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#! /usr/bin/perl -w use strict; while (1) { print "Please enter a number or expression: "; my $num = eval(scalar <STDIN>); print "How many iterations: "; chomp(my $count = <STDIN>); print "Doing $count iterations of approximations to $num.\n"; my $f = ret_frac_iter($num); for (1..$count) { my ($n, $m) = $f->(); my $approx = $n/$m; print "$n/$m = $approx\n"; } print "\n"; } # Takes a number, returns the best integer approximation and (in list # context) the error. sub best_int { my $x = shift; my $approx = sprintf '%.0f', $x; if (wantarray) { return ($approx, $x - $approx); } else { return $approx; } } # Takes a numerator and denominator, in scalar context returns # the best fraction describing them, in list the numerator and # denominator sub frac_standard { my $n = best_int(shift); my $m = best_int(shift); my $k = gcd($n, $m); $n /= $k; $m /= $k; if ($m < 0) { $n *= -1; $m *= -1; } if (wantarray) { return ($n, $m); } else { return "$n/$m"; } } # Euclidean algorithm for calculating a GCD. # Takes two integers, returns the greatest common divisor. sub gcd { my ($n, $m) = @_; while ($m) { my $k = $n % $m; ($n, $m) = ($m, $k); } return $n; } # Takes a list of terms in a continued fraction, and converts it # into a fraction. sub ints_to_frac { my ($n, $m) = (0, 1); # Start with 0 while (@_) { my $k = pop; if ($n) { # Want frac for $k + 1/($n/$m) ($n, $m) = frac_standard($k*$n + $m, $n); } else { # Want $k ($n, $m) = frac_standard($k, 1); } } return frac_standard($n, $m); } # Takes a number, returns an anon sub which iterates through a set of # fractional approximations that converges very quickly to the number. sub ret_frac_iter { my $x = shift; my $term_iter = ret_next_term_iter($x); my @ints; return sub { push @ints, $term_iter->(); return ints_to_frac(@ints); } } # terms of a continued fraction converging on that number. sub ret_next_term_iter { my $x = shift; return sub { (my $n, $x) = best_int($x); if (0 != $x) { $x = 1/$x; } return $n; }; }

In reply to Continued Fractions by tilly

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