Bit tricks and strength reduction

Replace expensive operations with cheap ones: shifts for divisions, popcount and count-leading-zeros, multiply-by-reciprocal, bit masks instead of sets.

1,973proven techniques

29pitfalls: tried, then slower

838repositories

107from papers

Examples from real commits

openfheorg/openfhe-development 56× Extract all base-2^d digits in one pass: bias once by H, then each digit is a shift-and-mask window minus h, top window unmasked. proof: commit → apache/doris 7× For constant exponent 2, replace libm pow with x*x for the leading block prefix whose bases are integers with |x|<=2^26, where the square is exact. proof: commit → NVIDIA/cudf 6.6× Represent NFA state as a single uint64_t bitmask to eliminate per-thread global memory access. proof: commit → rui314/mold 5.1× Compile 64+ complex glob patterns into one bit-parallel NFA, one bit per state, advancing 64 states per machine word per input byte. proof: commit → apache/arrow-rs 3.4× Constant-time byte-parallel compress: three SWAR suffix-network shift rounds on all bytes at once, then one multiply by 0x0101..01 to place each byte. proof: commit → sgl-project/sglang 3× Extract int4 nibbles with lop3 mask-and-OR against a fp16 magic constant, then fix the bias with one half2 sub or fma, avoiding per-element shifts and converts. proof: commit → VcDevel/Vc 3× Use inline assembly vmovd instead of _mm_cvtsi128_si32 to extract the first 32-bit lane. proof: commit → rive-app/rive-runtime 1.9× Evaluate the normal curve as exp2(-t_*t_) by pre-scaling the argument by sqrt(log2(e)), replacing natural exp with the cheaper base-2 exponential. proof: commit →

Languages

C++848
C515
Rust187
CUDA77
Go50
Python40

Hardware

x86605
CPU479
ARM201
NVIDIA GPU107
GPU60

Fields

general520
data & compression379
math299
graphics224
CPU204

Where these come from

Repositories with the most techniques on this topic in the database:

z88dk/z88dk · 14zeux/meshoptimizer · 12simdjson/simdjson · 10WojciechMula/base64simd · 10abseil/abseil-cpp · 10ptitSeb/box64 · 10v8/v8 · 9flagos-ai/FlagGems · 9stenzek/duckstation · 9torvalds/linux · 8

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