Imaginary base numbers: Difference between revisions
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Thundergnat (talk | contribs) m →{{header|Perl 6}}: fix some spacing issues, minor rewording |
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=={{header|Perl 6}}== |
=={{header|Perl 6}}== |
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{{works with|Rakudo|2017.01}} |
{{works with|Rakudo|2017.01}} |
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These are generalized imaginary-base conversion routines. They only work for imaginary bases, not complex. (Any real |
These are generalized imaginary-base conversion routines. They only work for imaginary bases, not complex. (Any real portion of the radix must be zero.) Theoretically they could be made to work for any imaginary base; in practice, they are limited to bases from -6i to -2i and 2i to 6i since those bases will fit within standard base 36 digit representations. Bases -1i and 1i exist but require special caseing and are not supported. Bases larger than 6i (or -6i) require digits outside of base 36 to express them, so aren't as standardized, are implementation dependent and are not supported here. |
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<lang perl6>multi sub base ( Real $num, Int $radix where -37 < * < -1, :$precision = -5 ) { |
<lang perl6>multi sub base ( Real $num, Int $radix where -37 < * < -1, :$precision = -5 ) { |
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multi sub base (Numeric $value, Complex $base where *.re == 0 ) { |
multi sub base (Numeric $value, Complex $base where *.re == 0 ) { |
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die "Base $base out of range" unless -6 <= $base.im <= -2 or 2 <= $base.im <= 6; |
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my ($re, $im) = $value.Complex.reals; |
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$re .= &base((-($base.im)²).Int); |
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$im = ($im/($base.im)).&base((-($base.im)²).Int); |
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my ($re-wh, $re-fr, $im-wh, $im-fr); |
my ($re-wh, $re-fr, $im-wh, $im-fr); |
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($re-wh, $re-fr) = $re.split: '.'; |
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($im-wh, $im-fr) = $im.split: '.'; |
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$_ //= '' for ($re-wh, $re-fr, $im-wh, $im-fr); |
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my @whole = do given $re-wh.chars cmp $im-wh.chars { |
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when Less { flat (flat $re-wh.flip.comb, '0' xx *) Z flat $im-wh.flip.comb } |
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when More { flat $re-wh.flip.comb Z flat (flat $im-wh.flip.comb, '0' xx $re-wh.chars - $im-wh.chars) } |
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default { flat $re-wh.flip.comb Z flat $im-wh.flip.comb } |
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} |
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} |
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my @fraction = do given $re-fr.chars cmp $im-fr.chars { |
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when More { flat (flat $im-fr.comb, '0' xx *) Z flat $re-fr.comb } |
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when Less { flat $im-fr.comb Z flat (flat $re-fr.comb, '0' xx $im-fr.chars - $re-fr.chars) } |
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default { flat $im-fr.comb Z flat $re-fr.comb } |
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} |
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} |
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@whole.pop if +@whole and @whole.tail eq '0'; |
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@fraction.pop while +@fraction and @fraction.tail eq '0'; |
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+@fraction ?? |
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@whole.reverse.join ~ '.' ~ @fraction.join !! |
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@whole.reverse.join |
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} |
} |
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