Baymine commented on PR #66391:
URL: https://github.com/apache/doris/pull/66391#issuecomment-5395114243
# Wide-Integer 256-bit Division Fast-Path Benchmark
## Environment
- **CPU**: 128 vCPUs @ 3.5 GHz (L1d 48 KiB, L2 1280 KiB, L3 49 MB × 2)
- **Compiler**: Clang++, `-O2`, Release build
- **Benchmark**: Google Benchmark with `--benchmark_min_time=2s
--benchmark_repetitions=3 --benchmark_report_aggregates_only=true`
- **Wall-clock stability**: Each case ran ≥ 6 seconds total (2 s per rep × 3
reps)
- **Batch**: 65536 random operand pairs per state-iteration (L2-resident,
amortizes cache effects)
## Results — `operator/` (Division)
Per-element time in nanoseconds (median time ÷ 65536 = ns / div):
| Case | Legacy Generic | Default (fast path) |
Speedup | Fast path hit |
|---------------------------------|---------------:|--------------------:|---------:|----------------------------------------|
| `BothFit128` (n,d < 2^128) | 27.4 ns | **11.7 ns** |
**2.34×** | Path 1 — single `__int128` divide |
| `SingleLimb` (d = 10^k) | 2128 ns | **13.7 ns** |
**155×** | Path 2 — schoolbook limb-by-limb |
| `TwoLimbKnuth` (2^64 ≤ d < 2^128) | 1559 ns | **154.9 ns** |
**10.1×** | Path 3 — Knuth Algorithm D (base 2^32) |
| `TrulyWide` (d ≥ 2^128) | 881 ns | **857 ns** |
**1.03×** ✓ | No fast path (unchanged code path) |
## Results — `operator%` (Modulo)
| Case | Legacy Generic | Default (fast path) |
Speedup |
|---------------------------------|---------------:|--------------------:|---------:|
| `BothFit128` | 28.0 ns | **14.2 ns** |
**1.97×** |
| `SingleLimb` (d = 10^k) | 2111 ns | **15.1 ns** |
**140×** |
| `TwoLimbKnuth` | 1563 ns | **156.5 ns** |
**10.0×** |
| `TrulyWide` | 876 ns | **860 ns** |
**1.02×** |
## Comparison with Short-Burst Measurement
To validate these numbers aren't an artifact of the larger batch, here are
the same cases run in "short-burst" mode (2000 iterations of 1 div each, ~30 µs
total per case):
| Case | Short-burst speedup | 6-second speedup |
|--------------------------|--------------------:|-----------------:|
| SingleLimb Div | 110× | **155×** |
| TwoLimbKnuth Div | 7.8× | **10.1×** |
| BothFit128 Div | 2.4× | **2.34×** |
| TrulyWide Div | 1.05× | **1.03×** |
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