From a11b7c32253acf1da8090ea60d0e27e80dda24eb Mon Sep 17 00:00:00 2001
From: Zhihua Lai <zhihualai@microsoft.com>
Date: Mon, 23 Feb 2026 13:08:50 +0000
Subject: [PATCH 1/2] Add Pi Monte Carlo Parallel Simulation

---
 README.md               |  1 +
 pi-monte-carlo/Makefile | 30 ++++++++++++++++++++
 pi-monte-carlo/main.cpp | 61 +++++++++++++++++++++++++++++++++++++++++
 pi-monte-carlo/tests.sh | 12 ++++++++
 4 files changed, 104 insertions(+)
 create mode 100644 pi-monte-carlo/Makefile
 create mode 100644 pi-monte-carlo/main.cpp
 create mode 100755 pi-monte-carlo/tests.sh

diff --git a/README.md b/README.md
index 082497b..7033920 100644
--- a/README.md
+++ b/README.md
@@ -35,6 +35,7 @@ Examples include (and will expand to):
     * Encoding
         * [rot47](./rot47/)
     * [prefix-sum](./prefix-sum/)
+    * [pi-monte-carlo](./pi-monte-carlo/)
 * Data Structures
     * [map-with-unknown-key](./map-with-unknown-key/)
 * OOP
diff --git a/pi-monte-carlo/Makefile b/pi-monte-carlo/Makefile
new file mode 100644
index 0000000..172da2f
--- /dev/null
+++ b/pi-monte-carlo/Makefile
@@ -0,0 +1,30 @@
+# pull in shared compiler settings
+include ../common.mk
+
+# per-example flags
+# CXXFLAGS += -pthread
+
+## get it from the folder name
+TARGET := $(notdir $(CURDIR))
+SRCS   := $(wildcard *.cpp)
+OBJS   := $(SRCS:.cpp=.o)
+
+all: $(TARGET)
+
+$(TARGET): $(OBJS)
+	$(CXX) $(CXXFLAGS) -o $@ $^
+
+%.o: %.cpp
+	$(CXX) $(CXXFLAGS) -c $< -o $@
+
+run: $(TARGET)
+	./$(TARGET) $(ARGS)
+
+clean:
+	rm -f $(OBJS) $(TARGET)
+
+# Delegates to top-level Makefile
+check-format:
+	$(MAKE) -f ../Makefile check-format DIR=$(CURDIR)
+
+.PHONY: all clean run check-format
diff --git a/pi-monte-carlo/main.cpp b/pi-monte-carlo/main.cpp
new file mode 100644
index 0000000..534847f
--- /dev/null
+++ b/pi-monte-carlo/main.cpp
@@ -0,0 +1,61 @@
+#include <algorithm>
+#include <cstdint>
+#include <iostream>
+#include <numeric>
+#include <random>
+#include <thread>
+#include <vector>
+
+static std::uint64_t
+count_hits(std::uint64_t n, std::uint64_t seed)
+{
+    std::mt19937_64 rng(seed);
+    std::uniform_real_distribution<double> dist(0.0, 1.0);
+
+    std::uint64_t hits = 0;
+    for (std::uint64_t i = 0; i < n; ++i) {
+        const double x = dist(rng);
+        const double y = dist(rng);
+        if (x * x + y * y <= 1.0)
+            ++hits;
+    }
+    return hits;
+}
+
+int
+main(int argc, char* argv[])
+{
+    int threads = 2;
+    std::uint64_t n = 1'000'000;
+
+    if (argc > 1)
+        threads = std::max(1, std::atoi(argv[1]));
+    if (argc > 2)
+        n = std::max<std::uint64_t>(1, std::strtoull(argv[2], nullptr, 10));
+
+    const std::uint64_t base = n / threads;
+    const std::uint64_t rem = n % threads;
+
+    std::vector<std::thread> pool;
+    std::vector<std::uint64_t> hits(threads, 0);
+
+    // a single nondeterministic seed source; each thread gets a different seed
+    std::random_device rd;
+    const std::uint64_t master_seed = (static_cast<std::uint64_t>(rd()) << 32) ^ static_cast<std::uint64_t>(rd());
+
+    for (int i = 0; i < threads; ++i) {
+        const std::uint64_t points = base + (static_cast<std::uint64_t>(i) < rem ? 1 : 0);
+        const std::uint64_t seed = master_seed + 0x9e3779b97f4a7c15ULL * static_cast<std::uint64_t>(i + 1);
+
+        pool.emplace_back([&, i, points, seed] { hits[i] = count_hits(points, seed); });
+    }
+
+    for (auto& t : pool)
+        t.join();
+
+    const std::uint64_t total_hits = std::accumulate(hits.begin(), hits.end(), std::uint64_t{0});
+    const long double pi = 4.0 * static_cast<long double>(total_hits) / static_cast<long double>(n);
+
+    std::cout << pi << "\n";
+    return 0;
+}
\ No newline at end of file
diff --git a/pi-monte-carlo/tests.sh b/pi-monte-carlo/tests.sh
new file mode 100755
index 0000000..337fb84
--- /dev/null
+++ b/pi-monte-carlo/tests.sh
@@ -0,0 +1,12 @@
+#!/bin/bash
+
+set -ex
+
+./rot47
+
+helloworld=$(./rot47 'w6==@ (@C=5P')
+
+if [ "$helloworld" != "Hello World!" ]; then
+    echo "Test failed: expected 'Hello World!' but got '$helloworld'"
+    exit 1
+fi

From 196a5044e48be995928dbe0a4496a79cdd0e07b6 Mon Sep 17 00:00:00 2001
From: Zhihua Lai <zhihualai@microsoft.com>
Date: Mon, 23 Feb 2026 13:10:28 +0000
Subject: [PATCH 2/2] Fix tests

---
 pi-monte-carlo/tests.sh | 13 ++++++++-----
 1 file changed, 8 insertions(+), 5 deletions(-)

diff --git a/pi-monte-carlo/tests.sh b/pi-monte-carlo/tests.sh
index 337fb84..24e28b6 100755
--- a/pi-monte-carlo/tests.sh
+++ b/pi-monte-carlo/tests.sh
@@ -2,11 +2,14 @@
 
 set -ex
 
-./rot47
+# Run the tests
+pi=$(./pi-monte-carlo)
 
-helloworld=$(./rot47 'w6==@ (@C=5P')
-
-if [ "$helloworld" != "Hello World!" ]; then
-    echo "Test failed: expected 'Hello World!' but got '$helloworld'"
+# Check that the result is within a reasonable range
+if (( $(echo "$pi < 3.0" | bc -l) )) ||
+   (( $(echo "$pi > 3.2" | bc -l) )); then
+    echo "Test failed: pi is out of range: $pi"
     exit 1
+else
+    echo "Test passed: pi is within range: $pi"
 fi