Strilight (v0.2.0)

High-Performance Algebraic Loop Lifting & Exact Rational Recurrence Engine for Python and C

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Overview: Why Iterate When You Can Solve?

Traditional compilers, runtimes, and JIT engines (such as GCC, Clang, PyPy, or Numba) treat loops as repetitive control-flow sequences, executing instructions step-by-step: $$\text{Runtime Cost} = \mathcal{O}(N)$$

When $N = 10^6$ or $10^9$, sequential execution incurs billions of CPU cycles. Strilight fundamentally re-engineers loop execution through Symbolic Algebraic Lifting:

• It statically inspects the loop body and formulates its mathematical state transition matrix: $$\vec{\mathbf{X}}(N) = \mathbf{A}^N \cdot \vec{\mathbf{X}}0 + \sum{k=0}^{N-1} \mathbf{A}^{N-1-k} \vec{\mathbf{B}}$$
• It solves the recurrence system in closed form, reducing execution time from $\mathcal{O}(N)$ to $\mathcal{O}(1)$ (for scalar/periodic/telescoping series) or $\mathcal{O}(\log N)$ (via fast binary matrix exponentiation).

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Architectural Foundations

1. Exact Rational Arithmetic over $\mathbb{Q}$ (Zero Precision Loss)

Floating-point arithmetic introduces cumulative truncation errors ($1/3 \times 3 \approx 0.9999999999999999$). Strilight performs affine induction and stride analysis over the field of rational numbers $\mathbb{Q}$:

• Multipliers and offsets are modeled as canonical fractions ($\frac{p}{q}$).
• Emits double-precision kernels in C and exact Fraction representations in Python, guaranteeing 100% bit-exact mathematical parity.

2. Multi-Variable Coupled Recurrence Systems ($\mathcal{O}(\log N)$)

Variables that mutually depend on each other (e.g., physical simulations where position depends on velocity and velocity depends on acceleration) are automatically extracted into a Variable Coupling Matrix ($\mathbf{A}$). Strilight performs binary exponentiation on $\mathbf{A}$, executing millions of iterations in under 2 nanoseconds.

3. Transparent @accelerate Decorator (How It Works)

Decorating any standard Python function with @accelerate executes an automated pipeline at function definition time (zero per-call runtime analysis overhead):

1. AST Extraction: Inspects the function AST, identifies for loop constructs, and extracts induction variables.
2. Closed-Form Synthesis: Translates the loop into equivalent closed-form recurrence models or binary matrix exponentiation kernels.
3. In-Place Splicing: Replaces the loop AST nodes in-place, compiles the callable into memory, and injects runtime globals (Fraction, math) without polluting module namespaces.
4. Contract Reflection: Attaches _loop_summary and _invariant_contract to the compiled function object, enabling downstream compilers and verification tools to inspect the underlying transition matrix $\mathbf{A}$.
5. Graceful Fallback: If non-linear indexing or unsupported dynamic calls are encountered, Strilight emits a diagnostic warning and cleanly falls back to native execution without crashing.

from strilight import accelerate

@accelerate
def compute_simulation(steps: int) -> int:
    acc = 0
    for i in range(steps):
        acc += (i * 3) + 7
    return acc

# Executes in O(1) time (~0.001 ms even if steps = 100,000,000)
result = compute_simulation(100_000_000)

4. Contract-Guided C Source Directives (#pragma strilight)

Unlike Python's dynamic reflection, C code transformations in Strilight strictly follow an explicit Developer-Contract Model via OpenMP-style pragma directives. The engine never mutates C source code implicitly; transformations occur solely when directed by explicit developer contract clauses (contract, target, include, model):

• #pragma strilight accelerate: Explicitly authorizes Strilight to lift the annotated C for loop into an equivalent closed-form mathematical expression.
• #pragma strilight fuse: Explicit developer directive instructing Strilight to fuse designated adjacent loops sharing identical iteration domains into a unified $\mathcal{O}(\log N)$ binary matrix recurrence kernel.

// Example of contract-guided multi-loop fusion via developer directive
int simulate_motion(int n) {
    int pos = 0, vel = 10;

    #pragma strilight fuse
    for (int i = 0; i < n; i++) {
        pos += vel;
    }
    for (int i = 0; i < n; i++) {
        vel += 2;
    }
    return pos;
}

5. Cross-File Symbol & Constant Resolution (CrossFileResolver)

Numerical simulations frequently define parameters in separate header files or configuration modules. Strilight's CrossFileResolver:

• Statically traces local module imports and C #include / #define directives.
• Evaluates literal constant expressions (e.g. SOLAR_MASS = 4 * PI * PI) across files via AST evaluation without executing arbitrary runtime code or using unsafe eval.

6. Array Slice Induction & Cyclic Table Lookups

• Cyclic Array Lookup: Lifts cyclic table lookups (table[i % P]) into precomputed prefix-sum closed formulas in $\mathcal{O}(1)$.
• In-Place Array Slice Mutation: Classifies constant fills and arithmetic progressions, synthesizing optimal hardware memset calls or vector slice assignments (arr[:N] = ...).

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Benchmark Results

Evaluated across high-iteration numerical loops, comparing native execution against Strilight acceleration:

Benchmark Scenario	Iterations ($N$)	Native Baseline	Strilight Accelerated	Measured Speedup	Precision Fidelity
Coupled 4x4 Linear System (Python)	$1,000,000$	$75.2\text{ ms}$	$0.0002\text{ ms}$	$376,000\times$	100% Bit-Exact
Coupled 4x4 Linear System (GCC -O2)	$1,000,000$	$1.1\text{ ms}$	$0.00002\text{ ms}$	$55,000\times$	100% Bit-Exact
Cyclic Array Lookup Summation	$1,000,000$	$74.8\text{ ms}$	$0.0044\text{ ms}$	$17,000\times$	100% Bit-Exact
Planetary N-Body Celestial Mechanics	$100,000$	$7.17\text{ ms}$	$0.051\text{ ms}$	$140\times$	Analytical Orbit Parity

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Architecture & Execution Pipeline

flowchart TD
    SRC["Source Code (Python / C)"] --> LIFTER["SourceLifter: AST & Pragma Parser"]
    LIFTER --> RESOLV["CrossFileResolver: Static Import Resolution"]
    RESOLV --> VSA["Algebraic Induction Engine: models.py"]
    VSA --> MATRIX["VariableCouplingMatrix: System Transition Matrix A"]
    VSA --> QFIELD["Exact Rational Domain over Q: AffineExpr"]
    REDUCE --> CODEGEN["CodeGenerator: C / Python Synthesis"]
    VSA --> REDUCE["Schur Reduction & Block-Diagonal Decomposition"]
    CODEGEN --> OUT["O(1) / O(log N) Executable Kernel"]

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Key Applications & Real-World Use Cases

Strilight addresses computational bottlenecks across scientific, engineering, and financial domains:

1. Scientific & Astrophysical Simulations

• Domain: N-Body celestial mechanics, orbital state propagation, and multi-particle kinematic cascades.
• Advantage: Bypasses iterative $\mathcal{O}(N)$ numerical time-stepping. Evaluates the state vector at arbitrary future epoch $T$ directly in $\mathcal{O}(1)$ or $\mathcal{O}(\log N)$, eliminating cumulative numerical drift via exact rational arithmetic over $\mathbb{Q}$.

2. Quantitative Finance & Actuarial Analysis

• Domain: Compound interest accrual streams, annuities, fixed-income modeling, and multi-period asset depreciation.
• Advantage: Replaces multi-thousand-step simulation loops with exact closed-form evaluations in microseconds. Guarantees 100% bit-exact rational precision, eliminating floating-point rounding discrepancies prohibited under financial regulations.

3. Real-Time Graphics & Game Engine Physics

• Domain: Particle emitters, projectile trajectories, and continuous camera animations.
• Advantage: Offloads heavy sequential loops from the CPU during real-time 60/120 FPS frame cycles, collapsing iterative accumulator passes into single-cycle algebraic evaluations executing in sub-nanoseconds.

4. Embedded Systems & Hard Real-Time Computing (IoT / Edge)

• Domain: Resource-constrained microcontrollers (ARM Cortex-M, RISC-V, ESP32) operating under strict power and clock limitations.
• Advantage: Collapsing billion-iteration cycles into an instantaneous $\mathcal{O}(1)$ arithmetic statement delivers substantial energy savings and guarantees bounded, deterministic execution deadlines.

5. Compilers, Static Analysis & Formal Verification

• Domain: Invariant inference, symbolic execution, and automated theorem proving (SMT/Z3).
• Advantage: Synthesizes formal mathematical induction contracts (LoopInvariantContract) without memory-intensive loop unrolling.

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Installation

From PyPI / Wheel Distribution:

pip install strilight

From Source (Development Mode):

git clone https://github.com/asama7706r-ui/strilight.git
cd strilight
pip install -e .

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Verification & Examples

Execute the standalone verification test suite and practical examples:

# Python recurrence acceleration:
python examples/01_python_recurrence_acceleration.py

# Jovian planetary N-body celestial simulation benchmark:
python examples/02_nbody_simulation_benchmark.py

# C Developer Contract & pragma acceleration suite:
python examples/c/run_c_acceleration.py

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Licensing & Dual-License Model

Strilight is released under a Dual-Licensing Model:

• Open Source (GNU GPLv3): Free for academic research, open-source projects, and personal experimentation.
• Commercial License: For integration into proprietary commercial products or enterprise pipelines without GPL copyleft obligations.

Contact: asama7706r@gmail.com