I encountered a problem with supppdf when I tried to rewrite Knuths "dangerous bend" as a MetaPost figure. Very little change was required to get a good picture, but the "reverse dangerous bend" (obtained by merely reflecting the currentpicture" produced a quite grotesquely distorted picture. I tracked this down to the method used to divide by the determinant of the scaling matrix in \doMPconcat. The division code is the following: \ifdim\dimen16=\onepoint \else \ifdim\dimen16>\MPconcatfactor \onepoint \relax \doMPreducedimen16 \divide \dimen18 \dimen16 \doMPexpanddimen18 \divide \dimen12 \dimen16 \doMPexpanddimen12 \else \divide \dimen18 \dimen16 \doMPexpanddimen18 \doMPexpanddimen18 \divide \dimen12 \dimen16 \doMPexpanddimen12 \doMPexpanddimen12 \fi \fi In the reverse dangerous bend symbol \dimen16 (the determinant in question) is 1 and \MPconcatfactor is 256, so the else part is taken. The division is integer division, so the accuracy (after the two \doMPexpanddimen) is +/ 1pt. This turns values like the following: 58.11118 61.6534 7.53143 11.0737 7.52731 11.06958 c 4.48691 8.02919 1.99252 4.2878 1.99252 0 c 1.99252 4.2878 4.48691 8.02919 7.52731 11.06958 c 7.53143 11.0737 58.11118 61.6534 58.1153 61.65752 c into (actual code in from uncompressed pdf output): 58.0 61.0 7.0 11.0 7.0 11.0 c 4.0 8.0 1.0 4.0 1.0 0.0 c 1.0 4.0 4.0 8.0 7.0 11.0 c 7.0 11.0 58.0 61.0 58.0 61.0 c Similar problems occur if the figure is rotated. (Theoretically, the determinant is 1, but with only 5 decimal accuracy, the same branch is taken.) Also the \if tests above don't take the sign of \dimen16 into account. There is a lesser problem with multiplication when numbers are less than around 1pt. The predivision by 256 (\doMPreducedimen) reduce accuracy to less than 3 significant decimal digits (i.e., 8 binary digits). I have written some modifications for supppdf that avoid all of these. No predivision is used because multiplication is accomplished by something like \dimen16 = \withoutpt\the\dimen0 \dimen6 and division is accomplished by computing 1/D and multiplying. Since the numerator (1) is fixed, this one division can be arranged for maximum accuracy. I do this by halving D until it is less than 1pt, keeping track of the number of halvings required. Then I divide 2^30 by D, then double the result 2 fewer times than than D was halved. This guarantees at least 14 binary places accuracy, or the number of places in D, whichever is smaller. My speed tests show that the resulting code is as fast or slightly faster than the current code. Further efficiency could be gained by performing the calculation of D outside the loop of calls to \doMPconcat (I have not done this yet). The current state of my code can be found at http://comp.uark.edu/~luecking/tex/supppdf.mod and a stripped down version of the reverse dangerous bend code that shows the problem is http://comp.uark.edu/~luecking/tex/rdbend.mp Comments are welcome. I hope at least the division can be made more accurate in the context distribution. Dan Luecking Daniel H. Luecking Department of Mathematical Sciences University of Arkansas
Hi Dan,
of the scaling matrix in \doMPconcat.
ah, doMPconcat ... indeed a problematic one ...
I have written some modifications for supppdf that avoid all of these.
good, we needed a mathematician to do this )
The current state of my code can be found at http://comp.uark.edu/~luecking/tex/supppdf.mod
interesting
Comments are welcome. I hope at least the division can be made more accurate in the context distribution.
sure, but i will probably comment the old and insret the new code (i often keep older slower worse code in there as example); let me know when you've frozen the code so that i can merge it one thing you can consider playing with is an etex variant; i attach a local experimental file (it build on the old code, but keeping the calculations within a \dimexpr may give even more accuracy because internally double precission is used thanks for taking the time to look into that messy part of the converter ) Hans  Hans Hagen  PRAGMA ADE Ridderstraat 27  8061 GH Hasselt  The Netherlands tel: 038 477 53 69  fax: 038 477 53 74  www.pragmaade.com  www.pragmapod.nl 
participants (2)

Dan Luecking

Hans Hagen