL_R(RE(Z1[k + N8]), scale);
IM(Z1[k + N8]) = MUL_R(IM(Z1[k + N8]), scale);
}
/* complex FFT, any non-scaling FFT can be used here */
cfftf(mdct->cfft, Z1);
/* post-FFT complex multiplication */
for (k = 0; k < N4; k++)
{
uint16_t n = k << 1;
ComplexMult(&RE(x), &IM(x),
RE(Z1[k]), IM(Z1[k]), RE(sincos[k]), IM(sincos[k]));
X_out[ n] = -RE(x);
X_out[N2 - 1 - n] = IM(x);
X_out[N2 + n] = -IM(x);
X_out[N - 1 - n] = RE(x);
}
}
int cfftf(int *n, doublecomplex *c, double *wsave) {
// Casting (doublecomplex*) to (double*) is probably OK.
return cfftf(n, (double *)c, wsave);
}
/* Main program */ int MAIN__(void)
{
/* Initialized data */
static integer nd[10] = { 120,54,49,32,4,3,2 };
/* Format strings */
static char fmt_1001[] = "(\0020N\002,i5,\002 RFFTF \002,e10.3,\002 RFF"
"TB \002,e10.3,\002 RFFTFB \002,e10.3,\002 SINT \002,e10.3,"
"\002 SINTFB \002,e10.3,\002 COST \002,e10.3/7x,\002 COSTFB "
"\002,e10.3,\002 SINQF \002,e10.3,\002 SINQB \002,e10.3,\002 SI"
"NQFB \002,e10.3,\002 COSQF \002,e10.3,\002 COSQB \002,e10.3/7x,"
"\002 COSQFB \002,e10.3,\002 DEZF \002,e10.3,\002 DEZB \002,e"
"10.3,\002 DEZFB \002,e10.3,\002 CFFTF \002,e10.3,\002 CFFTB "
" \002,e10.3/7x,\002 CFFTFB \002,e10.3)";
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5, i__6;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
double sqrt(doublereal), sin(doublereal), cos(doublereal);
integer pow_ii(integer *, integer *);
double atan(doublereal), z_abs(doublecomplex *);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
doublereal a[100], b[100];
integer i__, j, k, n;
doublereal w[2000], x[200], y[200], ah[100], bh[100], cf, fn, dt, pi;
doublecomplex cx[200], cy[200];
doublereal xh[200];
integer nz, nm1, np1, ns2;
doublereal arg, tfn, tpi;
integer nns;
doublereal sum, arg1, arg2;
integer ns2m;
doublereal sum1, sum2, dcfb;
integer ifac[64], modn;
doublereal rftb, rftf;
extern /* Subroutine */ void cost(integer *, doublereal *, doublereal *,
integer *), sint(integer *, doublereal *, doublereal *, integer *
);
doublereal dezb1, dezf1, sqrt2;
extern /* Subroutine */ void cfftb(integer *, doublecomplex *, doublereal
*, integer *), cfftf(integer *, doublecomplex *, doublereal *,
integer *);
doublereal dezfb;
extern /* Subroutine */ void cffti(integer *, doublereal *, integer *),
rfftb(integer *, doublereal *, doublereal *, integer *);
doublereal rftfb;
extern /* Subroutine */ void rfftf(integer *, doublereal *, doublereal *,
integer *), cosqb(integer *, doublereal *, doublereal *, integer
*), rffti(integer *, doublereal *, integer *), cosqf(integer *,
doublereal *, doublereal *, integer *), sinqb(integer *,
doublereal *, doublereal *, integer *), cosqi(integer *,
doublereal *, integer *), sinqf(integer *, doublereal *,
doublereal *, integer *), costi(integer *, doublereal *, integer
*);
doublereal azero;
extern /* Subroutine */ void sinqi(integer *, doublereal *, integer *),
sinti(integer *, doublereal *, integer *);
doublereal costt, sintt, dcfftb, dcfftf, cosqfb, costfb;
extern /* Subroutine */ void ezfftb(integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *);
doublereal sinqfb;
extern /* Subroutine */ void ezfftf(integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *);
doublereal sintfb;
extern /* Subroutine */ void ezffti(integer *, doublereal *, integer *);
doublereal azeroh, cosqbt, cosqft, sinqbt, sinqft;
/* Fortran I/O blocks */
static cilist io___58 = { 0, 6, 0, fmt_1001, 0 };
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/* VERSION 4 APRIL 1985 */
/* A TEST DRIVER FOR */
/* A PACKAGE OF FORTRAN SUBPROGRAMS FOR THE FAST FOURIER */
/* TRANSFORM OF PERIODIC AND OTHER SYMMETRIC SEQUENCES */
/* BY */
/* PAUL N SWARZTRAUBER */
/* NATIONAL CENTER FOR ATMOSPHERIC RESEARCH BOULDER,COLORADO 80307 */
/* WHICH IS SPONSORED BY THE NATIONAL SCIENCE FOUNDATION */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/* THIS PROGRAM TESTS THE PACKAGE OF FAST FOURIER */
/* TRANSFORMS FOR BOTH COMPLEX AND REAL PERIODIC SEQUENCES AND */
/* CERTIAN OTHER SYMMETRIC SEQUENCES THAT ARE LISTED BELOW. */
/* 1. RFFTI INITIALIZE RFFTF AND RFFTB */
/* 2. RFFTF FORWARD TRANSFORM OF A REAL PERIODIC SEQUENCE */
/* 3. RFFTB BACKWARD TRANSFORM OF A REAL COEFFICIENT ARRAY */
/* 4. EZFFTI INITIALIZE EZFFTF AND EZFFTB */
/* 5. EZFFTF A SIMPLIFIED REAL PERIODIC FORWARD TRANSFORM */
/* 6. EZFFTB A SIMPLIFIED REAL PERIODIC BACKWARD TRANSFORM */
/* 7. SINTI INITIALIZE SINT */
/* 8. SINT SINE TRANSFORM OF A REAL ODD SEQUENCE */
/* 9. COSTI INITIALIZE COST */
/* 10. COST COSINE TRANSFORM OF A REAL EVEN SEQUENCE */
/* 11. SINQI INITIALIZE SINQF AND SINQB */
/* 12. SINQF FORWARD SINE TRANSFORM WITH ODD WAVE NUMBERS */
/* 13. SINQB UNNORMALIZED INVERSE OF SINQF */
/* 14. COSQI INITIALIZE COSQF AND COSQB */
/* 15. COSQF FORWARD COSINE TRANSFORM WITH ODD WAVE NUMBERS */
/* 16. COSQB UNNORMALIZED INVERSE OF COSQF */
/* 17. CFFTI INITIALIZE CFFTF AND CFFTB */
/* 18. CFFTF FORWARD TRANSFORM OF A COMPLEX PERIODIC SEQUENCE */
/* 19. CFFTB UNNORMALIZED INVERSE OF CFFTF */
sqrt2 = sqrt(2.0);
nns = 7;
i__1 = nns;
for (nz = 1; nz <= i__1; ++nz) {
n = nd[nz - 1];
modn = n % 2;
fn = (real) n;
tfn = fn + fn;
np1 = n + 1;
nm1 = n - 1;
i__2 = np1;
for (j = 1; j <= i__2; ++j) {
x[j - 1] = sin((real) j * sqrt2);
y[j - 1] = x[j - 1];
xh[j - 1] = x[j - 1];
/* L101: */
}
/* TEST SUBROUTINES RFFTI,RFFTF AND RFFTB */
rffti(&n, w, ifac);
pi = 3.141592653589793238462643383279502884197169399375108209749445923;
dt = (pi + pi) / fn;
ns2 = (n + 1) / 2;
if (ns2 < 2) {
goto L104;
}
i__2 = ns2;
for (k = 2; k <= i__2; ++k) {
sum1 = 0.0;
sum2 = 0.0;
arg = (real) (k - 1) * dt;
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
arg1 = (real) (i__ - 1) * arg;
sum1 += x[i__ - 1] * cos(arg1);
sum2 += x[i__ - 1] * sin(arg1);
/* L102: */
}
y[(k << 1) - 3] = sum1;
y[(k << 1) - 2] = -sum2;
/* L103: */
}
L104:
sum1 = 0.0;
sum2 = 0.0;
i__2 = nm1;
for (i__ = 1; i__ <= i__2; i__ += 2) {
sum1 += x[i__ - 1];
sum2 += x[i__];
/* L105: */
}
if (modn == 1) {
sum1 += x[n - 1];
}
y[0] = sum1 + sum2;
if (modn == 0) {
y[n - 1] = sum1 - sum2;
}
rfftf(&n, x, w, ifac);
rftf = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = rftf, d__3 = (d__1 = x[i__ - 1] - y[i__ - 1], abs(d__1));
rftf = max(d__2,d__3);
x[i__ - 1] = xh[i__ - 1];
/* L106: */
}
rftf /= fn;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
sum = x[0] * 0.5;
arg = (real) (i__ - 1) * dt;
if (ns2 < 2) {
goto L108;
}
i__3 = ns2;
for (k = 2; k <= i__3; ++k) {
arg1 = (real) (k - 1) * arg;
sum = sum + x[(k << 1) - 3] * cos(arg1) - x[(k << 1) - 2] *
sin(arg1);
/* L107: */
}
L108:
if (modn == 0) {
i__3 = i__ - 1;
sum += (real) pow_ii(&c_n1, &i__3) * 0.5 * x[n - 1];
}
y[i__ - 1] = sum + sum;
/* L109: */
}
rfftb(&n, x, w, ifac);
rftb = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = rftb, d__3 = (d__1 = x[i__ - 1] - y[i__ - 1], abs(d__1));
rftb = max(d__2,d__3);
x[i__ - 1] = xh[i__ - 1];
y[i__ - 1] = xh[i__ - 1];
/* L110: */
}
rfftb(&n, y, w, ifac);
rfftf(&n, y, w, ifac);
cf = 1.0 / fn;
rftfb = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = rftfb, d__3 = (d__1 = cf * y[i__ - 1] - x[i__ - 1], abs(
d__1));
rftfb = max(d__2,d__3);
/* L111: */
}
/* TEST SUBROUTINES SINTI AND SINT */
dt = pi / fn;
i__2 = nm1;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__ - 1] = xh[i__ - 1];
/* L112: */
}
i__2 = nm1;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__ - 1] = 0.0;
arg1 = (real) i__ * dt;
i__3 = nm1;
for (k = 1; k <= i__3; ++k) {
y[i__ - 1] += x[k - 1] * sin((real) k * arg1);
/* L113: */
}
y[i__ - 1] += y[i__ - 1];
/* L114: */
}
sinti(&nm1, w, ifac);
sint(&nm1, x, w, ifac);
cf = 0.5 / fn;
sintt = 0.0;
i__2 = nm1;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = sintt, d__3 = (d__1 = x[i__ - 1] - y[i__ - 1], abs(d__1));
sintt = max(d__2,d__3);
x[i__ - 1] = xh[i__ - 1];
y[i__ - 1] = x[i__ - 1];
/* L115: */
}
sintt = cf * sintt;
sint(&nm1, x, w, ifac);
sint(&nm1, x, w, ifac);
sintfb = 0.0;
i__2 = nm1;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = sintfb, d__3 = (d__1 = cf * x[i__ - 1] - y[i__ - 1], abs(
d__1));
sintfb = max(d__2,d__3);
/* L116: */
}
/* TEST SUBROUTINES COSTI AND COST */
i__2 = np1;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__ - 1] = xh[i__ - 1];
/* L117: */
}
i__2 = np1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + 1;
y[i__ - 1] = (x[0] + (real) pow_ii(&c_n1, &i__3) * x[n]) * 0.5;
arg = (real) (i__ - 1) * dt;
i__3 = n;
for (k = 2; k <= i__3; ++k) {
y[i__ - 1] += x[k - 1] * cos((real) (k - 1) * arg);
/* L118: */
}
y[i__ - 1] += y[i__ - 1];
/* L119: */
}
costi(&np1, w, ifac);
cost(&np1, x, w, ifac);
costt = 0.0;
i__2 = np1;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = costt, d__3 = (d__1 = x[i__ - 1] - y[i__ - 1], abs(d__1));
costt = max(d__2,d__3);
x[i__ - 1] = xh[i__ - 1];
y[i__ - 1] = xh[i__ - 1];
/* L120: */
}
costt = cf * costt;
cost(&np1, x, w, ifac);
cost(&np1, x, w, ifac);
costfb = 0.0;
i__2 = np1;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = costfb, d__3 = (d__1 = cf * x[i__ - 1] - y[i__ - 1], abs(
d__1));
costfb = max(d__2,d__3);
/* L121: */
}
/* TEST SUBROUTINES SINQI,SINQF AND SINQB */
cf = 0.25 / fn;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__ - 1] = xh[i__ - 1];
/* L122: */
}
dt = pi / (fn + fn);
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__ - 1] = 0.0;
arg = dt * (real) i__;
i__3 = n;
for (k = 1; k <= i__3; ++k) {
x[i__ - 1] += y[k - 1] * sin((real) (k + k - 1) * arg);
/* L123: */
}
x[i__ - 1] *= 4.0;
/* L124: */
}
sinqi(&n, w, ifac);
sinqb(&n, y, w, ifac);
sinqbt = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = sinqbt, d__3 = (d__1 = y[i__ - 1] - x[i__ - 1], abs(d__1));
sinqbt = max(d__2,d__3);
x[i__ - 1] = xh[i__ - 1];
/* L125: */
}
sinqbt = cf * sinqbt;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
arg = (real) (i__ + i__ - 1) * dt;
i__3 = i__ + 1;
y[i__ - 1] = (real) pow_ii(&c_n1, &i__3) * 0.5 * x[n - 1];
i__3 = nm1;
for (k = 1; k <= i__3; ++k) {
y[i__ - 1] += x[k - 1] * sin((real) k * arg);
/* L126: */
}
y[i__ - 1] += y[i__ - 1];
/* L127: */
}
sinqf(&n, x, w, ifac);
sinqft = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = sinqft, d__3 = (d__1 = x[i__ - 1] - y[i__ - 1], abs(d__1));
sinqft = max(d__2,d__3);
y[i__ - 1] = xh[i__ - 1];
x[i__ - 1] = xh[i__ - 1];
/* L128: */
}
sinqf(&n, y, w, ifac);
sinqb(&n, y, w, ifac);
sinqfb = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = sinqfb, d__3 = (d__1 = cf * y[i__ - 1] - x[i__ - 1], abs(
d__1));
sinqfb = max(d__2,d__3);
/* L129: */
}
/* TEST SUBROUTINES COSQI,COSQF AND COSQB */
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__ - 1] = xh[i__ - 1];
/* L130: */
}
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__ - 1] = 0.0;
arg = (real) (i__ - 1) * dt;
i__3 = n;
for (k = 1; k <= i__3; ++k) {
x[i__ - 1] += y[k - 1] * cos((real) (k + k - 1) * arg);
/* L131: */
}
x[i__ - 1] *= 4.0;
/* L132: */
}
cosqi(&n, w, ifac);
cosqb(&n, y, w, ifac);
cosqbt = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = cosqbt, d__3 = (d__1 = x[i__ - 1] - y[i__ - 1], abs(d__1));
cosqbt = max(d__2,d__3);
x[i__ - 1] = xh[i__ - 1];
/* L133: */
}
cosqbt = cf * cosqbt;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
y[i__ - 1] = x[0] * 0.5;
arg = (real) (i__ + i__ - 1) * dt;
i__3 = n;
for (k = 2; k <= i__3; ++k) {
y[i__ - 1] += x[k - 1] * cos((real) (k - 1) * arg);
/* L134: */
}
y[i__ - 1] += y[i__ - 1];
/* L135: */
}
cosqf(&n, x, w, ifac);
cosqft = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = cosqft, d__3 = (d__1 = y[i__ - 1] - x[i__ - 1], abs(d__1));
cosqft = max(d__2,d__3);
x[i__ - 1] = xh[i__ - 1];
y[i__ - 1] = xh[i__ - 1];
/* L136: */
}
cosqft = cf * cosqft;
cosqb(&n, x, w, ifac);
cosqf(&n, x, w, ifac);
cosqfb = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = cosqfb, d__3 = (d__1 = cf * x[i__ - 1] - y[i__ - 1], abs(
d__1));
cosqfb = max(d__2,d__3);
/* L137: */
}
/* TEST PROGRAMS EZFFTI,EZFFTF,EZFFTB */
ezffti(&n, w, ifac);
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__ - 1] = xh[i__ - 1];
/* L138: */
}
tpi = atan(1.0) * 8.0;
dt = tpi / (real) n;
ns2 = (n + 1) / 2;
cf = 2.0 / (real) n;
ns2m = ns2 - 1;
if (ns2m <= 0) {
goto L141;
}
i__2 = ns2m;
for (k = 1; k <= i__2; ++k) {
sum1 = 0.0;
sum2 = 0.0;
arg = (real) k * dt;
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
arg1 = (real) (i__ - 1) * arg;
sum1 += x[i__ - 1] * cos(arg1);
sum2 += x[i__ - 1] * sin(arg1);
/* L139: */
}
a[k - 1] = cf * sum1;
b[k - 1] = cf * sum2;
/* L140: */
}
L141:
nm1 = n - 1;
sum1 = 0.0;
sum2 = 0.0;
i__2 = nm1;
for (i__ = 1; i__ <= i__2; i__ += 2) {
sum1 += x[i__ - 1];
sum2 += x[i__];
/* L142: */
}
if (modn == 1) {
sum1 += x[n - 1];
}
azero = cf * 0.5 * (sum1 + sum2);
if (modn == 0) {
a[ns2 - 1] = cf * 0.5 * (sum1 - sum2);
}
ezfftf(&n, x, &azeroh, ah, bh, w, ifac);
dezf1 = (d__1 = azeroh - azero, abs(d__1));
if (modn == 0) {
/* Computing MAX */
d__2 = dezf1, d__3 = (d__1 = a[ns2 - 1] - ah[ns2 - 1], abs(d__1));
dezf1 = max(d__2,d__3);
}
if (ns2m <= 0) {
goto L144;
}
i__2 = ns2m;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__3 = dezf1, d__4 = (d__1 = ah[i__ - 1] - a[i__ - 1], abs(d__1)),
d__3 = max(d__3,d__4), d__4 = (d__2 = bh[i__ - 1] - b[
i__ - 1], abs(d__2));
dezf1 = max(d__3,d__4);
/* L143: */
}
L144:
ns2 = n / 2;
if (modn == 0) {
b[ns2 - 1] = 0.0;
}
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
sum = azero;
arg1 = (real) (i__ - 1) * dt;
i__3 = ns2;
for (k = 1; k <= i__3; ++k) {
arg2 = (real) k * arg1;
sum = sum + a[k - 1] * cos(arg2) + b[k - 1] * sin(arg2);
/* L145: */
}
x[i__ - 1] = sum;
/* L146: */
}
ezfftb(&n, y, &azero, a, b, w, ifac);
dezb1 = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = dezb1, d__3 = (d__1 = x[i__ - 1] - y[i__ - 1], abs(d__1));
dezb1 = max(d__2,d__3);
x[i__ - 1] = xh[i__ - 1];
/* L147: */
}
ezfftf(&n, x, &azero, a, b, w, ifac);
ezfftb(&n, y, &azero, a, b, w, ifac);
dezfb = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = dezfb, d__3 = (d__1 = x[i__ - 1] - y[i__ - 1], abs(d__1));
dezfb = max(d__2,d__3);
/* L148: */
}
/* TEST CFFTI,CFFTF,CFFTB */
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ - 1;
d__1 = cos(sqrt2 * (real) i__);
d__2 = sin(sqrt2 * (real) (i__ * i__));
z__1.r = d__1, z__1.i = d__2;
cx[i__3].r = z__1.r, cx[i__3].i = z__1.i;
/* L149: */
}
dt = (pi + pi) / fn;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
arg1 = -((real) (i__ - 1)) * dt;
i__3 = i__ - 1;
cy[i__3].r = 0.0, cy[i__3].i = 0.0;
i__3 = n;
for (k = 1; k <= i__3; ++k) {
arg2 = (real) (k - 1) * arg1;
i__4 = i__ - 1;
i__5 = i__ - 1;
d__1 = cos(arg2);
d__2 = sin(arg2);
z__3.r = d__1, z__3.i = d__2;
i__6 = k - 1;
z__2.r = z__3.r * cx[i__6].r - z__3.i * cx[i__6].i, z__2.i =
z__3.r * cx[i__6].i + z__3.i * cx[i__6].r;
z__1.r = cy[i__5].r + z__2.r, z__1.i = cy[i__5].i + z__2.i;
cy[i__4].r = z__1.r, cy[i__4].i = z__1.i;
/* L150: */
}
/* L151: */
}
cffti(&n, w, ifac);
cfftf(&n, cx, w, ifac);
dcfftf = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ - 1;
i__4 = i__ - 1;
z__1.r = cx[i__3].r - cy[i__4].r, z__1.i = cx[i__3].i - cy[i__4]
.i;
d__1 = dcfftf, d__2 = z_abs(&z__1);
dcfftf = max(d__1,d__2);
i__3 = i__ - 1;
i__4 = i__ - 1;
z__1.r = cx[i__4].r / fn, z__1.i = cx[i__4].i / fn;
cx[i__3].r = z__1.r, cx[i__3].i = z__1.i;
/* L152: */
}
dcfftf /= fn;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
arg1 = (real) (i__ - 1) * dt;
i__3 = i__ - 1;
cy[i__3].r = 0.0, cy[i__3].i = 0.0;
i__3 = n;
for (k = 1; k <= i__3; ++k) {
arg2 = (real) (k - 1) * arg1;
i__4 = i__ - 1;
i__5 = i__ - 1;
d__1 = cos(arg2);
d__2 = sin(arg2);
z__3.r = d__1, z__3.i = d__2;
i__6 = k - 1;
z__2.r = z__3.r * cx[i__6].r - z__3.i * cx[i__6].i, z__2.i =
z__3.r * cx[i__6].i + z__3.i * cx[i__6].r;
z__1.r = cy[i__5].r + z__2.r, z__1.i = cy[i__5].i + z__2.i;
cy[i__4].r = z__1.r, cy[i__4].i = z__1.i;
/* L153: */
}
/* L154: */
}
cfftb(&n, cx, w, ifac);
dcfftb = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ - 1;
i__4 = i__ - 1;
z__1.r = cx[i__3].r - cy[i__4].r, z__1.i = cx[i__3].i - cy[i__4]
.i;
d__1 = dcfftb, d__2 = z_abs(&z__1);
dcfftb = max(d__1,d__2);
i__3 = i__ - 1;
i__4 = i__ - 1;
cx[i__3].r = cy[i__4].r, cx[i__3].i = cy[i__4].i;
/* L155: */
}
cf = 1.0 / fn;
cfftf(&n, cx, w, ifac);
cfftb(&n, cx, w, ifac);
dcfb = 0.0;
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ - 1;
z__2.r = cf * cx[i__3].r, z__2.i = cf * cx[i__3].i;
i__4 = i__ - 1;
z__1.r = z__2.r - cy[i__4].r, z__1.i = z__2.i - cy[i__4].i;
d__1 = dcfb, d__2 = z_abs(&z__1);
dcfb = max(d__1,d__2);
/* L156: */
}
s_wsfe(&io___58);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&rftf, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&rftb, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&rftfb, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&sintt, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&sintfb, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&costt, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&costfb, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&sinqft, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&sinqbt, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&sinqfb, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&cosqft, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&cosqbt, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&cosqfb, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&dezf1, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&dezb1, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&dezfb, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&dcfftf, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&dcfftb, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&dcfb, (ftnlen)sizeof(doublereal));
e_wsfe();
/* L157: */
}
return 0;
} /* MAIN__ */
void bluestein (size_t n, double *data, double *tstorage, int isign)
{
size_t n2=*((size_t *)tstorage);
size_t m;
double *bk, *bkf, *akf, *work;
bk = tstorage+2;
bkf = tstorage+2+2*n;
work= tstorage+2+2*(n+n2);
akf = tstorage+2+2*n+6*n2+16;
/* initialize a_k and FFT it */
if (isign>0)
for (m=0; m<2*n; m+=2)
{
akf[m] = data[m]*bk[m] - data[m+1]*bk[m+1];
akf[m+1] = data[m]*bk[m+1] + data[m+1]*bk[m];
}
else
for (m=0; m<2*n; m+=2)
{
akf[m] = data[m]*bk[m] + data[m+1]*bk[m+1];
akf[m+1] =-data[m]*bk[m+1] + data[m+1]*bk[m];
}
for (m=2*n; m<2*n2; ++m)
akf[m]=0;
cfftf (n2,akf,work);
/* do the convolution */
if (isign>0)
for (m=0; m<2*n2; m+=2)
{
double im = -akf[m]*bkf[m+1] + akf[m+1]*bkf[m];
akf[m ] = akf[m]*bkf[m] + akf[m+1]*bkf[m+1];
akf[m+1] = im;
}
else
for (m=0; m<2*n2; m+=2)
{
double im = akf[m]*bkf[m+1] + akf[m+1]*bkf[m];
akf[m ] = akf[m]*bkf[m] - akf[m+1]*bkf[m+1];
akf[m+1] = im;
}
/* inverse FFT */
cfftb (n2,akf,work);
/* multiply by b_k* */
if (isign>0)
for (m=0; m<2*n; m+=2)
{
data[m] = bk[m] *akf[m] - bk[m+1]*akf[m+1];
data[m+1] = bk[m+1]*akf[m] + bk[m] *akf[m+1];
}
else
for (m=0; m<2*n; m+=2)
{
data[m] = bk[m] *akf[m] + bk[m+1]*akf[m+1];
data[m+1] =-bk[m+1]*akf[m] + bk[m] *akf[m+1];
}
}
/* compare results with the regular fftpack */
void pffft_validate_N(int N, int cplx) {
int Nfloat = N*(cplx?2:1);
int Nbytes = Nfloat * sizeof(float);
float *ref, *in, *out, *tmp, *tmp2;
PFFFT_Setup *s = pffft_new_setup(N, cplx ? PFFFT_COMPLEX : PFFFT_REAL);
int pass;
if (!s) { printf("Skipping N=%d, not supported\n", N); return; }
ref = pffft_aligned_malloc(Nbytes);
in = pffft_aligned_malloc(Nbytes);
out = pffft_aligned_malloc(Nbytes);
tmp = pffft_aligned_malloc(Nbytes);
tmp2 = pffft_aligned_malloc(Nbytes);
for (pass=0; pass < 2; ++pass) {
float ref_max = 0;
int k;
//printf("N=%d pass=%d cplx=%d\n", N, pass, cplx);
// compute reference solution with FFTPACK
if (pass == 0) {
float *wrk = malloc(2*Nbytes+15*sizeof(float));
for (k=0; k < Nfloat; ++k) {
ref[k] = in[k] = frand()*2-1;
out[k] = 1e30;
}
if (!cplx) {
rffti(N, wrk);
rfftf(N, ref, wrk);
// use our ordering for real ffts instead of the one of fftpack
{
float refN=ref[N-1];
for (k=N-2; k >= 1; --k) ref[k+1] = ref[k];
ref[1] = refN;
}
} else {
cffti(N, wrk);
cfftf(N, ref, wrk);
}
free(wrk);
}
for (k = 0; k < Nfloat; ++k) ref_max = MAX(ref_max, fabs(ref[k]));
// pass 0 : non canonical ordering of transform coefficients
if (pass == 0) {
// test forward transform, with different input / output
pffft_transform(s, in, tmp, 0, PFFFT_FORWARD);
memcpy(tmp2, tmp, Nbytes);
memcpy(tmp, in, Nbytes);
pffft_transform(s, tmp, tmp, 0, PFFFT_FORWARD);
for (k = 0; k < Nfloat; ++k) {
assert(tmp2[k] == tmp[k]);
}
// test reordering
pffft_zreorder(s, tmp, out, PFFFT_FORWARD);
pffft_zreorder(s, out, tmp, PFFFT_BACKWARD);
for (k = 0; k < Nfloat; ++k) {
assert(tmp2[k] == tmp[k]);
}
pffft_zreorder(s, tmp, out, PFFFT_FORWARD);
} else {
// pass 1 : canonical ordering of transform coeffs.
pffft_transform_ordered(s, in, tmp, 0, PFFFT_FORWARD);
memcpy(tmp2, tmp, Nbytes);
memcpy(tmp, in, Nbytes);
pffft_transform_ordered(s, tmp, tmp, 0, PFFFT_FORWARD);
for (k = 0; k < Nfloat; ++k) {
assert(tmp2[k] == tmp[k]);
}
memcpy(out, tmp, Nbytes);
}
{
for (k=0; k < Nfloat; ++k) {
if (!(fabs(ref[k] - out[k]) < 1e-3*ref_max)) {
printf("%s forward PFFFT mismatch found for N=%d\n", (cplx?"CPLX":"REAL"), N);
exit(1);
}
}
if (pass == 0) pffft_transform(s, tmp, out, 0, PFFFT_BACKWARD);
else pffft_transform_ordered(s, tmp, out, 0, PFFFT_BACKWARD);
memcpy(tmp2, out, Nbytes);
memcpy(out, tmp, Nbytes);
if (pass == 0) pffft_transform(s, out, out, 0, PFFFT_BACKWARD);
else pffft_transform_ordered(s, out, out, 0, PFFFT_BACKWARD);
for (k = 0; k < Nfloat; ++k) {
assert(tmp2[k] == out[k]);
out[k] *= 1.f/N;
}
for (k = 0; k < Nfloat; ++k) {
if (fabs(in[k] - out[k]) > 1e-3 * ref_max) {
printf("pass=%d, %s IFFFT does not match for N=%d\n", pass, (cplx?"CPLX":"REAL"), N); break;
exit(1);
}
}
}
// quick test of the circular convolution in fft domain
{
float conv_err = 0, conv_max = 0;
pffft_zreorder(s, ref, tmp, PFFFT_FORWARD);
memset(out, 0, Nbytes);
pffft_zconvolve_accumulate(s, ref, ref, out, 1.0);
pffft_zreorder(s, out, tmp2, PFFFT_FORWARD);
for (k=0; k < Nfloat; k += 2) {
float ar = tmp[k], ai=tmp[k+1];
if (cplx || k > 0) {
tmp[k] = ar*ar - ai*ai;
tmp[k+1] = 2*ar*ai;
} else {
tmp[0] = ar*ar;
tmp[1] = ai*ai;
}
}
for (k=0; k < Nfloat; ++k) {
float d = fabs(tmp[k] - tmp2[k]), e = fabs(tmp[k]);
if (d > conv_err) conv_err = d;
if (e > conv_max) conv_max = e;
}
if (conv_err > 1e-5*conv_max) {
printf("zconvolve error ? %g %g\n", conv_err, conv_max); exit(1);
}
}
}
printf("%s PFFFT is OK for N=%d\n", (cplx?"CPLX":"REAL"), N); fflush(stdout);
pffft_destroy_setup(s);
pffft_aligned_free(ref);
pffft_aligned_free(in);
pffft_aligned_free(out);
pffft_aligned_free(tmp);
pffft_aligned_free(tmp2);
}
void benchmark_ffts(int N, int cplx) {
int Nfloat = (cplx ? N*2 : N);
int Nbytes = Nfloat * sizeof(float);
float *X = pffft_aligned_malloc(Nbytes), *Y = pffft_aligned_malloc(Nbytes), *Z = pffft_aligned_malloc(Nbytes);
double t0, t1, flops;
int k;
int max_iter = 5120000/N*4;
#ifdef __arm__
max_iter /= 4;
#endif
int iter;
for (k = 0; k < Nfloat; ++k) {
X[k] = 0; //sqrtf(k+1);
}
// FFTPack benchmark
{
float *wrk = malloc(2*Nbytes + 15*sizeof(float));
int max_iter_ = max_iter/pffft_simd_size(); if (max_iter_ == 0) max_iter_ = 1;
if (cplx) cffti(N, wrk);
else rffti(N, wrk);
t0 = uclock_sec();
for (iter = 0; iter < max_iter_; ++iter) {
if (cplx) {
cfftf(N, X, wrk);
cfftb(N, X, wrk);
} else {
rfftf(N, X, wrk);
rfftb(N, X, wrk);
}
}
t1 = uclock_sec();
free(wrk);
flops = (max_iter_*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
show_output("FFTPack", N, cplx, flops, t0, t1, max_iter_);
}
#ifdef HAVE_VECLIB
int log2N = (int)(log(N)/log(2) + 0.5f);
if (N == (1<<log2N)) {
FFTSetup setup;
setup = vDSP_create_fftsetup(log2N, FFT_RADIX2);
DSPSplitComplex zsamples;
zsamples.realp = &X[0];
zsamples.imagp = &X[Nfloat/2];
t0 = uclock_sec();
for (iter = 0; iter < max_iter; ++iter) {
if (cplx) {
vDSP_fft_zip(setup, &zsamples, 1, log2N, kFFTDirection_Forward);
vDSP_fft_zip(setup, &zsamples, 1, log2N, kFFTDirection_Inverse);
} else {
vDSP_fft_zrip(setup, &zsamples, 1, log2N, kFFTDirection_Forward);
vDSP_fft_zrip(setup, &zsamples, 1, log2N, kFFTDirection_Inverse);
}
}
t1 = uclock_sec();
vDSP_destroy_fftsetup(setup);
flops = (max_iter*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
show_output("vDSP", N, cplx, flops, t0, t1, max_iter);
} else {
show_output("vDSP", N, cplx, -1, -1, -1, -1);
}
#endif
#ifdef HAVE_FFTW
{
fftwf_plan planf, planb;
fftw_complex *in = (fftw_complex*) fftwf_malloc(sizeof(fftw_complex) * N);
fftw_complex *out = (fftw_complex*) fftwf_malloc(sizeof(fftw_complex) * N);
memset(in, 0, sizeof(fftw_complex) * N);
int flags = (N < 40000 ? FFTW_MEASURE : FFTW_ESTIMATE); // measure takes a lot of time on largest ffts
//int flags = FFTW_ESTIMATE;
if (cplx) {
planf = fftwf_plan_dft_1d(N, (fftwf_complex*)in, (fftwf_complex*)out, FFTW_FORWARD, flags);
planb = fftwf_plan_dft_1d(N, (fftwf_complex*)in, (fftwf_complex*)out, FFTW_BACKWARD, flags);
} else {
planf = fftwf_plan_dft_r2c_1d(N, (float*)in, (fftwf_complex*)out, flags);
planb = fftwf_plan_dft_c2r_1d(N, (fftwf_complex*)in, (float*)out, flags);
}
t0 = uclock_sec();
for (iter = 0; iter < max_iter; ++iter) {
fftwf_execute(planf);
fftwf_execute(planb);
}
t1 = uclock_sec();
fftwf_destroy_plan(planf);
fftwf_destroy_plan(planb);
fftwf_free(in); fftwf_free(out);
flops = (max_iter*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
show_output((flags == FFTW_MEASURE ? "FFTW (meas.)" : " FFTW (estim)"), N, cplx, flops, t0, t1, max_iter);
}
#endif
// PFFFT benchmark
{
PFFFT_Setup *s = pffft_new_setup(N, cplx ? PFFFT_COMPLEX : PFFFT_REAL);
if (s) {
t0 = uclock_sec();
for (iter = 0; iter < max_iter; ++iter) {
pffft_transform(s, X, Z, Y, PFFFT_FORWARD);
pffft_transform(s, X, Z, Y, PFFFT_BACKWARD);
}
t1 = uclock_sec();
pffft_destroy_setup(s);
flops = (max_iter*2) * ((cplx ? 5 : 2.5)*N*log((double)N)/M_LN2); // see http://www.fftw.org/speed/method.html
show_output("PFFFT", N, cplx, flops, t0, t1, max_iter);
}
}
if (!array_output_format) {
printf("--\n");
}
pffft_aligned_free(X);
pffft_aligned_free(Y);
pffft_aligned_free(Z);
}