Introduction. The \.{TFtoPL utility program converts \TeX\ font metric (“\.{TFM”) files into equivalent property-list (“\.{PL”) files. It also makes a thorough check of the given \.{TFM file, using essentially the same algorithm as \TeX. Thus if \TeX\ complains that a \.{TFM file is “bad,” this program will pinpoint the source or sources of badness. A \.{PL file output by this program can be edited with a normal text editor, and the result can be converted back to \.{TFM format using the companion program \.{PLtoTF.

The first \.{TFtoPL program was designed by Leo Guibas in the summer of 1978. Contributions by Frank Liang, Doug Wyatt, and Lyle Ramshaw also had a significant effect on the evolution of the present code.

Extensions for an enhanced ligature mechanism were added by the author in 1989.

The |banner| string defined here should be changed whenever \.{TFtoPL gets modified.

@d banner==’This is TFtoPL, Version 3.1’ {printed when the program starts

 This program is written entirely in standard \PASCAL, except that it occasionally has lower case letters in strings that are output. Such letters can be converted to upper case if necessary. The input is read from |tfm_file|, and the output is written on |pl_file|; error messages and other remarks are written on the |output| file, which the user may choose to assign to the terminal if the system permits it. ŝystem dependencies@>

The term |print| is used instead of |write| when this program writes on the |output| file, so that all such output can be easily deflected.

@d print(#)==write(#) @d print_ln(#)==write_ln(#)

@p program TFtoPL(!tfm_file,!pl_file,!output); label @<Labels in the outer block@> const @<Constants in the outer block@> type @<Types in the outer block@> var @<Globals in the outer block@> procedure initialize; {this procedure gets things started properly begin print_ln(banner); @<Set initial values@> end;

 If the program has to stop prematurely, it goes to the ‘|final_end|’.

@d final_end=9999 {label for the end of it all

@<Labels...@>=final_end;

 The following parameters can be changed at compile time to extend or reduce \.{TFtoPL’s capacity.

@<Constants...@>= !tfm_size=30000; {maximum length of |tfm| data, in bytes !lig_size=5000; {maximum length of |lig_kern| program, in words !hash_size=5003; {preferably a prime number, a bit larger than the number of character pairs in lig/kern steps

 Here are some macros for common programming idioms.

@d incr(#) == #:=#+1 {increase a variable by unity @d decr(#) == #:=#-1 {decrease a variable by unity @d do_nothing == {empty statement

Font metric data. The idea behind \.{TFM files is that typesetting routines like \TeX\ need a compact way to store the relevant information about several dozen fonts, and computer centers need a compact way to store the relevant information about several hundred fonts. \.{TFM files are compact, and most of the information they contain is highly relevant, so they provide a solution to the problem.

The information in a \.{TFM file appears in a sequence of 8-bit bytes. Since the number of bytes is always a multiple of 4, we could also regard the file as a sequence of 32-bit words; but \TeX\ uses the byte interpretation, and so does \.{TFtoPL. Note that the bytes are considered to be unsigned numbers.

@<Glob...@>= !tfm_file:packed file of 0..255;

 On some systems you may have to do something special to read a packed file of bytes. For example, the following code didn’t work when it was first tried at Stanford, because packed files have to be opened with a special switch setting on the \PASCAL\ that was used. ŝystem dependencies@>

@<Set init...@>= reset(tfm_file);

 The first 24 bytes (6 words) of a \.{TFM file contain twelve 16-bit integers that give the lengths of the various subsequent portions of the file. These twelve integers are, in order: $$\vbox{\halign{\hfil#&$\null=\null$#\hfil\cr |!lf|&length of the entire file, in words;\cr |!lh|&length of the header data, in words;\cr |!bc|&smallest character code in the font;\cr |!ec|&largest character code in the font;\cr |!nw|&number of words in the width table;\cr |!nh|&number of words in the height table;\cr |!nd|&number of words in the depth table;\cr |!ni|&number of words in the italic correction table;\cr |!nl|&number of words in the lig/kern table;\cr |!nk|&number of words in the kern table;\cr |!ne|&number of words in the extensible character table;\cr |!np|&number of font parameter words.\cr$$ They are all nonnegative and less than $2^{15$. We must have |bc-1<=ec<=255|, |ne<=256|, and $$\hbox{|lf=6+lh+(ec-bc+1)+nw+nh+nd+ni+nl+nk+ne+np|.$$ Note that a font may contain as many as 256 characters (if |bc=0| and |ec=255|), and as few as 0 characters (if |bc=ec+1|).

Incidentally, when two or more 8-bit bytes are combined to form an integer of 16 or more bits, the most significant bytes appear first in the file. This is called BigEndian order.

@<Glob...@>= !lf,!lh,!bc,!ec,!nw,!nh,!nd,!ni,!nl,!nk,!ne,!np:0..7'7777; {subfile sizes

 The rest of the \.{TFM file may be regarded as a sequence of ten data arrays having the informal specification $$\def\arr$[#1]#2${\&{array $[#1]$ \&{of #2 \vbox{\halign{\hfil\\{#&$\,:\,$\arr#\hfil\cr header&|[0..lh-1]stuff|\cr char\_info&|[bc..ec]char_info_word|\cr width&|[0..nw-1]fix_word|\cr height&|[0..nh-1]fix_word|\cr depth&|[0..nd-1]fix_word|\cr italic&|[0..ni-1]fix_word|\cr lig\_kern&|[0..nl-1]lig_kern_command|\cr kern&|[0..nk-1]fix_word|\cr exten&|[0..ne-1]extensible_recipe|\cr param&|[1..np]fix_word|\cr$$ The most important data type used here is a |!fix_word|, which is a 32-bit representation of a binary fraction. A |fix_word| is a signed quantity, with the two’s complement of the entire word used to represent negation. Of the 32 bits in a |fix_word|, exactly 12 are to the left of the binary point; thus, the largest |fix_word| value is $2048-2^{-20$, and the smallest is $-2048$. We will see below, however, that all but one of the |fix_word| values will lie between $-16$ and $+16$.

 The first data array is a block of header information, which contains general facts about the font. The header must contain at least two words, and for \.{TFM files to be used with Xerox printing software it must contain at least 18 words, allocated as described below. When different kinds of devices need to be interfaced, it may be necessary to add further words to the header block.

\yskip\hang|header[0]| is a 32-bit check sum that \TeX\ will copy into the \.{DVI output file whenever it uses the font. Later on when the \.{DVI file is printed, possibly on another computer, the actual font that gets used is supposed to have a check sum that agrees with the one in the \.{TFM file used by \TeX. In this way, users will be warned about potential incompatibilities. (However, if the check sum is zero in either the font file or the \.{TFM file, no check is made.) The actual relation between this check sum and the rest of the \.{TFM file is not important; the check sum is simply an identification number with the property that incompatible fonts almost always have distinct check sums. ĉheck sum@>

\yskip\hang|header[1]| is a |fix_word| containing the design size of the font, in units of \TeX\ points (7227 \TeX\ points = 254 cm). This number must be at least 1.0; it is fairly arbitrary, but usually the design size is 10.0 for a “10 point” font, i.e., a font that was designed to look best at a 10-point size, whatever that really means. When a \TeX\ user asks for a font ‘\.{at $\delta$ \.{pt’, the effect is to override the design size and replace it by $\delta$, and to multiply the $x$ and~$y$ coordinates of the points in the font image by a factor of $\delta$ divided by the design size. {\sl All other dimensions in the\/\ \.{TFM file are |fix_word|\kern-1pt\ numbers in design-size units. Thus, for example, the value of |param[6]|, one \.{em or \.{\\quad, is often the |fix_word| value $2^{20=1.0$, since many fonts have a design size equal to one em. The other dimensions must be less than 16 design-size units in absolute value; thus, |header[1]| and |param[1]| are the only |fix_word| entries in the whole \.{TFM file whose first byte might be something besides 0 or 255. d^esign size@>

\yskip\hang|header[2..11]|, if present, contains 40 bytes that identify the character coding scheme. The first byte, which must be between 0 and 39, is the number of subsequent ASCII bytes actually relevant in this string, which is intended to specify what character-code-to-symbol convention is present in the font. Examples are \.{ASCII for standard ASCII, \.{TeX text for fonts like \.{cmr10 and \.{cmti9, \.{TeX math extension for \.{cmex10, \.{XEROX text for Xerox fonts, \.{GRAPHIC for special-purpose non-alphabetic fonts, \.{UNSPECIFIED for the default case when there is no information. Parentheses should not appear in this name. (Such a string is said to be in {\mc BCPL format.) ĉoding scheme@>

\yskip\hang|header[12..16]|, if present, contains 20 bytes that name the font family (e.g., \.{CMR or \.{HELVETICA), in {\mc BCPL format. This field is also known as the “font identifier.” f^amily name@> f^ont identifier@>

\yskip\hang|header[17]|, if present, contains a first byte called the |seven_bit_safe_flag|, then two bytes that are ignored, and a fourth byte called the |face|. If the value of the fourth byte is less than 18, it has the following interpretation as a “weight, slope, and expansion”: Add 0 or 2 or 4 (for medium or bold or light) to 0 or 1 (for roman or italic) to 0 or 6 or 12 (for regular or condensed or extended). For example, 13 is 0+1+12, so it represents medium italic extended. A three-letter code (e.g., \.{MIE) can be used for such |face| data.

\yskip\hang|header[18..@twhatever@>]| might also be present; the individual words are simply called |header[18]|, |header[19]|, etc., at the moment.

 Next comes the |char_info| array, which contains one |char_info_word| per character. Each |char_info_word| contains six fields packed into four bytes as follows.

\yskip\hang first byte: |width_index| (8 bits)\par \hang second byte: |height_index| (4 bits) times 16, plus |depth_index| (4~bits)\par \hang third byte: |italic_index| (6 bits) times 4, plus |tag| (2~bits)\par \hang fourth byte: |remainder| (8 bits)\par \yskip\noindent The actual width of a character is |width[width_index]|, in design-size units; this is a device for compressing information, since many characters have the same width. Since it is quite common for many characters to have the same height, depth, or italic correction, the \.{TFM format imposes a limit of 16 different heights, 16 different depths, and 64 different italic corrections.

Incidentally, the relation |width[0]=height[0]=depth[0]=italic[0]=0| should always hold, so that an index of zero implies a value of zero. The |width_index| should never be zero unless the character does not exist in the font, since a character is valid if and only if it lies between |bc| and |ec| and has a nonzero |width_index|.

 The |tag| field in a |char_info_word| has four values that explain how to interpret the |remainder| field.

\yskip\hang|tag=0| (|no_tag|) means that |remainder| is unused.\par \hang|tag=1| (|lig_tag|) means that this character has a ligature/kerning program starting at |lig_kern[remainder]|.\par \hang|tag=2| (|list_tag|) means that this character is part of a chain of characters of ascending sizes, and not the largest in the chain. The |remainder| field gives the character code of the next larger character.\par \hang|tag=3| (|ext_tag|) means that this character code represents an extensible character, i.e., a character that is built up of smaller pieces so that it can be made arbitrarily large. The pieces are specified in |exten[remainder]|.\par

@d no_tag=0 {vanilla character @d lig_tag=1 {character has a ligature/kerning program @d list_tag=2 {character has a successor in a charlist @d ext_tag=3 {character is extensible

 The |lig_kern| array contains instructions in a simple programming language that explains what to do for special letter pairs. Each word is a |lig_kern_command| of four bytes.

\yskip\hang first byte: |skip_byte|, indicates that this is the final program step if the byte is 128 or more, otherwise the next step is obtained by skipping this number of intervening steps.\par \hang second byte: |next_char|, “if |next_char| follows the current character, then perform the operation and stop, otherwise continue.”\par \hang third byte: |op_byte|, indicates a ligature step if less than~128, a kern step otherwise.\par \hang fourth byte: |remainder|.\par \yskip\noindent In a kern step, an additional space equal to |kern[256*(op_byte-128)+remainder]| is inserted between the current character and |next_char|. This amount is often negative, so that the characters are brought closer together by kerning; but it might be positive.

There are eight kinds of ligature steps, having |op_byte| codes $4a+2b+c$ where $0\le a\le b+c$ and $0\le b,c\le1$. The character whose code is |remainder| is inserted between the current character and |next_char|; then the current character is deleted if $b=0$, and |next_char| is deleted if $c=0$; then we pass over $a$~characters to reach the next current character (which may have a ligature/kerning program of its own).

Notice that if $a=0$ and $b=1$, the current character is unchanged; if $a=b$ and $c=1$, the current character is changed but the next character is unchanged. \.{TFtoPL will check to see that infinite loops are avoided.

If the very first instruction of the |lig_kern| array has |skip_byte=255|, the |next_char| byte is the so-called right boundary character of this font; the value of |next_char| need not lie between |bc| and~|ec|. If the very last instruction of the |lig_kern| array has |skip_byte=255|, there is a special ligature/kerning program for a left boundary character, beginning at location |256*op_byte+remainder|. The interpretation is that \TeX\ puts implicit boundary characters before and after each consecutive string of characters from the same font. These implicit characters do not appear in the output, but they can affect ligatures and kerning.

If the very first instruction of a character’s |lig_kern| program has |skip_byte>128|, the program actually begins in location |256*op_byte+remainder|. This feature allows access to large |lig_kern| arrays, because the first instruction must otherwise appear in a location |<=255|.

Any instruction with |skip_byte>128| in the |lig_kern| array must have |256*op_byte+remainder<nl|. If such an instruction is encountered during normal program execution, it denotes an unconditional halt; no ligature command is performed.

@d stop_flag=128 {value indicating ‘\.{STOP’ in a lig/kern program @d kern_flag=128 {op code for a kern step

 Extensible characters are specified by an |extensible_recipe|, which consists of four bytes called |top|, |mid|, |bot|, and |rep| (in this order). These bytes are the character codes of individual pieces used to build up a large symbol. If |top|, |mid|, or |bot| are zero, they are not present in the built-up result. For example, an extensible vertical line is like an extensible bracket, except that the top and bottom pieces are missing.

 The final portion of a \.{TFM file is the |param| array, which is another sequence of |fix_word| values.

\yskip\hang|param[1]=!slant| is the amount of italic slant, which is used to help position accents. For example, |slant=.25| means that when you go up one unit, you also go .25 units to the right. The |slant| is a pure number; it’s the only |fix_word| other than the design size itself that is not scaled by the design size.

\hang|param[2]=space| is the normal spacing between words in text. Note that character |" "| in the font need not have anything to do with blank spaces.

\hang|param[3]=space_stretch| is the amount of glue stretching between words.

\hang|param[4]=space_shrink| is the amount of glue shrinking between words.

\hang|param[5]=x_height| is the height of letters for which accents don’t have to be raised or lowered.

\hang|param[6]=quad| is the size of one em in the font.

\hang|param[7]=extra_space| is the amount added to |param[2]| at the ends of sentences.

When the character coding scheme is \.{TeX math symbols, the font is supposed to have 15 additional parameters called |num1|, |num2|, |num3|, |denom1|, |denom2|, |sup1|, |sup2|, |sup3|, |sub1|, |sub2|, |supdrop|, |subdrop|, |delim1|, |delim2|, and |axis_height|, respectively. When the character coding scheme is \.{TeX math extension, the font is supposed to have six additional parameters called |default_rule_thickness| and |big_op_spacing1| through |big_op_spacing5|.

 So that is what \.{TFM files hold. The next question is, “What about \.{PL files?” A complete answer to that question appears in the documentation of the companion program, \.{PLtoTF, so it will not be repeated here. Suffice it to say that a \.{PL file is an ordinary \PASCAL\ text file, and that the output of \.{TFtoPL uses only a subset of the possible constructions that might appear in a \.{PL file. Furthermore, hardly anybody really wants to look at the formal definition of \.{PL format, because it is almost self-explanatory when you see an example or two.

@<Glob...@>= !pl_file:text;

 @<Set init...@>= rewrite(pl_file);

Unpacked representation. The first thing \.{TFtoPL does is read the entire |tfm_file| into an array of bytes, |tfm[0..(4*lf-1)]|.

@<Types...@>= !byte=0..255; {unsigned eight-bit quantity !index=0..tfm_size; {address of a byte in |tfm|

 @<Glob...@>= !tfm:array [-1000..tfm_size] of byte; {the input data all goes here {the negative addresses avoid range checks for invalid characters

 The input may, of course, be all screwed up and not a \.{TFM file at all. So we begin cautiously.

@d abort(#)==begin print_ln(#); print_ln(’Sorry, but I can”t go on; are you sure this is a TFM?’); goto final_end; end

@<Read the whole input file@>= read(tfm_file,tfm[0]); if tfm[0]>127 then abort(’The first byte of the input file exceeds 127!’); .The first byte...@> if eof(tfm_file) then abort(’The input file is only one byte long!’); .The input...one byte long@> read(tfm_file,tfm[1]); lf:=tfm[0]*4'00+tfm[1]; if lf=0 then abort(’The file claims to have length zero, but that”s impossible!’); .The file claims...@> if 4*lf-1>tfm_size then abort(’The file is bigger than I can handle!’); .The file is bigger...@> for tfm_ptr:=2 to 4*lf-1 do begin if eof(tfm_file) then abort(’The file has fewer bytes than it claims!’); .The file has fewer bytes...@> read(tfm_file,tfm[tfm_ptr]); end; if not eof(tfm_file) then begin print_ln(’There”s some extra junk at the end of the TFM file,’); .There’s some extra junk...@> print_ln(’but I”ll proceed as if it weren”t there.’); end

 After the file has been read successfully, we look at the subfile sizes to see if they check out.

@d eval_two_bytes(#)==begin if tfm[tfm_ptr]>127 then abort(’One of the subfile sizes is negative!’); .One of the subfile sizes...@> #:=tfm[tfm_ptr]*4'00+tfm[tfm_ptr+1]; tfm_ptr:=tfm_ptr+2; end

@<Set subfile sizes |lh|, |bc|, \dots, |np|@>= begin tfm_ptr:=2; eval_two_bytes(lh); eval_two_bytes(bc); eval_two_bytes(ec); eval_two_bytes(nw); eval_two_bytes(nh); eval_two_bytes(nd); eval_two_bytes(ni); eval_two_bytes(nl); eval_two_bytes(nk); eval_two_bytes(ne); eval_two_bytes(np); if lh<2 then abort(’The header length is only ’,lh:1,’!’); .The header length...@> if nl>4*lig_size then abort(’The lig/kern program is longer than I can handle!’); .The lig/kern program...@> if (bc>ec+1)or(ec>255) then abort(’The character code range ’, .The character code range...@> bc:1,’..’,ec:1,’is illegal!’); if (nw=0)or(nh=0)or(nd=0)or(ni=0) then abort(’Incomplete subfiles for character dimensions!’); .Incomplete subfiles...@> if ne>256 then abort(’There are ’,ne:1,’ extensible recipes!’); .There are ... recipes@> if lf<>6+lh+(ec-bc+1)+nw+nh+nd+ni+nl+nk+ne+np then abort(’Subfile sizes don”t add up to the stated total!’); .Subfile sizes don’t add up...@> end

 Once the input data successfully passes these basic checks, \.{TFtoPL believes that it is a \.{TFM file, and the conversion to \.{PL format will take place. Access to the various subfiles is facilitated by computing the following base addresses. For example, the |char_info| for character |c| will start in location |4*(char_base+c)| of the |tfm| array.

@<Globals...@>= !char_base,!width_base,!height_base,!depth_base,!italic_base, !lig_kern_base,!kern_base,!exten_base,!param_base:integer; {base addresses for the subfiles

 @<Compute the base addresses@>= begin char_base:=6+lh-bc; width_base:=char_base+ec+1; height_base:=width_base+nw; depth_base:=height_base+nh; italic_base:=depth_base+nd; lig_kern_base:=italic_base+ni; kern_base:=lig_kern_base+nl; exten_base:=kern_base+nk; param_base:=exten_base+ne-1; end

 Of course we want to define macros that suppress the detail of how the font information is actually encoded. Each word will be referred to by the |tfm| index of its first byte. For example, if |c| is a character code between |bc| and |ec|, then |tfm[char_info(c)]| will be the first byte of its |char_info|, i.e., the |width_index|; furthermore |width(c)| will point to the |fix_word| for |c|’s width.

@d check_sum=24 @d design_size=check_sum+4 @d scheme=design_size+4 @d family=scheme+40 @d random_word=family+20 @d char_info(#)==4*(char_base+#) @d width_index(#)==tfm[char_info(#)] @d nonexistent(#)==((#<bc)or(#>ec)or(width_index(#)=0)) @d height_index(#)==(tfm[char_info(#)+1] div 16) @d depth_index(#)==(tfm[char_info(#)+1] mod 16) @d italic_index(#)==(tfm[char_info(#)+2] div 4) @d tag(#)==(tfm[char_info(#)+2] mod 4) @d reset_tag(#)==tfm[char_info(#)+2]:=4*italic_index(#)+no_tag @d remainder(#)==tfm[char_info(#)+3] @d width(#)==4*(width_base+width_index(#)) @d height(#)==4*(height_base+height_index(#)) @d depth(#)==4*(depth_base+depth_index(#)) @d italic(#)==4*(italic_base+italic_index(#)) @d exten(#)==4*(exten_base+remainder(#)) @d lig_step(#)==4*(lig_kern_base+(#)) @d kern(#)==4*(kern_base+#) {here \#\ is an index, not a character @d param(#)==4*(param_base+#) {likewise

 One of the things we would like to do is take cognizance of fonts whose character coding scheme is \.{TeX math symbols or \.{TeX math extension; we will set the |font_type| variable to one of the three choices |vanilla|, |mathsy|, or |mathex|.

@d vanilla=0 {not a special scheme @d mathsy=1 {\.{TeX math symbols scheme @d mathex=2 {\.{TeX math extension scheme

@<Glob...@>= !font_type:vanilla..mathex; {is this font special?

Basic output subroutines. Let us now define some procedures that will reduce the rest of \.{TFtoPL’s work to a triviality.

First of all, it is convenient to have an abbreviation for output to the \.{PL file:

@d out(#)==write(pl_file,#)

 In order to stick to standard \PASCAL, we use three strings called |ASCII_04|, |ASCII_10|, and |ASCII_14|, in terms of which we can do the appropriate conversion of ASCII codes. Three other little strings are used to produce |face| codes like \.{MIE.

@<Glob...@>= !ASCII_04,!ASCII_10,!ASCII_14: packed array [1..32] of char; {strings for output in the user’s external character set !MBL_string,!RI_string,!RCE_string:packed array [1..3] of char; {handy string constants for |face| codes

 @<Set init...@>= ASCII_04:=’ !"#$%&”()*+,-./0123456789:;<=>?’; ASCII_10:=’@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_’; ASCII_14:=’‘abcdefghijklmnopqrstuvwxyz{|~ ’; MBL_string:=’MBL’; RI_string:=’RI ’; RCE_string:=’RCE’;

 The array |dig| will hold a sequence of digits to be output.

@<Glob...@>= !dig:array[0..11] of 0..9;

 Here, in fact, are two procedures that output |dig[j-1]|$\,\ldots\,$|dig[0]|, given $j>0$.

@p procedure out_digs(j:integer); {outputs |j| digits begin repeat decr(j); out(dig[j]:1); until j=0; end; @# procedure print_digs(j:integer); {prints |j| digits begin repeat decr(j); print(dig[j]:1); until j=0; end;

 The |print_octal| procedure indicates how |print_digs| can be used. Since this procedure is used only to print character codes, it always produces three digits.

@p procedure print_octal(c:byte); {prints octal value of |c| var j:0..2; {index into |dig| begin print(””); {an apostrophe indicates the octal notation for j:=0 to 2 do begin dig[j]:=c mod 8; c:=c div 8; end; print_digs(3); end;

 A \.{PL file has nested parentheses, and we want to format the output so that its structure is clear. The |level| variable keeps track of the depth of nesting.

@<Glob...@>= !level:0..5;

 @<Set init...@>= level:=0;

 Three simple procedures suffice to produce the desired structure in the output.

@p procedure out_ln; {finishes one line, indents the next var l:0..5; begin write_ln(pl_file); for l:=1 to level do out(’ ’); end; @# procedure left; {outputs a left parenthesis begin incr(level); out(’(’); end; @# procedure right; {outputs a right parenthesis and finishes a line begin decr(level); out(’)’); out_ln; end;

 The value associated with a property can be output in a variety of ways. For example, we might want to output a {\mc BCPL string that begins in |tfm[k]|:

@p procedure out_BCPL(!k:index); {outputs a string, preceded by a blank space var l:0..39; {the number of bytes remaining begin out(’ ’); l:=tfm[k]; while l>0 do begin incr(k); decr(l); case tfm[k] div 4'0 of 1: out(ASCII_04[1+(tfm[k] mod 4'0)]); 2: out(ASCII_10[1+(tfm[k] mod 4'0)]); 3: out(ASCII_14[1+(tfm[k] mod 4'0)]); end; end; end;

 The property value might also be a sequence of |l| bytes, beginning in |tfm[k]|, that we would like to output in octal notation. The following procedure assumes that |l<=4|, but larger values of |l| could be handled easily by enlarging the |dig| array and increasing the upper bounds on |b| and |j|.

@p procedure out_octal(!k,!l:index); {outputs |l| bytes in octal var a:0..1'777; {accumulator for bits not yet output !b:0..32; {the number of significant bits in |a| !j:0..11; {the number of digits of output begin out(’ O ’); {specify octal format a:=0; b:=0; j:=0; while l>0 do @<Reduce \(1)|l| by one, preserving the invariants@>; while (a>0)or(j=0) do begin dig[j]:=a mod 8; a:=a div 8; incr(j); end; out_digs(j); end;

 @<Reduce \(1)|l|...@>= begin decr(l); if tfm[k+l]<>0 then begin while b>2 do begin dig[j]:=a mod 8; a:=a div 8; b:=b-3; incr(j); end; case b of 0: a:=tfm[k+l]; 1:a:=a+2*tfm[k+l]; 2:a:=a+4*tfm[k+l]; end; end; b:=b+8; end

 The property value may be a character, which is output in octal unless it is a letter or a digit. This procedure is the only place where a lowercase letter will be output to the \.{PL file. ŝystem dependencies@>

@p procedure out_char(!c:byte); {outputs a character begin if font_type>vanilla then begin tfm[0]:=c; out_octal(0,1) end else if (c>="0")and(c<="9") then out(’ C ’,c-"0":1) else if (c>="A")and(c<="Z") then out(’ C ’,ASCII_10[c-"A"+2]) else if (c>="a")and(c<="z") then out(’ C ’,ASCII_14[c-"a"+2]) else begin tfm[0]:=c; out_octal(0,1); end; end;

 The property value might be a “face” byte, which is output in the curious code mentioned earlier, provided that it is less than 18.

@p procedure out_face(!k:index); {outputs a |face| var s:0..1; {the slope !b:0..8; {the weight and expansion begin if tfm[k]>=18 then out_octal(k,1) else begin out(’ F ’); {specify face-code format s:=tfm[k] mod 2; b:=tfm[k] div 2; out(MBL_string[1+(b mod 3)]); out(RI_string[1+s]); out(RCE_string[1+(b div 3)]); end; end;

 And finally, the value might be a |fix_word|, which is output in decimal notation with just enough decimal places for \.{PLtoTF to recover every bit of the given |fix_word|.

All of the numbers involved in the intermediate calculations of this procedure will be nonnegative and less than $10\cdot2^{24$.

@p procedure out_fix(!k:index); {outputs a |fix_word| var a:0..7'777; {accumulator for the integer part !f:integer; {accumulator for the fraction part !j:0..12; {index into |dig| !delta:integer; {amount if allowable inaccuracy begin out(’ R ’); {specify real format a:=(tfm[k]*16)+(tfm[k+1] div 16); f:=((tfm[k+1] mod 16)*4'00+tfm[k+2])*4'00+tfm[k+3]; if a>3'777 then @<Reduce \(2)negative to positive@>; @<Output the integer part, |a|, in decimal notation@>; @<Output the fraction part, $|f|/2^{20$, in decimal notation@>; end;

 The following code outputs at least one digit even if |a=0|.

@<Output the integer...@>= begin j:=0; repeat dig[j]:=a mod 10; a:=a div 10; incr(j); until a=0; out_digs(j); end

 And the following code outputs at least one digit to the right of the decimal point.

@<Output the fraction...@>= begin out(’.’); f:=10*f+5; delta:=10; repeat if delta>4'000000 then f:=f+2'000000-(delta div 2); out(f div 4'000000:1); f:=10*(f mod 4'000000); delta:=delta*10; until f<=delta; end;

 @<Reduce \(2)negative to positive@>= begin out(’-’); a:=1'0000-a; if f>0 then begin f:=4'000000-f; decr(a); end; end

Doing it. \TeX\ checks the information of a \.{TFM file for validity as the file is being read in, so that no further checks will be needed when typesetting is going on. And when it finds something wrong, it justs calls the file “bad,” without identifying the nature of the problem, since \.{TFM files are supposed to be good almost all of the time.

Of course, a bad file shows up every now and again, and that’s where \.{TFtoPL comes in. This program wants to catch at least as many errors as \TeX\ does, and to give informative error messages besides. All of the errors are corrected, so that the \.{PL output will be correct (unless, of course, the \.{TFM file was so loused up that no attempt is being made to fathom it).

 Just before each character is processed, its code is printed in octal notation. Up to eight such codes appear on a line; so we have a variable to keep track of how many are currently there. We also keep track of whether or not any errors have had to be corrected.

@<Glob...@>= !chars_on_line:0..8; {the number of characters printed on the current line !perfect:boolean; {was the file free of errors?

 @<Set init...@>= chars_on_line:=0; perfect:=true; {innocent until proved guilty

 Error messages are given with the help of the |bad| and |range_error| and |bad_char| macros:

@d bad(#)==begin perfect:=false; if chars_on_line>0 then print_ln(’ ’); chars_on_line:=0; print_ln(’Bad TFM file: ’,#); end .Bad TFM file@> @d range_error(#)==begin perfect:=false; print_ln(’ ’); print(#,’ index for character ’); print_octal(c); print_ln(’ is too large;’); print_ln(’so I reset it to zero.’); end @d bad_char_tail(#)==print_octal(#); print_ln(’.’); end @d bad_char(#)==begin perfect:=false; if chars_on_line>0 then print_ln(’ ’); chars_on_line:=0; print(’Bad TFM file: ’,#,’ nonexistent character ’); bad_char_tail @d correct_bad_char_tail(#)==print_octal(tfm[#]); print_ln(’.’); tfm[#]:=bc; end @d correct_bad_char(#)== begin perfect:=false; if chars_on_line>0 then print_ln(’ ’); chars_on_line:=0; print(’Bad TFM file: ’,#,’ nonexistent character ’); correct_bad_char_tail

@<Glob...@>= !i:0..7'7777; {an index to words of a subfile !c:0..256; {a random character !d:0..3; {byte number in a word !k:index; {a random index !r:0..65535; {a random two-byte value !count:0..127; {for when we need to enumerate a small set

 There are a lot of simple things to do, and they have to be done one at a time, so we might as well get down to business. The first things that \.{TFtoPL will put into the \.{PL file appear in the header part.

@<Do the header@>= begin font_type:=vanilla; if lh>=12 then begin @<Set the true |font_type|@>; if lh>=17 then begin @<Output the family name@>; if lh>=18 then @<Output the rest of the header@>; end; @<Output the character coding scheme@>; end; @<Output the design size@>; @<Output the check sum@>; @<Output the |seven_bit_safe_flag|@>; end

 @<Output the check sum@>= left; out(’CHECKSUM’); out_octal(check_sum,4); right

 Incorrect design sizes are changed to 10 points.

@d bad_design(#)==begin bad(’Design size ’,#,’!’); .Design size wrong@> print_ln(’I”ve set it to 10 points.’); out(’ D 10’); end

 @<Output the design size@>= left; out(’DESIGNSIZE’); if tfm[design_size]>127 then bad_design(’negative’) else if (tfm[design_size]=0)and(tfm[design_size+1]<16) then bad_design(’too small’) else out_fix(design_size); right; out(’(COMMENT DESIGNSIZE IS IN POINTS)’); out_ln; out(’(COMMENT OTHER SIZES ARE MULTIPLES OF DESIGNSIZE)’); out_ln .DESIGNSIZE IS IN POINTS@>

 Since we have to check two different {\mc BCPL strings for validity, we might as well write a subroutine to make the check.

@p procedure check_BCPL(!k,!l:index); {checks a string of length |<l| var j:index; {runs through the string !c:byte; {character being checked begin if tfm[k]>=l then begin bad(’String is too long; I”ve shortened it drastically.’); .String is too long...@> tfm[k]:=1; end; for j:=k+1 to k+tfm[k] do begin c:=tfm[j]; if (c="(")or(c=")") then begin bad(’Parenthesis in string has been changed to slash.’); .Parenthesis...changed to slash@> tfm[j]:="/"; end else if (c<" ")or(c>"~") then begin bad(’Nonstandard ASCII code has been blotted out.’); .Nonstandard ASCII code...@> tfm[j]:="?"; end else if (c>="a")and(c<="z") then tfm[j]:=c+"A"-"a"; {upper-casify letters end; end;

 The |font_type| starts out |vanilla|; possibly we need to reset it.

@<Set the true |font_type|@>= begin check_BCPL(scheme,40); if (tfm[scheme]>=11)and(tfm[scheme+1]="T")and (tfm[scheme+2]="E")and(tfm[scheme+3]="X")and (tfm[scheme+4]=" ")and(tfm[scheme+5]="M")and (tfm[scheme+6]="A")and(tfm[scheme+7]="T")and (tfm[scheme+8]="H")and(tfm[scheme+9]=" ") then begin if (tfm[scheme+10]="S")and(tfm[scheme+11]="Y") then font_type:=mathsy else if (tfm[scheme+10]="E")and(tfm[scheme+11]="X") then font_type:=mathex; end; end

 @<Output the character coding scheme@>= left; out(’CODINGSCHEME’); out_BCPL(scheme); right

 @<Output the family name@>= left; out(’FAMILY’); check_BCPL(family,20); out_BCPL(family); right

 @<Output the rest of the header@>= begin left; out(’FACE’); out_face(random_word+3); right; for i:=18 to lh-1 do begin left; out(’HEADER D ’,i:1); out_octal(check_sum+4*i,4,); right; end; end

 This program does not check to see if the |seven_bit_safe_flag| has the correct setting, i.e., if it really reflects the seven-bit-safety of the \.{TFM file; the stated value is merely put into the \.{PL file. The \.{PLtoTF program will store a correct value and give a warning message if a file falsely claims to be safe.

@<Output the |seven_bit_safe_flag|@>= if (lh>17) and (tfm[random_word]>127) then begin left; out(’SEVENBITSAFEFLAG TRUE’); right; end

 The next thing to take care of is the list of parameters.

@<Do the parameters@>= if np>0 then begin left; out(’FONTDIMEN’); out_ln; for i:=1 to np do @<Check and output the $i$th parameter@>; right; end; @<Check to see if |np| is complete for this font type@>;

 @<Check to see if |np|...@>= if (font_type=mathsy)and(np<>22) then print_ln(’Unusual number of fontdimen parameters for a math symbols font (’, .Unusual number of fontdimen...@> np:1,’ not 22).’) else if (font_type=mathex)and(np<>13) then print_ln(’Unusual number of fontdimen parameters for an extension font (’, np:1,’ not 13).’)

 All |fix_word| values except the design size and the first parameter will be checked to make sure that they are less than 16.0 in magnitude, using the |check_fix| macro:

@d check_fix_tail(#)==bad(#,’ ’,i:1,’ is too big;’); print_ln(’I have set it to zero.’); end @d check_fix(#)==if (tfm[#]>0)and(tfm[#]<255) then begin tfm[#]:=0; tfm[(#)+1]:=0; tfm[(#)+2]:=0; tfm[(#)+3]:=0; check_fix_tail

@<Check and output the $i$th parameter@>= begin left; if i=1 then out(’SLANT’) {this parameter is not checked else begin check_fix(param(i))(’Parameter’); .Parameter n is too big@> @<Output the name of parameter $i$@>; end; out_fix(param(i)); right; end

 @<Output the name...@>= if i<=7 then case i of 2:out(’SPACE’);@+3:out(’STRETCH’);@+4:out(’SHRINK’); 5:out(’XHEIGHT’);@+6:out(’QUAD’);@+7:out(’EXTRASPACE’)@+end else if (i<=22)and(font_type=mathsy) then case i of 8:out(’NUM1’);@+9:out(’NUM2’);@+10:out(’NUM3’); 11:out(’DENOM1’);@+12:out(’DENOM2’); 13:out(’SUP1’);@+14:out(’SUP2’);@+15:out(’SUP3’); 16:out(’SUB1’);@+17:out(’SUB2’); 18:out(’SUPDROP’);@+19:out(’SUBDROP’); 20:out(’DELIM1’);@+21:out(’DELIM2’); 22:out(’AXISHEIGHT’)@+end else if (i<=13)and(font_type=mathex) then if i=8 then out(’DEFAULTRULETHICKNESS’) else out(’BIGOPSPACING’,i-8:1) else out(’PARAMETER D ’,i:1)

 We need to check the range of all the remaining |fix_word| values, and to make sure that |width[0]=0|, etc.

@d nonzero_fix(#)==(tfm[#]>0)or(tfm[#+1]>0)or(tfm[#+2]>0)or(tfm[#+3]>0)

@<Check the |fix_word| entries@>= if nonzero_fix(4*width_base) then bad(’width[0] should be zero.’); .should be zero@> if nonzero_fix(4*height_base) then bad(’height[0] should be zero.’); if nonzero_fix(4*depth_base) then bad(’depth[0] should be zero.’); if nonzero_fix(4*italic_base) then bad(’italic[0] should be zero.’); for i:=0 to nw-1 do check_fix(4*(width_base+i))(’Width’); .Width n is too big@> for i:=0 to nh-1 do check_fix(4*(height_base+i))(’Height’); .Height n is too big@> for i:=0 to nd-1 do check_fix(4*(depth_base+i))(’Depth’); .Depth n is too big@> for i:=0 to ni-1 do check_fix(4*(italic_base+i))(’Italic correction’); .Italic correction n is too big@> if nk>0 then for i:=0 to nk-1 do check_fix(kern(i))(’Kern’); .Kern n is too big@>

 The ligature/kerning program comes next. Before we can put it out in \.{PL format, we need to make a table of “labels” that will be inserted into the program. For each character |c| whose |tag| is |lig_tag| and whose starting address is |r|, we will store the pair |(c,r)| in the |label_table| array. If there’s a boundary-char program starting at~|r|, we also store the pair |(256,r)|. This array is sorted by its second components, using the simple method of straight insertion.

@<Glob...@>= !label_table:array[0..258] of record@t@>!cc:0..256;!rr:0..lig_size;end; !label_ptr: 0..257; {the largest entry in |label_table| !sort_ptr:0..257; {index into |label_table| !boundary_char:0..256; {boundary character, or 256 if none !bchar_label:0..7'7777; {beginning of boundary character program

 @<Set init...@>= boundary_char:=256; bchar_label:=7'7777; label_ptr:=0; label_table[0].rr:=0; {a sentinel appears at the bottom

 We’ll also identify and remove inaccessible program steps, using the |activity| array.

@d unreachable=0 {a program step not known to be reachable @d pass_through=1 {a program step passed through on initialization @d accessible=2 {a program step that can be relevant

@<Glob...@>= !activity:array[0..lig_size] of unreachable..accessible; !ai,!acti:0..lig_size; {indices into |activity|

 @<Do the ligatures and kerns@>= if nl>0 then begin for ai:=0 to nl-1 do activity[ai]:=unreachable; @<Check for a boundary char@>; end; @<Build the label table@>; if nl>0 then begin left; out(’LIGTABLE’); out_ln; @<Compute the |activity| array@>; @<Output and correct the ligature/kern program@>; right; @<Check for ligature cycles@>; end

 We build the label table even when |nl=0|, because this catches errors that would not otherwise be detected.

@<Build...@>= for c:=bc to ec do if tag(c)=lig_tag then begin r:=remainder(c); if r<nl then begin if tfm[lig_step(r)]>stop_flag then begin r:=256*tfm[lig_step(r)+2]+tfm[lig_step(r)+3]; if r<nl then if activity[remainder(c)]=unreachable then activity[remainder(c)]:=pass_through; end; end; if r>=nl then begin perfect:=false; print_ln(’ ’); print(’Ligature/kern starting index for character ’); print_octal(c); print_ln(’ is too large;’); print_ln(’so I removed it.’); reset_tag(c); .Ligature/kern starting index...@> end else @<Insert |(c,r)| into |label_table|@>; end; label_table[label_ptr+1].rr:=lig_size; {put “infinite” sentinel at the end

 @<Insert |(c,r)|...@>= begin sort_ptr:=label_ptr; {there’s a hole at position |sort_ptr+1| while label_table[sort_ptr].rr>r do begin label_table[sort_ptr+1]:=label_table[sort_ptr]; decr(sort_ptr); {move the hole end; label_table[sort_ptr+1].cc:=c; label_table[sort_ptr+1].rr:=r; {fill the hole incr(label_ptr); activity[r]:=accessible; end

 @<Check for a bound...@>= if tfm[lig_step(0)]=255 then begin left; out(’BOUNDARYCHAR’); boundary_char:=tfm[lig_step(0)+1]; out_char(boundary_char); right; activity[0]:=pass_through; end; if tfm[lig_step(nl-1)]=255 then begin r:=256*tfm[lig_step(nl-1)+2]+tfm[lig_step(nl-1)+3]; if r>=nl then begin perfect:=false; print_ln(’ ’); print(’Ligature/kern starting index for boundarychar is too large;’); print_ln(’so I removed it.’); .Ligature/kern starting index...@> end else begin label_ptr:=1; label_table[1].cc:=256; label_table[1].rr:=r; bchar_label:=r; activity[r]:=accessible; end; activity[nl-1]:=pass_through; end

 @<Compute the |activity| array@>= for ai:=0 to nl-1 do if activity[ai]=accessible then begin r:=tfm[lig_step(ai)]; if r<stop_flag then begin r:=r+ai+1; if r>=nl then begin bad(’Ligature/kern step ’,ai:1,’ skips too far;’); .Lig...skips too far@> print_ln(’I made it stop.’); tfm[lig_step(ai)]:=stop_flag; end else activity[r]:=accessible; end; end

 We ignore |pass_through| items, which don’t need to be mentioned in the \.{PL file.

@<Output and correct the ligature...@>= sort_ptr:=1; {point to the next label that will be needed for acti:=0 to nl-1 do if activity[acti]<>pass_through then begin i:=acti; @<Take care of commenting out unreachable steps@>; @<Output any labels for step $i$@>; @<Output step $i$ of the ligature/kern program@>; end; if level=2 then right {the final step was unreachable

 @<Output any labels...@>= while i=label_table[sort_ptr].rr do begin left; out(’LABEL’); if label_table[sort_ptr].cc=256 then out(’ BOUNDARYCHAR’) else out_char(label_table[sort_ptr].cc); right; incr(sort_ptr); end

 @<Take care of commenting out...@>= if activity[i]=unreachable then begin if level=1 then begin left; out(’COMMENT THIS PART OF THE PROGRAM IS NEVER USED!’); out_ln; end end else if level=2 then right

 @<Output step $i$...@>= begin k:=lig_step(i); if tfm[k]>stop_flag then begin if 256*tfm[k+2]+tfm[k+3]>=nl then bad(’Ligature unconditional stop command address is too big.’); .Ligature unconditional stop...@> end else if tfm[k+2]>=kern_flag then @<Output a kern step@> else @<Output a ligature step@>; if tfm[k]>0 then if level=1 then @<Output either \.{SKIP or \.{STOP@>; end

 The \.{SKIP command is a bit tricky, because we will be omitting all inaccessible commands.

@<Output either...@>= begin if tfm[k]>=stop_flag then out(’(STOP)’) else begin count:=0; for ai:=i+1 to i+tfm[k] do if activity[ai]=accessible then incr(count); out(’(SKIP D ’,count:1,’)’); {possibly $count=0$, so who cares end; out_ln; end

 @<Output a kern step@>= begin if nonexistent(tfm[k+1]) then if tfm[k+1]<>boundary_char then correct_bad_char(’Kern step for’)(k+1); .Kern step for nonexistent...@> left; out(’KRN’); out_char(tfm[k+1]); r:=256*(tfm[k+2]-kern_flag)+tfm[k+3]; if r>=nk then begin bad(’Kern index too large.’); .Kern index too large@> out(’ R 0.0’); end else out_fix(kern(r)); right; end

 @<Output a ligature step@>= begin if nonexistent(tfm[k+1]) then if tfm[k+1]<>boundary_char then correct_bad_char(’Ligature step for’)(k+1); .Ligature step for nonexistent...@> if nonexistent(tfm[k+3]) then correct_bad_char(’Ligature step produces the’)(k+3); .Ligature step produces...@> left; r:=tfm[k+2]; if (r=4)or((r>7)and(r<>11)) then begin print_ln(’Ligature step with nonstandard code changed to LIG’); r:=0; tfm[k+2]:=0; end; if r mod 4>1 then out(’/’); out(’LIG’); if odd(r) then out(’/’); while r>3 do begin out(’>’); r:=r-4; end; out_char(tfm[k+1]); out_char(tfm[k+3]); right; end

 The last thing on \.{TFtoPL’s agenda is to go through the list of |char_info| and spew out the information about each individual character.

@<Do the characters@>= sort_ptr:=0; {this will suppress ‘\.{STOP’ lines in ligature comments for c:=bc to ec do if width_index(c)>0 then begin if chars_on_line=8 then begin print_ln(’ ’); chars_on_line:=1; end else begin if chars_on_line>0 then print(’ ’); incr(chars_on_line); end; print_octal(c); {progress report left; out(’CHARACTER’); out_char(c); out_ln; @<Output the character’s width@>; if height_index(c)>0 then @<Output the character’s height@>; if depth_index(c)>0 then @<Output the character’s depth@>; if italic_index(c)>0 then @<Output the italic correction@>; case tag(c) of no_tag: do_nothing; lig_tag: @<Output the applicable part of the ligature/kern program as a comment@>; list_tag: @<Output the character link unless there is a problem@>; ext_tag: @<Output an extensible character recipe@>; end; {there are no other cases right; end

 @<Output the character’s width@>= begin left; out(’CHARWD’); if width_index(c)>=nw then range_error(’Width’) else out_fix(width(c)); right; end

 @<Output the character’s height@>= if height_index(c)>=nh then range_error(’Height’) .Height index for char...@> else begin left; out(’CHARHT’); out_fix(height(c)); right; end

 @<Output the character’s depth@>= if depth_index(c)>=nd then range_error(’Depth’) .Depth index for char@> else begin left; out(’CHARDP’); out_fix(depth(c)); right; end

 @<Output the italic correction@>= if italic_index(c)>=ni then range_error(’Italic correction’) .Italic correction index for char...@> else begin left; out(’CHARIC’); out_fix(italic(c)); right; end

 @<Output the applicable part of the ligature...@>= begin left; out(’COMMENT’); out_ln; i:=remainder(c); r:=lig_step(i); if tfm[r]>stop_flag then i:=256*tfm[r+2]+tfm[r+3]; repeat @<Output step...@>; if tfm[k]>=stop_flag then i:=nl else i:=i+1+tfm[k]; until i>=nl; right; end

 We want to make sure that there is no cycle of characters linked together by |list_tag| entries, since such a cycle would get \TeX\ into an endless loop. If such a cycle exists, the routine here detects it when processing the largest character code in the cycle.

@<Output the character link unless there is a problem@>= begin r:=remainder(c); if nonexistent(r) then begin bad_char(’Character list link to’)(r); reset_tag(c); .Character list link...@> end else begin while (r<c)and(tag(r)=list_tag) do r:=remainder(r); if r=c then begin bad(’Cycle in a character list!’); .Cycle in a character list@> print(’Character ’); print_octal(c); print_ln(’ now ends the list.’); reset_tag(c); end else begin left; out(’NEXTLARGER’); out_char(remainder(c)); right; end; end; end

 @<Output an extensible character recipe@>= if remainder(c)>=ne then begin range_error(’Extensible’); reset_tag(c); .Extensible index for char@> end else begin left; out(’VARCHAR’); out_ln; @<Output the extensible pieces that exist@>; right; end

 @<Output the extensible pieces that...@>= for k:=0 to 3 do if (k=3)or(tfm[exten(c)+k]>0) then begin left; case k of 0:out(’TOP’);@+1:out(’MID’);@+2:out(’BOT’);@+3:out(’REP’)@+end; if nonexistent(tfm[exten(c)+k]) then out_char(c) else out_char(tfm[exten(c)+k]); right; end

 Some of the extensible recipes may not actually be used, but \TeX\ will complain about them anyway if they refer to nonexistent characters. Therefore \.{TFtoPL must check them too.

@<Check the extensible recipes@>= if ne>0 then for c:=0 to ne-1 do for d:=0 to 3 do begin k:=4*(exten_base+c)+d; if (tfm[k]>0)or(d=3) then begin if nonexistent(tfm[k]) then begin bad_char(’Extensible recipe involves the’)(tfm[k]); .Extensible recipe involves...@> if d<3 then tfm[k]:=0; end; end; end

Checking for ligature loops. We have programmed almost everything but the most interesting calculation of all, which has been saved for last as a special treat. \TeX’s extended ligature mechanism allows unwary users to specify sequences of ligature replacements that never terminate. For example, the pair of commands $$\.{(/LIG $x$ $y$) (/LIG $y$ $x$)$$ alternately replaces character $x$ by character $y$ and vice versa. A similar loop occurs if \.{(LIG/ $z$ $y$) occurs in the program for $x$ and \.{(LIG/ $z$ $x$) occurs in the program for $y$.

More complicated loops are also possible. For example, suppose the ligature programs for $x$ and $y$ are $$\vcenter{\halign{#\hfil\cr \.{(LABEL $x$)(/LIG/ $z$ $w$)(/LIG/> $w$ $y$) \dots,\cr \.{(LABEL $y$)(LIG $w$ $x$) \dots;\cr$$ then the adjacent characters $xz$ change to $xwz$, $xywz$, $xxz$, $xxwz$, \dots, ad infinitum.

 To detect such loops, \.{TFtoPL attempts to evaluate the function $f(x,y)$ for all character pairs $x$ and~$y$, where $f$ is defined as follows: If the current character is $x$ and the next character is $y$, we say the “cursor” is between $x$ and $y$; when the cursor first moves past $y$, the character immediately to its left is $f(x,y)$. This function is defined if and only if no infinite loop is generated when the cursor is between $x$ and~$y$.

The function $f(x,y)$ can be defined recursively. It turns out that all pairs $(x,y)$ belong to one of five classes. The simplest class has $f(x,y)=y$; this happens if there’s no ligature between $x$ and $y$, or in the cases \.{LIG/> and \.{/LIG/>>. Another simple class arises when there’s a \.{LIG or \.{/LIG> between $x$ and~$y$, generating the character~$z$; then $f(x,y)=z$. Otherwise we always have $f(x,y)$ equal to either $f(x,z)$ or $f(z,y)$ or $f(f(x,z),y)$, where $z$ is the inserted ligature character.

The first two of these classes can be merged; we can also consider $(x,y)$ to belong to the simple class when $f(x,y)$ has been evaluated. For technical reasons we allow $x$ to be 256 (for the boundary character at the left) or 257 (in cases when an error has been detected).

For each pair $(x,y)$ having a ligature program step, we store $(x,y)$ in a hash table from which the values $z$ and $class$ can be read.

@d simple=0 {$f(x,y)=z$ @d left_z=1 {$f(x,y)=f(z,y)$ @d right_z=2 {$f(x,y)=f(x,z)$ @d both_z=3 {$f(x,y)=f(f(x,z),y)$ @d pending=4 {$f(x,y)$ is being evaluated

@<Glob...@>= !hash:array[0..hash_size] of 0..66048; {$256x+y+1$ for $x\le257$ and $y\le255$ !class:array[0..hash_size] of simple..pending; !lig_z:array[0..hash_size] of 0..257; !hash_ptr:0..hash_size; {the number of nonzero entries in |hash| !hash_list:array[0..hash_size] of 0..hash_size; {list of those nonzero entries !h,!hh:0..hash_size; {indices into the hash table !x_lig_cycle,!y_lig_cycle:0..256; {problematic ligature pair

 @<Check for ligature cycles@>= hash_ptr:=0; y_lig_cycle:=256; for hh:=0 to hash_size do hash[hh]:=0; {clear the hash table for c:=bc to ec do if tag(c)=lig_tag then begin i:=remainder(c); if tfm[lig_step(i)]>stop_flag then i:=256*tfm[lig_step(i)+2]+tfm[lig_step(i)+3]; @<Enter data for character $c$ starting at location |i| in the hash table@>; end; if bchar_label<nl then begin c:=256; i:=bchar_label; @<Enter data for character $c$ starting at location |i| in the hash table@>; end; if hash_ptr=hash_size then begin print_ln(’Sorry, I haven”t room for so many ligature/kern pairs!’); .Sorry, I haven’t room...@> goto final_end; end; for hh:=1 to hash_ptr do begin r:=hash_list[hh]; if class[r]>simple then {make sure $f$ is defined r:=f(r,(hash[r]-1)div 256,(hash[r]-1)mod 256); end; if y_lig_cycle<256 then begin print(’Infinite ligature loop starting with ’); .Infinite ligature loop...@> if x_lig_cycle=256 then print(’boundary’)@+else print_octal(x_lig_cycle); print(’ and ’); print_octal(y_lig_cycle); print_ln(’!’); out(’(INFINITE LIGATURE LOOP MUST BE BROKEN!)’); goto final_end; end

 @<Enter data for character $c$...@>= repeat hash_input; k:=tfm[lig_step(i)]; if k>=stop_flag then i:=nl else i:=i+1+k; until i>=nl

 We use an “ordered hash table” with linear probing, because such a table is efficient when the lookup of a random key tends to be unsuccessful.

@p procedure hash_input; {enter data for character |c| and command |i| label 30; {go here for a quick exit var !cc:simple..both_z; {class of data being entered !zz:0..255; {function value or ligature character being entered !y:0..255; {the character after the cursor !key:integer; {value to be stored in |hash| !t:integer; {temporary register for swapping begin if hash_ptr=hash_size then goto 30; @<Compute the command parameters |y|, |cc|, and |zz|@>; key:=256*c+y+1; h:=(1009*key) mod hash_size; while hash[h]>0 do begin if hash[h]<=key then begin if hash[h]=key then goto 30; {unused ligature command t:=hash[h]; hash[h]:=key; key:=t; {do ordered-hash-table insertion t:=class[h]; class[h]:=cc; cc:=t; {namely, do a swap t:=lig_z[h]; lig_z[h]:=zz; zz:=t; end; if h>0 then decr(h)@+else h:=hash_size; end; hash[h]:=key; class[h]:=cc; lig_z[h]:=zz; incr(hash_ptr); hash_list[hash_ptr]:=h; 30:end;

 We must store kern commands as well as ligature commands, because the former might make the latter inapplicable.

@<Compute the command param...@>= k:=lig_step(i); y:=tfm[k+1]; t:=tfm[k+2]; cc:=simple; zz:=tfm[k+3]; if t>=kern_flag then zz:=y else begin case t of 0,6:do_nothing; {\.{LIG,\.{/LIG> 5,11:zz:=y; {\.{LIG/>, \.{/LIG/>> 1,7:cc:=left_z; {\.{LIG/, \.{/LIG/> 2:cc:=right_z; {\.{/LIG 3:cc:=both_z; {\.{/LIG/ end; {there are no other cases end

 Evaluation of $f(x,y)$ is handled by two mutually recursive procedures. Kind of a neat algorithm, generalizing a depth-first search.

@p function f(!h,!x,!y:index):index; forward;@t\2@> {compute $f$ for arguments known to be in |hash[h]| function eval(!x,!y:index):index; {compute $f(x,y)$ with hashtable lookup var !key:integer; {value sought in hash table begin key:=256*x+y+1; h:=(1009*key) mod hash_size; while hash[h]>key do if h>0 then decr(h)@+else h:=hash_size; if hash[h]<key then eval:=y {not in ordered hash table else eval:=f(h,x,y); end;

 Pascal’s beastly convention for |forward| declarations prevents us from saying |function f(h,x,y:index):index| here.

@p function f; begin case class[h] of simple: do_nothing; left_z: begin class[h]:=pending; lig_z[h]:=eval(lig_z[h],y); class[h]:=simple; end; right_z: begin class[h]:=pending; lig_z[h]:=eval(x,lig_z[h]); class[h]:=simple; end; both_z: begin class[h]:=pending; lig_z[h]:=eval(eval(x,lig_z[h]),y); class[h]:=simple; end; pending: begin x_lig_cycle:=x; y_lig_cycle:=y; lig_z[h]:=257; class[h]:=simple; end; {the value 257 will break all cycles, since it’s not in |hash| end; {there are no other cases f:=lig_z[h]; end;

The main program. The routines sketched out so far need to be packaged into separate procedures, on some systems, since some \PASCAL\ compilers place a strict limit on the size of a routine. The packaging is done here in an attempt to avoid some system-dependent changes.

First comes the |organize| procedure, which reads the input data and gets ready for subsequent events. If something goes wrong, the routine returns |false|.

@p function organize:boolean; label final_end, 30; var tfm_ptr:index; {an index into |tfm| begin @<Read the whole input file@>; @<Set subfile sizes |lh|, |bc|, \dots, |np|@>; @<Compute the base addresses@>; organize:=true; goto 30; final_end: organize:=false; 30: end;

 Next we do the simple things.

@p procedure do_simple_things; var i:0..7'7777; {an index to words of a subfile begin @<Do the header@>; @<Do the parameters@>; @<Check the |fix_word| entries@> end;

 And then there’s a routine for individual characters.

@p procedure do_characters; var !c:byte; {character being done !k:index; {a random index !ai:0..lig_size; {index into |activity| begin @<Do the characters@>; end;

 Here is where \.{TFtoPL begins and ends. @p begin initialize; if not organize then goto final_end; do_simple_things; @<Do the ligatures and kerns@>; @<Check the extensible recipes@>; do_characters; print_ln(’.’); if level<>0 then print_ln(’This program isn”t working!’); .This program isn’t working@> if not perfect then out(’(COMMENT THE TFM FILE WAS BAD, SO THE DATA HAS BEEN CHANGED!)’); .THE TFM FILE WAS BAD...@> final_end:end.

System-dependent changes. This section should be replaced, if necessary, by changes to the program that are necessary to make \.{TFtoPL work at a particular installation. It is usually best to design your change file so that all changes to previous sections preserve the section numbering; then everybody’s version will be consistent with the printed program. More extensive changes, which introduce new sections, can be inserted here; then only the index itself will get a new section number. ŝystem dependencies@>

Index. Pointers to error messages appear here together with the section numbers where each ident\-i\-fier is used.

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