static void PmlTableGen(int bw,
int m,
double *storeplm,
double *workspace)
{
double *prev, *prevprev, *temp1, *temp2, *temp3, *temp4, *x_i, *eval_args;
int i;
/* double *storeplm_ptr; */
prevprev = workspace;
prev = prevprev + (2*bw);
temp1 = prev + (2*bw);
temp2 = temp1 + (2*bw);
temp3 = temp2 + (2*bw);
temp4 = temp3 + (2*bw);
x_i = temp4 + (2*bw);
eval_args = x_i + (2*bw);
/* storeplm_ptr = storeplm; */
/* get the evaluation nodes */
EvalPts(2*bw,x_i);
ArcCosEvalPts(2*bw,eval_args);
/* set initial values of first two Pmls */
for (i=0; i<2*bw; i++)
prevprev[i] = 0.0;
if (m == 0)
for (i=0; i<2*bw; i++) {
/* prev[i] = 0.5; */
prev[i] = 0.707106781186547 ; /* 1/sqrt(2) */
}
else
Pmm_L2(m, eval_args, 2*bw, prev);
memcpy(storeplm, prev, (size_t) sizeof(double) * 2 * bw);
for(i = 0; i < bw - m - 1; i++)
{
vec_mul(L2_cn(m,m+i),prevprev,temp1,2*bw);
vec_pt_mul(prev, x_i, temp2, 2*bw);
vec_mul(L2_an(m,m+i), temp2, temp3, 2*bw);
vec_add(temp3, temp1, temp4, 2*bw); /* temp4 now contains P(m,m+i+1) */
storeplm += (2 * bw);
memcpy(storeplm, temp4, (size_t) sizeof(double) * 2 * bw);
memcpy(prevprev, prev, (size_t) sizeof(double) * 2 * bw);
memcpy(prev, temp4, (size_t) sizeof(double) * 2 * bw);
}
/* storeplm = storeplm_ptr; */
}
void CosPmlTableGen(int bw,
int m,
double *tablespace,
double *workspace)
{
double *prev, *prevprev, *temp1, *temp2, *temp3, *temp4;
double *x_i, *eval_args;
double *tableptr, *cosres ;
int i, j, k;
/* fftw stuff now */
double fudge ;
fftw_plan p ;
prevprev = workspace;
prev = prevprev + bw;
temp1 = prev + bw;
temp2 = temp1 + bw;
temp3 = temp2 + bw;
temp4 = temp3 + bw;
x_i = temp4 + bw;
eval_args = x_i + bw;
cosres = eval_args + bw;
tableptr = tablespace;
/* make fftw plan */
p = fftw_plan_r2r_1d( bw, temp4, cosres,
FFTW_REDFT10, FFTW_ESTIMATE ) ;
/* main loop */
/* Set the initial number of evaluation points to appropriate
amount */
/* now get the evaluation nodes */
EvalPts(bw,x_i);
ArcCosEvalPts(bw,eval_args);
/* set initial values of first two Pmls */
for (i=0; i<bw; i++)
prevprev[i] = 0.0;
if (m == 0)
for (i=0; i<bw; i++)
prev[i] = 0.707106781186547; /* sqrt(1/2) */
else
Pmm_L2(m, eval_args, bw, prev);
if ( m % 2 ) /* need to divide out sin x */
for (i=0; i<bw; i++)
prev[i] /= sin(eval_args[i]);
/* set k to highest degree coefficient */
if ((m % 2) == 0)
k = m;
else
k = m-1;
/* now compute cosine transform */
memcpy( temp4, prev, sizeof(double) * bw );
fftw_execute( p );
cosres[0] *= 0.707106781186547 ;
fudge = 1. / sqrt(((double) bw ) );
for ( i = 0 ; i < bw ; i ++ )
cosres[i] *= fudge ;
/* store what I've got so far */
for (i=0; i<=k; i+=2)
tableptr[i/2] = cosres[i];
/* update tableptr */
tableptr += k/2+1;
/* now generate remaining pmls */
for (i=0; i<bw-m-1; i++)
{
vec_mul(L2_cn(m,m+i),prevprev,temp1,bw);
vec_pt_mul(prev, x_i, temp2, bw);
vec_mul(L2_an(m,m+i), temp2, temp3, bw);
vec_add(temp3, temp1, temp4, bw); /* temp4 now contains P(m,m+i+1) */
/* compute cosine transform */
fftw_execute( p );
cosres[0] *= 0.707106781186547 ;
for ( j = 0 ; j < bw ; j ++ )
cosres[j] *= fudge ;
/* update degree counter */
k++;
/* now put decimated result into table */
if ( i % 2 )
for (j=0; j<=k; j+=2)
tableptr[j/2] = cosres[j];
else
for (j=1; j<=k; j+=2)
tableptr[j/2] = cosres[j];
/* update tableptr */
tableptr += k/2+1;
/* now update Pi and P(i+1) */
memcpy(prevprev, prev, sizeof(double) * bw);
memcpy(prev, temp4, sizeof(double) * bw);
}
fftw_destroy_plan( p );
}
void InvFST_semi_memo(double *rcoeffs, double *icoeffs,
double *rdata, double *idata,
int bw,
double **transpose_seminaive_naive_table,
double *workspace,
int dataformat,
int cutoff,
fftw_plan *idctPlan,
fftw_plan *ifftPlan )
{
int size, m, i, n;
double *rdataptr, *idataptr;
double *rfourdata, *ifourdata;
double *rinvfltres, *iminvfltres, *scratchpad;
double *sin_values, *eval_pts;
double tmpA ;
size = 2*bw ;
rfourdata = workspace; /* needs (size * size) */
ifourdata = rfourdata + (size * size); /* needs (size * size) */
rinvfltres = ifourdata + (size * size); /* needs (2 * bw) */
iminvfltres = rinvfltres + (2 * bw); /* needs (2 * bw) */
sin_values = iminvfltres + (2 * bw); /* needs (2 * bw) */
eval_pts = sin_values + (2 * bw); /* needs (2 * bw) */
scratchpad = eval_pts + (2 * bw); /* needs (2 * bw) */
/* total workspace = (8 * bw^2) + (10 * bw) */
/* load up the sin_values array */
n = 2*bw;
ArcCosEvalPts(n, eval_pts);
for (i=0; i<n; i++)
sin_values[i] = sin(eval_pts[i]);
/* Now do all of the inverse Legendre transforms */
rdataptr = rcoeffs;
idataptr = icoeffs;
for (m=0; m<bw; m++)
{
/*
fprintf(stderr,"m = %d\n",m);
*/
if(m < cutoff)
{
/* do real part first */
InvSemiNaiveReduced(rdataptr,
bw,
m,
rinvfltres,
transpose_seminaive_naive_table[m],
sin_values,
scratchpad,
idctPlan );
/* now do imaginary part */
InvSemiNaiveReduced(idataptr,
bw,
m,
iminvfltres,
transpose_seminaive_naive_table[m],
sin_values,
scratchpad,
idctPlan);
/* will store normal, then tranpose before doing inverse fft */
memcpy(rfourdata+(m*size), rinvfltres, sizeof(double) * size);
memcpy(ifourdata+(m*size), iminvfltres, sizeof(double) * size);
/* move to next set of coeffs */
rdataptr += bw-m;
idataptr += bw-m;
}
else
{
/* first do the real part */
Naive_SynthesizeX(rdataptr,
bw,
m,
rinvfltres,
transpose_seminaive_naive_table[m]);
/* now do the imaginary */
Naive_SynthesizeX(idataptr,
bw,
m,
iminvfltres,
transpose_seminaive_naive_table[m]);
/* will store normal, then tranpose before doing inverse fft */
memcpy(rfourdata+(m*size), rinvfltres, sizeof(double) * size);
memcpy(ifourdata+(m*size), iminvfltres, sizeof(double) * size);
/* move to next set of coeffs */
rdataptr += bw-m;
idataptr += bw-m;
}
}
/* closes m loop */
/* now fill in zero values where m = bw (from problem definition) */
memset(rfourdata + (bw * size), 0, sizeof(double) * size);
memset(ifourdata + (bw * size), 0, sizeof(double) * size);
/* now if the data is real, we don't have to compute the
coefficients whose order is less than 0, i.e. since
the data is real, we know that
invf-hat(l,-m) = conjugate(invf-hat(l,m)),
so use that to get the rest of the real data
dataformat =0 -> samples are complex, =1 -> samples real
*/
if(dataformat == 0){
/* now do negative m values */
for (m=bw+1; m<size; m++)
{
/*
fprintf(stderr,"m = %d\n",-(size-m));
*/
if ( (size-m) < cutoff )
{
/* do real part first */
InvSemiNaiveReduced(rdataptr,
bw,
size - m,
rinvfltres,
transpose_seminaive_naive_table[size - m],
sin_values,
scratchpad,
idctPlan);
/* now do imaginary part */
InvSemiNaiveReduced(idataptr,
bw,
size - m,
iminvfltres,
transpose_seminaive_naive_table[size - m],
sin_values,
scratchpad,
idctPlan );
/* will store normal, then tranpose before doing inverse fft */
if ((m % 2) != 0)
for(i=0; i< size; i++){
rinvfltres[i] = -rinvfltres[i];
iminvfltres[i] = -iminvfltres[i];
}
memcpy(rfourdata + (m*size), rinvfltres, sizeof(double) * size);
memcpy(ifourdata + (m*size), iminvfltres, sizeof(double) * size);
/* move to next set of coeffs */
rdataptr += bw-(size-m);
idataptr += bw-(size-m);
}
else
{
/* first do the real part */
Naive_SynthesizeX(rdataptr,
bw,
size-m,
rinvfltres,
transpose_seminaive_naive_table[size-m]);
/* now do the imaginary */
Naive_SynthesizeX(idataptr,
bw,
size-m,
iminvfltres,
transpose_seminaive_naive_table[size-m]);
/* will store normal, then tranpose before doing inverse fft */
if ((m % 2) != 0)
for(i=0; i< size; i++){
rinvfltres[i] = -rinvfltres[i];
iminvfltres[i] = -iminvfltres[i];
}
memcpy(rfourdata + (m*size), rinvfltres, sizeof(double) * size);
memcpy(ifourdata + (m*size), iminvfltres, sizeof(double) * size);
/* move to next set of coeffs */
rdataptr += bw-(size-m);
idataptr += bw-(size-m);
}
} /* closes m loop */
}
else {
for(m = bw + 1; m < size; m++){
memcpy(rfourdata+(m*size), rfourdata+((size-m)*size),
sizeof(double) * size);
memcpy(ifourdata+(m*size), ifourdata+((size-m)*size),
sizeof(double) * size);
for(i = 0; i < size; i++)
ifourdata[(m*size)+i] *= -1.0;
}
}
/* normalize */
tmpA = 1./(sqrt(2.*M_PI) );
for(i=0;i<4*bw*bw;i++)
{
rfourdata[i] *= tmpA ;
ifourdata[i] *= tmpA ;
}
fftw_execute_split_dft( *ifftPlan,
ifourdata, rfourdata,
idata, rdata );
/* amscray */
}
void CosPmlTableGenLim( int bw,
int m,
int lim,
double *tablespace,
double *workspace)
{
double *prev, *prevprev, *temp1, *temp2, *temp3, *temp4;
double *x_i, *eval_args;
double *tableptr, *cosres, *cosworkspace;
int i, j, k;
prevprev = workspace;
prev = prevprev + bw;
temp1 = prev + bw;
temp2 = temp1 + bw;
temp3 = temp2 + bw;
temp4 = temp3 + bw;
x_i = temp4 + bw;
eval_args = x_i + bw;
cosres = eval_args + bw;
cosworkspace = cosres + bw;
tableptr = tablespace;
/* main loop */
/* Set the initial number of evaluation points to appropriate
amount */
/* now get the evaluation nodes */
EvalPts(bw,x_i);
ArcCosEvalPts(bw,eval_args);
/* set initial values of first two Pmls */
for (i=0; i<bw; i++)
prevprev[i] = 0.0;
if (m == 0) {
for (i=0; i<bw; i++) {
prev[i] = 1.0;
}
}
else
Pmm_L2(m, eval_args, bw, prev);
if ((m % 2) == 1) { /* need to divide out sin x */
for (i=0; i<bw; i++)
prev[i] /= sin(eval_args[i]);
}
/* set k to highest degree coefficient */
if ((m % 2) == 0)
k = m;
else
k = m-1;
/* now compute cosine transform */
kFCT(prev, cosres, cosworkspace, bw, bw, 1);
for (i=0; i<=k; i+=2)
tableptr[i/2] = cosres[i];
/* update tableptr */
tableptr += k/2+1;
/* now generate remaining pmls */
for (i = 0 ; i < lim - m - 1 ; i ++) {
vec_mul(L2_cn(m,m+i),prevprev,temp1,bw);
vec_pt_mul(prev, x_i, temp2, bw);
vec_mul(L2_an(m,m+i), temp2, temp3, bw);
vec_add(temp3, temp1, temp4, bw); /* temp4 now contains P(m,m+i+1) */
/* compute cosine transform */
kFCT(temp4, cosres, cosworkspace, bw, bw, 1);
/* update degree counter */
k++;
/* now put decimated result into table */
if ((i % 2) == 1) {
for (j=0; j<=k; j+=2)
tableptr[j/2] = cosres[j];
}
else {
for (j=1; j<=k; j+=2)
tableptr[j/2] = cosres[j];
}
/* update tableptr */
tableptr += k/2+1;
/* now update Pi and P(i+1) */
memcpy(prevprev, prev, sizeof(double) * bw);
memcpy(prev, temp4, sizeof(double) * bw);
}
}
