simd: mask_ternlog_popcount / mask_ternlog_any — Boolean membership ends in Count/Any with no mask written

[AdaWorldAPI]

What

Two slice functions in simd_masking_ops.rs, re-exported from ndarray::simd:

• mask_ternlog_popcount::<IMM>(a, b, c) -> u64: Σ popcount(ternlog(a, b, c))
• mask_ternlog_any::<IMM>(a, b, c) -> bool: is any bit of ternlog(a, b, c) set?

A 2- or 3-input Boolean membership can now end in Count or Any without writing a mask. Two-input functions are the same call with a table that ignores c.

The question it answers

Is a new T1 primitive needed for "Boolean membership → Count/Any", or can the existing U64x8 operations already do it without touching memory?

Measured answer: nothing new is needed below the slice loop. U64x8::{ternlog, popcnt, +, |, reduce_sum} already exist in every backend (avx512, avx2-polyfill, scalar, neon, wasm). These two functions are loops over those methods, so no backend code, cfg or intrinsics are added.

Contract

• Word-level: the result is identical to mask_ternlog + popcount_batch_u64 / mask_any over the materialized mask.
• Odd truth tables: an odd IMM sets the dead tail bits of the last word, and those bits are counted. The caller masks the last word, the same rule mask_ternlog already documents for its output.
• Register padding is never counted. An odd table turns an all-zero padding lane into all-ones. The tail therefore runs through the packed op, and only the real lanes are read.
• mask_ternlog_any checks once per block of 8 chunks, not once per chunk. A per-chunk check lost to the materializing pair on avx2 (0.91×).

Evidence

Probe: examples/ternlog_fold_probe.rs. Truth table AND2_OR; timings are medians; "M/R" is the speed-up over materializing the mask and then reducing it.

backend	words	Count M/R	Any M/R
avx2 (config-v3)	16 384	1.27	3.24
avx2	262 144	1.50	6.18
avx512 (config-v4, no vpopcntdq)	16 384	1.90	2.59
avx512	262 144	1.94	4.39

A plain scalar fused loop roughly ties the register fold on avx2 and at the memory-bound size on avx512. The win comes from not writing the mask, not from SIMD as such.

Tests

• Differential: mask_ternlog_folds_match_the_materializing_pair_for_all_256_tables compares each fold against the exact pair it replaces. It covers all 256 truth tables × 14 lengths (0 … 129) × dense and sparse inputs.
• Padding: mask_ternlog_folds_never_count_register_padding covers NOR3 over 9 words (7 padding lanes), hits that sit only in the tail, and hits past the first block.
• Length-mismatch panics for both functions.
• Disable runs, each failing when broken as intended: counting padding lanes, testing padding lanes in the Any tail, and removing Any's block check.
• Parity: crates/simd-masking-parity slice_ternlog! now checks both folds (codes 0x69x count, 0x65x any). It passes on native v4, native v3, neon-qemu, wasm and wasm-scalar.
• clippy -D warnings passes on v3 and v4.

Consumer

lance-graph-mask-risc will use these for its fused terminal path MaskOp::{And, Or, Xor, AndNot, Ternlog} → Count/Any, in a follow-up lance-graph PR.

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• src/simd_masking_ops.rs

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