Fractran: Difference between revisions

Content added Content deleted
(→‎Revised Code: Output of zero powers is replaced by spaces.)
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END TYPE FACTORED !Rather than as a simple number multiplied out.
END TYPE FACTORED !Rather than as a simple number multiplied out.
TYPE(FACTORED) FP(ENUFF),FQ(ENUFF) !Thus represent a factored fraction, P(i)/Q(i).
TYPE(FACTORED) FP(ENUFF),FQ(ENUFF) !Thus represent a factored fraction, P(i)/Q(i).
INTEGER PLIVE(ENUFF),NL !Helps subroutine SHOWN display NPPOW.
CONTAINS !Now for the details.
CONTAINS !Now for the details.
SUBROUTINE SHOWFACTORS(N) !First, to show an internal data structure.
SUBROUTINE SHOWFACTORS(N) !First, to show an internal data structure.
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END DO !This relies on ALL(zero tests) yielding true, as when Q = 1.
END DO !This relies on ALL(zero tests) yielding true, as when Q = 1.
FRACTRAN = 0 !No hit.
FRACTRAN = 0 !No hit.
END FUNCTION FRACTRAN !No massive milti-precision arithmetic!
END FUNCTION FRACTRAN !No massive multi-precision arithmetic!

SUBROUTINE SHOWN(S,F) !Service routine to show the state after a step is calculated.
Could imaging a function I6FMT(23) that returns " 23" and " " for non-positive numbers.
Can't do it, as if this were invoked via a WRITE statement, re-entrant use of WRITE usually fails.
INTEGER S,F !Step number, Fraction number.
INTEGER I !A stepper.
CHARACTER*(9+4+1 + NL*6) ALINE !A scratchpad matching FORMAT 103.
⚫
WRITE (ALINE,103) S,F,NPPOW(PLIVE(1:NL)) !Show it!
⚫
103 FORMAT (I9,I4,":",<NL>I6) !As a sequence of powers of primes.
IF (F.LE.0) ALINE(10:13) = "" !Scrub when no fraction is fingered.
DO I = 1,NL !Step along the live primes.
IF (NPPOW(PLIVE(I)).GT.0) CYCLE !Ignoring the empowered ones.
ALINE(15 + (I - 1)*6:14 + I*6) = "" !Blank out zero powers.
⚫
END DO !On to the next.
WRITE (MSG,"(A)") ALINE !Reveal at last.
END SUBROUTINE SHOWN !A struggle.
END MODULE CONWAYSIDEA !Simple...
END MODULE CONWAYSIDEA !Simple...


PROGRAM POKE
PROGRAM POKE
USE CONWAYSIDEA
USE CONWAYSIDEA !But, where does he get his ideas from?
INTEGER P(ENUFF),Q(ENUFF) !Holds the fractions as P(i)/Q(i).
INTEGER P(ENUFF),Q(ENUFF) !Holds the fractions as P(i)/Q(i).
INTEGER N !The working number.
INTEGER N !The working number.
INTEGER I,IT,L,M !Assistants.
INTEGER LF !Last fraction given.
INTEGER LP !Last prime needed.
INTEGER LP !Last prime needed.
INTEGER MS !Maximum number of steps.
INTEGER I,IT !Assistants.
LOGICAL*1 PUSED(ENUFF) !Track the usage of prime numbers,


MSG = 6 !Standard output.
MSG = 6 !Standard output.
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Chew into an example programme.
Chew into an example programme.
10 OPEN (10,FILE = "Fractran.txt",STATUS="OLD",ACTION="READ") !Rather than compiled-in stuff.
10 OPEN (10,FILE = "Fractran.txt",STATUS="OLD",ACTION="READ") !Rather than compiled-in stuff.
READ (10,*) L !I need to know this without having to scan the input.
READ (10,*) LF !I need to know this without having to scan the input.
WRITE (MSG,11) L !Reveal in case of trouble.
WRITE (MSG,11) LF !Reveal in case of trouble.
11 FORMAT (I0," fractions, as follow:") !Should the input evoke problems.
11 FORMAT (I0," fractions, as follow:") !Should the input evoke problems.
READ (10,*) (P(I),Q(I),I = 1,L) !Ask for the specified number of P,Q pairs.
READ (10,*) (P(I),Q(I),I = 1,LF) !Ask for the specified number of P,Q pairs.
WRITE (MSG,12) (P(I),Q(I),I = 1,L) !Show what turned up.
WRITE (MSG,12) (P(I),Q(I),I = 1,LF) !Show what turned up.
12 FORMAT (24(I0,"/",I0:", ")) !As P(i)/Q(i) pairs. The colon means that there will be no trailing comma.
12 FORMAT (24(I0,"/",I0:", ")) !As P(i)/Q(i) pairs. The colon means that there will be no trailing comma.
READ (10,*) N,M !The start value, and the step limit.
READ (10,*) N,MS !The start value, and the step limit.
CLOSE (10) !Finished with input.
CLOSE (10) !Finished with input.
WRITE (MSG,13) N,M !Hopefully, all went well.
WRITE (MSG,13) N,MS !Hopefully, all went well.
13 FORMAT ("Start with N = ",I0,", step limit ",I0)
13 FORMAT ("Start with N = ",I0,", step limit ",I0)
IF (.NOT.GRASPPRIMEBAG(66)) STOP "Gan't grab my file of primes!" !Attempt in hope.
IF (.NOT.GRASPPRIMEBAG(66)) STOP "Gan't grab my file of primes!" !Attempt in hope.
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NPPOW(FP(1).PNUM(I)) = FP(1).PPOW(I) !Convert from a variable-length list
NPPOW(FP(1).PNUM(I)) = FP(1).PPOW(I) !Convert from a variable-length list
END DO !To a fixed-length random-access array.
END DO !To a fixed-length random-access array.
LP = FP(1).PNUM(FP(1).PNUM(0)) !Recall the last prime required.
PUSED = NPPOW.GT.0 !Note which primes have been used.
LP = FP(1).PNUM(FP(1).PNUM(0)) !Recall the last prime required. More later.
Convert the supplied P(i)/Q(i) fractions to lists of prime number factors and powers in FP(i) and FQ(i).
Convert the supplied P(i)/Q(i) fractions to lists of prime number factors and powers in FP(i) and FQ(i).
DO I = 1,L !Step through the fractions.
DO I = 1,LF !Step through the fractions.
IT = GCD(P(I),Q(I)) !Suspicion.
IT = GCD(P(I),Q(I)) !Suspicion.
IF (IT.GT.1) THEN !Justified?
IF (IT.GT.1) THEN !Justified?
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Q(I) = Q(I)/IT !And, as N is factorised in NPPOW
Q(I) = Q(I)/IT !And, as N is factorised in NPPOW
END IF !And Q in FQ, subtractions of powers only is needed.
END IF !And Q in FQ, subtractions of powers only is needed.
FP(I) = FACTOR(P(I)) !Righto, form the factor list for P.
FP(I) = FACTOR(P(I)) !Righto, form the factor list for P.
LP = MAX(LP,FP(I).PNUM(FP(I).PNUM(0))) !One has no prime factors: PNUM(0) = 0.
PUSED(FP(I).PNUM(1:FP(I).PNUM(0))) = .TRUE. !Mark which primes it fingers.
FQ(I) = FACTOR(Q(I)) !And likewise for Q.
LP = MAX(LP,FP(I).PNUM(FP(I).PNUM(0))) !One has no prime factors: PNUM(0) = 0.
FQ(I) = FACTOR(Q(I)) !And likewise for Q.
⚫
LP = MAX(LP,FQ(I).PNUM(FQ(I).PNUM(0))) !If zero prime factors, PNUM(0) fingers element zero, which is zero.
PUSED(FQ(I).PNUM(1:FQ(I).PNUM(0))) = .TRUE. !Some primes may be omitted.
⚫
LP = MAX(LP,FQ(I).PNUM(FQ(I).PNUM(0))) !If no prime factors, PNUM(0) fingers element zero, which is zero.
END DO !All this messing about saves on multiplication and division.
END DO !All this messing about saves on multiplication and division.
Check which primes are in use, preparing an index of live primes..
⚫
WRITE (MSG,22) LP,PRIME(LP)
NL = 0 !No live primes.
⚫
22 FORMAT ("Require primes only up to Prime(",I0,") = ",I0)
⚫
DO I = 1,LP !Check up to the last prime.
IF (PUSED(I)) THEN !This one used?
NL = NL + 1 !Yes. Another.
PLIVE(NL) = I !Fingered.
END IF !So much for that prime.
END DO !On to the next.
⚫
WRITE (MSG,22) NL,LP,PRIME(LP) !Remark on usage.
⚫
22 FORMAT ("Require ",I0," primes only, up to Prime(",I0,") = ",I0) !Presume always more than one prime.
IF (LP.GT.LASTP) STOP "But, that's too many for array NPPOW!"
IF (LP.GT.LASTP) STOP "But, that's too many for array NPPOW!"


Commence with a heading.
Cast forth a heading.
100 WRITE (MSG,101) (PRIME(I), I = 1,LP),0,NPPOW(1:LP) !Splat a heading.
100 WRITE (MSG,101) (PRIME(PLIVE(I)), I = 1,NL) !Splat a heading.
101 FORMAT (/,14X,"N as powers of prime factors",/, !The prime heading,
101 FORMAT (/,14X,"N as powers of prime factors",/, !The prime heading,
1 5X,"Step F#:",<LP>I6,/,I9,4X,":",<LP>I6) !With primes beneath.
1 5X,"Step F#:",<LP>I6) !With primes beneath.
CALL SHOWN(0,0)

⚫
DO I = 1,M !Here we go!
⚫
IT = FRACTRAN(L) !Do it!
⚫
WRITE (6,103) I,IT,NPPOW(1:LP) !Show it!
⚫
103 FORMAT (I9,I4,":",<LP>I6) !As a sequence of powers of primes.
⚫
END DO !The next step.


Commence!
⚫
END !Whee!</lang>
DO I = 1,MS !Here we go!
⚫
IT = FRACTRAN(LF) !Do it!
CALL SHOWN(I,IT) !Show it!
END DO !The next step.
Complete!
⚫
END !Whee!
</lang>


===Revised Results===
===Revised Results===
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