Performance & Benchmarks
simd-f128 is designed to out-perform software-emulated __float128 routines by utilizing Double-Double arithmetic packed into hardware vector registers.
Accuracy and ULP Testing
Beyond speed, the library maintains strict correctness verified against the GNU MPFR library (Multiple Precision Floating-Point Reliable). Integration tests (test_mpfr_accuracy.cpp) assert that the unit in the last place (ULP) drift remains within acceptable boundaries (~4-16 ULP) for all transcendental functions (sin, cos, exp, log, sqrt) across edge cases and subnormals.
Benchmark Methodology
All C/C++ benchmarks execute via Google Benchmark. Latency measurements test isolated operations through 10,000,000 iterations.
Flags used: -O3 -march=native -ffast-math.
Hardware: 12-core x86_64, 3.2GHz, AVX2 enabled.
Latency Comparison
| Data Type | Add (ms) | Mul (ms) | Div (ms) | Relative Multiplication Speed |
|---|---|---|---|---|
double (64-bit) |
8.80 | 8.07 | 33.06 | 1.00x (Baseline) |
long double (x87) |
16.66 | 17.28 | 38.58 | 0.47x |
__float128 (GCC) |
152.31 | 189.81 | 276.00 | 0.04x |
| simd-f128 (SIMD) | 73.60 | 56.15 | 159.70 | 0.14x (3.38x faster than GCC) |
Advanced Math Functions (Latency)
This chart illustrates the nanosecond latency for extended mathematical functions (simd_f128_sin, simd_f128_exp, etc.) processing 128-bit precision floats.
WebAssembly Performance
WebAssembly execution is split into two variants. When running in a modern V8 environment (Node.js/Chrome) with WASM-SIMD128 enabled, the library maps Double-Double operations to native 128-bit WASM instructions (v128).
| Environment | 1M Multiplications | Notes |
|---|---|---|
| WASM-SIMD128 | ~310 ms | Standard behavior in modern V8 contexts. |
| WASM-Scalar | ~481 ms | Fallback for legacy environments lacking SIMD. |
Reproducibility
To run the local C benchmark suite and verify the performance on target hardware:
mkdir build_bench && cd build_bench
cmake .. -DCMAKE_BUILD_TYPE=Release -DSIMD_F128_BUILD_BENCHMARKS=ON
cmake --build .
./benchmarks/bench_compare
./benchmarks/bench_arithmetic