qfall-math 0.1.1

// Copyright © 2023 Marvin Beckmann
//
// 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/>.

//! Implementations to approximate the exponential function using a [`PolyOverQ`] polynomial.

use crate::rational::PolyOverQ;
use flint_sys::fmpq_poly::fmpq_poly_exp_series;
use std::str::FromStr;

impl PolyOverQ {
    /// Creates the Taylor approximation as a polynomial with the provided length.
    ///
    /// Parameters:
    /// - `length`: the length of the taylor series approximation of the exponential function
    ///
    /// Returns the Taylor approximation of the exponential function.
    ///
    /// # Examples
    /// ```compile_fail
    /// use qfall_math::rational::PolyOverQ;
    ///
    /// // sum_{k=0}^{length-1} x^k/k!
    /// let taylor_approximation_exponential_function = PolyOverQ::exp_function_taylor(1000_u32);
    /// ```
    pub(crate) fn exp_function_taylor(length: impl Into<u32>) -> Self {
        let mut out = Self::default();
        let x_poly = PolyOverQ::from_str("2  0 1").unwrap();

        unsafe { fmpq_poly_exp_series(&mut out.poly, &x_poly.poly, length.into().into()) };
        out
    }
}

#[cfg(test)]
mod test_exp_series {
    use crate::{
        rational::{PolyOverQ, Q},
        traits::GetCoefficient,
    };

    /// Ensures that the coefficients of the Taylor polynomial for the
    /// exponential function are set correctly.
    #[test]
    fn coefficient_set_correctly() {
        let length: u32 = 1000;
        let poly = PolyOverQ::exp_function_taylor(length);
        let mut fac_value = Q::ONE;
        assert_eq!(fac_value, poly.get_coeff(0).unwrap());
        for i in 1..length {
            fac_value *= Q::from((1, i));
            assert_eq!(fac_value, poly.get_coeff(i).unwrap());
        }
    }

    /// Ensures that the length of the Taylor polynomial for the exponential function
    /// is correct
    #[test]
    fn correct_len() {
        let length: u32 = 170;
        let poly = PolyOverQ::exp_function_taylor(length);
        assert_eq!(length as i64, poly.poly.length);
    }
}