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Full Discussion: Slow FFT in ksh93 and awk.
Operating Systems OS X (Apple) Slow FFT in ksh93 and awk. Post 303023145 by wisecracker on Wednesday 12th of September 2018 12:11:57 PM
Old 09-12-2018
Hi all...

Well guys, it took a while because of the serious limitations of ARexx for a stock AMIGA A1200 but here is a working FFT for it. ARexx has no ARRAY facility but there is a workaround. ;o)
Boy oh boy, ARexx's arithmetic is so convoluted and floating point precision is not the best.
This was a challenge. I could have generated SIN, COS and SQRT in pure ARexx but decided to use an external ARexx math(s) library instead...
It would be just as easy to create SIN, COS and SQRT in ksh too eliminating awk entirely but awk just made it easier...
Just for the record the AMIGA shell/terminal has a large subset of xterm's escape codes.
An exercise in futility? Maybe but serious fun nevertheless...
This is through FS-UAE AMIGA emulation and my real A1200 setup for easy transfer from this Macbook Pro.
ARexx code:
Code:
/* Simple_FFT_DEMO.rexx */

/* This ARexx version needs this dependency: */
/* http://aminet.net/package/util/rexx/RexxMathLib */
CALL ADDLIB('rexxmathlib.library',0,-30,0)

NUMERIC DIGITS 14

SAY ""
SAY "An experimental method to do an FFT in ARexx using the standard test values."
SAY "It requires rexxmathlib.library for the SIN and COS."
SAY "$VER Simple_FFT_DEMO.rexx_(C)06-09-2018_B.Walker_issued_under_GPL2."
SAY ""

/* Create standard test _ARRAYS_ REAL and IMAGINARY. */
/* These MUST be powers of 2 and greater than 2 in size. */
/* Real values, '1.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0' */
/* Imag values, '0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0' */
/* Not really ARRAYS but good enough for this DEMO! */
DO N=0 TO 3 BY 1
	REAL_ARRAY.N=1.0
END
DO N=4 TO 7 BY 1
	REAL_ARRAY.N=0.0
END
DO N=0 TO 7 BY 1
	IMAG_ARRAY.N=0.0
END

/* Display them. */
SAY "Input, REAL: IMAG:"
DO N=0 TO 7 BY 1
	SAY "        "||REAL_ARRAY.N||"   "||IMAG_ARRAY.N
END

/* Only constant required, 14 decimal places. */
PI=3.14159265358979 
/* N should be 8 by default in this DEMO. */
/* SAY "Number of elements = "||N||"..." */
N=N-1

CALL FFT

SAY ""
DO N=0 TO 7 BY 1
	SAY "REAL: "||+OUT_REAL.N||",    IMAG: "||+OUT_IMAG.N
END

SAY ""
SAY "Final FFT values to 5 decimal places:"
STR=""
DO N=0 TO 7 BY 1
	CALL ABS_COMPLEX
	NUMERIC DIGITS 14
	IF +ABS <= 0.000000000001
	THEN
		ABS=0
	ENDIF
	NUMERIC DIGITS 6
	STR=STR||+ABS||" "
END
SAY STR
SAY ""
EXIT

/* Create the subroutines required. */
/* FFT subroutine. */
FFT:
DO K=0 TO N BY 1
	SUMREAL=0.0
	SUMIMAG=0.0
	DO T=0 TO N BY 1
		ANGLE=(2.0*PI*T*K)/(N+1)
		SUMREAL=SUMREAL+(REAL_ARRAY.T*COS(ANGLE))+(IMAG_ARRAY.T*SIN(ANGLE))
		SUMIMAG=SUMIMAG-(REAL_ARRAY.T*SIN(ANGLE))+(IMAG_ARRAY.T*COS(ANGLE))
	END
	OUT_REAL.K=SUMREAL
	OUT_IMAG.K=SUMIMAG
END
RETURN
/* FFT subroutine end. */

/* Absolute value of complex number subroutine. */
ABS_COMPLEX:
	ABS=SQRT( (OUT_REAL.N**2)+(OUT_IMAG.N**2) )
RETURN
/* Absolute value of complex number subroutine end. */

 

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MPI_Waitsome(3OpenMPI)													    MPI_Waitsome(3OpenMPI)

NAME
MPI_Waitsome - Waits for some given communications to complete. SYNTAX
C Syntax #include <mpi.h> int MPI_Waitsome(int incount, MPI_Request *array_of_requests, int *outcount, int *array_of_indices, MPI_Status *array_of_statuses) Fortran Syntax INCLUDE 'mpif.h' MPI_WAITSOME(INCOUNT, ARRAY_OF_REQUESTS, OUTCOUNT, ARRAY_OF_INDICES, ARRAY_OF_STATUSES, IERROR) INTEGER INCOUNT, ARRAY_OF_REQUESTS(*), OUTCOUNT INTEGER ARRAY_OF_INDICES(*) INTEGER ARRAY_OF_STATUSES(MPI_STATUS_SIZE*) INTEGER IERROR C++ Syntax #include <mpi.h> static int Request::Waitsome(int incount, Request array_of_requests[], int array_of_indices[], Status array_of_statuses[]) static int Request::Waitsome(int incount, Request array_of_requests[], int array_of_indices[]) INPUT PARAMETERS
incount Length of array_of_requests (integer). array_of_requests Array of requests (array of handles). OUTPUT PARAMETERS
outcount Number of completed requests (integer). array_of_indices Array of indices of operations that completed (array of integers). array_of_statuses Array of status objects for operations that completed (array of status). IERROR Fortran only: Error status (integer). DESCRIPTION
Waits until at least one of the operations associated with active handles in the list have completed. Returns in outcount the number of requests from the list array_of_requests that have completed. Returns in the first outcount locations of the array array_of_indices the indices of these operations (index within the array array_of_requests; the array is indexed from 0 in C and from 1 in Fortran). Returns in the first outcount locations of the array array_of_status the status for these completed operations. If a request that completed was allo- cated by a nonblocking communication call, then it is deallocated, and the associated handle is set to MPI_REQUEST_NULL. If the list contains no active handles, then the call returns immediately with outcount = MPI_UNDEFINED. When one or more of the communications completed by MPI_Waitsome fails, then it is desirable to return specific information on each commu- nication. The arguments outcount, array_of_indices, and array_of_statuses will be adjusted to indicate completion of all communications that have succeeded or failed. The call will return the error code MPI_ERR_IN_STATUS and the error field of each status returned will be set to indicate success or to indicate the specific error that occurred. The call will return MPI_SUCCESS if no request resulted in an error, and will return another error code if it failed for other reasons (such as invalid arguments). In such cases, it will not update the error fields of the statuses. If your application does not need to examine the array_of_statuses field, you can save resources by using the predefined constant MPI_STA- TUSES_IGNORE can be used as a special value for the array_of_statuses argument. Example: Same code as the example in the MPI_Waitany man page, but using MPI_Waitsome. CALL MPI_COMM_SIZE(comm, size, ierr) CALL MPI_COMM_RANK(comm, rank, ierr) IF(rank .GT. 0) THEN ! client code DO WHILE(.TRUE.) CALL MPI_ISEND(a, n, MPI_REAL, 0, tag, comm, request, ierr) CALL MPI_WAIT(request, status, ierr) END DO ELSE ! rank=0 -- server code DO i=1, size-1 CALL MPI_IRECV(a(1,i), n, MPI_REAL, i, tag, comm, requests(i), ierr) END DO DO WHILE(.TRUE.) CALL MPI_WAITSOME(size, request_list, numdone, indices, statuses, ierr) DO i=1, numdone CALL DO_SERVICE(a(1, indices(i))) CALL MPI_IRECV(a(1, indices(i)), n, MPI_REAL, 0, tag, comm, requests(indices(i)), ierr) END DO END DO END IF NOTES
The array of indices are in the range 0 to incount-1 for C and in the range 1 to incount for Fortran. ERRORS
For each invocation of MPI_Waitsome, if one or more requests generate an MPI exception, only the first MPI request that caused an exception will be passed to its corresponding error handler. No other error handlers will be invoked (even if multiple requests generated excep- tions). However, all requests that generate an exception will have a relevant error code set in the corresponding status.MPI_ERROR field (unless MPI_IGNORE_STATUSES was used). The default error handler aborts the MPI job, except for I/O function errors. The error handler may be changed with MPI_Comm_set_errhan- dler, MPI_File_set_errhandler, or MPI_Win_set_errhandler (depending on the type of MPI handle that generated the MPI request); the prede- fined error handler MPI_ERRORS_RETURN may be used to cause error values to be returned. Note that MPI does not guarantee that an MPI pro- gram can continue past an error. If the invoked error handler allows MPI_Waitsome to return to the caller, the value MPI_ERR_IN_STATUS will be returned in the C and Fortran bindings. In C++, if the predefined error handler MPI::ERRORS_THROW_EXCEPTIONS is used, the value MPI::ERR_IN_STATUS will be contained in the MPI::Exception object. The MPI_ERROR field can then be examined in the array of returned statuses to determine exactly which request(s) generated an exception. SEE ALSO
MPI_Comm_set_errhandler MPI_File_set_errhandler MPI_Test MPI_Testall MPI_Testany MPI_Testsome MPI_Wait MPI_Waitall MPI_Waitany MPI_Win_set_errhandler Open MPI 1.2 September 2006 MPI_Waitsome(3OpenMPI)
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