From 44e933e35901329b69a607da2dc65d10b1420c86 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Thu, 15 Jul 2021 19:58:54 +0000 Subject: texdimens (15jul21) git-svn-id: svn://tug.org/texlive/trunk@59939 c570f23f-e606-0410-a88d-b1316a301751 --- .../texmf-dist/tex/generic/texdimens/texdimens.sty | 2 +- .../texmf-dist/tex/generic/texdimens/texdimens.tex | 278 ++++++++++++++++----- 2 files changed, 218 insertions(+), 62 deletions(-) (limited to 'Master/texmf-dist/tex/generic') diff --git a/Master/texmf-dist/tex/generic/texdimens/texdimens.sty b/Master/texmf-dist/tex/generic/texdimens/texdimens.sty index c29f1458e0b..dbf39c72f80 100644 --- a/Master/texmf-dist/tex/generic/texdimens/texdimens.sty +++ b/Master/texmf-dist/tex/generic/texdimens/texdimens.sty @@ -1,5 +1,5 @@ % 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)] +\ProvidesPackage{texdimens}[2021/07/15 v0.9delta 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 index 471a07f807d..189caca95d0 100644 --- a/Master/texmf-dist/tex/generic/texdimens/texdimens.tex +++ b/Master/texmf-dist/tex/generic/texdimens/texdimens.tex @@ -1,101 +1,257 @@ % 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 +% 2021/07/15 v0.9delta \edef\texdimensendinput{\endlinechar\the\endlinechar\catcode`\noexpand _=\the\catcode`\_\relax\noexpand\endinput}% \endlinechar13\relax% \catcode`\_=11 +% +% Mathematics +% =========== +% % 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: % -% If Tsp>0 is not attainable, this R can produce either N or N+1 (=M+1). +% 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 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. +% 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. % -% 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. +% 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. % -% 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. +% This way we find the maximal dimension at most T sp exactly +% representable in "uu" unit. % -% 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. +% 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. % -% 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 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. % -% 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. +% If psi > 0.5 +% ------------ % -% 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. +% 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. +% +% 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 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, +% +% there was some hesitation about whether or not using the simpler +% round(T psi) approach for units > 2pt and the \texdimin 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. +% +% Implementation +% ============== +% +\def\texdimenfirstofone#1{#1}% +{\catcode`p 12\catcode`t 12 + \csname expandafter\endcsname\gdef\csname texdimenstrippt\endcsname#1pt{#1}}% % -% 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. +% down macros: +% for units with phi < 2: +\def\texdimendown_A#1{\if-#1\texdimendown_neg\fi\texdimendown_B#1}% +\def\texdimendown_B#1;#2;{\expandafter\texdimendown_c\the\numexpr(2*#1+1)#2;#1;}% +% for units with phi > 2: +\def\texdimendown_a#1{\if-#1\texdimendown_neg\fi\texdimendown_b#1}% +\def\texdimendown_b#1;#2;{\expandafter\texdimendown_c\the\numexpr#1#2;#1;}% +% shared macros: +\def\texdimendown_c#1;{\expandafter\texdimendown_d\the\dimexpr#1sp;#1;}% +{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdimendown_d#1PT};#2;#3;#4;% + {\ifdim#1#4>#3sp \texdimendown_e{#2}\fi\texdimenfirstofone{#1}}% +}% +% this #2 will be \fi +\def\texdimendown_e#1#2#3#4{#2\expandafter\texdimenstrippt\the\dimexpr\numexpr#1-1sp\relax}% +% negative branch: +% The problem here is that if input very small, output can be 0.0, and we +% do not want -0.0 as output. +% So let's do this somewhat brutally and non-efficiently. +% Anyhow, negative inputs are not our priority. +% #1 is \fi here and #2 is \texdimendown_b or _B: +\def\texdimendown_neg#1#2-#3;#4;#5;{#1\expandafter\texdimenstrippt\the\dimexpr-#2#3;#4;#5;pt\relax}% +% +% up macros: +\def\texdimenup_A#1{\if-#1\texdimenup_neg\fi\texdimenup_B#1}% +\def\texdimenup_B#1;#2;{\expandafter\texdimenup_c\the\numexpr(2*#1+1)#2;#1;}% +\def\texdimenup_a#1{\if-#1\texdimenup_neg\fi\texdimenup_b#1}% +\def\texdimenup_b#1;#2;{\expandafter\texdimenup_c\the\numexpr#1#2;#1;}% +\def\texdimenup_c#1;{\expandafter\texdimenup_d\the\dimexpr#1sp;#1;}% +{\catcode`P 12\catcode`T 12\lowercase{\gdef\texdimenup_d#1PT};#2;#3;#4;% + {\ifdim#1#4<#3sp \texdimenup_e{#2}\fi\texdimenfirstofone{#1}}% +}% +% this #2 will be \fi +\def\texdimenup_e#1#2#3#4{#2\expandafter\texdimenstrippt\the\dimexpr\numexpr#1+1sp\relax}% +% negative branch: +% Here we can me more expeditive than for the "down" macros. +% But this breaks f-expandability. +% #1 will be \fi and #2 is \texdimenup_b or _B: +\def\texdimenup_neg#1#2-{#1-#2}% +% +% pt +% +\def\texdiminpt#1{\expandafter\texdimenstrippt\the\dimexpr#1\relax}% % -% 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}}% +\def\texdiminbp_#1#2;{% + \expandafter\texdimenstrippt\the\dimexpr\numexpr(2*#1#2+\if-#1-\fi1)*400/803sp\relax +}% +% \texdiminbpdown: maximal dim exactly expressible in bp and at most equal to input +\def\texdiminbpdown#1{\expandafter\texdimendown_A\the\numexpr\dimexpr#1;*400/803;bp;}% +% \texdiminbpup: minimal dim exactly expressible in bp and at least equal to input +\def\texdiminbpup#1{\expandafter\texdimenup_A\the\numexpr\dimexpr#1;*400/803;bp;}% +% % 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}}% +\def\texdiminnd_#1#2;{% + \expandafter\texdimenstrippt\the\dimexpr\numexpr(2*#1#2+\if-#1-\fi1)*321/685sp\relax +}% +% \texdiminnddown: maximal dim exactly expressible in nd and at most equal to input +\def\texdiminnddown#1{\expandafter\texdimendown_A\the\numexpr\dimexpr#1;*321/685;nd;}% +% \texdiminndup: minimal dim exactly expressible in nd and at least equal to input +\def\texdiminndup#1{\expandafter\texdimenup_A\the\numexpr\dimexpr#1;*321/685;nd;}% +% % 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}}% +\def\texdimindd_#1#2;{% + \expandafter\texdimenstrippt\the\dimexpr\numexpr(2*#1#2+\if-#1-\fi1)*1157/2476sp\relax +}% +% \texdimindddown: maximal dim exactly expressible in dd and at most equal to input +\def\texdimindddown#1{\expandafter\texdimendown_A\the\numexpr\dimexpr#1;*1157/2476;dd;}% +% \texdiminddup: minimal dim exactly expressible in dd and at least equal to input +\def\texdiminddup#1{\expandafter\texdimenup_A\the\numexpr\dimexpr#1;*1157/2476;dd;}% +% % mm 7227/2540 phi now >2, use from here on the simpler approach -\def\texdiminmm#1{\texdiminpt{(#1)*2540/7227}}% +% +\def\texdiminmm#1{\expandafter\texdimenstrippt\the\dimexpr(#1)*2540/7227\relax}% +% \texdiminmmdown: maximal dim exactly expressible in mm and at most equal to input +\def\texdiminmmdown#1{\expandafter\texdimendown_a\the\numexpr\dimexpr#1;*2540/7227;mm;}% +% \texdiminmmup: minimal dim exactly expressible in mm and at least equal to input +\def\texdiminmmup#1{\expandafter\texdimenup_a\the\numexpr\dimexpr#1;*2540/7227;mm;}% +% % pc 12/1 -\def\texdiminpc#1{\texdiminpt{(#1)/12}}% +% +\def\texdiminpc#1{\expandafter\texdimenstrippt\the\dimexpr(#1)/12\relax}% +% \texdiminpcdown: maximal dim exactly expressible in pc and at most equal to input +\def\texdiminpcdown#1{\expandafter\texdimendown_a\the\numexpr\dimexpr#1;/12;pc;}% +% \texdiminpcup: minimal dim exactly expressible in pc and at least equal to input +\def\texdiminpcup#1{\expandafter\texdimenup_a\the\numexpr\dimexpr#1;/12;pc;}% +% % nc 1370/107 -\def\texdiminnc#1{\texdiminpt{(#1)*107/1370}}% +% +\def\texdiminnc#1{\expandafter\texdimenstrippt\the\dimexpr(#1)*107/1370\relax}% +% \texdiminncdown: maximal dim exactly expressible in nc and at most equal to input +\def\texdiminncdown#1{\expandafter\texdimendown_a\the\numexpr\dimexpr#1;*107/1370;nc;}% +% \texdiminncup: minimal dim exactly expressible in nc and at least equal to input +\def\texdiminncup#1{\expandafter\texdimenup_a\the\numexpr\dimexpr#1;*107/1370;nc;}% +% % cc 14856/1157 -\def\texdimincc#1{\texdiminpt{(#1)*1157/14856}}% +% +\def\texdimincc#1{\expandafter\texdimenstrippt\the\dimexpr(#1)*1157/14856\relax}% +% \texdiminccdown: maximal dim exactly expressible in cc and at most equal to input +\def\texdiminccdown#1{\expandafter\texdimendown_a\the\numexpr\dimexpr#1;*1157/14856;cc;}% +% \texdiminccup: minimal dim exactly expressible in cc and at least equal to input +\def\texdiminccup#1{\expandafter\texdimenup_a\the\numexpr\dimexpr#1;*1157/14856;cc;}% +% % cm 7227/254 -\def\texdimincm#1{\texdiminpt{(#1)*254/7227}}% +% +\def\texdimincm#1{\expandafter\texdimenstrippt\the\dimexpr(#1)*254/7227\relax}% +% \texdimincmdown: maximal dim exactly expressible in cm and at most equal to input +\def\texdimincmdown#1{\expandafter\texdimendown_a\the\numexpr\dimexpr#1;*254/7227;cm;}% +% \texdimincmup: minimal dim exactly expressible in cm and at least equal to input +\def\texdimincmup#1{\expandafter\texdimenup_a\the\numexpr\dimexpr#1;*254/7227;cm;}% +% % in 7227/100 -\def\texdiminin#1{\texdiminpt{(#1)*100/7227}}% +% +\def\texdiminin#1{\expandafter\texdimenstrippt\the\dimexpr(#1)*100/7227\relax}% +% \texdiminindown: maximal dim exactly expressible in in and at most equal to input +\def\texdiminindown#1{\expandafter\texdimendown_a\the\numexpr\dimexpr#1;*100/7227;in;}% +% \texdimininup: minimal dim exactly expressible in in and at least equal to input +\def\texdimininup#1{\expandafter\texdimenup_a\the\numexpr\dimexpr#1;*100/7227;in;}% +% \texdimensendinput -- cgit v1.2.3