Auto merge of rust-lang#85406 - VillSnow:integrate_binary_search, r=JohnTitor

Integrate binary search codes of binary_search_by and partition_point

For now partition_point has own binary search code piece.
It is because binary_search_by had called the comparer more times and the author (=me) wanted to avoid it.

However, now binary_search_by uses the comparer minimum times. (rust-lang#74024)
So it's time to integrate them.

The appearance of the codes are a bit different but both use completely same logic.

Author: bors

core/src/slice/mod.rs

@@ -3468,27 +3468,7 @@ impl<T> [T] {
     where
         P: FnMut(&T) -> bool,
     {
-        let mut left = 0;
-        let mut right = self.len();
-
-        while left != right {
-            let mid = left + (right - left) / 2;
-            // SAFETY: When `left < right`, `left <= mid < right`.
-            // Therefore `left` always increases and `right` always decreases,
-            // and either of them is selected. In both cases `left <= right` is
-            // satisfied. Therefore if `left < right` in a step, `left <= right`
-            // is satisfied in the next step. Therefore as long as `left != right`,
-            // `0 <= left < right <= len` is satisfied and if this case
-            // `0 <= mid < len` is satisfied too.
-            let value = unsafe { self.get_unchecked(mid) };
-            if pred(value) {
-                left = mid + 1;
-            } else {
-                right = mid;
-            }
-        }
-
-        left
+        self.binary_search_by(|x| if pred(x) { Less } else { Greater }).unwrap_or_else(|i| i)
     }
 }