Function horner::eval_any_rank_polynomial[−][src]

pub fn eval_any_rank_polynomial<T: Zero + MulAddAssign + Copy>(
    x: T, 
    coefficients: &[T]
) -> T

Expand description

Evaluate a polynomial of arbitrary rank using Horner’s method.

Horner’s method goes like this: to find 𝑎𝑥³+𝑏𝑥²+𝑐𝑥+𝑑, you evaluate 𝑥(𝑥(𝑎𝑥+𝑏)+𝑐)+𝑑.

That’s what this function does too.

You provide a value for 𝑥 and a slice of values for the coefficients &[𝑎, 𝑏, 𝑐, 𝑑, …]. The cardinality of the slice of coefficients must equal the degree of the polynomial plus one, except for the special case of the whole expression being just 0 in which case a slice of length zero means the same (gives you the same result) as if the slice was equal to &[0] or any other number of all zeros.

Here are some examples demonstrating use of eval_polynomial:

use horner::eval_any_rank_polynomial;

// Evaluating the polynomial 72𝑥²+81𝑥+99 with 𝑥 = 5
let val = eval_any_rank_polynomial(5, &[72, 81, 99]);

// Traditional calculation.
let trad = 72 * 5_i32.pow(2) + 81 * 5 + 99;

assert_eq!(val, trad);

// Here we have the "polynomial" 42, which is to say, 42𝑥⁰. Evaluated with 𝑥 = 9000
assert_eq!(42, eval_any_rank_polynomial(9000, &[42]));

// 23𝑥⁹+0𝑥⁸+27𝑥⁷+0𝑥⁶-5𝑥⁵+0𝑥⁴+0𝑥³+0𝑥²+0𝑥ⁱ+0𝑥⁰
// Written simply: 23𝑥⁹+27𝑥⁷-5𝑥⁵
// Evaluated with 𝑥 = 99

let val = eval_any_rank_polynomial(99_i128, &[23, 0, 27, 0, -5, 0, 0, 0, 0, 0]);
let trad = 23 * 99_i128.pow(9) + 27 * 99_i128.pow(7) - 5 * 99_i128.pow(5);

assert_eq!(val, trad);

// The "polynomial" 0. Represented in it's simplest form, the list of coefficents is empty.
// Evaluated with 𝑥 = 222
assert_eq!(0, eval_any_rank_polynomial(222, &[]));