Is there a bug in gftype.web's description of character widths?

Question

Under https://www.ctan.org/tex-archive/systems/knuth/dist/mfware we find gftype.web.

On line 574 of gftype.web it says:

The character width~|w| duplicates the information in the \.{TFM} file; it is $2^{24}$ times the ratio of the true width to the font's design size.

But in other places, for instance in mf.web under https://www.ctan.org/tex-archive/systems/knuth/dist/mf or in https://tug.org/TUGboat/tb02-1/tb02fuchstfm.pdf the TFM width is described as being a fix_word number scaled by 2^20 in design-size units.

In mf.web it says:

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 $-2048$.

And mf.web also says:

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]|, which defines the \.{em} unit, is often the |fix_word| value $2^{20}=1.0$, since many fonts have a design size equal to one em.

And then mf.web describes the actual width stored in the GF-file:

The character width~|w| duplicates the information in the \.{TFM} file; it is a |fix_word| value relative to the design size, and it should be independent of magnification.

Note that the first part of this text is the same as in gftype.web.

So should the formula $2^{24}$ really be $2^{20}$ instead?

Answer 1

Nothing better than doing an experiment. In TeX Live we find

/usr/local/texlive/2012/texmf-dist/doc/fonts/yannisgr/rgrsc10.300gf

and the corresponding tfm file. Upon running gftype, we read

Character 0: dx 1376256 (21), width 524290 (20.75554), loc 8275

With tftopl rgrsc10, we read

(CHARACTER O 0
   (CHARWD R 0.500002)
   (CHARHT R 0.444445)
   (CHARIC R 0.027779)
   )

and 0.500002*2^20 = 524290.097152, which matches the value 524290 in the gf file.

Typo.