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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_Waitany(3OpenMPI)													     MPI_Waitany(3OpenMPI)

NAME
MPI_Waitany - Waits for any specified send or receive to complete. SYNTAX
C Syntax #include <mpi.h> int MPI_Waitany(int count, MPI_Request *array_of_requests, int *index, MPI_Status *status) Fortran Syntax INCLUDE 'mpif.h' MPI_WAITANY(COUNT, ARRAY_OF_REQUESTS, INDEX, STATUS, IERROR) INTEGER COUNT, ARRAY_OF_REQUESTS(*), INDEX INTEGER STATUS(MPI_STATUS_SIZE), IERROR C++ Syntax #include <mpi.h> static int Request::Waitany(int count, Request array_of_requests[], Status& status) static int Request::Waitany(int count, Request array_of_requests[]) INPUT PARAMETERS
count List length (integer). array_of_requests Array of requests (array of handles). OUTPUT PARAMETERS
index Index of handle for operation that completed (integer). In the range 0 to count-1. In Fortran, the range is 1 to count. status Status object (status). IERROR Fortran only: Error status (integer). DESCRIPTION
A call to MPI_Waitany can be used to wait for the completion of one out of several requests. The array_of_requests list may contain null or inactive handles. If the list contains no active handles (list has length zero or all entries are null or inactive), then the call returns immediately with index = MPI_UNDEFINED, and an empty status. The execution of MPI_Waitany(count, array_of_requests, index, status) has the same effect as the execution of MPI_Wait(&array_of_requests[i], status), where i is the value returned by index (unless the value of index is MPI_UNDEFINED). MPI_Waitany with an array containing one active entry is equivalent to MPI_Wait. If your application does not need to examine the status field, you can save resources by using the predefined constant MPI_STATUS_IGNORE as a special value for the status argument. Example: Client-server code (starvation can occur). 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, request_list(i), ierr) END DO DO WHILE(.TRUE.) CALL MPI_WAITANY(size-1, request_list, index, status, ierr) CALL DO_SERVICE(a(1,index)) ! handle one message CALL MPI_IRECV(a(1, index), n, MPI_REAL, index, tag, comm, request_list(index), ierr) END DO END IF ERRORS
Almost all MPI routines return an error value; C routines as the value of the function and Fortran routines in the last argument. C++ func- tions do not return errors. If the default error handler is set to MPI::ERRORS_THROW_EXCEPTIONS, then on error the C++ exception mechanism will be used to throw an MPI::Exception object. Before the error value is returned, the current MPI error handler is called. By default, this error handler aborts the MPI job, except for I/O function errors. The error handler may be changed with MPI_Comm_set_errhandler, MPI_File_set_errhandler, or MPI_Win_set_errhandler (depending on the type of MPI handle that generated the request); the predefined error handler MPI_ERRORS_RETURN may be used to cause error values to be returned. Note that MPI does not guarantee that an MPI program can continue past an error. Note that per MPI-1 section 3.2.5, MPI exceptions on requests passed to MPI_WAITANY do not set the status.MPI_ERROR field in the returned status. The error code is passed to the back-end error handler and may be passed back to the caller through the return value of MPI_WAIT- ANY if the back-end error handler returns it. The pre-defined MPI error handler MPI_ERRORS_RETURN exhibits this behavior, for example. SEE ALSO
MPI_Comm_set_errhandler MPI_File_set_errhandler MPI_Test MPI_Testall MPI_Testany MPI_Testsome MPI_Wait MPI_Waitall MPI_Waitsome MPI_Win_set_errhandler Open MPI 1.2 September 2006 MPI_Waitany(3OpenMPI)
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