qfall-math 0.1.1

// Copyright © 2023 Niklas Siemer
//
// This file is part of qFALL-math.
//
// qFALL-math is free software: you can redistribute it and/or modify it under
// the terms of the Mozilla Public License Version 2.0 as published by the
// Mozilla Foundation. See <https://mozilla.org/en-US/MPL/2.0/>.

//! This module contains sampling algorithms for uniform distributions.

use crate::{
    error::MathError,
    integer::{MatPolyOverZ, PolyOverZ, Z},
    traits::{MatrixDimensions, MatrixSetEntry},
    utils::index::evaluate_index,
};
use std::fmt::Display;

impl MatPolyOverZ {
    /// Outputs a [`MatPolyOverZ`] instance with polynomials as entries,
    /// whose coefficients were chosen uniform at random in `[lower_bound, upper_bound)`.
    ///
    /// The internally used uniform at random chosen bytes are generated
    /// by [`ThreadRng`](rand::rngs::ThreadRng), which uses ChaCha12 and
    /// is considered cryptographically secure.
    ///
    /// Parameters:
    /// - `num_rows`: specifies the number of rows the new matrix should have
    /// - `num_cols`: specifies the number of columns the new matrix should have
    /// - `max_degree`: specifies the maximum length of all polynomials in the matrix,
    ///   i.e. the maximum number of coefficients any polynomial in the matrix can have
    /// - `lower_bound`: specifies the included lower bound of the
    ///   interval over which is sampled
    /// - `upper_bound`: specifies the excluded upper bound of the
    ///   interval over which is sampled
    ///
    /// Returns a new [`MatPolyOverZ`] instance with polynomials as entries,
    /// whose coefficients were chosen uniformly at random in
    /// `[lower_bound, upper_bound)` or a [`MathError`]
    /// if the interval was chosen too small or the `max_degree` of the polynomials
    /// is negative or too large to fit into [`i64`].
    ///
    /// # Examples
    /// ```
    /// use qfall_math::integer::MatPolyOverZ;
    ///
    /// let matrix = MatPolyOverZ::sample_uniform(3, 3, 5, 17, 26).unwrap();
    /// ```
    ///
    /// # Errors and Failures
    /// - Returns a [`MathError`] of type [`InvalidInterval`](MathError::InvalidInterval)
    ///   if the given `upper_bound` isn't at least larger than `lower_bound`.
    /// - Returns a [`MathError`] of type [`OutOfBounds`](MathError::OutOfBounds) if
    ///   the `max_degree` is negative or it does not fit into an [`i64`].
    ///
    /// # Panics ...
    /// - if the provided number of rows and columns are not suited to create a matrix.
    ///   For further information see [`MatPolyOverZ::new`].
    pub fn sample_uniform(
        num_rows: impl TryInto<i64> + Display,
        num_cols: impl TryInto<i64> + Display,
        max_degree: impl TryInto<i64> + Display,
        lower_bound: impl Into<Z>,
        upper_bound: impl Into<Z>,
    ) -> Result<Self, MathError> {
        let lower_bound: Z = lower_bound.into();
        let upper_bound: Z = upper_bound.into();
        let max_degree = evaluate_index(max_degree)?;
        let mut matrix = MatPolyOverZ::new(num_rows, num_cols);

        for row in 0..matrix.get_num_rows() {
            for col in 0..matrix.get_num_columns() {
                let sample = PolyOverZ::sample_uniform(max_degree, &lower_bound, &upper_bound)?;
                unsafe { matrix.set_entry_unchecked(row, col, sample) };
            }
        }

        Ok(matrix)
    }
}

#[cfg(test)]
mod test_sample_uniform {
    use crate::traits::{GetCoefficient, MatrixDimensions, MatrixGetEntry};
    use crate::{
        integer::{MatPolyOverZ, Z},
        integer_mod_q::Modulus,
    };

    /// Checks whether the boundaries of the interval are kept for small intervals.
    #[test]
    fn boundaries_kept_small() {
        let lower_bound = Z::from(17);
        let upper_bound = Z::from(32);
        for _ in 0..32 {
            let matrix = MatPolyOverZ::sample_uniform(1, 1, 0, &lower_bound, &upper_bound).unwrap();
            let sample = matrix.get_entry(0, 0).unwrap();
            let coeff = sample.get_coeff(0).unwrap();

            assert!(lower_bound <= coeff);
            assert!(coeff < upper_bound);
        }
    }

    /// Checks whether the boundaries of the interval are kept for large intervals.
    #[test]
    fn boundaries_kept_large() {
        let lower_bound = Z::from(i64::MIN) - Z::from(u64::MAX);
        let upper_bound = Z::from(i64::MIN);
        for _ in 0..256 {
            let matrix = MatPolyOverZ::sample_uniform(1, 1, 0, &lower_bound, &upper_bound).unwrap();
            let sample = matrix.get_entry(0, 0).unwrap();
            let coeff = sample.get_coeff(0).unwrap();

            assert!(lower_bound <= coeff);
            assert!(coeff < upper_bound);
        }
    }

    /// Checks whether the number of coefficients is correct.
    #[test]
    fn nr_coeffs() {
        let degrees = [1, 3, 7, 15, 32, 120];
        for degree in degrees {
            let matrix = MatPolyOverZ::sample_uniform(1, 1, degree, 1, 15).unwrap();
            let poly = matrix.get_entry(0, 0).unwrap();

            assert_eq!(degree, poly.get_degree());
        }
    }

    /// Checks whether matrices with at least one dimension chosen smaller than `1`
    /// or too large for an [`i64`] results in an error.
    #[should_panic]
    #[test]
    fn false_size() {
        let lower_bound = Z::from(-15);
        let upper_bound = Z::from(15);

        let _ = MatPolyOverZ::sample_uniform(0, 3, 1, &lower_bound, &upper_bound);
    }

    /// Checks whether providing an invalid interval results in an error.
    #[test]
    fn invalid_interval() {
        let lb_0 = Z::from(i64::MIN);
        let lb_1 = Z::from(i64::MIN);
        let lb_2 = Z::ZERO;
        let upper_bound = Z::from(i64::MIN);

        let mat_0 = MatPolyOverZ::sample_uniform(3, 3, 0, &lb_0, &upper_bound);
        let mat_1 = MatPolyOverZ::sample_uniform(4, 1, 0, &lb_1, &upper_bound);
        let mat_2 = MatPolyOverZ::sample_uniform(1, 5, 0, &lb_2, &upper_bound);

        assert!(mat_0.is_err());
        assert!(mat_1.is_err());
        assert!(mat_2.is_err());
    }

    /// Checks whether providing a length smaller than `0` results in an error.
    #[test]
    fn invalid_max_degree() {
        let lower_bound = Z::from(0);
        let upper_bound = Z::from(15);

        let res_0 = MatPolyOverZ::sample_uniform(1, 1, -1, &lower_bound, &upper_bound);
        let res_1 = MatPolyOverZ::sample_uniform(1, 1, i64::MIN, &lower_bound, &upper_bound);

        assert!(res_0.is_err());
        assert!(res_1.is_err());
    }

    /// Checks whether `sample_uniform` is available for all types
    /// implementing [`Into<Z>`], i.e. u8, u16, u32, u64, i8, ...
    #[test]
    fn availability() {
        let modulus = Modulus::from(7);
        let z = Z::from(7);

        let _ = MatPolyOverZ::sample_uniform(1, 1, 0u8, 0u16, 7u8);
        let _ = MatPolyOverZ::sample_uniform(1, 1, 0u16, 0u32, 7u16);
        let _ = MatPolyOverZ::sample_uniform(1, 1, 0u32, 0u64, 7u32);
        let _ = MatPolyOverZ::sample_uniform(1, 1, 0u64, 0i8, 7u64);
        let _ = MatPolyOverZ::sample_uniform(1, 1, 0i8, 0i16, 7i8);
        let _ = MatPolyOverZ::sample_uniform(1, 1, 0i16, 0i32, 7i16);
        let _ = MatPolyOverZ::sample_uniform(1, 1, 0i32, 0i64, 7i32);
        let _ = MatPolyOverZ::sample_uniform(1, 1, 0i64, &Z::ZERO, 7i64);
        let _ = MatPolyOverZ::sample_uniform(1, 1, 0, 0u8, &modulus);
        let _ = MatPolyOverZ::sample_uniform(1, 1, Z::ZERO, 0, &z);
    }

    /// Checks whether the size of uniformly random sampled matrices
    /// fits the specified dimensions.
    #[test]
    fn matrix_size() {
        let lower_bound = Z::from(-15);
        let upper_bound = Z::from(15);

        let mat_0 = MatPolyOverZ::sample_uniform(3, 3, 0, &lower_bound, &upper_bound).unwrap();
        let mat_1 = MatPolyOverZ::sample_uniform(4, 1, 0, &lower_bound, &upper_bound).unwrap();
        let mat_2 = MatPolyOverZ::sample_uniform(1, 5, 0, &lower_bound, &upper_bound).unwrap();
        let mat_3 = MatPolyOverZ::sample_uniform(15, 20, 0, &lower_bound, &upper_bound).unwrap();

        assert_eq!(3, mat_0.get_num_rows());
        assert_eq!(3, mat_0.get_num_columns());
        assert_eq!(4, mat_1.get_num_rows());
        assert_eq!(1, mat_1.get_num_columns());
        assert_eq!(1, mat_2.get_num_rows());
        assert_eq!(5, mat_2.get_num_columns());
        assert_eq!(15, mat_3.get_num_rows());
        assert_eq!(20, mat_3.get_num_columns());
    }
}