lib/int_sqrt.c: optimize square root algorithm

Optimize the current version of the shift-and-subtract (hardware)
algorithm, described by John von Newmann[1] and Guy L Steele.

Iterating 1,000,000 times, perf shows for the current version:

Performance counter stats for './sqrt-curr' (10 runs):

27.170996 task-clock # 0.979 CPUs utilized ( +- 3.19% )
3 context-switches # 0.103 K/sec ( +- 4.76% )
0 cpu-migrations # 0.004 K/sec ( +-100.00% )
104 page-faults # 0.004 M/sec ( +- 0.16% )
64,921,199 cycles # 2.389 GHz ( +- 0.03% )
28,967,789 stalled-cycles-frontend # 44.62% frontend cycles idle ( +- 0.18% )
<not supported> stalled-cycles-backend
104,502,623 instructions # 1.61 insns per cycle
# 0.28 stalled cycles per insn ( +- 0.00% )
34,088,368 branches # 1254.587 M/sec ( +- 0.00% )
4,901 branch-misses # 0.01% of all branches ( +- 1.32% )

0.027763015 seconds time elapsed ( +- 3.22% )

And for the new version:

Performance counter stats for './sqrt-new' (10 runs):

0.496869 task-clock # 0.519 CPUs utilized ( +- 2.38% )
0 context-switches # 0.000 K/sec
0 cpu-migrations # 0.403 K/sec ( +-100.00% )
104 page-faults # 0.209 M/sec ( +- 0.15% )
590,760 cycles # 1.189 GHz ( +- 2.35% )
395,053 stalled-cycles-frontend # 66.87% frontend cycles idle ( +- 3.67% )
<not supported> stalled-cycles-backend
398,963 instructions # 0.68 insns per cycle
# 0.99 stalled cycles per insn ( +- 0.39% )
70,228 branches # 141.341 M/sec ( +- 0.36% )
3,364 branch-misses # 4.79% of all branches ( +- 5.45% )

0.000957440 seconds time elapsed ( +- 2.42% )

Furthermore, this saves space in instruction text:

text data bss dec hex filename
111 0 0 111 6f lib/int_sqrt-baseline.o
89 0 0 89 59 lib/int_sqrt.o

[1] http://en.wikipedia.org/wiki/First_Draft_of_a_Report_on_the_EDVAC

Signed-off-by: Davidlohr Bueso <[e-mail]>
Reviewed-by: Jonathan Gonzalez <[e-mail]>
Tested-by: Jonathan Gonzalez <[e-mail]>
Signed-off-by: Andrew Morton <[e-mail]>
Signed-off-by: Linus Torvalds <[e-mail]>

lib/int_sqrt.c

···
+/*
+ * Copyright (C) 2013 Davidlohr Bueso <[e-mail]>
+ *
+ *  Based on the shift-and-subtract algorithm for computing integer
+ *  square root from Guy L. Steele.
+ */
 
 #include <linux/kernel.h>
 #include <linux/export.h>
···
  */
 unsigned long int_sqrt(unsigned long x)
 {
-	unsigned long op, res, one;
+	unsigned long b, m, y = 0;
 
-	op = x;
-	res = 0;
+	if (x <= 1)
+		return x;
 
-	one = 1UL << (BITS_PER_LONG - 2);
-	while (one > op)
-		one >>= 2;
+	m = 1UL << (BITS_PER_LONG - 2);
+	while (m != 0) {
+		b = y + m;
+		y >>= 1;
 
-	while (one != 0) {
-		if (op >= res + one) {
-			op = op - (res + one);
-			res = res +  2 * one;
+		if (x >= b) {
+			x -= b;
+			y += m;
 		}
-		res /= 2;
-		one /= 4;
+		m >>= 2;
 	}
-	return res;
+
+	return y;
 }
 EXPORT_SYMBOL(int_sqrt);