Improve the performance of binary_search by reducing the number of

unpredictable conditional branches in the loop. In addition improve the
benchmarks to test performance in l1, l2 and l3 caches on sorted arrays
with or without dups.

Before:

```
test slice::binary_search_l1                               ... bench:  48 ns/iter (+/- 1)
test slice::binary_search_l2                               ... bench:  63 ns/iter (+/- 0)
test slice::binary_search_l3                               ... bench: 152 ns/iter (+/- 12)
test slice::binary_search_l1_with_dups                     ... bench:  36 ns/iter (+/- 0)
test slice::binary_search_l2_with_dups                     ... bench:  64 ns/iter (+/- 1)
test slice::binary_search_l3_with_dups                     ... bench: 153 ns/iter (+/- 6)
```

After:

```
test slice::binary_search_l1                               ... bench:  15 ns/iter (+/- 0)
test slice::binary_search_l2                               ... bench:  23 ns/iter (+/- 0)
test slice::binary_search_l3                               ... bench: 100 ns/iter (+/- 17)
test slice::binary_search_l1_with_dups                     ... bench:  15 ns/iter (+/- 0)
test slice::binary_search_l2_with_dups                     ... bench:  23 ns/iter (+/- 0)
test slice::binary_search_l3_with_dups                     ... bench:  98 ns/iter (+/- 14)
```

Author: Alkis Evlogimenos

src/libcore/benches/lib.rs

@@ -20,6 +20,6 @@ extern crate test;
 mod any;
 mod hash;
 mod iter;
-mod mem;
 mod num;
 mod ops;
+mod slice;

src/libcore/benches/slice.rs

@@ -0,0 +1,67 @@
+// Copyright 2017 The Rust Project Developers. See the COPYRIGHT
+// file at the top-level directory of this distribution and at
+// http://rust-lang.org/COPYRIGHT.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+use test::black_box;
+use test::Bencher;
+
+enum Cache {
+    L1,
+    L2,
+    L3,
+}
+
+fn binary_search<F>(b: &mut Bencher, cache: Cache, mapper: F)
+    where F: Fn(usize) -> usize
+{
+    let size = match cache {
+        Cache::L1 => 1000, // 8kb
+        Cache::L2 => 10_000, // 80kb
+        Cache::L3 => 1_000_000, // 8Mb
+    };
+    let v = (0..size).map(&mapper).collect::<Vec<_>>();
+    let mut r = 0usize;
+    b.iter(move || {
+        // LCG constants from https://en.wikipedia.org/wiki/Numerical_Recipes.
+        r = r.wrapping_mul(1664525).wrapping_add(1013904223);
+        // Lookup the whole range to get 50% hits and 50% misses.
+        let i = mapper(r % size);
+        black_box(v.binary_search(&i).is_ok());
+    })
+}
+
+#[bench]
+fn binary_search_l1(b: &mut Bencher) {
+    binary_search(b, Cache::L1, |i| i * 2);
+}
+
+#[bench]
+fn binary_search_l2(b: &mut Bencher) {
+    binary_search(b, Cache::L2, |i| i * 2);
+}
+
+#[bench]
+fn binary_search_l3(b: &mut Bencher) {
+    binary_search(b, Cache::L3, |i| i * 2);
+}
+
+#[bench]
+fn binary_search_l1_with_dups(b: &mut Bencher) {
+    binary_search(b, Cache::L1, |i| i / 16 * 16);
+}
+
+#[bench]
+fn binary_search_l2_with_dups(b: &mut Bencher) {
+    binary_search(b, Cache::L2, |i| i / 16 * 16);
+}
+
+#[bench]
+fn binary_search_l3_with_dups(b: &mut Bencher) {
+    binary_search(b, Cache::L3, |i| i / 16 * 16);
+}

src/libcore/slice/mod.rs

@@ -394,23 +394,25 @@ impl<T> SliceExt for [T] {
     fn binary_search_by<'a, F>(&'a self, mut f: F) -> Result<usize, usize>
         where F: FnMut(&'a T) -> Ordering
     {
-        let mut base = 0usize;
-        let mut s = self;
-
-        loop {
-            let (head, tail) = s.split_at(s.len() >> 1);
-            if tail.is_empty() {
-                return Err(base)
-            }
-            match f(&tail[0]) {
-                Less => {
-                    base += head.len() + 1;
-                    s = &tail[1..];
-                }
-                Greater => s = head,
-                Equal => return Ok(base + head.len()),
-            }
+        let s = self;
+        let mut size = s.len();
+        if size == 0 {
+            return Err(0);
         }
+        let mut base = 0usize;
+        while size > 1 {
+            let half = size / 2;
+            let mid = base + half;
+            // mid is always in [0, size).
+            // mid >= 0: by definition
+            // mid < size: mid = size / 2 + size / 4 + size / 8 ...
+            let cmp = f(unsafe { s.get_unchecked(mid) });
+            base = if cmp == Greater { base } else { mid };
+            size -= half;
+        }
+        // base is always in [0, size) because base <= mid.
+        let cmp = f(unsafe { s.get_unchecked(base) });
+        if cmp == Equal { Ok(base) } else { Err(base + (cmp == Less) as usize) }
     }
 
     #[inline]

src/libcore/tests/slice.rs

@@ -15,22 +15,59 @@ use rand::{Rng, XorShiftRng};
 
 #[test]
 fn test_binary_search() {
+    let b: [i32; 0] = [];
+    assert_eq!(b.binary_search(&5), Err(0));
+
+    let b = [4];
+    assert_eq!(b.binary_search(&3), Err(0));
+    assert_eq!(b.binary_search(&4), Ok(0));
+    assert_eq!(b.binary_search(&5), Err(1));
+
     let b = [1, 2, 4, 6, 8, 9];
-    assert!(b.binary_search_by(|v| v.cmp(&6)) == Ok(3));
-    assert!(b.binary_search_by(|v| v.cmp(&5)) == Err(3));
-    let b = [1, 2, 4, 6, 7, 8, 9];
-    assert!(b.binary_search_by(|v| v.cmp(&6)) == Ok(3));
-    assert!(b.binary_search_by(|v| v.cmp(&5)) == Err(3));
-    let b = [1, 2, 4, 6, 8, 9];
-    assert!(b.binary_search_by(|v| v.cmp(&8)) == Ok(4));
-    assert!(b.binary_search_by(|v| v.cmp(&7)) == Err(4));
+    assert_eq!(b.binary_search(&5), Err(3));
+    assert_eq!(b.binary_search(&6), Ok(3));
+    assert_eq!(b.binary_search(&7), Err(4));
+    assert_eq!(b.binary_search(&8), Ok(4));
+
+    let b = [1, 2, 4, 5, 6, 8];
+    assert_eq!(b.binary_search(&9), Err(6));
+
     let b = [1, 2, 4, 6, 7, 8, 9];
-    assert!(b.binary_search_by(|v| v.cmp(&8)) == Ok(5));
+    assert_eq!(b.binary_search(&6), Ok(3));
+    assert_eq!(b.binary_search(&5), Err(3));
+    assert_eq!(b.binary_search(&8), Ok(5));
+
     let b = [1, 2, 4, 5, 6, 8, 9];
-    assert!(b.binary_search_by(|v| v.cmp(&7)) == Err(5));
-    assert!(b.binary_search_by(|v| v.cmp(&0)) == Err(0));
-    let b = [1, 2, 4, 5, 6, 8];
-    assert!(b.binary_search_by(|v| v.cmp(&9)) == Err(6));
+    assert_eq!(b.binary_search(&7), Err(5));
+    assert_eq!(b.binary_search(&0), Err(0));
+
+    let b = [1, 3, 3, 3, 7];
+    assert_eq!(b.binary_search(&0), Err(0));
+    assert_eq!(b.binary_search(&1), Ok(0));
+    assert_eq!(b.binary_search(&2), Err(1));
+    assert!(match b.binary_search(&3) { Ok(1...3) => true, _ => false });
+    assert!(match b.binary_search(&3) { Ok(1...3) => true, _ => false });
+    assert_eq!(b.binary_search(&4), Err(4));
+    assert_eq!(b.binary_search(&5), Err(4));
+    assert_eq!(b.binary_search(&6), Err(4));
+    assert_eq!(b.binary_search(&7), Ok(4));
+    assert_eq!(b.binary_search(&8), Err(5));
+}
+
+#[test]
+// Test implementation specific behavior when finding equivalent elements.
+// It is ok to break this test but when you do a crater run is highly advisable.
+fn test_binary_search_implementation_details() {
+    let b = [1, 1, 2, 2, 3, 3, 3];
+    assert_eq!(b.binary_search(&1), Ok(1));
+    assert_eq!(b.binary_search(&2), Ok(3));
+    assert_eq!(b.binary_search(&3), Ok(6));
+    let b = [1, 1, 1, 1, 1, 3, 3, 3, 3];
+    assert_eq!(b.binary_search(&1), Ok(4));
+    assert_eq!(b.binary_search(&3), Ok(8));
+    let b = [1, 1, 1, 1, 3, 3, 3, 3, 3];
+    assert_eq!(b.binary_search(&1), Ok(3));
+    assert_eq!(b.binary_search(&3), Ok(8));
 }
 
 #[test]