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| 1 | +macro_rules! tests { |
| 2 | + ($isqrt_consistency_check_fn_macro:ident : $($T:ident)+) => { |
| 3 | + $( |
| 4 | + mod $T { |
| 5 | + $isqrt_consistency_check_fn_macro!($T); |
| 6 | + |
| 7 | + // Check that the following produce the correct values from |
| 8 | + // `isqrt`: |
| 9 | + // |
| 10 | + // * the first and last 128 nonnegative values |
| 11 | + // * powers of two, minus one |
| 12 | + // * powers of two |
| 13 | + // |
| 14 | + // For signed types, check that `checked_isqrt` and `isqrt` |
| 15 | + // either produce the same numeric value or respectively |
| 16 | + // produce `None` and a panic. Make sure to do a consistency |
| 17 | + // check for `<$T>::MIN` as well, as no nonnegative values |
| 18 | + // negate to it. |
| 19 | + // |
| 20 | + // For unsigned types check that `isqrt` produces the same |
| 21 | + // numeric value for `$T` and `NonZero<$T>`. |
| 22 | + #[test] |
| 23 | + fn isqrt() { |
| 24 | + isqrt_consistency_check(<$T>::MIN); |
| 25 | + |
| 26 | + for n in (0..=127) |
| 27 | + .chain(<$T>::MAX - 127..=<$T>::MAX) |
| 28 | + .chain((0..<$T>::MAX.count_ones()).map(|exponent| (1 << exponent) - 1)) |
| 29 | + .chain((0..<$T>::MAX.count_ones()).map(|exponent| 1 << exponent)) |
| 30 | + { |
| 31 | + isqrt_consistency_check(n); |
| 32 | + |
| 33 | + let isqrt_n = n.isqrt(); |
| 34 | + assert!( |
| 35 | + isqrt_n |
| 36 | + .checked_mul(isqrt_n) |
| 37 | + .map(|isqrt_n_squared| isqrt_n_squared <= n) |
| 38 | + .unwrap_or(false), |
| 39 | + "`{n}.isqrt()` should be lower than {isqrt_n}." |
| 40 | + ); |
| 41 | + assert!( |
| 42 | + (isqrt_n + 1) |
| 43 | + .checked_mul(isqrt_n + 1) |
| 44 | + .map(|isqrt_n_plus_1_squared| n < isqrt_n_plus_1_squared) |
| 45 | + .unwrap_or(true), |
| 46 | + "`{n}.isqrt()` should be higher than {isqrt_n})." |
| 47 | + ); |
| 48 | + } |
| 49 | + } |
| 50 | + |
| 51 | + // Check the square roots of: |
| 52 | + // |
| 53 | + // * the first 1,024 perfect squares |
| 54 | + // * halfway between each of the first 1,024 perfect squares |
| 55 | + // and the next perfect square |
| 56 | + // * the next perfect square after the each of the first 1,024 |
| 57 | + // perfect squares, minus one |
| 58 | + // * the last 1,024 perfect squares |
| 59 | + // * the last 1,024 perfect squares, minus one |
| 60 | + // * halfway between each of the last 1,024 perfect squares |
| 61 | + // and the previous perfect square |
| 62 | + #[test] |
| 63 | + // Skip this test on Miri, as it takes too long to run. |
| 64 | + #[cfg(not(miri))] |
| 65 | + fn isqrt_extended() { |
| 66 | + // The correct value is worked out by using the fact that |
| 67 | + // the nth nonzero perfect square is the sum of the first n |
| 68 | + // odd numbers: |
| 69 | + // |
| 70 | + // 1 = 1 |
| 71 | + // 4 = 1 + 3 |
| 72 | + // 9 = 1 + 3 + 5 |
| 73 | + // 16 = 1 + 3 + 5 + 7 |
| 74 | + // |
| 75 | + // Note also that the last odd number added in is two times |
| 76 | + // the square root of the previous perfect square, plus |
| 77 | + // one: |
| 78 | + // |
| 79 | + // 1 = 2*0 + 1 |
| 80 | + // 3 = 2*1 + 1 |
| 81 | + // 5 = 2*2 + 1 |
| 82 | + // 7 = 2*3 + 1 |
| 83 | + // |
| 84 | + // That means we can add the square root of this perfect |
| 85 | + // square once to get about halfway to the next perfect |
| 86 | + // square, then we can add the square root of this perfect |
| 87 | + // square again to get to the next perfect square, minus |
| 88 | + // one, then we can add one to get to the next perfect |
| 89 | + // square. |
| 90 | + // |
| 91 | + // This allows us to, for each of the first 1,024 perfect |
| 92 | + // squares, test that the square roots of the following are |
| 93 | + // all correct and equal to each other: |
| 94 | + // |
| 95 | + // * the current perfect square |
| 96 | + // * about halfway to the next perfect square |
| 97 | + // * the next perfect square, minus one |
| 98 | + let mut n: $T = 0; |
| 99 | + for sqrt_n in 0..1_024.min((1_u128 << (<$T>::MAX.count_ones()/2)) - 1) as $T { |
| 100 | + isqrt_consistency_check(n); |
| 101 | + assert_eq!( |
| 102 | + n.isqrt(), |
| 103 | + sqrt_n, |
| 104 | + "`{sqrt_n}.pow(2).isqrt()` should be {sqrt_n}." |
| 105 | + ); |
| 106 | + |
| 107 | + n += sqrt_n; |
| 108 | + isqrt_consistency_check(n); |
| 109 | + assert_eq!( |
| 110 | + n.isqrt(), |
| 111 | + sqrt_n, |
| 112 | + "{n} is about halfway between `{sqrt_n}.pow(2)` and `{}.pow(2)`, so `{n}.isqrt()` should be {sqrt_n}.", |
| 113 | + sqrt_n + 1 |
| 114 | + ); |
| 115 | + |
| 116 | + n += sqrt_n; |
| 117 | + isqrt_consistency_check(n); |
| 118 | + assert_eq!( |
| 119 | + n.isqrt(), |
| 120 | + sqrt_n, |
| 121 | + "`({}.pow(2) - 1).isqrt()` should be {sqrt_n}.", |
| 122 | + sqrt_n + 1 |
| 123 | + ); |
| 124 | + |
| 125 | + n += 1; |
| 126 | + } |
| 127 | + |
| 128 | + // Similarly, for each of the last 1,024 perfect squares, |
| 129 | + // check: |
| 130 | + // |
| 131 | + // * the current perfect square |
| 132 | + // * the current perfect square, minus one |
| 133 | + // * about halfway to the previous perfect square |
| 134 | + // |
| 135 | + // `MAX`'s `isqrt` return value is verified in the `isqrt` |
| 136 | + // test function above. |
| 137 | + let maximum_sqrt = <$T>::MAX.isqrt(); |
| 138 | + let mut n = maximum_sqrt * maximum_sqrt; |
| 139 | + |
| 140 | + for sqrt_n in (maximum_sqrt - 1_024.min((1_u128 << (<$T>::MAX.count_ones()/2)) - 1) as $T..maximum_sqrt).rev() { |
| 141 | + isqrt_consistency_check(n); |
| 142 | + assert_eq!( |
| 143 | + n.isqrt(), |
| 144 | + sqrt_n + 1, |
| 145 | + "`{0}.pow(2).isqrt()` should be {0}.", |
| 146 | + sqrt_n + 1 |
| 147 | + ); |
| 148 | + |
| 149 | + n -= 1; |
| 150 | + isqrt_consistency_check(n); |
| 151 | + assert_eq!( |
| 152 | + n.isqrt(), |
| 153 | + sqrt_n, |
| 154 | + "`({}.pow(2) - 1).isqrt()` should be {sqrt_n}.", |
| 155 | + sqrt_n + 1 |
| 156 | + ); |
| 157 | + |
| 158 | + n -= sqrt_n; |
| 159 | + isqrt_consistency_check(n); |
| 160 | + assert_eq!( |
| 161 | + n.isqrt(), |
| 162 | + sqrt_n, |
| 163 | + "{n} is about halfway between `{sqrt_n}.pow(2)` and `{}.pow(2)`, so `{n}.isqrt()` should be {sqrt_n}.", |
| 164 | + sqrt_n + 1 |
| 165 | + ); |
| 166 | + |
| 167 | + n -= sqrt_n; |
| 168 | + } |
| 169 | + } |
| 170 | + } |
| 171 | + )* |
| 172 | + }; |
| 173 | +} |
| 174 | + |
| 175 | +macro_rules! signed_check { |
| 176 | + ($T:ident) => { |
| 177 | + /// This takes an input and, if it's nonnegative or |
| 178 | + #[doc = concat!("`", stringify!($T), "::MIN`,")] |
| 179 | + /// checks that `isqrt` and `checked_isqrt` produce equivalent results |
| 180 | + /// for that input and for the negative of that input. |
| 181 | + /// |
| 182 | + /// # Note |
| 183 | + /// |
| 184 | + /// This cannot check that negative inputs to `isqrt` cause panics if |
| 185 | + /// panics abort instead of unwind. |
| 186 | + fn isqrt_consistency_check(n: $T) { |
| 187 | + // `<$T>::MIN` will be negative, so ignore it in this nonnegative |
| 188 | + // section. |
| 189 | + if n >= 0 { |
| 190 | + assert_eq!( |
| 191 | + Some(n.isqrt()), |
| 192 | + n.checked_isqrt(), |
| 193 | + "`{n}.checked_isqrt()` should match `Some({n}.isqrt())`.", |
| 194 | + ); |
| 195 | + } |
| 196 | + |
| 197 | + // `wrapping_neg` so that `<$T>::MIN` will negate to itself rather |
| 198 | + // than panicking. |
| 199 | + let negative_n = n.wrapping_neg(); |
| 200 | + |
| 201 | + // Zero negated will still be nonnegative, so ignore it in this |
| 202 | + // negative section. |
| 203 | + if negative_n < 0 { |
| 204 | + assert_eq!( |
| 205 | + negative_n.checked_isqrt(), |
| 206 | + None, |
| 207 | + "`({negative_n}).checked_isqrt()` should be `None`, as {negative_n} is negative.", |
| 208 | + ); |
| 209 | + |
| 210 | + // `catch_unwind` only works when panics unwind rather than abort. |
| 211 | + #[cfg(panic = "unwind")] |
| 212 | + { |
| 213 | + std::panic::catch_unwind(core::panic::AssertUnwindSafe(|| (-n).isqrt())).expect_err( |
| 214 | + &format!("`({negative_n}).isqrt()` should have panicked, as {negative_n} is negative.") |
| 215 | + ); |
| 216 | + } |
| 217 | + } |
| 218 | + } |
| 219 | + }; |
| 220 | +} |
| 221 | + |
| 222 | +macro_rules! unsigned_check { |
| 223 | + ($T:ident) => { |
| 224 | + /// This takes an input and, if it's nonzero, checks that `isqrt` |
| 225 | + /// produces the same numeric value for both |
| 226 | + #[doc = concat!("`", stringify!($T), "` and ")] |
| 227 | + #[doc = concat!("`NonZero<", stringify!($T), ">`.")] |
| 228 | + fn isqrt_consistency_check(n: $T) { |
| 229 | + // Zero cannot be turned into a `NonZero` value, so ignore it in |
| 230 | + // this nonzero section. |
| 231 | + if n > 0 { |
| 232 | + assert_eq!( |
| 233 | + n.isqrt(), |
| 234 | + core::num::NonZero::<$T>::new(n) |
| 235 | + .expect( |
| 236 | + "Was not able to create a new `NonZero` value from a nonzero number." |
| 237 | + ) |
| 238 | + .isqrt() |
| 239 | + .get(), |
| 240 | + "`{n}.isqrt` should match `NonZero`'s `{n}.isqrt().get()`.", |
| 241 | + ); |
| 242 | + } |
| 243 | + } |
| 244 | + }; |
| 245 | +} |
| 246 | + |
| 247 | +tests!(signed_check: i8 i16 i32 i64 i128); |
| 248 | +tests!(unsigned_check: u8 u16 u32 u64 u128); |
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