4 title => 'number bases',
7 "Cheat sheets summarising various software programs and standards.",
10 sheet cheat reference software overview summary help keyboard map unicode
14 my @cols = (2, 6, 8, 9, 10, 12, 16, 18, 20);
15 my @morecols = (2 .. 6, 8, 9, 10, 12, 16, 18, 20, 24, 32, 36, 64);
16 my @char = (0..9, 'A'..'Z', 'a'..'z');
26 12 => 'dozenal', # duodecimal
29 #36 => 'double-senary',
31 #64 => 'double-octal',
36 <h2>Radix economy</h2>
42 $spans[ $_ > 10 ]++ for @_;
43 print "<colgroup span=$_>" for @spans;
44 print '<thead><tr><th>';
46 print '<th>', $_ < 36 ? $char[$_] : $char[35].'+'.$char[$_ - 35];
47 print " <small>($_)</small>" for join(', ',
49 $_ >= 10 ? "base$_" : (),
56 my ($val, $radix) = @_;
57 return $radix * int(log($val) / log($radix) + 1);
62 showcolhead(@morecols);
64 for my $max (100, 255, 1024) {
65 print '<tr><th>⍳', $max;
66 for my $radix (@morecols) {
67 printf '<td style="text-align:right">%.1f',
68 sum(map { radix_economy($_, $radix) } 1 .. $max) / $max;
73 <h2>Reciprocal fractions (n⁻¹)</h2>
79 my $places = $count<<1;
82 my ($num, $radix) = @_;
89 for my $place (1 .. $places) {
90 # add a digit in requested base (left shift)
91 $out .= $char[ $num->blsft(1, $radix) ];
93 # no remaining fractional part
94 $class = $out eq '1' ? 'l5' : $place == 1 ? 'l4' : 'l3';
97 $zeros++ if $out =~ /^0+$/;
99 for my $check ($zeros .. length($out)>>1) {
100 if (substr($out, -$check) eq substr($out, -$check*2, $check)) {
101 $class = $check == 1 ? 'l2' : 'l1';
102 substr($out, -$check) = '';
103 substr($out, -$check, 0) = '<span style="text-decoration:overline">';
109 printf '<td%s style="text-align:left">%s', $class && qq( class="$class"), $out;
114 for my $n (2 .. $count) {
115 print '<tbody>' if $n % 8 == 1;
118 for my $radix (@cols) {
119 my $accuracy = int($places * log($radix) / log(10));
120 Math::BigFloat->accuracy($accuracy);
121 showfrac(scalar Math::BigFloat->new(1)->bdiv($n, $accuracy+1), $radix);
130 <h2>Duplication (2ⁿ)</h2>
134 my ($int, $radix) = @_;
137 push @digits, $char[$int % $radix];
140 splice @digits, 3 * $_, 0, ' ' for reverse 1 .. @digits/3;
141 return join '', reverse @digits;
144 @cols = grep { not $_ ~~ [2,8,16] } @cols, 36;
147 for my $n (0, 3 .. 16, 0, 18, 20, 24, 30, 32, 36, 40, 48, 50, 60, 64) {
154 for my $radix (@cols) {
155 print '<td style="text-align:right">', showint(2 ** $n, $radix);