X-Git-Url: http://git.shiar.net/sheet.git/blobdiff_plain/1107366d212418d8f8a6a80c54115387816ef2a2..HEAD:/base.plp

diff --git a/base.plp b/base.plp
index ad6961b..a68a71f 100644
--- a/base.plp
+++ b/base.plp
@@ -1,8 +1,8 @@
 <(common.inc.plp)><:
 
 Html({
-	title => 'fractions',
-	version => 'v1.0',
+	title => 'number bases',
+	version => '1.2',
 	description => [
 		"Cheat sheets summarising various software programs and standards.",
 	],
@@ -12,48 +12,166 @@ Html({
 	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');
+my %RADIXNAME = (
+	 2 => 'binary',
+	 3 => 'ternary',
+	#4 => 'quaternary',
+	#5 => 'quinary',
+	 6 => 'senary',
+	 8 => 'octal',
+	#9 => 'nonary',
+	10 => 'decimal',
+	12 => 'dozenal', # duodecimal
+	16 => 'hexadecimal',
+	20 => 'vigesimal',
+	#36 => 'double-senary',
+	60 => 'sexagesimal',
+	#64 => 'double-octal',
+);
 :>
-<h1>Fractions</h1>
+<h1>Number bases</h1>
 
-<table>
+<h2>Radix economy</h2>
+<table class=mapped>
+<:
+sub showcolhead {
+	print '<col>';
+	my @spans;
+	$spans[ $_ > 10 ]++ for @_;
+	print "<colgroup span=$_>" for @spans;
+	print '<thead><tr><th>';
+	for (@_) {
+		print '<th>', $_ < 36 ? $char[$_] : $char[35].'+'.$char[$_ - 35];
+		print " <small>($_)</small>" for join(', ',
+			$RADIXNAME{$_} // (),
+			$_ >= 10 ? "base$_" : (),
+		) || ();
+	}
+	say '</thead>';
+}
+
+sub radix_economy {
+	my ($val, $radix) = @_;
+	return $radix * int(log($val) / log($radix) + 1);
+}
+
+use List::Util 'sum';
+
+showcolhead(@morecols);
+
+for my $max (100, 255, 1024) {
+	print '<tr><th>⍳', $max;
+	for my $radix (@morecols) {
+		printf '<td style="text-align:right">%.1f',
+			sum(map { radix_economy($_, $radix) } 1 .. $max) / $max;
+	}
+}
+:></table>
+
+<h2>Reciprocal fractions (n⁻¹)</h2>
+<table class=mapped>
 <:
 use Math::BigFloat;
 
-my @cols = (2, 6, 8, 9, 10, 12, 16, 18, 60);
-print '<tr><th>';
-print '<th>', $_ for @cols;
+my $count = 40;
+my $places = $count<<1;
 
-my @char = (0..9, 'A'..'Z', 'a'..'z');
-my $places = 48;
+sub showfrac {
+	my ($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 $n (2 .. 25) {
+		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) = '<span style="text-decoration:overline">';
+				$check .= '</span>';
+				last ADD_DIGITS;
+			}
+		}
+	}
+	printf '<td%s style="text-align:left">%s', $class && qq( class="$class"), $out;
+}
+
+showcolhead(@cols);
+
+for my $n (2 .. $count) {
+	print '<tbody>' if $n % 8 == 1;
 	print '<tr>';
 	print '<th>', $n;
 	for my $radix (@cols) {
 		my $accuracy = int($places * log($radix) / log(10));
 		Math::BigFloat->accuracy($accuracy);
-		my $frac = Math::BigFloat->new(1)->bdiv($n, $accuracy+1);
-		my $out = '';
-		my $class = '';
-ADD_DIGITS:
-		for my $place (1 .. $places) {
-			$out .= $char[ $frac->blsft(1, $radix) ];
-			$frac->bmod(1) or do {
-				$class = $n == $radix ? 'l5' : $place == 1 ? 'l4' : 'l3';
-				last;
-			};
-			for my $check (log($n)/log($radix) .. length($out)>>1) {
-				if ($out =~ /[^0]/ and substr($out, -$check) eq substr($out, -$check*2, $check)) {
-					$class = $check == 1 ? 'l2' : 'l1';
-					substr($out, -$check) = '';
-					substr($out, -$check, 0) = '(';
-					last ADD_DIGITS;
-				}
-			}
-		}
-		printf '<td%s>%s', $class && qq( class="$class"), $out;
+		showfrac(scalar Math::BigFloat->new(1)->bdiv($n, $accuracy+1), $radix);
 	}
-#	\x{305}
+	say '';
 }
+
 :></table>
 
+<hr>
+
+<h2>Duplication (2ⁿ)</h2>
+<table class=mapped>
+<:
+sub showint {
+	my ($int, $radix) = @_;
+	my @digits;
+	while ($int >= 1) {
+		push @digits, $char[$int % $radix];
+		$int /= $radix;
+	}
+	splice @digits, 3 * $_, 0, '&nbsp;' for reverse 1 .. @digits/3;
+	return join '', reverse @digits;
+}
+
+@cols = grep { not $_ ~~ [2,8,16] } @cols, 36;
+showcolhead(@cols);
+
+for my $n (0, 3 .. 16, 0, 18, 20, 24, 30, 32, 36, 40, 48, 50, 60, 64) {
+	if (!$n) {
+		print '<tbody>';
+		next;
+	}
+	print '<tr>';
+	print '<th>', $n;
+	for my $radix (@cols) {
+		print '<td style="text-align:right">', showint(2 ** $n, $radix);
+	}
+	say '<th>', {
+		 4 => 'nibble',
+		 8 => 'octet',
+		16 => '2o',
+		24 => '3o',
+		32 => '4o',
+		40 => '5o, Tebi',
+		48 => '6o',
+		64 => 'o²',
+		10 => 'kibi',
+		20 => 'Mebi',
+		30 => 'Gibi',
+		50 => 'Pebi',
+		60 => 'Exbi',
+		70 => 'Zebi',
+		80 => 'Yobi',
+	}->{$n} // '';
+}
+
+:></table>