On Mon, Aug 3, 2026 at 5:57 PM Konstantinos Eleftheriou
<[email protected]> wrote:
>
>
> This patch series teaches GCC to recognize longhand 64x64->128
> wide-multiplication idioms and replace them with native multiply
> instructions: a widening multiply followed by a right shift for the
> high part, and a plain MULT_EXPR for the low part.
>
> Portable C/C++ code that needs a 128-bit product on a 64-bit target
> often resorts to a longhand decomposition: split operands into 32-bit
> halves, compute four partial products, and propagate carries manually.
> This pattern appears in a number of real-world codebases, including
> SPEC2026's 750.sealcrypto_r (seal/util/uintarith.h) and several
> examples from Hacker's Delight. Targets like AArch64 (mul/umulh) and
> x86-64 can compute the full 128-bit product in one or two instructions,
> but GCC does not currently fold the longhand sequence back to these.
>
> The recognizer emits the canonical widening shape
>
> (N)(((2N) a * (2N) b) >> N)
>
> for the high part and a plain MULT_EXPR for the low part. The high
> part is emitted as a shift of the wide product, not as a bare
> (2N) a * (2N) b: the `>> N' form is the MULT_HIGHPART idiom, so
> pass_optimize_widening_mul rewrites it to the target's native high-part
> multiply (e.g. umulh) without ever forming the full 2N product. A bare
> widening product would also compute the unwanted low half, and where 2N
> has no native multiply -- the 128x128 case, 2N = OImode, which the mode
> table carries but the target cannot expand -- there is no way to form
> it at all. For that case the final patch resynthesizes the longhand at
> narrow precision from (N/2)-wide partial products, so the fold never
> depends on a 2N multiply the target lacks.
>
> The series is split into seven patches:
>
> 1/7 forwprop: Match and fold the long-multiply carry form
> [PR107090]
>
> Adds the match.pd atom patterns and the forwprop framework:
> linearize the outer add/ior chain, classify each summand, and
> match the multiset against a table of decomposed variants.
> Carries the base carry form, a single overflow comparison on
> the cross-sum. Matching starts only at the end of a chain, and
> leaves that are not long-multiply summands are preserved and
> re-applied on top of the fold, so a chain that mixes the idiom
> with unrelated addends still folds.
>
> 2/7 - 5/7 Add the remaining recognized variants: carry-low-sum,
> two-carry, ladder, and low-plus.
>
> 6/7 match.pd, forwprop: Recognize long-multiply carries written as
> 2-arg PHI
>
> Hand-written code often writes the carry as a 2-arg PHI
> (`if (overflow) result += pow2;`) with no top-level + at the
> result. Adds cond_carry_add / cond_carry_add_neg recognizers
> for that shape and a match_long_mul_phi entry that synthesizes
> the carry summand from the PHI bindings and reuses the table
> walk and emit path.
>
> 7/7 widening_mul: Lower long-multiply chains to inline longhand
>
> Lowers the high-part chain to a longhand high-part at narrow
> precision when the target has no expansion path for the 2N
> form, using (N/2)-by-(N/2)->N widening multiplies where the
> optab exists and plain N-bit multiplies otherwise. Operands
> that are themselves wider than N are split into N-bit halves
> rather than truncated, and a 2N product left with only low-half
> uses is narrowed to an N-bit multiply rather than reaching
> expansion. When an operand holds a product's high N bits, those
> come from the product's own operands instead of the 2N shift.
> Paired with pass_optimize_widening_mul so the chain is emitted
> only when the pass will run to rescue an unsupported 2N shape.
>
> On SPEC2026's 750.sealcrypto_r:
>
> - AArch64 Neoverse-N1: 25% improvement
> - x86-64 Zen4: 59% improvement
>
> Compile-time impact is negligible: recompiling gcc/*.cc
> (checking=yes,extra) with the series compiler versus its base adds
> about 0.1% overall, confined to forwprop, where the recognizer runs
> and grows the pass by a few percent.
>
> Bootstrapped/regtested on AArch64, x86-64, ARM and PowerPC.
This is OK. Please squash the series before pushing, there seems to
be unused code in earlier parts of the series and possibly failing
testcases.
Thanks,
Richard.
> Changes in v8:
> - 1/7 starts matching only at chain ends and sets aside leaves that are
> not long-multiply summands, re-applying them on top of the fold. The
> two go together. Either alone regresses a foldable chain. Now folds
> shapes such as `acc += mulh (x, y)`.
> - 1/7 factors out build_mul_high_seq, long_mul_classify_match and
> long_mul_classify_chain for the PHI entry in 6/7 to reuse, and takes
> a gassign * in the matcher and the emitters.
> - The long_mul_high_chain atom binds each mult operand through
> `(convert? @X)`, so a PRE-hoisted cast into a PHI still matches. An
> operand wider than N is now split into N-bit halves rather than
> rejected, which previously left the 2N multiply for expansion.
> - optimize_widening_mul_active_p returns false for optimize_debug: -Og
> runs no widening_mul pass to lower the emitted chain, so the
> unexpandable multiply reached expand.
> - Add narrow_long_mul_low_half: when a 2N `res = a * b` has uses only in
> its low N bits and the target cannot expand 2N, rewrite it to
> `res = (2N) ((N)a * (N)b)`. The split-based lowering covers a chained
> 2N operand by recursing into it, but not a shared 2N product left with
> only low-half uses, which is what ICEs libgo's p521_fiat64.go on ARM32.
> - long_mul_split_operand resolves a 2N value shifted down by N to the
> high half of what was shifted, instead of truncating the shift. The
> truncation read the shift and so kept a chained product live past its
> own lowering, aborting expand_mult on a target without a 2N multiply.
> Reachable from Go on ARM32 as bits.Mul64 (bits.Mul64 (x, y), z), where
> the unexpandable mode is TImode, and on aarch64 and x86-64 from a
> chained __int128 longhand, where it is OImode.
> - New coverage: near misses of the idiom, checked at runtime against
> their literal meaning, a signed narrow-cast operand on Thumb-1, and
> chained longhands through both halves on ARM32.
>
> Changes in v7:
> - Split the single long-multiply fold (was 1/2) into five patches: a
> base patch carrying the framework and the carry form, then one
> patch each for the carry-low-sum, two-carry, ladder and low-plus
> variants. Easier to review and to bisect a variant in isolation.
> The PHI-form recognition follows as 6/7, unchanged from v6's 2/2.
> - New 7/7: lower the emitted high-part chain to inline longhand at
> narrow precision when the target has no expansion path for the 2N
> form. v6 only emitted a HIGH_PART when the 2N scalar mode existed
> and skipped it otherwise; v7 emits it and pairs the recognizer with
> lower_long_mul_high_chain via optimize_widening_mul_active_p, so a
> 128x128 high part on a target whose mode table has OImode but no
> scalar OImode support is now built from (N/2)-wide partial products
> instead of a 2N multiply the target cannot expand.
> - Refuse the HIGH_PART emit and the chain lowering for BITINT_TYPE,
> keeping the recognizer and the lowering gate symmetric.
> - Add per-variant tree-ssa tests, 128-bit torture and runtime tests,
> arm thumb1 / umull inline tests, and a check_effective_target
> _oi_mode helper.
>
> Changes in v6:
> - Reorder so the long-multiply fold (was 2/2) is now 1/2 and a new
> PHI-form recognition pass is 2/2. Reverting 2/2 leaves a working
> long-multiply fold for the flat-shifted-compare carry form.
> - Drop v5's standalone flatten_cond_carry_add driver. The same
> cond_carry_add / cond_carry_add_neg match.pd recognizers now feed
> a match_long_mul_phi entry inside the long-multiply fold, so a
> PHI-shaped carry folds straight to the wide-multiply output.
> - Factor long_mul_classify_chain, long_mul_classify_match and
> build_mul_high_seq for sharing between match_long_mul and the new
> match_long_mul_phi.
> - cond_carry_add_neg uses le / ge instead of gt / lt to encode the
> carry condition strictly. v5 inverted the compare via
> invert_tree_comparison in the flatten driver; v6 synthesises the
> carry summand directly inside match_long_mul_phi and so requires
> the recogniser to encode the strict form.
> - Delete forwprop-44/45/46.c; add PHI-form coverage in
> long-mul-carry.c, long-mul-two-carry.c, long-mul-boundary.c
> and long-mul-boundary-64.c.
> - Add PHI-form near-miss tests in long-mul-partial.c and
> operand-swap polarity coverage in long-mul-boundary{,-64}.c.
> - Refresh stale long-mul comment references (check_hilo_and_ops,
> fold_mul_low_plus) and reword mul_carry_low's :c-on-gt note to
> the correct LT form (a + b < a).
>
> Changes in v5:
> - 1/2:
> - Replace the match.pd simplify on COND_EXPR with cond_carry_add
> / cond_carry_add_neg match recognizers (cond^), split by gcond
> polarity, plus a flatten_cond_carry_add driver in
> tree-ssa-forwprop.cc. The driver inverts the gcond's
> comparison for the _neg form. Modelled on match_saturation_add.
> - Remove fold_cond_carry_add_profitable_p and the tm_p.h /
> predict.h includes from gimple-match-head.cc. The width >
> MAX_FIXED_MODE_SIZE and width % 2 != 0 guards were
> prerequisites for the can_mult_highpart_p fallback path, not
> soundness checks. type_has_mode_precision_p subsumes them.
> - Retarget the test scans from phiopt2 to forwprop1. Add
> forwprop-46.c covering all four arm/comparison polarities.
> - forwprop-45.c uses __UINT64_TYPE__ instead of unsigned long
> and drops the lp64 restriction, covering the type > word_mode
> regime on 32-bit targets.
> - 2/2:
> - Lower the high-part as (N)(((2N) op1 * (2N) op2) >> N).
> pass_optimize_widening_mul rewrites this to WIDEN_MULT_EXPR /
> MULT_HIGHPART_EXPR on supporting targets. Removes
> can_mult_highpart_p queries from forwprop.
> - Replace the can_mult_highpart_p prefilter in match_long_mul
> with a targetm.scalar_mode_supported_p check on the 2N mode.
> Test scans select on int128, mirroring the gate, instead of
> lp64.
> - Drop the m_long_mul_fold_p pass parameter and its passes.def
> arguments. The long-mul fold runs in every forwprop instance.
> Test scans retargeted from forwprop2 to forwprop1.
> - Stop restricting forwprop-44.c to lp64. With the
> can_mult_highpart_p gating gone, the fold is target-independent
> and the test passes on ilp32 targets too.
>
> Changes in v4:
> - 1/2:
> - Rebuild the guard with per-conjunct reasoning: require both
> operands to be SSA names (drops degenerate one-side-constant
> cases that fold trivially elsewhere), require the type to
> have_mode_precision_p (excludes BITINT_TYPE precision != mode
> and similar oddities), drop the explicit MAX_FIXED_MODE_SIZE
> width cap (subsumed by have_mode_precision_p), and gate on the
> flat optab via can_mult_highpart_p of the 2N mode.
> - Retain BRANCH_COST >= 2: keep the flatten conditional on a
> target where the branchless form is generally cheaper.
> - Rewrite the cover letter to describe the gate as the
> composition of these conjuncts and to clarify that the
> transformation now only ever introduces a (mul_hi-like)
> can_mult_highpart_p shape, not a libgcc multi-precision call.
> - 2/2:
> - Convert per-variant fold_mul_* functions into a
> table-driven long_mul fold framework.
> - Migrate each variant into a row in long_mul_table (six
> HIGH_PART, six LOW_PART rows) keyed by (kind, extract).
> - Add cross-summand consistency checks
> (long_mul_check_consistency, long_mul_check_two_carries,
> long_mul_check_low_plus_defer) shared across rows.
> - Drop emission to a libgcc multi-precision call from RTL
> expansion; defer to pass_optimize_widening_mul / RTL
> expansion to pick native umul_highpart, a widening multiply, or
> a synthesised sequence. Emission is gated on
> can_mult_highpart_p.
> - Structural redesign: per-variant fold_mul_* functions
> consolidated into a single linearise + classify + table-lookup
> framework (long_mul_table, match_long_mul,
> long_mul_classify_summand, long_mul_check_consistency). Each
> variant is now a row in long_mul_table; consistency checks are
> shared across rows.
> - Fast-fail prefilters in match_long_mul: LHS-type prefilter at
> entry (no legitimate long-mul leaf has a signed / pointer /
> float / odd-width type) and a can_mult_highpart_p probe before
> the row loop to skip HIGH_PART rows on unsupported targets.
> - Bound long_mul_linearize_chain mid-walk by LONG_MUL_MAX_SUMMANDS
> so an overlong addition / BIT_IOR chain bails immediately rather
> than after a full traversal.
> - Emit a dump-file hint pointing at the shared inner addition when
> long-mul folding rejects a chain because of a multi-used
> intermediate (caching the partial sum into a single-use SSA
> name normally enables the fold).
>
> Changes in v3:
> - Moved carry-diamond flattening from forwprop to match.pd,
> replacing ~460 lines of C++ with a 17-line match.pd pattern.
> - Two-carry test scans forwprop3 (the first forwprop after phiopt2,
> since early phiopt restricts which tree codes are allowed).
> - Set location for new sequences.
> - Updated mul_carry_low pattern.
> - Added the `mul_low_plus` pattern.
> - Fixed formatting issues.
>
> Changes in v2:
> - Fixed the testcases by separating the high part's fold count for
> 32-bit and 64-bit targets.
>
> Konstantinos Eleftheriou (7):
> forwprop: Match and fold the long-multiply carry form [PR107090]
> forwprop: Add long-multiply carry-low-sum variant
> forwprop: Add long-multiply two-carry variant
> forwprop: Add long-multiply ladder variants
> forwprop: Add long-multiply low-plus variant
> match.pd, forwprop: Recognize long-multiply carries written as 2-arg
> PHI
> widening_mul: Lower long-multiply chains to inline longhand
>
> gcc/match.pd | 198 +++
> gcc/testsuite/gcc.dg/long-mul-128-Og.c | 26 +
> gcc/testsuite/gcc.dg/torture/long-mul-128.c | 121 ++
> .../gcc.dg/torture/long-mul-64-run.c | 180 +++
> .../gcc.dg/tree-ssa/long-mul-boundary-64.c | 417 ++++++
> .../gcc.dg/tree-ssa/long-mul-boundary.c | 394 ++++++
> .../gcc.dg/tree-ssa/long-mul-carry.c | 385 ++++++
> .../gcc.dg/tree-ssa/long-mul-chain-cse-128.c | 52 +
> .../tree-ssa/long-mul-chain-trunc-128.c | 80 ++
> .../gcc.dg/tree-ssa/long-mul-extra-addend.c | 63 +
> .../gcc.dg/tree-ssa/long-mul-ladder.c | 333 +++++
> .../gcc.dg/tree-ssa/long-mul-low-plus.c | 54 +
> .../gcc.dg/tree-ssa/long-mul-partial.c | 193 +++
> .../gcc.dg/tree-ssa/long-mul-two-carry.c | 140 ++
> gcc/testsuite/gcc.target/aarch64/long_mul.c | 100 ++
> .../gcc.target/arm/long-mul-thumb1-inline.c | 47 +
> gcc/testsuite/gcc.target/arm/long-mul-umull.c | 73 +
> gcc/testsuite/gcc.target/i386/long_mul.c | 100 ++
> .../gcc.target/i386/widen_mult_high_chain.c | 32 +
> gcc/testsuite/lib/target-supports.exp | 20 +
> gcc/tree-ssa-forwprop.cc | 1197 ++++++++++++++++-
> gcc/tree-ssa-math-opts.cc | 492 ++++++-
> gcc/tree-ssa-math-opts.h | 2 +
> 23 files changed, 4690 insertions(+), 9 deletions(-)
> create mode 100644 gcc/testsuite/gcc.dg/long-mul-128-Og.c
> create mode 100644 gcc/testsuite/gcc.dg/torture/long-mul-128.c
> create mode 100644 gcc/testsuite/gcc.dg/torture/long-mul-64-run.c
> create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/long-mul-boundary-64.c
> create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/long-mul-boundary.c
> create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/long-mul-carry.c
> create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/long-mul-chain-cse-128.c
> create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/long-mul-chain-trunc-128.c
> create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/long-mul-extra-addend.c
> create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/long-mul-ladder.c
> create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/long-mul-low-plus.c
> create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/long-mul-partial.c
> create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/long-mul-two-carry.c
> create mode 100644 gcc/testsuite/gcc.target/aarch64/long_mul.c
> create mode 100644 gcc/testsuite/gcc.target/arm/long-mul-thumb1-inline.c
> create mode 100644 gcc/testsuite/gcc.target/arm/long-mul-umull.c
> create mode 100644 gcc/testsuite/gcc.target/i386/long_mul.c
> create mode 100644 gcc/testsuite/gcc.target/i386/widen_mult_high_chain.c
>
> --
> 2.55.0
