mdct_info *faad_mdct_init(uint16_t N)
{
mdct_info *mdct = (mdct_info*)faad_malloc(sizeof(mdct_info));
assert(N % 8 == 0);
mdct->N = N;
/* NOTE: For "small framelengths" in FIXED_POINT the coefficients need to be
* scaled by sqrt("(nearest power of 2) > N" / N) */
/* RE(mdct->sincos[k]) = scale*(real_t)(cos(2.0*M_PI*(k+1./8.) / (real_t)N));
* IM(mdct->sincos[k]) = scale*(real_t)(sin(2.0*M_PI*(k+1./8.) / (real_t)N)); */
/* scale is 1 for fixed point, sqrt(N) for floating point */
switch (N)
{
case 2048:
mdct->sincos = (complex_t*)mdct_tab_2048;
break;
case 256:
mdct->sincos = (complex_t*)mdct_tab_256;
break;
#ifdef LD_DEC
case 1024:
mdct->sincos = (complex_t*)mdct_tab_1024;
break;
#endif
#ifdef ALLOW_SMALL_FRAMELENGTH
case 1920:
mdct->sincos = (complex_t*)mdct_tab_1920;
break;
case 240:
mdct->sincos = (complex_t*)mdct_tab_240;
break;
#ifdef LD_DEC
case 960:
mdct->sincos = (complex_t*)mdct_tab_960;
break;
#endif
#endif
#ifdef SSR_DEC
case 512:
mdct->sincos = (complex_t*)mdct_tab_512;
break;
case 64:
mdct->sincos = (complex_t*)mdct_tab_64;
break;
#endif
}
/* initialise fft */
mdct->cfft = cffti(N/4);
#ifdef PROFILE
mdct->cycles = 0;
mdct->fft_cycles = 0;
#endif
return mdct;
}
mdct_info *faad_mdct_init(uint16_t N)
{
uint16_t k;
#ifdef FIXED_POINT
uint16_t N_idx;
real_t cangle, sangle, c, s, cold;
#endif
real_t scale;
mdct_info *mdct = (mdct_info*)faad_malloc(sizeof(mdct_info));
assert(N % 8 == 0);
mdct->N = N;
mdct->sincos = (complex_t*)faad_malloc(N/4*sizeof(complex_t));
#ifdef FIXED_POINT
N_idx = map_N_to_idx(N);
scale = const_tab[N_idx][0];
cangle = const_tab[N_idx][1];
sangle = const_tab[N_idx][2];
c = const_tab[N_idx][3];
s = const_tab[N_idx][4];
#else
scale = (real_t)sqrt(2.0 / (real_t)N);
#endif
/* (co)sine table build using recurrence relations */
/* this can also be done using static table lookup or */
/* some form of interpolation */
for (k = 0; k < N/4; k++)
{
#ifdef FIXED_POINT
RE(mdct->sincos[k]) = c; //MUL_C_C(c,scale);
IM(mdct->sincos[k]) = s; //MUL_C_C(s,scale);
cold = c;
c = MUL_F(c,cangle) - MUL_F(s,sangle);
s = MUL_F(s,cangle) + MUL_F(cold,sangle);
#else
/* no recurrence, just sines */
RE(mdct->sincos[k]) = scale*(real_t)(cos(2.0*M_PI*(k+1./8.) / (real_t)N));
IM(mdct->sincos[k]) = scale*(real_t)(sin(2.0*M_PI*(k+1./8.) / (real_t)N));
#endif
}
/* initialise fft */
mdct->cfft = cffti(N/4);
#ifdef PROFILE
mdct->cycles = 0;
mdct->fft_cycles = 0;
#endif
return mdct;
}
complex_plan make_complex_plan (int length)
{
complex_plan plan = (complex_plan) malloc(sizeof(complex_plan_i));
int pfsum = prime_factor_sum(length);
double comp1 = length*pfsum;
double comp2 = 2*3*length*log(3.*length);
plan->length=length;
plan->bluestein = (comp2<comp1);
if (plan->bluestein)
bluestein_i (length,&(plan->work));
else
{
plan->work=(double *)malloc((4*length+15)*sizeof(double));
cffti(length, plan->work);
}
return plan;
}
complex_plan make_complex_plan (size_t length)
{
complex_plan plan = RALLOC(complex_plan_i,1);
size_t pfsum = prime_factor_sum(length);
double comp1 = length*pfsum;
double comp2 = 2*3*length*log(3.*length);
comp2*=3.; /* fudge factor that appears to give good overall performance */
plan->length=length;
plan->bluestein = (comp2<comp1);
if (plan->bluestein)
bluestein_i (length,&(plan->work));
else
{
plan->work=RALLOC(double,4*length+15);
cffti(length, plan->work);
}
return plan;
}
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);
}
static PyObject *
fftpack_cffti(PyObject *NPY_UNUSED(self), PyObject *args)
{
PyArrayObject *op;
npy_intp dim;
long n;
if (!PyArg_ParseTuple(args, "l", &n)) {
return NULL;
}
/*Magic size needed by cffti*/
dim = 4*n + 15;
/*Create a 1 dimensional array of dimensions of type double*/
op = (PyArrayObject *)PyArray_SimpleNew(1, &dim, NPY_DOUBLE);
if (op == NULL) {
return NULL;
}
NPY_SIGINT_ON;
cffti(n, (double *)PyArray_DATA((PyArrayObject*)op));
NPY_SIGINT_OFF;
return (PyObject *)op;
}
Datum
fft_main(PG_FUNCTION_ARGS)
{
int i,n;
double sgn;
double *w;
double wtime;
double *x,*y,*z;
int32 arg = PG_GETARG_INT32(0);
timestamp();
ereport(INFO,(errmsg(" Number of processors available = %d\n", omp_get_num_procs())));
ereport(INFO,(errmsg(" Number of threads = %d\n", omp_get_max_threads())));
//Prepare for tests.
ereport(INFO,(errmsg(" N Time\n")));
n = 4;
w = (double *) malloc( n * sizeof(double));
x = (double *) malloc(2 * n * sizeof(double));
y = (double *) malloc(2 * n * sizeof(double));
z = (double *) malloc(2 * n * sizeof(double));
//初始化数据
x[0]=1.0; x[1]=0.0;
x[2]=2.0; x[3]=0.0;
x[4]=4.0; x[5]=0.0;
x[6]=3.0; x[7]=0.0;
ereport(INFO,(errmsg("x=")));
for(i=0; i<2*n; i++){
ereport(INFO,(errmsg("%f,",x[i])));
}
//Initialize the sine and cosine tables.
cffti(n, w);
wtime = omp_get_wtime();
//Transform forward
sgn = + 1.0;
//fft计算
cfft2( n, x, y, w, sgn );
//输出结果
ereport(INFO,(errmsg("y=")));
for(i=0; i<2*n; i++){
ereport(INFO,(errmsg("%f,",y[i])));
}
//元素个数
ereport(INFO,(errmsg(" %12d", n)));
//运行时间
wtime = omp_get_wtime() - wtime;
ereport(INFO,(errmsg(" %12e\n", wtime)));
free(w);
free(x);
free(y);
//Terminate.
ereport(INFO,(errmsg(" Normal end of execution.\n")));
timestamp();
PG_RETURN_INT32(arg);
}
int main()
{
/*
SSE version of cfft2 - uses INTEL intrinsics
W. Petersen, SAM. Math. ETHZ 2 May, 2002
*/
int first,i,icase,it,n;
float seed,error,fnm1,sign,z0,z1,ggl();
float t1,ln2,mflops;
void cffti(),cfft2();
first = 1;
seed = 331.0;
for(icase=0;icase<2;icase++){
if(first){
for(i=0;i<2*N;i+=2){
z0 = ggl(&seed); /* real part of array */
z1 = ggl(&seed); /* imaginary part of array */
x[i] = z0;
z[i] = z0; /* copy of initial real data */
x[i+1] = z1;
z[i+1] = z1; /* copy of initial imag. data */
}
} else {
for(i=0;i<2*N;i+=2){
z0 = 0; /* real part of array */
z1 = 0; /* imaginary part of array */
x[i] = z0;
z[i] = z0; /* copy of initial real data */
x[i+1] = z1;
z[i+1] = z1; /* copy of initial imag. data */
}
}
/* initialize sine/cosine tables */
n = N;
cffti(n,w);
/* transform forward, back */
if(first){
sign = 1.0;
cfft2(n,x,y,w,sign);
sign = -1.0;
cfft2(n,y,x,w,sign);
/* results should be same as initial multiplied by N */
fnm1 = 1.0/((float) n);
error = 0.0;
for(i=0;i<2*N;i+=2){
error += (z[i] - fnm1*x[i])*(z[i] - fnm1*x[i]) +
(z[i+1] - fnm1*x[i+1])*(z[i+1] - fnm1*x[i+1]);
}
error = sqrt(fnm1*error);
printf(" for n=%d, fwd/bck error=%e\n",N,error);
first = 0;
} else {
unsigned j = 0;
for(it=0;it<20000;it++){
sign = +1.0;
cfft2(n,x,y,w,sign);
sign = -1.0;
cfft2(n,y,x,w,sign);
}
printf(" for n=%d\n",n);
for (i = 0; i<N; ++i) {
printf("%g ", w[i]);
j++;
if (j == 4) {
printf("\n");
j = 0;
}
}
}
}
return 0;
}
main()
{
/*
Example of Apple Altivec coded binary radix FFT
using intrinsics from Petersen and Arbenz "Intro.
to Parallel Computing," Section 3.6
This is an expanded version of a generic work-space
FFT: steps are in-line. cfft2(n,x,y,w,sign) takes complex
n-array "x" (Fortran real,aimag,real,aimag,... order)
and writes its DFT in "y". Both input "x" and the
original contents of "y" are destroyed. Initialization
for array "w" (size n/2 complex of twiddle factors
(exp(twopi*i*k/n), for k=0..n/2-1)) is computed once
by cffti(n,w).
WPP, SAM. Math. ETHZ, 1 June, 2002
*/
int first,i,icase,it,ln2,n;
int nits=1000000;
static float seed = 331.0;
float error,fnm1,sign,z0,z1,ggl();
float *x,*y,*z,*w;
double t1,mflops;
/* allocate storage for x,y,z,w on 4-word bndr. */
x = (float *) malloc(8*N);
y = (float *) malloc(8*N);
z = (float *) malloc(8*N);
w = (float *) malloc(4*N);
n = 2;
for(ln2=1; ln2<21; ln2++) {
first = 1;
for(icase=0; icase<2; icase++) {
if(first) {
for(i=0; i<2*n; i+=2) {
z0 = ggl(&seed); /* real part of array */
z1 = ggl(&seed); /* imaginary part of array */
x[i] = z0;
z[i] = z0; /* copy of initial real data */
x[i+1] = z1;
z[i+1] = z1; /* copy of initial imag. data */
}
} else {
for(i=0; i<2*n; i+=2) {
z0 = 0; /* real part of array */
z1 = 0; /* imaginary part of array */
x[i] = z0;
z[i] = z0; /* copy of initial real data */
x[i+1] = z1;
z[i+1] = z1; /* copy of initial imag. data */
}
}
/* initialize sine/cosine tables */
cffti(n,w);
/* transform forward, back */
if(first) {
sign = 1.0;
cfft2(n,x,y,w,sign);
sign = -1.0;
cfft2(n,y,x,w,sign);
/* results should be same as initial multiplied by n */
fnm1 = 1.0/((float) n);
error = 0.0;
for(i=0; i<2*n; i+=2) {
error += (z[i] - fnm1*x[i])*(z[i] - fnm1*x[i]) +
(z[i+1] - fnm1*x[i+1])*(z[i+1] - fnm1*x[i+1]);
}
error = sqrt(fnm1*error);
printf(" for n=%d, fwd/bck error=%e\n",n,error);
first = 0;
} else {
for(it=0; it<nits; it++) {
sign = +1.0;
cfft2(n,x,y,w,sign);
sign = -1.0;
cfft2(n,y,x,w,sign);
}
}
}
if((ln2%4)==0) nits /= 10;
n *= 2;
}
return 0;
}
/* 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__ */
int main ( void )
/******************************************************************************/
/*
Purpose:
MAIN is the main program for FFT_SERIAL.
Discussion:
The "complex" vector A is actually stored as a double vector B.
The "complex" vector entry A[I] is stored as:
B[I*2+0], the real part,
B[I*2+1], the imaginary part.
Modified:
23 March 2009
Author:
Original C version by Wesley Petersen.
This C version by John Burkardt.
Reference:
Wesley Petersen, Peter Arbenz,
Introduction to Parallel Computing - A practical guide with examples in C,
Oxford University Press,
ISBN: 0-19-851576-6,
LC: QA76.58.P47.
*/
{
double ctime;
double ctime1;
double ctime2;
double error;
int first;
double flops;
double fnm1;
int i;
int icase;
int it;
int ln2;
double mflops;
int n;
int nits = 10000;
static double seed;
double sgn;
double *w;
double *x;
double *y;
double *z;
double z0;
double z1;
timestamp ( );
printf ( "\n" );
printf ( "FFT_SERIAL\n" );
printf ( " C version\n" );
printf ( "\n" );
printf ( " Demonstrate an implementation of the Fast Fourier Transform\n" );
printf ( " of a complex data vector.\n" );
/*
Prepare for tests.
*/
printf ( "\n" );
printf ( " Accuracy check:\n" );
printf ( "\n" );
printf ( " FFT ( FFT ( X(1:N) ) ) == N * X(1:N)\n" );
printf ( "\n" );
printf ( " N NITS Error Time Time/Call MFLOPS\n" );
printf ( "\n" );
seed = 331.0;
n = 1;
/*
LN2 is the log base 2 of N. Each increase of LN2 doubles N.
*/
for ( ln2 = 1; ln2 <= 20; ln2++ )
{
n = 2 * n;
/*
Allocate storage for the complex arrays W, X, Y, Z.
We handle the complex arithmetic,
and store a complex number as a pair of doubles, a complex vector as a doubly
dimensioned array whose second dimension is 2.
*/
w = ( double * ) malloc ( n * sizeof ( double ) );
x = ( double * ) malloc ( 2 * n * sizeof ( double ) );
y = ( double * ) malloc ( 2 * n * sizeof ( double ) );
z = ( double * ) malloc ( 2 * n * sizeof ( double ) );
first = 1;
for ( icase = 0; icase < 2; icase++ )
{
if ( first )
{
for ( i = 0; i < 2 * n; i = i + 2 )
{
z0 = ggl ( &seed );
z1 = ggl ( &seed );
x[i] = z0;
z[i] = z0;
x[i+1] = z1;
z[i+1] = z1;
}
}
else
{
for ( i = 0; i < 2 * n; i = i + 2 )
{
z0 = 0.0; /* real part of array */
z1 = 0.0; /* imaginary part of array */
x[i] = z0;
z[i] = z0; /* copy of initial real data */
x[i+1] = z1;
z[i+1] = z1; /* copy of initial imag. data */
}
}
/*
Initialize the sine and cosine tables.
*/
cffti ( n, w );
/*
Transform forward, back
*/
if ( first )
{
sgn = + 1.0;
cfft2 ( n, x, y, w, sgn );
sgn = - 1.0;
cfft2 ( n, y, x, w, sgn );
/*
Results should be same as the initial data multiplied by N.
*/
fnm1 = 1.0 / ( double ) n;
error = 0.0;
for ( i = 0; i < 2 * n; i = i + 2 )
{
error = error
+ pow ( z[i] - fnm1 * x[i], 2 )
+ pow ( z[i+1] - fnm1 * x[i+1], 2 );
}
error = sqrt ( fnm1 * error );
printf ( " %12d %8d %12e", n, nits, error );
first = 0;
}
else
{
ctime1 = cpu_time ( );
for ( it = 0; it < nits; it++ )
{
sgn = + 1.0;
cfft2 ( n, x, y, w, sgn );
sgn = - 1.0;
cfft2 ( n, y, x, w, sgn );
}
ctime2 = cpu_time ( );
ctime = ctime2 - ctime1;
flops = 2.0 * ( double ) nits * ( 5.0 * ( double ) n * ( double ) ln2 );
mflops = flops / 1.0E+06 / ctime;
printf ( " %12e %12e %12f\n", ctime, ctime / ( double ) ( 2 * nits ), mflops );
}
}
if ( ( ln2 % 4 ) == 0 )
{
nits = nits / 10;
}
if ( nits < 1 )
{
nits = 1;
}
free ( w );
free ( x );
free ( y );
free ( z );
}
printf ( "\n" );
printf ( "FFT_SERIAL:\n" );
printf ( " Normal end of execution.\n" );
printf ( "\n" );
timestamp ( );
return 0;
}
/* 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);
}
