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use std::cmp::Ordering;
pub type Number = f32;
pub type Poly = Vec<Number>;
pub fn eval_poly(p: &Poly, t: Number) -> Number {
let mut r = 0.0;
for i in 0..p.len() {
r += p[i] * t.powi(i as i32);
}
r
}
pub fn sub(a: &Poly, b: &Poly) -> Poly {
let mut r = a.clone();
for i in 0..r.len() {
r[i] -= b[i];
}
r
}
pub fn skewed_sum(a: Poly, b: Poly) -> Poly {
let mut r = a.clone();
for i in 0..r.len() - 1 {
r[i + 1] += b[i];
}
r.push(b[b.len() - 1]);
r
}
fn is_zero(p: &Poly) -> bool {
for i in 0..p.len() {
if p[i] != 0.0 {
return false
}
}
true
}
fn degree(p: &Poly) -> usize {
let mut i = p.len() - 1;
while p[i] == 0.0 && i > 0 {
i -= 1;
}
i
}
fn prod(p: &Poly, n: Number) -> Poly {
let mut r = p.clone();
for i in 0..r.len() {
r[i] *= n;
}
r
}
fn shift(p: &Poly, amount: usize) -> Poly {
let mut r = vec![0.0; p.len()];
for i in 0..p.len() {
if i + amount < r.len() {
r[i + amount] = p[i];
}
}
r
}
fn rem(a: &Poly, b: &Poly) -> Poly {
let an = a[degree(a)];
let bn = b[degree(b)];
match degree(a).cmp(°ree(b)) {
Ordering::Equal => sub(a, &prod(b, an / bn)),
Ordering::Greater => sub(a, &prod(&shift(b, (degree(a) - degree(b)) as usize), an / bn)),
Ordering::Less => vec![0.0; b.len()]
}
}
pub fn gcd(a: &Poly, b: &Poly) -> Poly {
let c = rem(a, b);
if is_zero(&c) {
b.clone()
} else {
gcd(b, &c)
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn poly_is_zero() {
let p = vec![0.0; 5];
assert_eq!(is_zero(&p), true);
}
#[test]
fn poly_is_not_zero() {
let mut p = vec![0.0; 5];
p[2] = 8.0;
assert_eq!(is_zero(&p), false);
}
#[test]
fn degree_is_five() {
let mut p = vec![0.0; 6];
p[5] = 2.0;
assert_eq!(degree(&p), 5);
}
#[test]
fn degree_is_zero() {
let p = vec![0.0; 6];
assert_eq!(degree(&p), 0);
}
#[test]
fn prod_test() {
let p = vec![1.0, 2.0, 3.0, 4.0, 5.0];
assert_eq!(prod(&p, 2.0), vec![2.0, 4.0, 6.0, 8.0, 10.0]);
}
#[test]
fn shift_test() {
let p = vec![1.0, 2.0, 3.0, 0.0, 0.0];
assert_eq!(shift(&p, 2), vec![0.0, 0.0, 1.0, 2.0, 3.0]);
}
#[test]
fn rem_equal() {
let a = vec![6.0, 7.0, 1.0];
let b = vec![-6.0, -5.0, 1.0];
assert_eq!(rem(&a, &b), vec![12.0, 12.0, 0.0]);
}
#[test]
fn rem_greater() {
let a = vec![-6.0, -5.0, 1.0];
let b = vec![12.0, 12.0, 0.0];
assert_eq!(rem(&a, &b), vec![-6.0, -6.0, 0.0]);
}
#[test]
fn gcd_test() {
let a = vec![6.0, 7.0, 1.0];
let b = vec![-6.0, -5.0, 1.0];
assert_eq!(gcd(&a, &b), vec![-6.0, -6.0, 0.0]);
}
}
|
