[cbeck88]

Motivation

batched::msm uses double-and-add below 15 bases.
From 15 to 31 bases, it uses the bucket method with a window of one bit.
That is 253 windows, and each window does its own batched inversions over a few points.
At 32 bases and above, the window grows, and the cost drops again.

Verification of a private fee does one G1 MSM of 25 bases, for the record's inclusion circuit.
A public fee and a transfer_public execution do G1 MSMs of 13 bases or fewer.

This PR uses double-and-add below 32 bases. The bucket method with a one-bit window is then not reachable, so the PR removes it.

Commits:

• test: cover MSM sizes at the batched path's thresholds adds 14, 15, 25, 31, 32 and 33 bases to test_msm. The test passes before and after the change.
• perf: use double-and-add for MSMs below 32 bases raises the cutoff from 15 to 32.

One G1 MSM, one core (taskset, RAYON_NUM_THREADS=1), median of 300 interleaved repetitions. Host: Intel Xeon w9-3475X.

bases	staging	standard::msm	double-and-add
13	1367 µs	1422 µs	1372 µs
15	8585 µs	1133 µs	1077 µs
25	10687 µs	1747 µs	1696 µs
31	11828 µs	2162 µs	2095 µs
32	2806 µs	2068 µs	2159 µs
64	4050 µs	3551 µs	4236 µs

check_transaction of a credits.aleo/transfer_public at ConsensusVersion::V22 (Varuna V3), with the verified-transaction cache cleared before each call, one core, pinned. Both arms include #3591. Each row is 6 interleaved blocks.

	before	after	change	blocks faster
check_fee, private fee	19.21 ms	10.21 ms	−46.8%	6 of 6
check_transaction, private fee	26.89 ms	18.16 ms	−32.8%	6 of 6
check_fee, public fee	7.88 ms	7.85 ms	−1.0%	4 of 6
check_transaction, public fee	15.87 ms	15.50 ms	−1.1%	6 of 6

On 72 threads, each iteration checks 72 transactions in parallel. Each row is 6 interleaved blocks.

	before	after	change	blocks faster
private fee	922 tx/s	1155 tx/s	+25%	6 of 6
public fee	1317 tx/s	1331 tx/s	+1%	3 of 6

The public-fee rows do no MSM in the changed range.

Test Plan

• cargo test --release -p snarkvm-algorithms (115 passed)
• cargo clippy -p snarkvm-algorithms --all-targets [--features serial] -- -D warnings
• cargo +nightly-2026-04-02 fmt --all -- --check
• The end-to-end numbers use ledger/benches/verify_transaction.rs from bench: measure transaction verification without the verified-transaction cache #3592: cargo bench -p snarkvm-ledger --bench verify_transaction --features test_consensus_heights.

Documentation

None.

Backwards compatibility

No consensus change. An MSM returns the same group element; test_msm compares both paths with a naive MSM at every size above.

🤖 Generated with Claude Code

https://claude.ai/code/session_017omPAWn5XC7EA2aMFGn7FC