XProfan

English

p.specht

The n-over-k function (Binomialkoeffizienten the Pascal´schen Dreiecks) lead rasch To gigant numbers, The The double-precision floats of XProfan überfordern. here therefore my attempt, The Zahlendarstellung with separated Exponenten To to charge: Float-numbers over 10^154 threatening namely in the next step überzulaufen, and go here then aufgesplittet. The Number of therefore additional compel Kommaverschiebungen becomes then additional angeschrieben. in the everywhere known Pascalschen Dreieck is n The 'N-th basement-Ebene' and k the place in the jeweiligen row, of left ex 1 counted. demonstration without Gewähr!

Compile Mark Separation

Window Title "BinCoeff(n over k) = n!/((n-k)!*k!)"
var f!=10^154'1.3407807929942596324916056014016*10^154
declare n!,k!,p!,q!,i&:font 2: rpt:
set("decimals",0):cls rgb(0,240,255)
print " n = ";:input n!: loop:
locate 2,1:print " k = ";:input k!:case k!=0:goto "rpt"

if k!>n!:beep:goto "rpt":endif :case 2*k!>n!:k!=n!-k!

    i&=int(k!+0.00000000000005):p!=1:q!=0

    whileloop i&,1,-1:p!=p!*(n!+1-&Loop):p!=p!/&Loop

        if p!>f!:p!=p!/f!:q!=q!+1:endif

        endwhile

        print "= BinCoeff(";n!;" over ";k!;") = "
        case (p!>10000000000) or (q!>0): set("decimals",17)
        print p! :case q!:print " *10^";154*q!
        goto "loop"