sched: fix/optimise calculation of weight-inverse

If the inverse loadweight should be zero, function "calc_delta_mine" calculates the inverse of "lw->weight" (in 32bit integer ops).

This calculation is actually a little bit impure (because it is inverting something around "lw-weight"+1), especially when "lw->weight" becomes smaller. (This could explain some aritmetical issues for small shares...)

The correct inverse would be 1/lw->weight multiplied by "WMULT_CONST" for fixcomma-scaling it into integers. (So WMULT_CONST/lw->weight ...)

For safety it is also important to check if division by zero could happen...

The old, impure algorithm took two divisions for inverting lw->weight, the new, more exact one only takes one and an additional unlikely-if.

---
 kernel/sched.c |   12 +++++++++---
 1 files changed, 9 insertions(+), 3 deletions(-)

index 312f8b9..bb55996 100644
@@ -1307,15 +1307,21 @@ calc_delta_mine(unsigned long delta_exec,

unsigned long weight,

 {
     u64 tmp;

+ tmp = (u64)delta_exec * weight;
+
+ // actually we would have to trap - division by zero - but we stay
and pretend the limit of the operation...
+ if (unlikely(lw->weight == 0)) {
+ if (unlikely(tmp == ((u64)0))) return (unsigned long)0;
+ else return (unsigned long)LONG_MAX;
+ }
+

     if (!lw->inv_weight) {
         if (BITS_PER_LONG > 32 && unlikely(lw->weight >= WMULT_CONST))
             lw->inv_weight = 1;
         else
-            lw->inv_weight = 1 + (WMULT_CONST-lw->weight/2)
-                / (lw->weight+1);
+            lw->inv_weight = WMULT_CONST / lw->weight;
     }

-    tmp = (u64)delta_exec * weight;
     /*
      * Check whether we'd overflow the 64-bit multiplication:
      */

1.7.3.4



--
Dipl.-Inf. Stephan Bärwolf
Ilmenau University of Technology, Integrated Communication Systems Group
Phone: +49 (0)3677 69 2821,  FAX: +49 (0)3677 69 1614
Email: [email protected],
Web: http://www.tu-ilmenau.de/iks

From: Stephan Baerwolf <[email protected]>
Date: Wed, 11 May 2011 17:36:26 +0200
Subject: [PATCH] sched: fix/optimise calculation of weight-inverse

If the inverse loadweight should be zero, function "calc_delta_mine" calculates the inverse of "lw->weight" (in 32bit integer ops).

This calculation is actually a little bit impure (because it is inverting something around "lw-weight"+1), especially when "lw->weight" becomes smaller. (This could explain some aritmetical issues for small shares...)

The correct inverse would be 1/lw->weight multiplied by "WMULT_CONST" for fixcomma-scaling it into integers. (So WMULT_CONST/lw->weight ...)

For safety it is also important to check if division by zero could happen...

The old, impure algorithm took two divisions for inverting lw->weight, the new, more exact one only takes one and an additional unlikely-if.

---
 kernel/sched.c |   12 +++++++++---
 1 files changed, 9 insertions(+), 3 deletions(-)

index 312f8b9..bb55996 100644
@@ -1307,15 +1307,21 @@ calc_delta_mine(unsigned long delta_exec, unsigned long weight,
 {
 	u64 tmp;
 
+	tmp = (u64)delta_exec * weight;
+
+	// actually we would have to trap - division by zero - but we stay and pretend the limit of the operation...
+	if (unlikely(lw->weight == 0)) {
+		if (unlikely(tmp == ((u64)0))) return (unsigned long)0;
+		else return (unsigned long)LONG_MAX;
+	}
+
 	if (!lw->inv_weight) {
 		if (BITS_PER_LONG > 32 && unlikely(lw->weight >= WMULT_CONST))
 			lw->inv_weight = 1;
 		else
-			lw->inv_weight = 1 + (WMULT_CONST-lw->weight/2)
-				/ (lw->weight+1);
+			lw->inv_weight = WMULT_CONST / lw->weight;
 	}
 
-	tmp = (u64)delta_exec * weight;
 	/*
 	 * Check whether we'd overflow the 64-bit multiplication:
 	 */

1.7.3.4

I agree that moving this multiplication early in the sequence is better for micro-performance regardless of the lw->weight optimization you do: it can be executed in parallel.

Thanks,

Ingo

I suspect I might be the idiot,

I think what we wanted to do was minimize the error:
err = weight - inv*WMULT_CONST

by adding another term. But we could well have simply made a mess of it instead.

Hi all,
thanks for your fast response.
I think what you mean is:

err = | WMULT_CONST - inv*weight | --> min

right?

But the following table(s) shows the difference in the inverses:
(assuming WMULT_CONST = 2**32 as on x64)

weight oldway
inv_weigth new inv_weight

1 2147483649 (=1+2**31)
4294967295 [=(2**32)-1]
2
1431655766 2147483647
3 (= WEIGHT_IDLEPRIO) 1073741824 1431655765
15 (= nice 19)
268435456 286331153
1024 (=nice 0)
4190212 4194304
...
...
88761 (=nice -20)
48387 48388

----

weight err
oldway err newway

1 2147483647 (=2**31 - 1)
1
2 1431655764

                        2

3 (= WEIGHT_IDLEPRIO) 1073741824 1
15 (= nice 19) 268435456 1
1024 (=nice 0)
4190208 0
...
...
88761 (=nice -20) 88789

                                  28

Thus the "err" of the old way can become very large (up to about 2^31 ). And of course the new error increases with increasing weight, it is still alway
smaller than the oldway err (because oldway inv converts to newway inv)...

regards Stephan

--
Dipl.-Inf. Stephan Bärwolf
Ilmenau University of Technology, Integrated Communication Systems Group
Phone: +49 (0)3677 69 2821, FAX: +49 (0)3677 69 1614
Email: [email protected],
Web: http://www.tu-ilmenau.de/iks

Your table got white-space mungled, but I'll take your word for it. I'll give the patch a spin tomorrow (without the weight==0 bits), since by brain officially gave up for today ;-)