TFM Specification

TFM File Format

0. Foreword

The purpose of this page is to provide documentation for the TFM file format. Much of the content of this page was taken directly from the tftopl.web program, written by Donal Knuth (this explains the several references to the TFtoPL program; these can be ignored).

1. The TFM File Formant

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.

2. File Header

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:

TFM Length Data

Name	Description
lf	length of the entire file, in words
lh	length of the header data, in words
bc	smallest character code in the font
ec	largest character code in the font
nw	number of words in the width table
nh	number of words in the height table
nd	number of words in the depth table
ni	number of words in the italic correction table
nl	number of words in the lig/kern table
nk	number of words in the kern table
ne	number of words in the extensible character table
n

number of font parameter words

They are all nonnegative and less than 2^15. We must have

bc-1 <= ec < =255

ne <=256

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.

3. File Body

The rest of the TFM file may be regarded as a sequence of ten data arrays having the informal specification

TFM File Body Structure

Name	Range	Type
header	[0..lh-1]	stuff
char_info	[bc..ec]	char_info_word
width	[0..nw-1]	fix_word
height	[0..nh-1]	fix_word
depth	[0..nd-1]	fix_word
italic	[0..ni-1]	fix_word
lig_kern	[0..nl-1]	lig_kern_command
kern	[0..nk-1]	fix_word
exten	[0..ne-1]	extensible_recipe
param	[1..np]	fix_word

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.

3.1 The header Array

---

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.

• 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.
• 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. 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.
• 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 BCPL format.)
• header[12..16], if present, contains 20 bytes that name the font family (e.g., CMR or HELVETICA), in BCPL format. This field is also known as the ``font identifier.''
• 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.
• header[18..whatever] might also be present; the individual words are simply called header[18], header[19], etc., at the moment.

3.2 The char_info Array

---

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.

char_info_word Data Type

Byte no.	Name	Size
1	width_index	8 bits
2	height_index (times 16)	4 bits
	depth_index	4 bits
3	italic_index (times 4)	6 bits
	tag	2 bits
4	remainder	8 bits

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.

The tag field in char_info_word

tag value

Tag Value	Name	Description
0	no_tag	means that remainder is unused.
1	lig_tag	means that this character has a ligature/kerning program starting
	at lig_kern[remainder].
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.
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].

3.3 The lig_kern Array

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.

lig_kern_command Data Type

Byte no.	Field Name	Description
1	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.
2	next_char	if next_char follows the current character, then perform
		the operation and stop, otherwise continue.''
3	op_byte	indicates a ligature step if less than 128, a kern step otherwise.
4	remainder

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 <= a <= b+c and 0 <= b,c <= 1. 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.

3.4 The extensible_recipe Array

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.

3.5 The param Array

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

• 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.
• 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.
• param[3]=space_stretch is the amount of glue stretching between words.
• param[4]=space_shrink is the amount of glue shrinking between words.
• param[5]=x_height is the height of letters for which accents don't have to be raised or lowered.
• param[6]=quad is the size of one em in the font.
• 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.