Yiming Jing | cf21fc4 | 2021-07-16 13:23:26 -0700 | [diff] [blame] | 1 | mod biguint { |
| 2 | use num_bigint::BigUint; |
| 3 | use num_traits::{One, Zero}; |
| 4 | use std::{i32, u32}; |
| 5 | |
| 6 | fn check<T: Into<BigUint>>(x: T, n: u32) { |
| 7 | let x: BigUint = x.into(); |
| 8 | let root = x.nth_root(n); |
| 9 | println!("check {}.nth_root({}) = {}", x, n, root); |
| 10 | |
| 11 | if n == 2 { |
| 12 | assert_eq!(root, x.sqrt()) |
| 13 | } else if n == 3 { |
| 14 | assert_eq!(root, x.cbrt()) |
| 15 | } |
| 16 | |
| 17 | let lo = root.pow(n); |
| 18 | assert!(lo <= x); |
| 19 | assert_eq!(lo.nth_root(n), root); |
| 20 | if !lo.is_zero() { |
| 21 | assert_eq!((&lo - 1u32).nth_root(n), &root - 1u32); |
| 22 | } |
| 23 | |
| 24 | let hi = (&root + 1u32).pow(n); |
| 25 | assert!(hi > x); |
| 26 | assert_eq!(hi.nth_root(n), &root + 1u32); |
| 27 | assert_eq!((&hi - 1u32).nth_root(n), root); |
| 28 | } |
| 29 | |
| 30 | #[test] |
| 31 | fn test_sqrt() { |
| 32 | check(99u32, 2); |
| 33 | check(100u32, 2); |
| 34 | check(120u32, 2); |
| 35 | } |
| 36 | |
| 37 | #[test] |
| 38 | fn test_cbrt() { |
| 39 | check(8u32, 3); |
| 40 | check(26u32, 3); |
| 41 | } |
| 42 | |
| 43 | #[test] |
| 44 | fn test_nth_root() { |
| 45 | check(0u32, 1); |
| 46 | check(10u32, 1); |
| 47 | check(100u32, 4); |
| 48 | } |
| 49 | |
| 50 | #[test] |
| 51 | #[should_panic] |
| 52 | fn test_nth_root_n_is_zero() { |
| 53 | check(4u32, 0); |
| 54 | } |
| 55 | |
| 56 | #[test] |
| 57 | fn test_nth_root_big() { |
| 58 | let x = BigUint::from(123_456_789_u32); |
| 59 | let expected = BigUint::from(6u32); |
| 60 | |
| 61 | assert_eq!(x.nth_root(10), expected); |
| 62 | check(x, 10); |
| 63 | } |
| 64 | |
| 65 | #[test] |
| 66 | fn test_nth_root_googol() { |
| 67 | let googol = BigUint::from(10u32).pow(100u32); |
| 68 | |
| 69 | // perfect divisors of 100 |
| 70 | for &n in &[2, 4, 5, 10, 20, 25, 50, 100] { |
| 71 | let expected = BigUint::from(10u32).pow(100u32 / n); |
| 72 | assert_eq!(googol.nth_root(n), expected); |
| 73 | check(googol.clone(), n); |
| 74 | } |
| 75 | } |
| 76 | |
| 77 | #[test] |
| 78 | fn test_nth_root_twos() { |
| 79 | const EXP: u32 = 12; |
| 80 | const LOG2: usize = 1 << EXP; |
| 81 | let x = BigUint::one() << LOG2; |
| 82 | |
| 83 | // the perfect divisors are just powers of two |
| 84 | for exp in 1..=EXP { |
| 85 | let n = 2u32.pow(exp); |
| 86 | let expected = BigUint::one() << (LOG2 / n as usize); |
| 87 | assert_eq!(x.nth_root(n), expected); |
| 88 | check(x.clone(), n); |
| 89 | } |
| 90 | |
| 91 | // degenerate cases should return quickly |
| 92 | assert!(x.nth_root(x.bits() as u32).is_one()); |
| 93 | assert!(x.nth_root(i32::MAX as u32).is_one()); |
| 94 | assert!(x.nth_root(u32::MAX).is_one()); |
| 95 | } |
| 96 | |
| 97 | #[test] |
| 98 | fn test_roots_rand1() { |
| 99 | // A random input that found regressions |
| 100 | let s = "575981506858479247661989091587544744717244516135539456183849\ |
| 101 | 986593934723426343633698413178771587697273822147578889823552\ |
| 102 | 182702908597782734558103025298880194023243541613924361007059\ |
| 103 | 353344183590348785832467726433749431093350684849462759540710\ |
| 104 | 026019022227591412417064179299354183441181373862905039254106\ |
| 105 | 4781867"; |
| 106 | let x: BigUint = s.parse().unwrap(); |
| 107 | |
| 108 | check(x.clone(), 2); |
| 109 | check(x.clone(), 3); |
| 110 | check(x.clone(), 10); |
| 111 | check(x, 100); |
| 112 | } |
| 113 | } |
| 114 | |
| 115 | mod bigint { |
| 116 | use num_bigint::BigInt; |
| 117 | use num_traits::Signed; |
| 118 | |
| 119 | fn check(x: i64, n: u32) { |
| 120 | let big_x = BigInt::from(x); |
| 121 | let res = big_x.nth_root(n); |
| 122 | |
| 123 | if n == 2 { |
| 124 | assert_eq!(&res, &big_x.sqrt()) |
| 125 | } else if n == 3 { |
| 126 | assert_eq!(&res, &big_x.cbrt()) |
| 127 | } |
| 128 | |
| 129 | if big_x.is_negative() { |
| 130 | assert!(res.pow(n) >= big_x); |
| 131 | assert!((res - 1u32).pow(n) < big_x); |
| 132 | } else { |
| 133 | assert!(res.pow(n) <= big_x); |
| 134 | assert!((res + 1u32).pow(n) > big_x); |
| 135 | } |
| 136 | } |
| 137 | |
| 138 | #[test] |
| 139 | fn test_nth_root() { |
| 140 | check(-100, 3); |
| 141 | } |
| 142 | |
| 143 | #[test] |
| 144 | #[should_panic] |
| 145 | fn test_nth_root_x_neg_n_even() { |
| 146 | check(-100, 4); |
| 147 | } |
| 148 | |
| 149 | #[test] |
| 150 | #[should_panic] |
| 151 | fn test_sqrt_x_neg() { |
| 152 | check(-4, 2); |
| 153 | } |
| 154 | |
| 155 | #[test] |
| 156 | fn test_cbrt() { |
| 157 | check(8, 3); |
| 158 | check(-8, 3); |
| 159 | } |
| 160 | } |