From: L. David Baron <dbaron@dbaron.org>

Date: Tue, 25 Oct 2011 10:16:00 -0700

To: www-style@w3.org

Message-ID: <20111025171600.GA19568@pickering.dbaron.org>

Date: Tue, 25 Oct 2011 10:16:00 -0700

To: www-style@w3.org

Message-ID: <20111025171600.GA19568@pickering.dbaron.org>

I've been asked a few times why min() and max() are hard to implement. For a start, let me explain what they allow: percentages normally allow the CSS author to specify that a value (V) is some percentage of the percentage basis (P) for that property. For example, on width, the percentage basis is the width of the parent element. Thus, without calc(), percentages allow values to be linear functions that intersect the origin, V = a * P, whereas lengths allow specifying a constant, V = b. With calc(), but without min() and max(), we extend this to allow affine functions of the percentage basis, V = a * P + b. With min() and max(), instead of these simple functions I believe we would allow all continuous and piecewise-linear functions mapping the percentage basis to the resulting value. I think the algorithm for constructing a min/max/calc expression for such a function recursively works roughly like this (though as I note below, I haven't worked out the whole thing and thus it doesn't constitute a proof): * if constructing a linear function, construct based on slope and intercept, V = a * P + b. * otherwise, partition the function into a sequence of linear segments, split those segments at a segment boundary (though you need to be careful to pick one that works (i.e., where the extended segment doesn't intersect the other half), and I haven't worked out the right rule here, and thus haven't proven that this is possible), extend the segments at the split point straight in each direction, and construct the function min() (if the segment for values just below the split has larger slope than the one above) or max() (otherwise) with two arguments, constructing those recursively for each of the two halves of the split. This means that it is no longer possible to find the percentage basis that yields a particular result, since there may be none, one, or many such percentage bases (and I don't know of an efficient way to figure that out, either, though there may well be one). This type of computation is needed: * when computing the intrinsic width of a table from cells or columns that have a percentage width, which influence the width of the table in two different ways, as described in bullets (2) and (3) in http://dbaron.org/css/intrinsic/20110309#autotableintrinsic * when computing the intrinsic width of any element from margin or padding that has a percentage value (though for padding we already have this problem for calc() without min() and max(), since padding is constrained to be nonnegative) It's actually important that things work this way because it leads to results that don't have overlap/overflow, which is one of the reasons for using intrinsic width calculation. We could define an alternative, but I don't see how to do so in a way that avoids overlap/overflow. At the very least, however, we should agree on what alternative behavior is correct (and it should be one that produces correct results without min()/max()) before encouraging implementors to implement calc() and locking us in to a bad one. -David -- 𝄞 L. David Baron http://dbaron.org/ 𝄂 𝄢 Mozilla http://www.mozilla.org/ 𝄂Received on Tuesday, 25 October 2011 17:16:24 UTC

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