<(common.inc.plp)><: Html({ title => 'number bases', version => '1.1', description => [ "Cheat sheets summarising various software programs and standards.", ], keywords => [qw' sheet cheat reference software overview summary help keyboard map unicode '], stylesheet => [qw'light dark circus mono red'], }); my @cols = (2, 6, 8, 9, 10, 12, 16, 18, 20); my @morecols = (2 .. 6, 8, 9, 10, 12, 16, 18, 20, 24, 32, 36, 64); my @char = (0..9, 'A'..'Z', 'a'..'z'); :>

Number bases

Radix economy

<: sub radix_economy { my ($val, $radix) = @_; return $radix * int(log($val) / log($radix) + 1); } use List::Util 'sum'; print '
'; print '', $_ for @morecols; for my $max (100, 255, 1024) { print '
⍳', $max; for my $radix (@morecols) { printf '%.1f', sum(map { radix_economy($_, $radix) } 1 .. $max) / $max; } } :>

Reciprocal fractions (n⁻¹)

<: print ''; print '
'; print '', $_ for @cols; use Math::BigFloat; my $count = 40; my $places = $count<<1; sub showfrac { my ($num, $radix) = @_; my $out = ''; my $class = ''; my $zeros = 0; ADD_DIGITS: for my $place (1 .. $places) { # add a digit in requested base (left shift) $out .= $char[ $num->blsft(1, $radix) ]; $num->bmod(1) or do { # no remaining fractional part $class = $out eq '1' ? 'l5' : $place == 1 ? 'l4' : 'l3'; last; }; $zeros++ if $out =~ /^0+$/; for my $check ($zeros .. length($out)>>1) { if (substr($out, -$check) eq substr($out, -$check*2, $check)) { $class = $check == 1 ? 'l2' : 'l1'; substr($out, -$check) = ''; substr($out, -$check, 0) = ''; $check .= ''; last ADD_DIGITS; } } } printf '%s', $class && qq( class="$class"), $out; } for my $n (2 .. $count) { print '
', $n; for my $radix (@cols) { my $accuracy = int($places * log($radix) / log(10)); Math::BigFloat->accuracy($accuracy); showfrac(scalar Math::BigFloat->new(1)->bdiv($n, $accuracy+1), $radix); } } :>

Duplication (2ⁿ)

<: use 5.010; sub showint { my ($int, $radix) = @_; my @digits; while ($int >= 1) { push @digits, $char[$int % $radix]; $int /= $radix; } splice @digits, 3 * $_, 0, ' ' for reverse 1 .. @digits/3; return join '', reverse @digits; } @cols = grep { not $_ ~~ [2,8,16] } @cols, 36; print ''; print '
'; print '', $_ for @cols; for my $n (3 .. 16, 18, 20, 24, 30, 32, 36, 40, 48, 50, 60, 64) { print '
', $n; for my $radix (@cols) { print '', showint(2 ** $n, $radix); } print '', { 4 => 'nibble', 8 => 'octet', 16 => '2o', 24 => '3o', 32 => '4o', 40 => '5o, Tebi', 48 => '6o', 64 => 'o²', 10 => 'kibi', 20 => 'Mebi', 30 => 'Gibi', 50 => 'Pebi', 60 => 'Exbi', 70 => 'Zebi', 80 => 'Yobi', }->{$n} // ''; } :>