ぴょん's comment on 格子点の列挙

格子点の列挙 (Nested Flatten)

Perl がなかったので。力技。

use strict;

my $PI = atan2(1, 1) * 4;
my $MAXR = int(sqrt(1000 / $PI) + sqrt(2) + 0.5);
my @res = ();

for (my $i = 0; $i <= $MAXR; $i++) {
    for (my $j = 0; $j <= $MAXR; $j++) {
        my $r = sqrt($i * $i + $j * $j);
        push(@res, [$i, $j, $r, atan2($j, $i)]);
        ($i != 0) && push(@res, [-$i, $j, $r, atan2($j, -$i)]);
        ($j != 0) && push(@res, [$i, -$j, $r, atan2(-$j, $i) + 2 * $PI]);
        ($i * $j != 0) && push(@res, [-$i, -$j, $r, atan2(-$j, -$i) + 2 * $PI]);
    }
}

foreach my $p (sort {($a->[2] <=> $b->[2]) || ($a->[3] <=> $b->[3])} @res) {
    printf("%3d, %3d\n", splice(@{$p}, 0, 2));
}

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かも's comment on 立方根の計算

立方根の計算 (Nested Flatten)

もっと精度が必要な場合は、Math::BigFloatを使うとよいと思います。(check, improveはまったく同じです。)

use Math::BigFloat;

my $d = Math::BigFloat->new("1E-12");

sub check($$$){
  my ($x, $y, $d) = @_;
  return abs($y - $x ** 3) < $d;
}

sub improve($$){
  my ($x, $a) = @_;
  return (2 * $x ** 3 + $a) / (3 * $x ** 2);
}

sub cube_root($){
  my $a = Math::BigFloat->new($_[0]);
  my $p = Math::BigFloat->bone();
  my $q;
  until(check($p, $a, $d)){
    $q = $p;
    $p = improve($p, $a);
  }
  $p->ffround(-12);
}

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Latest comments replied to かも

ぴょん's comment on 格子点の列挙

かも's comment on 立方根の計算