texdimens (30jun21)

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+License for texdimens package
+=======
+
+Copyright (c) 2021 Jean-François Burnol
+
+This Work may be distributed and/or modified under the conditions of the
+LaTeX Project Public License version 1.3c. This version of this license
+is in
+
+> <http://www.latex-project.org/lppl/lppl-1-3c.txt>
+
+and version 1.3 or later is part of all distributions of LaTeX version
+2005/12/01 or later.
+
+This Work has the LPPL maintenance status author-maintained.
+
+The Author of this Work is Jean-François Burnol
+
+This Work consists of the package files `texdimens.tex`, `texdimens.sty`,
+`README.md` and `LICENSE.md`.
+
diff --git a/Master/texmf-dist/doc/generic/texdimens/README.md b/Master/texmf-dist/doc/generic/texdimens/README.md
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+texdimens
+=========
+
+## Copyright and License
+
+Copyright (c) 2021 Jean-François Burnol
+
+This file is part of the texdimens package distributed under the
+LPPL 1.3c.  See file LICENSE.md.
+
+Development: https://github.com/jfbu/texdimens
+
+## Aim of this package
+
+Utilities and documentation related to TeX dimensional units, usable
+both with Plain (\input texdimens) and with LaTeX (\usepackage{texdimens}).
+
+The aim of this package is to address the issue of expressing dimensions
+(or dimension expressions evaluated by `\dimexpr`) in the various TeX
+units, to the extent possible.
+
+The descriptions that follow do not explain the details of the exact
+internal TeX procedures of parsing dimensional input, they only describe
+in a faithful manner the exact outcome of those internal procedures.
+The reader is supposed to be familiar with TeX basics.
+
+This project requires the e-TeX extensions `\dimexpr` and `\numexpr`.
+
+Notice that this is WIP and inaccuracies may exist even relative to
+descriptions of TeX handlings due to  limited time available for the project.
+
+## TeX points and scaled points
+
+TeX dimensions are represented internally by a signed integer which is
+in absolute value at most `0x3FFFFFFF`, i.e. `1073741823`.  The
+corresponding unit is called the "scaled point", i.e. `1sp` is `1/65536`
+of one TeX point `1pt`, or rather `1pt` is represented internally as `65536`.
+
+If `\foo` is a dimen register:
+
+- `\number\foo` produces the integer `N` such as `\foo` is the same as `N sp`,
+
+- inside `\numexpr`, `\foo` is replaced by `N`,
+
+- `\the\foo` produces a decimal `D` (with at most five places) followed
+with `pt` (catcode 12 tokens) and this output `D pt` can serve as input
+in a dimen assignment to produce the same dimension as `\foo`.  One can
+also use the catcode 11 characters `pt` for this.  Digits and decimal
+mark must have their standard catcode 12.
+
+When TeX encounters a dimen denotation of the type `D pt` it will
+compute `N` in a way equivalent to `N = round(65536 D)` where ties are
+rounded away from zero.  Only 17 decimal places of `D` are
+kept as it can be shown that going beyond can not change the result.
+
+When `\foo` has been assigned as `D pt`, `\the\foo` will produce some
+`E pt` where `E` is not necessarily the same as `D`.  But it is guaranteed
+that `E pt` defines the same dimension as `D pt̀`.
+
+
+## Further units known to TeX on input
+
+TeX understands on input further units: `bp`, `cm`, `mm`, `in`, `pc`,
+`cc`, `dd` and `nd`.  It also understands font-dependent units `ex` and
+`em`, and PDFTeX adds the `px` dimension unit.  Japanese engines also
+add specific units.
+
+`ex`, `em`, `px` and other engine-dependent units, are all currently
+excluded from consideration in this project and the rest of this
+documentation is only for the `bp`, `cm`, `mm`, `in`, `pc`, `cc`, `dd`
+and `nd` units. When we say "unit" we mean one of those or the `pt` (the
+`sp` is a special case and will be included or not tacitly in the "unit"
+denomination depending on the case).
+
+TeX associates to each such unit `uu` a fraction `phi` which is a conversion
+factor.  It is always `>1`:
+
+    uu     phi      reduced  real approximation  1uu in sp=   x=[65536phi]/65536  \the<1uu>
+                                                 [65536phi]  (real approximation)
+    --  ----------  -------  ------------------   ---------  -------------------- ----------
+    bp  7227/7200   803/800   1.00375                 65781    1.0037384033203125  1.00374pt
+    nd  685/642     same      1.0669781931464175      69925    1.0669708251953125  1.06697pt
+    dd  1238/1157   same      1.070008643042351       70124    1.07000732421875    1.07pt   
+    mm  7227/2540   same      2.8452755905511813     186467    2.8452606201171875  2.84526pt
+    pc  12/1        12       12.0                    786432   12.0                12.0pt    
+    nc  1370/107    same     12.80373831775701       839105   12.803726196289062  12.80373pt
+    cc  14856/1157  same     12.84010371650821       841489   12.840103149414062  12.8401pt 
+    cm  7227/254    same     28.45275590551181      1864679   28.452743530273438  28.45274pt
+    in  7227/100    same     72.27                  4736286   72.26998901367188   72.26999pt
+
+When TeX parses an assignment `U uu` with a decimal `U` and a unit `uu`,
+among those listed above, it first handles `U` as with the `pt` unit.
+This means that it computes `N = round(65536*U)`. It then multiplies
+this `N` by the conversion factor `phi` and truncates towards zero the
+mathematically exact result to obtain an integer `T`:
+`T=trunc(N*phi)`. The assignment `U uu` is concluded by defining the
+value of the dimension to be `T sp`.
+
+Attention that although the mnemotic is `phi=1uu/1pt`, this formula
+definitely does not apply with numerator and denominator interpreted as
+TeX dimensions.  See the above table.  Also, the last column looks like
+`round(.,5)` is applied to the previous one, but `\the\dimexpr1dd\relax`
+is an exception (in the table `[x]` is the integer part, aka for
+non-negative values, the `\trunc()` function).  Notice also that
+`1.00375` is the exact value of the `phi` factor for the `bp` unit but
+`1.00375pt>1bp` (`65782>65781`).
+
+As `phi>1` (and is not exceedingly close to `1`), the increasing
+sequence `0<=trunc(phi)<=trunc(2phi)<=...` is *strictly increasing* and
+**it has jumps**: not all TeX dimensions can be obtained from an
+assignment not using the `pt` unit.
+
+The "worst" unit is the largest i.e. the `in` whose conversion factor is
+`72.27`.  The simplest unit to understand is the `pc` as it corresponds
+to an integer ratio `12`: only dimensions which in scaled points are
+multiple of `12` are exactly representable in the `pc` unit.
+
+This also means that some dimensions expressible in one unit may not be
+available with another unit.  For example, it turns out that `0.6in` can
+not be expressed as `D cm`, whatever the `D`.  More surprisingly perhaps
+is that `1in==2.54cm` is **false** in TeX! But it is true that
+`100in==254cm`! It is also false that `10in==25.4cm` but it is true that
+`10in==254mm`! It is false though that `1in==25.4mm`!
+
+    >>> (\dimexpr1in, \dimexpr2.54cm);
+    @_1     4736286, 4736274
+    >>> (\dimexpr10in, \dimexpr25.4cm);
+    @_2     47362867, 47362855
+    >>> (\dimexpr100in, \dimexpr254cm);
+    @_3     473628672, 473628672
+    
+    >>> (\dimexpr1in, \dimexpr25.4mm);
+    @_4     4736286, 4736285
+    >>> (\dimexpr10in, \dimexpr254mm);
+    @_5     47362867, 47362867
+
+`\maxdimen` can be expressed only with `pt`, `bp`, and `nd`.  For the
+other units the maximal attainable dimensions are given in this table:
+
+    16322.78954 bp  (\maxdimen = 1073741823 sp)
+    15355.51532 nd  (\maxdimen = 1073741823 sp)
+    15312.02583 dd  (1073741822 sp)
+     5758.31741 mm  (1073741822 sp)
+     1365.33333 pc  (1073741820 sp)
+     1279.62627 nc  (1073741814 sp)
+     1276.00215 cc  (1073741821 sp)
+      575.83174 cm  (1073741822 sp)
+      226.7054  in  (1073741768 sp)
+
+Perhaps for these various peculiarities with dimensional units, TeX does
+not provide an output facility for them similar to what `\the` achieves for
+the `pt`.
+
+## Macros of this package
+
+All macros are expandable.  At time of writing they may not be
+f-expandable, but (perhaps) in future final versions will expand fully
+in two steps.  This refinement is anyhow not really important as TeX
+engines now support the `\expanded` primitive.
+
+All macros handle negative dimensions via their absolute value then
+taking the opposite.
+
+1. At time of writing only the `\texdimin<uu>` macros are implemented,
+The envisioned "down" and "up" variants are not done yet.
+
+2. For `dd`, `nc` and `in`, input equal to (or sufficiently close to)
+`\maxdimen` will produce also with `\texdimin<uu>` an output `D`
+representing the next "attainable" dimension above `\maxdimen` hence
+using `Duu` will trigger "Dimension too large error".
+
+3. (not yet) For input equal to (or sufficiently close to) `\maxdimen` and those
+units `uu` for which `\maxdimen` is not exactly representable, i.e. all
+units except `pt`, `bp` and `nd`, the output `D` of the "up" variants
+`\texdimin<uu>u` if used as `Duu` in a dimension assignment or
+expression will (naturally) trigger "Dimension too large" error.
+
+4. (not yet) For some units the "down" and "up" macros may trigger "Dimension too
+large" during their execution if used with an input too close to
+`\maxdimen`. "Safe" variants which are guaranteed never to trigger this
+error but have some extra overhead to filter out inputs too close to
+`\maxdimen` will *perhaps* be provided. But see 2. and 3. regarding the
+usability of the output anyhow.
+
+`\texdiminpt{<dim. expr.>}`
+
+> Does `\the\dimexpr <dim. expr.> \relax` then removes the `pt`.
+
+`\texdiminbp{<dim. expr.>}`
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> bp` represents the dimension exactly if possible. If not possible it
+> will differ by `1sp` from the original dimension, but it is not
+> known in advance if it will be above or below.
+
+> `\maxdimen` on input produces `16322.78954` and indeed is realized as `16322.78954bp`.
+
+`\texdiminbpd{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> bp` represents the dimension exactly if possible. If not possible it
+> will be smaller by `1sp` from the original dimension.
+
+`\texdiminbpu{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> bp` represents the dimension exactly if possible. If not possible it
+> will be larger by `1sp` from the original dimension.
+
+`\texdiminnd{<dim. expr.>}`
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> nd` represents the dimension exactly if possible. If not possible it
+> will differ by `1sp` from the original dimension, but it is not
+> known in advance if it will be above or below.
+
+> `\maxdimen` on input produces `15355.51532` and indeed is realized as `15355.51532nd`.
+
+`\texdiminndd{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> nd` represents the dimension exactly if possible. If not possible it
+> will be smaller by `1sp` from the original dimension.
+
+`\texdiminndu{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> nd` represents the dimension exactly if possible. If not possible it
+> will be larger by `1sp` from the original dimension.
+
+`\texdimindd{<dim. expr.>}`
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> dd` represents the dimension exactly if possible. If not possible it
+> will differ by `1sp` from the original dimension, but it is not
+> known in advance if it will be above or below.
+
+> Warning: the output for `\maxdimen` is `15312.02585` but `15312.02585dd`
+> will trigger "Dimension too large" error.
+> `\maxdimen-1sp` is atteignable via `15312.02583dd`.
+
+`\texdiminddd{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> dd` represents the dimension exactly if possible. If not possible it
+> will be smaller by `1sp` from the original dimension.
+
+`\texdiminddu{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> dd` represents the dimension exactly if possible. If not possible it
+> will be larger by `1sp` from the original dimension.
+
+`\texdiminmm{<dim. expr.>}`
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> mm` represents the dimension exactly if possible. If not possible it
+> will either be the closest from below or from above, but it is not
+> known in advance which one (and it is not known if the other choice
+> would have been closer).
+
+> `\maxdimen` as input produces on output `5758.31741` and indeed the
+> maximal attainable dimension is `5758.31741mm` (`1073741822sp`).
+
+`\texdiminmmd{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> mm` represents the dimension exactly if possible. If not possible it
+> will be largest representable dimension smaller than the original one.
+
+`\texdiminmmu{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> mm` represents the dimension exactly if possible. If not possible it
+> will be smallest representable dimension larger than the original one.
+
+`\texdiminpc{<dim. expr.>}`
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> pc` represents the dimension exactly if possible. If not possible it
+> will be the closest representable one (in case of tie, the approximant
+> from above is chosen).
+
+> `\maxdimen` as input produces on output `1365.33333` and indeed the
+> maximal attainable dimension is `1365.33333pc` (`1073741820sp`).
+
+`\texdiminpcd{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> pc` represents the dimension exactly if possible. If not possible it
+> will be largest representable dimension smaller than the original one.
+
+`\texdiminpcu{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> pc` represents the dimension exactly if possible. If not possible it
+> will be smallest representable dimension larger than the original one.
+
+`\texdiminnc{<dim. expr.>}`
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> nc` represents the dimension exactly if possible. If not possible it
+> will either be the closest from below or from above, but it is not
+> known in advance which one (and it is not known if the other choice
+> would have been closer).
+
+> Warning: the output for `\maxdimen` is `1279.62628` but `1279.62628nc`
+> will trigger "Dimension too large" error.
+> `\maxdimen-9sp` is attainable via `1279.62627nc`.
+
+`\texdiminncd{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> nc` represents the dimension exactly if possible. If not possible it
+> will be largest representable dimension smaller than the original one.
+
+`\texdiminncu{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> nc` represents the dimension exactly if possible. If not possible it
+> will be smallest representable dimension larger than the original one.
+
+`\texdimincc{<dim. expr.>}`
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> cc` represents the dimension exactly if possible. If not possible it
+> will either be the closest from below or from above, but it is not
+> known in advacce which one (and it is not known if the other choice
+> would have been closer).
+
+> `\maxdimen` as input produces on output `1276.00215` and indeed the
+> maximal attainable dimension is `1276.00215cc` (`1073741821sp`).
+
+`\texdiminccd{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> cc` represents the dimension exactly if possible. If not possible it
+> will be largest representable dimension smaller than the original one.
+
+`\texdiminccu{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> cc` represents the dimension exactly if possible. If not possible it
+> will be smallest representable dimension larger than the original one.
+
+`\texdimincm{<dim. expr.>}`
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> cm` represents the dimension exactly if possible. If not possible it
+> will either be the closest from below or from above, but it is not
+> known in advance which one (and it is not known if the other choice
+> would have been closer).
+
+> `\maxdimen` as input produces on output `575.83174` and indeed the
+> maximal attainable dimension is `575.83174cm` (`1073741822sp`).
+
+`\texdimincmd{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> cm` represents the dimension exactly if possible. If not possible it
+> will be largest representable dimension smaller than the original one.
+
+`\texdimincmu{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> cm` represents the dimension exactly if possible. If not possible it
+> will be smallest representable dimension larger than the original one.
+
+`\texdiminin{<dim. expr.>}`
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> in` represents the dimension exactly if possible. If not possible it
+> will either be the closest from below or from above, but it is not
+> known in advance which one (and it is not known if the other choice
+> would have been closer).
+
+> Warning: the output for `\maxdimen` is `226.70541` but `226.70541in`
+> will trigger "Dimension too large" error.
+> `\maxdimen-55sp` is maximal attainable dimension (via `226.7054in`).
+
+`\texdiminind{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> in` represents the dimension exactly if possible. If not possible it
+> will be largest representable dimension smaller than the original one.
+
+`\texdimininu{<dim. expr.>}` NOT YET
+
+> Produces a decimal (with up to five decimal places) `D` such that `D
+> in` represents the dimension exactly if possible. If not possible it
+> will be smallest representable dimension larger than the original one.
+
+
+## TODO
+
+Implement the "up" and "down" variants.
+
+Provide a macro `\texdimnearest{in,cm}{<dim.expr.>}` which provides the
+nearest dimension simultaneously representable both in `in` and in `cm`?
+According to a reference on the web by an anonymous contributor the
+available positive dimensions in scaled points have the shape
+`floor(3613.5*k) sp` for some integer `k`. So we basically may have a
+delta up to about `1800sp` which is about `0.0275pt` and is still small
+(less than one hundredth of a millimeter), so perhaps such a utility for
+"safe dimensions" may be useful. Simpler however and more efficient
+would be for people to finally adopt the French revolution Système
+Métrique (rather than setting up giant financial paradises).
+
+<!--
+-->
diff --git a/Master/texmf-dist/tex/generic/texdimens/texdimens.sty b/Master/texmf-dist/tex/generic/texdimens/texdimens.sty
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+% This is file texdimens.tex, part of texdimens package, which
+% is distributed under the LPPL 1.3c. Copyright (c) 2021 Jean-François Burnol
+\ProvidesPackage{texdimens}[2021/06/30 v0.9beta conversion of TeX dimensions to decimals (JFB)]
+\@@input texdimens.tex\relax
+\endinput
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/generic/texdimens/texdimens.tex b/Master/texmf-dist/tex/generic/texdimens/texdimens.tex
new file mode 100644
index 00000000000..471a07f807d
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/texdimens/texdimens.tex
@@ -0,0 +1,101 @@
+% This is file texdimens.tex, part of texdimens package, which
+% is distributed under the LPPL 1.3c. Copyright (c) 2021 Jean-François Burnol
+% 2021/06/30 v0.9beta
+\edef\texdimensendinput{\endlinechar\the\endlinechar\catcode`\noexpand _=\the\catcode`\_\relax\noexpand\endinput}%
+\endlinechar13\relax%
+\catcode`\_=11
+% Is T sp attainable from unit "uu"?. Here we suppose T>0.
+% phi>1, psi=1/phi, psi<1
+% U(N,phi)=floor(N phi) is strictly increasing
+%     U(N)<= T <  U(N+1)    iff    N = ceil((T+1)psi) - 1
+%     U(M)<  T <= U(M+1)    iff    M = ceil(T psi)    - 1
+% Either:
+% -  M = N, i.e. T is not attainable, M=N < T psi < (T+1) psi <= N+1
+% -  M = N - 1, i.e. T is attained, T psi <= N < (T+1) psi, T = floor(N phi) 
+%
+% In the latter case:
+% - as psi<1, |N - (T+0.5) psi| < 0.5, hence N = R := round((T+0.5) psi).
+%   Also works for T=0 but T<0 would need -0.5.
+%
+% - if psi<1/2, then N = round(T psi) is simpler formula which works
+%   also for attainable T<0.
+%
+% This R=round((T+0.5) psi) can always be computed via \numexpr because 2T+1
+% will not trigger arithmetic overflow.
+%
+% If Tsp>0 is not attainable, this R can produce either N or N+1 (=M+1).
+%
+% If we try computing ceil(x) via round(x+0.5) (\numexpr rounds up)
+% this means for N, we need round((T+1)psi + 0.5), for example with
+% psi = 100/7227 for "in", this gives round((((T+1)200)+7227)/14454)
+% feasible via \numexpr only for (circa) 100 T less than \maxdimen.
+%
+% We could rather compute round(T psi) but we don't know if it gives
+% N or N+1. We know it is N if round(T psi)< round((T+1) psi)
+% but if the two are the same we don't know if they are both N or
+% both N+1.
+%
+% It is slightly less costly to compute X = round(T psi) than R,
+% but if we then realize that X uu < T sp we do not yet know
+% if (X+1) uu = T sp or is > Tsp, except if psi<1/2, because
+% if T sp is attainable then X = round(T psi) is then necessarily N
+% so if X uu < T sp we now that T sp was not attainable.
+%
+% We decide with some hesitation to not split whether psi<1/2 or
+% psi>1/2. Reverted! Currently following done only for psi>1/2,
+% i.e. bp, nd, dd.
+%
+% 1. compute R = round((T+0.5) psi) in \numexpr. This forces
+%    to check for negative T because then we would want here (T-0.5)psi
+%
+% 2. check for the "up" and "down" variants whether R uu is <, =, or > T sp.
+%    But we have to choose here what "up" and "down" mean for T<0.
+%    Also, computation of R uu
+%    may trigger Dimension too large if T sp is not attainable,
+%    close to \maxdimen, and \maxdimen itself is not attainable.
+%
+% For the envisioned "safe versions" we would tabulate first per unit
+% what is Rmax such that Rmax uu <= \maxdimen. Then the "safe" versions
+% would have an extra check of R. But for \texdimeninuuu it will
+% then not be compliant to its definition for inputs close to
+% non-attainable \maxdimen.
+%
+% After having written the macros we will tabulate what is for each unit
+% the maximal attainable dimension.
+%
+% Hesitation about whether using simpler round(T psi) approach
+% for units > 2pt and the \texdimin<uu> macros.
+%
+% Testing shows that this would not change output for \maxdimen
+% with "nc" and "in": still N+1 is returned... but it has great
+% advantage to not have to check the sign.
+%
+% OK let's do this,
+% especially as I don't know if I will ever implement "up" and "down".
+\def\texdiminpt#1{\expandafter\texdiminpt_\the\dimexpr#1\relax}%
+{\catcode`p 12\catcode`t 12\csname expandafter\endcsname\gdef\csname texdiminpt_\endcsname#1pt{#1}}%
+% bp 7227/7200 = 803/800
+% complications and annoying overhead caused by sign
+% and we don't want to evaluate #1 twice in a \dimexpr; if #1 was
+% restricted to be a dimen register, we would avoid "\the and re-grab" step.
+\def\texdiminbp#1{\expandafter\texdiminbp_\the\numexpr\dimexpr#1;}%
+\def\texdiminbp_#1#2;{\texdiminpt{\numexpr(2*#1#2+\if-#1-\fi1)*400/803sp}}%
+% nd 685/642
+\def\texdiminnd#1{\expandafter\texdiminnd_\the\numexpr\dimexpr#1;}%
+\def\texdiminnd_#1#2;{\texdiminpt{\numexpr(2*#1#2+\if-#1-\fi1)*321/685sp}}%
+% dd 1238/1157
+\def\texdimindd#1{\expandafter\texdimindd_\the\numexpr\dimexpr#1;}%
+\def\texdimindd_#1#2;{\texdiminpt{\numexpr(2*#1#2+\if-#1-\fi1)*1157/2476sp}}%
+% mm 7227/2540 phi now >2, use from here on the simpler approach
+\def\texdiminmm#1{\texdiminpt{(#1)*2540/7227}}%
+% pc 12/1
+\def\texdiminpc#1{\texdiminpt{(#1)/12}}%
+% nc 1370/107
+\def\texdiminnc#1{\texdiminpt{(#1)*107/1370}}%
+% cc 14856/1157
+\def\texdimincc#1{\texdiminpt{(#1)*1157/14856}}%
+% cm 7227/254
+\def\texdimincm#1{\texdiminpt{(#1)*254/7227}}%
+% in 7227/100
+\def\texdiminin#1{\texdiminpt{(#1)*100/7227}}%
+\texdimensendinput