Scrupuli: rad50.pl - interpret quadragesimal numbers

rad50.pl - interpret quadragesimal numbers

by Scrvpvlvs
Nov 19, 2010 6:43 AM–


  1 #! /usr/bin/perl

  2 

  3 # Title:

  4 #   rad50.pl

  5 #

  6 # Author:

  7 #   MetaEd

  8 #

  9 # Version:

 10 #   November 22, 3732

 11 #

 12 # This document is a Perl 5 program which will:

 13 #

 14 #   1. take a line of text as input

 15 #

 16 #   2. interpret it as a string of three-digit quadragesimal numbers

 17 #

 18 #        NOTE: Quadragesimal notation is analogous to octal,

 19 #        decimal, and hexadecimal notation. Octal uses eight symbols

 20 #        (numerals), decimal uses ten, hexadecimal uses sixteen, and

 21 #        quadragesimal notation uses forty numerals.

 22 #

 23 #   3. convert each such number to six-digit octal numbers

 24 #

 25 #   4. type the octal numbers as a line of text

 26 #

 27 #   5. stop

 28 #

 29 # Sample input:

 30 #   "Nothing sucks like a VAX."

 31 #

 32 # Interpretation as quadragesimal numbers:

 33 #   "NOT/HIN/G S/UCK/S L/IKE/ A /VAX/.  "

 34 #

 35 #     NOTE: The interpretation is not case sensitive. If the last

 36 #     number is incomplete, it is padded on the right with space.

 37 #

 38 # Sample output:

 39 #   054754 031566 025723 101703 073314 034775 000050 104700 127400\n

 40 

 41 # First, we declare the forty symbols we recognize as quadragesimal

 42 # numerals.

 43 

 44 $_ =

 45 $numerals =

 46 $digital020 = ' ABCDEFGHIJKLMNOPQRSTUVWXYZ$.%0123456789' ;

 47   # ' ' (space) = zero, 'A' = one, ..., 'V' = twenty-two, ...

 48 

 49 $digital044 = ' 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ.$%' ;

 50   # ' ' (space) = zero, 'A' = eleven, ..., 'V' = thirty-two, ...

 51 

 52 #   NOTE: Two different notation schemes are commonly used. These

 53 #   originate from Digital Equipment Corporation (DEC) sixteen bit

 54 #   systems and DEC thirty-six bit systems, respectively. The same

 55 #   symbols are used by both schemes, but the ordering is different.

 56 #   For our purpose, we adapt the sixteen bit ordering.

 57 

 58 # We create a hash table which maps each numeral to its number.

 59 

 60 %rad050 = map( ($_ => $i++), split // ) ;

 61 

 62 #   NOTE: These schemes (both of them) are better known to systems

 63 #   programmers as Radix 50. Why Radix 50, not Radix 40? Because 50

 64 #   (octal) = 40 (decimal). Ask a silly question, get a silly

 65 #   answer.

 66 

 67 # We read input from a literal string, and transform it to valid

 68 # input.

 69 

 70 $_ = "Nothing sucks like a VAX." ;

 71 tr/[a-z]/[A-Z]/ ;                 # convert lower case to UPPER CASE

 72 eval "tr/$numerals//cd" ;         # delete any illegal character

 73 $_ .= '  ' ;                      # pad the last number with space

 74 

 75 # We create an accumulator to hold intermediate values during

 76 # interpretation, a place counter to keep track of what place of the

 77 # quadragesimal number we're on, and a string to hold the result.

 78 

 79 $accum = 0 ;

 80 $place = 0 ;

 81 $output = '' ;

 82 

 83 # We consider each numeral in turn from left to right.

 84 

 85 foreach( split // ) {

 86 

 87   # As a failsafe, we assert that the current numeral can be

 88   # interpreted quadragesimally. If not, we construct an identifying

 89   # error message and stop.

 90 

 91   index( $numerals, $_ ) >= 0

 92     or

 93   die "$0: current numeral: "

 94   . ( /^[[:graph:]]$/ ? $_ : sprintf("<%#o>",ord($_)))

 95   . "\nILLEGAL FILE NAME\n" ;

 96 

 97   # We shift the accumulated value left one quadragesimal place to

 98   # make room for the value corresponding to the current numeral,

 99   # taken from the hash table.

100 

101   $accum = $accum * 050 + $rad050{$_} ;

102 

103   # If the place counter tells us the number is complete, we write

104   # it in octal with a space separator, and reset the accumulator

105   # and the place counter.

106 

107   if ( $place++ == 2 ) {

108     $output .= sprintf "%06o ", $accum ;

109     $accum = 0 ;

110     $place = 0 ;

111   }

112 

113 }

114 

115 # At the end, we type the line of output.

116 

117 print $output, "\n" ;

118 

119 # HISTORICAL NOTE: Systems programmers used quadragesimal (Radix 50)

120 # numbers to economize on memory needed to store text: for example,

121 # file names in the disk index. Consider the file name "NONAME".

122 # Storing it as a string of six ASCII codes would cost forty-eight

123 # bits:

124 #

125 #   N        O        N        A        M        E

126 #   01001110 01001111 01001110 01000001 01001101 00100101

127 #

128 # But storing it as a string of two three-digit quadragecimal

129 # numbers would cost sixteen fewer bits:

130 #

131 #   NON               AME

132 #   01011001 11100110 00001000 01001101

133 #

134 # Economy was traded for convenience. File names were limited to the

135 # repertoire of forty quadragesimal numerals. And conversions to and

136 # from quadragesimal were arcane, despite the availability of tools

137 # in the system library. For example, here's how the PDP-11 RSTS/E

138 # systems programmer could store a file name as a quadragesimal

139 # number with this technique, saving sixteen bits of memory:

140 #

141 # 1000    T$ = "NONAME"                                     ! ASCII

142 # 1010    T$ = MID(SYS(CHR$(6%) + CHR$(-10%) + T$), 7%, 4%) ! RAD50

143 #

144 # And here's how the programmer could recover the file name as text:

145 #

146 # 2000    CHANGE T$ TO T%

147 # 2010    T$ = RAD$(      T%(0%)

148 #                 + SWAP%(T%(1%))

149 #            + RAD$(      T%(2%)

150 #                 + SWAP%(T%(3%))

151 #

152 # Or:

153 #

154 # 2000    T$ = RAD$(      ASCII(MID(T$,0%,1%))

155 #                 + SWAP%(ASCII(MID(T$,1%,1%))))

156 #            + RAD$(      ASCII(MID(T$,2%,1%))

157 #                 + SWAP%(ASCII(MID(T$,3%,1%))))

158 

159 # vim:set sw=2 sts=2 tw=68 : Instructions for Vim, the text editor.