85 lines
1.9 KiB
Rust
85 lines
1.9 KiB
Rust
use std::f64::consts::{E, PI};
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/// Calculate the value of a factorial iteratively
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///
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/// Can calculate up to 34! using native unsigned 128 bit integers.
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///
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/// Example:
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/// ```rust
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/// use rusty_fib_facts::factorial;
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///
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/// let valid = factorial(3); // Some(6)
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/// # assert_eq!(6, valid.unwrap());
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///
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/// let invalid = factorial(35); // None
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/// # assert!(invalid.is_none());
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/// ```
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#[inline]
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pub fn it_factorial(n: usize) -> Option<u128> {
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let mut total: u128 = 1;
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if matches!(n, 0 | 1) {
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Some(1u128)
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} else {
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for x in 1..=n {
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total = total.checked_mul(x as u128)?;
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}
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Some(total)
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}
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}
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/// Calculate the value of a factorial recursively
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///
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/// Can calculate up to 34! using native unsigned 128 bit integers.
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///
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/// Example:
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/// ```rust
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/// use rusty_fib_facts::factorial;
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///
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/// let valid = factorial(3); // Some(6)
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/// # assert_eq!(6, valid.unwrap());
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///
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/// let invalid = factorial(35); // None
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/// # assert!(invalid.is_none());
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/// ```
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#[inline]
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pub fn factorial(n: usize) -> Option<u128> {
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if matches!(n, 0 | 1) {
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Some(1u128)
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} else {
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let prev = factorial(n - 1)?;
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(n as u128).checked_mul(prev)
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}
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}
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/// Approximates a factorial using Stirling's approximation
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///
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/// Based on https://en.wikipedia.org/wiki/Stirling's_approximation
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///
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/// Can approximate up to ~ 170.624!
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///
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/// Example:
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/// ```rust
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/// use rusty_fib_facts::approx_factorial;
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///
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/// let valid = approx_factorial(170.6); // Some(..)
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/// # assert!(valid.is_some());
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///
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/// let invalid = approx_factorial(171.0); // None
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/// # assert!(invalid.is_none());
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/// ```
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#[inline]
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pub fn approx_factorial(n: f64) -> Option<f64> {
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let power = (n / E).powf(n);
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let root = (PI * 2.0 * n).sqrt();
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let res = power * root;
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if res >= std::f64::MIN && res <= std::f64::MAX {
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Some(res)
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} else {
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None
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}
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} |