hybrid_phi

High-accuracy numerical approximation using a φ-based hybrid method.

This Rust library provides a fast, compact and reversible approximation for real numbers using a precomputed exponential φ-basis and a smooth linear correction.

✨ Features

• ⚡ Machine-level precision (~1e-14)
• 📐 φ-basis from exponential series (precomputed φ[1..32])
• 🧠 Smooth correction preserves reversibility
• 🔢 1 multiplication + 1 correction: ideal for embedded/AI/inference
• ✅ Zero allocation, pure f64

📦 Usage

Add to your Cargo.toml:

[dependencies]
hybrid_phi = "0.1.0"

🔧 Example (Library)

use hybrid_phi::hybrid_phi_approximate;

fn main() {
    let x = 123.456;
    let approx = hybrid_phi_approximate(x, 10);
    println!("Approximated value: {}", approx);
}

🚀 Example (CLI)

cargo run --example demo -- --n=32

Hybrid φ-approximation with N = 32

w                approx    recovered   approx_err    recon_err
-1000.000  -1000.000000 -1000.000000      0.000e0      0.000e0
-100.000    -100.000000  -100.000000    4.121e-13    4.121e-13
0.000          0.000000     0.000000      0.000e0      0.000e0
42.000        42.000000    42.000000      0.000e0      0.000e0
123.456      123.456000   123.456000      0.000e0      0.000e0
999.990      999.990000   999.990000      0.000e0      0.000e0

📚 Algorithm

We approximate:

w ≈ a · φ(N) · (1 - r + r / √2)

Where:

• φ(N) = ∑_{j=1}^N j · exp(1 / (2j))
• a = w / φ(N), r = w - aφ(N)

This approximation is reversible:

use hybrid_phi::{hybrid_phi_approximate, hybrid_phi_inverse};

let w = 123.456;
let approx = hybrid_phi_approximate(w, 10);
let recovered = hybrid_phi_inverse(approx, 10);
let error = (w - recovered).abs();

🔢 φ(N) Lookup Table (excerpt)

🔐 License

🚫 Commercial use requires a separate license.
Please contact info@paxintrade.com for licensing options.

© 2025 Idan Kaminer — author of the method and implementation.