Rundungsexperimente mit BigRat.

tests/ratround.pl

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+#!/usr/bin/env perl
+
+use strict;
+use warnings;
+
+use Math::BigRat;
+use Math::Trig;
+
+my $x = abs(Math::BigRat->new(-1/3));
+
+print "$x\n";
+
+for my $s(0..6) {
+  my $pi = ratFromFloatSteps($s, pi);
+
+  print "$s -> $pi\n";
+}
+
+my $pi = ratFromFloatEpsilon(0.000001, pi);
+print "  $pi\n";
+
+sub ratFromFloatEpsilon {
+  my ($epsilon, $inp) = @_;
+  my $steps = 0;
+  my $old = ratFromFloatSteps($steps, $inp);
+  for(;;) {
+    $steps++;
+    my $n = ratFromFloatSteps($steps, $inp);
+    if(abs($old-$n) < $epsilon) {
+      return $n
+    } else {
+      $old = $n
+    }
+  }
+}
+
+sub ratFromFloatSteps {
+  my ($steps, $inp) = @_;
+  #print "  [[ $steps $inp ]]\n";
+  if($inp < 0) { return ratFromFloatSteps($steps, -$inp) }
+  if(0 == $inp) { return Math::BigRat->new(0) }
+  if($steps <= 0) {
+    return Math::BigRat->new(int $inp);
+  }
+  my $prop = int $inp;
+  my $rem = $inp - $prop;
+  $prop = Math::BigRat->new($prop);
+  $rem = 1/ratFromFloatSteps($steps-1, 1/$rem);
+  return $prop + $rem;
+}