From c8bfa5bda1270e2850b86a4e93cf1a21489461ec Mon Sep 17 00:00:00 2001
From: Georgiana Mania <mania@dkrz.de>
Date: Mon, 27 May 2024 17:12:21 +0200
Subject: [PATCH] add slide 26
---
lectures/parallelism/slides.qmd | 63 +++++++++++++++++++++++++++++++--
1 file changed, 61 insertions(+), 2 deletions(-)
diff --git a/lectures/parallelism/slides.qmd b/lectures/parallelism/slides.qmd
index 37ce200..5747f35 100644
--- a/lectures/parallelism/slides.qmd
+++ b/lectures/parallelism/slides.qmd
@@ -217,8 +217,11 @@ Wikipedia
## Types of parallelism
-* Data-level parallelism - what we've been discussing
-* Task-level parallelism - Example: Atmosphere ocean coupling
+
+* Data-level parallelism
+ * what we've been discussing
+* Task-level parallelism
+ * Example: Atmosphere ocean coupling
## Precondition for parallel execution
@@ -331,6 +334,62 @@ d = c - b; // S2
```
:::
+## Bernstein's parallelism conditions {.alignleft}
+
+:::{.fragment .semi-fade-out}
+```c++
+c = a + b; // S1
+d = a - b; // S2
+```
+:::
+
+
+:::{.fragment}
+Replace `a` with `c` in statement 2
+```c++
+c = a + b; // S1
+d = c - b; // S2
+```
+:::
+
+:::{.smaller}
+
+:::: {.columns}
+
+::: {.column width="50%"}
+
+:::{.fragment}
+
+Read and write sets for S1 and S2:
+$$
+R_1 = \{a,b\} ; W_1 = \{c\} \\
+R_2 = \{c,b\} ; W_2 = \{d\} \\
+$$
+
+:::
+:::
+
+::: {.column width="50%"}
+
+:::{.fragment}
+Bernstein's conditions:
+
+$$
+R_1 \cap W_2 = \emptyset \\
+W_1 \cap R_2 = \{c\} \\
+W_1 \cap W_2 = \emptyset
+$$
+:::
+
+:::
+:::
+::::
+
+:::{.fragment}
+S1 and S2 can NOT be executed in parallel!
+:::
+
+
## Best practices
* Parallelisation should not change the results! Exceptions to be discussed next week!
--
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