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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal>Hi,<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I’m trying expand the Float2Int pass in order to make it able to optimize<o:p></o:p></p><p class=MsoNormal>expressions like f * x > y, where x and y are integers (we’ll assume unsigned for<o:p></o:p></p><p class=MsoNormal>simplicity) and f is a floating point constant. The optimization would convert<o:p></o:p></p><p class=MsoNormal>the expression to something like:<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal> (a * x)/b > y<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>where a and b are integers guessed by the compiler (currently using continued<o:p></o:p></p><p class=MsoNormal>fractions, but some other method could also be used). The exact expression<o:p></o:p></p><p class=MsoNormal>would depend on the comparison type and on the type of input integers.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Note that dividing by an integer constant should be a cheap operation<o:p></o:p></p><p class=MsoNormal>compared to FP multiplication and comparison as this would get lowered to a<o:p></o:p></p><p class=MsoNormal>multiply+subtract+shift sequence (and should certainly be true on cores with no<o:p></o:p></p><p class=MsoNormal>FP unit)<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The change will add some machinery to Float2Int in order to be able to<o:p></o:p></p><p class=MsoNormal>match certain known patterns. All patterns will have exactly representable<o:p></o:p></p><p class=MsoNormal>inputs and outputs. In this case, the FCMP will have two inputs, x and y and<o:p></o:p></p><p class=MsoNormal>one output (the result of the comparison). This allows us to use the existing<o:p></o:p></p><p class=MsoNormal>Float2Int infrastructure to track the integer length that would be required<o:p></o:p></p><p class=MsoNormal>for the conversion.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The main difficulty I can see with this is validating the transformation. Ideally<o:p></o:p></p><p class=MsoNormal>the property that we want to prove for the guessed integers a and b would be<o:p></o:p></p><p class=MsoNormal>that (a*x)/b == round_to_zero(f * to_float(x)), for every integer x in a given<o:p></o:p></p><p class=MsoNormal>range. The problem with this is that we would need to come up with a reasonably<o:p></o:p></p><p class=MsoNormal>quick method of proving this.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>My best guess (still need to work out the exact details) would be that we only<o:p></o:p></p><p class=MsoNormal>need to check the first and last b numbers of the range. A hand-wavy argument<o:p></o:p></p><p class=MsoNormal>for this would be that since errors increase on the extremities of the range, so if<o:p></o:p></p><p class=MsoNormal>an error appears anywhere it must also appear at the edges of the range.<o:p></o:p></p><p class=MsoNormal>I still need to prove this. If there are any floating-point experts that can help<o:p></o:p></p><p class=MsoNormal>with this, I would greatly appreciate it.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Any other comments about the overall merits of the idea and the approach are<o:p></o:p></p><p class=MsoNormal>of course also welcome!<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Thanks,<o:p></o:p></p><p class=MsoNormal>Silviu<o:p></o:p></p></div></body></html>