sub factorial_gosper { # sqrt(2*n*PI + 1/3)*n**n/exp(n) my \$n = shift; return exp(\$n*log(\$n) - \$n + 0.5*log(2*\$n*PI + 1.0/3.0)); } ##```## #!/usr/bin/perl -w use strict; my \$h =8; my \$pure = factorial_pure(\$h); my \$stirling = factorial_stirling(\$h); my \$real_stirling = real_stirling(\$h); my \$gosper = factorial_gosper(\$h); print "PURE : \$pure\n"; print "STIRLING : \$stirling\n"; print "REAL : \$real_stirling\n"; print "GOSPER : \$gosper\n"; #------Subroutines------------ sub factorial_stirling{ my \$n = shift; use constant PI => 4*atan2 (1,1); use constant e => exp(1); my \$log_nfact = \$n * log (\$n) - e* log(\$n) + 0.5 * (log(2*PI)+log(\$n)); # Below is Tilly's suggestion, with less accuracy # \$n * log (\$n) - (\$n) + (0.5 * (log(2+ log(PI))+log(\$n))); return exp(\$log_nfact); } sub factorial_pure { my (\$n,\$res) = (shift,1); return undef unless \$n>=0 and \$n == int(\$n); \$res *= \$n-- while \$n>1; return \$res; } sub real_stirling { my \$n = shift; my \$log_nfact = \$n*log(\$n) - \$n + 0.5*(log(2) + log(PI)+ log(\$n)); return exp(\$log_nfact); } sub factorial_gosper { # sqrt(2*n*PI + 1/3)*n**n/exp(n) my \$n = shift; return exp(\$n*log(\$n) - \$n + 0.5*log(2*\$n*PI + 1.0/3.0)); } ##``````## PURE : 40320 STIRLING : 417351.253768542 REAL : 39902.3954526567 GOSPER : 40034.4823215513 ```