diff options
author | Karl Berry <karl@freefriends.org> | 2021-11-04 20:41:38 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2021-11-04 20:41:38 +0000 |
commit | e1d0124de719fd58f51853021760056b10315f38 (patch) | |
tree | b4dbd14a424827736e33e0198e4a0930b490baa5 /Master/texmf-dist/tex/generic | |
parent | 5e2519e504edda48b83a1b5f05151693d98dd147 (diff) |
texdimens (4nov21)
git-svn-id: svn://tug.org/texlive/trunk@60948 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/tex/generic')
-rw-r--r-- | Master/texmf-dist/tex/generic/texdimens/texdimens.sty | 2 | ||||
-rw-r--r-- | Master/texmf-dist/tex/generic/texdimens/texdimens.tex | 93 |
2 files changed, 73 insertions, 22 deletions
diff --git a/Master/texmf-dist/tex/generic/texdimens/texdimens.sty b/Master/texmf-dist/tex/generic/texdimens/texdimens.sty index 1b41c47d68e..88e67741e00 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}[2021/11/02 v0.99 conversion of TeX dimensions to decimals (JFB)] +\ProvidesPackage{texdimens}[2021/11/04 v0.99a 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 d8bf99e0bc4..bc4acf26485 100644 --- a/Master/texmf-dist/tex/generic/texdimens/texdimens.tex +++ b/Master/texmf-dist/tex/generic/texdimens/texdimens.tex @@ -1,18 +1,18 @@ % This is file texdimens.tex, part of texdimens package, which % is distributed under the LPPL 1.3c. Copyright (c) 2021 Jean-François Burnol -% 2021/11/02 v0.99 -% All macros from 0.9delta release have changed names: \texdimen prefix -% has replaced \texdimin. -\edef\texdimensendinput{\endlinechar\the\endlinechar\catcode`\noexpand _=\the\catcode`\_\relax\noexpand\endinput}% +% 2021/11/04 v0.99a +\edef\texdimensendinput{\endlinechar\the\endlinechar% +\catcode`\noexpand _=\the\catcode`\_% +\catcode`\noexpand @=\the\catcode`\@\relax\noexpand\endinput}% \endlinechar13\relax% -\catcode`\_=11 +\catcode`\_=11 \catcode`\@=11 % only for using \p@ of Plain. Check exists? % % Mathematics ("down" and "up" macros) % =========== % % In the entire discussion here, "uu" stands for some core unit, % or some unit corresponding to a dimension > 1pt. For the case -% of a unit corresponding to a dimension < 1pt, i.e. to +% of a unit corresponding to a dimension < 1pt, i.e. to % \texdimenwithunit macro added at 0.99, refer to the % comments of issue #2 on the tracker site. % @@ -378,19 +378,65 @@ % Mathematics % =========== % -% <comments to be added> (see discussion #2) -% +% As explained in the README.md, the ex and em units are +% handled by TeX as if multiplying by a conversion factor f/65536 +% (here f sp = 1ex resp. = 1em). +% In particular, for any decimal D, input "D em" is handled the exact +% same way as input "D\dimexpr 1em\relax"; this is not +% the case for the core units except for pt and pc (and sp), whose +% conversion factors are the sole ones with a power of 2 denominator +% (respectively 1, 1, and 65536). The further difference is that +% for the core units apart from sp, the conversion factor is >1. +% +% We assume for this discussion T is non-negative. +% If f/65536 > 1, the analysis is as above : some dimensions T sp +% are not attainable as D uu, but the formula +% N=round((2T+1)*32768/f) +% will give a suitable decimal D via \the\dimexpr N sp\relax. +% This D will let TeX convert D uu into T sp, if the dimension +% is attainable else it will be a closest match +% either from above or below (not necessarily nearest overall). +% +% If f/65536<1, all dimensions Tsp are attainable as D uu. Indeed +% D uu is parsed by TeX via N=round(D*65536), then T=trunc(N*phi), +% with phi=f/65536. Starting from T we need to find an N such that +% T/phi <= N< (T+1)/phi. We first consider v=(T+0.5)/phi. As its +% distance to the extremities is 0.5/phi>0.5, its rounding M +% to an integer verifies automatically T/phi < M < (T+1)/phi, so +% is a candidate. The TeX core conversion of Msp to a Dpt with +% D a decimal of at most 5 fractional digits will provide a D +% such that indeed M=round(D*65536). +% % Implementation % ============== % -% <comments to be added> (see discussion #2) -% #2 is unit, assumed positive. We will need to branch whether -% #2 is <1pt or >1pt. +% \texdimenwithunit{dim1}{dim2}. dim2>0 assumed. +% We first get f from dim2 and branch according to whether f>=65536 or +% f<65536. We will also need to check the sign of T (dim1=T sp). +% We then compute in both branches round((2T+1)*32768/f), but +% in an indirect way in the f<65536 branch to avoid overflow. +% +% In the f<65536 branch we first do the Euclidean division +% 2T+1 = k*2*f + R with 0<=R<2f. The k is obtained as round((2T+1-f)/(2f)) +% which can be computed in a numexpr (and never gives -1 even for T=0) +% Then (2T+1)*32768/f=65536*k + R*32768/f +% Then R*32768/f<=65536-32768/f<65536-32768/65536=65536-0.5 +% Hence the numexpr evaluation gives an integer B<65536. +% +% N.B.: if f>=65536, we still have R*32768/f<65536 as R<2f +% so the only difference is that the B could be here 65536 +% +% From \the\dimexpr Bsp, we get a decimal E < 1, so E=0.ddddd +% (or less digits) and the looked for D will be the contatenation +% k.ddddd with k as obtained earlier. This procedure has no possible +% arithmetic overflow. +% +% #2 is assumed positive. % pre-multiplication of #1 by 2 here \def\texdimenwithunit#1#2{\expandafter\texdimenwithunit_ \the\numexpr\dimexpr#2\expandafter;\the\numexpr2*\dimexpr#1;}% -\def\texdimenwithunit_#1;#2{\ifnum#1>65535 - \expandafter\texdimenwithunit_A\else\expandafter\texdimenwithunit_B\fi +\def\texdimenwithunit_#1;#2{\ifnum#1<\p@ + \expandafter\texdimenwithunit_B\else\expandafter\texdimenwithunit_A\fi #2#1;% }% % unit>=1pt, handle this as for bp @@ -398,19 +444,24 @@ \the\dimexpr\numexpr(#1#3+\if-#1-\fi1)*32768/#2sp\relax }% % unit<1pt -% if dim1<0, simply negate result for dim1>0 as it can not be 0.0 +% if dim1<0, simply negate result for dim1>0 as it can not possibly be 0.0 +% Indeed (2T+1)*32768/f will be at least 3*32768/f so its rounding at least 2. \def\texdimenwithunit_B#1{\if-#1\expandafter\texdimenwithunit_Bneg\fi\texdimenwithunit_Ba#1}% \def\texdimenwithunit_Ba#1#2;#3;{\expandafter\texdimenwithunit_Bb\the\numexpr#1#3+1;#2;}% \def\texdimenwithunit_Bb#1;#2;{\expandafter\texdimenwithunit_Bc\the\numexpr(#1-#2)/(2*#2);#1;#2;}% -% not adding f-expandability slight overhead here -% oh well, let's do \the\numexpr..+0.ddddd which does the trick and allows -% recycling strippt here with no need of another utility -% (thinking about it it means we could do this for unit >1pt as this method -% works even for \the\dimexpr producing 1pt or more... (as TeX outputs 1.0pt, not 1pt -% so the dot remains to stop the \numexpr scan) +% I was hesitating between leaving k in the stream (breaking f-expandability) +% and then remove the "0" and trailing "pt" from 0.ddddd pt, but opted +% finally for doing \the\numexpr..+0.ddddd which is f-expandable and allows +% recycling strippt here with no need of another utility. +% +% This means (see the nota bene above) that we could apply this procedure +% also for f>=65536, because at worst we will get a \the\numexprk+1.0, which +% gives the correct result. I tested and found about 39% longer execution time +% if dim2>1pt does same calculations as for dim2<1pt, and at the same time +% dim2<1pt was improved about 11% from skipping the conditional \def\texdimenwithunit_Bc#1;#2;#3;{\the\numexpr#1+\expandafter\texdimenstrippt \the\dimexpr\numexpr(#2-#1*2*#3)*32768/#3sp\relax}% -% definitly not caring about f-expandability here +% Here, definitely not caring about f-expandability \def\texdimenwithunit_Bneg\texdimenwithunit_Ba-#1;#2;% {-\expandafter\texdimenwithunit_Bb\the\numexpr#2+1;#1;}% \texdimensendinput |