From 5adda84099fc337424be73c71874473e577ec300 Mon Sep 17 00:00:00 2001
From: Chao Zhan <chao.zhan@fu-berlin.de>
Date: Wed, 14 Jun 2023 19:53:29 +0200
Subject: [PATCH] add amdahl's law exercises

---
 slides/images/execution-model.png | Bin 0 -> 9891 bytes
 slides/pages/recap.md             |  44 ++++++++++++++++++++++++++++--
 2 files changed, 42 insertions(+), 2 deletions(-)
 create mode 100644 slides/images/execution-model.png

diff --git a/slides/images/execution-model.png b/slides/images/execution-model.png
new file mode 100644
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diff --git a/slides/pages/recap.md b/slides/pages/recap.md
index 12fa0b6..8d6a926 100644
--- a/slides/pages/recap.md
+++ b/slides/pages/recap.md
@@ -155,10 +155,10 @@ title: Recap IV
 </div>
 
 ---
-title: Recap III
+title: Recap IV
 ---
 
-### Amdahl's Law II
+### Amdahl's Law (cont.)
 
 **What happens when $n \rightarrow \infty$?**
 
@@ -191,3 +191,43 @@ title: Recap III
 
 </v-click>
 
+
+---
+title: Recap V
+---
+
+### Amdahl's Law - Exercise 1
+
+How is **system performance** altered when **some component** is changed?
+
+
+Program execution time is made up of **75% CPU time** and **25% I/O time**. Which is the better enhancement:
+
+- a) Increasing  the CPU speed by 50% or
+- b) Reducing the I/O time by 50%? 
+
+<div class="container flex justify-center mt-5">
+    <img src="/images/execution-model.png" class="block w-lg"/>
+</div>
+
+**Hint:** Use Amdahl's Law and derive the speedup for each case.
+
+
+---
+title: Recap V
+---
+
+### Amdahl's Law - Exercise 2
+
+A program made up of **10% serial initialization and finalization code** and it has a **fully parallelizable loop of N iterations**.
+
+Assumption: **fork/join** overhead is negligible, execution time for parallelizable loop is scales linearly with N, that is:
+
+- For p processors, each processor executes $N/p$ iterations
+- Parallel time for executing the loop is: $T_{serial} = \frac{N}{p}$
+
+Given: $T_{serial} = 0.1T$ and $T_{loop} = 0.9T$, answer the following questions:
+
+- a) What is the speedup of the program with 4 processors?
+- b) What is the maximum speedup of the program? 
+- c) What can we conclude from this?
-- 
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