4.4 MILLIONx
Faster than mpmath. EXACT results.
NumPy gives WRONG ANSWERS on Hilbert matrices. VLA gives CORRECT ones.
4.4M
Speedup vs mpmath
4
NumPy Wrong Signs
0
VLA Wrong Signs
v6.3.6
Latest Release
VLA vs mpmath Speedup
Click any bar for details. mpmath is the gold standard for exact arithmetic.
mpmath is NEVER reproducible
We tested mpmath at 15, 50, 100, and 500 decimal precision. Every single run produced different results. VLA produces identical checksums every time.
Benchmarked on Tesla T4 (Kaggle), v6.3.6, March 2026
NumPy Gets WRONG Answers
Hilbert matrices are a classic ill-conditioned test. The determinant is ALWAYS positive. NumPy gives wrong signs at n≥14.
| n | NumPy det(H) | NumPy Sign | VLA Sign | Correct? |
|---|---|---|---|---|
| 10 | 2.16e-53 | + | + | |
| 12 | 2.72e-78 | + | + | |
| 14 | -3.44e-106 | - | + | |
| 15 | -2.43e-122 | - | + | |
| 16 | -4.93e-135 | - | + | |
| 18 | 3.84e-164 | + | + | |
| 20 | -2.23e-194 | - | + |
4
NumPy wrong signs
n = 14, 15, 16, 20
0
VLA wrong signs
All positive, as mathematically required
For quantum simulation, financial modeling, and scientific computing: wrong signs can be catastrophic.
Cross-GPU Reproducibility
Same checksum on completely different architectures. This is unprecedented.
Matrix Multiply Checksums (SHA-256)
32x32 Matrix
ca242dbb106174d4a2f637d77e2d8cf2fd4b9c57c10139e76475fdafed5a3622
64x64 Matrix
f5eac2fd06b2b14bcb26cac85a9ef688fdfa78a088a9a916eedf47ece344eae7
128x128 Matrix
d8e7492022a1a18b9101e71f93a21f7bf5f1ea22c0b785efcf3e48879361d83c
BIT-IDENTICAL ACROSS GPUs
RTX 4070 (sm_89) and Tesla T4 (sm_75) produce identical results
100%
Reproducible
2
GPU architectures verified
0
Bit differences
Exact Linear Algebra
New in v6.3: Exact determinant, inverse, solve, rank, null space for ANY matrix size.
Exact Solve
0
Residual
A @ x = b exactly
Exact Inverse
I
A @ inv(A)
True identity matrix
Exact Null Space
0
A @ v
True null vectors
Quantum simulation requires unitarity. VLA guarantees U @ U† = I EXACTLY.
Real-World Impact
Quantum Computing
1000+ Gates
Unitarity preserved perfectly
Financial Transactions
$881,143,573.77
1 million transactions summed
Scientific Computing
Hilbert n=20
Classic ill-conditioned problem
AI/ML Training
Gradient Sums
Large batch accumulation
See The Proof
All benchmarks are reproducible. Verify on Kaggle or discuss your use case.