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rayon::prelude::*; + +/// Computes the integer nth-root of `value` using binary search. +/// Returns the largest integer `r` such that `r^n <= value`. +fn integer_root(value: u64, n: u32) -> u64 { + if value == 0 { + return 0; + } + if n == 0 { + panic!("0th root is undefined"); + } + if n == 1 { + return value; + } + + // Binary search for the integer nth-root + let mut low: u64 = 1; + let mut high: u64 = value; + + // Narrow down the upper bound to avoid overflow + // The nth root of u64::MAX is at most 2^(64/n) + let max_root = 1u64 << (64 / n as u64 + 1); + if high > max_root { + high = max_root; + } + + while low < high { + let mid = low + (high - low + 1) / 2; + + // Check if mid^n <= value, handling potential overflow + match checked_pow(mid, n) { + Some(pow) if pow <= value => low = mid, + _ => high = mid - 1, + } + } + + low +} + +/// Computes base^exp with overflow checking +fn checked_pow(base: u64, exp: u32) -> Option { + let mut result: u64 = 1; + let mut b = base; + let mut e = exp; + + while e > 0 { + if e & 1 == 1 { + result = result.checked_mul(b)?; + } + e >>= 1; + if e > 0 { + b = b.checked_mul(b)?; + } + } + + Some(result) +} + +/// Benchmark: compute the sum of integer roots for many values +fn sum_integer_roots(values: &[u64], root_degrees: &[u32]) -> u64 { + values + .iter() + .flat_map(|&v| root_degrees.iter().map(move |&n| integer_root(v, n))) + .sum() +} + +/// Parallel version using rayon +fn sum_integer_roots_parallel(values: &[u64], root_degrees: &[u32]) -> u64 { + values + .par_iter() + .flat_map(|&v| root_degrees.par_iter().map(move |&n| integer_root(v, n))) + .sum() +} + +fn benchmark_integer_roots(c: &mut Criterion) { + // Limit thread count to avoid ThreadPoolBuilder bug + rayon::ThreadPoolBuilder::new() + .num_threads(4) + .build_global() + .ok(); // Ignore error if pool already initialized + + // Generate test data: a range of values to compute roots for + let values: Vec = (1..=10000).collect(); + let root_degrees: Vec = vec![2, 3, 4, 5, 6, 7, 8]; // square, cube, 4th, 5th, 6th, 7th, 8th roots + + c.bench_function("sum_integer_roots_sequential", |b| { + b.iter(|| sum_integer_roots(black_box(&values), black_box(&root_degrees))) + }); + + c.bench_function("sum_integer_roots_parallel", |b| { + b.iter(|| sum_integer_roots_parallel(black_box(&values), black_box(&root_degrees))) + }); + + // Benchmark individual root operations + c.bench_function("integer_sqrt_10000_values", |b| { + b.iter(|| { + values + .iter() + .map(|&v| integer_root(black_box(v), 2)) + .sum::() + }) + }); + + c.bench_function("integer_cbrt_10000_values", |b| { + b.iter(|| { + values + .iter() + .map(|&v| integer_root(black_box(v), 3)) + .sum::() + }) + }); + + // Benchmark with larger values + let large_values: Vec = (1..=1000).map(|x| x * 1_000_000).collect(); + + c.bench_function("sum_roots_large_values", |b| { + b.iter(|| sum_integer_roots(black_box(&large_values), black_box(&root_degrees))) + }); +} + +criterion_group!(benches, benchmark_integer_roots); +criterion_main!(benches);