Use better initial guesses for Roots

Cargo.toml

@@ -24,6 +24,9 @@ name = "factorial"
 [[bench]]
 name = "gcd"
 
+[[bench]]
+name = "roots"
+
 [[bench]]
 harness = false
 name = "shootout-pidigits"

benches/bigint.rs

@@ -343,27 +343,3 @@ fn modpow_even(b: &mut Bencher) {
 
     b.iter(|| base.modpow(&e, &m));
 }
-
-#[bench]
-fn roots_sqrt(b: &mut Bencher) {
-    let mut rng = get_rng();
-    let x = rng.gen_biguint(2048);
-
-    b.iter(|| x.sqrt());
-}
-
-#[bench]
-fn roots_cbrt(b: &mut Bencher) {
-    let mut rng = get_rng();
-    let x = rng.gen_biguint(2048);
-
-    b.iter(|| x.cbrt());
-}
-
-#[bench]
-fn roots_nth_100(b: &mut Bencher) {
-    let mut rng = get_rng();
-    let x = rng.gen_biguint(2048);
-
-    b.iter(|| x.nth_root(100));
-}

benches/roots.rs

@@ -0,0 +1,176 @@
+#![feature(test)]
+#![cfg(feature = "rand")]
+
+extern crate num_bigint;
+extern crate num_traits;
+extern crate rand;
+extern crate test;
+
+use num_bigint::{BigUint, RandBigInt};
+use num_traits::Pow;
+use rand::{SeedableRng, StdRng};
+use test::Bencher;
+
+// The `big64` cases demonstrate the speed of cases where the value
+// can be converted to a `u64` primitive for faster calculation.
+//
+// The `big1k` cases demonstrate those that can convert to `f64` for
+// a better initial guess of the actual value.
+//
+// The `big2k` and `big4k` cases are too big for `f64`, and use a simpler guess.
+
+fn get_rng() -> StdRng {
+    let mut seed = [0; 32];
+    for i in 1..32 {
+        seed[usize::from(i)] = i;
+    }
+    SeedableRng::from_seed(seed)
+}
+
+fn check(x: &BigUint, n: u32) {
+    let root = x.nth_root(n);
+    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);
+    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);
+}
+
+fn bench_sqrt(b: &mut Bencher, bits: usize) {
+    let x = get_rng().gen_biguint(bits);
+    eprintln!("bench_sqrt({})", x);
+
+    check(&x, 2);
+    b.iter(|| x.sqrt());
+}
+
+#[bench]
+fn big64_sqrt(b: &mut Bencher) {
+    bench_sqrt(b, 64);
+}
+
+#[bench]
+fn big1k_sqrt(b: &mut Bencher) {
+    bench_sqrt(b, 1024);
+}
+
+#[bench]
+fn big2k_sqrt(b: &mut Bencher) {
+    bench_sqrt(b, 2048);
+}
+
+#[bench]
+fn big4k_sqrt(b: &mut Bencher) {
+    bench_sqrt(b, 4096);
+}
+
+fn bench_cbrt(b: &mut Bencher, bits: usize) {
+    let x = get_rng().gen_biguint(bits);
+    eprintln!("bench_cbrt({})", x);
+
+    check(&x, 3);
+    b.iter(|| x.cbrt());
+}
+
+#[bench]
+fn big64_cbrt(b: &mut Bencher) {
+    bench_cbrt(b, 64);
+}
+
+#[bench]
+fn big1k_cbrt(b: &mut Bencher) {
+    bench_cbrt(b, 1024);
+}
+
+#[bench]
+fn big2k_cbrt(b: &mut Bencher) {
+    bench_cbrt(b, 2048);
+}
+
+#[bench]
+fn big4k_cbrt(b: &mut Bencher) {
+    bench_cbrt(b, 4096);
+}
+
+fn bench_nth_root(b: &mut Bencher, bits: usize, n: u32) {
+    let x = get_rng().gen_biguint(bits);
+    eprintln!("bench_{}th_root({})", n, x);
+
+    check(&x, n);
+    b.iter(|| x.nth_root(n));
+}
+
+#[bench]
+fn big64_nth_10(b: &mut Bencher) {
+    bench_nth_root(b, 64, 10);
+}
+
+#[bench]
+fn big1k_nth_10(b: &mut Bencher) {
+    bench_nth_root(b, 1024, 10);
+}
+
+#[bench]
+fn big1k_nth_100(b: &mut Bencher) {
+    bench_nth_root(b, 1024, 100);
+}
+
+#[bench]
+fn big1k_nth_1000(b: &mut Bencher) {
+    bench_nth_root(b, 1024, 1000);
+}
+
+#[bench]
+fn big1k_nth_10000(b: &mut Bencher) {
+    bench_nth_root(b, 1024, 10000);
+}
+
+#[bench]
+fn big2k_nth_10(b: &mut Bencher) {
+    bench_nth_root(b, 2048, 10);
+}
+
+#[bench]
+fn big2k_nth_100(b: &mut Bencher) {
+    bench_nth_root(b, 2048, 100);
+}
+
+#[bench]
+fn big2k_nth_1000(b: &mut Bencher) {
+    bench_nth_root(b, 2048, 1000);
+}
+
+#[bench]
+fn big2k_nth_10000(b: &mut Bencher) {
+    bench_nth_root(b, 2048, 10000);
+}
+
+#[bench]
+fn big4k_nth_10(b: &mut Bencher) {
+    bench_nth_root(b, 4096, 10);
+}
+
+#[bench]
+fn big4k_nth_100(b: &mut Bencher) {
+    bench_nth_root(b, 4096, 100);
+}
+
+#[bench]
+fn big4k_nth_1000(b: &mut Bencher) {
+    bench_nth_root(b, 4096, 1000);
+}
+
+#[bench]
+fn big4k_nth_10000(b: &mut Bencher) {
+    bench_nth_root(b, 4096, 10000);
+}