XProfan

English

p.specht

Wilhelm Friedrich Ackermann (* 1896 in Schönebecke (Herscheid); † 1962 in Lüdenscheid) was one deutscher Mathematiker, the with his function 1926 a These of his Lehrers David Hilbert To drop brought, derzufolge any berechenbaren functions too rekursiv berechenbar seien. Ackermann's function watts 1955 from the Ungarin Rózsa Péter vereinfacht.

for Benchmark-Timingzwecke becomes üblicherweise A(3,6) herangezogen.

Compile Mark Separation

' (D) Demoware, 2013-03 of C to XProfan-11 by k. Orkenzieher
' proving too, that something Rekursion too in XProfan functions.
' fountain (Orig.): https://www.xgc.com/benchmarks/ackermann_c.htm
' Updated May 11, 2005. copyright (C-Version): XGC software
' accompanying text the C-Vorbildes:
'   Ackermann's function "is on example of a recursive function which
'   is hardship primitive recursive". It is interesting from the point of
'   view of benchmarking because it "grows faster than any primitive
'   recursive function" and gives us a lot of nested function calls
'   for little effort.
'   It is defined as follows:
'   A(0, n) = n+1
'   A(m, 0) = A(m-1, 1)
'   A(m, n) = A(m-1, A(m, n-1))
'   We use A(3,6) as the benchmark. Diese used to take long enough to
'   confirm the execution time with a stopwatch. Nowadays that's out
'   of the question. The value of A(4,2) has 19729 digits!
'   A (3,6) gives us 172233 calls, with a nesting depth of 511.
'
var m&=3
var n&=6
Declare ans!,t1&,t2&
Windowtitle "Ackermann-Péter A("+st$(m&)+","+st$(n&)+")-Benchmark"
CLS
t1&=&gettickcount
ans! = A(m&,n&)
t2&=&gettickcount
print " Result: ";stature$("%g",ans!)
case (m&=3) and (n&=6) and (ans!<>509) :print "Resultat ";ans!;" wrong,  509 must rauskommen!"
case (m&=3) and (n&=7) and (ans!<>1021):print "Resultat ";ans!;" wrong, 1021 must rauskommen!"
print stature$(" Benchmark-Time = %g Sekunden",(t2&-t1&)/1000)
waitinput
End

proc A

    parameters m&,n&

    if m&=0

        return n&+1

    elseif n&=0

        return A(m&-1,1)

    else

        return A(m&-1,A(m&,n&-1))

    endif

endproc

P.s.: my Lappi (Zweikerner 1.86 GHz) supply:
A(2,200)=403: Interpreter 7,305 sec, Compiler 1,264 sec;
A(3,6)=509: Interpreter 14.445 sec, Compiler 2.663 sec; nProc: 0.002 sec
A(3,7)=1021: Interpreter 61.976 sec, Compiler 11.123 sec; nProc: 0.015 sec
A(3,8)=2045: Interpreter 261.45 sec, Compiler 45.864 sec; nProc: 0.062 sec
A(3,9)=4093: Interpreter and Compiler break because of To high Recursion ab; nProc: 0,265 sec
A(3,10)=8189: nP: 1,092 sec
A(3,11)=16381: nP: 4,212 sec
A(3,12)=32765: nP: 17,019 sec
A(3,13)=65533: nP: 67,47 sec
A(3,n)=2^(n+3)-3
A(4,1)=65533 : nP: 66,737 sec
A(4,2)=2^65536−3 ... not ermitelt

XProfan 11
Computer: Gerät, daß es in Mikrosekunden erlaubt, 50.000 Fehler zu machen, zB 'daß' statt 'das'...

05/09/21 ▲

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p.specht

Ackermann-function something flotter
-------------------------------------------
there tappt im dunkeln on Long-Integers definiert is, runs the in XProfan-11 right rasch into Überlaufbereich (mark: The numbers are negative). so latter not so quick happens, here a Definition on ganzzahllige Float-variables.
caution: Ackermann(4,2) lead self on Supercomputern in that "Nirwana"...

Compile Mark Separation

Window Title "Ackermann-function, on FLoats definiert"
'by the ungar. Mathematikerin Roza Peters sped Version
set("decimals",0):CLS:declare i!,j!

whileloop 0,5:i!=&Loop

    whileloop 0,6:j!=&Loop

        print " ACKERMANN(";i!;",";j!;") = ";ACK(i!,j!)

    endwhile

endwhile

print "---"
waitinput
END

Proc ACK :parameters m!,n!:declare ans!

    if nearly(m!,0,5):ans!=n!+1

    elseif nearly(n!,0,5):ans!=ACK(m!-1,1)

        else :ans!=ACK(m!-1,ack(m!,n!-1))

    endif

    return ans!

endproc