lib/bsearch.c: micro-optimize pivot position calculation

There is a slightly faster way (in terms of the number of instructions
being used) to calculate the position of a middle element, preserving
integer overflow safeness.

./scripts/bloat-o-meter lib/bsearch.o.old lib/bsearch.o.new
add/remove: 0/0 grow/shrink: 0/1 up/down: 0/-24 (-24)
function                                     old     new   delta
bsearch                                      122      98     -24

TEST

INT array of size 100001, elements [0..100000]. gcc 7.1, Os, x86_64.

a) bsearch() of existing key "100001 - 2":

BASE
====

$ perf stat ./a.out

 Performance counter stats for './a.out':

        619.445196      task-clock:u (msec)       #    0.999 CPUs utilized
                 0      context-switches:u        #    0.000 K/sec
                 0      cpu-migrations:u          #    0.000 K/sec
               133      page-faults:u             #    0.215 K/sec
     1,949,517,279      cycles:u                  #    3.147 GHz                      (83.06%)
       181,017,938      stalled-cycles-frontend:u #    9.29% frontend cycles idle     (83.05%)
        82,959,265      stalled-cycles-backend:u  #    4.26% backend cycles idle      (67.02%)
     4,355,706,383      instructions:u            #    2.23  insn per cycle
                                                  #    0.04  stalled cycles per insn  (83.54%)
     1,051,539,242      branches:u                # 1697.550 M/sec                    (83.54%)
        15,263,381      branch-misses:u           #    1.45% of all branches          (83.43%)

       0.620082548 seconds time elapsed

PATCHED
=======

$ perf stat ./a.out

 Performance counter stats for './a.out':

        475.097316      task-clock:u (msec)       #    0.999 CPUs utilized
                 0      context-switches:u        #    0.000 K/sec
                 0      cpu-migrations:u          #    0.000 K/sec
               135      page-faults:u             #    0.284 K/sec
     1,487,467,717      cycles:u                  #    3.131 GHz                      (82.95%)
       186,537,162      stalled-cycles-frontend:u #   12.54% frontend cycles idle     (82.93%)
        28,797,869      stalled-cycles-backend:u  #    1.94% backend cycles idle      (67.10%)
     3,807,564,203      instructions:u            #    2.56  insn per cycle
                                                  #    0.05  stalled cycles per insn  (83.57%)
     1,049,344,291      branches:u                # 2208.693 M/sec                    (83.60%)
             5,485      branch-misses:u           #    0.00% of all branches          (83.58%)

       0.475760235 seconds time elapsed

b) bsearch() of un-existing key "100001 + 2":

BASE
====

$ perf stat ./a.out

 Performance counter stats for './a.out':

        499.244480      task-clock:u (msec)       #    0.999 CPUs utilized
                 0      context-switches:u        #    0.000 K/sec
                 0      cpu-migrations:u          #    0.000 K/sec
               132      page-faults:u             #    0.264 K/sec
     1,571,194,855      cycles:u                  #    3.147 GHz                      (83.18%)
        13,450,980      stalled-cycles-frontend:u #    0.86% frontend cycles idle     (83.18%)
        21,256,072      stalled-cycles-backend:u  #    1.35% backend cycles idle      (66.78%)
     4,171,197,909      instructions:u            #    2.65  insn per cycle
                                                  #    0.01  stalled cycles per insn  (83.68%)
     1,009,175,281      branches:u                # 2021.405 M/sec                    (83.79%)
             3,122      branch-misses:u           #    0.00% of all branches          (83.37%)

       0.499871144 seconds time elapsed

PATCHED
=======

$ perf stat ./a.out

 Performance counter stats for './a.out':

        399.023499      task-clock:u (msec)       #    0.998 CPUs utilized
                 0      context-switches:u        #    0.000 K/sec
                 0      cpu-migrations:u          #    0.000 K/sec
               134      page-faults:u             #    0.336 K/sec
     1,245,793,991      cycles:u                  #    3.122 GHz                      (83.39%)
        11,529,273      stalled-cycles-frontend:u #    0.93% frontend cycles idle     (83.46%)
        12,116,311      stalled-cycles-backend:u  #    0.97% backend cycles idle      (66.92%)
     3,679,710,005      instructions:u            #    2.95  insn per cycle
                                                  #    0.00  stalled cycles per insn  (83.47%)
     1,009,792,625      branches:u                # 2530.660 M/sec                    (83.46%)
             2,590      branch-misses:u           #    0.00% of all branches          (83.12%)

       0.399733539 seconds time elapsed

Link: http://lkml.kernel.org/r/20170607150457.5905-1-sergey.senozhatsky@gmail.com
Signed-off-by: Sergey Senozhatsky <sergey.senozhatsky@gmail.com>
Cc: Peter Zijlstra <peterz@infradead.org>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

lib/bsearch.c

@@ -33,19 +33,21 @@
 void *bsearch(const void *key, const void *base, size_t num, size_t size,
 	      int (*cmp)(const void *key, const void *elt))
 {
-	size_t start = 0, end = num;
+	const char *pivot;
 	int result;
 
-	while (start < end) {
-		size_t mid = start + (end - start) / 2;
+	while (num > 0) {
+		pivot = base + (num >> 1) * size;
+		result = cmp(key, pivot);
 
-		result = cmp(key, base + mid * size);
-		if (result < 0)
-			end = mid;
-		else if (result > 0)
-			start = mid + 1;
-		else
-			return (void *)base + mid * size;
+		if (result == 0)
+			return (void *)pivot;
+
+		if (result > 0) {
+			base = pivot + size;
+			num--;
+		}
+		num >>= 1;
 	}
 
 	return NULL;