A fixed-point arithmetic library providing constrained fixed-point operations for Stwo-based circuits. The library implements fixed-point arithmetic using M31 field elements with configurable decimal precision.

• Type-level scale parameter using Rust's const generics
• Fixed-point operations (addition, subtraction, multiplication, reciprocal, square root)
• Circuit constraints for all operations
• Zero memory overhead for scale information

// Using 15 bits of precision
let a = Fixed::<15>::from_f64(3.14);
let b = Fixed::<15>::from_f64(2.0);

// Basic arithmetic operations
let sum = a + b;
let diff = a - b;
let (prod, rem) = a * b;

// Convert between scales
let converted = a.convert_to::<8>();

To use fixed-point operations in your Stwo Prover circuit, use the constraint evaluation functions:

use numerair::eval::EvalFixedPoint;

// In your circuit component's evaluate function:
fn evaluate<E: EvalAtRow>(&self, mut eval: E) -> E {
    let lhs = eval.next_trace_mask();
    let rhs = eval.next_trace_mask();
    let rem = eval.next_trace_mask();
    let res = eval.next_trace_mask();
    
    // Get scale factor for the specific scale you're using
    let scale_factor = E::F::from(M31::from_u32_unchecked(1 << 15)); // For Fixed<15>

    // Constrain mul using EvalFixedPoint trait
    eval.eval_fixed_mul(lhs, rhs, scale_factor, res, rem);

    eval
}

The fixed-point representation uses a const generic parameter to determine the number of bits used for the fractional part:

• SCALE: Type-level constant that defines the number of bits for decimal precision
• SCALE_FACTOR: The value 2^SCALE (automatically calculated), represents 1.0 in fixed-point
• HALF_SCALE_FACTOR: The value 2^(SCALE-1) (automatically calculated), used for rounding

A value x in floating point is represented as floor(x * 2^SCALE) in fixed-point.

Contributions are welcome! Please submit pull requests with:

• New arithmetic operations
• Improved constraints
• Additional tests
• Documentation improvements
• Performance optimizations

raphaelDkhn 💻

Mario Karagiorgas 💻

Mahmoud Mohajer 💻