406 lines
10 KiB
Rust
406 lines
10 KiB
Rust
//! # Rusty Fib Facts
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//!
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//! Implementations of common math algorithms to benchmark
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#![forbid(unsafe_code)]
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#![no_std]
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use core::cmp::{max, min};
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#[cfg(all(feature = "alloc", not(feature = "std")))]
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#[macro_use]
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extern crate alloc;
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#[cfg(feature = "std")]
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#[macro_use]
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extern crate std;
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#[cfg(feature = "std")]
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use core::f64::consts::{E, PI};
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/// Calculate a number in the fibonacci sequence,
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/// using recursion and a lookup table
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///
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/// Can calculate up to 186 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::mem_fibonacci;
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///
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/// let valid = mem_fibonacci(45); // Some(1134903170)
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/// # assert_eq!(1134903170, mem_fibonacci(45).unwrap());
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/// # assert!(valid.is_some());
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///
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/// let invalid = mem_fibonacci(187); // None
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/// # assert!(invalid.is_none());
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/// ```
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#[inline]
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pub fn mem_fibonacci(n: usize) -> Option<u128> {
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let mut table = [0u128; 187];
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table[0] = 0;
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table[1] = 1;
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table[2] = 1;
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/// Actual calculating function for `fibonacci`
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fn f(n: usize, table: &mut [u128]) -> Option<u128> {
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if n < 2 {
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// The first values are predefined.
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return Some(table[n]);
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}
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if n > 186 {
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return None;
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}
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match table[n] {
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// The lookup array starts out zeroed, so a zero
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// is a not yet calculated value
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0 => {
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let a = f(n - 1, table)?;
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let b = f(n - 2, table)?;
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table[n] = a + b;
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Some(table[n])
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}
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x => Some(x),
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}
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}
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f(n, &mut table)
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}
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/// Calculate a number in the fibonacci sequence,
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/// using naive recursion
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///
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/// REALLY SLOW
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///
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/// Can calculate up to 186 using native unsigned 128 bit integers.
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#[inline]
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pub fn rec_fibonacci(n: usize) -> Option<u128> {
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if matches!(n, 0 | 1) {
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Some(n as u128)
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} else {
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let a = rec_fibonacci(n - 1)?;
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let b = rec_fibonacci(n - 2)?;
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a.checked_add(b)
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}
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}
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/// Calculate a number in the fibonacci sequence,
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///
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/// Can calculate up to 186 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::fibonacci;
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///
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/// let valid = fibonacci(45); // Some(1134903170)
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/// # assert_eq!(1134903170, fibonacci(45).unwrap());
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/// # assert!(valid.is_some());
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///
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/// let invalid = fibonacci(187); // None
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/// # assert!(invalid.is_none());
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/// ```
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#[inline]
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pub fn fibonacci(n: usize) -> Option<u128> {
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let mut a: u128 = 0;
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let mut b: u128 = 1;
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if matches!(n, 0 | 1) {
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Some(n as u128)
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} else {
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for _ in 0..n - 1 {
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let c: u128 = a.checked_add(b)?;
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a = b;
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b = c;
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}
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Some(b)
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}
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}
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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 recrursively
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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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#[cfg(feature = "std")]
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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 >= core::f64::MIN && res <= core::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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}
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pub trait UnsignedGCD {
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/// Find the greatest common denominator of two numbers
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fn gcd(a: Self, b: Self) -> Self;
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/// Euclid gcd algorithm
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fn e_gcd(a: Self, b: Self) -> Self;
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/// Stein gcd algorithm
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fn stein_gcd(a: Self, b: Self) -> Self;
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/// Find the least common multiple of two numbers
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fn lcm(a: Self, b: Self) -> Self;
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}
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macro_rules! impl_unsigned {
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($($Type: ty),* ) => {
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$(
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impl UnsignedGCD for $Type {
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/// Implementation based on
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/// [Binary GCD algorithm](https://en.wikipedia.org/wiki/Binary_GCD_algorithm)
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fn gcd(a: $Type, b: $Type) -> $Type {
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if a == b {
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return a;
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} else if a == 0 {
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return b;
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} else if b == 0 {
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return a;
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}
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let a_even = a % 2 == 0;
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let b_even = b % 2 == 0;
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if a_even {
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if b_even {
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// Both a & b are even
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return Self::gcd(a >> 1, b >> 1) << 1;
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} else if !b_even {
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// b is odd
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return Self::gcd(a >> 1, b);
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}
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}
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// a is odd, b is even
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if (!a_even) && b_even {
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return Self::gcd(a, b >> 1);
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}
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if a > b {
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return Self::gcd((a - b) >> 1, b);
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}
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Self::gcd((b - a) >> 1, a)
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}
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fn e_gcd(x: $Type, y: $Type) -> $Type {
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let mut x = x;
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let mut y = y;
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while y != 0 {
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let t = y;
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y = x % y;
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x = t;
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}
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x
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}
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fn stein_gcd(a: Self, b: Self) -> Self {
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match ((a, b), (a & 1, b & 1)) {
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((x, y), _) if x == y => y,
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((0, x), _) | ((x, 0), _) => x,
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((x, y), (0, 1)) | ((y, x), (1, 0)) => Self::stein_gcd(x >> 1, y),
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((x, y), (0, 0)) => Self::stein_gcd(x >> 1, y >> 1) << 1,
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((x, y), (1, 1)) => {
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let (x, y) = (min(x, y), max(x, y));
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Self::stein_gcd((y - x) >> 1, x)
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}
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_ => unreachable!(),
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}
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}
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fn lcm(a: $Type, b: $Type) -> $Type {
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if (a == 0 && b == 0) {
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return 0;
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}
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a * b / Self::gcd(a, b)
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}
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}
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)*
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};
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}
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impl_unsigned!(u8, u16, u32, u64, u128, usize);
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#[cfg(test)]
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#[cfg(not(tarpaulin_include))]
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mod tests {
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use super::*;
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#[test]
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fn test_factorial() {
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for pair in [[1usize, 0], [1, 1], [2, 2], [6, 3]].iter() {
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assert_eq!(
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Some(pair[0] as u128),
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factorial(pair[1]),
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"{}! should be {}",
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pair[1],
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pair[0]
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);
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assert_eq!(
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Some(pair[0] as u128),
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it_factorial(pair[1]),
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"{}! should be {}",
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pair[1],
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pair[0]
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);
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}
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// Verify each implementation returns the same results
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let res = factorial(34);
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let res2 = it_factorial(34);
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assert!(res.is_some());
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assert!(res2.is_some());
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assert_eq!(res, res2);
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// Bounds checks
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assert!(factorial(35).is_none());
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assert!(it_factorial(35).is_none());
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}
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#[cfg(feature = "std")]
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#[test]
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fn test_approx_factorial() {
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assert!(approx_factorial(170.624).is_some());
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assert!(approx_factorial(1.0).is_some());
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assert!(approx_factorial(170.7).is_none());
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}
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#[test]
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fn test_fibonacci() {
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// Sanity checking
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for pair in [[0usize, 0], [1, 1], [1, 2], [2, 3]].iter() {
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assert_eq!(
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Some(pair[0] as u128),
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fibonacci(pair[1]),
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"fibonacci({}) should be {}",
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pair[1],
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pair[0]
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);
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assert_eq!(
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Some(pair[0] as u128),
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mem_fibonacci(pair[1]),
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"fibonacci({}) should be {}",
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pair[1],
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pair[0]
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);
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assert_eq!(
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Some(pair[0] as u128),
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rec_fibonacci(pair[1]),
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"fibonacci({}) should be {}",
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pair[1],
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pair[0]
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);
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}
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// Verify each implementation returns the same results
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let res = fibonacci(186);
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let res2 = mem_fibonacci(186);
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assert!(res.is_some());
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assert!(res2.is_some());
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assert_eq!(res, res2);
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// Bounds checks
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assert!(fibonacci(187).is_none());
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assert!(mem_fibonacci(187).is_none());
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}
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#[test]
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fn test_gcd() {
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assert_eq!(u8::gcd(5, 0), 5);
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assert_eq!(u8::gcd(0, 5), 5);
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assert_eq!(u8::gcd(2, 3), 1);
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assert_eq!(u8::gcd(2, 2), 2);
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assert_eq!(u8::gcd(2, 8), 2);
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assert_eq!(u16::gcd(36, 48), 12);
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assert_eq!(u16::e_gcd(36, 48), 12);
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assert_eq!(u16::stein_gcd(36, 48), 12);
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}
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#[test]
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fn test_lcm() {
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assert_eq!(u32::lcm(2, 8), 8);
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assert_eq!(u16::lcm(2, 3), 6);
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assert_eq!(usize::lcm(15, 30), 30);
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assert_eq!(u128::lcm(1, 5), 5);
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assert_eq!(0u8, u8::lcm(0, 0));
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}
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}
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