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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_Probe(3OpenMPI)													       MPI_Probe(3OpenMPI)

NAME
MPI_Probe - Blocking test for a message. SYNTAX
C Syntax #include <mpi.h> int MPI_Probe(int source, int tag, MPI_Comm comm, MPI_Status *status) Fortran Syntax INCLUDE 'mpif.h' MPI_PROBE(SOURCE, TAG, COMM, STATUS, IERROR) INTEGER SOURCE, TAG, COMM, STATUS(MPI_STATUS_SIZE), IERROR C++ Syntax #include <mpi.h> void Comm::Probe(int source, int tag, Status& status) const void Comm::Probe(int source, int tag) const INPUT PARAMETERS
source Source rank or MPI_ANY_SOURCE (integer). tag Tag value or MPI_ANY_TAG (integer). comm Communicator (handle). OUTPUT PARAMETERS
status Status object (status). IERROR Fortran only: Error status (integer). DESCRIPTION
The MPI_Probe and MPI_Iprobe operations allow checking of incoming messages, without actual receipt of them. The user can then decide how to receive them, based on the information returned by the probe in the status variable. For example, the user may allocate memory for the receive buffer, according to the length of the probed message. MPI_Probe behaves like MPI_Iprobe except that it is a blocking call that returns only after a matching message has been found. 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. The semantics of MPI_Probe and MPI_Iprobe guarantee progress: If a call to MPI_Probe has been issued by a process, and a send that matches the probe has been initiated by some process, then the call to MPI_Probe will return, unless the message is received by another concurrent receive operation (that is executed by another thread at the probing process). Similarly, if a process busy waits with MPI_Iprobe and a matching message has been issued, then the call to MPI_Iprobe will eventually return flag = true unless the message is received by another concurrent receive operation. Example 1: Use blocking probe to wait for an incoming message. CALL MPI_COMM_RANK(comm, rank, ierr) IF (rank.EQ.0) THEN CALL MPI_SEND(i, 1, MPI_INTEGER, 2, 0, comm, ierr) ELSE IF(rank.EQ.1) THEN CALL MPI_SEND(x, 1, MPI_REAL, 2, 0, comm, ierr) ELSE ! rank.EQ.2 DO i=1, 2 CALL MPI_PROBE(MPI_ANY_SOURCE, 0, comm, status, ierr) IF (status(MPI_SOURCE) = 0) THEN 100 CALL MPI_RECV(i, 1, MPI_INTEGER, 0, 0, status, ierr) ELSE 200 CALL MPI_RECV(x, 1, MPI_REAL, 1, 0, status, ierr) END IF END DO END IF Each message is received with the right type. Example 2: A program similar to the previous example, but with a problem. CALL MPI_COMM_RANK(comm, rank, ierr) IF (rank.EQ.0) THEN CALL MPI_SEND(i, 1, MPI_INTEGER, 2, 0, comm, ierr) ELSE IF(rank.EQ.1) THEN CALL MPI_SEND(x, 1, MPI_REAL, 2, 0, comm, ierr) ELSE DO i=1, 2 CALL MPI_PROBE(MPI_ANY_SOURCE, 0, comm, status, ierr) IF (status(MPI_SOURCE) = 0) THEN 100 CALL MPI_RECV(i, 1, MPI_INTEGER, MPI_ANY_SOURCE, 0, status, ierr) ELSE 200 CALL MPI_RECV(x, 1, MPI_REAL, MPI_ANY_SOURCE, 0, status, ierr) END IF END DO END IF We slightly modified Example 2, using MPI_ANY_SOURCE as the source argument in the two receive calls in statements labeled 100 and 200. The program is now incorrect: The receive operation may receive a message that is distinct from the message probed by the preceding call to MPI_Probe. 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; 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. SEE ALSO
MPI_Iprobe MPI_Cancel Open MPI 1.2 September 2006 MPI_Probe(3OpenMPI)
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