design: add initial conditions section to GC pacer redesign
I realized I neglected to talk about initial conditions, even though all
the simulations clearly set *something*.
For golang/go#44167.
Change-Id: Ia1727d5c068847e9192bf87bc1b6a5f0bb832303
Reviewed-on: https://go-review.googlesource.com/c/proposal/+/295509
Reviewed-by: Michael Pratt <mpratt@google.com>
diff --git a/design/44167-gc-pacer-redesign.md b/design/44167-gc-pacer-redesign.md
index 8bb27f9..23b4242 100644
--- a/design/44167-gc-pacer-redesign.md
+++ b/design/44167-gc-pacer-redesign.md
@@ -565,6 +565,27 @@
It's not important to put these limits in the rest of the pacer because it no
longer tries to compute the trigger point ahead of time.
+### Initial conditions
+
+Like today, the pacer has to start somewhere for the first GC.
+I propose we carry forward what we already do today: set the trigger point at
+7/8ths of the first heap goal, which will always be the minimum heap size.
+If GC 1 is the first GC, then in terms of the math above, we choose to avoid
+defining , and instead directly define
+
+
+
+The definition of  is necessary for the GC assist
+pacer.
+
+Furthermore, the PI controller's state will be initialized to zero otherwise.
+
+These choices are somewhat arbitrary, but the fact is that the pacer has no
+knowledge of the progam's past behavior for the first GC.
+Naturally the behavior of the GC will always be a little odd, but it should, in
+general, stabilize quite quickly (note that this is the case in each scenario
+for the [simulations](#simulations).
+
## A note about CPU utilization
This document uses the term "GC CPU utilization" quite frequently, but so far
@@ -591,7 +612,7 @@
The latter is computed directly, but is just the difference between the start
and end time in the critical section; it does not try to account for context
switches forced by the underlying system, or anything like that.
-Now take this value we just computed and divide it by .
+Now take this value we just computed and divide it by .
That's our GC CPU utilization.
This approximation is mostly accurate in the common case, but is prone to skew
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diff --git a/design/44167/gc-pacer-redesign.src.md b/design/44167/gc-pacer-redesign.src.md
index 3268a56..1420b34 100644
--- a/design/44167/gc-pacer-redesign.src.md
+++ b/design/44167/gc-pacer-redesign.src.md
@@ -573,6 +573,32 @@
It's not important to put these limits in the rest of the pacer because it no
longer tries to compute the trigger point ahead of time.
+### Initial conditions
+
+Like today, the pacer has to start somewhere for the first GC.
+I propose we carry forward what we already do today: set the trigger point at
+7/8ths of the first heap goal, which will always be the minimum heap size.
+If GC 1 is the first GC, then in terms of the math above, we choose to avoid
+defining `$M_0$`, and instead directly define
+
+```render-latex
+\begin{aligned}
+N_1 & = \textrm{minimum heap size} \\
+T_1 & = \frac{7}{8} N_1 \\
+P_0 & = 0
+\end{aligned}
+```
+
+The definition of `$P_0$` is necessary for the GC assist pacer.
+
+Furthermore, the PI controller's state will be initialized to zero otherwise.
+
+These choices are somewhat arbitrary, but the fact is that the pacer has no
+knowledge of the progam's past behavior for the first GC.
+Naturally the behavior of the GC will always be a little odd, but it should, in
+general, stabilize quite quickly (note that this is the case in each scenario
+for the [simulations](#simulations).
+
## A note about CPU utilization
This document uses the term "GC CPU utilization" quite frequently, but so far
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