' Cino Hilliard, 1/31/2003
' !3.bas BCX bignums Factorial routine.
' Program outputs the factorial of N <= 126000, and number of 2's in it.
' digits = int((n+.5)*log10(n) - n*log10(exp(1))+.3992)+1  'estimate of digits in n!
' I derived this formula by counting the digits in this program and
' Stirling's formula for N!. It is correct for N <= 100000.

$nowin
#include <bignums.h>
cls
 dim dummy$
 dim n1$
 dim  n
 dim n2   as long
 dim prec as long
 dim one  as pBignum
 dim a    as pBignum
 dim b    as pBignum
 dim tmp  as pBignum
 dim bigbuff[100000001] as char
 dim digits as long
 dim d[20] as long
  n1$ = Command$
  print "                         BCX bignums Factorial."
  print "             Use dos redirect > filename.txt to save to file"
  print
 IF n1$ = "" THEN
 input "number ",n1$
 END IF
 n = VAL(n1$)
 n2 = n/2
 digits = int((n+.5)*log10(n) - n*log10(exp(1))+.3992)+1  'estimate of digits in n!
 print "Computing ";n;"!. Estimated digits = ";digits
for n = 0 to 100
 if n <  1000   then prec = digits/2
 if n >= 1000   and n  <= 5000    then prec = digits/7
 if n >  5000   and n  <= 20000   then prec = digits/8
 if n >  20000  and n  <= 50000   then prec = digits/7
 if n >  50000  and n  <= 100000  then prec = digits/4
 if n >  100000 then prec = digits
 BignumPrecision(prec)
 one = newBignum(1)
 a   = quadnew(2)
 b   = newBignum(n2)
 tmp = newBignum(0)
a = fact(n)
 quadformat(a,bigbuff)
d[2] = tally(bigbuff$,"2")
print d[2];
next n
print

 input "enter to end",dummy$