qfall_math/integer/z/arithmetic/
exp.rs

1// Copyright © 2023 Marvin Beckmann
2//
3// This file is part of qFALL-math.
4//
5// qFALL-math is free software: you can redistribute it and/or modify it under
6// the terms of the Mozilla Public License Version 2.0 as published by the
7// Mozilla Foundation. See <https://mozilla.org/en-US/MPL/2.0/>.
8
9//! Implementations to call the exponential function on a [`Z`] integer.
10
11use crate::{
12    integer::Z,
13    rational::{PolyOverQ, Q},
14    traits::Evaluate,
15};
16
17impl Z {
18    /// Computes `e^self` using taylor series approximation of the exponential function.
19    ///
20    /// Parameters:
21    /// - `length_taylor_polynomial`: the length of the taylor series
22    ///   approximation of the exponential function
23    ///
24    /// Returns `e^self`.
25    ///
26    /// # Examples
27    /// ```
28    /// use qfall_math::integer::Z;
29    ///
30    /// // sum_{k=0}^999 17^k/k!
31    /// let evaluation = Z::from(17).exp_taylor(1000_u32);
32    /// ```
33    pub fn exp_taylor(&self, length_taylor_polynomial: impl Into<u32>) -> Q {
34        let exp_taylor_series = PolyOverQ::exp_function_taylor(length_taylor_polynomial);
35        exp_taylor_series.evaluate(self)
36    }
37}
38
39#[cfg(test)]
40mod test_exp {
41    use crate::{integer::Z, rational::Q};
42
43    /// Ensure that `0` is returned if the length `0` is provided
44    #[test]
45    fn zero_length() {
46        let z = Z::from(17);
47
48        assert_eq!(Q::default(), z.exp_taylor(0_u32));
49    }
50
51    /// Test correct evaluation for some explicit values
52    #[test]
53    fn ten_length_value() {
54        assert_eq!(Q::from((98641, 36288)), Z::ONE.exp_taylor(10_u32));
55        assert_eq!(Q::from((22471, 1120)), Z::from(3).exp_taylor(10_u32));
56        assert_eq!(Q::from((83, 2240)), Z::from(-3).exp_taylor(10_u32));
57    }
58}
qfall_math/integer/z/arithmetic/exp.rs

qfall_math/integer/z/arithmetic/
exp.rs
