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 <davidlohr.bueso@hp.com>
Reviewed-by: Jonathan Gonzalez <jgonzlez@linets.cl>
Tested-by: Jonathan Gonzalez <jgonzlez@linets.cl>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
diff --git a/lib/int_sqrt.c b/lib/int_sqrt.c
index fc2eeb7..1ef4cc3 100644
--- a/lib/int_sqrt.c
+++ b/lib/int_sqrt.c
@@ -1,3 +1,9 @@
+/*
+ * Copyright (C) 2013 Davidlohr Bueso <davidlohr.bueso@hp.com>
+ *
+ * Based on the shift-and-subtract algorithm for computing integer
+ * square root from Guy L. Steele.
+ */
#include <linux/kernel.h>
#include <linux/export.h>
@@ -10,23 +16,23 @@
*/
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);
