mathru/elementary/
exponential.rs

1use crate::algebra::abstr::{Complex, Real, Sign};
2use std::{f32, f64};
3
4/// Exponential function and its inverse
5///
6///<https://en.wikipedia.org/wiki/Exponential_function>
7pub trait Exponential {
8    /// Euler's number
9    fn e() -> Self;
10
11    ///Exponential function
12    fn exp(self) -> Self;
13
14    /// Natural logarithm function
15    fn ln(self) -> Self;
16}
17
18macro_rules! exponential_impl {
19    ($t:ty, $e: expr) => {
20        impl Exponential for $t {
21            fn e() -> Self {
22                $e
23            }
24
25            ///Exponential function
26            fn exp(self) -> Self {
27                self.exp()
28            }
29
30            ///Logarithm function
31            fn ln(self) -> Self {
32                self.ln()
33            }
34        }
35    };
36}
37
38exponential_impl!(f32, f32::consts::E);
39exponential_impl!(f64, f64::consts::E);
40
41impl<T> Exponential for Complex<T>
42where
43    T: Real,
44{
45    /// Returns the euler number represented as a complex number
46    fn e() -> Self {
47        Complex {
48            re: T::e(),
49            im: T::zero(),
50        }
51    }
52
53    ///Exponential function
54    ///
55    /// # Example
56    ///
57    /// ```
58    /// use mathru::{elementary::Exponential};
59    /// use mathru::algebra::abstr::Complex;
60    ///
61    /// let z: Complex<f64> = Complex::new(1.0, 2.0);
62    /// let a: Complex<f64> = z.exp();
63    /// ```
64    fn exp(self) -> Self {
65        let k: T = self.re.exp();
66        Complex {
67            re: k * self.im.cos(),
68            im: k * self.im.sin(),
69        }
70    }
71
72    ///Logiarithm function
73    ///
74    /// # Example
75    ///
76    /// ```
77    /// use mathru::{elementary::Exponential};
78    /// use mathru::algebra::abstr::Complex;
79    ///
80    /// let a: Complex<f64> = Complex::new(1.0_f64, 2.0_f64);
81    /// let refer: Complex<f64> = Complex::new(5.0_f64.powf(0.5_f64).ln(), 2.0_f64.atan());
82    ///
83    /// assert_eq!(refer, a.ln());
84    /// ```
85    fn ln(self) -> Self {
86        Complex {
87            re: self.abs().re.ln(),
88            im: self.arg().re,
89        }
90    }
91}
mathru/elementary/exponential.rs

mathru/elementary/
exponential.rs
