Simplify (x*c0 + y)/c1 to x/(c1/c0) when 0 <= y < c0 by alexreinking · Pull Request #9520 · halide/Halide

alexreinking · 2026-10-06T19:33:48Z

Adds a Div simplifier rule (and its commuted form):

rewrite((x * c0 + y) / c1, x / fold(c1 / c0), c0 > 0 && c1 % c0 == 0 && in_range(y, 0, c0, this))

An offset y in [0, c0) can't carry into the next multiple of c1. This makes per-block factor indices such as scale((lane*4 + ki) / 32) invariant in ki, so hoist_invariants() can hoist them (#9521).

in_range is a new allocation-free IRMatch predicate, since can_prove is too expensive in rule predicates. It only reads constant bounds of an IntImm, a bare Variable (from bounds_and_alignment_info), or a Broadcast of either, so compound offsets like y % 4 don't fire. It reuses #9400's bound_node/bound_const_int building blocks verbatim; whichever PR lands second gets one trivial conflict (keep #9400's side).

Verified with apps/simplifier_rule_verifier: true and correctly ordered under no-overflow (the rule is in the no_overflow block), false with wraparound.

Tests: positive and negative cases in correctness_simplify.

Authored by GitHub Copilot

abadams · 2026-10-06T20:08:54Z

We're trying to delete all can_prove usage from the simplifier, as it's very expensive and not guaranteed to terminate.

abadams · 2026-10-06T20:09:35Z

In general I'd like to be able to retrieve what the computed ConstantInterval was for subexpressions in rewrite rules, as those were already available while mutating the LHS of the division. But currently they've been dropped.

codecov · 2026-10-06T22:43:52Z

Codecov Report

❌ Patch coverage is 91.30435% with 2 lines in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (alexreinking/struct-let-loads@af07f26). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
src/Simplify_Exprs.cpp	81.81%	0 Missing and 2 partials ⚠️

Additional details and impacted files

@@                       Coverage Diff                        @@
##             alexreinking/struct-let-loads    #9520   +/-   ##
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mcourteaux · 2026-10-07T06:00:09Z

This is trivially done right once the can-prove-facts branch is in.

alexreinking · 2026-10-07T06:38:45Z

This is trivially done right once the can-prove-facts branch is in.

How would you do this in terms of #9400's (linear_)?(min|max)_diff?

alexreinking · 2026-10-07T20:35:03Z

This PR no longer uses can_prove

abadams · 2026-10-16T19:33:50Z

I think this PR should also drop the last term in this predicate, because the new rules bundle in this transformation but omitting this last term. After discussion we decided the last term was a relic from before when we defined division by zero.

abadams · 2026-10-16T19:34:27Z

+           // in_range only looks up the bounds already known for y, without
+           // simplifying anything, so it recognizes y only as a constant or a
+           // variable with constant bounds (from loops, lets, learned facts,
+           // or the caller's bounds), or a broadcast of one.


Please drop comment entirely. The rule is easier to read than the comment.

abadams

Approved pending two requested changes

When c0 > 0 divides the denominator c1, x*c0 % c1 is a multiple of c0 no greater than |c1| - c0, so an offset y in [0, c0) can never carry into the next multiple of c1 and doesn't affect the quotient. For example, (x*4 + y) / 32 == x / 8 for y in [0, 4). This form arises when a reduction is split twice (e.g. into blocks of 32 and then lanes of 4) and a per-block factor is indexed by r / 32: after rfactor, the factor's index is ((lane*4 + rxi) / 32) + u, which this rule reduces to lane/8 + u so it can be recognized as invariant in the innermost loop. The bound on y is established with can_prove(y / c0 == 0), which is equivalent to 0 <= y < c0 for c0 > 0 and mentions y only once, following the existing ramp rule in Simplify_Mod.cpp. The rule is restricted to integer types (it is false for floats) and applies lanewise to vectors. It holds under the no-overflow assumption only, and is placed inside the existing no_overflow block. To be revisited when #9400 lands, which bounds can_prove's recursion depth and may offer an allocation-free alternative. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

The (x*c0 + y)/c1 -> x/(c1/c0) rule checked 0 <= y < c0 with can_prove(y / c0 == 0), which builds and simplifies IR every time the rule's cheaper predicates pass. Replace it with a new IRMatch predicate, in_range(y, lo, hi, this), which tests y against the half-open range [lo, hi) without building, simplifying, or reference counting any IR. in_range requires y to be a wildcard and lo/hi to be WildConsts or integer literals (enforced by static_assert), and accepts only an integer constant, a variable whose constant bounds the simplifier already tracks (from loops, lets, learned facts, or the caller's bounds), or a broadcast of either. Anything else fails the predicate, so the rule no longer fires for compound offsets such as y % 4 or clamp(y, 0, 3). Wild::bound_node, WildConst::bound_const_int, IntLiteral::bound_const_int and the has_bound_node/has_bound_const_int traits are taken unchanged from #9400, which needs the same allocation-free access to matched terms. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Remove the obsolete nonzero quotient predicate and the explanatory comment on bounded-offset division rules. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Parse half-open range predicates with an optional matcher context, document their interpretation, and cover boundaries and bounded-offset division rules. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

alexreinking added this pull request to stack #9522 October 6, 2026 19:34

alexreinking mentioned this pull request Oct 6, 2026

hoist_invariants: decide invariance modulo the RVar bounds #9521

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alexreinking mentioned this pull request Oct 6, 2026

apps/ggml: GGML quantized kernels on Approximations #9511

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alexreinking removed this pull request from stack #9522 October 7, 2026 16:08

alexreinking added this pull request to stack #9524 October 7, 2026 16:08

alexreinking removed this pull request from stack #9524 October 7, 2026 19:21

alexreinking added this pull request to stack #9527 October 7, 2026 19:26

alexreinking marked this pull request as ready for review October 7, 2026 20:35

alexreinking requested a review from abadams October 7, 2026 20:35

alexreinking assigned shoaibkamil Oct 7, 2026

alexreinking removed this pull request from stack #9527 October 8, 2026 11:09

alexreinking added this pull request to stack #9529 October 8, 2026 11:10

alexreinking removed this pull request from stack #9529 October 8, 2026 14:37

alexreinking added this pull request to stack #9531 October 8, 2026 14:38

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alexreinking added this pull request to stack #9540 October 9, 2026 07:12

abadams reviewed Oct 16, 2026

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Comment thread src/Simplify_Div.cpp

abadams approved these changes Oct 16, 2026

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alexreinking force-pushed the alexreinking/simplify-div-bounded-offset branch from 505b388 to f73276e Compare October 16, 2026 19:45

alexreinking force-pushed the alexreinking/simplify-div-bounded-offset branch from bc38e1e to 29dcc55 Compare October 16, 2026 19:50

alexreinking added this pull request to stack #9560 October 16, 2026 19:50

alexreinking force-pushed the alexreinking/simplify-div-bounded-offset branch from 29dcc55 to a5dbfc2 Compare October 16, 2026 20:33

alexreinking removed this pull request from stack #9560 October 16, 2026 22:00

alexreinking added this pull request to stack #9561 October 16, 2026 22:00

alexreinking force-pushed the alexreinking/simplify-div-bounded-offset branch from a5dbfc2 to a471315 Compare October 17, 2026 16:07

alexreinking force-pushed the alexreinking/simplify-div-bounded-offset branch from a471315 to 36e1bee Compare October 19, 2026 19:49

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alexreinking removed this pull request from stack #9561 October 23, 2026 00:07

alexreinking added this pull request to stack #9597 October 23, 2026 00:08

alexreinking and others added 4 commits October 22, 2026 20:19

Address review feedback on division simplification

ba238a4

Remove the obsolete nonzero quotient predicate and the explanatory comment on bounded-offset division rules. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Support in_range predicates in the simplifier rule verifier

6692ec4

Parse half-open range predicates with an optional matcher context, document their interpretation, and cover boundaries and bounded-offset division rules. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

alexreinking removed this pull request from stack #9597 October 23, 2026 00:38

alexreinking force-pushed the alexreinking/simplify-div-bounded-offset branch from f7490c3 to 6692ec4 Compare October 23, 2026 00:38

alexreinking added this pull request to stack #9598 October 23, 2026 00:38

alexreinking mentioned this pull request Oct 23, 2026

Split ARM64 prefetches at the cache line size #9599

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Simplify (x*c0 + y)/c1 to x/(c1/c0) when 0 <= y < c0 - #9520

Simplify (x*c0 + y)/c1 to x/(c1/c0) when 0 <= y < c0#9520
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