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|
mod biguint {
use num_bigint::BigUint;
use num_traits::{One, Zero};
fn check<T: Into<BigUint>>(x: T, n: u32) {
let x: BigUint = x.into();
let root = x.nth_root(n);
println!("check {}.nth_root({}) = {}", x, n, root);
if n == 2 {
assert_eq!(root, x.sqrt())
} else if n == 3 {
assert_eq!(root, x.cbrt())
}
let lo = root.pow(n);
assert!(lo <= x);
assert_eq!(lo.nth_root(n), root);
if !lo.is_zero() {
assert_eq!((&lo - 1u32).nth_root(n), &root - 1u32);
}
let hi = (&root + 1u32).pow(n);
assert!(hi > x);
assert_eq!(hi.nth_root(n), &root + 1u32);
assert_eq!((&hi - 1u32).nth_root(n), root);
}
#[test]
fn test_sqrt() {
check(99u32, 2);
check(100u32, 2);
check(120u32, 2);
}
#[test]
fn test_cbrt() {
check(8u32, 3);
check(26u32, 3);
}
#[test]
fn test_nth_root() {
check(0u32, 1);
check(10u32, 1);
check(100u32, 4);
}
#[test]
#[should_panic]
fn test_nth_root_n_is_zero() {
check(4u32, 0);
}
#[test]
fn test_nth_root_big() {
let x = BigUint::from(123_456_789_u32);
let expected = BigUint::from(6u32);
assert_eq!(x.nth_root(10), expected);
check(x, 10);
}
#[test]
fn test_nth_root_googol() {
let googol = BigUint::from(10u32).pow(100u32);
// perfect divisors of 100
for &n in &[2, 4, 5, 10, 20, 25, 50, 100] {
let expected = BigUint::from(10u32).pow(100u32 / n);
assert_eq!(googol.nth_root(n), expected);
check(googol.clone(), n);
}
}
#[test]
fn test_nth_root_twos() {
const EXP: u32 = 12;
const LOG2: usize = 1 << EXP;
let x = BigUint::one() << LOG2;
// the perfect divisors are just powers of two
for exp in 1..=EXP {
let n = 2u32.pow(exp);
let expected = BigUint::one() << (LOG2 / n as usize);
assert_eq!(x.nth_root(n), expected);
check(x.clone(), n);
}
// degenerate cases should return quickly
assert!(x.nth_root(x.bits() as u32).is_one());
assert!(x.nth_root(i32::MAX as u32).is_one());
assert!(x.nth_root(u32::MAX).is_one());
}
#[test]
fn test_roots_rand1() {
// A random input that found regressions
let s = "575981506858479247661989091587544744717244516135539456183849\
986593934723426343633698413178771587697273822147578889823552\
182702908597782734558103025298880194023243541613924361007059\
353344183590348785832467726433749431093350684849462759540710\
026019022227591412417064179299354183441181373862905039254106\
4781867";
let x: BigUint = s.parse().unwrap();
check(x.clone(), 2);
check(x.clone(), 3);
check(x.clone(), 10);
check(x, 100);
}
}
mod bigint {
use num_bigint::BigInt;
use num_traits::Signed;
fn check(x: i64, n: u32) {
let big_x = BigInt::from(x);
let res = big_x.nth_root(n);
if n == 2 {
assert_eq!(&res, &big_x.sqrt())
} else if n == 3 {
assert_eq!(&res, &big_x.cbrt())
}
if big_x.is_negative() {
assert!(res.pow(n) >= big_x);
assert!((res - 1u32).pow(n) < big_x);
} else {
assert!(res.pow(n) <= big_x);
assert!((res + 1u32).pow(n) > big_x);
}
}
#[test]
fn test_nth_root() {
check(-100, 3);
}
#[test]
#[should_panic]
fn test_nth_root_x_neg_n_even() {
check(-100, 4);
}
#[test]
#[should_panic]
fn test_sqrt_x_neg() {
check(-4, 2);
}
#[test]
fn test_cbrt() {
check(8, 3);
check(-8, 3);
}
}
|
