```1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
```
``````use num::rational::Ratio;

/// Expand a float to a continued fraction expansion
///
/// # Arguments
///
/// * `n`:  The float to expand
/// * `min`:  Numbers less than this value are treated as zero
///
/// returns: [usize; N] where N is the number of terms in the expansion
///
/// # Examples
///
/// ```
/// # use rationalize::continued_fraction_expansion;
/// let cfe = continued_fraction_expansion::<10>(std::f64::consts::PI, 1e-10);
/// assert_eq!(cfe, [3, 7, 15, 1, 292, 1, 1, 1, 2, 1]);
/// ```
pub fn continued_fraction_expansion<const N: usize>(n: f64, min: f64) -> [usize; N] {
let mut out = [0; N];
let mut n = n;
for i in 0..N {
let integer = n.floor() as usize;
out[i] = integer;
n -= integer as f64;
if n <= min {
break;
}
n = 1.0 / n;
}
out
}

/// Convert a float to a rational number
///
/// # Arguments
///
/// * `n`:  The float to convert
/// * `min`:  Numbers less than this value are treated as zero
///
/// returns: Ratio<usize>
///
/// # Examples
///
/// ```
/// use num::rational::Ratio;
/// use rationalize::float2ratio;
/// let cfe = float2ratio::<4>(std::f64::consts::PI, 1e-10);
/// assert_eq!(cfe, Ratio::new(355, 113));
/// ```
pub fn float2ratio<const N: usize>(n: f64, min: f64) -> Ratio<isize> {
match n.is_sign_negative() {
true => {
let cfe = continued_fraction_expansion::<N>(-n, min);
let (numer, denom) = build_ratio(&cfe).into();
-Ratio::new(numer as isize, denom as isize)
}
false => {
let cfe = continued_fraction_expansion::<N>(n, min);
let (numer, denom) = build_ratio(&cfe).into();
Ratio::new(numer as isize, denom as isize)
}
}
}

// build ratio from continued fraction expansion
pub fn build_ratio(cfe: &[usize]) -> Ratio<usize> {
let seq = trim_tail_zeros(cfe);
let mut out = Ratio::new(seq[seq.len() - 1], 1);
for i in (0..seq.len() - 1).rev() {
out = Ratio::new(seq[i], 1) + out.recip();
}
out
}

pub fn trim_tail_zeros(cfe: &[usize]) -> &[usize] {
let mut i = cfe.len() - 1;
while i > 0 && cfe[i] == 0 {
i -= 1;
}
&cfe[0..=i]
}
``````