On 14-07-04 03:09 PM, Alexei Podtelezhnikov wrote: > > > You force me to think, man. To avoid any overflow it is sufficient to satisfy > this inequality > > a + b < 2 * sqrt(X - c/2) > > where X is 2^31 - 1. Using Taylor series it can replaces with a *stronger* > inequality > > a + b < 2 * sqrt(X) - c / (2 * sqrt(X)) > > or > > a + b < 92681.9 - c / 92681.9 > > Now we get rid of impractical division > > a + b < 92681.9 - (c >> 16) + (c >> 18) > > where the right side got a bit smaller again as the denominator became > 87381.3. We can finally turn the whole thing integer > > a + b < 92681 - (c >> 16) + ((c+ 235935) >> 18) > > Therefore, we do not need a special limit on c. The whole thing becomes more > permissive.
You could write it with <= instead of <. No? How about the simpler: a + b <= 92681 - (c >> 16) This has the same number of operations as my previous patch, but more permissive for all practical purposes though not *completely* covering the previous case. -- behdad http://behdad.org/ _______________________________________________ Freetype-devel mailing list [email protected] https://lists.nongnu.org/mailman/listinfo/freetype-devel
