4b08b2e400
Improved `checked_isqrt` and `isqrt` methods ### Improved tests of `isqrt` and `checked_isqrt` implementations * Inputs chosen more thoroughly and systematically. * Checks that `isqrt` and `checked_isqrt` have equivalent results for signed types, either equivalent numerically or equivalent as a panic and a `None`. * Checks that `isqrt` has numerically-equivalent results for unsigned types and their `NonZero` counterparts. ### Added benchmarks for `isqrt` implementations ### Greatly sped up `checked_isqrt` and `isqrt` methods * Uses a lookup table for 8-bit integers and then the Karatsuba square root algorithm for larger integers. * Includes optimization hints that give the compiler the exact numeric range of results. ### Feature tracking issue `isqrt` is an unstable feature tracked at #116226. <details><summary>Benchmarked improvements</summary> ### Command used to benchmark ./x bench library/core -- int_sqrt ### Before benchmarks: num::int_sqrt::i128::isqrt 439591.65/iter +/- 6652.70 num::int_sqrt::i16::isqrt 5302.97/iter +/- 160.93 num::int_sqrt::i32::isqrt 62999.11/iter +/- 2022.05 num::int_sqrt::i64::isqrt 125248.81/iter +/- 1674.43 num::int_sqrt::i8::isqrt 123.56/iter +/- 1.87 num::int_sqrt::isize::isqrt 125356.56/iter +/- 1017.03 num::int_sqrt::non_zero_u128::isqrt 437443.75/iter +/- 3535.43 num::int_sqrt::non_zero_u16::isqrt 8604.58/iter +/- 94.76 num::int_sqrt::non_zero_u32::isqrt 62933.33/iter +/- 517.30 num::int_sqrt::non_zero_u64::isqrt 125076.38/iter +/- 11340.61 num::int_sqrt::non_zero_u8::isqrt 221.51/iter +/- 1.58 num::int_sqrt::non_zero_usize::isqrt 136005.21/iter +/- 2020.35 num::int_sqrt::u128::isqrt 439014.55/iter +/- 3920.45 num::int_sqrt::u16::isqrt 8575.08/iter +/- 148.06 num::int_sqrt::u32::isqrt 63008.89/iter +/- 803.67 num::int_sqrt::u64::isqrt 125088.09/iter +/- 879.29 num::int_sqrt::u8::isqrt 230.18/iter +/- 2.04 num::int_sqrt::usize::isqrt 125237.51/iter +/- 4747.83 ### After benchmarks: num::int_sqrt::i128::isqrt 105184.89/iter +/- 1171.38 num::int_sqrt::i16::isqrt 1910.26/iter +/- 78.50 num::int_sqrt::i32::isqrt 34260.34/iter +/- 960.84 num::int_sqrt::i64::isqrt 45939.19/iter +/- 2525.65 num::int_sqrt::i8::isqrt 22.87/iter +/- 0.45 num::int_sqrt::isize::isqrt 45884.17/iter +/- 595.49 num::int_sqrt::non_zero_u128::isqrt 106344.27/iter +/- 780.99 num::int_sqrt::non_zero_u16::isqrt 2790.19/iter +/- 53.43 num::int_sqrt::non_zero_u32::isqrt 33613.99/iter +/- 362.96 num::int_sqrt::non_zero_u64::isqrt 46235.42/iter +/- 429.69 num::int_sqrt::non_zero_u8::isqrt 31.78/iter +/- 0.75 num::int_sqrt::non_zero_usize::isqrt 46208.75/iter +/- 375.27 num::int_sqrt::u128::isqrt 106385.94/iter +/- 1649.95 num::int_sqrt::u16::isqrt 2747.69/iter +/- 28.72 num::int_sqrt::u32::isqrt 33627.09/iter +/- 475.68 num::int_sqrt::u64::isqrt 46182.29/iter +/- 311.16 num::int_sqrt::u8::isqrt 33.10/iter +/- 0.30 num::int_sqrt::usize::isqrt 46165.00/iter +/- 388.41 </details> Tracking Issue for {u8,i8,...}::isqrt #116226 try-job: test-various
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