SCFFT(3S)SCFFT(3S)NAME
SCFFT, DZFFT, CSFFT, ZDFFT - Computes a real-to-complex or complex-to-
real Fast Fourier Transform (FFT)
SYNOPSIS
Single precision -> Single precision complex
Fortran:
CALL SCFFT (isign, n, scale, x, y, table, work, isys)
C/C++:
#include <scsl_fft.h>
int scfft (int isign, int n, float scale, float *x,
scsl_complex *y, float *table, float *work, int *isys);
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
int scfft (int isign, int n, float scale, float *x,
complex<float> *y, float*table, float *work, int *isys);
Double precision -> Double precision complex
Fortran:
CALL DZFFT (isign, n, scale, x, y, table, work, isys)
C/C++:
#include <scsl_fft.h>
int dzfft (int isign, int n, double scale, float *x,
scsl_zomplex *y, double *table, double *work, int *isys);
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
int dzfft (int isign, int n, double scale, double *x,
complex<double> *y, double *table, double *work, int *isys);
Single precision complex -> Single precision
Fortran:
CALL CSFFT (isign, n, scale, x, y, table, work, isys)
C/C++:
#include <scsl_fft.h>
int csfft (int isign, int n, float scale, scsl_complex *x,
float *y, float *table, float *work, int *isys);
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
int csfft (int isign, int n, float scale, complex<float> *x,
float *y, float *table, float *work, int *isys);
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SCFFT(3S)SCFFT(3S)
Double precision complex -> Double precision
Fortran:
CALL ZDFFT (isign, n, scale, x, y, table, work, isys)
C/C++:
#include <scsl_fft.h>
int zdfft (int isign, int n, double scale, scsl_zomplex *x,
double *y, double *table, double *work, int *isys);
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
int zdfft (int isign, int n, double scale, complex<double> *x,
double *y, double *table, double *work, int *isys);
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
The C and C++ prototypes shown above are appropriate for the 4-byte
integer version of SCSL. When using the 8-byte integer version, the
variables of type int become long long and the <scsl_fft_i8.h> header
file should be included.
DESCRIPTION
SCFFT/DZFFT computes the FFT of the real array X, and it stores the
results in the complex array Y. CSFFT/ZDFFT computes the corresponding
inverse complex-to-real transform.
It is customary in FFT applications to use zero-based subscripts; the
formulas are simpler that way. For these routines, suppose that the
arrays are declared as follows:
Fortran:
REAL X(0:n-1)
COMPLEX Y(0:n/2)
C/C++:
float x[n];
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SCFFT(3S)SCFFT(3S)
scsl_complex y[n/2+1];
C++ STL:
float x[n];
complex<float> y[n/2+1];
Then the output array is the FFT of the input array, using the following
formula for the FFT:
n-1
Y(k) = scale * Sum [ X(j)*w**(isign*j*k) ] for k = 0, ..., n/2
j=0
where:
w = exp(2*pi*i/n),
i = + sqrt(-1),
pi = 3.14159...,
isign = +1 or -1.
Different authors use different conventions for which of the transforms,
isign = +1 or isign = -1, is the forward or inverse transform, and what
the scale factor should be in either case. You can make these routines
compute any of the various possible definitions, however, by choosing the
appropriate values for isign and scale.
The relevant fact from FFT theory is this: If you call SCFFT with any
particular values of isign and scale, the mathematical inverse function
is computed by calling CSFFT with -isign and 1/(n*scale). In particular,
if you use isign = +1 and scale = 1.0 in SCFFT for the forward FFT, you
can compute the inverse FFT by using CSFFT with isign = -1 and
scale = 1.0/n.
See the NOTES section of this man page for information about the
interpretation of the data types described in the following arguments.
These routines have the following arguments:
isign Integer. (input)
Specifies whether to initialize the table array or to do the
forward or inverse Fourier transform, as follows:
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SCFFT(3S)SCFFT(3S)
If isign = 0, the routine initializes the table array and
returns. In this case, the only arguments used or checked are
isign, n, and table.
If isign = +1 or -1, the value of isign is the sign of the
exponent used in the FFT formula.
n Integer. (input)
Size of transform. If n is not positive, the routine returns
without calculating the transform.
scale Scale factor. (input)
SCFFT: Single precision.
DZFFT: Double precision.
CSFFT: Single precision.
ZDFFT: Double precision.
Each element of the output array is multiplied by scale after
taking the Fourier transform, as defined in the preceding
formula.
x Input array of values to be transformed. (input)
SCFFT: Single precision array of dimension n.
DZFFT: Double precision array of dimension n.
CSFFT: Single precision complex array of dimension n/2 + 1.
(input)
ZDFFT: Double precision complex array of dimension n/2 + 1.
(input)
y Output array of transformed values. (output)
SCFFT: Single precision complex array of dimension n/2 + 1.
(input)
DZFFT: Double precision complex array of dimension n/2 + 1.
(input)
CSFFT: Single precision array of dimension n.
ZDFFT: Double precision array of dimension n.
The output array, y, is the FFT of the the input array, x,
computed according to the preceding formula. The output array
may be equivalenced to the input array in the calling program.
Be careful when dimensioning the arrays, in this case, to allow
for the fact that the complex array contains two (real) words
more than the real array.
table Array of dimension (n + NFR) (input or output)
SCFFT, CSFFT: Single precision array.
DZFFT, ZDFFT: Double precision array.
Table of factors and roots of unity. See the description of
the isys argument for the value of NFR.
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SCFFT(3S)SCFFT(3S)
If isign = 0, the routine initializes table (table is output
only).
If isign = +1 or -1, the values in table are assumed to be
initialized already by a prior call with isign = 0 (table is
input only).
work Array of dimension n + 2
SCFFT, CSFFT: Single precision array.
DZFFT, ZDFFT: Double precision array.
Work array used for intermediate calculations. Its address
space must be different from that of the input and output
arrays.
isys Integer array dimensioned 0..isys(0).
An array that gives implementation-specific information. All
features and functions of the FFT routines specific to any
particular implementation are confined to this isys array.
In the Origin series implementation, isys(0)=0 and isys(0)=1
are supported. In SCSL versions prior to 1.3, only isys(0)=0
was allowed. For isys(0)=0, NFR=15, and for isys(0)=1, NFR=256.
The NFR words of storage in the table array contain a
factorization of the length of the transform.
The smaller value of NFR for isys(0)=0 is historical. It is too
small to store all the required factors for the highest
performing FFT, so when isys(0)=0, extra space is allocated
when the table array is initialized. To avoid memory leaks,
this extra space must be deallocated when the table array is no
longer needed. The SCFFTF routine is used to release this
memory. Due to the potential for memory leaks, the use of
isys(0)=0 should be avoided.
For isys(0)=1, the value of NFR is large enough so that no
extra memory needs to be allocated, and there is no need to
call SCFFTF to release memory. If called, it does nothing.
NOTE: isys(0)=1 means that isys is an integer array with two
elements. The second element, isys(1), will not be accessed.
NOTES
The following data types are described in this documentation:
Term Used Data type
Fortran:
Array dimensioned 0..n-1 x(0:n-1)
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SCFFT(3S)SCFFT(3S)
Array of dimensions (m,n) x(m,n)
Array of dimensions (m,n,p) x(m,n,p)
Integer INTEGER (INTEGER*8 for -lscs_i8[_mp])
Single precision REAL
Double precision DOUBLE PRECISION
Single precision complex COMPLEX
Double precision complex DOUBLE COMPLEX
C/C++:
Array dimensioned 0..n-1 x[n]
Array of dimensions (m,n) x[m*n] or x[n][m]
Array of dimensions (m,n,p) x[m*n*p] or x[p][n][m]
Integer int (long long for -lscs_i8[_mp])
Single precision float
Double precision double
Single precision complex scsl_complex
Double precision complex scsl_zomplex
C++ STL:
Array dimensioned 0..n-1 x[n]
Array of dimensions (m,n) x[m*n] or x[n][m]
Array of dimensions (m,n,p) x[m*n*p] or x[p][n][m]
Integer int (long long for -lscs_i8[_mp])
Single precision float
Double precision double
Single precision complex complex<float>
Double precision complex complex<double>
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SCFFT(3S)SCFFT(3S)CAUTIONS
Transform sizes with a prime factor exceeding 232-1 are not supported for
the 8-byte integer version of the library.
In addition to the work array, the FFT routines also dynamically allocate
scratch space from the stack. The amount of space allocated can be
slightly bigger than the size of the largest processor cache. For single
processor runs, the default stack size is large enough that these
allocations generally cause no problems. But for parallel runs, you need
to ensure that the stack size of slave threads is big enough to hold this
scratch space. Failure to reserve sufficient stack space will cause
programs to dump core due to stack overflows. The stack size of MP
library slave threads is controlled via the MP_SLAVE_STACKSIZE
environment variable or the mp_set_slave_stacksize() library routine. See
the mp(3C), mp(3F) and pe_environ(5) reference pages for more information
on controlling the slave stack size. For pthreads applications, the
thread's stack size is specified as one of many creation attributes
provided in the pthread_attr_t argument to pthread_create(3P). The
stacksize attribute should be set explicitly to a non-default value using
the pthread_attr_setstacksize(3P) call, described in the
pthread_attr_init(3P) man page.
Care must be exercised if copies of the table array are used: even though
a copy exists, the original must persist. As an example, the following
code will not work:
#include <scsl_fft.h>
float x[1024];
scsl_complex y[513];
float table[1024+256];
float work[1024+2];
int isys[2];
isys[0] = 1;
{
float table_orig[1024+256];
scfft(0, 1024, 1.0f, x, y, table_orig, work, isys)
bcopy(table_orig, table, (1024+256)*sizeof(float));
}
scfft(1, 1024, 1.0f, x, y, table, work, isys)
In this example, because table_orig is a stack variable that does not
persist outside of the code block delimited by the braces, the data in
the copy, table, are not guaranteed to be valid. However, the following
code will work because table_orig is persistent:
#include <scsl_fft.h>
float x[1024];
scsl_complex y[513];
float table_orig[1024+256];
float table[1024+256];
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float work[1024+2];
int isys[2];
isys[0] = 1;
scfft(0, 1024, 1.0f, x, y, table_orig, work, isys)
bcopy(table_orig, table, (1024+256)*sizeof(float));
scfft(1, 1024, 1.0f, x, y, table, work, isys)
EXAMPLES
These examples use the table and workspace sizes appropriate to Origin
series.
Example 1: Initialize the TABLE array in preparation for doing an FFT of
size 1024. In this case only the arguments isign, n, and table are used.
You can use dummy arguments or zeros for the other arguments in the
subroutine call.
Fortran:
REAL TABLE(1024+256)
INTEGER ISYS(0:1)
ISYS(0) = 1
CALL SCFFT(0, 1024, 0.0, DUMMY, DUMMY, TABLE, DUMMY, ISYS)
C/C++:
#include <scsl_fft.h>
float table[1024+256];
int isys[2];
isys[0] = 1;
scfft(0, 1024, 0.0f, NULL, NULL, table, NULL, isys);
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
float table[1024+256];
int isys[2];
isys[0] = 1;
scfft(0, 1024, 0.0f, NULL, NULL, table, NULL, isys);
Example 2: X is a real array dimensioned (0...1023), and Y is a complex
array dimensioned (0...:512). Take the FFT of X and store the results in
Y. Before taking the FFT, initialize the TABLE array, as in example 1.
Fortran:
REAL X(0:1023)
COMPLEX Y(0:512)
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SCFFT(3S)SCFFT(3S)
REAL TABLE(1024+256)
REAL WORK(1024+2)
INTEGER ISYS(0:1)
ISYS(0) = 1
CALL SCFFT(0, 1024, 1.0, X, Y, TABLE, WORK, ISYS)
CALL SCFFT(1, 1024, 1.0, X, Y, TABLE, WORK, ISYS)
C/C++:
#include <scsl_fft.h>
float x[1024];
scsl_complex y[513];
float table[1024+256];
float work[1024+2];
int isys[2];
isys[0] = 1;
scfft(0, 1024, 1.0f, x, y, table, work, isys)
scfft(1, 1024, 1.0f, x, y, table, work, isys)
C++ STL:
#include <complex.h>
#include <scsl_fft.h>
float x[1024];
complex<float> y[513];
float table[1024+256];
float work[1024+2];
int isys[2];
isys[0] = 1;
scfft(0, 1024, 1.0f, x, y, table, work, isys)
scfft(1, 1024, 1.0f, x, y, table, work, isys)
Example 3: With X and Y as in example 2, take the inverse FFT of Y and
store it back in X. The scale factor 1/1024 is used. Assume that the
TABLE array is initialized already.
Fortran:
CALL CSFFT(-1, 1024, 1.0/1024.0, Y, X, TABLE, WORK, ISYS)
C/C++ and C++ STL:
csfft(-1, 1024, 1.0f/1024.0f, y, x, table, work, isys)
Example 4: Perform the same computation as in example 2, but equivalence
the input and output arrays to save storage space. Use the 8-byte
integer version of SCSL.
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SCFFT(3S)SCFFT(3S)
Fortran:
REAL X(0:1023)
COMPLEX Y(0:512)
EQUIVALENCE ( X(1), Y(1) )
REAL TABLE(1024+256)
REAL WORK(1024+2)
INTEGER*8 ISYS(0:1)
ISYS(0) = 1_8
CALL SCFFT(0_8, 1024_8, 1.0, X, Y, TABLE, WORK, ISYS)
CALL SCFFT(1_8, 1024_8, 1.0, X, Y, TABLE, WORK, ISYS)
C/C++:
#include <scsl_fft_i8.h>
float *x;
scsl_complex y[513];
float table[1024+256];
float work[1024+2];
long long isys[2];
isys[0] = 1LL;
x = (float *) &y[0];
scfft(0LL, 1024LL, 1.0f, x, y, table, work, isys)
scfft(1LL, 1024LL, 1.0f, x, y, table, work, isys)
C++ STL:
#include <complex.h>
#include <scsl_fft_i8.h>
float *x;
complex<float> y[513];
float table[1024+256];
float work[1024+2];
long long isys[2];
isys[0] = 1LL;
x = (float *) &y[0];
scfft(0LL, 1024LL, 1.0f, x, y, table, work, isys)
scfft(1LL, 1024LL, 1.0f, x, y, table, work, isys)
Example 5: Perform the same computation as in example 2, but assume that
the lower bound of each Fortran array is 1, rather than 0. The
subroutine calls are not changed.
Fortran:
REAL X(1024)
COMPLEX Y(513)
CALL SCFFT(0, 1024, 1.0, X, Y, TABLE, WORK, ISYS)
CALL SCFFT(1, 1024, 1.0, X, Y, TABLE, WORK, ISYS)
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SCFFT(3S)SCFFT(3S)SEE ALSOINTRO_FFT(3S), INTRO_SCSL(3S), CCFFT(3S), CCFFTM(3S), SCFFTM(3S)
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