This file is a log of changes made to the "new generation" of Computer Modern
fonts, after the first output proofs were ready. I had a great deal of
advice from Neenie Billawala, Matthew Carter, and Richard Southall while
I was making these revisions.

Entries are in chronological order; thus the most recent news appears
at the bottom of the file.

-------------------------------------------------------------------------------
Changes based on the proofsheets of April 26, 1985
ACCENT.MF:
 lower the idots, umlauts, and tilde (MC)
 Polish ell cross: longer stroke in bold
CMBASE.MF:
COMLIG.MF:
 double quotes too close together in bold (MC)
CSCSPU.MF:
 SS made from two S's
GREEKU.MF:
 Gamma: .25u longer arm
 Lambda: too narrow (MC,NB)
 Xi: 1u wider; shorten middle serifs (MC)
  top and bottom strokes to be arms (NB)
 Psi: more super; thin the lower curve (MC)
  add points 3' and 7' for crisp sans
 Omega: redo the bottom, curl 0 becomes vertical (MC)
  thin from hair to vair at points 3 and 5
PUNCT.MF:
 Monospace period, comma, colon, semicolon made heavier (MC)
ROMAN.MF:
 ligs=2 gets ff, fi, etc.; ligs=1 gets only --, '', etc.
 II kerning introduced
 kern between a and ' in csc
ROMAND.MF:
 0: med_curve decreased to curve; y2l and y4l raised
 1: cap_bar changed to bar in the top stroke
  sans-serif serifs also use bar as the slab height
 2: lighten cap_curve and cap_stem slightly (RS)
  move point 3 down by .5vair (MC)
 4: thin the diagonal still more (NB)
  bar line moves up one pixel when there's a serif below it
 6: move bulb to the right (MC)
  make the lower left curve more_super (RS,NB)
 9: make the upper right curve more_super (RS,NB)
ROMANL.MF:
 a: bulb positioned by its center rather than the left (MC)
 c: right terminals moved closer to the edge (MC,NB)
  more pull on the inside left (RS)
 e: less left sidebar in monospace (MC)
  bold versions to be wider (MC)
  more pull on inside left (MC,RS)
 g: lower edge of loop goes one pixel lower
 varg: point 6 raised above baseline (MC)
  y0 calculated so that it works when x7l=stem_edge
  lower arc goes one pixel lower
 i: monospace version gets more left sidebar (MC)
  dot moves slightly right (NB)
  stem'' increased to stem' (MC,RS,NB)
  slab replaces tiny in correction for dot-too-close
 j: diminish monospace sidebars (MC)
  shift slightly to right (MC)
 k: serif right_jut decreased .8 to .6
  bug fixed in alpha2 (had y1 not y11)(MC,RS,NB)
  decreased diagonal weights
  "if abs(angle(z3-z4)-45)<2:y4:=y3-(x3-x4);fi" rejected; moves y4 down too much
 n: omit pull inside the arch (MC,RS)
  introduce stem_shift, shifts this character and others slightly right (MC)
 o: raise y2l and y4l (RS)
 s: reduced sidebearing in sans (MC)
  increased thickness at edges (.35 to .5) (RS)
  changed to super_arc, and made it more_super (RS)
  raised the top of upper barb to equal top of the character (RS)
  removed typo (`tiny' for `fine')
  reduced flare in upper terminal of sans, and rounded it properly
 t: width to grow in bold case
  height made independent of bar_height
  slightly longer bar (MC)
 v: decreased left stem (RS)
 w: decreased stems (MC,RS)
  monospace version drops middle from 2/3 to .6 and lengthens inner serifs
 x: decreased left stem
 y: decreased left stem
 z: lighter diagonal, longer upper arm (MC,RS,NB)
ROMANP.MF:
 $: tau eliminated
ROMANU.MF:
 A: decrease right stem (MC)
  make the bar thinner (MC,NB)
  bar position based on y0 rather than bar_height
 C: use cap_band instead of vair' at top and bottom (RS)
  correct typo: x2l to be reset, not y2l
 E: middle arm .35u longer, but beak reduced from .7 to .6 (MC)
 F: top arm .25u longer; middle arm as E (MC)
 G: same as C; also the bar is raised one pixel
 J: slightly longer upper left serif
 K: lower diagonal thinned and moved outward
 M: monospace version raised still more in middle
 N: diagonal thinned (MC,RS)
 O: y2l and y4l raised
 R: tail should move to the right (MC,RS,NB)
  bold case gets wider (RS,NB)
 S: changed as s (RS)
 V: took stem_corr off the left stem (MC)
 W: monospace version takes center down from 2/3 to .6, lengthens inner jut
 X: took stem_corr off the left stem (MC)
 Y: took stem_corr off the left stem (MC)
 Z: diagonal made lighter in sans (MC)
  upper arm made longer (MC,RS)
ROMLIG.MF:
 equalize stem weights (RS,NB)
ROMSPL.MF:
 ae, oe: incorporate changes of a and e and o
 ss: more stem weight, less curve weight, less bulb (MC,NB)
 dotless i,j: see i,j
ROMSPU.MF:
 AE: middle arm changes as E (MC)
  if hefty and monospace, avoid the serif on middle arm
  bars not aligned if hefty
  if monospace, middle stem moves to right
 OE: middle arm changes as in AE (MC)
  middle stem lightened
ROMSUB.MF:
 blankspace: not so close to sides
SYM.MF:
CMR10.MF etc:
 bar_height raised in the quote and bold fonts (MC,NB)
 comma_depth in cmtt10 increased from 40 to 50 (MC)
 cap_notch_cut decreased in cmsc10, cmsx10
 apex_o decreased in cmr10, cmb10, cmbx10, cmbx5, cmcsc10, cmtt10
 o decreased in cmb10
 cap_jut decreased from 39 to 34 in cmb10; cap_serif_fit increased 5 to 6
 cmbx5 gets smaller beak, fudge, cap_ess; more apex_corr
GENERAL:
 "robustness" added when points like x8r of "a" are calculated
  (this affects a,b,d,varg,j,p,q,t,u,dj,ae,6,9,f_stroke)
 "robustness" also added to avoid curl at end of paths
  (this affects c,e,s,C,G,S,1,5,ae,oe,breve,parens)
 "term" subroutine adds robustness for sans-serif terminals
  (this affects C,G,J,S,f_stroke,j,ss,ae,oe,2,3,5,6,9,$,&,?,@)
 code revised to use "pos" instead of "penpos" when possible
Changes based on the proofsheets of May and June, 1985
ROMAND.MF:
 1: use o instead of apex_o
 4: bar line height shouldn't depend on bar_height
 5: sans-serif lower terminal position raised; depends on upper left edge
    bug in arm at top (0 for 90) made all hefty arms too small
 9: disappears at link
ROMANU.MF:
 B: middle bar positioned by its middle, not its bottom (RS)
    serifed lobes thickened slightly at bottom (RS)
 C: lower terminal is tilted the other way
 C,G: upper terminal in sans-serif is tilted slightly
    upper barb is darkened
 J: tilt the lower terminal
 K: lighten the main diagonal (serif case) (RS)
    lighten the upper diagonal (sans-serif case) (RS)
 M: remove apex_corr (RS)
 N: lighten the diagonal
 P: too light below counter (RS)
 Q: sharpen upper right corner of sans-serif tail (RS)
    top of tail thickened and moved slightly left
 S: less super at upper left and lower right (MC)
    barb to go below baseline
    barbs darkened
    add weight at top, bottom in sans_serif version (RS)
    tilt the lower terminal like the upper one
    top weight needs to be maxed with fine.breadth
 W: top middle stems allowed to overlap in serifed case
    second inner serif made no longer than left outer serif (MC)
    ceiling must become floor, to ensure that x5r>=x4r-mid_corr
 Z: diagonal still too heavy, because previous change was ineffective
    beaks made darker
    better positioning of y2 and y3 when tiny is zero
CSCSPU.MF:
 J,SS: changes from J and S
ROMANL.MF:
 a: inappropriate uses of "fine" are removed
    bh introduced to guard against "wild" bar heights
    thin_join introduced at point 9
    robustness logic changed so that x8l-x8r<=u
 c: too much weight constrast between strokes in sans_serif (RS)
    top terminal lowered to match a
    bottom terminal tilted the other way
 d: fine.breadth should have been thin_join as in b, p, q
 e: 1+xpart changed to xpart
    bottom terminal tilted the other way
 g: sans-serif ear to use z0l and z0r
 h,m,n: left inner serifs stay at jut length
 i,l: mod_width for better fit at lowres
 j: reposition stem for better fit (use .5w+2.5u, not w-2.5u)
    remove bug in "pos" change
 k: upper diagonal serif lengthened from 1.2jut to 1.4jut (RS)
    diagonals made still lighter
 r: thin_join introduced
 s: barb to go below baseline
    barbs darkened
    add weight at top, bottom in sans_serif version (RS)
    tilt the lower terminal like the upper one (RS)
    top weight needs to be maxed with fine.breadth
 t: bar extended still more at right (RS)
 v: decreased the width by .25width_adj#
 w: overlap allowed as in W
    second inner serif made no longer than left outer serif (MC)
    ceiling must become floor, to ensure that x5r>=x4r-mid_corr
 x: decreased the width by .5width_adj# (RS)
 y: sans-serif tail curls up too far (RS)
 z: beaks too light; decrease the diagonal to compensate (RS)
    better positioning of y2 and y3 when tiny is zero
ROMSPL.MF:
 dotless i and j: as i and j
 ae and oe: bottom terminal tilted the other way
 ae: corrected as a
ROMSPU.MF:
 AE: x12 based on x1l rather than x1, works better in bold cases (RS)
 OE: left curve not to be pulled
GREEKU.MF:
 Phi and Psi: middle parts must keep away from the serifs
ROMANP.MF:
 $: strengthened the terminals in sans-serif case, and tilted them
 &: opened the eye by moving point 8 left .5u (RS)
 ?: tilted the sans-serif terminal and moved it down a little more
PUNCT.MF:
 %: move the diagonal a bit left at the top
 ( and ): 3.5( changed to 3(.
 [ and ]: round changed to ceiling and floor, avoids disappearing brackets
 @: inner a placed by its edges instead of its stem centers (RS)
ITALL.MF:
 f: lower bulb moved left; .5 changed to .6 between bulb and stem
 k: bug in lower right stroke (missing e's)
 l: bug in italic correction for math fitting (u not u#)
 m: avoid hooks in monospace version
 p: lengthed left serif at bottom from .5jut to .75jut
 x: bulbs moved .25u further out; .5 used between bulb and stem
 w: avoid hook in monospace version
ITALIG.MF:
 all five: changed like f
 fi: made 1u less wide
 fl,ffl: made .5u less wide, bulb now touches the l stem
 ffi: made .75u less wide
GREEKL.MF:
 beta, gamma, zeta, xi, omega, varepsilon: +eps at the tight turns
 gamma: final diagonal should be more slanted (MC)
 zeta: as tall as xi, shallower diagonal slant (MC)
 kappa: bug in lower right stroke (missing e's)
 xi: raise the bottom diagonal and distort arc slightly (MC)
 chi: introduce slight curve in main diagonal stroke
 varphi: too wide at right half bowl (MC)
ITALMS.MF:
 wp: bulb smaller, bottom a little more open
ITALD.MF:
 5: changed like 5 in ROMAND
OLDDIG.MF:
 2: top a bit narrower, bottom a bit wider (MC)
 5: changed like 5 in ROMAND
SYM.MF:
 plus-minus: shift depends on u not asc_height
SYMBOL.MF:
 minus-plus: shift depends on u not asc_height
 up-and-down arrows (characters '154 and '155): taller and deeper
 clubsuit: wider
 spadesuit: y1+1 changed to y1+.75 (also in clubsuit)
ROMAN.MF:
 eliminated kerning between L and O,C,G,Q,U (also in TEXTIT and CSC)
MATHEX.MF:
 font_x_height needed to be set, for positioning of accents
CMB10.MF:
 dishing is too much (on all bold fonts)
CMR5.MF:
 letter_fit decreased 10 to 5
CMBX5.MF:
 fudge should be 1 (cap_stem 8=:7 in aps mode was too much)
 decrease letter_fit drastically; this means f-ligatures must come back
 lowercase parameters increased by 2/36
CMBI10.MF:
 lowercase serifs too short. (same change to all the italic fonts)
CMSX10.MF:
 decrease `ess' (RS)
CMTC10.MF:
 fudge is too much in lowercase
CMCC10.MF:
 lowercase more extended
 much less letterspace in caps
 increase lower.cap_curve, decrease lower.o
CMSQI8.MF:
 slope shouldn't be so much (RS)
 increase `ess' (RS)

GENERAL:
 serif-abutment corrections changed to +1 instead of +2
 vround used for vertical rounding

CMBASE.MF:
 new way to set shrink_fit (0,1,2) for monotonicity with letter_fit
 letter_fit not included in mono_charwd
 fine must be positive (else we lose barbs)
 thin_join must be positive (else h_stroke gives a bad pos)
Changes based on the `version 0' test fonts of July 12
[not showing hundreds of changes to the `typography' of the programs]

Driver files in general:
Frequency info (from MANUAL.TEX[tex,dek]) was used to order the ligtables
font_xheight changed to font_x_height (a change to PLAIN.MF)

Program files in general:
 use `hround' instead of `round' wherever granularity might be wanted
 less_rounded was taken out; autorounded occasionally put in
 arm($,$$,...), the value of y$$ was adjusted by eps (lower) or -eps (upper)

Parameter files in general:
 new 12pt and 17+pt fonts; more sans serif fonts
 new comment at bottom of all parameter files: `switch to the driver file'

ACCENT.MF:
 ^: eps subtracted from y1 (helps avoid degenerate equations in ultralowres)
 '`: eps added to y1

ROMAN.MF:
 kern entry for gj had the wrong sign
 kerns for v removed in sans serif
 new kern for aj in serif case
 new kern for ar in sans serif

ROMAND.MF:
 3: pos3 needed to be maxed with fine.breadth
    y1r,y9r needed to be adjusted by eps
 6,9: keep x1 on the correct side of x2 at lowlowres
    (this change also affects OLDDIG, ITALD, and ITALMS partial sign)

ROMANP.MF:
 $: less_tense bulbs

ROMSPL.MF:
 ss: ensure x5 not > x4l at low resolutions

ROMLIG.MF:
 itc shouldn't include the slant...

COMLIG.MF:
 em dash should be one em wide (add letter_fit# to the adjustments)

BIGOP.MF:
 \displaystyle coproduct sign had 1.2bracket instead of 1.8bracket
 charlist syntax changed from commas to colons

BIGDEL.MF:
 extensible double arrow: position wasn't computed as in top and bottom
 charlist syntax changed from commas to colons

BIGACC.MF:
 charlist syntax changed from commas to colons

ITALL.MF:
 c: point 1 made definitely greater than point 2, for lowlowres
 q: x4 increased by eps, for lowlowres path intersection
 r: x4 based on w, not 5u
 s: max(ess,fine.breadth)
    add eps and 2eps for lowlowres case (cmmi6 at 100/in)

ITALMS.MF:
 wp: x6r must not be less than x1r at lowlowres

TSETSL.MF:
 gamma: last time's bugfix from GREEKL needs to be here too

GREEKL.MF:
 omega: add 2eps to x4-x6
 lambda: make sure that y3>y4 at lowlowres
 zeta: make sure that x2>x0 at lowlowres
 varsigma: make sure that x1>x2 at lowlowres

CMFIB8.MF:
 decreased serif_fit, cap_serif_fit; increased curve, cap_curve

CMBASE.MF:
 l,r made newinternals
 serif darkness and skew switches now done with boolean variables
 comma and ammoc: 2eps addedto/subtractedfrom position of x@2
 mod_width now called change_width
 ess and cap_ess initialized to preserve ratios with stem and cap_stem
 mode="string" had to be handled properly
 ^ and ! changed to t_ and o_, as per new PLAIN conventions
 make cmchar "outer"
 t_ is now `relaxed' if it is useless
 soft is now softjoin in PLAIN (we must set join_radius:=u)
 eps is now in PLAIN
 vair is vrounded but at least 1; also slab, etc.
 cal nibs, yscaled by cap_hair not vair
 autorounding and smoothing turned off

ROMANL.MF:
 a: `footed' version is .25u tighter at the right
 b,d,varg,p,q: x4l position relative to .5(w-serif_fit) not 5u
 e: testpath uses .r not .l (because of cmss10)
 f: added 1 at right for monospace lowres versions
 varg: robust sans-serif terminal at tail
 m: missing `round' in r adjustment caused noninteger chardx
 r: x4 based on w, not 5.25u
 s: watch out that ess isn't so small that badpos error occurs (also ROMANU)
    barbs made longer; based on middle stroke not just h
 t: sans-serif terminal made more robust in extreme cases
 w: in non-monospace hefty serif case, the middle point comes to .8h not h
 y: robust sans-serif terminal at tail

ROMANU.MF:
 E: good.y used in y9

PUNCT.MF:
 []: side_thickness needed to be maxed with crisp.breadth
     +1 or -1 makes lowres versions more distinctive
 #: tricky part lost at low resolution

SYMBOL.MF:
 angle brackets: +1 and -1 to make lowres versions more distinctive
 aleph: eps added so that y5 will be well defined at lowlowres

SYM.MF:
 integral sign: bulbs need to be in right direction at lowlowres

CALU.MF:
 A: apex moved slightly down
 D: less flat at top, slightly lower lobe
 F: u less right sidebar
 H: soft corner at upper left
 I: middle stroke more like J, upper bar a little further right
 K: introduce t_ in case of aspect_ratio
 L: darker
 M: lighter first diagonal; clean the joins
 N: lighter diagonal; clean bottom right; .5u less right sidebar
 O: shortened the inner stroke
 P: stem comes lower
 Q: tail not so long at left
 R: not so flat at top; diagonal less tense; tail less high
 T: narrower, also changed like I, .5u less right sidebar,
     heavier, not so high at right
 U: less extreme curve at lower left
 V: cleaned up at bottom; lighter first diagonal; slightly wider
 W: changed like V, but double
 X: new design, less rigid
 Y: new design based more on V than U
 Z: tighter at right, heavier at top and bottom

CMSS10.MF:
 decreased notch_cut and bar_height

%Note: The following can presumably be deleted; I removed it from CMBASE because
%  I don't think it is used any more:
vardef parallel_pos(expr d,u,v,w) = % point at distance $d$ from $u$,
  % on the line through $w$ that's parallel to |u..v|
 pair p_; p_=w+whatever*(u-v)=u+whatever*(u-v) rotated 90;
 numeric d_; d_=length(u-p_);  % distance from $w$ to |u..v|
 if d_>=d: p_ else: p_+(d+-+d_)*unitvector(v-u) fi enddef;
Changes subsequent to `Version 1' as released on October 7, 1985.

1. thin_join should be subject to blacker:
@x in CMBASE.MF, the font_setup routine
 define_whole_pixels(letter_fit,thin_join,fine,crisp,tiny);
 define_whole_vertical_pixels(body_height,asc_height,
  cap_height,fig_height,x_height,comma_depth,desc_depth,serif_drop);
 define_whole_blacker_pixels(hair,stem,curve,flare,
@y
 define_whole_pixels(letter_fit,fine,crisp,tiny);
 define_whole_vertical_pixels(body_height,asc_height,
  cap_height,fig_height,x_height,comma_depth,desc_depth,serif_drop);
 define_whole_blacker_pixels(thin_join,hair,stem,curve,flare,
@z
@x
 if thin_join=0: thin_join:=1; fi
@y
@z
[Note, December 11: My first correction also introduced the statement
 if fine<thin_join: fine:=thin_join; fi
in place of
 if fine=0: fine:=1; fi
but I can't understand why I would do such a stupid thing!]

2. A new subroutine needed in CMBASE.MF (for cases with aspect_ratio<>1):
vardef Vround primary y = y_:=vround y;
 if y_<min_Vround: min_Vround else: y_ fi enddef;
newinternal y_,min_Vround;

@x related changes to the font_setup routine (in CMBASE.MF):
 forsuffixes $=vair,bar,slab,cap_bar,cap_band:
  $:=vround($.#*hppp+blacker); if $<=1: $:=1; fi endfor
@y
 define_whole_vertical_blacker_pixels(vair,bar,slab,cap_bar,cap_band);
@z
@x
 vair':=max(1,vround(vair+vair_corr));
 vstem:=max(1,vround .8[vair,stem]);
 cap_vstem:=max(1,vround .8[vair,cap_stem]);
@y
 vair':=vround(vair+vair_corr);
 vstem:=vround .8[vair,stem]; cap_vstem:=vround .8[vair,cap_stem];
@z
@x
 pickup pencircle scaled rule_thickness; rule.nib:=savepen;
@y
 min_Vround:=max(fine.breadth,crisp.breadth,tiny.breadth);
 forsuffixes $=vair,bar,slab,cap_bar,cap_band,vair',vstem,cap_vstem:
  if $<min_Vround: $:=min_Vround; fi endfor
 pickup pencircle scaled rule_thickness; rule.nib:=savepen;
@z

The Vround routine is substituted for vround in the programs for
  Macron, line 6 (in ACCENT.MF)
  Variant epsilon, line 5 (in GREEKL.MF)
  Sigma, line 6 (in GREEKU.MF)
  Omega, line 14 (in GREEKU.MF)
  2, line 6 (in OLDDIG.MF and ROMAND.MF)
  7, lines 6 and 8 (in OLDDIG.MF and ROMAND.MF)
  g, lines 6 and 8 (in ROMANL.MF)
  s, line 6 (in ROMANL.MF)
  y, line 9 (in ROMANL.MF)
  z, line 6 (in ROMANL.MF)
  &, line 39 (in ROMANP.MF)
  ?, line 18 (in ROMANP.MF)
  Spanish open ?, line 17 (in ROMANP.MF)
  Z, line 6 (in ROMANU.MF)
  smile and frown, line 4 (in ROMMS.MF)

3. Typo in program for oe ligature.
@x in file ROMSPL.MF
else: left_curve=max(tiny.breadth,hround(curve-2stem_corr));
@y
else: left_curve=max(fine.breadth,hround(curve-2stem_corr));
@z

4. Forgotten update to program for SS.
@x in file CSCSPU.MF
pickup fine.nib; pos2(max(fine.breadth,s_slab-vround vair_corr),-90);
pos0(cap_ess,theta); pos7(s_slab,-90);
x2+x7=2x0=w; x7-x2=if serifs: u else: 0 fi; top y2l=h+o; bot y7r=-o;
y0=.52h; lft x3l=hround u; rt x6r=hround(w-u);
x3r-x3l=x6r-x6l=hround .5[s_slab,cap_ess] -fine;
@y
numeric ess'; ess'=max(fine.breadth,cap_ess);
pickup fine.nib; pos2(max(fine.breadth,s_slab-vround vair_corr),-90);
pos0(ess',theta); pos7(s_slab,-90);
x2+x7=2x0=w; x7-x2=if serifs: u else: 0 fi; top y2l=h+o; bot y7r=-o;
y0=.52h; lft x3l=hround u; rt x6r=hround(w-u);
x3r-x3l=x6r-x6l=hround .5[s_slab,ess']-fine;
@z

5. Hairline in `k' was overcorrected. (Pavel Curtis)
@x in file ROMANL.MF
stem3=max(tiny.breadth,hround(fudged.hair-4stem_corr));
@y
stem3=max(tiny.breadth,hround(fudged.hair if hefty:-\\4stem_corr fi));
@z

6. Too much kerning in "We", etc., in sans-serif fonts
@x in file ROMAN.MF and TEXSET.MF
 ligtable "F": "V": "W": "o" kern kk#, "e" kern kk#, "u" kern kk#,
   "r" kern kk#, "a" kern kk#, "A" kern kkk#,
@y
 ligtable "F": "V": "W": if serifs: "o" kern kk#, "e" kern kk#, "u" kern kk#,
    "r" kern kk#, "a" kern kk#, "A" kern kkk#,
   else: "o" kern k#, "e" kern k#, "u" kern k#,
    "r" kern k#, "a" kern k#, "A" kern kk#, fi
@z
@x in file TITLE.MF
 ligtable "F": "V": "W": "A" kern kkk#,
@y
 ligtable "F": "V": "W": "A" kern if serifs: kkk# else: kk#\\fi,
@z
@x in file CSC.MF
 ligtable "F": "V": "W": "a" kern kkk#, "A" kern kkk#,
@y
 ligtable "F": "V": "W": if serifs: "a" kern kkk#, "A" kern kkk#,
  else: "a" kern kk#, "A" kern kk#, fi
@z
@x in file CSC.MF
 ligtable "f": "v": "w": "a" kern kkk#,
@y
 ligtable "f": "v": "w": "a" kern if serifs: kkk# else: kk#\\fi,
@z

7. dish serifs need to be more robust when dishing is very small.
@x in file CMBASE.MF
  if y$<y$$: dish_out=bot y$; dish_in=dish_out+dish;
  else: dish_out=top y$; dish_in=dish_out-dish; fi
  erase fill\\(x@1,dish_out)..(x$,dish_in){right}..(x@@1,dish_out)--cycle;
@y
  if y$<y$$: dish_out=bot y$; dish_in=dish_out+dish; let rev_=reverse;
  else: dish_out=top y$; dish_in=dish_out-dish; let rev_=relax; fi
  erase fill rev_
   ((x@1,dish_out)..(x$,dish_in){right}..(x@@1,dish_out)--cycle);
@z

8. more robustness in case thin_join is too big
@x in file ROMANL.MF, program for "b"
pos4(vair,90); pos5(curve,0);
pos6(vair,-90); penpos7(x3l-x3r,-180);
rt x3l=1/3[rt x2,edge]; y3=1/8[bar_height,x_height];
@y
pos4(vair,90); pos5(curve,0); pos6(vair,-90); penpos7(x3l-x3r,-180);
rt x3l=max(rt x3l-(lft x3r-tiny.lft x2l),1/3[rt x2,edge]);
y3=1/8[bar_height,x_height];
@z
@x ibid, program for "d"
pos4(vair,90); pos5(curve,180);
pos6(vair,270); penpos7(x3r-x3l,360);
lft x3l=1/3[lft x2,edge]; y3=1/8[bar_height,x_height];
@y
pos4(vair,90); pos5(curve,180); pos6(vair,270); penpos7(x3r-x3l,360);
lft x3l=min(lft x3l-(rt x3r-tiny.rt x2r),1/3[lft x2,edge]);
y3=1/8[bar_height,x_height];
@z
@x ibid, program for variant "g"
pos4(vair,90); pos5(curve,180);
pos6(vair,270); penpos7(x3r-x3l,360);
lft x3l=2/3[lft x2,edge]; y3=bar_height;
@y
pos4(vair,90); pos5(curve,180); pos6(vair,270); penpos7(x3r-x3l,360);
lft x3l=min(lft x3l-(rt x3r-tiny.rt x2r),2/3[lft x2,edge]); y3=bar_height;
@z
@x ibid, program for "p"
rt x3l=1/3[rt x2,edge]; y3=1/8[bar_height,x_height];
@y
rt x3l=max(rt x3l-(lft x3r-tiny.lft x2l), 1/3[rt x2,edge]);
y3=1/8[bar_height,x_height];
@z
@x ibid, program for "q"
lft x3l=2/3[lft x2,edge]; y3=bar_height;
@y
lft x3l=min(lft x3l-(rt x3r-tiny.rt x2r),2/3[lft x2,edge]); y3=bar_height;
@z
@x ibid, proram for "q"
x6l=x4l-.2u; bot y6r=-oo;
lft x7l=1/3[lft x2,edge]; y7=min(y3,y6+y4-y3+.6vair);
@y
x6l=x4l-.2u; bot y6r=-oo; y7=min(y3,y6+y4-y3+.6vair);
lft x7l=min(lft x7l-(rt x7r-tiny.rt x2r),1/3[lft x2,edge]);
@z

9. More robust "c" and "e" and "C"
@x in file ROMANL.MF, program for "c"
 (x,y4l)=whatever[z4r,z5l]; x4l:=x;
@y
 (x,y4l)=whatever[z4r,z5l]; x4l:=min(x,x4l+.5u);
@z
@x ibid, program for "e"
 (x,y4l)=whatever[z4r,z5]; x4l:=x;
@y
 (x,y4l)=whatever[z4r,z5]; x4l:=min(x,x4l+.5u);
@z
@x in file ROMSPL.MF, programs for "ae" and "oe"
 (x,y14l)=whatever[z14r,z15]; x14l:=x;
@y
 (x,y14l)=whatever[z14r,z15]; x14l:=min(x,x14l+.5u);
@z
@x in file ROMANU.MF, programs for "C" and "G"
 (x2l',y2l)=whatever[z2r,z1l]; x2l:=x2l';
 (x4l',y4l)=whatever[z4r,z5l]; x4l:=x4l';
@y
 (x2l',y2l)=whatever[z2r,z1l]; x2l:=min(x2l',x2l+.5u);
 (x4l',y4l)=whatever[z4r,z5l]; x4l:=min(x4l',x4l+.5u);
@z

10. More robust foot in "a"
@x in file ROMANL.MF
  filldraw stroke z5'e---z10e...z11e{right};  % foot
@y
  pos12(shaved_stem,0); x11=x12; top y12=slab+eps;
  filldraw z5'l---z10l...z11l{right}--z11r
   --z12r{left}...z10r+.75(z12-z11)---z5'r--cycle;  % foot
@z

11. Barbs less sharp
@x in file ROMANU.MF, programs for "C" and "G"
 x6=x1r; top y6=h+o; x1r-x1'=2cap_curve-fine; y1'=y1;
 path upper_arc; upper_arc=z1{x2-x1,10(y2-y1)}..z2{left};
 numeric t; t=xpart(upper_arc intersectiontimes (z6--z1'));
 filldraw z1r--z6--subpath(t,0) of upper_arc--cycle; % barb
@y [actually "G" had something similar but not identical]
 pos6(.3[fine.breadth,cap_hair],0); x6r=x1r; top y6=h+o;
 x1r-x1'=2cap_curve-fine; y1'=y1;
 path upper_arc; upper_arc=z1{x2-x1,10(y2-y1)}..z2{left};
 numeric t; t=xpart(upper_arc intersectiontimes (z6l--z1'));
 filldraw z1r--z6r--z6l--subpath(t,0) of upper_arc--cycle; % barb
@z
@x ibid, program for "S"
 x10=x1l; top y10=top y2l; x9=x8r; bot y9=bot y7r;
 x1l-x1'=x8'-x8r=1.6cap_curve-fine; y1'=y1; y8'=y8;
 numeric t; t=xpart(upper_arc intersectiontimes(z10--z1'));
 filldraw z1l--z10--subpath(t,0) of upper_arc--cycle;  % upper barb
 t:=xpart(lower_arc intersectiontimes(z9--z8'));
 filldraw z8r--z9--subpath(t,1) of lower_arc--cycle;  % lower barb
@y
 pos10(.3[fine.breadth,cap_hair],0); pos9(.3[fine.breadth,cap_hair],0);
 x10r=x1l; top y10=top y2l; x9l=x8r; bot y9=bot y7r;
 x1l-x1'=x8'-x8r=1.6cap_curve-fine; y1'=y1; y8'=y8;
 numeric t; t=xpart(upper_arc intersectiontimes(z10l--z1'));
 filldraw z1l--z10r--z10l--subpath(t,0) of upper_arc--cycle;  % upper barb
 t:=xpart(lower_arc intersectiontimes(z9r--z8'));
 filldraw z8r--z9l--z9r--subpath(t,1) of lower_arc--cycle;  % lower barb
@z [the same change goes into file CSCSPU.MF, the program for two S's]
@x in file ROMANL.MF, program for "s"
 x10=x1l; top y10=top y2l; x9=x8r; bot y9=bot y7r;
 x1l-x1'=x8'-x8r=1.6curve-fine; y1'=y1; y8'=y8;
 numeric t; t=xpart(upper_arc intersectiontimes(z10--z1'));
 filldraw z1l--z10--subpath(t,0) of upper_arc--cycle;  % upper barb
 t:=xpart(lower_arc intersectiontimes(z9--z8'));
 filldraw z8r--z9--subpath(t,1) of lower_arc--cycle;  % lower barb
@y
 pos10(.3[fine.breadth,cap_hair],0); pos9(.3[fine.breadth,cap_hair],0);
 x10r=x1l; top y10=top y2l; x9l=x8r; bot y9=bot y7r;
 x1l-x1'=x8'-x8r=1.6cap_curve-fine; y1'=y1; y8'=y8;
 numeric t; t=xpart(upper_arc intersectiontimes(z10l--z1'));
 filldraw z1l--z10r--z10l--subpath(t,0) of upper_arc--cycle;  % upper barb
 t:=xpart(lower_arc intersectiontimes(z9r--z8'));
 filldraw z8r--z9l--z9r--subpath(t,1) of lower_arc--cycle;  % lower barb
@z

12. Italic ampersand more robust
@x in file ITALP
 & pulled_arc.e(9,10)...{dir(theta+90)}z11e;  % bowls, loop, and stem
@y
 & {{interim superness:=more_super; pulled_arc.e(9,10)}}
 ..tension .9 and 1..{dir(theta+100)}z11e;  % bowls, loop, and stem
@z

13. h_stroke more robust (esp in case of typewriter-style m)
@x in file CMBASE
 pickup fine.nib; pos@0(thin_join,180);
@y
 penpos@0(min(rt x$r-lft x$l,thin_join)-fine,180); pickup fine.nib;
@z

14. eliminate dishing in conflict with arm.
Put a new subroutine into CMBASE.MF:
def nodish_serif(suffix $,$$,@)(expr left_darkness,left_jut)
  (suffix @@)(expr right_darkness,right_jut) suffix modifier =
 serif($,$$,@,left_darkness,-left_jut) modifier;
 serif($,$$,@@,right_darkness,right_jut) modifier; enddef;

Now use this instead of dish_serif in the following places:
GREEKU:  Gamma, upper serif
  Pi, both upper serifs (fix erroneous comments!)
SYMBOL:  Amalgamation, both lower serifs (fix erroneous comments!)
ROMANU:  B, both serifs
  D, both serifs
  E, both serifs
  F, upper serif
  L, lower serif
  P, upper serif
  R, upper serif
  T, upper bracketing
ROMSPU: AE, upper and lower middle serifs

15. Change #2 wasn't quite good enough!
@x in CMBASE
 min_Vround:=max(fine.breadth,crisp.breadth,tiny.breadth);
@y
 min_Vround:=max(fine.breadth,crisp.breadth,tiny.breadth);
 if min_Vround<vround min_Vround: min_Vround:=vround min_Vround; fi
 if flare<vround flare: flare:=vround flare; fi
@z

16. body_depth# is now called paren_depth#, since body_depth is
computed differently. (This is a cosmetic change only; it affects
files CMBASE, PUNCT, SYM, SYMBOL, and ROMMS.)

17. more robust Sigma
@x in GREEKU, page 9
top y1=h; bot y2=h-slab; bot y4=0; x3l-x1l=4/11(w-2u); y3=.5h;
@y
top y1=h; bot y2=h-slab-eps; bot y4=0; x3l-x1l=4/11(w-2u); y3=.5h;
@z
@x in BIGOP, page 7
top_arm_thickness=rule_thickness;
@y
top_arm_thickness=Vround rule_thickness;
@z
@x in BIGOP, page 7 (this change needed twice)
top y1=0; bot y2=-top_arm_thickness; bot y4=-d; y3=-.5d;
@y
top y1=0; bot y2=-top_arm_thickness-eps; bot y4=-d; y3=-.5d;
@z

18. yet another refinement of change #2
@x in CMBASE
 forsuffixes $=vair,bar,slab,cap_bar,cap_band,vair',vstem,cap_vstem:
@y
 forsuffixes $=vair,bar,slab,cap_bar,cap_band,vair',vstem,cap_vstem,bold:
@z

19. slightly more robust `k'
@x in ROMANL
top y3=x_height; rt x3r=hround(r-letter_fit-.7u-right_jut);
bot y6=0; rt x6r=hround(r-letter_fit-.3u-right_jut);
@y
top y3=x_height; rt x3r=hround(r-letter_fit-.7u-right_jut)+eps;
bot y6=0; rt x6r=hround(r-letter_fit-.3u-right_jut)+eps;
@z

20. small parameter changes for consistency
@x in CMBX6
dish#:=.9/36pt#;    % amount erased at top or bottom of serifs
@y
dish#:=.8/36pt#;    % amount erased at top or bottom of serifs
@z
@x in CMBX5
dish#:=.75/36pt#;    % amount erased at top or bottom of serifs
@y
dish#:=.7/36pt#;    % amount erased at top or bottom of serifs
@z
@x in CMSS9 and CMSSI9 [these two lines are not consecutive in the files!]
notch_cut#:=23/36pt#;    % maximum breadth above or below notches
cap_notch_cut#:=29/36pt#;  % max breadth above/below uppercase notches
@y
notch_cut#:=17/36pt#;    % maximum breadth above or below notches
cap_notch_cut#:=24/36pt#;  % max breadth above/below uppercase notches
@z
@x in CMSS8 and CMSSI8 [these two lines are not consecutive in the files!]
notch_cut#:=21/36pt#;    % maximum breadth above or below notches
cap_notch_cut#:=27/36pt#;  % max breadth above/below uppercase notches
@y
notch_cut#:=16/36pt#;    % maximum breadth above or below notches
cap_notch_cut#:=22/36pt#;  % max breadth above/below uppercase notches
@z
@x in CMTI9
cap_hair#:=10/36pt#;    % uppercase hairline breadth
@y
cap_hair#:=11/36pt#;    % uppercase hairline breadth
@z
@x in CMTI8
cap_hair#:=9.5/36pt#;    % uppercase hairline breadth
@y
cap_hair#:=11/36pt#;    % uppercase hairline breadth
@z
@x in CMTI7
cap_hair#:=9/36pt#;    % uppercase hairline breadth
@y
cap_hair#:=10.5/36pt#;    % uppercase hairline breadth
@z
@x in CMTCSC10
lower.cap_notch_cut#:=24pt#;  % max breadth above/below uppercase notches
@y
lower.cap_notch_cut#:=24/36pt#;  % max breadth above/below uppercase notches
@z

21. New parameter file CMFI10 was added; font_identifier is "CMFI".
Also changed the name `cmit10' to `cmitt10'; font_identifier is "CMITT".

22. Still more changes for robustness (based on resolution h120 x v108).
@x in ROMAND and ITALD, "5"
bot y5=vround(.53h-vair); top y6r=vround .61803h+o;
@y
bot y5=vround(.53h-vair); top y6r=max(vround .61803h+o,top y6r+y5+eps-y6l);
@z
@x in OLDDIG, "5"
bot y5=vround(.53[-d,h]-vair); top y6r=(vround .61803[-d,h])+o;
@y
bot y5=vround(.53[-d,h]-vair);
top y6r=max((vround .61803[-d,h])+o,top y6r+y5+eps-y6l);
@z
@x in ROMANU, "C"
 bot y1=vround max(.6h,x_height-.5vair); y5=good.y .95(h-y1);
@y
 bot y1=min(vround max(.6h,x_height-.5vair),bot y2l-eps);
 y5=max(good.y .95(h-y1),y4l+eps);
@z
@x in ROMANU, "G"
 bot y1=vround max(.6h,x_height-.5vair);
@y
 bot y1=min(vround max(.6h,x_height-.5vair),bot y2l-eps);
@z
@x in GREEKL page 6 and TSETSL page 8
y1=.9h; top y2l=h+oo; top y8r=x_height+oo; y4=y8;
@y
top y2l=h+oo; y1=min(.9h,y2r-eps); top y8r=x_height+oo; y4=y8;
@z
@x in GREEKL page 16
x6=x7=w-2u; x8=.5w+.5u; y6=-.3d; y8=-3/4d-oo; bot y7r=-d-oo;
@y
x6=x7=w-2u; x8=.5w+.5u; y6=-.3d; bot y7r=-d-oo; y8=max(-3/4d-oo,y7l);
@z
@x in ITALL page 12, ITALMS page 6, ITALSP page 4
lft x5r=hround-.5u; x4=1/3(w-u);
@y
x4=1/3(w-u); lft x5r=min(hround-.5u,lft x5r+x4-x5l-eps);
@z
@x in ROMANL, "g"
x11=x13=.5w; bot y13r=-d-oo-1; x14=w-x12; z10'l=z10l;
@y
x11=x13=max(.5w,x10+eps); bot y13r=-d-oo-1; x14=w-x12; z10'l=z10l;
@z
@x in ROMANL, "s"
 filldraw stroke z1e..tension.9..{left}z2e;  % upper arc and terminal
 filldraw stroke z7e{left}..z8e; fi  % lower arc and terminal
@y
 filldraw stroke term.e(2,1,right,.9,4);  % upper arc and terminal
 filldraw stroke term.e(7,8,left,1,4); fi  % lower arc and terminal
@z
@x in ROMANL, "c"
 filldraw stroke pulled_super_arc.e(2,3)(.7superpull)
  & pulled_super_arc.e(3,4)(.5superpull)
  ..tension .9 and 1..z5e; fi  % arc and lower terminal
@y
 forsuffixes e=l,r: path p.e; p.e=z4e{right}..tension .9 and 1..z5e;
  if angle direction 1 of p.e>75:
   p.e:=z4e{right}..tension atleast.9 and 1..{dir 75}z5e; fi endfor
 filldraw stroke pulled_super_arc.e(2,3)(.7superpull)
  & pulled_super_arc.e(3,4)(.5superpull) & p.e; fi  % arc and lower terminal
@z
@x in ROMSPL, page 5
lft x8r=hround(stem_edge+.5u+1); x7=max(x8l+eps,.4[lft x8r,x6]);
@y
lft x8r=min(hround(stem_edge+.5u+1),lft x8r+x6r-2eps-x8l);
x7=max(x8l+eps,.4[lft x8r,x6]);
@z
@x in ROMAND and OLDDIG, "2"
 lft x1r=hround .75u; bot y1l=vround .7h; y1r:=good.y y1r; x1l:=good.x x1l;
@y
 lft x1r=hround .75u; bot y1l=vround .7h; y1r:=good.y y1r+eps; x1l:=good.x x1l;
@z
@x in SYMBOL, page 42 (Fraktur R)
z=(z20{up}...{right}z21)intersectionpoint(z22l--z22l+(h,0) rotated theta);
@y
path p; p=z20{up}...(z21--(w,y21));
z=p intersectionpoint(z22l--z22l+(h,0) rotated theta);
@z

23. Another consequence of change 2:
"vround" should be "Vround" in the BIGDEL programs for extensible arrows
(five times).
Also five times in the BIGOP programs for summation, product, coproduct.

24. Cosmetic change to bring CMBASE in line with PLAIN.
@x in CMBASE.MF
def pickup secondary q =
 if numeric q: currentpen:=pen_[q];
  pen_top:=pen_top_[q];  pen_bot:=pen_bot_[q];
  pen_lft:=pen_lft_[q];  pen_rt:=pen_rt_[q];
  currentpen_path:=pen_path_[q];
  if known breadth_[q]: currentbreadth:=breadth_[q]; fi
 else: currentpen:=q yscaled aspect_ratio;
  pen_top:=(ypart penoffset left of currentpen)_o_;
  pen_bot:=(ypart penoffset right of currentpen)_o_;
  pen_lft:=xpart penoffset down of currentpen;
  pen_rt:=xpart penoffset up of currentpen;
  path currentpen_path;
 fi enddef;
@y
def numeric_pickup_ primary q =
 currentpen:=pen_[q];
 pen_lft:=pen_lft_[q];  pen_rt:=pen_rt_[q];
 pen_top:=pen_top_[q];  pen_bot:=pen_bot_[q];
 currentpen_path:=pen_path_[q];
 if known breadth_[q]: currentbreadth:=breadth_[q]; fi enddef;
@z

25. false italic correction in lambda of texset fonts (Feb 25, 1986)
@x in TEXSET
mode_setup; font_setup;
@y
mode_setup; font_setup; mono_charic#:=0;
@z
@x ibid
slant:=mono_charic#:=0;  % the remaining characters will not be slanted
@y
slant:=0;  % the remaining characters will not be slanted
@z
[now remove the occurrences of `charic:=0;' in TSETSL, as they are unnecessary]

*** The above changes are incorporated into the published book,
*** Computer Modern Typefaces; this is "Version 2" (released March 5, 1986).
Changes subsequent to `Version 2' as published in C&T, Volume E:

@x in GREEKU
numeric shaved_stem; shaved_stem=hround .9[vair,.85cap_stem];
@y
numeric shaved_stem; shaved_stem=hround .9[vair,.85cap_stem];
if shaved_stem<crisp.breadth: shaved_stem:=crisp.breadth; fi
@z

@x in CMSS9 [this affects the TFM file to a small extent!]
fig_height#:=236/36pt#;    % height of numerals
@y
fig_height#:=212/36pt#;    % height of numerals
@z

@x in CMSSI9 [this affects the TFM file in ten hts and eleven italcorrs]
fig_height#:=236/36pt#;    % height of numerals
@y
fig_height#:=212/36pt#;    % height of numerals
@z

@x in CMR17 [no change to TFM file]
curve#:=41/36pt#;    % lowercase curve breadth
@y
curve#:=40/36pt#;    % lowercase curve breadth
@z
@x
cap_stem#:=40/36pt#;    % uppercase stem breadth
cap_curve#:=48/36pt#;    % uppercase curve breadth
@y
cap_stem#:=41/36pt#;    % uppercase stem breadth
cap_curve#:=47/36pt#;    % uppercase curve breadth
@z
@x
serif_drop#:=17/36pt#;    % vertical drop of sloped serifs
@y
serif_drop#:=7/36pt#;    % vertical drop of sloped serifs
@z

@x in ROMAND [this fixes the `disappearing hairline' in some lowres 8's]
 lower_side=hround(.5[hair,stem]+stem_corr);
@y
 lower_side=hround(.5[hair,stem]+stem_corr);
 if lower_side>1.2upper_side: upper_side:=lower_side; fi
@z
% Note: the SAME change should also be made in files ITALD and OLDDIG

@x in ITALL [this fixes italic ell especially at low resolutions]
top y1=h; x1=x2; filldraw stroke z1e--z2e;  % stem
@y
top y1=h; x1=x2; filldraw stroke z1e--z2'e;  % stem
@z

@x in SYM, the plus-or-minus character
x1=x2=.5w; lft x3=lft=x5=hround u-eps; x4=x6=w-x3;
@y
x1=x2=.5w; lft x3=lft x5=hround u-eps; x4=x6=w-x3;
@z actually the code worked but it was "infelicitous"

@x in SYMBOL, the minus-or-plus character
x1=x2=.5w; lft x3=lft=x5=hround u-eps; x4=x6=w-x3;
@y
x1=x2=.5w; lft x3=lft x5=hround u-eps; x4=x6=w-x3;
@z actually the code worked but it was "infelicitous"

@x in ROMANU, letter J [fixes a bug if dish=0 and crisp<tiny and serifs]
 bulb(3,4,5);  % bulb
@y
 pickup tiny.nib; bulb(3,4,5);  % bulb
@z

@x in ROMANL, letter w [makes notch_cut more useful]
 else: fill diag_end(6r,5r,1,1,5l,6l)--.5[z5l,z6l]
   --.5[z5r,z6r]--cycle;% middle stem
@y
 else: fill diag_end(6r,5r,1,1,5l,6l)--.9[z5l,z6l]
   ..{z5-z6}.1[z5r,z6r]--cycle; % middle stem
@z the same change applies also to letter W in ROMANU

@x in CMBASE, makes lowres types (especially TT) look better
 define_blacker_pixels(notch_cut,cap_notch_cut);
@y
 define_blacker_pixels(notch_cut,cap_notch_cut);
 forsuffixes $=notch_cut,cap_notch_cut: if $<3: $:=3; fi endfor
@z

@x in BIGOP, the \displaystyle coproduct sign
lft x11=hround u; x1l-x11=x2l-x12=x22-x2r=hround cap_jut;
@y
lft x11=hround u; x1l-x11=x2l-x12=x22-x2r=hround 1.6cap_jut;
@z

@x in ROMANL, the letter m
lft x1l=hround(2.5u-.5stem); x1l=x1'l=x2l=x2'l;
lft x3l=hround(.5w-.5stem); x5-x3=x3-x1;
if not monospace: r:=hround(x5+x1)-l; fi  % change width for better fit
@y
lft x1l=hround(2.5u-.5stem); x1l=x1'l=x2l=x2'l; % stem, sic
lft x3l=hround(.5w-.5mfudged.stem); x5-x3=x3-x1;
if not monospace: r:=hround(x5+x1)+r-w; fi  % change width for better fit
@z

@x a new routine for CMBASE, following change_width
@y
def center_on(expr x) = if not monospace: % change width for symmetric fit
 r:=r+2x-w; w:=2x; fi enddef;
@z
@x in SYMBOL, the elementary division operator
x3-.5dot_size=hround(.5w-.5dot_size); w:=r:=2x3;
@y
x3-.5dot_size=hround(.5w-.5dot_size); center_on(x3);
@z
Similarly, whenever the construction "w:=r:=2x*" appears, change it to
"center_on(x*)". This happens in the programs for elementary division operator
(as noted above), large triangle, large inverted triangle, lattice top,
lattice bottom, dagger mark, double dagger mark, club/diamond/heart/spade suit
(all in SYMBOL), plus the diamond operator and universal quantifier in SYM.
The following additional change needs to be made in the programs
for lattice top and lattice bottom:
@x
x1=x2=good.x .5w; center_on(x1); lft x3=hround u; x4=r-x3;
@y
x1=x2=good.x .5w; center_on(x1); lft x3=hround u; x4=w-x3;
@z

@x in SYMBOL, at end of zero-width slash
labels(1,2); zero_width; endchar;
@y
labels(5,6); zero_width; endchar;
@z

@x in ROMANU, the letter Q (this change simply labels point 8 on proofs)
math_fit(-.3cap_height#*slant-.5u#,ic#); penlabels(1,2,3,4,5,6,7); endchar;
@y
math_fit(-.3cap_height#*slant-.5u#,ic#);
penlabels(1,2,3,4,5,6,7,8); endchar;
@z

@x in ROMANL, the letter i (this change by Jonathan Kew makes the dot rounder)
if serifs: x3r=max(x1r,x1+.5(dot_diam-tiny)-.2jut) else: x3=x1-.5 fi;
@y
if serifs: x3r=max(x1r,hround(x1+.5dot_diam-.2jut)-.5tiny)
else: x3=x1-.5 fi;
@z

-----------Improvements made in January 1992
[No change to TFM files]
@x in cmbase (improve lowres as suggested by John Hobby)
def normal_adjust_fit(expr left_adjustment,right_adjustment) =
 l:=-hround(left_adjustment*hppp)-letter_fit;
 interim xoffset:=-l;
 charwd:=charwd+2letter_fit#+left_adjustment+right_adjustment;
 r:=l+hround(charwd*hppp)-shrink_fit;
 w:=r-hround(right_adjustment*hppp)-letter_fit;
 enddef;

def mono_adjust_fit(expr left_adjustment,right_adjustment) =
 numeric expansion_factor;
 mono_charwd#=2letter_fit#
   +expansion_factor*(charwd+left_adjustment+right_adjustment);
 forsuffixes $=u,jut,cap_jut,beak_jut,apex_corr:
   $:=$.#*expansion_factor*hppp; endfor
 l:=-hround(left_adjustment*expansion_factor*hppp)-letter_fit;
 interim xoffset:=-l;
 r:=l+mono_charwd-shrink_fit;
 w:=r-hround(right_adjustment*expansion_factor*hppp)-letter_fit;
 charwd:=mono_charwd#; charic:=mono_charic#;
 enddef;
@y
def do_expansion(expr expansion_factor) =
 forsuffixes $=u,jut,cap_jut,beak_jut,apex_corr:
   $:=$.#*expansion_factor*hppp; endfor
enddef;

def normal_adjust_fit(expr left_adjustment,right_adjustment) =
 numeric charwd_in; charwd_in=charwd;
 l:=-hround(left_adjustment*hppp)-letter_fit;
 interim xoffset:=-l;
 charwd:=charwd+2letter_fit#+left_adjustment+right_adjustment;
 r:=l+hround(charwd*hppp)-shrink_fit;
 w:=r-hround(right_adjustment*hppp)-letter_fit;
 do_expansion(w/(charwd_in*hppp));
 enddef;

def mono_adjust_fit(expr left_adjustment,right_adjustment) =
 numeric charwd_in; charwd_in=charwd;
 numeric expansion_factor;
 mono_charwd#=2letter_fit#
   +expansion_factor*(charwd+left_adjustment+right_adjustment);
 l:=-hround(left_adjustment*expansion_factor*hppp)-letter_fit;
 interim xoffset:=-l;
 r:=l+mono_charwd-shrink_fit;
 w:=r-hround(right_adjustment*expansion_factor*hppp)-letter_fit;
 charwd:=mono_charwd#; charic:=mono_charic#;
 do_expansion(w/(charwd_in*hppp));
 enddef;
@z
@x in SYM, Downward arrow
pos3(bar,90); pos4(bar,90);
lft x1l=hround(.5w-.5rule_thickness); y1+.5rule_thickness=h;
x0=x1=x2; bot y0=-d; x0-x3=x4-x0=3u+eps;
y3=y4=y0+.24asc_height+eps;
pos5(bar,angle(z4-z0)); z5l=z0;
pos6(bar,angle(z3-z0)); z6l=z0;
z9=.381966[.5[z3,z4],z0];
@y (make arrowheads heavier, as suggested by Zapf)
pos3(rule_thickness,90); pos4(rule_thickness,90);
lft x1l=hround(.5w-.5rule_thickness); y1+.5rule_thickness=h;
x0=x1=x2; bot y0=-d; x0-x3=x4-x0=if monospace:3u else:4u fi+eps;
y3=y4=y0+if monospace:.24 else:.36 fi asc_height+eps;
pos5(rule_thickness,angle(z4-z0)); z5l=z0;
pos6(rule_thickness,angle(z3-z0)); z6l=z0;
z9=.2[.5[z3,z4],z0];
@z
@x in SYM, Upward arrow
pos3(bar,90); pos4(bar,90);
lft x1l=hround(.5w-.5rule_thickness); y1-.5rule_thickness=-d;
x0=x1=x2; top y0=h; x0-x3=x4-x0=3u+eps;
y3=y4=y0-.24asc_height-eps;
pos5(bar,angle(z4-z0)); z5l=z0;
pos6(bar,angle(z3-z0)); z6l=z0;
z9=.381966[.5[z3,z4],z0];
@y
pos3(rule_thickness,90); pos4(rule_thickness,90);
lft x1l=hround(.5w-.5rule_thickness); y1-.5rule_thickness=-d;
x0=x1=x2; top y0=h; x0-x3=x4-x0=if monospace:3u else:4u fi+eps;
y3=y4=y0-if monospace:.24 else:.36 fi asc_height-eps;
pos5(rule_thickness,angle(z4-z0)); z5l=z0;
pos6(rule_thickness,angle(z3-z0)); z6l=z0;
z9=.2[.5[z3,z4],z0];
@z
@x in SYM, Leftward arrow
pos1(rule_thickness,90); pos2(rule_thickness,90); pos3(bar,0); pos4(bar,0);
y0=y1=y2=math_axis; x1+.5rule_thickness=hround(w-u); lft x0=hround u;
y3-y0=y0-y4=.24asc_height+eps; x3=x4=x0+3u+eps;
pos5(bar,angle(z4-z0)); z5l=z0; pos6(bar,angle(z3-z0)); z6l=z0;
z9=.381966[.5[z3,z4],z0];
@y
pos1(rule_thickness,90); pos2(rule_thickness,90);
pos3(rule_thickness,0); pos4(rule_thickness,0);
y0=y1=y2=math_axis; x1+.5rule_thickness=hround(w-u); lft x0=hround u;
y3-y0=y0-y4=if monospace:.24 else:.36 fi asc_height+eps;
x3=x4=x0+if monospace:3u else:4u fi+eps;
pos5(rule_thickness,angle(z4-z0)); z5l=z0;
pos6(rule_thickness,angle(z3-z0)); z6l=z0;
z9=.2[.5[z3,z4],z0];
@z
@x in SYM, Rightward arrow
pos1(rule_thickness,90); pos2(rule_thickness,90); pos3(bar,0); pos4(bar,0);
y0=y1=y2=math_axis; x1-.5rule_thickness=hround u; rt x0=hround(w-u);
y3-y0=y0-y4=.24asc_height+eps; x3=x4=x0-4u-eps;
pos5(bar,angle(z4-z0)); z5l=z0; pos6(bar,angle(z3-z0)); z6l=z0;
z9=.381966[.5[z3,z4],z0];
@y
pos1(rule_thickness,90); pos2(rule_thickness,90);
pos3(rule_thickness,0); pos4(rule_thickness,0);
y0=y1=y2=math_axis; x1-.5rule_thickness=hround u; rt x0=hround(w-u);
y3-y0=y0-y4=if monospace:.24 else:.36 fi asc_height+eps;
x3=x4=x0-if monospace:3u else:4u fi-eps;
pos5(rule_thickness,angle(z4-z0)); z5l=z0;
pos6(rule_thickness,angle(z3-z0)); z6l=z0;
z9=.2[.5[z3,z4],z0];
@z
@x in SYM, Left-and-right arrow
pos1(rule_thickness,90); pos2(rule_thickness,90); pos3(bar,0); pos4(bar,0);
y0=y1=y2=math_axis if monospace:+vround.3asc_height fi; lft x0=hround u;
if monospace: x1+.5rule_thickness=hround(w-u) else: x1=.5w fi;
y3-y0=y0-y4=.24asc_height+eps; x3=x4=x0+3u+eps;
pos5(bar,angle(z4-z0)); z5l=z0; pos6(bar,angle(z3-z0)); z6l=z0;
z9=.381966[.5[z3,z4],z0];
@y
pos1(rule_thickness,90); pos2(rule_thickness,90);
pos3(rule_thickness,0); pos4(rule_thickness,0);
y0=y1=y2=math_axis if monospace:+vround.3asc_height fi; lft x0=hround u;
if monospace: x1+.5rule_thickness=hround(w-u) else: x1=.5w fi;
y3-y0=y0-y4=if monospace:.24 else:.36 fi asc_height+eps;
x3=x4=x0+if monospace:3u else:4u fi+eps;
pos5(rule_thickness,angle(z4-z0)); z5l=z0;
pos6(rule_thickness,angle(z3-z0)); z6l=z0;
z9=.2[.5[z3,z4],z0];
@z
@x ibid
pos11(rule_thickness,90); pos12(rule_thickness,90); pos13(bar,0); pos14(bar,0);
y10=y11=y12=math_axis if monospace:-vround.3asc_height fi;
rt x10=hround(w-u);
if monospace: x11-.5rule_thickness=hround u else: x11=.5w fi;
y13-y10=y10-y14=.24asc_height+eps; x13=x14=x10-3u-eps;
pos15(bar,angle(z14-z10)); z15l=z10; pos16(bar,angle(z13-z10)); z16l=z10;
z19=.381966[.5[z13,z14],z10];
@y
pos11(rule_thickness,90); pos12(rule_thickness,90);
pos13(rule_thickness,0); pos14(rule_thickness,0);
y10=y11=y12=math_axis if monospace:-vround.3asc_height fi;
rt x10=hround(w-u);
if monospace: x11-.5rule_thickness=hround u else: x11=.5w fi;
y13-y10=y10-y14=if monospace:.24 else:.36 fi asc_height+eps;
x13=x14=x10-if monospace:3u else:4u fi-eps;
pos15(rule_thickness,angle(z14-z10)); z15l=z10;
pos16(rule_thickness,angle(z13-z10)); z16l=z10;
z19=.2[.5[z13,z14],z10];
@z
@x in SYMBOL, Up-and-down arrow
pos3(bar,90); pos4(bar,90);
lft x1l=hround(.5w-.5rule_thickness); y1=.5[-d,h];
x0=x1=x2; bot y0=-d-o; x0-x3=x4-x0=3u+eps;
y3=y4=y0+.24asc_height+eps;
pos5(bar,angle(z4-z0)); z5l=z0; pos6(bar,angle(z3-z0)); z6l=z0;
z9=.381966[.5[z3,z4],z0];
@y
pos3(rule_thickness,90); pos4(rule_thickness,90);
lft x1l=hround(.5w-.5rule_thickness); y1=.5[-d,h];
x0=x1=x2; bot y0=-d-o; x0-x3=x4-x0=4u+eps;
y3=y4=y0+.36asc_height+eps;
pos5(rule_thickness,angle(z4-z0)); z5l=z0;
pos6(rule_thickness,angle(z3-z0)); z6l=z0;
z9=.2[.5[z3,z4],z0];
@z
@x ibid
pos13(bar,90); pos14(bar,90);
x10=x11=x12; top y10=h+o; x10-x13=x14-x10=3u+eps;
y13=y14=y10-.36asc_height-eps;
pos15(bar,angle(z14-z10)); z15l=z10;
pos16(bar,angle(z13-z10)); z16l=z10;
z19=.381966[.5[z13,z14],z10];
@y
pos13(rule_thickness,90); pos14(rule_thickness,90);
x10=x11=x12; top y10=h+o; x10-x13=x14-x10=4u+eps;
y13=y14=y10-.24asc_height-eps;
pos15(rule_thickness,angle(z14-z10)); z15l=z10;
pos16(rule_thickness,angle(z13-z10)); z16l=z10;
z19=.2[.5[z13,z14],z10];
@z
@x in SYMBOL, Northeast arrow
pos3(bar,theta); pos4(bar,theta);
y3=y0; x4=x0; x0-x3=y0-y4=delta+eps;
pos5(bar,-90); z5l=z0; pos6(bar,-180); z6l=z0;
z9=.381966[.5[z3,z4],z0];
@y
pos3(rule_thickness,theta); pos4(rule_thickness,theta);
z3-z0=(-4u,.36asc_height) rotated theta;
z4-z0=(-4u,-.36asc_height) rotated theta;
pos5(rule_thickness,-90); z5l=z0; pos6(rule_thickness,-180); z6l=z0;
z9=.2[.5[z3,z4],z0];
@z
@x in SYMBOL, Southeast arrow
pos3(bar,theta); pos4(bar,theta);
x3=x0; y4=y0; y3-y0=x0-x4=delta+eps;
pos5(bar,180); z5l=z0; pos6(bar,90); z6l=z0;
z9=.381966[.5[z3,z4],z0];
@y
pos3(rule_thickness,theta); pos4(rule_thickness,theta);
z3-z0=(-4u,.36asc_height) rotated theta;
z4-z0=(-4u,-.36asc_height) rotated theta;
pos5(rule_thickness,180); z5l=z0; pos6(rule_thickness,90); z6l=z0;
z9=.2[.5[z3,z4],z0];
@z
@x in SYMBOL, Northwest arrow
pos3(bar,-180+theta); pos4(bar,-180+theta);
x3=x0; y4=y0; x4-x0=y0-y3=delta+eps;
pos5(bar,0); z5l=z0; pos6(bar,-90); z6l=z0;
z9=.381966[.5[z3,z4],z0];
@y
pos3(rule_thickness,-180+theta); pos4(rule_thickness,-180+theta);
z4-z0=(4u,.36asc_height) rotated theta;
z3-z0=(4u,-.36asc_height) rotated theta;
pos5(rule_thickness,0); z5l=z0; pos6(rule_thickness,-90); z6l=z0;
z9=.2[.5[z3,z4],z0];
@z
@x in SYMBOL, Southwest arrow
pos3(bar,-180+theta); pos4(bar,-180+theta);
y3=y0; x4=x0; x3-x0=y4-y0=delta+eps;
pos5(bar,90); z5l=z0; pos6(bar,0); z6l=z0;
z9=.381966[.5[z3,z4],z0];
@y
pos3(rule_thickness,-180+theta); pos4(rule_thickness,-180+theta);
z4-z0=(4u,.36asc_height) rotated theta;
z3-z0=(4u,-.36asc_height) rotated theta;
pos5(rule_thickness,90); z5l=z0; pos6(rule_thickness,0); z6l=z0;
z9=.2[.5[z3,z4],z0];
@z
@x in ROMMS, Leftward top half arrow
pos1(rule_thickness,90); pos2(rule_thickness,90); pos3(bar,0); pos4(bar,0);
y0=y1=y2=math_axis; x1+.5rule_thickness=hround(w-u); lft x0=hround u;
y3-y0=y0-y4=.24asc_height+eps; x3=x4=x0+3u+eps;
pos5(bar,angle(z4-z0)); z5l=z0; pos6(bar,angle(z3-z0)); z6l=z0;
@y
pos1(rule_thickness,90); pos2(rule_thickness,90);
pos3(rule_thickness,0); pos4(rule_thickness,0);
y0=y1=y2=math_axis; x1+.5rule_thickness=hround(w-u); lft x0=hround u;
y3-y0=y0-y4=.36asc_height+eps; x3=x4=x0+4u+eps;
pos5(rule_thickness,angle(z4-z0)); z5l=z0;
pos6(rule_thickness,angle(z3-z0)); z6l=z0;
@z
@x in ROMMS, Leftward bottom half arrow
pos1(rule_thickness,90); pos2(rule_thickness,90); pos3(bar,0); pos4(bar,0);
y0=y1=y2=math_axis; x1+.5rule_thickness=hround(w-u); lft x0=hround u;
y3-y0=y0-y4=.24asc_height+eps; x3=x4=x0+3u+eps;
pos5(bar,angle(z4-z0)); z5l=z0; pos6(bar,angle(z3-z0)); z6l=z0;
@y
pos1(rule_thickness,90); pos2(rule_thickness,90);
pos3(rule_thickness,0); pos4(rule_thickness,0);
y0=y1=y2=math_axis; x1+.5rule_thickness=hround(w-u); lft x0=hround u;
y3-y0=y0-y4=.36asc_height+eps; x3=x4=x0+4u+eps;
pos5(rule_thickness,angle(z4-z0)); z5l=z0;
pos6(rule_thickness,angle(z3-z0)); z6l=z0;
@z
@x in ROMMS, Rightward top half arrow
pos1(rule_thickness,90); pos2(rule_thickness,90); pos3(bar,0); pos4(bar,0);
y0=y1=y2=math_axis; x1-.5rule_thickness=hround u; rt x0=hround(w-u);
y3-y0=y0-y4=.24asc_height+eps; x3=x4=x0-3u-eps;
pos5(bar,angle(z4-z0)); z5l=z0; pos6(bar,angle(z3-z0)); z6l=z0;
@y
pos1(rule_thickness,90); pos2(rule_thickness,90);
pos3(rule_thickness,0); pos4(rule_thickness,0);
y0=y1=y2=math_axis; x1-.5rule_thickness=hround u; rt x0=hround(w-u);
y3-y0=y0-y4=.36asc_height+eps; x3=x4=x0-4u-eps;
pos5(rule_thickness,angle(z4-z0)); z5l=z0;
pos6(rule_thickness,angle(z3-z0)); z6l=z0;
@z
@x in ROMMS, Rightward bottom half arrow
pos1(rule_thickness,90); pos2(rule_thickness,90); pos3(bar,0); pos4(bar,0);
y0=y1=y2=math_axis; x1-.5rule_thickness=hround u; rt x0=hround(w-u);
y3-y0=y0-y4=.asc_height+eps; x3=x4=x0-3u-eps;
pos5(bar,angle(z4-z0)); z5l=z0; pos6(bar,angle(z3-z0)); z6l=z0;
@y
pos1(rule_thickness,90); pos2(rule_thickness,90);
pos3(rule_thickness,0); pos4(rule_thickness,0);
y0=y1=y2=math_axis; x1-.5rule_thickness=hround u; rt x0=hround(w-u);
y3-y0=y0-y4=.36asc_height+eps; x3=x4=x0-4u-eps;
pos5(rule_thickness,angle(z4-z0)); z5l=z0;
pos6(rule_thickness,angle(z3-z0)); z6l=z0;
@z
@x in CALU, Calligraphic F
top y1=top y6=h; z2=.5[z3,z1]+bend;
bot y3=-o; y4=.1h; y5=y2; y7=.9h;
draw flex(z1,z2,z3) softjoin (z3...{x4-x3,5(y4-y3)}z4);  % stem
draw z1-flourish_change{up}...z1---z6...{down}z7;  %  upper bar
@y
top y1=top y6=h; z2=.5[z3,z1]+1.2bend;
bot y3=-o; y4=.1h; y5=y2; y7=.9h;
draw flex(z1,z2,z3) softjoin (z3...{x4-x3,5(y4-y3)}z4);  % stem
draw z1-flourish_change{up}...(z1-(u,0))---z6...{down}z7;  %  upper bar
@z
@x in CALU, Calligraphic H
lft x1=lft x3=0; rt x4=rt x6=.8w; rt x9=w;
top y1=top y4=h; bot y3=-o; bot y6=bot_flourish_line; y9=y6+.1h;
z2=.6[z3,z1]+bend; z5=.4[z6,z4]-2bend;
path p[]; p1=flex(z1,z2,z3); p2=flex(z4,z5,z6);
p3=(-w,.55h)--(2w,.55h);
lft z7=p3 intersectionpoint p1; rt z8=p3 intersectionpoint p2;
draw (z1-flourish_change{up}....z1-(u,0)---z1) softjoin p1;  % left stem
@y
lft x1=lft x3=.5u; rt x4=rt x6=.8w-.6u; rt x9=w;
top y1=top y4=h; bot y3=-.06h; bot y6=bot_flourish_line; y9=y6+.1h;
z2=.6[z3,z1]+bend; z5=.4[z6,z4]-bend;
path p[]; p1=flex(z1,z2,z3); p2=flex(z4,z5,z6);
p3=(-w,.45h)--(2w,.45h);
rt z7+2bend=p3 intersectionpoint p1; rt z8=p3 intersectionpoint p2;
draw (z1-flourish_change-bend{curl2}....z1-(u,0)---z1) softjoin p1;  % left stem
@z
@x in CALU, Calligraphic I
lft x0=0; x1=.9w; x2=x4=.5w; x5=.2w; x6=.75w; rt x7=w;
@y
lft x0=0; x1=.9w; x2=x4=.5w; x5=.2w; x6=.8w; rt x7=1.05w;
@z
@x in CALU, Calligraphic T
x1=x3=.5w; lft x4=0; x5=w-x6=.25w; rt x7=w;
x1=.47w; x3=.5w; lft x4=0; x5=w-x6=.25w; rt x7=1.05w;
z2=.5[z3,z1]+bend;
x1-x8=x9-x1=2u; y8=y9=y3;
z0=1/3[z1,z6];
draw z0{left}...z2{down}...{left}z8;  % stem
draw z8--z9;  % foot
draw z4{up}...z5{right}...z6{right}...{up}z7;  % arms
math_fit(.5u#-5/7h#*slant,-u#); labels(1,2,3,4,5,6,7,8,9); endchar;
@y
x1=.47w; x3=.5w; lft x4=0; x5=.25w; x6=.85w; rt x7=1.05w;
top y1=h; bot y3=-.1h; y4=3/4h; top y5=top y6=h; top y7=1.05h;
z2=.3[z3,z1]+bend;
top y0=y1; x0=x2;
z8=(2u,.2h);
draw z0---z2...z3;  % stem
draw z4{curl 2}...z5{right}...z6{right}...{up}z7;  % arms
math_fit(.5u#-5/7h#*slant,-u#); labels(1,2,3,4,5,6,7); endchar;
@z
@x in GREEKL, lowercase delta
pos1(hair,-180); pos2(vair,-90);
numeric theta; theta=angle(18u,-h);
pos3(stem,theta+90); pos4(stem,theta+90); pos5(1/4[hair,stem],20);
pos6(vair,-90); pos7(curve,-180); pos8(vair,-270);
rt x1l=hround(w-2u+.5hair); x2=.5w; x3r=3u; rt x5r=hround(w-u);
x4=x6=x8=.5w+.5u; lft x7r=hround(1.5u-.5curve);
top y2l=h+oo; y1=min(.9h,y2r-eps); top y8r=x_height+oo; y4=y8;
z4-z3=whatever*(18u,-h); y5=y7=.5[y6,y8]; bot y6=-oo;
filldraw stroke z1e{x2-x1,3(y2-y1)}...z2e{left}...z3e---z4e
 ....z5e{down}...pulled_arc.e(6,7) & pulled_arc.e(7,8);  % hook and bowl
math_fit(-.3x_height#*slant+.5curve#-u#,.7x_height#*slant-.5u#);
penlabels(1,2,3,4,5,6,7,8); endchar;
@y
x0=-u; y0=1.1h;
numeric light_flare; light_flare=2/3[vair,flare];
x1=w-2u-.5light_flare; y1=h-.5light_flare;
numeric theta; theta=angle (z1-z0);
pos1(light_flare,theta-90); pos2(.2[vair,light_flare],-90); pos3(vair,theta);
x2=x3+u; y2=h;
x4=x6=.5w+.5u; top y8r=x_height+oo; z4=z8;
pos6(vair,-90); pos7(stem,-180); pos8(vair,-270);
pos4(stem,angle(z4-z0)+90); pos5(stem,30);
z3=.5[.5[z1,z4],z0];
y5+.1x_height=y7=.5[y6,y8]; bot y6=-oo;
lft x7r=hround(1.4u-.5stem); rt x5r=hround(w-u);
filldraw stroke z1e{z0-z1e}....z2e....z3e{(z0-z1)rotated 90}
 ...z4e{z4e-.8[z4,z0]}
 ....z5e{down}...pulled_arc.e(6,7) & pulled_arc.e(7,8);  % hook and bowl
filldraw z1r{z1r-z0}...z1l{z0-z1l}--cycle; % bulb
math_fit(-.3x_height#*slant+.5curve#-u#,.7x_height#*slant-.5u#);
penlabels(0,1,2,3,4,5,6,7,8); endchar;
@z
@x in TSETSL, lowercase delta for extended ASCII
pos1(hair,-180); pos2(vair,-90);
numeric theta; theta=angle(18u,-h);
pos3(stem,theta+90); pos4(stem,theta+90); pos5(1/4[hair,stem],20);
pos6(vair,-90); pos7(curve,-180); pos8(vair,-270);
rt x1l=hround(w-2u+.5hair); x2=.5w; x3r=3u; rt x5r=hround(w-u);
x4=x6=x8=.5w+.5u; lft x7r=hround(1.5u-.5curve);
top y2l=h+oo; y1=min(.9h,y2r-eps); top y8r=x_height+oo; y4=y8;
z4-z3=whatever*(18u,-h); y5=y7=.5[y6,y8]; bot y6=-oo;
filldraw stroke z1e{x2-x1,3(y2-y1)}...z2e{left}...z3e---z4e
 ....z5e{down}...pulled_arc.e(6,7) & pulled_arc.e(7,8);  % hook and bowl
penlabels(1,2,3,4,5,6,7,8); endchar;
@y this next line differs from GREEKL, but the other lines agree
x0=-u; y0=1.05h;
numeric light_flare; light_flare=2/3[vair,flare];
x1=w-2u-.5light_flare; y1=h-.5light_flare;
numeric theta; theta=angle (z1-z0);
pos1(light_flare,theta-90); pos2(.2[vair,light_flare],-90); pos3(vair,theta);
x2=x3+u; y2=h;
x4=x6=.5w+.5u; top y8r=x_height+oo; z4=z8;
pos6(vair,-90); pos7(stem,-180); pos8(vair,-270);
pos4(stem,angle(z4-z0)+90); pos5(stem,30);
z3=.5[.5[z1,z4],z0];
y5+.1x_height=y7=.5[y6,y8]; bot y6=-oo;
lft x7r=hround(1.4u-.5stem); rt x5r=hround(w-u);
filldraw stroke z1e{z0-z1e}....z2e....z3e{(z0-z1)rotated 90}
 ...z4e{z4e-.8[z4,z0]}
 ....z5e{down}...pulled_arc.e(6,7) & pulled_arc.e(7,8);  % hook and bowl
filldraw z1r{z1r-z0}...z1l{z0-z1l}--cycle; % bulb
penlabels(0,1,2,3,4,5,6,7,8); endchar;
@z

----------- Changes made after the fourth printing (1993) of Volume E

@x in CSCSPU, letter J [fixes a bug if dish=0 and crisp<tiny and serifs]
 bulb(3,4,5);  % bulb
@y
 pickup tiny.nib; bulb(3,4,5);  % bulb
@z

@x in BIGDEL, two harmless bugs caught by Robert Hunt
"Extensible vertical arrow--extension module";
@y
cmchar "Extensible vertical arrow--extension module";
@z
@x
"Extensible double vertical arrow--extension module";
@y
cmchar "Extensible double vertical arrow--extension module";
@z

@x in GREEKU, letter Phi (hi-res glitch found by Robert Hunt)
lft x1l=lft x2l=hround(.5w-.5cap_stem); top y1=h; bot y2=0;
@y
lft x1l=lft x2l=hround(.5w-.5shaved_stem); top y1=h; bot y2=0;
@z
@x in GREEKU, letter Psi similarly
lft x1l=lft x2l=hround(.5w-.5cap_stem); top y1=h; bot y2=0;
@y
lft x1l=lft x2l=hround(.5w-.5shaved_stem); top y1=h; bot y2=0;
@z

@x in BIGOP, teststyle integral sign
x5=.5[x4,x6]; x4-x6=1.2u; lft x5r=hround(.5w-.5stem);
@y
x5=.5[x4,x6]; x4-x6=1.2u; lft x5r=hround(.5w-.5curve);
@z
@x same, displaystyle integral sign
x5=.5[x4,x6]; x4-x6=4.8u; lft x5r=hround(.5w-.5stem);
@y
x5=.5[x4,x6]; x4-x6=4.8u; lft x5r=hround(.5w-.5max_size);
@z
@x same, textstyle contour integral sign
x5=.5[x4,x6]; x4-x6=1.2u; lft x5r=hround(.5w-.5stem);
@y
x5=.5[x4,x6]; x4-x6=1.2u; lft x5r=hround(.5w-.5curve);
@z
@x same, displaystyle contour integral sign
x5=.5[x4,x6]; x4-x6=4.8u; lft x5r=hround(.5w-.5stem);
@y
x5=.5[x4,x6]; x4-x6=4.8u; lft x5r=hround(.5w-.5max_size);
@z

@x in ITALMS, the partial differential sign
path p; p=pulled_super_arc.l(3,4)(pull);
@y
path p; {{interim superness:=more_super; p=pulled_super_arc.l(3,4)(pull)}};
@z

@x in SYMBOL, the elementary division operator
beginarithchar(oct"004"); pickup rule.nib;
x3-.5dot_size=hround(.5w-.5dot_size); center_on(x3);
y3+.5dot_size=vround(math_axis+math_spread[.5x_height,.6x_height]+.5dot_size);
@y note that pickup rule.nib leaves currentbreadth unchanged
beginarithchar(oct"004"); pickup fine.nib; pickup rule.nib;
numeric del; del=dot_size-currentbreadth; % currentbreadth=fine
x3-.5del=good.x(.5w-.5del); center_on(x3);
y3+.5del=good.y(math_axis+math_spread[.5x_height,.6x_height]+.5del);
@z

@x in CMBASE, compute_spread can force even spreads for better rounding
 spread:=ceiling(spread#*hppp)+eps; enddef;
@y
 spread:=2ceiling(spread#*hppp/2)+eps; enddef;
@z

@x in CMBASE, better diag_ratio routine avoids overflow in hi-res chars
 numeric a_,b_; b_=b/y; a_=a*a-b_*b_;
 (a*(c++y*sqrt a_)-b_*c)/a_/y enddef;
@y
 numeric a_,b_,c_; b_=b/y; c_=c/y; a_=a*a-b_*b_;
 (a*(c_++sqrt a_)-b_*c_)/a_ enddef;
@z

@x in ROMAND, numeral 3, allow hi-res cminch to run without overflow (MacKay)
x4=1/3[x5,x3l]; z4=z5+whatever*(150u,h);
@y
x4=1/3[x5,x3l]; z4=z5+whatever*(15u,.1h);
@z

@x in ITALP, the Sterling sign (bug caught by Yannis Haralambous)
lft x6r=hround u; x7=3u; x8=w-3.5u; rt x9r=hround(w-u);
@y
lft x6r=hround u; x7=3u; x8=w-3.5u; rt x9l=hround(w-u);
@z

@x in GREEKL, lowercase omega, I made minor changes for new edition of TAOCP:
y1+.5hair=h; x1=x2+.75u; pos1(hair,angle(2(x1-x2),y1-y2)+90);
@y
y1+.5hair=h; x1=x2+.75u; pos1(hair+dw,angle(2(x1-x2),y1-y2)+90);
@z
@x
x3=.5[x2,x4]; x7+.25u=.5[x6,x8]; rt x8r=hround(w-.5u);
@y
x3=.5[x2,x4]; x7-.25u=.5[x6,x8]; rt x8r=hround(w-.5u);
@z

@x in GREEKL, lowercase beta, I made minor changes for new edition of TAOCP:
pos3(stem,0); pos4(vair,-90); pos5(hair,-180);
pos6(vair,-270); pos7(curve,-360); pos8(vair,-450); pos9(hair,-540);
x0=x1=x9; lft x0l=hround(1.5u-.5hair); x2=x4=x6=x8=.5w+.25u;
rt x3r=hround(w-1.5u); rt x7r=hround(w-1.5u+.5curve); rt x5l=hround(x4-u);
bot y0=-d; y1=top y6r=x_height; top y2r=h+oo; y3=.5[y2,y4];
y5=.5[y4,y6]; top y6r-bot y4r=vstem+eps; bot y8=-oo; y7=y9=.5[y6,y8];
@y (this change also is made in TSETSL)
pos3(.8[hair,stem],0); pos4(vair,-90); pos5(hair,-180);
pos6(vair,-270); pos7(stem,-360); pos8(vair,-450); pos9(hair,-540);
x0=x1=x9; lft x0l=hround(1.5u-.5hair); x2=x4=x6=x8=.5w-.25u;
rt x3r=hround(w-1.75u); rt x7r=hround(w-u); rt x5l=hround(x4-u);
bot y0=-d; y1=top y6r=x_height; top y2r=h+oo; y3=.5[y2,y4];
y5=.5[y4,y6]; top y6r-bot y4r=vstem+eps; bot y8=-oo; y7=y9=.55[y6,y8];
@z

@x in ROMANU, less overshoot on uppercase sans serif C (for Vol 2 of TAOCP)
 top y1r=vround .95h+o; top y2r=h+o; y3=.5h;
 bot y4r=-o; bot y5r=vround .08h-o; y5l:=good.y y5l; x5l:=good.x x5l;
@y
 top y1r=vround .95h+oo; top y2r=h+oo; y3=.5h;
 bot y4r=-oo; bot y5r=vround .08h-oo; y5l:=good.y y5l; x5l:=good.x x5l;
@z

@x in ROMANU, likewise for G
 top y1r=vround .93h+o; top y2r=h+o; y3=.5h;
 bot y4r=-o; bot y5r=vround .07h-o;
@y
 top y1r=vround .93h+oo; top y2r=h+oo; y3=.5h;
 bot y4r=-oo; bot y5r=vround .07h-oo;
@z

@x in SYMBOL, spade suit, a cosmetic change that doesn't affect any fonts:
labels(1,2,3,5,6,10,11,12,13,14,15); endchar;
@y
labels(1,2,3,5,6,7,8,9,10,11,12,13,14,15); endchar;
@z

@x in CMBASE, sloped_serif.l never used $$ except rarely in letter p
 y@0=max(y@2l-bracket,y$$)-eps;
@y and in letter p, it was wrong to do so! (but not in any normal font)
 y@0=y@2l-bracket-eps;
@z
@x sloped_serif.r never used $$ in any reasonable way at all
 y@0=min(y@2l+bracket,y$$)+eps;
@y
 y@0=y@2l+bracket+eps;
@z

in ITALD, programs for 6 and 9: same change as above for partial derivative
in OLDDIG, programs for 6 and 9: same change as above for partial derivative
in ROMAND, programs for 6 and 9: same change as above for partial derivative
in TSETSL, program for partial derivative: same change as above

@x in ROMANL, slight change to cmss10 and cmssbx10 `g' improves meta-ness
loop_top=Vround .77[vair,fudged.stem];
@y
loop_top=if serifs: Vround .77[vair,fudged.stem] else: vair fi;
@z

@x in CMBASE, recent change shouldn't clobber a_, b_, and c_ of plain.mf
 numeric a_,b_,c_; b_=b/y; c_=c/y; a_=a*a-b_*b_;
 (a*(c_++sqrt a_)-b_*c_)/a_ enddef;
@y
 numeric aa_,bb_,cc_; bb_=b/y; cc_=c/y; aa_=a*a-bb_*bb_;
 (a*(cc_++sqrt aa_)-bb_*cc_)/aa_ enddef;
@z

@x in ITALMS, Arrow (vector) accent
lft x1=hround .5u; x2=w-x1; y1=y2=good.x .7[x_height,asc_height];
@y a correction of almost purely academic interest
lft x1=hround .5u; x2=w-x1; y1=y2=good.y .7[x_height,asc_height];
@z

the following patches make the arrows more robust, but essentially unchanged
@x in SYM, Downward arrow
 --z2r---z1r..z1l---z2l--subpath (t,0) of\\(z3r{z9-z3}..z5r)
@y
 ---z1r..z1l---subpath (t,0) of\\(z3r{z9-z3}..z5r)
@z
@x in SYM, Upward arrow
 --z2r---z1r..z1l---z2l--subpath (t,0) of\\(z3l{z9-z3}..z5r)
@y
 ---z1r..z1l---subpath (t,0) of\\(z3l{z9-z3}..z5r)
@z
@x in SYM, Leftward arrow
 --z2l---z1l..z1r---z2r--subpath (t,0) of\\(z3r{z9-z3}..z5r)
@y
 ---z1l..z1r---subpath (t,0) of\\(z3r{z9-z3}..z5r)
@z
@x in SYM, Rightward arrow
 --z2l---z1l..z1r---z2r--subpath (t,0) of\\(z3l{z9-z3}..z5r)
@y
 ---z1l..z1r---subpath (t,0) of\\(z3l{z9-z3}..z5r)
@z
@x in SYM, Left-and-right arrow
 --z2l---z1l..z1r---z2r--subpath (t,0) of\\(z3r{z9-z3}..z5r)
@y
 ---z1l..z1r---subpath (t,0) of\\(z3r{z9-z3}..z5r)
@z
@x ibid
 --z12l---z11l..z11r---z12r--subpath (t,0) of\\(z13l{z19-z13}..z15r)
@y
 ---z11l..z11r---subpath (t,0) of\\(z13l{z19-z13}..z15r)
@z
@x in SYMBOL, Up-and-down arrow
 --z2r---z1r..z1l---z2l--subpath (t,0) of\\(z3r{z9-z3}..z5r)
@y
 ---z1r..z1l---subpath (t,0) of\\(z3r{z9-z3}..z5r)
@z
@x ibid
 --z12r---z11r..z11l---z12l--subpath (t,0) of\\(z13l{z19-z13}..z15r)
@y
 ---z11r..z11l---subpath (t,0) of\\(z13l{z19-z13}..z15r)
@z
@x in SYMBOL, Northeast arrow
 --z2l---z1l..z1r---z2r--subpath (t,0) of\\(z3l{z9-z3}..z5r)
@y
 ---z1l..z1r---subpath (t,0) of\\(z3l{z9-z3}..z5r)
@z
@x in SYMBOL, Southeast arrow
 --z2l---z1l..z1r---z2r
 --subpath (t,0) of\\(z3l{z9-z3}..z5r)
@y
 ---z1l..z1r---subpath (t,0) of\\(z3l{z9-z3}..z5r)
@z
@x in SYMBOL, Northwest arrow
 --z2l---z1l..z1r---z2r--subpath (t,0) of\\(z3l{z9-z3}..z5r)
@y
 ---z1l..z1r---subpath (t,0) of\\(z3l{z9-z3}..z5r)
@z
@x in SYMBOL, Southwest arrow
 --z2l---z1l..z1r---z2r
 --subpath (t,0) of\\(z3l{z9-z3}..z5r)
@y
 ---z1l..z1r---subpath (t,0) of\\(z3l{z9-z3}..z5r)
@z
@x in ROMMS, Leftward top half arrow
filldraw z0--(x0,y2l)---z1l..z1r---z2r
 ..subpath (t,0) of\\(z3r..{2(x0-x3),y0-y3}z5r)
@y
filldraw z0--(x0,y2l)--z1l{right}..{left}z1r
 --subpath (t,0) of\\(z3r..{2(x0-x3),y0-y3}z5r)
@z
@x in ROMMS, Leftward bottom half arrow
filldraw z0{2(x4-x0),y4-y0}..z4l
 --subpath (0,t) of\\(z4r..{2(x0-x4),y0-y4}z6r)
@y
 --z1l{right}..{left}z1r--(x0,y2r)--cycle;  % arrowhead and stem
@z
@x in ROMMS, Rightward top half arrow
filldraw z0--(x0,y2l)---z1l..z1r---z2r
 ..subpath (t,0) of\\(z3l..{2(x0-x3),y0-y3}z5r)
@y
filldraw z0--(x0,y2l)--z1l{left}..{right}z1r
 --subpath (t,0) of\\(z3l..{2(x0-x3),y0-y3}z5r)
@z
@x in ROMMS, Rightward bottom half arrow
 ..z2l---z1l..z1r---(x0,y2r)--cycle;  % arrowhead and stem
@y
 --z1l{left}..{right}z1r--(x0,y2r)--cycle;  % arrowhead and stem
@z
@x in BIGDEL, Extensible vertical arrow--top
 --z2r---z1r--z1l---z2l--subpath (t,0) of\\(z3l{z9-z3}..z5r)
@y
 --z1r--z1l--subpath (t,0) of\\(z3l{z9-z3}..z5r)
@z
@x in BIGDEL, Extensible vertical arrow--bottom
 --z2r---z1r--z1l---z2l--subpath (t,0) of\\(z3r{z9-z3}..z5r)
@y
 --z1r--z1l--subpath (t,0) of\\(z3r{z9-z3}..z5r)
@z

@x in ROMLIG, the ligature fi
 x13=x11-.5; top y14r=min(2x_height,h+1); top y11=x_height;
@y make the center of the dot consistent with ordinary i, in sans-serif fonts
 x13=x11-.5; top y14r=min(10/7x_height+.5bulb_diam,h)+1; top y11=x_height;
@z
@x in ROMLIG, the ligature ffi
 x23=x21-.5; top y24r=min(2x_height,h+1); top y21=x_height;
@y same corrections as to fi
 x23=x21-.5; top y24r=min(10/7x_height+.5bulb_diam,h)+1; top y21=x_height;
@z

@x in SYMBOL, the circle operator
lft x6=hround u; x2=w-x6; top y8=h; y2=math_axis;
@y this correction makes it a circle even at small size, low resolution
lft x6=hround u; x2=w-x6; top y8=h; y8-y4=x2-x6;
@z
@x in SYMBOL, the bullet
lft x6=hround u; x2=w-x6; top y8=h; y2=math_axis; circle_points;
@y likewise
lft x6=hround u; x2=w-x6; top y8=h; y8-y4=x2-x6; circle_points;
@z

@x in ROMAND, the numeral 2
 ..z3e{down}.. z4e---z5e--z6e;  % stroke
@y it's more robust to avoid --- next to -- (in case of tiny loops)
 ..z3e{down}..{z5e-z4e}z4e--z5e--z6e;  % stroke
@z
@x in OLDDIG, oldstyle numeral 2
 ..z3e{down}.. z4e---z5e--z6e;  % stroke
@y likewise
 ..z3e{down}..{z5e-z4e}z4e--z5e--z6e;  % stroke
@z

@x in CSC, after the second font_setup
extra_endchar:=extra_endchar&"charcode:=charcode+code_offset";
@y
extra_endchar:=extra_endchar&"charcode:=charcode+code_offset;";
@z

@x in ACCENT, in program for Breve
numeric mid_thickness; mid_thickness=vround 1/3[vair,stem];
@y
numeric mid_thickness; mid_thickness=Vround 1/3[vair,stem];
@z

@x in CMBASE, a more robust arm routine fixes the 7 in cmbx5,6,7,8
  filldraw z$$l{z@1-z$$l}...darkness[z@1,.5[z@2,z$$l] ]...z@2
   ---z$l--z$r--z@0--z$$r--cycle; % arm and beak
@y
  path p_; p_= z$$l{z@1-z$$l}...darkness[z@1,.5[z@2,z$$l] ]...z@2
    ---z$l--z$r--z@0--z$$r--cycle;
  if (y$$>y$) <> (ypart precontrol 1 of p_ > ypart postcontrol 1 of p_):
    p_:=z$$l{z@1-z$$l}...darkness[z@1,.5[z@2,z$$l] ]
     ---z$l--z$r--z@0--z$$r--cycle; fi
  filldraw p_; % arm and beak
@z

@x in CALU, I decided in July 2005 that I really wanted a less swashy F
top y1=top y6=h; z2=.5[z3,z1]+1.2bend;
bot y3=-o; y4=.1h; y5=y2; y7=.9h;
draw flex(z1,z2,z3) softjoin (z3...{x4-x3,5(y4-y3)}z4);  % stem
draw z1-flourish_change{up}...(z1-(u,0))---z6...{down}z7;  %  upper bar
@y
top y1=top y6=h; z2=.5[z3,z1]+bend;
bot y3=-o; y4=.1h; y5=y2; y7=.9h;
draw flex(z1,z2,z3) softjoin (z3...{x4-x3,5(y4-y3)}z4);  % stem
draw z1-flourish_change+(0,.15asc_height){up}...{right}(z1-(2u,0))
        ---z6...{down}z7;  %  upper bar
@z

@x in SYMBOL, two points of Hardy's asymptotic equivalence sign were unlabeled
labels(1,2,3,4); endchar;
@y
labels(1,2,3,4,5,6); endchar;
@z

@x in GREEKL, correct a tiny notch that can show up at hires (Charles Duan)
filldraw z1l--z2l--z--z1r--cycle;  % stem
@y
filldraw z1l--z2l...(x3,y2l)...z--z1r--cycle;  % stem
@z

@x in GREEKL, make almost-invisible semantic corrections to beta
x0=x1=x9; lft x0l=hround(1.5u-.5hair); x2=x4=x6=x8=.5w-.25u;
@y
x0=x1=x9; lft x0r=hround(1.5u-.5hair); x2=x4=x6=x8=.5w-.25u;
@z
@x
y5=.5[y4,y6]; top y6r-bot y4r=vstem+eps; bot y8=-oo; y7=y9=.55[y6,y8];
@y
y5=.5[y4,y6]; top y6r-bot y4r=vstem+eps; bot y8r=-oo; y7=y9=.55[y6,y8];
@z
@x and also to delta
y5+.1x_height=y7=.5[y6,y8]; bot y6=-oo;
@y
y5+.1x_height=y7=.5[y6,y8]; bot y6r=-oo;
@z
@x and also to phi
top y1=x_height+oo; y2=y4=.5[y1,y3]; bot y3=-oo;
@y
top y1r=x_height+oo; y2=y4=.5[y1,y3]; bot y3r=-oo;
@z

-----------Here I draw the line with respect to further changes

(I sincerely believe there won't be any more!)

I absolutely guarantee that the TFM files will never change again.
(Otherwise I would consider zeroing the depth of italic 7,
which I admit is strange... we can live with it.)
