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[PATCH v2 06/12] documentation: Add scheduler/sched-avg.txt

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This doc file has the programs to generate the constants to compute
sched averages.

Signed-off-by: Yuyang Du <yuyang.du@intel.com>
---
 Documentation/scheduler/sched-avg.txt |  137 +++++++++++++++++++++++++++++++++
 1 file changed, 137 insertions(+)
 create mode 100644 Documentation/scheduler/sched-avg.txt

diff --git a/Documentation/scheduler/sched-avg.txt b/Documentation/scheduler/sched-avg.txt
new file mode 100644
index 0000000..ae4132f
--- /dev/null
+++ b/Documentation/scheduler/sched-avg.txt
@@ -0,0 +1,137 @@
+The following programs are used to generate the constants for
+computing sched averages.
+
+==============================================================
+		C program (compile with -lm)
+==============================================================
+
+#include <math.h>
+#include <stdio.h>
+
+#define HALFLIFE 32
+#define SHIFT 32
+
+double y;
+
+void calc_decay_inv_multiply() {
+	int i;
+	unsigned int x;
+
+	printf("static const u32 __decay_inv_multiply_N[] = {");
+	for(i = 0; i < HALFLIFE; i++) {
+		x = ((1UL<<32)-1)*pow(y, i);
+
+		if (i % 6 == 0) printf("\n\t");
+		printf("0x%8x, ", x);
+	}
+	printf("\n};\n\n");
+}
+
+int sum = 1024;
+void calc_accumulated_sum() {
+	int i;
+
+	printf("static const u32 __accumulated_sum_N[] = {\n\t    0,");
+	for(i = 1; i <= HALFLIFE; i++) {
+		if (i == 1)
+			sum *= y;
+		else
+			sum = sum*y + 1024*y;
+
+		if (i % 11 == 0) printf("\n\t");
+		printf("%5d,", sum);
+	}
+	printf("\n};\n\n");
+}
+
+int n = 1;
+/* first period */
+long max = 1024;
+
+void calc_converged_max() {
+	long last = 0, y_inv = ((1UL<<32)-1)*y;
+
+	for (; ; n++) {
+		if (n > 1)
+			max = ((max*y_inv)>>SHIFT) + 1024;
+			/*
+			 * This is the same as:
+			 * max = max*y + 1024;
+			 */
+
+		if (last == max)
+			break;
+
+		last = max;
+	}
+	n--;
+	printf("#define SCHED_AVG_HALFLIFE %d\n", HALFLIFE);
+	printf("#define SCHED_AVG_MAX %ld\n", max);
+	printf("#define SCHED_AVG_MAX_N %d\n\n", n);
+}
+
+void calc_accumulated_sum_32() {
+	int i, x = sum;
+
+	printf("static const u32 __accumulated_sum_N32[] = {\n\t     0,");
+	for(i = 1; i <= n/HALFLIFE+1; i++) {
+		if (i > 1)
+			x = x/2 + sum;
+
+		if (i % 6 == 0) printf("\n\t");
+		printf("%6d,", x);
+	}
+	printf("\n};\n\n");
+}
+
+void main() {
+	y = pow(0.5, 1/(double)HALFLIFE);
+
+	calc_decay_inv_multiply();
+	calc_accumulated_sum();
+	calc_converged_max();
+	calc_accumulated_sum_32();
+}
+
+==============================================================
+		Python script if you speak snake
+==============================================================
+
+#!/usr/bin/env python
+
+print " #:     yN_inv   yN_sum"
+print "-----------------------"
+y = (0.5)**(1/32.0)
+x = 2**32
+xx = 1024
+for i in range(0, 32):
+	if i == 0:
+		x = x-1
+		xx = xx*y
+	else:
+		x = x*y
+		xx = int(xx*y + 1024*y)
+	print "%2d: %#x %8d" % (i, int(x), int(xx))
+
+print
+print " #:  sum_N32"
+print "------------"
+xxx = xx
+for i in range(0, 11):
+	if i > 0:
+		xxx = xxx/2 + xx
+	print "%2d: %8d" % (i, xxx)
+
+print
+print "  n:     max"
+print "------------"
+xxxx = 1024
+old = 0
+i = 2
+while (1):
+	xxxx = int(xxxx*y + 1024)
+	if old == xxxx:
+		break
+	i = i+1
+	old = xxxx
+print "%3d: %7d" % (i-1, xxxx)
-- 
1.7.9.5

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[PATCH v2 00/12] sched/fair: Optimize and clean up sched averages Yuyang Du <yuyang.du@intel.com> - 2016-05-03 07:40 +0200
  [PATCH v2 03/12] sched/fair: Change the variable to hold the number of periods to 32bit integer Yuyang Du <yuyang.du@intel.com> - 2016-05-03 07:40 +0200
    Re: [PATCH v2 03/12] sched/fair: Change the variable to hold the  number of periods to 32bit integer Peter Zijlstra <peterz@infradead.org> - 2016-05-03 10:50 +0200
  [PATCH v2 09/12] sched/fair: Add introduction to the sched average metrics Yuyang Du <yuyang.du@intel.com> - 2016-05-03 07:40 +0200
  [PATCH v2 08/12] sched/fair: Remove SCHED_LOAD_SHIFT and SCHED_LOAD_SCALE Yuyang Du <yuyang.du@intel.com> - 2016-05-03 07:40 +0200
  [PATCH v2 06/12] documentation: Add scheduler/sched-avg.txt Yuyang Du <yuyang.du@intel.com> - 2016-05-03 07:40 +0200
    Re: [PATCH v2 06/12] documentation: Add scheduler/sched-avg.txt Peter Zijlstra <peterz@infradead.org> - 2016-05-03 11:00 +0200

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