62 lines
1.7 KiB
Rust
62 lines
1.7 KiB
Rust
//! Approximation calculations
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use {
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num_traits::{CheckedAdd, CheckedDiv, One, Zero},
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std::cmp::Eq,
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};
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const SQRT_ITERATIONS: u8 = 50;
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/// Perform square root
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pub fn sqrt<T: CheckedAdd + CheckedDiv + One + Zero + Eq + Copy>(radicand: T) -> Option<T> {
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if radicand == T::zero() {
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return Some(T::zero());
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}
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// A good initial guess is the average of the interval that contains the
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// input number. For all numbers, that will be between 1 and the given number.
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let one = T::one();
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let two = one.checked_add(&one)?;
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let mut guess = radicand.checked_div(&two)?.checked_add(&one)?;
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let mut last_guess = guess;
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for _ in 0..SQRT_ITERATIONS {
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// x_k+1 = (x_k + radicand / x_k) / 2
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guess = last_guess
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.checked_add(&radicand.checked_div(&last_guess)?)?
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.checked_div(&two)?;
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if last_guess == guess {
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break;
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} else {
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last_guess = guess;
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}
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}
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Some(guess)
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}
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#[cfg(test)]
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mod tests {
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use {super::*, proptest::prelude::*};
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fn check_square_root(radicand: u128) {
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let root = sqrt(radicand).unwrap();
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let lower_bound = root.saturating_sub(1).checked_pow(2).unwrap();
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let upper_bound = root.checked_add(1).unwrap().checked_pow(2).unwrap();
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assert!(radicand as u128 <= upper_bound);
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assert!(radicand as u128 >= lower_bound);
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}
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#[test]
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fn test_square_root_min_max() {
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let test_roots = [0, u64::MAX];
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for i in test_roots.iter() {
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check_square_root(*i as u128);
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}
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}
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proptest! {
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#[test]
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fn test_square_root(a in 0..u64::MAX) {
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check_square_root(a as u128);
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}
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}
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}
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