On Tue, Jan 11, 2022 at 12:28 AM Andrew MacLeod via Gcc-patches <gcc-patches@gcc.gnu.org> wrote: > > This test case demonstrates an unnoticed exponential situation in range-ops. > > We end up unrolling the loop, and the pattern of code creates a set of > cascading multiplies for which we can precisely evaluate them with > sub-ranges. > > For instance, we calculated : > > _38 = int [8192, 8192][24576, 24576][40960, 40960][57344, 57344] > > so _38 has 4 sub-ranges, and then we calculate: > > _39 = _38 * _38; > > we do 16 sub-range multiplications and end up with: int [67108864, > 67108864][201326592, 201326592][335544320, 335544320][469762048, > 469762048][603979776, 603979776][1006632960, 1006632960][1409286144, > 1409286144][1677721600, 1677721600][+INF, +INF] > > This feeds other multiplies (_39 * _39) and progresses rapidly to blow > up the number of sub-ranges in subsequent operations. > > Folding of sub-ranges is an O(n*m) process. We perform the operation on > each pair of sub-ranges and union them. Values like _38 * _38 that > continue feeding each other quickly become exponential. > > Then combining that with union (an inherently linear operation over the > number of sub-ranges) at each step of the way adds an additional > quadratic operation on top of the exponential factor. > > This patch adjusts the wi_fold routine to recognize when the calculation > is moving in an exponential direction, simply produce a summary result > instead of a precise one. The attached patch does this if (#LH > sub-ranges * #RH sub-ranges > 12)... then it just performs the operation > with the lower and upper bound instead. We could choose a different > number, but that one seems to keep things under control, and allows us > to process up to a 3x4 operation for precision (there is a testcase in > the testsuite for this combination gcc.dg/tree-ssa/pr61839_2.c). > Longer term, we might want adjust this routine to be slightly smarter > than that, but this is a virtually zero-risk solution this late in the > release cycle.
I'm not sure we can do smarter in a good way other than maybe having a range helper that reduces a N component range to M components with maintaining as much precision as possible? Like for [1, 1] u [3, 3] u [100, 100] and requesting at most 2 elements merge [1, 1] and [3, 3] and not [100, 100]. That should eventually be doable in O(n log n). > This also a generalize ~1% speedup in the VRP2 pass across 380 gcc > source files, but I'm sure has much more dramatic results at -O3 that > this testcase exposes. > > Bootstraps on x86_64-pc-linux-gnu with no regressions. OK for trunk? OK. Thanks, Richard. > > Andrew
