IRIX Base Documentation 2002 November/SGI IRIX Base Documentation 2002 November.iso/usr/share/catman/p_man/cat3/SCSL/ccfft.z/ccfft

Text File | 2002-10-03 | 26.0 KB | 595 lines

CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))                                                            CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))



NNNNAAAAMMMMEEEE
     CCCCCCCCFFFFFFFFTTTT, ZZZZZZZZFFFFFFFFTTTT - Applies a complex-to-complex Fast Fourier Transform (FFT)

SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     Single precision complex -> Single precision complex

          Fortran:
               CCCCAAAALLLLLLLL CCCCCCCCFFFFFFFFTTTT ((((_i_s_i_g_n,,,, _n,,,, _s_c_a_l_e,,,, _x,,,, _y,,,, _t_a_b_l_e,,,, _w_o_r_k,,,, _i_s_y_s))))

          C/C++:
               ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>>
               iiiinnnntttt ccccccccfffffffftttt ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n,,,, ffffllllooooaaaatttt _s_c_a_l_e,,,, ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_x,,,,
               ssssccccssssllll____ccccoooommmmpppplllleeeexxxx *_y,,,, ffffllllooooaaaatttt *_t_a_b_l_e,,,, ffffllllooooaaaatttt *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;;

          C++ STL:
               ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>>
               ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>>
               iiiinnnntttt ccccccccfffffffftttt ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n,,,, ffffllllooooaaaatttt _s_c_a_l_e,,,, ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_x,,,,
               ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>> *_y,,,, ffffllllooooaaaatttt *_t_a_b_l_e,,,, ffffllllooooaaaatttt *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;;

     Double precision complex -> Double precision complex

          Fortran:
               CCCCAAAALLLLLLLL ZZZZZZZZFFFFFFFFTTTT ((((_i_s_i_g_n,,,, _n,,,, _s_c_a_l_e,,,, _x,,,, _y,,,, _t_a_b_l_e,,,, _w_o_r_k,,,, _i_s_y_s))))

          C/C++:
               ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>>
               iiiinnnntttt zzzzzzzzfffffffftttt ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n,,,, ddddoooouuuubbbblllleeee _s_c_a_l_e,,,, ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_x,,,,
               ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx *_y,,,, ddddoooouuuubbbblllleeee *_t_a_b_l_e,,,, ddddoooouuuubbbblllleeee *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;;

          C++ STL:
               ####iiiinnnncccclllluuuuddddeeee <<<<ccccoooommmmpppplllleeeexxxx....hhhh>>>>
               ####iiiinnnncccclllluuuuddddeeee <<<<ssssccccssssllll____fffffffftttt....hhhh>>>>
               iiiinnnntttt zzzzzzzzfffffffftttt ((((iiiinnnntttt _i_s_i_g_n,,,, iiiinnnntttt _n,,,, ddddoooouuuubbbblllleeee _s_c_a_l_e,,,, ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_x,,,,
               ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>> *_y,,,, ddddoooouuuubbbblllleeee *_t_a_b_l_e,,,, ddddoooouuuubbbblllleeee *_w_o_r_k,,,, iiiinnnntttt *_i_s_y_s))));;;;

IIIIMMMMPPPPLLLLEEEEMMMMEEEENNNNTTTTAAAATTTTIIIIOOOONNNN
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the ----llllssssccccssss or the ----llllssssccccssss____mmmmpppp option.  The ----llllssssccccssss____mmmmpppp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with ----llllssssccccssss or ----llllssssccccssss____mmmmpppp, 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 ----llllssssccccssss____iiii8888 option or the ----llllssssccccssss____iiii8888____mmmmpppp 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 iiiinnnntttt become lllloooonnnngggg lllloooonnnngggg and the <<<<ssssccccssssllll____fffffffftttt____iiii8888....hhhh>>>> header



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CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))                                                            CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))



     file should be included.

DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
     These routines compute the Fast Fourier Transform (FFT) of the complex
     vector _x, and store the result in vector _y.

     In FFT applications, it is customary to use zero-based subscripts; the
     formulas are simpler that way.  Suppose that the arrays are declared as
     follows:

          Fortran:

               COMPLEX X(0:N-1), Y(0:N-1)


          C/C++:

               scsl_complex x[n], y[n];


          C++ STL:

               complex<float> x[n], y[n];


     The output array is the FFT of the input array, using the following
     formula for the FFT:



                  n-1              isign * j * k
          Y k  = scale * Sum [X * w              ]
           k      j=0          j


     for _k = 0 ..., _n-1 where:

     _w         = exp(2*_p_i*_i/_n),

     _i         = + sqrt(-1),

     _p_i        = 3.14159...

     _i_s_i_g_n     = +1 or -1

     Different authors use different conventions for which of the transforms,
     _i_s_i_g_n = +1 or _i_s_i_g_n = -1, is the forward or inverse transform, and what
     the scale factor should be in either case.  You can make this routine
     compute any of the various possible definitions, however, by choosing the
     appropriate values for _i_s_i_g_n and _s_c_a_l_e.





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CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))                                                            CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))



     The relevant fact from FFT theory is this:  If you take the FFT with any
     particular values of _i_s_i_g_n and _s_c_a_l_e, the mathematical inverse function
     is computed by taking the FFT with -_i_s_i_g_n and nnnn 1111////((((_n*_s_c_a_l_e).  In
     particular, if you use _i_s_i_g_n = +1 and _s_c_a_l_e = 1.0 you can compute the
     inverse FFT by using _i_s_i_g_n = -1 and _s_c_a_l_e = 1.0/_n.

     The output array may be the same as the input array.

     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:

     _i_s_i_g_n     Integer.  (input)
               Specifies whether to initialize the table array or to do the
               forward or inverse Fourier transform, as follows:

               If _i_s_i_g_n = 0, the routine initializes the _t_a_b_l_e array and
               returns.  In this case, the only arguments used or checked are
               _i_s_i_g_n, _n, and _t_a_b_l_e.

               If _i_s_i_g_n = +1 or -1, the value of _i_s_i_g_n is the sign of the
               exponent used in the FFT formula.

     _n         Integer.  (input)
               Size of the transform (the number of values in the input
               array).  _n >= 0.

     _s_c_a_l_e     Scale factor. (input).
               CCCCCCCCFFFFFFFFTTTT: Single precision.
               ZZZZZZZZFFFFFFFFTTTT: Double precision.
               Each element of the output array is multiplied by _s_c_a_l_e after
               taking the Fourier transform, as defined by the previous
               formula.

     _x         Array of size _n.   (input)
               CCCCCCCCFFFFFFFFTTTT: Single precision complex array.
               ZZZZZZZZFFFFFFFFTTTT: Double precision complex array.

               Input array of values to be transformed.

     _y         Array of size _n.  (output)
               CCCCCCCCFFFFFFFFTTTT: Single precision complex array.
               ZZZZZZZZFFFFFFFFTTTT: Double precision complex array.
               Output array of transformed values.  The output array may be
               the same as the input array.  In that case, the transform is
               done in place and the input array is overwritten with the
               transformed values.

     _t_a_b_l_e     Array of size (2*_n + _N_F) (input or output)
               CCCCCCCCFFFFFFFFTTTT: Single precision array.
               ZZZZZZZZFFFFFFFFTTTT: Double precision array.



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CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))                                                            CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))



               Table of factors and roots of unity.  See the description of
               the _i_s_y_s argument for the value of _N_F.

               If _i_s_i_g_n = 0, the routine initializes _t_a_b_l_e (_t_a_b_l_e is output
               only).

               If _i_s_i_g_n = +1 or -1, the values in _t_a_b_l_e are assumed to be
               initialized already by a prior call with _i_s_i_g_n = 0 (_t_a_b_l_e is
               input only).

     _w_o_r_k      Array of size (2 * _n).
               CCCCCCCCFFFFFFFFTTTT: Single precision array.
               ZZZZZZZZFFFFFFFFTTTT: Double precision array.

               Work array.  This is a scratch array used for intermediate
               calculations.  Its address space must be different address
               space from that of the input and output arrays.

     _i_s_y_s      Integer array dimensioned 0000........_i_s_y_s((((0000))))
               An array that gives implementation-specific information.  All
               features and functions of the FFT routines specific to any
               particular implementation are confined to this _i_s_y_s array.

               In the Origin series implementation, _i_s_y_s((((0000))))====0000 and _i_s_y_s((((0000))))====1111
               are supported.  In SCSL versions prior to 1.3, only _i_s_y_s((((0000))))====0000
               was allowed. For _i_s_y_s((((0000))))====0000, _N_F====33330000, and for _i_s_y_s((((0000))))====1111, _N_F====222255556666.
               The _N_F words of storage in the _t_a_b_l_e array contain a
               factorization of the length of the transform.

               The smaller value of _N_F for _i_s_y_s((((0000))))====0000 is historical. It is too
               small to store all the required factors for the highest
               performing FFT, so when _i_s_y_s((((0000))))====0000, extra space is allocated
               when the _t_a_b_l_e array is initialized. To avoid memory leaks,
               this extra space must be deallocated when the _t_a_b_l_e array is no
               longer needed. The CCCCCCCCFFFFFFFFTTTTFFFF routine is used to release this
               memory. Due to the potential for memory leaks, the use of
               _i_s_y_s((((0000))))====0000 should be avoided.

               For _i_s_y_s((((0000))))====1111, the value of _N_F is large enough so that no extra
               memory needs to be allocated, and there is no need to call
               CCCCCCCCFFFFFFFFTTTTFFFF to release memory. If called, it does nothing.

               NOTE: _i_s_y_s((((0000))))====1111 means that _i_s_y_s is an integer array with two
               elements. The second element, _i_s_y_s((((1111)))), will not be accessed.

NNNNOOOOTTTTEEEESSSS
     The following data types are described in this documentation:

          TTTTeeeerrrrmmmm UUUUsssseeeedddd                     DDDDaaaattttaaaa ttttyyyyppppeeee






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CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))                                                            CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))



     Fortran:

          Array dimensioned _n           xxxx((((nnnn))))

          Array of dimensions (_m,_n)     xxxx((((mmmm,,,,nnnn))))

          Integer                       IIIINNNNTTTTEEEEGGGGEEEERRRR (IIIINNNNTTTTEEEEGGGGEEEERRRR****8888 for ----llllssssccccssss____iiii8888[[[[____mmmmpppp]]]])

          Single precision              RRRREEEEAAAALLLL

          Double precision              DDDDOOOOUUUUBBBBLLLLEEEE PPPPRRRREEEECCCCIIIISSSSIIIIOOOONNNN

          Single precision complex      CCCCOOOOMMMMPPPPLLLLEEEEXXXX

          Double precision complex      DDDDOOOOUUUUBBBBLLLLEEEE CCCCOOOOMMMMPPPPLLLLEEEEXXXX

     C/C++:

          Array dimensioned _n           xxxx[[[[_n]]]]

          Array of dimensions (_m,_n)     xxxx[[[[mmmm****nnnn]]]] oooorrrr xxxx[[[[nnnn]]]][[[[mmmm]]]]

          Integer                       iiiinnnntttt (lllloooonnnngggg lllloooonnnngggg for ----llllssssccccssss____iiii8888[[[[____mmmmpppp]]]])

          Single precision              ffffllllooooaaaatttt

          Double precision              ddddoooouuuubbbblllleeee

          Single precision complex      ssssccccssssllll____ccccoooommmmpppplllleeeexxxx

          Double precision complex      ssssccccssssllll____zzzzoooommmmpppplllleeeexxxx

     C++ STL:

          Array dimensioned _n           xxxx[[[[_n]]]]

          Array of dimensions (_m,_n)     xxxx[[[[mmmm****nnnn]]]] oooorrrr xxxx[[[[nnnn]]]][[[[mmmm]]]]

          Integer                       iiiinnnntttt (lllloooonnnngggg lllloooonnnngggg for ----llllssssccccssss____iiii8888[[[[____mmmmpppp]]]])

          Single precision              ffffllllooooaaaatttt

          Double precision              ddddoooouuuubbbblllleeee

          Single precision complex      ccccoooommmmpppplllleeeexxxx<<<<ffffllllooooaaaatttt>>>>

          Double precision complex      ccccoooommmmpppplllleeeexxxx<<<<ddddoooouuuubbbblllleeee>>>>

CCCCAAAAUUUUTTTTIIIIOOOONNNNSSSS
     Transform sizes with a prime factor exceeding 22223332222----1111 are not supported for
     the 8-byte integer version of the library.




                                                                        PPPPaaaaggggeeee 5555






CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))                                                            CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))



     In addition to the _w_o_r_k 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 MMMMPPPP____SSSSLLLLAAAAVVVVEEEE____SSSSTTTTAAAACCCCKKKKSSSSIIIIZZZZEEEE
     environment variable or the mmmmpppp____sssseeeetttt____ssssllllaaaavvvveeee____ssssttttaaaacccckkkkssssiiiizzzzeeee(((()))) library routine. See
     the mmmmpppp(3C), mmmmpppp(3F) and ppppeeee____eeeennnnvvvviiiirrrroooonnnn(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 pppptttthhhhrrrreeeeaaaadddd____ccccrrrreeeeaaaatttteeee(3P).  The
     stacksize attribute should be set explicitly to a non-default value using
     the pppptttthhhhrrrreeeeaaaadddd____aaaattttttttrrrr____sssseeeettttssssttttaaaacccckkkkssssiiiizzzzeeee(3P) call, described in the
     pppptttthhhhrrrreeeeaaaadddd____aaaattttttttrrrr____iiiinnnniiiitttt(3P) man page.

     Care must be exercised if copies of the _t_a_b_l_e array are used: even though
     a copy exists, the original must persist. As an example, the following
     code will nnnnooootttt work:

          #include <scsl_fft.h>
          scsl_complex x[1024], y[1024];
          float table[2048+256];
          float work[2048];
          int isys[2];
          isys[0] = 1;
          {
            float table_orig[2048+256];

            ccfft(0, 1024, 1.0f, x, y, table_orig, work, isys);
            bcopy(table_orig, table, (2048+256)*sizeof(float));
          }
          ccfft(1, 1024, 1.0f, x, y, table, work, isys);


     In this example, because _t_a_b_l_e__o_r_i_g is a stack variable that does not
     persist outside of the code block delimited by the braces, the data in
     the copy, _t_a_b_l_e, are not guaranteed to be valid. However, the following
     code will work because _t_a_b_l_e__o_r_i_g is persistent:

          #include <scsl_fft.h>
          scsl_complex x[1024], y[1024];
          float table_orig[2048+256], table[2048+256];
          float work[2048];
          int isys[2];
          isys[0] = 1;
          ccfft(0, 1024, 1.0f, x, y, table_orig, work, isys);
          bcopy(table_orig, table, (2048+256)*sizeof(float));
          ccfft(1, 1024, 1.0f, x, y, table, work, isys);




                                                                        PPPPaaaaggggeeee 6666






CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))                                                            CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))



EEEEXXXXAAAAMMMMPPPPLLLLEEEESSSS
     These examples use the table and workspace sizes appropriate to the
     Origin series.

     Example 1:  Initialize the _t_a_b_l_e array in preparation for doing an FFT of
     size 1024.  Only the _i_s_i_g_n, _n, and _t_a_b_l_e arguments are used in this case.
     You can use dummy arguments or zeros for the other arguments in the
     subroutine call.

     Fortran:

          REAL TABLE(2048+256)
          INTEGER ISYS(0:1)
          ISYS(0) = 1
          CALL CCFFT(0, 1024, 0.0, DUMMY, DUMMY, TABLE, DUMMY, ISYS)


     C/C++:

          #include <scsl_fft.h>
          float table[2048+256];
          int isys[2];
          isys[0] = 1;
          ccfft(0, 1024, 0.0f, NULL, NULL, table, NULL, isys);


     C++ STL:

     #include <complex.h>
     #include <scsl_fft.h>
     float table[2048+256];
     int isys[2];
     isys[0] = 1;
     ccfft(0, 1024, 0.0f, NULL, NULL, table, NULL, isys);


     Example 2:  _x and _y are complex arrays of dimension (0:1023).  Take the
     FFT of _x and store the results in _y.  Before taking the FFT, initialize
     the _t_a_b_l_e array, as in example 1.

     Fortran:

          COMPLEX X(0:1023), Y(0:1023)
          REAL TABLE(2048+256)
          REAL WORK(2048)
          INTEGER ISYS(0:1)
          ISYS(0) = 1
          CALL CCFFT(0, 1024, 1.0, X, Y, TABLE, WORK, ISYS)
          CALL CCFFT(1, 1024, 1.0, X, Y, TABLE, WORK, ISYS)






                                                                        PPPPaaaaggggeeee 7777






CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))                                                            CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))



     C/C++:

          #include <scsl_fft.h>
          scsl_complex x[1024], y[1024];
          float table[2048+256];
          float work[2048];
          int isys[2];
          isys[0] = 1;
          ccfft(0, 1024, 1.0f, x, y, table, work, isys);
          ccfft(1, 1024, 1.0f, x, y, table, work, isys);


     C++ STL:

          #include <complex.h>
          #include <scsl_fft.h>
          complex<float> x[1024], y[1024];
          float table[2048+256];
          float work[2048];
          int isys[2];
          isys[0] = 1;
          ccfft(0, 1024, 1.0f, x, y, table, work, isys);
          ccfft(1, 1024, 1.0f, x, y, table, work, isys);


     Example 3:  Using the same _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 _t_a_b_l_e array is already initialized.

     Fortran:

          CALL CCFFT(-1, 1024, 1.0/1024.0, Y, X, TABLE, WORK, ISYS)


     C/C++ and C++ STL:

          ccfft(-1, 1024, 1.0f/1024.0f, y, x, table, work, isys);


     Example 4:  Perform the same computation as in example 2, but put the
     output back in array _x to save storage space. Use the 8-byte integer
     version of SCSL.

     Fortran:

          COMPLEX X(0:1023)
          REAL TABLE(2048+256)
          REAL WORK(2048)
          INTEGER*8 ISYS(0:1)
          ISYS(0) = 1_8
          CALL CCFFT(0_8, 1024_8, 1.0, X, X, TABLE, WORK, ISYS)
          CALL CCFFT(1_8, 1024_8, 1.0, X, X, TABLE, WORK, ISYS)



                                                                        PPPPaaaaggggeeee 8888






CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))                                                            CCCCCCCCFFFFFFFFTTTT((((3333SSSS))))



     C/C++:

          #include <scsl_fft_i8.h>
          scsl_complex x[1024]
          float table[2048+256];
          float work[2048];
          long long isys[2];
          isys[0] = 1LL;
          ccfft(0LL, 1024LL, 1.0f, x, x, table, work, isys);
          ccfft(1LL, 1024LL, 1.0f, x, x, table, work, isys);


     C++ STL:

          #include <complex.h>
          #include <scsl_fft_i8.h>
          complex<float> x[1024]
          float table[2048+256];
          float work[2048];
          long long isys[2];
          isys[0] = 1LL;
          ccfft(0LL, 1024LL, 1.0f, x, x, table, work, isys);
          ccfft(1LL, 1024LL, 1.0f, x, x, 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.  No change is
     needed in the subroutine calls:

     Fortran:

          COMPLEX X(1024), Y(1024)
          CALL CCFFT(0, 1024, 1.0, X, Y, TABLE, WORK, ISYS)
          CALL CCFFT(1, 1024, 1.0, X, Y, TABLE, WORK, ISYS)


SSSSEEEEEEEE AAAALLLLSSSSOOOO
     IIIINNNNTTTTRRRROOOO____FFFFFFFFTTTT(3S), IIIINNNNTTTTRRRROOOO____SSSSCCCCSSSSLLLL(3S), CCCCCCCCFFFFFFFFTTTTMMMM(3S), SSSSCCCCFFFFFFFFTTTT(3S), SSSSCCCCFFFFFFFFTTTTMMMM(3S)














                                                                        PPPPaaaaggggeeee 9999