XProfan

Window Title upper$(\
"  Allg. Fibonacci-numbers:  Gültigkeitsbereich verschiedener Formeln (ua.: Moivre-Binet) testen")
'(CL) CopyLeft 2015-08 in XProfan11.2a by P.woodpecker, Wien (Austria), OHNE JEDWEDE GEWÄHR!
'Info-Base: https://de.wikipedia.org/wiki/Fibonacci-follow
Window 0,0-%maxx,%maxy-50:font 2:Set("decimals",0):declare n&,vz&,sg!
AppendMenubar 100,"N "+"_______ tab.1 "+"___________________________ tab.2 "+\
"__________________________________ Fib(%g) "+"____________________________ Fib(#) "+\
"_____________________ fibz_MoivreBinet() "+"_____________ Error "+\
"________________________________ n "
var f$="00,0,01,1,02,1,03,2,04,3,05,5,06,8,07,13,08,21,09,34,10,55,11,89,12,144,13,233,"+\
"14,377,15,610,16,987,17,1597,18,2584,19,4181,20,6765,21,10946,22,17711,23,28657,"+\
"24,46368,25,75025,26,121393,27,196418,28,317811,29,514229,30,832040,31,1346269,"+\
"32,2178309,33,3524578,34,5702887,35,9227465,36,14930352,37,24157817,38,39088169,"+\
"39,63245986,40,102334155,41,165580141,42,267914296,43,433494437,44,701408733,"+\
"45,1134903170,46,1836311903,47,2971215073,48,4807526976,49,7778742049,50,12586269025"
var fi$="0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,"+\
"28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,5702887,9227465,"+\
"14930352,24157817,39088169,63245986,102334155,165580141,267914296,433494437,701408733,"+\
"1134903170,1836311903,2971215073,4807526976,7778742049,12586269025,20365011074,32951280099,"+\
"53316291173,86267571272,139583862445,225851433717,365435296162,591286729879,956722026041,"+\
"1548008755920,2504730781961,4052739537881,6557470319842,10610209857723,17167680177565,"+\
"27777890035288,44945570212853,72723460248141,117669030460994,190392490709135,308061521170129,"+\
"498454011879264,806515533049393,1304969544928657,2111485077978050,3416454622906707,"+\
"5527939700884757,8944394323791464"

whileloop -80,80

    n&=&Loop:sg!=1:vz&=(n&>0)-(n&<0):case vz&=-1:vz&=if(int(0.5*n&)=(0.5*n&),-1,1)
    print if(n&<0,""," ");if(abs(n&)<1000," ","");if(abs(n&)<100," ","");if(abs(n&)<10," ","");n&,
    print tab(10);if(vz&<0,""," ");stature$("%g",vz&*val(substr$(f$,abs(n&)*2+2,","))),
    print tab(32);stature$("%g",fib(n&)),
    print tab(54);stature$(" ################0;-################0; 0",vz&*val(substr$(fi$,abs(n&)+1,","))),
    print tab(76);stature$(" ################0;-################0; 0",fib(n&)),
    print tab(98);stature$(" ################0;-################0; 0",fibz_MoivreBinet(n&)),
    font 0
    print tab(120);stature$("+################0;-################0; 0",fibz_MoivreBinet(n&)-vz&*val(substr$(fi$,abs(n&)+1,","))),
    font 2
    print tab(142);if(n&<0,""," ");if(abs(n&)<1000," ","");if(abs(n&)<100," ","");if(abs(n&)<10," ","");n&

    if %csrlin>49:print "   [Button]";:waitinput:cls:endif

    endwhile

    waitinput
    END

    Proc fib :parameters n&:declare i&,vz!,sg!,f0!,f1!,f2!

        sg!=1:vz!=(n&>0)-(n&<0):n&=abs(n&):f0!=1
        case vz&=-1:sg!=if(int(0.5*n&)=(0.5*n&),-1,1)

        while i&<n&:f2!=f1!+f0!:f0!=f1!:f1!=f2!:inc i&:endwhile

            return sg!*f2!

        endproc

        Proc fibz_MoivreBinet :parameters n&:case n&=0:return 0

            var vz!=(n&>0)-(n&<0):n&=abs(n&)
            var sg!=1:case vz&=-1:sg!=if(int(0.5*n&)=(0.5*n&),-1,1)
            var phi!=(1+sqrt(5))/2:var chi!=phi!-1
            return sg!*(phi!^n& + chi!^n&)/sqrt(5)

        endproc

Window Title " n. Fibonacci-number by Moivre-Binet-Näherung to charge (N=0..1474)"
'https://de.wikipedia.org/wiki/Fibonacci-follow#n%C3%A4herungsformel_f%C3%BCr_gro%C3%9Fe_Zahlen
Window Style 24:CLS:Font 2
declare n!

proc fib$ :parameters n!

    case n!<0:return "0"
    case n!>1474:return " ... > 5e+307 *** OVERFLOW ERROR *** "
    return stature$("######################0",(0.5+0.5*Sqrt(5))^n!/Sqrt(5))
    'works only, because stature$ rundet, means 0.5 dazuaddiert!

endproc

luuup:
locate 4,1
print "\n The wievielte Fibonacci-number to charge? n = ";:input n!
CLS
print "\n The ";int(n!);".te",tab(14);"Fibonacci-number ist",fib$(n!)
print "  Check through Aufaddieren with vorangehender number:",fibadd$(n!)
Goto "luuup"

proc fibadd$ :parameters n!

    declare fib!,last!,sum!
    last!=1

    Whileloop n!

        sum!=fib!+last!
        fib!=last!
        last!=sum!

    Endwhile

    return stature$("######################0",fib!)

endproc