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-rw-r--r--macros/generic/texdimens/texdimens.tex340
1 files changed, 284 insertions, 56 deletions
diff --git a/macros/generic/texdimens/texdimens.tex b/macros/generic/texdimens/texdimens.tex
index 471a07f807..7068d57db9 100644
--- a/macros/generic/texdimens/texdimens.tex
+++ b/macros/generic/texdimens/texdimens.tex
@@ -1,101 +1,329 @@
% 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
+% 2021/07/14 v0.9gamma
\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,phi)=trunc(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)
+% case1: M = N, i.e. T is not attainable, M=N < T psi < (T+1) psi <= N+1
+% case2: 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.
+% Let X = round(T psi). And let Y = trunc(X phi).
%
-% - if psi<1/2, then N = round(T psi) is simpler formula which works
-% also for attainable T<0.
+% case1: X can be N or N+1. It will be N+1 iff Y > T.
+% case2: X can be N or N-1. It will be N iff trunc((X+1)phi)>T.
%
-% This R=round((T+0.5) psi) can always be computed via \numexpr because 2T+1
-% will not trigger arithmetic overflow.
+% This is not convenient: if Y <= T it might still be that we are in case 2
+% and we must check then if trunc((X+1) phi) > T or not.
+%
+% If psi < 0.5
+% ------------
+%
+% The situation then simplifies:
+%
+% case1: X can be N or N+1. It will be N+1 iff Y = trunc(X phi) > T.
+% case2: X is necessarily N.
%
-% If Tsp>0 is not attainable, this R can produce either N or N+1 (=M+1).
+% Thus:
+% a) compute X = round(T psi)
+% b) compute Y = trunc(X phi) and test if Y > T. If true, we
+% were in case 1, replace X by X - 1, else we were either
+% in case 1 or case 2, but we can leave X as is.
+% We have thus found N.
%
-% 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.
+% The operation Y = trunc(X phi) can be achieved this way:
+% i) use \the\dimexpr to convert X sp into D pt,
+% ii) use \the\numexpr\dimexpr to convert "D uu" into sp.
+% These steps give Y.
%
-% 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.
+% This way we find the maximal dimension at most T sp exactly
+% representable in "uu" unit.
%
-% 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.
+% The computations of X and Y can be done independently of sign of T.
+% But the final test has to be changed to Y < T if T < 0 and then
+% one must replace X by X+1. So we must filter sign.
%
-% 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.
+% If the goal is only to find a decimal D such that "D uu" is
+% exactly T sp in the case this is possible, then things are simpler
+% because from X = round(T psi) we get D such as X sp is same as D pt
+% and "D uu" will work.
+% We don't have to take sign into account for this computation.
+% But if T sp was not atteignable we don't know if this X will give
+% a D such that D uu < T sp or D uu > T sp.
%
-% 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
+% If psi > 0.5
+% ------------
%
-% 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 example unit "bp" has phi=803/800.
+%
+% It is then not true that if T sp is atteignable, the X = round(T psi)
+% will always work.
+%
+% But it is true that R = round((T + 0.5) psi) will always work.
+% Here we must use -0.5 if T < 0, though.
+%
+% This R=round((T+0.5) psi) can always be computed via \numexpr because 2T+1
+% will not trigger arithmetic overflow.
%
-% 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.
+% So this gives an approach to find a D such that "D uu" is exactly
+% T sp when this is possible.
+%
+% If Tsp (positive) is not attainable, this R however can produce
+% either N or N+1.
+%
+% But we can decide what happened by computing Z = trunc(R phi).
+% If and only if Z > T this means R was N+1.
+%
+% It is slightly less costly to compute X = round(T psi) than
+% R = round((T + 0.5) psi),
+% but if we then realize that trunc(X phi) < T we do not yet know
+% if trunc((X+1) phi) = T or is > T.
+%
+% To recapitulate: we have our algorithm for all units to find out
+% maximal dimension exactly atteignable in "uu" unit and at most equal
+% to (positive) T sp.
+%
+% Unfortunately the check that Y (in case psi < 0.5) or Z (in case psi >
+% 0.5) may trigger a Dimension too large error if T sp was near
+% non-atteignable \maxdimen.
+%
+% For additional envisioned "safe versions" we would tabulate first per unit
+% what is the integer Rmax such that trunc(Rmax phi) <= \maxdimen. Then
+% the "safe" versions would have an extra check of X or R before
+% proceeding further. But the "up macros" supposed to give the next
+% dimension above Tsp and exactly atteignable in "uu" unit, if compliant
+% to their description can not avoid "Dimension too large" 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.
+% About the macros such as \texdiminbp whose constraints are:
+% - give a decimal D such that "Duu" = "T sp" for TeX if possible
+% - else give nearest from below or above without knowing
+% which one,
%
-% 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.
+% there was some hesitation about whether or not using the simpler
+% round(T psi) approach for units > 2pt and the \texdimin<uu> macros.
+% Testing showed that this did not change the output for \maxdimen
+% with the units "nc" and "in": still N+1 is returned...
+%
+% As it has great
+% advantage to not have to check the sign of the input, the
+% "simpler" approach was chosen for those units to which it
+% applies, i.e. the units uu > 2pt (phi>2, psi<1/2), i.e.
+% all units except bp, nd and dd.
+%
+\def\texdimfirstofone#1{#1}%
+% this #2 will be \fi
+\def\texdiminuudown_e#1#2#3#4{#2\expandafter\texdiminpt_\the\dimexpr\numexpr(#1-1)sp\relax}%
+\def\texdiminuuup_e#1#2#3#4{#2\expandafter\texdiminpt_\the\dimexpr\numexpr(#1+1)sp\relax}%
+% this #1 will be \fi
+\def\texdiminuuup_neg#1#2-{#1-#2}%
+%
+% pt
%
-% 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}}%
+% \texdiminbpdown: maximal dim exactly expressible in bp and at most equal to input
+\def\texdiminbpdown#1{\expandafter\texdiminbpdown_a\the\numexpr\dimexpr#1;}%
+\def\texdiminbpdown_a#1{\if-#1\texdiminbpdown_neg\fi\texdiminbpdown_b#1}%
+\def\texdiminbpdown_b#1;{\expandafter\texdiminbpdown_c\the\numexpr(2*#1+1)*400/803;#1;}%
+\def\texdiminbpdown_c#1;{\expandafter\texdiminbpdown_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminbpdown_d#1PT};#2;#3;%
+ {\ifdim#1bp>#3sp \texdiminuudown_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+% The problem here is that if close to 0sp, output can be 0.0, and we do not want
+% -0.0 as output. So let's do this somewhat brutally. Anyhow, negative inputs are
+% not our priority. #1 is \fi here:
+\def\texdiminbpdown_neg#1#2-#3;{#1\expandafter\texdiminpt_\the\dimexpr-\texdiminbpdown_b#3;pt\relax}%
+% \texdiminbpup: minimal dim exactly expressible in bp and at least equal to input
+\def\texdiminbpup#1{\expandafter\texdiminbpup_a\the\numexpr\dimexpr#1;}%
+\def\texdiminbpup_a#1{\if-#1\texdiminuuup_neg\fi\texdiminbpup_b#1}%
+\def\texdiminbpup_b#1;{\expandafter\texdiminbpup_c\the\numexpr(2*#1+1)*400/803;#1;}%
+\def\texdiminbpup_c#1;{\expandafter\texdiminbpup_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminbpup_d#1PT};#2;#3;%
+ {\ifdim#1bp<#3sp \texdiminuuup_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+%
% 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}}%
+% \texdiminnddown: maximal dim exactly expressible in nd and at most equal to input
+\def\texdiminnddown#1{\expandafter\texdiminnddown_a\the\numexpr\dimexpr#1;}%
+\def\texdiminnddown_a#1{\if-#1\texdiminnddown_neg\fi\texdiminnddown_b#1}%
+\def\texdiminnddown_b#1;{\expandafter\texdiminnddown_c\the\numexpr(2*#1+1)*321/685;#1;}%
+\def\texdiminnddown_c#1;{\expandafter\texdiminnddown_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminnddown_d#1PT};#2;#3;%
+ {\ifdim#1nd>#3sp \texdiminuudown_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+\def\texdiminnddown_neg#1#2-#3;{#1\expandafter\texdiminpt_\the\dimexpr-\texdiminnddown_b#3;pt\relax}%
+% \texdiminndup: minimal dim exactly expressible in nd and at least equal to input
+\def\texdiminndup#1{\expandafter\texdiminndup_a\the\numexpr\dimexpr#1;}%
+\def\texdiminndup_a#1{\if-#1\texdiminuuup_neg\fi\texdiminndup_b#1}%
+\def\texdiminndup_b#1;{\expandafter\texdiminndup_c\the\numexpr(2*#1+1)*321/685;#1;}%
+\def\texdiminndup_c#1;{\expandafter\texdiminndup_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminndup_d#1PT};#2;#3;%
+ {\ifdim#1nd<#3sp \texdiminuuup_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+%
% 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}}%
+% \texdimindddown: maximal dim exactly expressible in dd and at most equal to input
+\def\texdimindddown#1{\expandafter\texdimindddown_a\the\numexpr\dimexpr#1;}%
+\def\texdimindddown_a#1{\if-#1\texdimindddown_neg\fi\texdimindddown_b#1}%
+\def\texdimindddown_b#1;{\expandafter\texdimindddown_c\the\numexpr(2*#1+1)*1157/2476;#1;}%
+\def\texdimindddown_c#1;{\expandafter\texdimindddown_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdimindddown_d#1PT};#2;#3;%
+ {\ifdim#1dd>#3sp \texdiminuudown_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+\def\texdimindddown_neg#1#2-#3;{#1\expandafter\texdiminpt_\the\dimexpr-\texdimindddown_b#3;pt\relax}%
+% \texdiminddup: minimal dim exactly expressible in dd and at least equal to input
+\def\texdiminddup#1{\expandafter\texdiminddup_a\the\numexpr\dimexpr#1;}%
+\def\texdiminddup_a#1{\if-#1\texdiminuuup_neg\fi\texdiminddup_b#1}%
+\def\texdiminddup_b#1;{\expandafter\texdiminddup_c\the\numexpr(2*#1+1)*1157/2476;#1;}%
+\def\texdiminddup_c#1;{\expandafter\texdiminddup_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminddup_d#1PT};#2;#3;%
+ {\ifdim#1dd<#3sp \texdiminuuup_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+%
% mm 7227/2540 phi now >2, use from here on the simpler approach
-\def\texdiminmm#1{\texdiminpt{(#1)*2540/7227}}%
+%
+\def\texdiminmm#1{\expandafter\texdiminpt_\the\dimexpr(#1)*2540/7227\relax}%
+% \texdiminmmdown: maximal dim exactly expressible in mm and at most equal to input
+\def\texdiminmmdown#1{\expandafter\texdiminmmdown_a\the\numexpr\dimexpr#1;}%
+\def\texdiminmmdown_a#1{\if-#1\texdiminmmdown_neg\fi\texdiminmmdown_b#1}%
+\def\texdiminmmdown_b#1;{\expandafter\texdiminmmdown_c\the\numexpr#1*2540/7227;#1;}%
+\def\texdiminmmdown_c#1;{\expandafter\texdiminmmdown_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminmmdown_d#1PT};#2;#3;%
+ {\ifdim#1mm>#3sp \texdiminuudown_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+\def\texdiminmmdown_neg#1#2-#3;{#1\expandafter\texdiminpt_\the\dimexpr-\texdiminmmdown_b#3;pt\relax}%
+% \texdiminmmup: minimal dim exactly expressible in mm and at least equal to input
+\def\texdiminmmup#1{\expandafter\texdiminmmup_a\the\numexpr\dimexpr#1;}%
+\def\texdiminmmup_a#1{\if-#1\texdiminuuup_neg\fi\texdiminmmup_b#1}%
+\def\texdiminmmup_b#1;{\expandafter\texdiminmmup_c\the\numexpr#1*2540/7227;#1;}%
+\def\texdiminmmup_c#1;{\expandafter\texdiminmmup_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminmmup_d#1PT};#2;#3;%
+ {\ifdim#1mm<#3sp \texdiminuuup_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+%
% pc 12/1
-\def\texdiminpc#1{\texdiminpt{(#1)/12}}%
+%
+\def\texdiminpc#1{\expandafter\texdiminpt_\the\dimexpr(#1)/12\relax}%
+% \texdiminpcdown: maximal dim exactly expressible in pc and at most equal to input
+\def\texdiminpcdown#1{\expandafter\texdiminpcdown_a\the\numexpr\dimexpr#1;}%
+\def\texdiminpcdown_a#1{\if-#1\texdiminpcdown_neg\fi\texdiminpcdown_b#1}%
+\def\texdiminpcdown_b#1;{\expandafter\texdiminpcdown_c\the\numexpr#1/12;#1;}%
+\def\texdiminpcdown_c#1;{\expandafter\texdiminpcdown_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminpcdown_d#1PT};#2;#3;%
+ {\ifdim#1pc>#3sp \texdiminuudown_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+\def\texdiminpcdown_neg#1#2-#3;{#1\expandafter\texdiminpt_\the\dimexpr-\texdiminpcdown_b#3;pt\relax}%
+% \texdiminpcup: minimal dim exactly expressible in pc and at least equal to input
+\def\texdiminpcup#1{\expandafter\texdiminpcup_a\the\numexpr\dimexpr#1;}%
+\def\texdiminpcup_a#1{\if-#1\texdiminuuup_neg\fi\texdiminpcup_b#1}%
+\def\texdiminpcup_b#1;{\expandafter\texdiminpcup_c\the\numexpr#1/12;#1;}%
+\def\texdiminpcup_c#1;{\expandafter\texdiminpcup_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminpcup_d#1PT};#2;#3;%
+ {\ifdim#1pc<#3sp \texdiminuuup_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+%
% nc 1370/107
-\def\texdiminnc#1{\texdiminpt{(#1)*107/1370}}%
+%
+\def\texdiminnc#1{\expandafter\texdiminpt_\the\dimexpr(#1)*107/1370\relax}%
+% \texdiminncdown: maximal dim exactly expressible in nc and at most equal to input
+\def\texdiminncdown#1{\expandafter\texdiminncdown_a\the\numexpr\dimexpr#1;}%
+\def\texdiminncdown_a#1{\if-#1\texdiminncdown_neg\fi\texdiminncdown_b#1}%
+\def\texdiminncdown_b#1;{\expandafter\texdiminncdown_c\the\numexpr#1*107/1370;#1;}%
+\def\texdiminncdown_c#1;{\expandafter\texdiminncdown_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminncdown_d#1PT};#2;#3;%
+ {\ifdim#1nc>#3sp \texdiminuudown_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+\def\texdiminncdown_neg#1#2-#3;{#1\expandafter\texdiminpt_\the\dimexpr-\texdiminncdown_b#3;pt\relax}%
+% \texdiminncup: minimal dim exactly expressible in nc and at least equal to input
+\def\texdiminncup#1{\expandafter\texdiminncup_a\the\numexpr\dimexpr#1;}%
+\def\texdiminncup_a#1{\if-#1\texdiminuuup_neg\fi\texdiminncup_b#1}%
+\def\texdiminncup_b#1;{\expandafter\texdiminncup_c\the\numexpr#1*107/1370;#1;}%
+\def\texdiminncup_c#1;{\expandafter\texdiminncup_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminncup_d#1PT};#2;#3;%
+ {\ifdim#1nc<#3sp \texdiminuuup_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+%
% cc 14856/1157
-\def\texdimincc#1{\texdiminpt{(#1)*1157/14856}}%
+%
+\def\texdimincc#1{\expandafter\texdiminpt_\the\dimexpr(#1)*1157/14856\relax}%
+% \texdiminccdown: maximal dim exactly expressible in cc and at most equal to input
+\def\texdiminccdown#1{\expandafter\texdiminccdown_a\the\numexpr\dimexpr#1;}%
+\def\texdiminccdown_a#1{\if-#1\texdiminccdown_neg\fi\texdiminccdown_b#1}%
+\def\texdiminccdown_b#1;{\expandafter\texdiminccdown_c\the\numexpr#1*1157/14856;#1;}%
+\def\texdiminccdown_c#1;{\expandafter\texdiminccdown_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminccdown_d#1PT};#2;#3;%
+ {\ifdim#1cc>#3sp \texdiminuudown_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+\def\texdiminccdown_neg#1#2-#3;{#1\expandafter\texdiminpt_\the\dimexpr-\texdiminccdown_b#3;pt\relax}%
+% \texdiminccup: minimal dim exactly expressible in cc and at least equal to input
+\def\texdiminccup#1{\expandafter\texdiminccup_a\the\numexpr\dimexpr#1;}%
+\def\texdiminccup_a#1{\if-#1\texdiminuuup_neg\fi\texdiminccup_b#1}%
+\def\texdiminccup_b#1;{\expandafter\texdiminccup_c\the\numexpr#1*1157/14856;#1;}%
+\def\texdiminccup_c#1;{\expandafter\texdiminccup_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminccup_d#1PT};#2;#3;%
+ {\ifdim#1cc<#3sp \texdiminuuup_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+%
% cm 7227/254
-\def\texdimincm#1{\texdiminpt{(#1)*254/7227}}%
+%
+\def\texdimincm#1{\expandafter\texdiminpt_\the\dimexpr(#1)*254/7227\relax}%
+% \texdimincmdown: maximal dim exactly expressible in cm and at most equal to input
+\def\texdimincmdown#1{\expandafter\texdimincmdown_a\the\numexpr\dimexpr#1;}%
+\def\texdimincmdown_a#1{\if-#1\texdimincmdown_neg\fi\texdimincmdown_b#1}%
+\def\texdimincmdown_b#1;{\expandafter\texdimincmdown_c\the\numexpr#1*254/7227;#1;}%
+\def\texdimincmdown_c#1;{\expandafter\texdimincmdown_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdimincmdown_d#1PT};#2;#3;%
+ {\ifdim#1cm>#3sp \texdiminuudown_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+\def\texdimincmdown_neg#1#2-#3;{#1\expandafter\texdiminpt_\the\dimexpr-\texdimincmdown_b#3;pt\relax}%
+% \texdimincmup: minimal dim exactly expressible in cm and at least equal to input
+\def\texdimincmup#1{\expandafter\texdimincmup_a\the\numexpr\dimexpr#1;}%
+\def\texdimincmup_a#1{\if-#1\texdiminuuup_neg\fi\texdimincmup_b#1}%
+\def\texdimincmup_b#1;{\expandafter\texdimincmup_c\the\numexpr#1*254/7227;#1;}%
+\def\texdimincmup_c#1;{\expandafter\texdimincmup_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdimincmup_d#1PT};#2;#3;%
+ {\ifdim#1cm<#3sp \texdiminuuup_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+%
% in 7227/100
-\def\texdiminin#1{\texdiminpt{(#1)*100/7227}}%
+%
+\def\texdiminin#1{\expandafter\texdiminpt_\the\dimexpr(#1)*100/7227\relax}%
+% \texdiminindown: maximal dim exactly expressible in in and at most equal to input
+\def\texdiminindown#1{\expandafter\texdiminindown_a\the\numexpr\dimexpr#1;}%
+\def\texdiminindown_a#1{\if-#1\texdiminindown_neg\fi\texdiminindown_b#1}%
+\def\texdiminindown_b#1;{\expandafter\texdiminindown_c\the\numexpr#1*100/7227;#1;}%
+\def\texdiminindown_c#1;{\expandafter\texdiminindown_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdiminindown_d#1PT};#2;#3;%
+ {\ifdim#1in>#3sp \texdiminuudown_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+\def\texdiminindown_neg#1#2-#3;{#1\expandafter\texdiminpt_\the\dimexpr-\texdiminindown_b#3;pt\relax}%
+% \texdimininup: minimal dim exactly expressible in in and at least equal to input
+\def\texdimininup#1{\expandafter\texdimininup_a\the\numexpr\dimexpr#1;}%
+\def\texdimininup_a#1{\if-#1\texdiminuuup_neg\fi\texdimininup_b#1}%
+\def\texdimininup_b#1;{\expandafter\texdimininup_c\the\numexpr#1*100/7227;#1;}%
+\def\texdimininup_c#1;{\expandafter\texdimininup_d\the\dimexpr#1sp;#1;}%
+{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdimininup_d#1PT};#2;#3;%
+ {\ifdim#1in<#3sp \texdiminuuup_e{#2}\fi\texdimfirstofone{#1}}%
+}%
+%
\texdimensendinput