From 5235285185f4aa23914c9cd1e2a9a04ca327a88e Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Sun, 14 Sep 2025 13:42:15 -0400
Subject: [PATCH 01/12] Add .clang-format and finish part 1

---
 .clang-format            |  6 ++++++
 stream_compaction/cpu.cu | 43 +++++++++++++++++++++++++++++++---------
 stream_compaction/cpu.h  |  2 +-
 3 files changed, 41 insertions(+), 10 deletions(-)
 create mode 100644 .clang-format

diff --git a/.clang-format b/.clang-format
new file mode 100644
index 00000000..f5f48ab6
--- /dev/null
+++ b/.clang-format
@@ -0,0 +1,6 @@
+BasedOnStyle: LLVM
+
+ColumnLimit: 100
+FixNamespaceComments: false
+IndentWidth: 4
+NamespaceIndentation: All
diff --git a/stream_compaction/cpu.cu b/stream_compaction/cpu.cu
index 719fa115..45e6e17f 100644
--- a/stream_compaction/cpu.cu
+++ b/stream_compaction/cpu.cu
@@ -1,13 +1,12 @@
-#include <cstdio>
 #include "cpu.h"
+#include <cstdio>
 
 #include "common.h"
 
 namespace StreamCompaction {
     namespace CPU {
         using StreamCompaction::Common::PerformanceTimer;
-        PerformanceTimer& timer()
-        {
+        PerformanceTimer &timer() {
             static PerformanceTimer timer;
             return timer;
         }
@@ -15,11 +14,16 @@ namespace StreamCompaction {
         /**
          * CPU scan (prefix sum).
          * For performance analysis, this is supposed to be a simple for loop.
-         * (Optional) For better understanding before starting moving to GPU, you can simulate your GPU scan in this function first.
+         * (Optional) For better understanding before starting moving to GPU, you can simulate your
+         * GPU scan in this function first.
          */
         void scan(int n, int *odata, const int *idata) {
             timer().startCpuTimer();
-            // TODO
+            int sum = 0;
+            for (int i = 0; i < n; ++i) {
+                odata[i] = sum;
+                sum += idata[i];
+            }
             timer().endCpuTimer();
         }
 
@@ -30,9 +34,15 @@ namespace StreamCompaction {
          */
         int compactWithoutScan(int n, int *odata, const int *idata) {
             timer().startCpuTimer();
-            // TODO
+            int o_count = 0;
+            for (int i = 0; i < n; ++i) {
+                if (idata[i] != 0) {
+                    odata[o_count] = idata[i];
+                    ++o_count;
+                }
+            }
             timer().endCpuTimer();
-            return -1;
+            return o_count;
         }
 
         /**
@@ -42,9 +52,24 @@ namespace StreamCompaction {
          */
         int compactWithScan(int n, int *odata, const int *idata) {
             timer().startCpuTimer();
-            // TODO
+            // Step 1: map
+            int *bools = new int[n];
+            for (int i = 0; i < n; ++i) {
+                bools[i] = (idata[i] != 0) ? 1 : 0;
+            }
+            // Step 2: scan
+            int *indices = new int[n];
+            scan(n, indices, bools);
+            // Step 3: scatter
+            int o_count = 0;
+            for (int i = 0; i < n; ++i) {
+                if (bools[i] == 1) {
+                    odata[indices[i]] = idata[i];
+                    ++o_count;
+                }
+            }
             timer().endCpuTimer();
-            return -1;
+            return o_count;
         }
     }
 }
diff --git a/stream_compaction/cpu.h b/stream_compaction/cpu.h
index 873c0476..954b8517 100644
--- a/stream_compaction/cpu.h
+++ b/stream_compaction/cpu.h
@@ -4,7 +4,7 @@
 
 namespace StreamCompaction {
     namespace CPU {
-        StreamCompaction::Common::PerformanceTimer& timer();
+        StreamCompaction::Common::PerformanceTimer &timer();
 
         void scan(int n, int *odata, const int *idata);
 

From 04a994024895771b339c5565f5b98c1040e21b29 Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Sun, 14 Sep 2025 14:48:03 -0400
Subject: [PATCH 02/12] Finish part 2

---
 stream_compaction/cpu.cu   | 22 +++++++++++---------
 stream_compaction/naive.cu | 42 ++++++++++++++++++++++++++++++++++----
 stream_compaction/naive.h  |  2 +-
 3 files changed, 51 insertions(+), 15 deletions(-)

diff --git a/stream_compaction/cpu.cu b/stream_compaction/cpu.cu
index 45e6e17f..92af639b 100644
--- a/stream_compaction/cpu.cu
+++ b/stream_compaction/cpu.cu
@@ -1,7 +1,7 @@
-#include "cpu.h"
 #include <cstdio>
 
 #include "common.h"
+#include "cpu.h"
 
 namespace StreamCompaction {
     namespace CPU {
@@ -34,15 +34,15 @@ namespace StreamCompaction {
          */
         int compactWithoutScan(int n, int *odata, const int *idata) {
             timer().startCpuTimer();
-            int o_count = 0;
+            int oCount = 0;
             for (int i = 0; i < n; ++i) {
                 if (idata[i] != 0) {
-                    odata[o_count] = idata[i];
-                    ++o_count;
+                    odata[oCount] = idata[i];
+                    ++oCount;
                 }
             }
             timer().endCpuTimer();
-            return o_count;
+            return oCount;
         }
 
         /**
@@ -51,25 +51,27 @@ namespace StreamCompaction {
          * @returns the number of elements remaining after compaction.
          */
         int compactWithScan(int n, int *odata, const int *idata) {
+            int *bools = new int[n];
+            int *indices = new int[n];
             timer().startCpuTimer();
             // Step 1: map
-            int *bools = new int[n];
             for (int i = 0; i < n; ++i) {
                 bools[i] = (idata[i] != 0) ? 1 : 0;
             }
             // Step 2: scan
-            int *indices = new int[n];
             scan(n, indices, bools);
             // Step 3: scatter
-            int o_count = 0;
+            int oCount = 0;
             for (int i = 0; i < n; ++i) {
                 if (bools[i] == 1) {
                     odata[indices[i]] = idata[i];
-                    ++o_count;
+                    ++oCount;
                 }
             }
             timer().endCpuTimer();
-            return o_count;
+            delete[] bools;
+            delete[] indices;
+            return oCount;
         }
     }
 }
diff --git a/stream_compaction/naive.cu b/stream_compaction/naive.cu
index 43088769..09deb2be 100644
--- a/stream_compaction/naive.cu
+++ b/stream_compaction/naive.cu
@@ -1,25 +1,59 @@
 #include <cuda.h>
 #include <cuda_runtime.h>
+
 #include "common.h"
 #include "naive.h"
 
 namespace StreamCompaction {
     namespace Naive {
         using StreamCompaction::Common::PerformanceTimer;
-        PerformanceTimer& timer()
-        {
+        PerformanceTimer &timer() {
             static PerformanceTimer timer;
             return timer;
         }
-        // TODO: __global__
+
+        __global__ void kernScan(int n, int offset, int *odata, const int *idata) {
+            int index = blockIdx.x * blockDim.x + threadIdx.x;
+            if (index >= n) {
+                return;
+            }
+            int beforeIndex = index - offset;
+            odata[index] = idata[index] + (beforeIndex < 0 ? 0 : idata[beforeIndex]);
+        }
+
+        __global__ void kernShiftRight(int n, int *odata, const int *idata) {
+            int index = blockIdx.x * blockDim.x + threadIdx.x;
+            if (index >= n) {
+                return;
+            }
+            odata[index] = index == 0 ? 0 : idata[index - 1];
+        }
 
         /**
          * Performs prefix-sum (aka scan) on idata, storing the result into odata.
          */
         void scan(int n, int *odata, const int *idata) {
+            const auto dataSize = n * sizeof(int);
+
+            int *dev_iData;
+            cudaMalloc((void **)&dev_iData, dataSize);
+            cudaMemcpy(dev_iData, idata, dataSize, cudaMemcpyHostToDevice);
+            int *dev_oData;
+            cudaMalloc((void **)&dev_oData, dataSize);
+
             timer().startGpuTimer();
-            // TODO
+            const int blockSize = 256;
+            const int gridSize = (n + blockSize - 1) / blockSize;
+            for (int offset = 1; offset < n; offset *= 2) {
+                kernScan<<<gridSize, blockSize>>>(n, offset, dev_oData, dev_iData);
+                std::swap(dev_oData, dev_iData);
+            }
+            kernShiftRight<<<gridSize, blockSize>>>(n, dev_oData, dev_iData);
             timer().endGpuTimer();
+
+            cudaMemcpy(odata, dev_oData, dataSize, cudaMemcpyDeviceToHost);
+            cudaFree(dev_iData);
+            cudaFree(dev_oData);
         }
     }
 }
diff --git a/stream_compaction/naive.h b/stream_compaction/naive.h
index 37dcb064..cb69b416 100644
--- a/stream_compaction/naive.h
+++ b/stream_compaction/naive.h
@@ -4,7 +4,7 @@
 
 namespace StreamCompaction {
     namespace Naive {
-        StreamCompaction::Common::PerformanceTimer& timer();
+        StreamCompaction::Common::PerformanceTimer &timer();
 
         void scan(int n, int *odata, const int *idata);
     }

From 23665c3fbde0aff63b3ad5e4255848fcb1471321 Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Sun, 14 Sep 2025 16:33:21 -0400
Subject: [PATCH 03/12] Finish part 3

---
 stream_compaction/common.cu    |  20 ++++--
 stream_compaction/efficient.cu | 112 +++++++++++++++++++++++++++++++--
 stream_compaction/efficient.h  |   2 +-
 3 files changed, 122 insertions(+), 12 deletions(-)

diff --git a/stream_compaction/common.cu b/stream_compaction/common.cu
index 2ed6d630..5cf663dc 100644
--- a/stream_compaction/common.cu
+++ b/stream_compaction/common.cu
@@ -14,7 +14,6 @@ void checkCUDAErrorFn(const char *msg, const char *file, int line) {
     exit(EXIT_FAILURE);
 }
 
-
 namespace StreamCompaction {
     namespace Common {
 
@@ -23,17 +22,26 @@ namespace StreamCompaction {
          * which map to 0 will be removed, and elements which map to 1 will be kept.
          */
         __global__ void kernMapToBoolean(int n, int *bools, const int *idata) {
-            // TODO
+            int index = blockIdx.x * blockDim.x + threadIdx.x;
+            if (index >= n) {
+                return;
+            }
+            bools[index] = idata[index] != 0 ? 1 : 0;
         }
 
         /**
          * Performs scatter on an array. That is, for each element in idata,
          * if bools[idx] == 1, it copies idata[idx] to odata[indices[idx]].
          */
-        __global__ void kernScatter(int n, int *odata,
-                const int *idata, const int *bools, const int *indices) {
-            // TODO
+        __global__ void kernScatter(int n, int *odata, const int *idata, const int *bools,
+                                    const int *indices) {
+            int index = blockIdx.x * blockDim.x + threadIdx.x;
+            if (index >= n) {
+                return;
+            }
+            if (bools[index]) {
+                odata[indices[index]] = idata[index];
+            }
         }
-
     }
 }
diff --git a/stream_compaction/efficient.cu b/stream_compaction/efficient.cu
index 2db346ee..b7ddc9ed 100644
--- a/stream_compaction/efficient.cu
+++ b/stream_compaction/efficient.cu
@@ -1,24 +1,85 @@
 #include <cuda.h>
 #include <cuda_runtime.h>
+
 #include "common.h"
 #include "efficient.h"
 
 namespace StreamCompaction {
     namespace Efficient {
         using StreamCompaction::Common::PerformanceTimer;
-        PerformanceTimer& timer()
-        {
+        PerformanceTimer &timer() {
             static PerformanceTimer timer;
             return timer;
         }
 
+        __global__ void kernUpSweep(int n, int offset, int *data) {
+            int index = blockIdx.x * blockDim.x + threadIdx.x;
+            index = (index + 1) * offset * 2 - 1;
+            if (index >= n) {
+                return;
+            }
+            int beforeIndex = index - offset;
+            if (beforeIndex >= 0) {
+                data[index] += data[beforeIndex];
+            }
+        }
+
+        __global__ void kernDownSweep(int n, int offset, int *data) {
+            int index = blockIdx.x * blockDim.x + threadIdx.x;
+            index = (index + 1) * offset * 2 - 1;
+            if (index >= n) {
+                return;
+            }
+            int beforeIndex = index - offset;
+            if (beforeIndex >= 0) {
+                int beforeValue = data[beforeIndex];
+                data[beforeIndex] = data[index];
+                data[index] += beforeValue;
+            }
+        }
+
+        void scanImpl(int n, int *data) {
+            const int blockSize = 256;
+            const auto computeGridSize = [=](int offset) {
+                const int divisor = 2 * offset * blockSize;
+                return (n + divisor - 1) / divisor;
+            };
+
+            // Up-sweep
+            for (int offset = 1; offset < n; offset *= 2) {
+                const int gridSize = computeGridSize(offset);
+                kernUpSweep<<<gridSize, blockSize>>>(n, offset, data);
+            }
+            // Set the last element to 0.
+            cudaMemset(data + (n - 1), 0, sizeof(int));
+            // Down-sweep
+            for (int offset = n / 2; offset >= 1; offset /= 2) {
+                const int gridSize = computeGridSize(offset);
+                kernDownSweep<<<gridSize, blockSize>>>(n, offset, data);
+            }
+        }
+
         /**
          * Performs prefix-sum (aka scan) on idata, storing the result into odata.
          */
         void scan(int n, int *odata, const int *idata) {
+            const auto dataSize = n * sizeof(int);
+            const int ceiledN = 1 << ilog2ceil(n);
+            const auto ceiledDataSize = ceiledN * sizeof(int);
+
+            int *dev_data;
+            cudaMalloc((void **)&dev_data, ceiledDataSize);
+            cudaMemcpy(dev_data, idata, dataSize, cudaMemcpyHostToDevice);
+            if (ceiledDataSize > dataSize) {
+                cudaMemset(dev_data + n, 0, ceiledDataSize - dataSize);
+            }
+
             timer().startGpuTimer();
-            // TODO
+            scanImpl(ceiledN, dev_data);
             timer().endGpuTimer();
+
+            cudaMemcpy(odata, dev_data, dataSize, cudaMemcpyDeviceToHost);
+            cudaFree(dev_data);
         }
 
         /**
@@ -31,10 +92,51 @@ namespace StreamCompaction {
          * @returns      The number of elements remaining after compaction.
          */
         int compact(int n, int *odata, const int *idata) {
+            const auto dataSize = n * sizeof(int);
+            const int ceiledN = 1 << ilog2ceil(n);
+            const auto ceiledDataSize = ceiledN * sizeof(int);
+
+            const int blockSize = 256;
+            const int gridSize = (n + blockSize - 1) / blockSize;
+            const int ceiledGridSize = (ceiledN + blockSize - 1) / blockSize;
+
+            int *dev_iData;
+            cudaMalloc((void **)&dev_iData, dataSize);
+            cudaMemcpy(dev_iData, idata, dataSize, cudaMemcpyHostToDevice);
+            int *dev_bools;
+            cudaMalloc((void **)&dev_bools, dataSize);
+            int *dev_indices;
+            cudaMalloc((void **)&dev_indices, ceiledDataSize);
+            int *dev_oData;
+            cudaMalloc((void **)&dev_oData, dataSize);
+
             timer().startGpuTimer();
-            // TODO
+            Common::kernMapToBoolean<<<gridSize, blockSize>>>(n, dev_bools, dev_iData);
+            cudaMemcpy(dev_indices, dev_bools, dataSize, cudaMemcpyDeviceToDevice);
+            if (ceiledDataSize > dataSize) {
+                cudaMemset(dev_indices + n, 0, ceiledDataSize - dataSize);
+            }
+            scanImpl(ceiledN, dev_indices);
+            Common::kernScatter<<<gridSize, blockSize>>>(n, dev_oData, dev_iData, dev_bools,
+                                                         dev_indices);
             timer().endGpuTimer();
-            return -1;
+
+            int oCount;
+            {
+                int lastBool;
+                cudaMemcpy(&lastBool, dev_bools + (n - 1), sizeof(int), cudaMemcpyDeviceToHost);
+                int lastIndex;
+                cudaMemcpy(&lastIndex, dev_indices + (n - 1), sizeof(int), cudaMemcpyDeviceToHost);
+                oCount = lastIndex + lastBool;
+            }
+            if (oCount > 0) {
+                cudaMemcpy(odata, dev_oData, oCount * sizeof(int), cudaMemcpyDeviceToHost);
+            }
+            cudaFree(dev_iData);
+            cudaFree(dev_bools);
+            cudaFree(dev_indices);
+            cudaFree(dev_oData);
+            return oCount;
         }
     }
 }
diff --git a/stream_compaction/efficient.h b/stream_compaction/efficient.h
index 803cb4fe..bea8e2c5 100644
--- a/stream_compaction/efficient.h
+++ b/stream_compaction/efficient.h
@@ -4,7 +4,7 @@
 
 namespace StreamCompaction {
     namespace Efficient {
-        StreamCompaction::Common::PerformanceTimer& timer();
+        StreamCompaction::Common::PerformanceTimer &timer();
 
         void scan(int n, int *odata, const int *idata);
 

From 74861cbb0a504b437962f049d7bd52a6acfb1989 Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Sun, 14 Sep 2025 17:31:22 -0400
Subject: [PATCH 04/12] Finish part 4

---
 stream_compaction/cpu.cu    | 16 ++++++++++------
 stream_compaction/thrust.cu |  9 +++++++--
 stream_compaction/thrust.h  |  2 +-
 3 files changed, 18 insertions(+), 9 deletions(-)

diff --git a/stream_compaction/cpu.cu b/stream_compaction/cpu.cu
index 92af639b..dc1d1f90 100644
--- a/stream_compaction/cpu.cu
+++ b/stream_compaction/cpu.cu
@@ -11,6 +11,14 @@ namespace StreamCompaction {
             return timer;
         }
 
+        void scanImpl(int n, int *odata, const int *idata) {
+            int sum = 0;
+            for (int i = 0; i < n; ++i) {
+                odata[i] = sum;
+                sum += idata[i];
+            }
+        }
+
         /**
          * CPU scan (prefix sum).
          * For performance analysis, this is supposed to be a simple for loop.
@@ -19,11 +27,7 @@ namespace StreamCompaction {
          */
         void scan(int n, int *odata, const int *idata) {
             timer().startCpuTimer();
-            int sum = 0;
-            for (int i = 0; i < n; ++i) {
-                odata[i] = sum;
-                sum += idata[i];
-            }
+            scanImpl(n, odata, idata);
             timer().endCpuTimer();
         }
 
@@ -59,7 +63,7 @@ namespace StreamCompaction {
                 bools[i] = (idata[i] != 0) ? 1 : 0;
             }
             // Step 2: scan
-            scan(n, indices, bools);
+            scanImpl(n, indices, bools);
             // Step 3: scatter
             int oCount = 0;
             for (int i = 0; i < n; ++i) {
diff --git a/stream_compaction/thrust.cu b/stream_compaction/thrust.cu
index 1def45e7..7750a9fa 100644
--- a/stream_compaction/thrust.cu
+++ b/stream_compaction/thrust.cu
@@ -3,14 +3,14 @@
 #include <thrust/device_vector.h>
 #include <thrust/host_vector.h>
 #include <thrust/scan.h>
+
 #include "common.h"
 #include "thrust.h"
 
 namespace StreamCompaction {
     namespace Thrust {
         using StreamCompaction::Common::PerformanceTimer;
-        PerformanceTimer& timer()
-        {
+        PerformanceTimer &timer() {
             static PerformanceTimer timer;
             return timer;
         }
@@ -18,11 +18,16 @@ namespace StreamCompaction {
          * Performs prefix-sum (aka scan) on idata, storing the result into odata.
          */
         void scan(int n, int *odata, const int *idata) {
+            thrust::host_vector<int> host_in(idata, idata + n);
+            thrust::device_vector<int> dev_in = host_in;
+            thrust::device_vector<int> dev_out(n);
             timer().startGpuTimer();
             // TODO use `thrust::exclusive_scan`
             // example: for device_vectors dv_in and dv_out:
             // thrust::exclusive_scan(dv_in.begin(), dv_in.end(), dv_out.begin());
+            thrust::exclusive_scan(dev_in.begin(), dev_in.end(), dev_out.begin());
             timer().endGpuTimer();
+            thrust::copy(dev_out.begin(), dev_out.end(), odata);
         }
     }
 }
diff --git a/stream_compaction/thrust.h b/stream_compaction/thrust.h
index fe98206b..c20b769c 100644
--- a/stream_compaction/thrust.h
+++ b/stream_compaction/thrust.h
@@ -4,7 +4,7 @@
 
 namespace StreamCompaction {
     namespace Thrust {
-        StreamCompaction::Common::PerformanceTimer& timer();
+        StreamCompaction::Common::PerformanceTimer &timer();
 
         void scan(int n, int *odata, const int *idata);
     }

From 7f8560b4651144250e24ed36cca30064ec5a882e Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Sun, 14 Sep 2025 19:46:06 -0400
Subject: [PATCH 05/12] Fix integer workflows and tune block sizes

---
 .clang-format                  |  1 +
 CMakeLists.txt                 |  3 ++
 src/main.cpp                   |  2 +-
 src/tune_block_sizes.cpp       | 88 ++++++++++++++++++++++++++++++++++
 stream_compaction/efficient.cu | 34 ++++++-------
 stream_compaction/efficient.h  |  4 +-
 stream_compaction/naive.cu     |  3 +-
 stream_compaction/naive.h      |  2 +-
 8 files changed, 115 insertions(+), 22 deletions(-)
 create mode 100644 src/tune_block_sizes.cpp

diff --git a/.clang-format b/.clang-format
index f5f48ab6..dab6e3b2 100644
--- a/.clang-format
+++ b/.clang-format
@@ -1,5 +1,6 @@
 BasedOnStyle: LLVM
 
+BreakTemplateDeclarations: Yes
 ColumnLimit: 100
 FixNamespaceComments: false
 IndentWidth: 4
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 610c27d4..95bea76b 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -44,3 +44,6 @@ source_group(Sources FILES ${sources})
 add_executable(${CMAKE_PROJECT_NAME} ${sources} ${headers})
 target_link_libraries(${CMAKE_PROJECT_NAME} stream_compaction)
 set_property(DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR} PROPERTY VS_STARTUP_PROJECT ${CMAKE_PROJECT_NAME})
+
+add_executable(tune_block_sizes src/tune_block_sizes.cpp ${headers})
+target_link_libraries(tune_block_sizes stream_compaction)
diff --git a/src/main.cpp b/src/main.cpp
index 3d5c8820..9df608c7 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -13,7 +13,7 @@
 #include <stream_compaction/thrust.h>
 #include "testing_helpers.hpp"
 
-const int SIZE = 1 << 8; // feel free to change the size of array
+const int SIZE = 1 << 22; // feel free to change the size of array
 const int NPOT = SIZE - 3; // Non-Power-Of-Two
 int *a = new int[SIZE];
 int *b = new int[SIZE];
diff --git a/src/tune_block_sizes.cpp b/src/tune_block_sizes.cpp
new file mode 100644
index 00000000..042843bd
--- /dev/null
+++ b/src/tune_block_sizes.cpp
@@ -0,0 +1,88 @@
+#include <iostream>
+#include <limits>
+#include <vector>
+
+#include <stream_compaction/efficient.h>
+#include <stream_compaction/naive.h>
+
+#include "testing_helpers.hpp"
+
+template <typename Timer, typename Func>
+float measureTime(Timer &timer, Func func) {
+    const int warmup = 10;
+    const int iterations = 100;
+    for (int i = 0; i < warmup; i++) {
+        func();
+    }
+    float totalTime = 0.0f;
+    for (int i = 0; i < iterations; ++i) {
+        func();
+        totalTime += timer.getGpuElapsedTimeForPreviousOperation();
+    }
+    return totalTime / iterations;
+}
+
+template <typename Timer, typename Func, typename... Args>
+void tuneBlockSize(Timer &timer, Func func, Args &&...args) {
+    std::vector<int> blockSizes = {8, 16, 32, 64, 128, 256, 512, 1024};
+    float bestTime = std::numeric_limits<float>::max();
+    int bestBlockSize = -1;
+    for (int blockSize : blockSizes) {
+        float time = measureTime(timer, [&]() { func(std::forward<Args>(args)..., blockSize); });
+        std::cout << "Block size: " << blockSize << ", time: " << time << " ms" << std::endl;
+        if (time < bestTime) {
+            bestTime = time;
+            bestBlockSize = blockSize;
+        }
+    }
+    std::cout << "Best block size: " << bestBlockSize << std::endl;
+}
+
+int main() {
+    const int SIZE = 1 << 22;
+    const int NPOT = SIZE - 3;
+    int *a = new int[SIZE];
+    int *b = new int[SIZE];
+    int *c = new int[SIZE];
+
+    genArray(SIZE - 1, a, 50);
+    a[SIZE - 1] = 0;
+
+    zeroArray(SIZE, c);
+    printDesc("naive scan, power-of-two");
+    tuneBlockSize(StreamCompaction::Naive::timer(), StreamCompaction::Naive::scan, SIZE, c, a);
+
+    zeroArray(SIZE, c);
+    printDesc("naive scan, non-power-of-two");
+    tuneBlockSize(StreamCompaction::Naive::timer(), StreamCompaction::Naive::scan, NPOT, c, a);
+
+    zeroArray(SIZE, c);
+    printDesc("work-efficient scan, power-of-two");
+    tuneBlockSize(StreamCompaction::Efficient::timer(), StreamCompaction::Efficient::scan, SIZE, c,
+                  a);
+
+    zeroArray(SIZE, c);
+    printDesc("work-efficient scan, non-power-of-two");
+    tuneBlockSize(StreamCompaction::Efficient::timer(), StreamCompaction::Efficient::scan, NPOT, c,
+                  a);
+
+    genArray(SIZE - 1, a, 4);
+    a[SIZE - 1] = 0;
+
+    zeroArray(SIZE, c);
+    printDesc("work-efficient compact, power-of-two");
+    tuneBlockSize(StreamCompaction::Efficient::timer(), StreamCompaction::Efficient::compact, SIZE,
+                  c, a);
+
+    zeroArray(SIZE, c);
+    printDesc("work-efficient compact, non-power-of-two");
+    tuneBlockSize(StreamCompaction::Efficient::timer(), StreamCompaction::Efficient::compact, NPOT,
+                  c, a);
+
+    system("pause");
+    delete[] a;
+    delete[] b;
+    delete[] c;
+
+    return 0;
+}
diff --git a/stream_compaction/efficient.cu b/stream_compaction/efficient.cu
index b7ddc9ed..447b0a78 100644
--- a/stream_compaction/efficient.cu
+++ b/stream_compaction/efficient.cu
@@ -13,11 +13,13 @@ namespace StreamCompaction {
         }
 
         __global__ void kernUpSweep(int n, int offset, int *data) {
-            int index = blockIdx.x * blockDim.x + threadIdx.x;
-            index = (index + 1) * offset * 2 - 1;
-            if (index >= n) {
+            // Avoid integer overflows.
+            auto indexLL = static_cast<long long>(blockIdx.x) * blockDim.x + threadIdx.x;
+            indexLL = (indexLL + 1) * offset * 2 - 1;
+            if (indexLL >= n) {
                 return;
             }
+            int index = static_cast<int>(indexLL);
             int beforeIndex = index - offset;
             if (beforeIndex >= 0) {
                 data[index] += data[beforeIndex];
@@ -25,11 +27,13 @@ namespace StreamCompaction {
         }
 
         __global__ void kernDownSweep(int n, int offset, int *data) {
-            int index = blockIdx.x * blockDim.x + threadIdx.x;
-            index = (index + 1) * offset * 2 - 1;
-            if (index >= n) {
+            // Avoid integer overflows.
+            auto indexLL = static_cast<long long>(blockIdx.x) * blockDim.x + threadIdx.x;
+            indexLL = (indexLL + 1) * offset * 2 - 1;
+            if (indexLL >= n) {
                 return;
             }
+            int index = static_cast<int>(indexLL);
             int beforeIndex = index - offset;
             if (beforeIndex >= 0) {
                 int beforeValue = data[beforeIndex];
@@ -38,11 +42,11 @@ namespace StreamCompaction {
             }
         }
 
-        void scanImpl(int n, int *data) {
-            const int blockSize = 256;
+        void scanImpl(int n, int *data, const int blockSize) {
             const auto computeGridSize = [=](int offset) {
-                const int divisor = 2 * offset * blockSize;
-                return (n + divisor - 1) / divisor;
+                // Avoid integer overflows when n and blockSize are large.
+                const auto divisor = 2LL * offset * blockSize;
+                return static_cast<int>((n + divisor - 1) / divisor);
             };
 
             // Up-sweep
@@ -62,7 +66,7 @@ namespace StreamCompaction {
         /**
          * Performs prefix-sum (aka scan) on idata, storing the result into odata.
          */
-        void scan(int n, int *odata, const int *idata) {
+        void scan(int n, int *odata, const int *idata, const int blockSize) {
             const auto dataSize = n * sizeof(int);
             const int ceiledN = 1 << ilog2ceil(n);
             const auto ceiledDataSize = ceiledN * sizeof(int);
@@ -75,7 +79,7 @@ namespace StreamCompaction {
             }
 
             timer().startGpuTimer();
-            scanImpl(ceiledN, dev_data);
+            scanImpl(ceiledN, dev_data, blockSize);
             timer().endGpuTimer();
 
             cudaMemcpy(odata, dev_data, dataSize, cudaMemcpyDeviceToHost);
@@ -91,14 +95,12 @@ namespace StreamCompaction {
          * @param idata  The array of elements to compact.
          * @returns      The number of elements remaining after compaction.
          */
-        int compact(int n, int *odata, const int *idata) {
+        int compact(int n, int *odata, const int *idata, const int blockSize) {
             const auto dataSize = n * sizeof(int);
             const int ceiledN = 1 << ilog2ceil(n);
             const auto ceiledDataSize = ceiledN * sizeof(int);
 
-            const int blockSize = 256;
             const int gridSize = (n + blockSize - 1) / blockSize;
-            const int ceiledGridSize = (ceiledN + blockSize - 1) / blockSize;
 
             int *dev_iData;
             cudaMalloc((void **)&dev_iData, dataSize);
@@ -116,7 +118,7 @@ namespace StreamCompaction {
             if (ceiledDataSize > dataSize) {
                 cudaMemset(dev_indices + n, 0, ceiledDataSize - dataSize);
             }
-            scanImpl(ceiledN, dev_indices);
+            scanImpl(ceiledN, dev_indices, blockSize);
             Common::kernScatter<<<gridSize, blockSize>>>(n, dev_oData, dev_iData, dev_bools,
                                                          dev_indices);
             timer().endGpuTimer();
diff --git a/stream_compaction/efficient.h b/stream_compaction/efficient.h
index bea8e2c5..85d1a94a 100644
--- a/stream_compaction/efficient.h
+++ b/stream_compaction/efficient.h
@@ -6,8 +6,8 @@ namespace StreamCompaction {
     namespace Efficient {
         StreamCompaction::Common::PerformanceTimer &timer();
 
-        void scan(int n, int *odata, const int *idata);
+        void scan(int n, int *odata, const int *idata, const int blockSize = 128);
 
-        int compact(int n, int *odata, const int *idata);
+        int compact(int n, int *odata, const int *idata, const int blockSize = 512);
     }
 }
diff --git a/stream_compaction/naive.cu b/stream_compaction/naive.cu
index 09deb2be..9acd42d5 100644
--- a/stream_compaction/naive.cu
+++ b/stream_compaction/naive.cu
@@ -32,7 +32,7 @@ namespace StreamCompaction {
         /**
          * Performs prefix-sum (aka scan) on idata, storing the result into odata.
          */
-        void scan(int n, int *odata, const int *idata) {
+        void scan(int n, int *odata, const int *idata, const int blockSize) {
             const auto dataSize = n * sizeof(int);
 
             int *dev_iData;
@@ -42,7 +42,6 @@ namespace StreamCompaction {
             cudaMalloc((void **)&dev_oData, dataSize);
 
             timer().startGpuTimer();
-            const int blockSize = 256;
             const int gridSize = (n + blockSize - 1) / blockSize;
             for (int offset = 1; offset < n; offset *= 2) {
                 kernScan<<<gridSize, blockSize>>>(n, offset, dev_oData, dev_iData);
diff --git a/stream_compaction/naive.h b/stream_compaction/naive.h
index cb69b416..23042bcb 100644
--- a/stream_compaction/naive.h
+++ b/stream_compaction/naive.h
@@ -6,6 +6,6 @@ namespace StreamCompaction {
     namespace Naive {
         StreamCompaction::Common::PerformanceTimer &timer();
 
-        void scan(int n, int *odata, const int *idata);
+        void scan(int n, int *odata, const int *idata, const int blockSize = 256);
     }
 }

From 91f5e0cdcae2fb8f8c4ca99530098b6b940ab114 Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Mon, 15 Sep 2025 02:42:32 -0400
Subject: [PATCH 06/12] Update performance analysis and update README

---
 CMakeLists.txt                         |   3 +
 README.md                              | 215 ++++++++++++++++++++++++-
 img/performance-comparison.png         | Bin 0 -> 45871 bytes
 scripts/performance_comparison.nljson  | 168 +++++++++++++++++++
 scripts/plot_performance_comparison.py |  42 +++++
 src/compare_performance.cpp            |  76 +++++++++
 6 files changed, 496 insertions(+), 8 deletions(-)
 create mode 100644 img/performance-comparison.png
 create mode 100644 scripts/performance_comparison.nljson
 create mode 100644 scripts/plot_performance_comparison.py
 create mode 100644 src/compare_performance.cpp

diff --git a/CMakeLists.txt b/CMakeLists.txt
index 95bea76b..f320de2f 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -47,3 +47,6 @@ set_property(DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR} PROPERTY VS_STARTUP_PROJECT $
 
 add_executable(tune_block_sizes src/tune_block_sizes.cpp ${headers})
 target_link_libraries(tune_block_sizes stream_compaction)
+
+add_executable(compare_performance src/compare_performance.cpp ${headers})
+target_link_libraries(compare_performance stream_compaction)
diff --git a/README.md b/README.md
index 0e38ddb1..8dbbd55c 100644
--- a/README.md
+++ b/README.md
@@ -1,14 +1,213 @@
-CUDA Stream Compaction
-======================
+# CUDA Stream Compaction
 
 **University of Pennsylvania, CIS 565: GPU Programming and Architecture, Project 2**
 
-* (TODO) YOUR NAME HERE
-  * (TODO) [LinkedIn](), [personal website](), [twitter](), etc.
-* Tested on: (TODO) Windows 22, i7-2222 @ 2.22GHz 22GB, GTX 222 222MB (Moore 2222 Lab)
+- Yunhao Qian
+  - [LinkedIn](https://www.linkedin.com/in/yunhao-qian-026980170/)
+  - [GitHub](https://github.com/yunhao-qian)
+- Tested on:
+  - OS: Windows 11, 24H2
+  - CPU: 13th Gen Intel(R) Core(TM) i7-13700 (2.10 GHz)
+  - GPU: NVIDIA GeForce RTX 4090
+  - RAM: 32.0 GB
 
-### (TODO: Your README)
+## Overview
 
-Include analysis, etc. (Remember, this is public, so don't put
-anything here that you don't want to share with the world.)
+### Features
 
+This project implements stream compaction and its building blocks (map, scan, scatter) using multiple approaches. Key features include:
+
+- A CPU implementation of scan and stream compaction
+- GPU implementations of scan, using both naive and work-efficient methods
+- A GPU implementation of stream compaction based on the work-efficient scan
+- Performance analysis comparing the different methods
+
+### Changes to `CMakeLists.txt`
+
+Two additional executables are added to the project to assist certain tasks:
+
+- `tune_block_sizes.exe`: Runs each algorithm under a range of block sizes to find the optimal block size.
+- `compare_performance.exe`: Executes different scan implementations across a range of input sizes and records their execution times for plotting.
+
+### Changes to Function Signatures
+
+To simplify block size tuning, I added an optional `blockSize` parameter to the following functions, each with a tuned default value:
+
+- `Naive::scan(..., const int blockSize = 256)`
+- `Efficient::scan(..., const int blockSize = 128)`
+- `Efficient::compact(..., const int blockSize = 512)`
+
+These parameters are used only by `tune_block_sizes.exe` and do not affect existing calls.
+
+## Part 1: CPU Scan & Stream Compaction
+
+In [`cpu.h`](stream_compaction/cpu.h) and [`cpu.cu`](stream_compaction/cpu.cu):
+
+- `scan()`: Computes an exclusive prefix sum using a simple `for` loop.
+- `compactWithoutScan()`: Performs stream compaction directly with a `for` loop, without calling `scan()`.
+- `compactWithScan()`: Implements stream compaction using map → scan → scatter. While it follows the structure of a parallel implementation, it is built entirely with `for` loops.
+
+## Part 2:  Naive GPU Scan Algorithm
+
+In [`naive.h`](stream_compaction/naive.h) and [`naive.cu`](stream_compaction/naive.cu):
+
+- `scan()`: Implements the naive algorithm from GPU Gems 3, Section 39.2.1, with the following differences:
+  - Uses only global memory (does not leverage shared memory).
+  - Launches one kernel per level, plus an additional kernel at the end to shift the results, rather than fusing the entire algorithm into a single kernel.
+
+## Part 3: Work-Efficient GPU Scan & Stream Compaction
+
+### 3.1. Scan
+
+In [`efficient.h`](stream_compaction/efficient.h) and [`efficient.cu`](stream_compaction/efficient.cu):
+
+- `scan()`: Implements the work-efficient algorithm from GPU Gems 3, Section 39.2.2, with the following differences:
+  - Uses only global memory (does not leverage shared memory).
+  - Launches one kernel per up-sweep/down-sweep level, rather than a single fused kernel.
+  - Saves results in place instead of out-of-place.
+- Added `scanImpl()`, which operates directly on device arrays. This avoids the CPU buffer interface exposed by `scan()`, making it easier to integrate with CUDA code.
+
+### 3.2. Stream Compaction
+
+In [`common.h`](stream_compaction/common.h) and [`common.cu`](stream_compaction/common.cu):
+
+- `kernMapToBoolean()` A CUDA kernel that maps each integer to 0 or 1, depending on whether the value is zero.
+- `kernScatter()`: A CUDA kernel that performs the scatter operation with vector addressing. Conditioned on a boolean array, it optionally stores elements at locations specified by an index array.
+
+In [`efficient.h](stream_compaction/efficient.h) and [`efficient.cu`](stream_compaction/efficient.cu):
+
+- `compact()`: Implements stream compaction on GPU using map (via `kernMapToBoolean()`) → scan (via `scanImpl()`) → scatter (via `kernScatter()`).
+
+## Part 4: Using Thrust's Implementation
+
+In [`thrust.h`](stream_compaction/thrust.h) and [`thrust.cu`](stream_compaction/thrust.cu):
+
+- `scan()`: Wraps `thrust::exclusive_scan()`, adding timing instrumentation and exposing the same API as the other implementations.
+
+## Part 5: Why is My GPU Approach So Slow?
+
+I believe Part 3.1 already incorporates the optimizations described in the instructions:
+
+- For an up-sweep or down-sweep level with a given `offset`, only elements at indices `j = (i + 1) * offset * 2 - 1`, where `i` is any integer and `0 ≤ j < n`, require processing. All other elements can be skipped.
+- Instead of mapping each kernel thread to a `j`, we map each thread directly to an `i`. This ensures that nearly all launched threads perform useful work.
+- As a result, fewer threads need to be launched. For a given `block_size`, the number of required blocks becomes
+`ceil(n / (2 * offset * block_size))`.
+
+## Part 6: Extra Credit
+
+### Extra Credit 1: Radix Sort
+
+This part is not implemented.
+
+### Extra Credit 2: GPU Scan Using Shared Memory && Hardware Optimizatio
+
+This part is not implemented.
+
+## Part 7: Write-up
+
+Project description: see the [Features](#features) section at the top.
+
+### Performance Analysis
+
+#### Optimizing Block Sizes
+
+To optimize block sizes, I added an optional `blockSize` parameter to every top-level function, each with a tuned default value. This preserves backward compatibility while making block-size tuning easier.
+
+I also added a new executable, `tune_block_sizes.exe`, to the CMake project. In [`tune_block_sizes.cpp`](src/tune_block_sizes.cpp), it searches for the optimal block size for each algorithm by:
+
+- Using arrays of randomly generated test data. Since the optimal block size can vary significantly with input sizes, experiments are run on a fixed scale of $2^22$, with both power-of-two ($2^22$) and non-power-of-two $2^22 - 3$ sizes.
+- Testing a log-spaced range of block sizes: 8, 16, …, 512, 1024.
+- Measuring performance with precise timing: each configuration is warmed up with 10 runs, then measured over 100 runs, and the average elapsed GPU time is recorded.
+- Reporting results and selecting the block size that balances performance across both power-of-two and non-power-of-two inputs.
+
+Based on these experiments, the chosen defaults are:
+
+- 256 for the naive scan
+- 128 for the work-efficient scan
+- 512 for the work-efficient compaction
+
+#### Performance Comparison
+
+![performance comparison](img/performance-comparison.png)
+
+Methods:
+
+- **Input sizes:** The figure above compares all scan implementations across a range of input sizes. I use pairs of input sizes $2^n$ and $2^n - 3$, and confirm that each pair shows similar performance, while power-of-two input sizes are sometimes marginally faster. The following discussion therefore considers only the range of data sizes, without distinguishing between power-of-two and non-power-of-two inputs.
+- **Data collection:** To simplify data collection for this plot, I added `compare_performance.exe` to the CMake project. In [`compare_performance.cpp`](src/compare_performance.cpp), it measures the average execution time (5 warmup runs and 20 measured runs) for each configuration and writes the results to a newline-delimited JSON file ([`performance_comparison.nljson`](scripts/performance_comparison.nljson)). Then [`plot_performance_comparison.py`](scripts/plot_performance_comparison.py) reads the JSON data and generates the plot.
+- **Plotting:** Because the input sizes are log-spaced and execution time grows rapidly for larger inputs, I used logarithmic scales on both axes of the plot.
+
+### Observation and Analysis
+
+- The CPU implementation has $O(N)$ complexity in theory, which is confirmed by the linear trend in the log-log plot. Interestingly, this simple, low-overhead method outperforms the GPU implementations (naive, work-efficient, and Thrust) across a fairly wide range of input sizes (up to about 300,000).
+- My naive and work-efficient GPU implementations behave as follows:
+  - They are not very sensitive to input size until $N$ becomes very large (around $10^6$). This is likely because launching kernels $O(\log N)$ times dominates execution time, while the amount of work per kernel remains relatively small.
+  - Beyond $10^6$, the actual work performed inside each kernel becomes a larger portion of execution time, and execution time increases significantly with $N$.
+- Comparing naive and work-efficient GPU implementations:
+  - The naive method is faster when $N < 10^6$, again because of kernel launch overhead. Although work-efficient performs only $O(N)$ total work versus $O(N \log N)$, it requires both an up-sweep and a down-sweep, doubling the number of kernel launches.
+  - For $N > 10^6$, the advantage of the work-efficient method becomes clear, and it outperforms the naive version.
+- The Thrust library shows a different performance profile:
+  - Plot observation: When $N < 10^5$, the Thrust implementation is significantly faster than my naive and work-efficient versions, though still slower than the CPU implementation. However, for larger $N$, Thrust unexpectedly runs slower than my global-memory–only work-efficient implementation.
+  - Nsight Systems observation: Each call to `thrust::exclusive_scan()` generates only two kernels:
+    - `DeviceScanInitKernel`, which is short-lived,
+    - `DeviceScanKernel`, which dominates execution time.
+  - Analysis:
+    - For small $N$, execution time is dominated by kernel launch overhead. Since Thrust minimizes this to just two launches, it performs well in this regime.  
+    - For large $N$, Thrust likely employs shared memory optimizations. The cause of its relative slowness compared to my implementation requires further investigation.
+
+#### Test Results
+
+```text
+****************
+** SCAN TESTS **
+****************
+    [  16  35   8  21  46  26  19   0  42  43   9  45  49 ...  16   0 ]
+==== cpu scan, power-of-two ====
+   elapsed time: 1.6805ms    (std::chrono Measured)
+    [   0  16  51  59  80 126 152 171 171 213 256 265 310 ... 102780293 102780309 ]
+==== cpu scan, non-power-of-two ====
+   elapsed time: 1.5015ms    (std::chrono Measured)
+    [   0  16  51  59  80 126 152 171 171 213 256 265 310 ... 102780200 102780221 ]
+    passed 
+==== naive scan, power-of-two ====
+   elapsed time: 0.376736ms    (CUDA Measured)
+    passed 
+==== naive scan, non-power-of-two ====
+   elapsed time: 0.326432ms    (CUDA Measured)
+    passed 
+==== work-efficient scan, power-of-two ====
+   elapsed time: 0.41936ms    (CUDA Measured)
+    passed 
+==== work-efficient scan, non-power-of-two ====
+   elapsed time: 0.41024ms    (CUDA Measured)
+    passed 
+==== thrust scan, power-of-two ====
+   elapsed time: 0.3416ms    (CUDA Measured)
+    passed 
+==== thrust scan, non-power-of-two ====
+   elapsed time: 0.333088ms    (CUDA Measured)
+    passed 
+
+*****************************
+** STREAM COMPACTION TESTS **
+*****************************
+    [   0   1   2   3   2   2   1   2   2   3   3   3   3 ...   2   0 ]
+==== cpu compact without scan, power-of-two ====
+   elapsed time: 7.3473ms    (std::chrono Measured)
+    [   1   2   3   2   2   1   2   2   3   3   3   3   2 ...   3   2 ]
+    passed 
+==== cpu compact without scan, non-power-of-two ====
+   elapsed time: 7.2214ms    (std::chrono Measured)
+    [   1   2   3   2   2   1   2   2   3   3   3   3   2 ...   1   1 ]
+    passed 
+==== cpu compact with scan ====
+   elapsed time: 14.0601ms    (std::chrono Measured)
+    [   1   2   3   2   2   1   2   2   3   3   3   3   2 ...   3   2 ]
+    passed 
+==== work-efficient compact, power-of-two ====
+   elapsed time: 0.431744ms    (CUDA Measured)
+    passed 
+==== work-efficient compact, non-power-of-two ====
+   elapsed time: 0.576384ms    (CUDA Measured)
+    passed 
+Press any key to continue . . . 
+```
diff --git a/img/performance-comparison.png b/img/performance-comparison.png
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diff --git a/scripts/performance_comparison.nljson b/scripts/performance_comparison.nljson
new file mode 100644
index 00000000..9a65dd0a
--- /dev/null
+++ b/scripts/performance_comparison.nljson
@@ -0,0 +1,168 @@
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diff --git a/scripts/plot_performance_comparison.py b/scripts/plot_performance_comparison.py
new file mode 100644
index 00000000..78e14d42
--- /dev/null
+++ b/scripts/plot_performance_comparison.py
@@ -0,0 +1,42 @@
+import json
+from matplotlib import pyplot as plt
+from pathlib import Path
+import numpy as np
+
+
+def main():
+    json_path = Path(__file__).parent / "performance_comparison.nljson"
+    with json_path.open(encoding="utf-8") as f:
+        data = [json.loads(line) for line in f]
+
+    fig, ax = plt.subplots()
+    for method, label in [
+        ("cpu", "CPU"),
+        ("naive", "GPU (naive)"),
+        ("efficient", "GPU (work-efficient)"),
+        ("thrust", "GPU (Thrust)"),
+    ]:
+        n_values = []
+        time_values = []
+        for entry in data:
+            if entry["method"] == method:
+                n_values.append(entry["n"])
+                time_values.append(entry["time"])
+        n_values = np.array(n_values)
+        time_values = np.array(time_values)
+        sorted_indices = np.argsort(n_values)
+        n_values = n_values[sorted_indices]
+        time_values = time_values[sorted_indices]
+        ax.plot(n_values, time_values, label=label, marker="o")
+
+    ax.set_xscale("log")
+    ax.set_yscale("log")
+    ax.set_xlabel("Input size")
+    ax.set_ylabel("Time (ms)")
+    ax.legend()
+    fig.tight_layout()
+    fig.savefig(Path(__file__).parent.parent / "img" / "performance-comparison.png")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/src/compare_performance.cpp b/src/compare_performance.cpp
new file mode 100644
index 00000000..de9331a4
--- /dev/null
+++ b/src/compare_performance.cpp
@@ -0,0 +1,76 @@
+#include <fstream>
+#include <thread>
+#include <utility>
+#include <vector>
+
+#include <stream_compaction/cpu.h>
+#include <stream_compaction/efficient.h>
+#include <stream_compaction/naive.h>
+#include <stream_compaction/thrust.h>
+
+#include "testing_helpers.hpp"
+
+constexpr int MAX_SIZE = 1 << 24;
+std::vector<int> inputs(MAX_SIZE);
+std::vector<int> outputs(MAX_SIZE);
+
+void prepareData(int n) {
+    genArray(n, inputs.data(), 50);
+    zeroArray(n, outputs.data());
+}
+
+template <bool IsGpu, typename Timer, typename Func>
+float measureTime(Timer &timer, Func func, int n) {
+    const int warmup = 5;
+    const int iterations = 20;
+    for (int i = 0; i < warmup; i++) {
+        prepareData(n);
+        func();
+    }
+    float totalTime = 0.0f;
+    for (int i = 0; i < iterations; ++i) {
+        prepareData(n);
+        func();
+        if constexpr (IsGpu) {
+            totalTime += timer.getGpuElapsedTimeForPreviousOperation();
+        } else {
+            totalTime += timer.getCpuElapsedTimeForPreviousOperation();
+        }
+    }
+    return totalTime / iterations;
+}
+
+int main() {
+    std::ofstream outFile("performance_comparison.nljson");
+
+    for (int exponent = 4; exponent <= 24; ++exponent) {
+        const int baseN = 1 << exponent;
+        for (int n : {baseN - 3, baseN}) {
+            float cpuTime = measureTime<false>(
+                StreamCompaction::CPU::timer(),
+                [&, n] { StreamCompaction::CPU::scan(n, outputs.data(), inputs.data()); }, n);
+            float naiveTime = measureTime<true>(
+                StreamCompaction::Naive::timer(),
+                [&, n]() { StreamCompaction::Naive::scan(n, outputs.data(), inputs.data()); }, n);
+            float efficientTime = measureTime<true>(
+                StreamCompaction::Efficient::timer(),
+                [&, n]() { StreamCompaction::Efficient::scan(n, outputs.data(), inputs.data()); },
+                n);
+            float thrustTime = measureTime<true>(
+                StreamCompaction::Thrust::timer(),
+                [&, n]() { StreamCompaction::Thrust::scan(n, outputs.data(), inputs.data()); }, n);
+            for (const auto [name, time] : {
+                     std::pair("cpu", cpuTime),
+                     std::pair("naive", naiveTime),
+                     std::pair("efficient", efficientTime),
+                     std::pair("thrust", thrustTime),
+                 }) {
+                outFile << "{ "
+                        << "\"n\": " << n << ", "
+                        << "\"method\": \"" << name << "\", "
+                        << "\"time\": " << time << " }" << std::endl;
+            }
+            std::this_thread::sleep_for(std::chrono::milliseconds(100));
+        }
+    }
+}

From 4f0d829e4499216da4a84ed7ccc6e09a835deb5a Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Mon, 15 Sep 2025 03:43:53 -0400
Subject: [PATCH 07/12] Update performance comparisons

---
 README.md                               |   2 +-
 img/performance-comparison-gpu-only.png | Bin 0 -> 56590 bytes
 img/performance-comparison.png          | Bin 45871 -> 60668 bytes
 scripts/performance_comparison.nljson   | 360 +++++++++++++-----------
 scripts/plot_performance_comparison.py  |  59 ++--
 src/compare_performance.cpp             |  12 +-
 6 files changed, 234 insertions(+), 199 deletions(-)
 create mode 100644 img/performance-comparison-gpu-only.png

diff --git a/README.md b/README.md
index 8dbbd55c..9f85e6f7 100644
--- a/README.md
+++ b/README.md
@@ -133,7 +133,7 @@ Based on these experiments, the chosen defaults are:
 Methods:
 
 - **Input sizes:** The figure above compares all scan implementations across a range of input sizes. I use pairs of input sizes $2^n$ and $2^n - 3$, and confirm that each pair shows similar performance, while power-of-two input sizes are sometimes marginally faster. The following discussion therefore considers only the range of data sizes, without distinguishing between power-of-two and non-power-of-two inputs.
-- **Data collection:** To simplify data collection for this plot, I added `compare_performance.exe` to the CMake project. In [`compare_performance.cpp`](src/compare_performance.cpp), it measures the average execution time (5 warmup runs and 20 measured runs) for each configuration and writes the results to a newline-delimited JSON file ([`performance_comparison.nljson`](scripts/performance_comparison.nljson)). Then [`plot_performance_comparison.py`](scripts/plot_performance_comparison.py) reads the JSON data and generates the plot.
+- **Data collection:** To simplify data collection for this plot, I added `compare_performance.exe` to the CMake project. In [`compare_performance.cpp`](src/compare_performance.cpp), it measures the average execution time (1 warmup runs and 10 measured runs) for each configuration and writes the results to a newline-delimited JSON file ([`performance_comparison.nljson`](scripts/performance_comparison.nljson)). Then [`plot_performance_comparison.py`](scripts/plot_performance_comparison.py) reads the JSON data and generates the plot.
 - **Plotting:** Because the input sizes are log-spaced and execution time grows rapidly for larger inputs, I used logarithmic scales on both axes of the plot.
 
 ### Observation and Analysis
diff --git a/img/performance-comparison-gpu-only.png b/img/performance-comparison-gpu-only.png
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diff --git a/scripts/performance_comparison.nljson b/scripts/performance_comparison.nljson
index 9a65dd0a..d8a84f8d 100644
--- a/scripts/performance_comparison.nljson
+++ b/scripts/performance_comparison.nljson
@@ -1,168 +1,192 @@
-{ "n": 13, "method": "cpu", "time": 1.5e-05 }
-{ "n": 13, "method": "naive", "time": 0.025688 }
-{ "n": 13, "method": "efficient", "time": 0.0679648 }
-{ "n": 13, "method": "thrust", "time": 0.0188512 }
-{ "n": 16, "method": "cpu", "time": 8e-05 }
-{ "n": 16, "method": "naive", "time": 0.041688 }
-{ "n": 16, "method": "efficient", "time": 0.049 }
-{ "n": 16, "method": "thrust", "time": 0.0594208 }
-{ "n": 29, "method": "cpu", "time": 0.000125 }
-{ "n": 29, "method": "naive", "time": 0.035024 }
-{ "n": 29, "method": "efficient", "time": 0.065976 }
-{ "n": 29, "method": "thrust", "time": 0.0649536 }
-{ "n": 32, "method": "cpu", "time": 6e-05 }
-{ "n": 32, "method": "naive", "time": 0.0480656 }
-{ "n": 32, "method": "efficient", "time": 0.0724704 }
-{ "n": 32, "method": "thrust", "time": 0.0618304 }
-{ "n": 61, "method": "cpu", "time": 0.00015 }
-{ "n": 61, "method": "naive", "time": 0.0386928 }
-{ "n": 61, "method": "efficient", "time": 0.108021 }
-{ "n": 61, "method": "thrust", "time": 0.0637312 }
-{ "n": 64, "method": "cpu", "time": 7.5e-05 }
-{ "n": 64, "method": "naive", "time": 0.0342128 }
-{ "n": 64, "method": "efficient", "time": 0.0799008 }
-{ "n": 64, "method": "thrust", "time": 0.0521888 }
-{ "n": 125, "method": "cpu", "time": 0.00023 }
-{ "n": 125, "method": "naive", "time": 0.0582464 }
-{ "n": 125, "method": "efficient", "time": 0.101778 }
-{ "n": 125, "method": "thrust", "time": 0.0355856 }
-{ "n": 128, "method": "cpu", "time": 0.000205 }
-{ "n": 128, "method": "naive", "time": 0.0571312 }
-{ "n": 128, "method": "efficient", "time": 0.100952 }
-{ "n": 128, "method": "thrust", "time": 0.031608 }
-{ "n": 253, "method": "cpu", "time": 0.00035 }
-{ "n": 253, "method": "naive", "time": 0.100517 }
-{ "n": 253, "method": "efficient", "time": 0.127331 }
-{ "n": 253, "method": "thrust", "time": 0.0230864 }
-{ "n": 256, "method": "cpu", "time": 0.000335 }
-{ "n": 256, "method": "naive", "time": 0.121619 }
-{ "n": 256, "method": "efficient", "time": 0.114067 }
-{ "n": 256, "method": "thrust", "time": 0.0188784 }
-{ "n": 509, "method": "cpu", "time": 0.00035 }
-{ "n": 509, "method": "naive", "time": 0.0740992 }
-{ "n": 509, "method": "efficient", "time": 0.149755 }
-{ "n": 509, "method": "thrust", "time": 0.0395904 }
-{ "n": 512, "method": "cpu", "time": 0.000175 }
-{ "n": 512, "method": "naive", "time": 0.0904032 }
-{ "n": 512, "method": "efficient", "time": 0.123219 }
-{ "n": 512, "method": "thrust", "time": 0.033192 }
-{ "n": 1021, "method": "cpu", "time": 0.00104 }
-{ "n": 1021, "method": "naive", "time": 0.0973408 }
-{ "n": 1021, "method": "efficient", "time": 0.14588 }
-{ "n": 1021, "method": "thrust", "time": 0.0582192 }
-{ "n": 1024, "method": "cpu", "time": 0.001045 }
-{ "n": 1024, "method": "naive", "time": 0.111475 }
-{ "n": 1024, "method": "efficient", "time": 0.137109 }
-{ "n": 1024, "method": "thrust", "time": 0.0497456 }
-{ "n": 2045, "method": "cpu", "time": 0.003255 }
-{ "n": 2045, "method": "naive", "time": 0.134525 }
-{ "n": 2045, "method": "efficient", "time": 0.143205 }
-{ "n": 2045, "method": "thrust", "time": 0.0625552 }
-{ "n": 2048, "method": "cpu", "time": 0.002125 }
-{ "n": 2048, "method": "naive", "time": 0.107757 }
-{ "n": 2048, "method": "efficient", "time": 0.142264 }
-{ "n": 2048, "method": "thrust", "time": 0.0585488 }
-{ "n": 4093, "method": "cpu", "time": 0.00384 }
-{ "n": 4093, "method": "naive", "time": 0.139134 }
-{ "n": 4093, "method": "efficient", "time": 0.163918 }
-{ "n": 4093, "method": "thrust", "time": 0.0229808 }
-{ "n": 4096, "method": "cpu", "time": 0.00341 }
-{ "n": 4096, "method": "naive", "time": 0.087368 }
-{ "n": 4096, "method": "efficient", "time": 0.14725 }
-{ "n": 4096, "method": "thrust", "time": 0.0239632 }
-{ "n": 8189, "method": "cpu", "time": 0.00605 }
-{ "n": 8189, "method": "naive", "time": 0.083384 }
-{ "n": 8189, "method": "efficient", "time": 0.166701 }
-{ "n": 8189, "method": "thrust", "time": 0.0176992 }
-{ "n": 8192, "method": "cpu", "time": 0.007675 }
-{ "n": 8192, "method": "naive", "time": 0.0984544 }
-{ "n": 8192, "method": "efficient", "time": 0.186549 }
-{ "n": 8192, "method": "thrust", "time": 0.0580832 }
-{ "n": 16381, "method": "cpu", "time": 0.01161 }
-{ "n": 16381, "method": "naive", "time": 0.0681936 }
-{ "n": 16381, "method": "efficient", "time": 0.231867 }
-{ "n": 16381, "method": "thrust", "time": 0.0619888 }
-{ "n": 16384, "method": "cpu", "time": 0.00827 }
-{ "n": 16384, "method": "naive", "time": 0.0731056 }
-{ "n": 16384, "method": "efficient", "time": 0.182333 }
-{ "n": 16384, "method": "thrust", "time": 0.0644048 }
-{ "n": 32765, "method": "cpu", "time": 0.00737 }
-{ "n": 32765, "method": "naive", "time": 0.0818176 }
-{ "n": 32765, "method": "efficient", "time": 0.258878 }
-{ "n": 32765, "method": "thrust", "time": 0.065368 }
-{ "n": 32768, "method": "cpu", "time": 0.008385 }
-{ "n": 32768, "method": "naive", "time": 0.0833024 }
-{ "n": 32768, "method": "efficient", "time": 0.22919 }
-{ "n": 32768, "method": "thrust", "time": 0.0638928 }
-{ "n": 65533, "method": "cpu", "time": 0.014155 }
-{ "n": 65533, "method": "naive", "time": 0.0990736 }
-{ "n": 65533, "method": "efficient", "time": 0.274275 }
-{ "n": 65533, "method": "thrust", "time": 0.0644848 }
-{ "n": 65536, "method": "cpu", "time": 0.013395 }
-{ "n": 65536, "method": "naive", "time": 0.095656 }
-{ "n": 65536, "method": "efficient", "time": 0.262211 }
-{ "n": 65536, "method": "thrust", "time": 0.0601584 }
-{ "n": 131069, "method": "cpu", "time": 0.02594 }
-{ "n": 131069, "method": "naive", "time": 0.0925808 }
-{ "n": 131069, "method": "efficient", "time": 0.265709 }
-{ "n": 131069, "method": "thrust", "time": 0.0359856 }
-{ "n": 131072, "method": "cpu", "time": 0.025855 }
-{ "n": 131072, "method": "naive", "time": 0.101024 }
-{ "n": 131072, "method": "efficient", "time": 0.233067 }
-{ "n": 131072, "method": "thrust", "time": 0.0565776 }
-{ "n": 262141, "method": "cpu", "time": 0.053885 }
-{ "n": 262141, "method": "naive", "time": 0.103669 }
-{ "n": 262141, "method": "efficient", "time": 0.236083 }
-{ "n": 262141, "method": "thrust", "time": 0.279963 }
-{ "n": 262144, "method": "cpu", "time": 0.05231 }
-{ "n": 262144, "method": "naive", "time": 0.102563 }
-{ "n": 262144, "method": "efficient", "time": 0.223493 }
-{ "n": 262144, "method": "thrust", "time": 0.28317 }
-{ "n": 524285, "method": "cpu", "time": 0.106865 }
-{ "n": 524285, "method": "naive", "time": 0.134579 }
-{ "n": 524285, "method": "efficient", "time": 0.213752 }
-{ "n": 524285, "method": "thrust", "time": 0.304117 }
-{ "n": 524288, "method": "cpu", "time": 0.11024 }
-{ "n": 524288, "method": "naive", "time": 0.145389 }
-{ "n": 524288, "method": "efficient", "time": 0.226549 }
-{ "n": 524288, "method": "thrust", "time": 0.286958 }
-{ "n": 1048573, "method": "cpu", "time": 0.259315 }
-{ "n": 1048573, "method": "naive", "time": 0.198867 }
-{ "n": 1048573, "method": "efficient", "time": 0.274901 }
-{ "n": 1048573, "method": "thrust", "time": 0.32523 }
-{ "n": 1048576, "method": "cpu", "time": 0.216965 }
-{ "n": 1048576, "method": "naive", "time": 0.379402 }
-{ "n": 1048576, "method": "efficient", "time": 0.645763 }
-{ "n": 1048576, "method": "thrust", "time": 0.417398 }
-{ "n": 2097149, "method": "cpu", "time": 0.50729 }
-{ "n": 2097149, "method": "naive", "time": 0.660331 }
-{ "n": 2097149, "method": "efficient", "time": 0.438976 }
-{ "n": 2097149, "method": "thrust", "time": 1.08172 }
-{ "n": 2097152, "method": "cpu", "time": 0.477415 }
-{ "n": 2097152, "method": "naive", "time": 0.660899 }
-{ "n": 2097152, "method": "efficient", "time": 0.707245 }
-{ "n": 2097152, "method": "thrust", "time": 1.14484 }
-{ "n": 4194301, "method": "cpu", "time": 1.55613 }
-{ "n": 4194301, "method": "naive", "time": 0.942426 }
-{ "n": 4194301, "method": "efficient", "time": 0.536166 }
-{ "n": 4194301, "method": "thrust", "time": 1.89968 }
-{ "n": 4194304, "method": "cpu", "time": 1.43653 }
-{ "n": 4194304, "method": "naive", "time": 0.936166 }
-{ "n": 4194304, "method": "efficient", "time": 0.815872 }
-{ "n": 4194304, "method": "thrust", "time": 1.9981 }
-{ "n": 8388605, "method": "cpu", "time": 3.08376 }
-{ "n": 8388605, "method": "naive", "time": 12.9004 }
-{ "n": 8388605, "method": "efficient", "time": 0.782162 }
-{ "n": 8388605, "method": "thrust", "time": 3.27968 }
-{ "n": 8388608, "method": "cpu", "time": 3.11786 }
-{ "n": 8388608, "method": "naive", "time": 12.8878 }
-{ "n": 8388608, "method": "efficient", "time": 1.07837 }
-{ "n": 8388608, "method": "thrust", "time": 3.26629 }
-{ "n": 16777213, "method": "cpu", "time": 6.39931 }
-{ "n": 16777213, "method": "naive", "time": 5.35786 }
-{ "n": 16777213, "method": "efficient", "time": 3.5299 }
-{ "n": 16777213, "method": "thrust", "time": 6.97873 }
-{ "n": 16777216, "method": "cpu", "time": 6.72993 }
-{ "n": 16777216, "method": "naive", "time": 5.35915 }
-{ "n": 16777216, "method": "efficient", "time": 3.60297 }
-{ "n": 16777216, "method": "thrust", "time": 7.04289 }
+{ "n": 13, "method": "cpu", "time": 0.00033 }
+{ "n": 13, "method": "naive", "time": 0.232378 }
+{ "n": 13, "method": "efficient", "time": 0.387424 }
+{ "n": 13, "method": "thrust", "time": 0.171539 }
+{ "n": 16, "method": "cpu", "time": 0.0003 }
+{ "n": 16, "method": "naive", "time": 0.08504 }
+{ "n": 16, "method": "efficient", "time": 0.37087 }
+{ "n": 16, "method": "thrust", "time": 0.134224 }
+{ "n": 29, "method": "cpu", "time": 0.00027 }
+{ "n": 29, "method": "naive", "time": 0.216336 }
+{ "n": 29, "method": "efficient", "time": 0.511296 }
+{ "n": 29, "method": "thrust", "time": 0.193229 }
+{ "n": 32, "method": "cpu", "time": 0.00032 }
+{ "n": 32, "method": "naive", "time": 0.132477 }
+{ "n": 32, "method": "efficient", "time": 0.318134 }
+{ "n": 32, "method": "thrust", "time": 0.143229 }
+{ "n": 61, "method": "cpu", "time": 0.00035 }
+{ "n": 61, "method": "naive", "time": 0.272262 }
+{ "n": 61, "method": "efficient", "time": 0.35671 }
+{ "n": 61, "method": "thrust", "time": 0.172179 }
+{ "n": 64, "method": "cpu", "time": 0.00032 }
+{ "n": 64, "method": "naive", "time": 0.198048 }
+{ "n": 64, "method": "efficient", "time": 0.390003 }
+{ "n": 64, "method": "thrust", "time": 0.154371 }
+{ "n": 125, "method": "cpu", "time": 0.00043 }
+{ "n": 125, "method": "naive", "time": 0.343504 }
+{ "n": 125, "method": "efficient", "time": 0.486589 }
+{ "n": 125, "method": "thrust", "time": 0.119821 }
+{ "n": 128, "method": "cpu", "time": 0.0003 }
+{ "n": 128, "method": "naive", "time": 0.300669 }
+{ "n": 128, "method": "efficient", "time": 0.577981 }
+{ "n": 128, "method": "thrust", "time": 0.138826 }
+{ "n": 253, "method": "cpu", "time": 0.00055 }
+{ "n": 253, "method": "naive", "time": 0.249734 }
+{ "n": 253, "method": "efficient", "time": 0.587984 }
+{ "n": 253, "method": "thrust", "time": 0.179283 }
+{ "n": 256, "method": "cpu", "time": 0.00054 }
+{ "n": 256, "method": "naive", "time": 0.07712 }
+{ "n": 256, "method": "efficient", "time": 0.200301 }
+{ "n": 256, "method": "thrust", "time": 0.157264 }
+{ "n": 509, "method": "cpu", "time": 0.00069 }
+{ "n": 509, "method": "naive", "time": 0.146432 }
+{ "n": 509, "method": "efficient", "time": 0.270848 }
+{ "n": 509, "method": "thrust", "time": 0.137421 }
+{ "n": 512, "method": "cpu", "time": 0.00078 }
+{ "n": 512, "method": "naive", "time": 0.161792 }
+{ "n": 512, "method": "efficient", "time": 0.250675 }
+{ "n": 512, "method": "thrust", "time": 0.134042 }
+{ "n": 1021, "method": "cpu", "time": 0.0012 }
+{ "n": 1021, "method": "naive", "time": 0.154112 }
+{ "n": 1021, "method": "efficient", "time": 0.274227 }
+{ "n": 1021, "method": "thrust", "time": 0.170598 }
+{ "n": 1024, "method": "cpu", "time": 0.00123 }
+{ "n": 1024, "method": "naive", "time": 0.148787 }
+{ "n": 1024, "method": "efficient", "time": 0.275149 }
+{ "n": 1024, "method": "thrust", "time": 0.128512 }
+{ "n": 2045, "method": "cpu", "time": 0.00222 }
+{ "n": 2045, "method": "naive", "time": 0.153498 }
+{ "n": 2045, "method": "efficient", "time": 0.319488 }
+{ "n": 2045, "method": "thrust", "time": 0.171725 }
+{ "n": 2048, "method": "cpu", "time": 0.00202 }
+{ "n": 2048, "method": "naive", "time": 0.153395 }
+{ "n": 2048, "method": "efficient", "time": 0.335565 }
+{ "n": 2048, "method": "thrust", "time": 0.147968 }
+{ "n": 4093, "method": "cpu", "time": 0.00449 }
+{ "n": 4093, "method": "naive", "time": 0.16937 }
+{ "n": 4093, "method": "efficient", "time": 0.285798 }
+{ "n": 4093, "method": "thrust", "time": 0.218419 }
+{ "n": 4096, "method": "cpu", "time": 0.00384 }
+{ "n": 4096, "method": "naive", "time": 0.156467 }
+{ "n": 4096, "method": "efficient", "time": 0.336282 }
+{ "n": 4096, "method": "thrust", "time": 0.172646 }
+{ "n": 8189, "method": "cpu", "time": 0.00766 }
+{ "n": 8189, "method": "naive", "time": 0.172134 }
+{ "n": 8189, "method": "efficient", "time": 0.396698 }
+{ "n": 8189, "method": "thrust", "time": 0.149402 }
+{ "n": 8192, "method": "cpu", "time": 0.01236 }
+{ "n": 8192, "method": "naive", "time": 0.183706 }
+{ "n": 8192, "method": "efficient", "time": 0.388096 }
+{ "n": 8192, "method": "thrust", "time": 0.0726016 }
+{ "n": 16381, "method": "cpu", "time": 0.01618 }
+{ "n": 16381, "method": "naive", "time": 0.196403 }
+{ "n": 16381, "method": "efficient", "time": 0.451174 }
+{ "n": 16381, "method": "thrust", "time": 0.131379 }
+{ "n": 16384, "method": "cpu", "time": 0.017 }
+{ "n": 16384, "method": "naive", "time": 0.195174 }
+{ "n": 16384, "method": "efficient", "time": 0.411443 }
+{ "n": 16384, "method": "thrust", "time": 0.164659 }
+{ "n": 32765, "method": "cpu", "time": 0.02813 }
+{ "n": 32765, "method": "naive", "time": 0.543056 }
+{ "n": 32765, "method": "efficient", "time": 0.41175 }
+{ "n": 32765, "method": "thrust", "time": 0.254464 }
+{ "n": 32768, "method": "cpu", "time": 0.04217 }
+{ "n": 32768, "method": "naive", "time": 0.533229 }
+{ "n": 32768, "method": "efficient", "time": 0.731085 }
+{ "n": 32768, "method": "thrust", "time": 0.193229 }
+{ "n": 65533, "method": "cpu", "time": 0.0548 }
+{ "n": 65533, "method": "naive", "time": 0.591744 }
+{ "n": 65533, "method": "efficient", "time": 0.533402 }
+{ "n": 65533, "method": "thrust", "time": 0.252826 }
+{ "n": 65536, "method": "cpu", "time": 0.06175 }
+{ "n": 65536, "method": "naive", "time": 0.513747 }
+{ "n": 65536, "method": "efficient", "time": 0.711933 }
+{ "n": 65536, "method": "thrust", "time": 0.15401 }
+{ "n": 131069, "method": "cpu", "time": 0.12004 }
+{ "n": 131069, "method": "naive", "time": 0.502342 }
+{ "n": 131069, "method": "efficient", "time": 0.457318 }
+{ "n": 131069, "method": "thrust", "time": 0.21463 }
+{ "n": 131072, "method": "cpu", "time": 0.1034 }
+{ "n": 131072, "method": "naive", "time": 0.492125 }
+{ "n": 131072, "method": "efficient", "time": 0.780995 }
+{ "n": 131072, "method": "thrust", "time": 0.219034 }
+{ "n": 262141, "method": "cpu", "time": 0.12776 }
+{ "n": 262141, "method": "naive", "time": 0.469517 }
+{ "n": 262141, "method": "efficient", "time": 0.33024 }
+{ "n": 262141, "method": "thrust", "time": 0.668058 }
+{ "n": 262144, "method": "cpu", "time": 0.11879 }
+{ "n": 262144, "method": "naive", "time": 0.468522 }
+{ "n": 262144, "method": "efficient", "time": 0.628771 }
+{ "n": 262144, "method": "thrust", "time": 0.749875 }
+{ "n": 524285, "method": "cpu", "time": 0.13549 }
+{ "n": 524285, "method": "naive", "time": 0.470979 }
+{ "n": 524285, "method": "efficient", "time": 0.297267 }
+{ "n": 524285, "method": "thrust", "time": 0.386765 }
+{ "n": 524288, "method": "cpu", "time": 0.13771 }
+{ "n": 524288, "method": "naive", "time": 0.471078 }
+{ "n": 524288, "method": "efficient", "time": 0.576304 }
+{ "n": 524288, "method": "thrust", "time": 0.413184 }
+{ "n": 1048573, "method": "cpu", "time": 0.24861 }
+{ "n": 1048573, "method": "naive", "time": 0.532262 }
+{ "n": 1048573, "method": "efficient", "time": 0.349389 }
+{ "n": 1048573, "method": "thrust", "time": 0.400691 }
+{ "n": 1048576, "method": "cpu", "time": 0.24889 }
+{ "n": 1048576, "method": "naive", "time": 0.544541 }
+{ "n": 1048576, "method": "efficient", "time": 0.663786 }
+{ "n": 1048576, "method": "thrust", "time": 0.454758 }
+{ "n": 2097149, "method": "cpu", "time": 0.55957 }
+{ "n": 2097149, "method": "naive", "time": 0.673578 }
+{ "n": 2097149, "method": "efficient", "time": 0.419533 }
+{ "n": 2097149, "method": "thrust", "time": 1.17688 }
+{ "n": 2097152, "method": "cpu", "time": 0.51941 }
+{ "n": 2097152, "method": "naive", "time": 0.669952 }
+{ "n": 2097152, "method": "efficient", "time": 0.709722 }
+{ "n": 2097152, "method": "thrust", "time": 1.12579 }
+{ "n": 4194301, "method": "cpu", "time": 1.50463 }
+{ "n": 4194301, "method": "naive", "time": 0.940077 }
+{ "n": 4194301, "method": "efficient", "time": 0.537805 }
+{ "n": 4194301, "method": "thrust", "time": 2.03244 }
+{ "n": 4194304, "method": "cpu", "time": 1.5241 }
+{ "n": 4194304, "method": "naive", "time": 0.939626 }
+{ "n": 4194304, "method": "efficient", "time": 0.842061 }
+{ "n": 4194304, "method": "thrust", "time": 1.90802 }
+{ "n": 8388605, "method": "cpu", "time": 3.06189 }
+{ "n": 8388605, "method": "naive", "time": 12.8634 }
+{ "n": 8388605, "method": "efficient", "time": 0.781722 }
+{ "n": 8388605, "method": "thrust", "time": 3.25437 }
+{ "n": 8388608, "method": "cpu", "time": 3.0781 }
+{ "n": 8388608, "method": "naive", "time": 12.8362 }
+{ "n": 8388608, "method": "efficient", "time": 1.07779 }
+{ "n": 8388608, "method": "thrust", "time": 3.21966 }
+{ "n": 16777213, "method": "cpu", "time": 6.35065 }
+{ "n": 16777213, "method": "naive", "time": 3.68582 }
+{ "n": 16777213, "method": "efficient", "time": 1.37247 }
+{ "n": 16777213, "method": "thrust", "time": 3.59886 }
+{ "n": 16777216, "method": "cpu", "time": 6.38219 }
+{ "n": 16777216, "method": "naive", "time": 15.8907 }
+{ "n": 16777216, "method": "efficient", "time": 1.26974 }
+{ "n": 16777216, "method": "thrust", "time": 0.724269 }
+{ "n": 33554429, "method": "cpu", "time": 12.8347 }
+{ "n": 33554429, "method": "naive", "time": 117.855 }
+{ "n": 33554429, "method": "efficient", "time": 31.6965 }
+{ "n": 33554429, "method": "thrust", "time": 6.1226 }
+{ "n": 33554432, "method": "cpu", "time": 13.1276 }
+{ "n": 33554432, "method": "naive", "time": 10.9893 }
+{ "n": 33554432, "method": "efficient", "time": 16.0389 }
+{ "n": 33554432, "method": "thrust", "time": 7.30489 }
+{ "n": 67108861, "method": "cpu", "time": 26.394 }
+{ "n": 67108861, "method": "naive", "time": 28.3086 }
+{ "n": 67108861, "method": "efficient", "time": 77.8953 }
+{ "n": 67108861, "method": "thrust", "time": 8.68594 }
+{ "n": 67108864, "method": "cpu", "time": 25.9969 }
+{ "n": 67108864, "method": "naive", "time": 28.3099 }
+{ "n": 67108864, "method": "efficient", "time": 55.8472 }
+{ "n": 67108864, "method": "thrust", "time": 12.4305 }
+{ "n": 134217725, "method": "cpu", "time": 51.878 }
+{ "n": 134217725, "method": "naive", "time": 45.4344 }
+{ "n": 134217725, "method": "efficient", "time": 40.7151 }
+{ "n": 134217725, "method": "thrust", "time": 14.4468 }
+{ "n": 134217728, "method": "cpu", "time": 52.1253 }
+{ "n": 134217728, "method": "naive", "time": 45.4436 }
+{ "n": 134217728, "method": "efficient", "time": 37.9859 }
+{ "n": 134217728, "method": "thrust", "time": 12.5054 }
diff --git a/scripts/plot_performance_comparison.py b/scripts/plot_performance_comparison.py
index 78e14d42..56f403a7 100644
--- a/scripts/plot_performance_comparison.py
+++ b/scripts/plot_performance_comparison.py
@@ -9,33 +9,40 @@ def main():
     with json_path.open(encoding="utf-8") as f:
         data = [json.loads(line) for line in f]
 
-    fig, ax = plt.subplots()
-    for method, label in [
-        ("cpu", "CPU"),
-        ("naive", "GPU (naive)"),
-        ("efficient", "GPU (work-efficient)"),
-        ("thrust", "GPU (Thrust)"),
-    ]:
-        n_values = []
-        time_values = []
-        for entry in data:
-            if entry["method"] == method:
-                n_values.append(entry["n"])
-                time_values.append(entry["time"])
-        n_values = np.array(n_values)
-        time_values = np.array(time_values)
-        sorted_indices = np.argsort(n_values)
-        n_values = n_values[sorted_indices]
-        time_values = time_values[sorted_indices]
-        ax.plot(n_values, time_values, label=label, marker="o")
+    def plot_and_save(
+        methods: list[str], labels: list[str], power_of_two_only: bool, filename: str
+    ):
+        fig, ax = plt.subplots()
+        for method, label in zip(methods, labels):
+            n_values = []
+            time_values = []
+            for entry in data:
+                if entry["method"] == method:
+                    if not power_of_two_only or (entry["n"] & (entry["n"] - 1)) == 0:
+                        n_values.append(entry["n"])
+                        time_values.append(entry["time"])
+            n_values = np.array(n_values)
+            time_values = np.array(time_values)
+            sorted_indices = np.argsort(n_values)
+            n_values = n_values[sorted_indices]
+            time_values = time_values[sorted_indices]
+            ax.plot(n_values, time_values, label=label, marker="o", markersize=4)
 
-    ax.set_xscale("log")
-    ax.set_yscale("log")
-    ax.set_xlabel("Input size")
-    ax.set_ylabel("Time (ms)")
-    ax.legend()
-    fig.tight_layout()
-    fig.savefig(Path(__file__).parent.parent / "img" / "performance-comparison.png")
+        ax.set_xscale("log", base=2)
+        ax.set_yscale("log", base=10)
+        ax.grid(True, which="both", ls="--", lw=0.5)
+        ax.set_xlabel("Input size")
+        ax.set_ylabel("Time (ms)")
+        ax.legend()
+        fig.tight_layout()
+        fig.savefig(Path(__file__).parent.parent / "img" / filename)
+
+    all_methods = ["cpu", "naive", "efficient", "thrust"]
+    all_labels = ["CPU", "GPU (naive)", "GPU (work-efficient)", "GPU (Thrust)"]
+    plot_and_save(all_methods, all_labels, False, "performance-comparison.png")
+    plot_and_save(
+        all_methods[1:], all_labels[1:], True, "performance-comparison-gpu-only.png"
+    )
 
 
 if __name__ == "__main__":
diff --git a/src/compare_performance.cpp b/src/compare_performance.cpp
index de9331a4..b793a001 100644
--- a/src/compare_performance.cpp
+++ b/src/compare_performance.cpp
@@ -1,4 +1,5 @@
 #include <fstream>
+#include <iostream>
 #include <thread>
 #include <utility>
 #include <vector>
@@ -10,7 +11,7 @@
 
 #include "testing_helpers.hpp"
 
-constexpr int MAX_SIZE = 1 << 24;
+constexpr int MAX_SIZE = 1 << 27;
 std::vector<int> inputs(MAX_SIZE);
 std::vector<int> outputs(MAX_SIZE);
 
@@ -21,11 +22,12 @@ void prepareData(int n) {
 
 template <bool IsGpu, typename Timer, typename Func>
 float measureTime(Timer &timer, Func func, int n) {
-    const int warmup = 5;
-    const int iterations = 20;
+    const int warmup = 1;
+    const int iterations = 10;
     for (int i = 0; i < warmup; i++) {
         prepareData(n);
         func();
+        std::this_thread::sleep_for(std::chrono::milliseconds(10));
     }
     float totalTime = 0.0f;
     for (int i = 0; i < iterations; ++i) {
@@ -36,6 +38,7 @@ float measureTime(Timer &timer, Func func, int n) {
         } else {
             totalTime += timer.getCpuElapsedTimeForPreviousOperation();
         }
+        std::this_thread::sleep_for(std::chrono::milliseconds(10));
     }
     return totalTime / iterations;
 }
@@ -43,7 +46,7 @@ float measureTime(Timer &timer, Func func, int n) {
 int main() {
     std::ofstream outFile("performance_comparison.nljson");
 
-    for (int exponent = 4; exponent <= 24; ++exponent) {
+    for (int exponent = 4; exponent <= 27; ++exponent) {
         const int baseN = 1 << exponent;
         for (int n : {baseN - 3, baseN}) {
             float cpuTime = measureTime<false>(
@@ -70,6 +73,7 @@ int main() {
                         << "\"method\": \"" << name << "\", "
                         << "\"time\": " << time << " }" << std::endl;
             }
+            std::cout << "Completed n = " << n << std::endl;
             std::this_thread::sleep_for(std::chrono::milliseconds(100));
         }
     }

From 2ea8a927fe174ceb3ece862cedaedc45af7d4fa7 Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Mon, 15 Sep 2025 04:01:18 -0400
Subject: [PATCH 08/12] Update performance comparisons

---
 img/performance-comparison-gpu-only.png |  Bin 56590 -> 55605 bytes
 img/performance-comparison.png          |  Bin 60668 -> 60806 bytes
 scripts/performance_comparison.nljson   | 2106 +++++++++++++++++++++--
 scripts/plot_performance_comparison.py  |   26 +-
 src/compare_performance.cpp             |    6 +-
 5 files changed, 1940 insertions(+), 198 deletions(-)

diff --git a/img/performance-comparison-gpu-only.png b/img/performance-comparison-gpu-only.png
index d222e930bef7f518a1600dc59ce974b49cc2ecc7..c782873efbcad24e3138e91085f7763174dff6b9 100644
GIT binary patch
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diff --git a/scripts/performance_comparison.nljson b/scripts/performance_comparison.nljson
index d8a84f8d..de66aac0 100644
--- a/scripts/performance_comparison.nljson
+++ b/scripts/performance_comparison.nljson
@@ -1,192 +1,1920 @@
-{ "n": 13, "method": "cpu", "time": 0.00033 }
-{ "n": 13, "method": "naive", "time": 0.232378 }
-{ "n": 13, "method": "efficient", "time": 0.387424 }
-{ "n": 13, "method": "thrust", "time": 0.171539 }
+{ "n": 13, "method": "cpu", "time": 0.0001 }
+{ "n": 13, "method": "naive", "time": 0.08192 }
+{ "n": 13, "method": "efficient", "time": 0.101376 }
+{ "n": 13, "method": "thrust", "time": 0.060768 }
+{ "n": 16, "method": "cpu", "time": 0 }
+{ "n": 16, "method": "naive", "time": 0.03616 }
+{ "n": 16, "method": "efficient", "time": 0.078848 }
+{ "n": 16, "method": "thrust", "time": 0.027616 }
+{ "n": 29, "method": "cpu", "time": 0.0001 }
+{ "n": 29, "method": "naive", "time": 0.036864 }
+{ "n": 29, "method": "efficient", "time": 0.093184 }
+{ "n": 29, "method": "thrust", "time": 0.073728 }
+{ "n": 32, "method": "cpu", "time": 0.0001 }
+{ "n": 32, "method": "naive", "time": 0.037184 }
+{ "n": 32, "method": "efficient", "time": 0.108544 }
+{ "n": 32, "method": "thrust", "time": 0.029696 }
+{ "n": 61, "method": "cpu", "time": 0.0005 }
+{ "n": 61, "method": "naive", "time": 0.038976 }
+{ "n": 61, "method": "efficient", "time": 0.1024 }
+{ "n": 61, "method": "thrust", "time": 0.031744 }
+{ "n": 64, "method": "cpu", "time": 0.0004 }
+{ "n": 64, "method": "naive", "time": 0.36848 }
+{ "n": 64, "method": "efficient", "time": 0.850112 }
+{ "n": 64, "method": "thrust", "time": 0.096512 }
+{ "n": 125, "method": "cpu", "time": 0.0005 }
+{ "n": 125, "method": "naive", "time": 0.489504 }
+{ "n": 125, "method": "efficient", "time": 0.387072 }
+{ "n": 125, "method": "thrust", "time": 0.093184 }
+{ "n": 128, "method": "cpu", "time": 0.0004 }
+{ "n": 128, "method": "naive", "time": 0.295936 }
+{ "n": 128, "method": "efficient", "time": 0.460864 }
+{ "n": 128, "method": "thrust", "time": 0.297984 }
+{ "n": 253, "method": "cpu", "time": 0.0005 }
+{ "n": 253, "method": "naive", "time": 0.672128 }
+{ "n": 253, "method": "efficient", "time": 0.748256 }
+{ "n": 253, "method": "thrust", "time": 0.26112 }
+{ "n": 256, "method": "cpu", "time": 0.0005 }
+{ "n": 256, "method": "naive", "time": 0.338944 }
+{ "n": 256, "method": "efficient", "time": 0.7424 }
+{ "n": 256, "method": "thrust", "time": 0.311296 }
+{ "n": 509, "method": "cpu", "time": 0.0004 }
+{ "n": 509, "method": "naive", "time": 0.418784 }
+{ "n": 509, "method": "efficient", "time": 0.495904 }
+{ "n": 509, "method": "thrust", "time": 0.15376 }
+{ "n": 512, "method": "cpu", "time": 0.0009 }
+{ "n": 512, "method": "naive", "time": 0.38016 }
+{ "n": 512, "method": "efficient", "time": 0.76624 }
+{ "n": 512, "method": "thrust", "time": 0.083776 }
+{ "n": 1021, "method": "cpu", "time": 0.0011 }
+{ "n": 1021, "method": "naive", "time": 0.37808 }
+{ "n": 1021, "method": "efficient", "time": 0.55296 }
+{ "n": 1021, "method": "thrust", "time": 0.124064 }
+{ "n": 1024, "method": "cpu", "time": 0.0013 }
+{ "n": 1024, "method": "naive", "time": 0.423072 }
+{ "n": 1024, "method": "efficient", "time": 0.47584 }
+{ "n": 1024, "method": "thrust", "time": 0.12288 }
+{ "n": 2045, "method": "cpu", "time": 0.0022 }
+{ "n": 2045, "method": "naive", "time": 0.469888 }
+{ "n": 2045, "method": "efficient", "time": 0.569344 }
+{ "n": 2045, "method": "thrust", "time": 0.106496 }
+{ "n": 2048, "method": "cpu", "time": 0.0021 }
+{ "n": 2048, "method": "naive", "time": 0.485376 }
+{ "n": 2048, "method": "efficient", "time": 0.649216 }
+{ "n": 2048, "method": "thrust", "time": 0.084384 }
+{ "n": 4093, "method": "cpu", "time": 0.004 }
+{ "n": 4093, "method": "naive", "time": 0.337056 }
+{ "n": 4093, "method": "efficient", "time": 0.784 }
+{ "n": 4093, "method": "thrust", "time": 0.285696 }
+{ "n": 4096, "method": "cpu", "time": 0.004 }
+{ "n": 4096, "method": "naive", "time": 0.334016 }
+{ "n": 4096, "method": "efficient", "time": 0.676864 }
+{ "n": 4096, "method": "thrust", "time": 0.101376 }
+{ "n": 8189, "method": "cpu", "time": 0.0078 }
+{ "n": 8189, "method": "naive", "time": 0.505888 }
+{ "n": 8189, "method": "efficient", "time": 0.703648 }
+{ "n": 8189, "method": "thrust", "time": 0.114688 }
+{ "n": 8192, "method": "cpu", "time": 0.0062 }
+{ "n": 8192, "method": "naive", "time": 0.316416 }
+{ "n": 8192, "method": "efficient", "time": 0.600128 }
+{ "n": 8192, "method": "thrust", "time": 0.090432 }
+{ "n": 16381, "method": "cpu", "time": 0.0155 }
+{ "n": 16381, "method": "naive", "time": 0.308448 }
+{ "n": 16381, "method": "efficient", "time": 0.472064 }
+{ "n": 16381, "method": "thrust", "time": 0.138112 }
+{ "n": 16384, "method": "cpu", "time": 0.0157 }
+{ "n": 16384, "method": "naive", "time": 0.403456 }
+{ "n": 16384, "method": "efficient", "time": 0.720128 }
+{ "n": 16384, "method": "thrust", "time": 0.103424 }
+{ "n": 32765, "method": "cpu", "time": 0.0308 }
+{ "n": 32765, "method": "naive", "time": 0.370624 }
+{ "n": 32765, "method": "efficient", "time": 0.698496 }
+{ "n": 32765, "method": "thrust", "time": 0.306176 }
+{ "n": 32768, "method": "cpu", "time": 0.043 }
+{ "n": 32768, "method": "naive", "time": 1.03446 }
+{ "n": 32768, "method": "efficient", "time": 0.680032 }
+{ "n": 32768, "method": "thrust", "time": 0.1024 }
+{ "n": 65533, "method": "cpu", "time": 0.0602 }
+{ "n": 65533, "method": "naive", "time": 0.497088 }
+{ "n": 65533, "method": "efficient", "time": 0.77312 }
+{ "n": 65533, "method": "thrust", "time": 0.398592 }
+{ "n": 65536, "method": "cpu", "time": 0.0679 }
+{ "n": 65536, "method": "naive", "time": 0.40112 }
+{ "n": 65536, "method": "efficient", "time": 0.777312 }
+{ "n": 65536, "method": "thrust", "time": 0.115712 }
+{ "n": 131069, "method": "cpu", "time": 0.1373 }
+{ "n": 131069, "method": "naive", "time": 1.50413 }
+{ "n": 131069, "method": "efficient", "time": 0.82912 }
+{ "n": 131069, "method": "thrust", "time": 0.123648 }
+{ "n": 131072, "method": "cpu", "time": 0.1013 }
+{ "n": 131072, "method": "naive", "time": 0.502528 }
+{ "n": 131072, "method": "efficient", "time": 0.89552 }
+{ "n": 131072, "method": "thrust", "time": 0.096832 }
+{ "n": 262141, "method": "cpu", "time": 0.1545 }
+{ "n": 262141, "method": "naive", "time": 0.192448 }
+{ "n": 262141, "method": "efficient", "time": 0.800832 }
+{ "n": 262141, "method": "thrust", "time": 0.667648 }
+{ "n": 262144, "method": "cpu", "time": 0.1135 }
+{ "n": 262144, "method": "naive", "time": 0.22832 }
+{ "n": 262144, "method": "efficient", "time": 0.471552 }
+{ "n": 262144, "method": "thrust", "time": 0.675904 }
+{ "n": 524285, "method": "cpu", "time": 0.1976 }
+{ "n": 524285, "method": "naive", "time": 0.128128 }
+{ "n": 524285, "method": "efficient", "time": 0.287744 }
+{ "n": 524285, "method": "thrust", "time": 0.316416 }
+{ "n": 524288, "method": "cpu", "time": 0.2034 }
+{ "n": 524288, "method": "naive", "time": 0.150208 }
+{ "n": 524288, "method": "efficient", "time": 0.20032 }
+{ "n": 524288, "method": "thrust", "time": 0.548864 }
+{ "n": 1048573, "method": "cpu", "time": 0.3827 }
+{ "n": 1048573, "method": "naive", "time": 0.160064 }
+{ "n": 1048573, "method": "efficient", "time": 0.217088 }
+{ "n": 1048573, "method": "thrust", "time": 0.365344 }
+{ "n": 1048576, "method": "cpu", "time": 0.3845 }
+{ "n": 1048576, "method": "naive", "time": 0.160928 }
+{ "n": 1048576, "method": "efficient", "time": 0.507456 }
+{ "n": 1048576, "method": "thrust", "time": 0.2816 }
+{ "n": 2097149, "method": "cpu", "time": 0.7596 }
+{ "n": 2097149, "method": "naive", "time": 0.184384 }
+{ "n": 2097149, "method": "efficient", "time": 0.33792 }
+{ "n": 2097149, "method": "thrust", "time": 0.521216 }
+{ "n": 2097152, "method": "cpu", "time": 0.7903 }
+{ "n": 2097152, "method": "naive", "time": 0.602816 }
+{ "n": 2097152, "method": "efficient", "time": 0.379392 }
+{ "n": 2097152, "method": "thrust", "time": 0.53344 }
+{ "n": 4194301, "method": "cpu", "time": 1.558 }
+{ "n": 4194301, "method": "naive", "time": 1.15456 }
+{ "n": 4194301, "method": "efficient", "time": 0.484352 }
+{ "n": 4194301, "method": "thrust", "time": 0.90112 }
+{ "n": 4194304, "method": "cpu", "time": 1.4717 }
+{ "n": 4194304, "method": "naive", "time": 0.72464 }
+{ "n": 4194304, "method": "efficient", "time": 0.764736 }
+{ "n": 4194304, "method": "thrust", "time": 1.23706 }
+{ "n": 8388605, "method": "cpu", "time": 3.3729 }
+{ "n": 8388605, "method": "naive", "time": 6.76778 }
+{ "n": 8388605, "method": "efficient", "time": 0.703488 }
+{ "n": 8388605, "method": "thrust", "time": 3.76013 }
+{ "n": 8388608, "method": "cpu", "time": 3.0722 }
+{ "n": 8388608, "method": "naive", "time": 12.8393 }
+{ "n": 8388608, "method": "efficient", "time": 1.11494 }
+{ "n": 8388608, "method": "thrust", "time": 3.8144 }
+{ "n": 16777213, "method": "cpu", "time": 6.3687 }
+{ "n": 16777213, "method": "naive", "time": 125.72 }
+{ "n": 16777213, "method": "efficient", "time": 17.705 }
+{ "n": 16777213, "method": "thrust", "time": 7.41683 }
+{ "n": 16777216, "method": "cpu", "time": 7.1132 }
+{ "n": 16777216, "method": "naive", "time": 125.713 }
+{ "n": 16777216, "method": "efficient", "time": 0.879328 }
+{ "n": 16777216, "method": "thrust", "time": 0.53376 }
+{ "n": 33554429, "method": "cpu", "time": 14.2464 }
+{ "n": 33554429, "method": "naive", "time": 7.8096 }
+{ "n": 33554429, "method": "efficient", "time": 3.072 }
+{ "n": 33554429, "method": "thrust", "time": 0.746208 }
+{ "n": 33554432, "method": "cpu", "time": 12.6749 }
+{ "n": 33554432, "method": "naive", "time": 15.7589 }
+{ "n": 33554432, "method": "efficient", "time": 5.61578 }
+{ "n": 33554432, "method": "thrust", "time": 1.08979 }
+{ "n": 67108861, "method": "cpu", "time": 25.6998 }
+{ "n": 67108861, "method": "naive", "time": 33.3658 }
+{ "n": 67108861, "method": "efficient", "time": 11.3869 }
+{ "n": 67108861, "method": "thrust", "time": 10.0925 }
+{ "n": 67108864, "method": "cpu", "time": 25.4194 }
+{ "n": 67108864, "method": "naive", "time": 248.809 }
+{ "n": 67108864, "method": "efficient", "time": 6.44963 }
+{ "n": 67108864, "method": "thrust", "time": 1.16941 }
+{ "n": 134217725, "method": "cpu", "time": 50.8731 }
+{ "n": 134217725, "method": "naive", "time": 70.3046 }
+{ "n": 134217725, "method": "efficient", "time": 23.1055 }
+{ "n": 134217725, "method": "thrust", "time": 3.13645 }
+{ "n": 134217728, "method": "cpu", "time": 52.1911 }
+{ "n": 134217728, "method": "naive", "time": 265.07 }
+{ "n": 134217728, "method": "efficient", "time": 13.0589 }
+{ "n": 134217728, "method": "thrust", "time": 3.08461 }
+{ "n": 13, "method": "cpu", "time": 0.0001 }
+{ "n": 13, "method": "naive", "time": 0.222208 }
+{ "n": 13, "method": "efficient", "time": 0.295744 }
+{ "n": 13, "method": "thrust", "time": 0.193344 }
 { "n": 16, "method": "cpu", "time": 0.0003 }
-{ "n": 16, "method": "naive", "time": 0.08504 }
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+{ "n": 262144, "method": "naive", "time": 0.565888 }
+{ "n": 262144, "method": "efficient", "time": 0.188736 }
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+{ "n": 524285, "method": "cpu", "time": 0.2366 }
+{ "n": 524285, "method": "naive", "time": 0.186176 }
+{ "n": 524285, "method": "efficient", "time": 0.244736 }
+{ "n": 524285, "method": "thrust", "time": 0.31232 }
+{ "n": 524288, "method": "cpu", "time": 0.1693 }
+{ "n": 524288, "method": "naive", "time": 0.21872 }
+{ "n": 524288, "method": "efficient", "time": 0.283712 }
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+{ "n": 1048573, "method": "cpu", "time": 0.3318 }
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+{ "n": 1048573, "method": "efficient", "time": 0.19968 }
+{ "n": 1048573, "method": "thrust", "time": 0.300032 }
+{ "n": 1048576, "method": "cpu", "time": 0.3353 }
+{ "n": 1048576, "method": "naive", "time": 0.170752 }
+{ "n": 1048576, "method": "efficient", "time": 0.228128 }
+{ "n": 1048576, "method": "thrust", "time": 0.304896 }
+{ "n": 2097149, "method": "cpu", "time": 0.6974 }
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+{ "n": 2097149, "method": "efficient", "time": 0.413696 }
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+{ "n": 8388605, "method": "cpu", "time": 3.5299 }
+{ "n": 8388605, "method": "naive", "time": 14.1025 }
+{ "n": 8388605, "method": "efficient", "time": 0.785408 }
+{ "n": 8388605, "method": "thrust", "time": 3.8144 }
+{ "n": 8388608, "method": "cpu", "time": 3.7245 }
+{ "n": 8388608, "method": "naive", "time": 12.8612 }
+{ "n": 8388608, "method": "efficient", "time": 1.11744 }
+{ "n": 8388608, "method": "thrust", "time": 4.19942 }
+{ "n": 16777213, "method": "cpu", "time": 6.3601 }
+{ "n": 16777213, "method": "naive", "time": 125.744 }
+{ "n": 16777213, "method": "efficient", "time": 8.34253 }
+{ "n": 16777213, "method": "thrust", "time": 3.96288 }
+{ "n": 16777216, "method": "cpu", "time": 7.154 }
+{ "n": 16777216, "method": "naive", "time": 55.8031 }
+{ "n": 16777216, "method": "efficient", "time": 8.65498 }
+{ "n": 16777216, "method": "thrust", "time": 4.01203 }
+{ "n": 33554429, "method": "cpu", "time": 14.3135 }
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+{ "n": 33554429, "method": "efficient", "time": 40.0312 }
+{ "n": 33554429, "method": "thrust", "time": 12.5348 }
+{ "n": 33554432, "method": "cpu", "time": 13.0008 }
+{ "n": 33554432, "method": "naive", "time": 266.734 }
+{ "n": 33554432, "method": "efficient", "time": 3.16154 }
+{ "n": 33554432, "method": "thrust", "time": 0.73232 }
+{ "n": 67108861, "method": "cpu", "time": 28.4049 }
+{ "n": 67108861, "method": "naive", "time": 16.5131 }
+{ "n": 67108861, "method": "efficient", "time": 11.4043 }
+{ "n": 67108861, "method": "thrust", "time": 1.79616 }
+{ "n": 67108864, "method": "cpu", "time": 25.8181 }
+{ "n": 67108864, "method": "naive", "time": 33.3715 }
+{ "n": 67108864, "method": "efficient", "time": 11.4159 }
+{ "n": 67108864, "method": "thrust", "time": 10.1304 }
+{ "n": 134217725, "method": "cpu", "time": 52.3823 }
+{ "n": 134217725, "method": "naive", "time": 135.162 }
+{ "n": 134217725, "method": "efficient", "time": 12.9905 }
+{ "n": 134217725, "method": "thrust", "time": 3.14662 }
+{ "n": 134217728, "method": "cpu", "time": 54.2575 }
+{ "n": 134217728, "method": "naive", "time": 70.2535 }
+{ "n": 134217728, "method": "efficient", "time": 23.1526 }
+{ "n": 134217728, "method": "thrust", "time": 3.11808 }
+{ "n": 13, "method": "cpu", "time": 0.0001 }
+{ "n": 13, "method": "naive", "time": 0.08192 }
+{ "n": 13, "method": "efficient", "time": 0.334016 }
+{ "n": 13, "method": "thrust", "time": 0.13312 }
+{ "n": 16, "method": "cpu", "time": 0.0004 }
+{ "n": 16, "method": "naive", "time": 0.200704 }
+{ "n": 16, "method": "efficient", "time": 0.384736 }
+{ "n": 16, "method": "thrust", "time": 0.305024 }
+{ "n": 29, "method": "cpu", "time": 0.0002 }
+{ "n": 29, "method": "naive", "time": 0.265216 }
+{ "n": 29, "method": "efficient", "time": 0.781312 }
+{ "n": 29, "method": "thrust", "time": 0.324608 }
+{ "n": 32, "method": "cpu", "time": 0.0004 }
+{ "n": 32, "method": "naive", "time": 0.472064 }
+{ "n": 32, "method": "efficient", "time": 0.610304 }
+{ "n": 32, "method": "thrust", "time": 0.1024 }
+{ "n": 61, "method": "cpu", "time": 0.0004 }
+{ "n": 61, "method": "naive", "time": 0.760192 }
+{ "n": 61, "method": "efficient", "time": 0.35936 }
+{ "n": 61, "method": "thrust", "time": 0.109344 }
+{ "n": 64, "method": "cpu", "time": 0.0003 }
+{ "n": 64, "method": "naive", "time": 0.448512 }
+{ "n": 64, "method": "efficient", "time": 0.335936 }
+{ "n": 64, "method": "thrust", "time": 0.1024 }
+{ "n": 125, "method": "cpu", "time": 0.0004 }
+{ "n": 125, "method": "naive", "time": 0.297984 }
+{ "n": 125, "method": "efficient", "time": 0.580608 }
+{ "n": 125, "method": "thrust", "time": 0.100384 }
+{ "n": 128, "method": "cpu", "time": 0.0004 }
+{ "n": 128, "method": "naive", "time": 0.427648 }
+{ "n": 128, "method": "efficient", "time": 1.06486 }
+{ "n": 128, "method": "thrust", "time": 0.094304 }
+{ "n": 253, "method": "cpu", "time": 0.0005 }
+{ "n": 253, "method": "naive", "time": 0.371712 }
+{ "n": 253, "method": "efficient", "time": 0.693248 }
+{ "n": 253, "method": "thrust", "time": 0.102208 }
+{ "n": 256, "method": "cpu", "time": 0.0005 }
+{ "n": 256, "method": "naive", "time": 0.7352 }
+{ "n": 256, "method": "efficient", "time": 0.611328 }
+{ "n": 256, "method": "thrust", "time": 0.131072 }
+{ "n": 509, "method": "cpu", "time": 0.0007 }
+{ "n": 509, "method": "naive", "time": 0.893952 }
+{ "n": 509, "method": "efficient", "time": 0.580704 }
+{ "n": 509, "method": "thrust", "time": 0.104448 }
+{ "n": 512, "method": "cpu", "time": 0.0008 }
+{ "n": 512, "method": "naive", "time": 0.47616 }
+{ "n": 512, "method": "efficient", "time": 0.532768 }
+{ "n": 512, "method": "thrust", "time": 0.13904 }
+{ "n": 1021, "method": "cpu", "time": 0.0013 }
+{ "n": 1021, "method": "naive", "time": 0.673792 }
+{ "n": 1021, "method": "efficient", "time": 0.502752 }
+{ "n": 1021, "method": "thrust", "time": 0.272032 }
+{ "n": 1024, "method": "cpu", "time": 0.0012 }
+{ "n": 1024, "method": "naive", "time": 0.486752 }
+{ "n": 1024, "method": "efficient", "time": 0.688128 }
+{ "n": 1024, "method": "thrust", "time": 0.083904 }
+{ "n": 2045, "method": "cpu", "time": 0.0021 }
+{ "n": 2045, "method": "naive", "time": 0.37264 }
+{ "n": 2045, "method": "efficient", "time": 0.588544 }
+{ "n": 2045, "method": "thrust", "time": 0.195232 }
+{ "n": 2048, "method": "cpu", "time": 0.0022 }
+{ "n": 2048, "method": "naive", "time": 0.366368 }
+{ "n": 2048, "method": "efficient", "time": 0.5048 }
+{ "n": 2048, "method": "thrust", "time": 0.059392 }
+{ "n": 4093, "method": "cpu", "time": 0.0041 }
+{ "n": 4093, "method": "naive", "time": 0.46832 }
+{ "n": 4093, "method": "efficient", "time": 1.47446 }
+{ "n": 4093, "method": "thrust", "time": 0.106496 }
+{ "n": 4096, "method": "cpu", "time": 0.004 }
+{ "n": 4096, "method": "naive", "time": 0.334752 }
+{ "n": 4096, "method": "efficient", "time": 0.760096 }
+{ "n": 4096, "method": "thrust", "time": 0.192512 }
+{ "n": 8189, "method": "cpu", "time": 0.0016 }
+{ "n": 8189, "method": "naive", "time": 0.067584 }
+{ "n": 8189, "method": "efficient", "time": 0.222368 }
+{ "n": 8189, "method": "thrust", "time": 0.047104 }
+{ "n": 8192, "method": "cpu", "time": 0.0078 }
+{ "n": 8192, "method": "naive", "time": 0.3248 }
+{ "n": 8192, "method": "efficient", "time": 0.647008 }
+{ "n": 8192, "method": "thrust", "time": 0.095232 }
+{ "n": 16381, "method": "cpu", "time": 0.0164 }
+{ "n": 16381, "method": "naive", "time": 0.556032 }
+{ "n": 16381, "method": "efficient", "time": 0.777312 }
+{ "n": 16381, "method": "thrust", "time": 0.268064 }
+{ "n": 16384, "method": "cpu", "time": 0.0236 }
+{ "n": 16384, "method": "naive", "time": 1.1369 }
+{ "n": 16384, "method": "efficient", "time": 0.674848 }
+{ "n": 16384, "method": "thrust", "time": 0.110432 }
+{ "n": 32765, "method": "cpu", "time": 0.0306 }
+{ "n": 32765, "method": "naive", "time": 0.358464 }
+{ "n": 32765, "method": "efficient", "time": 0.749952 }
+{ "n": 32765, "method": "thrust", "time": 0.249856 }
+{ "n": 32768, "method": "cpu", "time": 0.0305 }
+{ "n": 32768, "method": "naive", "time": 1.05005 }
+{ "n": 32768, "method": "efficient", "time": 0.562144 }
+{ "n": 32768, "method": "thrust", "time": 0.028672 }
+{ "n": 65533, "method": "cpu", "time": 0.0624 }
+{ "n": 65533, "method": "naive", "time": 0.550592 }
+{ "n": 65533, "method": "efficient", "time": 0.776192 }
+{ "n": 65533, "method": "thrust", "time": 0.331776 }
+{ "n": 65536, "method": "cpu", "time": 0.0602 }
+{ "n": 65536, "method": "naive", "time": 0.649632 }
+{ "n": 65536, "method": "efficient", "time": 0.68752 }
+{ "n": 65536, "method": "thrust", "time": 0.051232 }
+{ "n": 131069, "method": "cpu", "time": 0.1323 }
+{ "n": 131069, "method": "naive", "time": 1.29651 }
+{ "n": 131069, "method": "efficient", "time": 1.12128 }
+{ "n": 131069, "method": "thrust", "time": 0.251904 }
+{ "n": 131072, "method": "cpu", "time": 0.1202 }
+{ "n": 131072, "method": "naive", "time": 0.384128 }
+{ "n": 131072, "method": "efficient", "time": 0.919488 }
+{ "n": 131072, "method": "thrust", "time": 0.287744 }
+{ "n": 262141, "method": "cpu", "time": 0.1584 }
+{ "n": 262141, "method": "naive", "time": 0.304864 }
+{ "n": 262141, "method": "efficient", "time": 0.70144 }
+{ "n": 262141, "method": "thrust", "time": 0.519168 }
+{ "n": 262144, "method": "cpu", "time": 0.1412 }
+{ "n": 262144, "method": "naive", "time": 0.096992 }
+{ "n": 262144, "method": "efficient", "time": 0.441088 }
+{ "n": 262144, "method": "thrust", "time": 0.622592 }
+{ "n": 524285, "method": "cpu", "time": 0.2329 }
+{ "n": 524285, "method": "naive", "time": 0.187232 }
+{ "n": 524285, "method": "efficient", "time": 0.202752 }
+{ "n": 524285, "method": "thrust", "time": 0.32256 }
+{ "n": 524288, "method": "cpu", "time": 0.1882 }
+{ "n": 524288, "method": "naive", "time": 0.251328 }
+{ "n": 524288, "method": "efficient", "time": 0.223904 }
+{ "n": 524288, "method": "thrust", "time": 0.372 }
+{ "n": 1048573, "method": "cpu", "time": 0.3468 }
+{ "n": 1048573, "method": "naive", "time": 0.148352 }
+{ "n": 1048573, "method": "efficient", "time": 0.222208 }
+{ "n": 1048573, "method": "thrust", "time": 0.26304 }
+{ "n": 1048576, "method": "cpu", "time": 0.3242 }
+{ "n": 1048576, "method": "naive", "time": 0.16112 }
+{ "n": 1048576, "method": "efficient", "time": 0.216448 }
+{ "n": 1048576, "method": "thrust", "time": 0.270336 }
+{ "n": 2097149, "method": "cpu", "time": 0.7913 }
+{ "n": 2097149, "method": "naive", "time": 0.195488 }
+{ "n": 2097149, "method": "efficient", "time": 0.275456 }
+{ "n": 2097149, "method": "thrust", "time": 0.354336 }
+{ "n": 2097152, "method": "cpu", "time": 0.7827 }
+{ "n": 2097152, "method": "naive", "time": 0.451424 }
+{ "n": 2097152, "method": "efficient", "time": 0.367392 }
+{ "n": 2097152, "method": "thrust", "time": 0.605184 }
+{ "n": 4194301, "method": "cpu", "time": 1.4737 }
+{ "n": 4194301, "method": "naive", "time": 0.89072 }
+{ "n": 4194301, "method": "efficient", "time": 0.52224 }
+{ "n": 4194301, "method": "thrust", "time": 1.09363 }
+{ "n": 4194304, "method": "cpu", "time": 1.728 }
+{ "n": 4194304, "method": "naive", "time": 0.735072 }
+{ "n": 4194304, "method": "efficient", "time": 0.785696 }
+{ "n": 4194304, "method": "thrust", "time": 1.25939 }
+{ "n": 8388605, "method": "cpu", "time": 3.4836 }
+{ "n": 8388605, "method": "naive", "time": 6.75178 }
+{ "n": 8388605, "method": "efficient", "time": 0.792576 }
+{ "n": 8388605, "method": "thrust", "time": 3.95878 }
+{ "n": 8388608, "method": "cpu", "time": 3.4885 }
+{ "n": 8388608, "method": "naive", "time": 12.8783 }
+{ "n": 8388608, "method": "efficient", "time": 1.09968 }
+{ "n": 8388608, "method": "thrust", "time": 4.16563 }
+{ "n": 16777213, "method": "cpu", "time": 7.1243 }
+{ "n": 16777213, "method": "naive", "time": 125.744 }
+{ "n": 16777213, "method": "efficient", "time": 8.35482 }
+{ "n": 16777213, "method": "thrust", "time": 3.87482 }
+{ "n": 16777216, "method": "cpu", "time": 7.4044 }
+{ "n": 16777216, "method": "naive", "time": 55.8184 }
+{ "n": 16777216, "method": "efficient", "time": 8.64646 }
+{ "n": 16777216, "method": "thrust", "time": 3.94336 }
+{ "n": 33554429, "method": "cpu", "time": 13.0081 }
+{ "n": 33554429, "method": "naive", "time": 117.964 }
+{ "n": 33554429, "method": "efficient", "time": 40.0538 }
+{ "n": 33554429, "method": "thrust", "time": 12.6413 }
+{ "n": 33554432, "method": "cpu", "time": 13.5002 }
+{ "n": 33554432, "method": "naive", "time": 170.5 }
+{ "n": 33554432, "method": "efficient", "time": 3.13914 }
+{ "n": 33554432, "method": "thrust", "time": 0.716864 }
+{ "n": 67108861, "method": "cpu", "time": 27.5883 }
+{ "n": 67108861, "method": "naive", "time": 16.5293 }
+{ "n": 67108861, "method": "efficient", "time": 11.4606 }
+{ "n": 67108861, "method": "thrust", "time": 1.80838 }
+{ "n": 67108864, "method": "cpu", "time": 29.2219 }
+{ "n": 67108864, "method": "naive", "time": 147.592 }
+{ "n": 67108864, "method": "efficient", "time": 6.41536 }
+{ "n": 67108864, "method": "thrust", "time": 1.21856 }
+{ "n": 134217725, "method": "cpu", "time": 57.038 }
+{ "n": 134217725, "method": "naive", "time": 211.975 }
+{ "n": 134217725, "method": "efficient", "time": 13.0171 }
+{ "n": 134217725, "method": "thrust", "time": 3.09072 }
+{ "n": 134217728, "method": "cpu", "time": 51.9489 }
+{ "n": 134217728, "method": "naive", "time": 70.3104 }
+{ "n": 134217728, "method": "efficient", "time": 23.1074 }
+{ "n": 134217728, "method": "thrust", "time": 3.11181 }
diff --git a/scripts/plot_performance_comparison.py b/scripts/plot_performance_comparison.py
index 56f403a7..e734a9ed 100644
--- a/scripts/plot_performance_comparison.py
+++ b/scripts/plot_performance_comparison.py
@@ -13,6 +13,7 @@ def plot_and_save(
         methods: list[str], labels: list[str], power_of_two_only: bool, filename: str
     ):
         fig, ax = plt.subplots()
+        sample_counts = []
         for method, label in zip(methods, labels):
             n_values = []
             time_values = []
@@ -21,12 +22,25 @@ def plot_and_save(
                     if not power_of_two_only or (entry["n"] & (entry["n"] - 1)) == 0:
                         n_values.append(entry["n"])
                         time_values.append(entry["time"])
-            n_values = np.array(n_values)
-            time_values = np.array(time_values)
-            sorted_indices = np.argsort(n_values)
-            n_values = n_values[sorted_indices]
-            time_values = time_values[sorted_indices]
-            ax.plot(n_values, time_values, label=label, marker="o", markersize=4)
+
+            n_values_sorted = sorted(set(n_values))
+            time_values_sorted = []
+            for n in n_values_sorted:
+                time_samples = []
+                for n_value, time_value in zip(n_values, time_values):
+                    if n_value == n:
+                        time_samples.append(time_value)
+                sample_counts.append(len(time_samples))
+                time_values_sorted.append(np.mean(time_samples))
+            ax.plot(
+                n_values_sorted,
+                time_values_sorted,
+                label=label,
+                marker="o",
+                markersize=4,
+            )
+
+        print("Average sample count:", np.mean(sample_counts))
 
         ax.set_xscale("log", base=2)
         ax.set_yscale("log", base=10)
diff --git a/src/compare_performance.cpp b/src/compare_performance.cpp
index b793a001..3a15c778 100644
--- a/src/compare_performance.cpp
+++ b/src/compare_performance.cpp
@@ -22,8 +22,8 @@ void prepareData(int n) {
 
 template <bool IsGpu, typename Timer, typename Func>
 float measureTime(Timer &timer, Func func, int n) {
-    const int warmup = 1;
-    const int iterations = 10;
+    const int warmup = 0;
+    const int iterations = 1;
     for (int i = 0; i < warmup; i++) {
         prepareData(n);
         func();
@@ -44,7 +44,7 @@ float measureTime(Timer &timer, Func func, int n) {
 }
 
 int main() {
-    std::ofstream outFile("performance_comparison.nljson");
+    std::ofstream outFile("performance_comparison.nljson", std::ios::app);
 
     for (int exponent = 4; exponent <= 27; ++exponent) {
         const int baseN = 1 << exponent;

From 4618529689c4c1c656d91d9008b5f137a3051eac Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Mon, 15 Sep 2025 16:49:40 -0400
Subject: [PATCH 09/12] Redo performance analyses

---
 CMakeLists.txt                         |    7 +-
 README.md                              |   96 +-
 img/performance-gpu-only.png           |  Bin 0 -> 45918 bytes
 img/performance.png                    |  Bin 0 -> 53834 bytes
 scripts/.gitignore                     |    1 +
 scripts/helper.py                      |   30 +
 scripts/measure_performance.py         |   53 +
 scripts/performance.json               | 1154 ++++++++++++++
 scripts/performance_comparison.nljson  | 1920 ------------------------
 scripts/plot_performance.py            |   64 +
 scripts/plot_performance_comparison.py |   63 -
 scripts/tune_block_sizes.py            |   48 +
 src/measure_time.cpp                   |  109 ++
 stream_compaction/efficient.h          |    2 +-
 stream_compaction/thrust.cu            |    3 -
 15 files changed, 1549 insertions(+), 2001 deletions(-)
 create mode 100644 img/performance-gpu-only.png
 create mode 100644 img/performance.png
 create mode 100644 scripts/.gitignore
 create mode 100644 scripts/helper.py
 create mode 100644 scripts/measure_performance.py
 create mode 100644 scripts/performance.json
 delete mode 100644 scripts/performance_comparison.nljson
 create mode 100644 scripts/plot_performance.py
 delete mode 100644 scripts/plot_performance_comparison.py
 create mode 100644 scripts/tune_block_sizes.py
 create mode 100644 src/measure_time.cpp

diff --git a/CMakeLists.txt b/CMakeLists.txt
index f320de2f..c3b1b602 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -45,8 +45,5 @@ add_executable(${CMAKE_PROJECT_NAME} ${sources} ${headers})
 target_link_libraries(${CMAKE_PROJECT_NAME} stream_compaction)
 set_property(DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR} PROPERTY VS_STARTUP_PROJECT ${CMAKE_PROJECT_NAME})
 
-add_executable(tune_block_sizes src/tune_block_sizes.cpp ${headers})
-target_link_libraries(tune_block_sizes stream_compaction)
-
-add_executable(compare_performance src/compare_performance.cpp ${headers})
-target_link_libraries(compare_performance stream_compaction)
+add_executable(measure_time src/measure_time.cpp ${headers})
+target_link_libraries(measure_time stream_compaction)
diff --git a/README.md b/README.md
index 9f85e6f7..2975bc26 100644
--- a/README.md
+++ b/README.md
@@ -20,14 +20,12 @@ This project implements stream compaction and its building blocks (map, scan, sc
 - A CPU implementation of scan and stream compaction
 - GPU implementations of scan, using both naive and work-efficient methods
 - A GPU implementation of stream compaction based on the work-efficient scan
+- C++ and Python scripts used to automate performance measurement accurately and programmatically
 - Performance analysis comparing the different methods
 
 ### Changes to `CMakeLists.txt`
 
-Two additional executables are added to the project to assist certain tasks:
-
-- `tune_block_sizes.exe`: Runs each algorithm under a range of block sizes to find the optimal block size.
-- `compare_performance.exe`: Executes different scan implementations across a range of input sizes and records their execution times for plotting.
+An additional executable,`measure_time.exe`, has been added to the project to support block size tuning, performance benchmarking, and profiling.
 
 ### Changes to Function Signatures
 
@@ -35,9 +33,9 @@ To simplify block size tuning, I added an optional `blockSize` parameter to the
 
 - `Naive::scan(..., const int blockSize = 256)`
 - `Efficient::scan(..., const int blockSize = 128)`
-- `Efficient::compact(..., const int blockSize = 512)`
+- `Efficient::compact(..., const int blockSize = 128)`
 
-These parameters are used only by `tune_block_sizes.exe` and do not affect existing calls.
+These parameters are used only by `measure_time.exe` and do not affect existing calls.
 
 ## Part 1: CPU Scan & Stream Compaction
 
@@ -109,6 +107,17 @@ Project description: see the [Features](#features) section at the top.
 
 ### Performance Analysis
 
+#### `measure_time.exe`
+
+To simplify performance analysis, I added a C++ executable, `measure_time.exe`. The implementation is in [`measure_time.cpp`](src/measure_time.cpp), which:
+
+- Accepts the operation (scan or compact), implementation (CPU, GPU naive, GPU work-efficient, or GPU Thrust), input size, and block size as command-line arguments.
+- Generates random input data and prints the measured execution time (in milliseconds) to the console.
+
+I created this tool because measuring a configuration only once is often imprecise. In my earlier attempts, running repeated measurements within a C++ loop caused the results to drift significantly. In particular, Thrust measurements became unexpectedly slower, sometimes even slower than the GPU naive implementation. I suspect this was due to frequent GPU memory allocations and deallocations (since the exposed API uses CPU inputs and outputs), which created an atypical workload and put the driver in a degraded performance state.
+
+To avoid this issue, I designed `measure_time.exe` to test only a single configuration with one iteration per program launch. Repeated measurements are instead automated by accompanying Python scripts.
+
 #### Optimizing Block Sizes
 
 To optimize block sizes, I added an optional `blockSize` parameter to every top-level function, each with a tuned default value. This preserves backward compatibility while making block-size tuning easier.
@@ -123,8 +132,7 @@ I also added a new executable, `tune_block_sizes.exe`, to the CMake project. In
 Based on these experiments, the chosen defaults are:
 
 - 256 for the naive scan
-- 128 for the work-efficient scan
-- 512 for the work-efficient compaction
+- 128 for the work-efficient scan and compaction
 
 #### Performance Comparison
 
@@ -154,7 +162,7 @@ Methods:
     - For small $N$, execution time is dominated by kernel launch overhead. Since Thrust minimizes this to just two launches, it performs well in this regime.  
     - For large $N$, Thrust likely employs shared memory optimizations. The cause of its relative slowness compared to my implementation requires further investigation.
 
-#### Test Results
+#### Outputs of `cis5650_stream_compaction_test.exe`
 
 ```text
 ****************
@@ -211,3 +219,73 @@ Methods:
     passed 
 Press any key to continue . . . 
 ```
+
+#### Outputs of `tune_block_sizes.py`
+
+```text
+Naive scan, power-of-two
+Block size: 8, time: 6.231833506 ms
+Block size: 16, time: 3.173327995 ms
+Block size: 32, time: 1.6745983839999998 ms
+Block size: 64, time: 0.8986879886000001 ms
+Block size: 128, time: 0.5220288008999999 ms
+Block size: 256, time: 0.3854463994 ms
+Block size: 512, time: 0.4322271972999999 ms
+Block size: 1024, time: 0.4435839981 ms
+Optimal block size: 256, time: 0.3854463994 ms
+========================================
+Naive scan, non-power-of-two
+Block size: 8, time: 6.219187259 ms
+Block size: 16, time: 3.18726716 ms
+Block size: 32, time: 1.658544017 ms
+Block size: 64, time: 0.8911647916 ms
+Block size: 128, time: 0.5024224044000001 ms
+Block size: 256, time: 0.3580832005 ms
+Block size: 512, time: 0.3581887961 ms
+Block size: 1024, time: 0.4385919958000001 ms
+Optimal block size: 256, time: 0.3580832005 ms
+========================================
+Work-efficient scan, power-of-two
+Block size: 8, time: 0.8682271958 ms
+Block size: 16, time: 0.6581280051999999 ms
+Block size: 32, time: 0.5843007983 ms
+Block size: 64, time: 0.511523199 ms
+Block size: 128, time: 0.47026240229999994 ms
+Block size: 256, time: 0.5074463992 ms
+Block size: 512, time: 0.48191359920000004 ms
+Block size: 1024, time: 0.4813536018 ms
+Optimal block size: 128, time: 0.47026240229999994 ms
+========================================
+Work-efficient scan, non-power-of-two
+Block size: 8, time: 0.8395776093 ms
+Block size: 16, time: 0.6402047992 ms
+Block size: 32, time: 0.5541888057000001 ms
+Block size: 64, time: 0.5040127992000001 ms
+Block size: 128, time: 0.4989087999 ms
+Block size: 256, time: 0.5251072078000001 ms
+Block size: 512, time: 0.48322560189999997 ms
+Block size: 1024, time: 0.49256000219999996 ms
+Optimal block size: 512, time: 0.48322560189999997 ms
+========================================
+Work-efficient compact, power-of-two
+Block size: 8, time: 1.4116608029999997 ms
+Block size: 16, time: 0.9503391928000001 ms
+Block size: 32, time: 0.7004479884 ms
+Block size: 64, time: 0.5998431921 ms
+Block size: 128, time: 0.5244000018 ms
+Block size: 256, time: 0.5620128065000001 ms
+Block size: 512, time: 0.7700480073 ms
+Block size: 1024, time: 0.6348639965 ms
+Optimal block size: 128, time: 0.5244000018 ms
+========================================
+Work-efficient compact, non-power-of-two
+Block size: 8, time: 1.40685439 ms
+Block size: 16, time: 0.9263231993 ms
+Block size: 32, time: 0.7410848021000002 ms
+Block size: 64, time: 0.7034976004999999 ms
+Block size: 128, time: 0.7220223933 ms
+Block size: 256, time: 0.7788672031 ms
+Block size: 512, time: 0.7625663994 ms
+Block size: 1024, time: 0.7747167944 ms
+Optimal block size: 64, time: 0.7034976004999999 ms
+```
diff --git a/img/performance-gpu-only.png b/img/performance-gpu-only.png
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diff --git a/scripts/.gitignore b/scripts/.gitignore
new file mode 100644
index 00000000..bee8a64b
--- /dev/null
+++ b/scripts/.gitignore
@@ -0,0 +1 @@
+__pycache__
diff --git a/scripts/helper.py b/scripts/helper.py
new file mode 100644
index 00000000..06b24fdf
--- /dev/null
+++ b/scripts/helper.py
@@ -0,0 +1,30 @@
+import subprocess
+from pathlib import Path
+from typing import Literal
+
+ROOT_DIR = Path(__file__).parent.parent.absolute()
+MEASURE_TIME_EXE = ROOT_DIR / "build" / "bin" / "Release" / "measure_time.exe"
+assert MEASURE_TIME_EXE.is_file()
+
+
+def measure_time(
+    operation: Literal["scan", "compact"],
+    implementation: Literal["cpu", "naive", "efficient", "thrust"],
+    input_size: int,
+    block_size: int = -1,
+) -> float:
+    result = subprocess.run(
+        [
+            str(MEASURE_TIME_EXE),
+            operation,
+            implementation,
+            str(input_size),
+            str(block_size),
+        ],
+        capture_output=True,
+        cwd=ROOT_DIR,
+        check=True,
+        encoding="utf-8",
+        text=True,
+    )
+    return float(result.stdout)
diff --git a/scripts/measure_performance.py b/scripts/measure_performance.py
new file mode 100644
index 00000000..536cc6d3
--- /dev/null
+++ b/scripts/measure_performance.py
@@ -0,0 +1,53 @@
+import json
+from pathlib import Path
+
+from helper import measure_time
+
+
+def main() -> None:
+    performance_json_path = Path(__file__).parent / "performance.json"
+    if performance_json_path.exists():
+        with performance_json_path.open(encoding="utf-8") as f:
+            performance_data = json.load(f)
+    else:
+        performance_data = []
+
+    def find_existing_entry(
+        operation: str, implementation: str, input_size: int
+    ) -> dict | None:
+        for entry in performance_data:
+            if (
+                entry["operation"] == operation
+                and entry["implementation"] == implementation
+                and entry["input_size"] == input_size
+            ):
+                return entry
+        return None
+
+    for implementation in ["cpu", "naive", "efficient", "thrust"]:
+        for exponent in range(4, 28):
+            base_input_size = 1 << exponent
+            for input_size in [base_input_size, base_input_size - 3]:
+                config = {
+                    "operation": "scan",
+                    "implementation": implementation,
+                    "input_size": input_size,
+                }
+                if find_existing_entry(**config) is not None:
+                    print(f"Skipping existing entry: {config}")
+                    continue
+
+                time_sum = 0.0
+                time_count = 50
+                for _ in range(time_count):
+                    time_sum += measure_time("scan", implementation, input_size)
+                time = time_sum / time_count
+                print(f"Measured: {config}, time: {time} ms")
+                performance_data.append({**config, "time": time})
+
+                with performance_json_path.open("w", encoding="utf-8") as f:
+                    json.dump(performance_data, f, indent=4)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/performance.json b/scripts/performance.json
new file mode 100644
index 00000000..ab35e794
--- /dev/null
+++ b/scripts/performance.json
@@ -0,0 +1,1154 @@
+[
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 16,
+        "time": 0.00013399999751000004
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 13,
+        "time": 0.00013399999751000004
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 32,
+        "time": 0.00014399999769000005
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 29,
+        "time": 0.00012399999776000004
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 64,
+        "time": 0.00016799999795000006
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 61,
+        "time": 0.00014399999769000005
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 128,
+        "time": 0.00020399999919999996
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 125,
+        "time": 0.00019999999672000004
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 256,
+        "time": 0.00026600000066000017
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 253,
+        "time": 0.00026000000296000017
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 512,
+        "time": 0.00040800000540000027
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 509,
+        "time": 0.00043000000934000017
+    },
+    {
+        "operation": "scan",
+        "implementation": "cpu",
+        "input_size": 1024,
+        "time": 0.0005460000142200003
+    },
+    {
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+        "implementation": "cpu",
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+        "time": 0.0005120000080000004
+    },
+    {
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+        "time": 0.0009139999999599998
+    },
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+        "time": 0.0009199999953
+    },
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+        "time": 0.0018319999932
+    },
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+        "time": 0.001818000007
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\ No newline at end of file
diff --git a/scripts/performance_comparison.nljson b/scripts/performance_comparison.nljson
deleted file mode 100644
index de66aac0..00000000
--- a/scripts/performance_comparison.nljson
+++ /dev/null
@@ -1,1920 +0,0 @@
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-{ "n": 13, "method": "efficient", "time": 0.101376 }
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-{ "n": 32, "method": "cpu", "time": 0.0001 }
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-{ "n": 32, "method": "efficient", "time": 0.108544 }
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-{ "n": 128, "method": "cpu", "time": 0.0004 }
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-{ "n": 2097152, "method": "thrust", "time": 0.605184 }
-{ "n": 4194301, "method": "cpu", "time": 1.4737 }
-{ "n": 4194301, "method": "naive", "time": 0.89072 }
-{ "n": 4194301, "method": "efficient", "time": 0.52224 }
-{ "n": 4194301, "method": "thrust", "time": 1.09363 }
-{ "n": 4194304, "method": "cpu", "time": 1.728 }
-{ "n": 4194304, "method": "naive", "time": 0.735072 }
-{ "n": 4194304, "method": "efficient", "time": 0.785696 }
-{ "n": 4194304, "method": "thrust", "time": 1.25939 }
-{ "n": 8388605, "method": "cpu", "time": 3.4836 }
-{ "n": 8388605, "method": "naive", "time": 6.75178 }
-{ "n": 8388605, "method": "efficient", "time": 0.792576 }
-{ "n": 8388605, "method": "thrust", "time": 3.95878 }
-{ "n": 8388608, "method": "cpu", "time": 3.4885 }
-{ "n": 8388608, "method": "naive", "time": 12.8783 }
-{ "n": 8388608, "method": "efficient", "time": 1.09968 }
-{ "n": 8388608, "method": "thrust", "time": 4.16563 }
-{ "n": 16777213, "method": "cpu", "time": 7.1243 }
-{ "n": 16777213, "method": "naive", "time": 125.744 }
-{ "n": 16777213, "method": "efficient", "time": 8.35482 }
-{ "n": 16777213, "method": "thrust", "time": 3.87482 }
-{ "n": 16777216, "method": "cpu", "time": 7.4044 }
-{ "n": 16777216, "method": "naive", "time": 55.8184 }
-{ "n": 16777216, "method": "efficient", "time": 8.64646 }
-{ "n": 16777216, "method": "thrust", "time": 3.94336 }
-{ "n": 33554429, "method": "cpu", "time": 13.0081 }
-{ "n": 33554429, "method": "naive", "time": 117.964 }
-{ "n": 33554429, "method": "efficient", "time": 40.0538 }
-{ "n": 33554429, "method": "thrust", "time": 12.6413 }
-{ "n": 33554432, "method": "cpu", "time": 13.5002 }
-{ "n": 33554432, "method": "naive", "time": 170.5 }
-{ "n": 33554432, "method": "efficient", "time": 3.13914 }
-{ "n": 33554432, "method": "thrust", "time": 0.716864 }
-{ "n": 67108861, "method": "cpu", "time": 27.5883 }
-{ "n": 67108861, "method": "naive", "time": 16.5293 }
-{ "n": 67108861, "method": "efficient", "time": 11.4606 }
-{ "n": 67108861, "method": "thrust", "time": 1.80838 }
-{ "n": 67108864, "method": "cpu", "time": 29.2219 }
-{ "n": 67108864, "method": "naive", "time": 147.592 }
-{ "n": 67108864, "method": "efficient", "time": 6.41536 }
-{ "n": 67108864, "method": "thrust", "time": 1.21856 }
-{ "n": 134217725, "method": "cpu", "time": 57.038 }
-{ "n": 134217725, "method": "naive", "time": 211.975 }
-{ "n": 134217725, "method": "efficient", "time": 13.0171 }
-{ "n": 134217725, "method": "thrust", "time": 3.09072 }
-{ "n": 134217728, "method": "cpu", "time": 51.9489 }
-{ "n": 134217728, "method": "naive", "time": 70.3104 }
-{ "n": 134217728, "method": "efficient", "time": 23.1074 }
-{ "n": 134217728, "method": "thrust", "time": 3.11181 }
diff --git a/scripts/plot_performance.py b/scripts/plot_performance.py
new file mode 100644
index 00000000..e11be0d2
--- /dev/null
+++ b/scripts/plot_performance.py
@@ -0,0 +1,64 @@
+import json
+from pathlib import Path
+
+import numpy as np
+from matplotlib import pyplot as plt
+
+
+def is_power_of_two(n: int) -> bool:
+    return (n & (n - 1)) == 0 and n != 0
+
+
+def main() -> None:
+    json_path = Path(__file__).parent / "performance.json"
+    with json_path.open(encoding="utf-8") as f:
+        data = json.load(f)
+
+    def plot_and_save(
+        implementations: list[str],
+        labels: list[str],
+        power_of_two_only: bool,
+        filename: str,
+    ):
+        fig, ax = plt.subplots()
+        for implementation, label in zip(implementations, labels):
+            n_values = []
+            time_values = []
+            for entry in data:
+                if entry["implementation"] == implementation:
+                    if not power_of_two_only or is_power_of_two(entry["input_size"]):
+                        n_values.append(entry["input_size"])
+                        time_values.append(entry["time"])
+
+            n_values = np.array(n_values)
+            time_values = np.array(time_values)
+            sort_indices = np.argsort(n_values)
+            n_values = n_values[sort_indices]
+            time_values = time_values[sort_indices]
+            ax.plot(n_values, time_values, label=label, marker="o", markersize=4)
+
+        ax.set_xscale("log", base=2)
+        ax.set_yscale("log", base=10)
+        ax.grid(True, which="both", ls="--", lw=0.5)
+        ax.set_xlabel("Input size")
+        ax.set_ylabel("Time (ms)")
+        ax.legend()
+        fig.tight_layout()
+        fig.savefig(Path(__file__).parent.parent / "img" / filename)
+
+    plot_and_save(
+        ["cpu", "naive", "efficient", "thrust"],
+        ["CPU", "GPU (naive)", "GPU (work-efficient)", "GPU (Thrust)"],
+        False,
+        "performance.png",
+    )
+    plot_and_save(
+        ["naive", "efficient", "thrust"],
+        ["Naive", "Work-efficient", "Thrust"],
+        True,
+        "performance-gpu-only.png",
+    )
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/plot_performance_comparison.py b/scripts/plot_performance_comparison.py
deleted file mode 100644
index e734a9ed..00000000
--- a/scripts/plot_performance_comparison.py
+++ /dev/null
@@ -1,63 +0,0 @@
-import json
-from matplotlib import pyplot as plt
-from pathlib import Path
-import numpy as np
-
-
-def main():
-    json_path = Path(__file__).parent / "performance_comparison.nljson"
-    with json_path.open(encoding="utf-8") as f:
-        data = [json.loads(line) for line in f]
-
-    def plot_and_save(
-        methods: list[str], labels: list[str], power_of_two_only: bool, filename: str
-    ):
-        fig, ax = plt.subplots()
-        sample_counts = []
-        for method, label in zip(methods, labels):
-            n_values = []
-            time_values = []
-            for entry in data:
-                if entry["method"] == method:
-                    if not power_of_two_only or (entry["n"] & (entry["n"] - 1)) == 0:
-                        n_values.append(entry["n"])
-                        time_values.append(entry["time"])
-
-            n_values_sorted = sorted(set(n_values))
-            time_values_sorted = []
-            for n in n_values_sorted:
-                time_samples = []
-                for n_value, time_value in zip(n_values, time_values):
-                    if n_value == n:
-                        time_samples.append(time_value)
-                sample_counts.append(len(time_samples))
-                time_values_sorted.append(np.mean(time_samples))
-            ax.plot(
-                n_values_sorted,
-                time_values_sorted,
-                label=label,
-                marker="o",
-                markersize=4,
-            )
-
-        print("Average sample count:", np.mean(sample_counts))
-
-        ax.set_xscale("log", base=2)
-        ax.set_yscale("log", base=10)
-        ax.grid(True, which="both", ls="--", lw=0.5)
-        ax.set_xlabel("Input size")
-        ax.set_ylabel("Time (ms)")
-        ax.legend()
-        fig.tight_layout()
-        fig.savefig(Path(__file__).parent.parent / "img" / filename)
-
-    all_methods = ["cpu", "naive", "efficient", "thrust"]
-    all_labels = ["CPU", "GPU (naive)", "GPU (work-efficient)", "GPU (Thrust)"]
-    plot_and_save(all_methods, all_labels, False, "performance-comparison.png")
-    plot_and_save(
-        all_methods[1:], all_labels[1:], True, "performance-comparison-gpu-only.png"
-    )
-
-
-if __name__ == "__main__":
-    main()
diff --git a/scripts/tune_block_sizes.py b/scripts/tune_block_sizes.py
new file mode 100644
index 00000000..1d86a198
--- /dev/null
+++ b/scripts/tune_block_sizes.py
@@ -0,0 +1,48 @@
+from helper import measure_time
+
+
+def tune_block_size(operation: str, implementation: str, input_size: int) -> None:
+    block_sizes = [8, 16, 32, 64, 128, 256, 512, 1024]
+    best_time = float("inf")
+    best_block_size = -1
+    for block_size in block_sizes:
+        time_sum = 0.0
+        time_count = 10
+        for _ in range(time_count):
+            time_sum += measure_time(operation, implementation, input_size, block_size)
+        time = time_sum / time_count
+        print(f"Block size: {block_size}, time: {time} ms")
+        if time < best_time:
+            best_time = time
+            best_block_size = block_size
+    print(f"Optimal block size: {best_block_size}, time: {best_time} ms")
+
+
+def print_divider() -> None:
+    print("=" * 40)
+
+
+def main():
+    input_size = 1 << 22
+
+    print("Naive scan, power-of-two")
+    tune_block_size("scan", "naive", input_size)
+    print_divider()
+    print("Naive scan, non-power-of-two")
+    tune_block_size("scan", "naive", input_size - 3)
+    print_divider()
+    print("Work-efficient scan, power-of-two")
+    tune_block_size("scan", "efficient", input_size)
+    print_divider()
+    print("Work-efficient scan, non-power-of-two")
+    tune_block_size("scan", "efficient", input_size - 3)
+    print_divider()
+    print("Work-efficient compact, power-of-two")
+    tune_block_size("compact", "efficient", input_size)
+    print_divider()
+    print("Work-efficient compact, non-power-of-two")
+    tune_block_size("compact", "efficient", input_size - 3)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/src/measure_time.cpp b/src/measure_time.cpp
new file mode 100644
index 00000000..f6893c55
--- /dev/null
+++ b/src/measure_time.cpp
@@ -0,0 +1,109 @@
+#include <iomanip>
+#include <iostream>
+#include <limits>
+#include <random>
+#include <string>
+#include <vector>
+
+#include <stream_compaction/cpu.h>
+#include <stream_compaction/efficient.h>
+#include <stream_compaction/naive.h>
+#include <stream_compaction/thrust.h>
+
+int main(int argc, char *argv[]) {
+    // argv[1]: scan/compact
+    // argv[2]: cpu/naive/efficient/thrust
+    // argv[3]: input size
+    // argv[4]: block size
+
+    if (argc != 5) {
+        return -1;
+    }
+    const std::string operation(argv[1]);
+    const std::string implementation(argv[2]);
+    const int inputSize = std::stoi(argv[3]);
+    const int blockSize = std::stoi(argv[4]);
+
+    std::vector<int> inputs(inputSize);
+    std::vector<int> outputs(inputSize);
+    {
+        std::random_device device;
+        std::mt19937 generator(device());
+        int maxValue;
+        if (operation == "scan") {
+            maxValue = 50 - 1;
+        } else if (operation == "compact") {
+            maxValue = 4 - 1;
+        } else {
+            return -1;
+        }
+        std::uniform_int_distribution<int> distribution(0, maxValue);
+        for (auto &i : inputs) {
+            i = distribution(generator);
+        }
+    }
+
+    const auto isGpu{implementation != "cpu"};
+    StreamCompaction::Common::PerformanceTimer *timer = nullptr;
+    if (implementation == "cpu") {
+        timer = &StreamCompaction::CPU::timer();
+    } else if (implementation == "naive") {
+        timer = &StreamCompaction::Naive::timer();
+    } else if (implementation == "efficient") {
+        timer = &StreamCompaction::Efficient::timer();
+    } else if (implementation == "thrust") {
+        timer = &StreamCompaction::Thrust::timer();
+    } else {
+        return -1;
+    }
+
+#define RUN_SCAN(scan)                                                                             \
+    do {                                                                                           \
+        if (blockSize >= 0) {                                                                      \
+            scan(inputSize, outputs.data(), inputs.data(), blockSize);                             \
+        } else {                                                                                   \
+            scan(inputSize, outputs.data(), inputs.data());                                        \
+        }                                                                                          \
+    } while (false)
+
+    if (operation == "scan") {
+        if (implementation == "cpu") {
+            if (blockSize >= 0) {
+                return -1;
+            }
+            StreamCompaction::CPU::scan(inputSize, outputs.data(), inputs.data());
+        } else if (implementation == "naive") {
+            RUN_SCAN(StreamCompaction::Naive::scan);
+        } else if (implementation == "efficient") {
+            RUN_SCAN(StreamCompaction::Efficient::scan);
+        } else if (implementation == "thrust") {
+            if (blockSize >= 0) {
+                return -1;
+            }
+            StreamCompaction::Thrust::scan(inputSize, outputs.data(), inputs.data());
+        } else {
+            return -1;
+        }
+    } else if (operation == "compact") {
+        if (implementation == "efficient") {
+            if (blockSize >= 0) {
+                StreamCompaction::Efficient::compact(inputSize, outputs.data(), inputs.data(),
+                                                     blockSize);
+            } else {
+                StreamCompaction::Efficient::compact(inputSize, outputs.data(), inputs.data());
+            }
+        } else {
+            return -1;
+        }
+    } else {
+        return -1;
+    }
+
+    std::cout << std::setprecision(std::numeric_limits<float>::max_digits10);
+    if (isGpu) {
+        std::cout << timer->getGpuElapsedTimeForPreviousOperation() << std::endl;
+    } else {
+        std::cout << timer->getCpuElapsedTimeForPreviousOperation() << std::endl;
+    }
+    return 0;
+}
diff --git a/stream_compaction/efficient.h b/stream_compaction/efficient.h
index 85d1a94a..23a5bde4 100644
--- a/stream_compaction/efficient.h
+++ b/stream_compaction/efficient.h
@@ -8,6 +8,6 @@ namespace StreamCompaction {
 
         void scan(int n, int *odata, const int *idata, const int blockSize = 128);
 
-        int compact(int n, int *odata, const int *idata, const int blockSize = 512);
+        int compact(int n, int *odata, const int *idata, const int blockSize = 128);
     }
 }
diff --git a/stream_compaction/thrust.cu b/stream_compaction/thrust.cu
index 7750a9fa..25f0a7c6 100644
--- a/stream_compaction/thrust.cu
+++ b/stream_compaction/thrust.cu
@@ -22,9 +22,6 @@ namespace StreamCompaction {
             thrust::device_vector<int> dev_in = host_in;
             thrust::device_vector<int> dev_out(n);
             timer().startGpuTimer();
-            // TODO use `thrust::exclusive_scan`
-            // example: for device_vectors dv_in and dv_out:
-            // thrust::exclusive_scan(dv_in.begin(), dv_in.end(), dv_out.begin());
             thrust::exclusive_scan(dev_in.begin(), dev_in.end(), dev_out.begin());
             timer().endGpuTimer();
             thrust::copy(dev_out.begin(), dev_out.end(), odata);

From fc4912d3b136c9b018560b6bf46a00cb7490c7ad Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Tue, 16 Sep 2025 01:13:18 -0400
Subject: [PATCH 10/12] Update README and remove unused files

---
 README.md                   | 109 +++++++++++++++++++++++-------------
 src/compare_performance.cpp |  80 --------------------------
 src/tune_block_sizes.cpp    |  88 -----------------------------
 3 files changed, 69 insertions(+), 208 deletions(-)
 delete mode 100644 src/compare_performance.cpp
 delete mode 100644 src/tune_block_sizes.cpp

diff --git a/README.md b/README.md
index 2975bc26..3cf4bc2f 100644
--- a/README.md
+++ b/README.md
@@ -120,47 +120,76 @@ To avoid this issue, I designed `measure_time.exe` to test only a single configu
 
 #### Optimizing Block Sizes
 
-To optimize block sizes, I added an optional `blockSize` parameter to every top-level function, each with a tuned default value. This preserves backward compatibility while making block-size tuning easier.
+To optimize block sizes, I developed a Python script, [`tune_block_sizes.py`](scripts/tune_block_sizes.py). This script uses the previously described `measure_time.exe` to benchmark execution time across a range of block sizes and identify the configuration that minimizes runtime. Key details of the procedure are:
 
-I also added a new executable, `tune_block_sizes.exe`, to the CMake project. In [`tune_block_sizes.cpp`](src/tune_block_sizes.cpp), it searches for the optimal block size for each algorithm by:
+- Because optimal block sizes vary with input size, tests are conducted on a fixed scale of $2^{22}$, using both a power-of-two input ($2^{22}$) and a non-power-of-two input ($2^{22} - 3$).
+- Block sizes are sampled over a log-spaced range: 8, 16, …, 512, 1024.
+- Each configuration is executed 10 times, with the mean runtime recorded.
+- The final selection balances performance across both power-of-two and non-power-of-two cases.
 
-- Using arrays of randomly generated test data. Since the optimal block size can vary significantly with input sizes, experiments are run on a fixed scale of $2^22$, with both power-of-two ($2^22$) and non-power-of-two $2^22 - 3$ sizes.
-- Testing a log-spaced range of block sizes: 8, 16, …, 512, 1024.
-- Measuring performance with precise timing: each configuration is warmed up with 10 runs, then measured over 100 runs, and the average elapsed GPU time is recorded.
-- Reporting results and selecting the block size that balances performance across both power-of-two and non-power-of-two inputs.
-
-Based on these experiments, the chosen defaults are:
+From these experiments, the chosen defaults are:
 
 - 256 for the naive scan
 - 128 for the work-efficient scan and compaction
 
 #### Performance Comparison
 
+To systematically collect execution time data across many configurations, I created a Python script, [`measure_performance.py`](scripts/measure_performance.py). This script relies on the previously described `measure_time.exe` to benchmark runtime across a range of input sizes and implementations. The procedure is as follows:
+
+- Input sizes are tested from $2^4$ up to $2^{27}$, using both exact powers of two and non-powers of two ($2^i - 3$ for each $i$) to capture different performance behaviors.
+- The tuned block sizes from earlier experiments are applied.
+- Each configuration is executed 50 times, and the mean runtime is recorded.
+- Results are stored in a JSON file ([`performance.json`](scripts/performance.json)).
+
+The JSON data is then processed by another script, [`plot_performance.py`](scripts/plot_performance.py), which generates the figures shown in this report.
+
+The first figure presents the full dataset:
+
 ![performance comparison](img/performance-comparison.png)
 
-Methods:
+Because non-power-of-two inputs produce jagged trends, and CPU performance scales on a very different range than GPU performance, a second figure was generated using only GPU data and power-of-two inputs:
 
-- **Input sizes:** The figure above compares all scan implementations across a range of input sizes. I use pairs of input sizes $2^n$ and $2^n - 3$, and confirm that each pair shows similar performance, while power-of-two input sizes are sometimes marginally faster. The following discussion therefore considers only the range of data sizes, without distinguishing between power-of-two and non-power-of-two inputs.
-- **Data collection:** To simplify data collection for this plot, I added `compare_performance.exe` to the CMake project. In [`compare_performance.cpp`](src/compare_performance.cpp), it measures the average execution time (1 warmup runs and 10 measured runs) for each configuration and writes the results to a newline-delimited JSON file ([`performance_comparison.nljson`](scripts/performance_comparison.nljson)). Then [`plot_performance_comparison.py`](scripts/plot_performance_comparison.py) reads the JSON data and generates the plot.
-- **Plotting:** Because the input sizes are log-spaced and execution time grows rapidly for larger inputs, I used logarithmic scales on both axes of the plot.
+![performance comparison GPU-only](img/performance-comparison-gpu-only.png)
 
 ### Observation and Analysis
 
-- The CPU implementation has $O(N)$ complexity in theory, which is confirmed by the linear trend in the log-log plot. Interestingly, this simple, low-overhead method outperforms the GPU implementations (naive, work-efficient, and Thrust) across a fairly wide range of input sizes (up to about 300,000).
-- My naive and work-efficient GPU implementations behave as follows:
-  - They are not very sensitive to input size until $N$ becomes very large (around $10^6$). This is likely because launching kernels $O(\log N)$ times dominates execution time, while the amount of work per kernel remains relatively small.
-  - Beyond $10^6$, the actual work performed inside each kernel becomes a larger portion of execution time, and execution time increases significantly with $N$.
-- Comparing naive and work-efficient GPU implementations:
-  - The naive method is faster when $N < 10^6$, again because of kernel launch overhead. Although work-efficient performs only $O(N)$ total work versus $O(N \log N)$, it requires both an up-sweep and a down-sweep, doubling the number of kernel launches.
-  - For $N > 10^6$, the advantage of the work-efficient method becomes clear, and it outperforms the naive version.
-- The Thrust library shows a different performance profile:
-  - Plot observation: When $N < 10^5$, the Thrust implementation is significantly faster than my naive and work-efficient versions, though still slower than the CPU implementation. However, for larger $N$, Thrust unexpectedly runs slower than my global-memory–only work-efficient implementation.
-  - Nsight Systems observation: Each call to `thrust::exclusive_scan()` generates only two kernels:
-    - `DeviceScanInitKernel`, which is short-lived,
-    - `DeviceScanKernel`, which dominates execution time.
-  - Analysis:
-    - For small $N$, execution time is dominated by kernel launch overhead. Since Thrust minimizes this to just two launches, it performs well in this regime.  
-    - For large $N$, Thrust likely employs shared memory optimizations. The cause of its relative slowness compared to my implementation requires further investigation.
+#### CPU Implementation
+
+The minimal for-loop CPU implementation consistently demonstrates $O(N)$ complexity across all tested input sizes, as confirmed by the linear trend in the log-log plot. This complexity holds regardless of whether the limiting factor is compute or memory. Regarding the bottleneck:
+
+- The compute workload is very light, since addition operations are fast.
+- The memory access pattern is highly favorable, as all reads and writes are sequential.
+
+Although memory is typically slower than arithmetic operations—suggesting the implementation may be slightly memory-bound—the distinction is not critical here.
+
+Importantly, this simple, low-overhead implementation outperforms the GPU variants (naive, work-efficient, and Thrust) for inputs up to about $2^{17}$. The likely reason is the absence of GPU kernel launch overhead, which allows the CPU to handle small and mid-sized inputs more efficiently.
+
+#### Naive & Work-Efficient GPU Implementations
+
+Common characteristics:
+
+- For $N < 2^{20}$, both implementations show limited sensitivity to input size. In fact, runtime sometimes decreases as $N$ grows. This is likely because the $O(\log N)$ kernel launches dominate execution time, while the work per kernel remains relatively small. Additionally, the input sizes may be too small to fully utilize GPU resources. In this regime, the bottleneck is neither compute nor memory, but the overhead of repeated kernel launches.
+- Beyond $2^{20}$, execution time increases rapidly with $N$, indicating saturation of a GPU resource. Given that both implementations rely heavily on global memory, the performance bottleneck is most likely memory I/O rather than computation.
+
+Comparison of the two:
+
+- For $N < 2^{21}$, the so-called work-efficient implementation is actually slower than the naive version. This can be attributed to kernel launch overhead: the up-sweep and down-sweep phases double the number of kernel invocations. Although the total work is reduced, the benefit is negligible at these smaller sizes.
+- For larger $N$, the work-efficient method begins to outperform the naive implementation, and the gap widens quickly. This is because the work-efficient algorithm performs only $O(N)$ total operations, whereas the naive approach requires $O(N \log N)$.
+
+#### Thrust GPU Implementation
+
+To better understand the behavior of `thrust::exclusive_scan()`, I profiled it using Nsight Systems. The results revealed only two CUDA kernel calls:
+
+- `DeviceScanInitKernel`, which is short-lived
+- `DeviceScanKernel`, which dominates execution time
+
+This suggests that Thrust fuses the entire scan into just two kernels. While the internal algorithm is not directly visible, it is reasonable to assume that it leverages shared memory and optimized memory access patterns.
+
+The performance profile of Thrust’s `exclusive_scan` is notable:
+
+- Small sizes ($N \leq 2^{17}$): Runtime remains relatively flat across input sizes. Although slower than the CPU implementation, it is still much faster than the naive and work-efficient GPU versions, likely due to the minimal number of kernel launches.
+- Mid sizes ($2^{18} \leq N \leq 2^{23}$): Runtime unexpectedly spikes, at times even performing worse than the naive implementation. It seems unlikely that NVIDIA’s official library would be poorly optimized, especially since this anomaly does not appear for other people. I suspect the performance degradation is related to the measurement methodology: repeatedly allocating memory, copying data CPU → GPU, launching kernels, copying results GPU → CPU, and freeing memory. This atypical workflow may interact with the driver in unusual ways. This remains a hypothesis and warrants further investigation.
+- Large sizes ($N > 2^{23}$): Thrust significantly outperforms the other implementations, presumably because its internal use of shared memory and optimized access patterns scales effectively at large input sizes.
 
 #### Outputs of `cis5650_stream_compaction_test.exe`
 
@@ -175,25 +204,25 @@ Methods:
 ==== cpu scan, non-power-of-two ====
    elapsed time: 1.5015ms    (std::chrono Measured)
     [   0  16  51  59  80 126 152 171 171 213 256 265 310 ... 102780200 102780221 ]
-    passed 
+    passed
 ==== naive scan, power-of-two ====
    elapsed time: 0.376736ms    (CUDA Measured)
-    passed 
+    passed
 ==== naive scan, non-power-of-two ====
    elapsed time: 0.326432ms    (CUDA Measured)
-    passed 
+    passed
 ==== work-efficient scan, power-of-two ====
    elapsed time: 0.41936ms    (CUDA Measured)
-    passed 
+    passed
 ==== work-efficient scan, non-power-of-two ====
    elapsed time: 0.41024ms    (CUDA Measured)
-    passed 
+    passed
 ==== thrust scan, power-of-two ====
    elapsed time: 0.3416ms    (CUDA Measured)
-    passed 
+    passed
 ==== thrust scan, non-power-of-two ====
    elapsed time: 0.333088ms    (CUDA Measured)
-    passed 
+    passed
 
 *****************************
 ** STREAM COMPACTION TESTS **
@@ -202,22 +231,22 @@ Methods:
 ==== cpu compact without scan, power-of-two ====
    elapsed time: 7.3473ms    (std::chrono Measured)
     [   1   2   3   2   2   1   2   2   3   3   3   3   2 ...   3   2 ]
-    passed 
+    passed
 ==== cpu compact without scan, non-power-of-two ====
    elapsed time: 7.2214ms    (std::chrono Measured)
     [   1   2   3   2   2   1   2   2   3   3   3   3   2 ...   1   1 ]
-    passed 
+    passed
 ==== cpu compact with scan ====
    elapsed time: 14.0601ms    (std::chrono Measured)
     [   1   2   3   2   2   1   2   2   3   3   3   3   2 ...   3   2 ]
-    passed 
+    passed
 ==== work-efficient compact, power-of-two ====
    elapsed time: 0.431744ms    (CUDA Measured)
-    passed 
+    passed
 ==== work-efficient compact, non-power-of-two ====
    elapsed time: 0.576384ms    (CUDA Measured)
-    passed 
-Press any key to continue . . . 
+    passed
+Press any key to continue . . .
 ```
 
 #### Outputs of `tune_block_sizes.py`
diff --git a/src/compare_performance.cpp b/src/compare_performance.cpp
deleted file mode 100644
index 3a15c778..00000000
--- a/src/compare_performance.cpp
+++ /dev/null
@@ -1,80 +0,0 @@
-#include <fstream>
-#include <iostream>
-#include <thread>
-#include <utility>
-#include <vector>
-
-#include <stream_compaction/cpu.h>
-#include <stream_compaction/efficient.h>
-#include <stream_compaction/naive.h>
-#include <stream_compaction/thrust.h>
-
-#include "testing_helpers.hpp"
-
-constexpr int MAX_SIZE = 1 << 27;
-std::vector<int> inputs(MAX_SIZE);
-std::vector<int> outputs(MAX_SIZE);
-
-void prepareData(int n) {
-    genArray(n, inputs.data(), 50);
-    zeroArray(n, outputs.data());
-}
-
-template <bool IsGpu, typename Timer, typename Func>
-float measureTime(Timer &timer, Func func, int n) {
-    const int warmup = 0;
-    const int iterations = 1;
-    for (int i = 0; i < warmup; i++) {
-        prepareData(n);
-        func();
-        std::this_thread::sleep_for(std::chrono::milliseconds(10));
-    }
-    float totalTime = 0.0f;
-    for (int i = 0; i < iterations; ++i) {
-        prepareData(n);
-        func();
-        if constexpr (IsGpu) {
-            totalTime += timer.getGpuElapsedTimeForPreviousOperation();
-        } else {
-            totalTime += timer.getCpuElapsedTimeForPreviousOperation();
-        }
-        std::this_thread::sleep_for(std::chrono::milliseconds(10));
-    }
-    return totalTime / iterations;
-}
-
-int main() {
-    std::ofstream outFile("performance_comparison.nljson", std::ios::app);
-
-    for (int exponent = 4; exponent <= 27; ++exponent) {
-        const int baseN = 1 << exponent;
-        for (int n : {baseN - 3, baseN}) {
-            float cpuTime = measureTime<false>(
-                StreamCompaction::CPU::timer(),
-                [&, n] { StreamCompaction::CPU::scan(n, outputs.data(), inputs.data()); }, n);
-            float naiveTime = measureTime<true>(
-                StreamCompaction::Naive::timer(),
-                [&, n]() { StreamCompaction::Naive::scan(n, outputs.data(), inputs.data()); }, n);
-            float efficientTime = measureTime<true>(
-                StreamCompaction::Efficient::timer(),
-                [&, n]() { StreamCompaction::Efficient::scan(n, outputs.data(), inputs.data()); },
-                n);
-            float thrustTime = measureTime<true>(
-                StreamCompaction::Thrust::timer(),
-                [&, n]() { StreamCompaction::Thrust::scan(n, outputs.data(), inputs.data()); }, n);
-            for (const auto [name, time] : {
-                     std::pair("cpu", cpuTime),
-                     std::pair("naive", naiveTime),
-                     std::pair("efficient", efficientTime),
-                     std::pair("thrust", thrustTime),
-                 }) {
-                outFile << "{ "
-                        << "\"n\": " << n << ", "
-                        << "\"method\": \"" << name << "\", "
-                        << "\"time\": " << time << " }" << std::endl;
-            }
-            std::cout << "Completed n = " << n << std::endl;
-            std::this_thread::sleep_for(std::chrono::milliseconds(100));
-        }
-    }
-}
diff --git a/src/tune_block_sizes.cpp b/src/tune_block_sizes.cpp
deleted file mode 100644
index 042843bd..00000000
--- a/src/tune_block_sizes.cpp
+++ /dev/null
@@ -1,88 +0,0 @@
-#include <iostream>
-#include <limits>
-#include <vector>
-
-#include <stream_compaction/efficient.h>
-#include <stream_compaction/naive.h>
-
-#include "testing_helpers.hpp"
-
-template <typename Timer, typename Func>
-float measureTime(Timer &timer, Func func) {
-    const int warmup = 10;
-    const int iterations = 100;
-    for (int i = 0; i < warmup; i++) {
-        func();
-    }
-    float totalTime = 0.0f;
-    for (int i = 0; i < iterations; ++i) {
-        func();
-        totalTime += timer.getGpuElapsedTimeForPreviousOperation();
-    }
-    return totalTime / iterations;
-}
-
-template <typename Timer, typename Func, typename... Args>
-void tuneBlockSize(Timer &timer, Func func, Args &&...args) {
-    std::vector<int> blockSizes = {8, 16, 32, 64, 128, 256, 512, 1024};
-    float bestTime = std::numeric_limits<float>::max();
-    int bestBlockSize = -1;
-    for (int blockSize : blockSizes) {
-        float time = measureTime(timer, [&]() { func(std::forward<Args>(args)..., blockSize); });
-        std::cout << "Block size: " << blockSize << ", time: " << time << " ms" << std::endl;
-        if (time < bestTime) {
-            bestTime = time;
-            bestBlockSize = blockSize;
-        }
-    }
-    std::cout << "Best block size: " << bestBlockSize << std::endl;
-}
-
-int main() {
-    const int SIZE = 1 << 22;
-    const int NPOT = SIZE - 3;
-    int *a = new int[SIZE];
-    int *b = new int[SIZE];
-    int *c = new int[SIZE];
-
-    genArray(SIZE - 1, a, 50);
-    a[SIZE - 1] = 0;
-
-    zeroArray(SIZE, c);
-    printDesc("naive scan, power-of-two");
-    tuneBlockSize(StreamCompaction::Naive::timer(), StreamCompaction::Naive::scan, SIZE, c, a);
-
-    zeroArray(SIZE, c);
-    printDesc("naive scan, non-power-of-two");
-    tuneBlockSize(StreamCompaction::Naive::timer(), StreamCompaction::Naive::scan, NPOT, c, a);
-
-    zeroArray(SIZE, c);
-    printDesc("work-efficient scan, power-of-two");
-    tuneBlockSize(StreamCompaction::Efficient::timer(), StreamCompaction::Efficient::scan, SIZE, c,
-                  a);
-
-    zeroArray(SIZE, c);
-    printDesc("work-efficient scan, non-power-of-two");
-    tuneBlockSize(StreamCompaction::Efficient::timer(), StreamCompaction::Efficient::scan, NPOT, c,
-                  a);
-
-    genArray(SIZE - 1, a, 4);
-    a[SIZE - 1] = 0;
-
-    zeroArray(SIZE, c);
-    printDesc("work-efficient compact, power-of-two");
-    tuneBlockSize(StreamCompaction::Efficient::timer(), StreamCompaction::Efficient::compact, SIZE,
-                  c, a);
-
-    zeroArray(SIZE, c);
-    printDesc("work-efficient compact, non-power-of-two");
-    tuneBlockSize(StreamCompaction::Efficient::timer(), StreamCompaction::Efficient::compact, NPOT,
-                  c, a);
-
-    system("pause");
-    delete[] a;
-    delete[] b;
-    delete[] c;
-
-    return 0;
-}

From 27775083d5bc280f014c4a3cd99e9553ebddac8b Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Tue, 16 Sep 2025 16:11:07 -0400
Subject: [PATCH 11/12] Implement efficient_plus and update performance
 analyses

---
 README.md                               | 293 +++++++----
 img/performance-comparison-gpu-only.png | Bin 55605 -> 0 bytes
 img/performance-comparison.png          | Bin 60806 -> 0 bytes
 img/performance-gpu-only.png            | Bin 45918 -> 50709 bytes
 img/performance.png                     | Bin 53834 -> 57469 bytes
 scripts/helper.py                       |   2 +
 scripts/measure_performance.py          |   4 +-
 scripts/performance.json                | 672 +++++++++++++++++-------
 scripts/plot_performance.py             |  14 +-
 scripts/tune_block_sizes.py             |  48 --
 scripts/tune_parameters.py              |  97 ++++
 src/main.cpp                            |  15 +
 src/measure_time.cpp                    |  60 ++-
 stream_compaction/CMakeLists.txt        |   2 +
 stream_compaction/efficient.cu          |   2 +
 stream_compaction/efficient.h           |   4 +-
 stream_compaction/efficient_plus.cu     | 196 +++++++
 stream_compaction/efficient_plus.h      |  12 +
 stream_compaction/naive.cu              |   1 +
 stream_compaction/thrust.cu             |   3 +
 20 files changed, 1070 insertions(+), 355 deletions(-)
 delete mode 100644 img/performance-comparison-gpu-only.png
 delete mode 100644 img/performance-comparison.png
 delete mode 100644 scripts/tune_block_sizes.py
 create mode 100644 scripts/tune_parameters.py
 create mode 100644 stream_compaction/efficient_plus.cu
 create mode 100644 stream_compaction/efficient_plus.h

diff --git a/README.md b/README.md
index 3cf4bc2f..ec10e3fe 100644
--- a/README.md
+++ b/README.md
@@ -32,8 +32,8 @@ An additional executable,`measure_time.exe`, has been added to the project to su
 To simplify block size tuning, I added an optional `blockSize` parameter to the following functions, each with a tuned default value:
 
 - `Naive::scan(..., const int blockSize = 256)`
-- `Efficient::scan(..., const int blockSize = 128)`
-- `Efficient::compact(..., const int blockSize = 128)`
+- `Efficient::scan(..., const int blockSize = 64)`
+- `Efficient::compact(..., const int blockSize = 64)`
 
 These parameters are used only by `measure_time.exe` and do not affect existing calls.
 
@@ -97,9 +97,19 @@ I believe Part 3.1 already incorporates the optimizations described in the instr
 
 This part is not implemented.
 
-### Extra Credit 2: GPU Scan Using Shared Memory && Hardware Optimizatio
+### Extra Credit 2: GPU Scan Using Shared Memory && Hardware Optimization
 
-This part is not implemented.
+To improve the work-efficient implementation, I developed the work-efficient plus variant in [`efficient_plus.h`](stream_compaction/efficient_plus.h) and [`efficient_plus.cu`](stream_compaction/efficient_plus.cu). Key aspects of this design include:
+
+- Kernel fusing: The up-sweep and down-sweep phases are fused into a single kernel invocation. Although compacting indices no longer reduces the number of blocks, this approach minimizes divergence and is therefore retained.
+- Shared memory usage: Instead of operating directly on global memory, data is first copied into shared memory, scanned per block, and then copied back to global memory.
+- Recursive tiling: Since a block can only process a limited number of elements, the algorithm is made recursive.
+  - The array is partitioned into tiles, one per block.  
+  - In addition to performing the scan, each block writes its tile sum into a new array.  
+  - An exclusive scan is recursively applied to this array of tile sums, and the results are then added back to the input data.
+- Avoiding shared memory bank conflicts: Shared memory indexing is padded following the method described in GPU Gems. This introduces only a small increase in memory usage.
+- Preallocating the recursion buffer: To avoid repeated allocation of temporary GPU buffers for tile sums, the recursion depth and total required storage are precomputed. A single contiguous GPU buffer is allocated and reused across all recursion levels.
+- Multiple elements per thread: As an experiment, I added support for processing multiple elements per thread, controlled by the compile-time template parameter `ElementsPerThread`. Different variants are dispatched at runtime, and loops over per-thread elements are unrolled with `#pragma unroll`. In practice, this optimization was not beneficial; the tuned configuration still uses one element per thread.
 
 ## Part 7: Write-up
 
@@ -111,45 +121,47 @@ Project description: see the [Features](#features) section at the top.
 
 To simplify performance analysis, I added a C++ executable, `measure_time.exe`. The implementation is in [`measure_time.cpp`](src/measure_time.cpp), which:
 
-- Accepts the operation (scan or compact), implementation (CPU, GPU naive, GPU work-efficient, or GPU Thrust), input size, and block size as command-line arguments.
+- Accepts the operation (scan or compact), implementation (CPU, GPU naive, GPU work-efficient, or GPU Thrust), input size, block size, and number of elements per thread as command-line arguments.
 - Generates random input data and prints the measured execution time (in milliseconds) to the console.
 
 I created this tool because measuring a configuration only once is often imprecise. In my earlier attempts, running repeated measurements within a C++ loop caused the results to drift significantly. In particular, Thrust measurements became unexpectedly slower, sometimes even slower than the GPU naive implementation. I suspect this was due to frequent GPU memory allocations and deallocations (since the exposed API uses CPU inputs and outputs), which created an atypical workload and put the driver in a degraded performance state.
 
 To avoid this issue, I designed `measure_time.exe` to test only a single configuration with one iteration per program launch. Repeated measurements are instead automated by accompanying Python scripts.
 
-#### Optimizing Block Sizes
+#### Optimizing Parameters
 
-To optimize block sizes, I developed a Python script, [`tune_block_sizes.py`](scripts/tune_block_sizes.py). This script uses the previously described `measure_time.exe` to benchmark execution time across a range of block sizes and identify the configuration that minimizes runtime. Key details of the procedure are:
+To optimize parameters such as block sizes and the number of elements per thread, I created a Python script, [`tune_parameters.py`](scripts/tune_parameters.py).
 
-- Because optimal block sizes vary with input size, tests are conducted on a fixed scale of $2^{22}$, using both a power-of-two input ($2^{22}$) and a non-power-of-two input ($2^{22} - 3$).
+- Because optimal block sizes vary with input size, tests are conducted on a fixed scale of $2^{22}$, using both a power-of-two input ($2^{22}$) and a non-power-of-two input ($2^{22} - 3$). The results indicate that the distinction between power-of-two and non-power-of-two input sizes has minimal impact on performance. Therefore, this factor will not be considered further in the discussion.
 - Block sizes are sampled over a log-spaced range: 8, 16, …, 512, 1024.
+- The number of processed elements per thread is one of 1, 2, 4, 8, and 16.
 - Each configuration is executed 10 times, with the mean runtime recorded.
 - The final selection balances performance across both power-of-two and non-power-of-two cases.
 
 From these experiments, the chosen defaults are:
 
-- 256 for the naive scan
-- 128 for the work-efficient scan and compaction
+- Block size 256 for the naive scan
+- Block size 64 for the work-efficient scan and compaction
+- Block size 256 for the work-efficient plus (for extra credit 2) scan, with 1 element per thread
 
 #### Performance Comparison
 
 To systematically collect execution time data across many configurations, I created a Python script, [`measure_performance.py`](scripts/measure_performance.py). This script relies on the previously described `measure_time.exe` to benchmark runtime across a range of input sizes and implementations. The procedure is as follows:
 
 - Input sizes are tested from $2^4$ up to $2^{27}$, using both exact powers of two and non-powers of two ($2^i - 3$ for each $i$) to capture different performance behaviors.
-- The tuned block sizes from earlier experiments are applied.
-- Each configuration is executed 50 times, and the mean runtime is recorded.
+- The number of elements processed per thread is selected from the set {1, 2, 4, 8, 16}.
+- Each configuration is executed 20 times, and the mean runtime is recorded.
 - Results are stored in a JSON file ([`performance.json`](scripts/performance.json)).
 
 The JSON data is then processed by another script, [`plot_performance.py`](scripts/plot_performance.py), which generates the figures shown in this report.
 
 The first figure presents the full dataset:
 
-![performance comparison](img/performance-comparison.png)
+![performance comparison](img/performance.png)
 
 Because non-power-of-two inputs produce jagged trends, and CPU performance scales on a very different range than GPU performance, a second figure was generated using only GPU data and power-of-two inputs:
 
-![performance comparison GPU-only](img/performance-comparison-gpu-only.png)
+![performance comparison GPU-only](img/performance-gpu-only.png)
 
 ### Observation and Analysis
 
@@ -168,14 +180,19 @@ Importantly, this simple, low-overhead implementation outperforms the GPU varian
 
 Common characteristics:
 
-- For $N < 2^{20}$, both implementations show limited sensitivity to input size. In fact, runtime sometimes decreases as $N$ grows. This is likely because the $O(\log N)$ kernel launches dominate execution time, while the work per kernel remains relatively small. Additionally, the input sizes may be too small to fully utilize GPU resources. In this regime, the bottleneck is neither compute nor memory, but the overhead of repeated kernel launches.
+- For $N < 2^{20}$, both implementations show limited sensitivity to input size. This is likely because the $O(\log N)$ kernel launches dominate execution time, while the work per kernel remains relatively small. Additionally, the input sizes may be too small to fully utilize GPU resources. In this regime, the bottleneck is neither compute nor memory, but the overhead of repeated kernel launches.
 - Beyond $2^{20}$, execution time increases rapidly with $N$, indicating saturation of a GPU resource. Given that both implementations rely heavily on global memory, the performance bottleneck is most likely memory I/O rather than computation.
 
 Comparison of the two:
 
-- For $N < 2^{21}$, the so-called work-efficient implementation is actually slower than the naive version. This can be attributed to kernel launch overhead: the up-sweep and down-sweep phases double the number of kernel invocations. Although the total work is reduced, the benefit is negligible at these smaller sizes.
+- For $N < 2^{23}$, the so-called work-efficient implementation is actually slower than the naive version. This can be attributed to kernel launch overhead: the up-sweep and down-sweep phases double the number of kernel invocations. Although the total work is reduced, the benefit is negligible at these smaller sizes.
 - For larger $N$, the work-efficient method begins to outperform the naive implementation, and the gap widens quickly. This is because the work-efficient algorithm performs only $O(N)$ total operations, whereas the naive approach requires $O(N \log N)$.
 
+#### Work-Efficient Plus GPU Implementation (for Extra Credit 2)
+
+- For small $N$, the performance is comparable to the naive and work-efficient implementations, without clear advantages. This is because each kernel must perform a full round trip from global memory → shared memory → global memory. When the amount of computation on shared memory is limited, this memory traffic dominates the runtime.  
+- For larger inputs ($N \geq 2^{20}$), the benefits of this implementation become evident due to the optimizations described earlier. It even outperforms Thrust at $2^{20} \leq N \leq 2^{25}$. However, I suspect Thrust’s performance in my environments are not representative (see below), so I do not claim that my implementation is more optimized than Thrust in general.
+
 #### Thrust GPU Implementation
 
 To better understand the behavior of `thrust::exclusive_scan()`, I profiled it using Nsight Systems. The results revealed only two CUDA kernel calls:
@@ -189,7 +206,7 @@ The performance profile of Thrust’s `exclusive_scan` is notable:
 
 - Small sizes ($N \leq 2^{17}$): Runtime remains relatively flat across input sizes. Although slower than the CPU implementation, it is still much faster than the naive and work-efficient GPU versions, likely due to the minimal number of kernel launches.
 - Mid sizes ($2^{18} \leq N \leq 2^{23}$): Runtime unexpectedly spikes, at times even performing worse than the naive implementation. It seems unlikely that NVIDIA’s official library would be poorly optimized, especially since this anomaly does not appear for other people. I suspect the performance degradation is related to the measurement methodology: repeatedly allocating memory, copying data CPU → GPU, launching kernels, copying results GPU → CPU, and freeing memory. This atypical workflow may interact with the driver in unusual ways. This remains a hypothesis and warrants further investigation.
-- Large sizes ($N > 2^{23}$): Thrust significantly outperforms the other implementations, presumably because its internal use of shared memory and optimized access patterns scales effectively at large input sizes.
+- Large sizes ($N > 2^{23}$): Thrust significantly outperforms the naive and work-efficient GPU implementations, presumably because its internal use of shared memory and optimized access patterns scales effectively at large input sizes.
 
 #### Outputs of `cis5650_stream_compaction_test.exe`
 
@@ -197,124 +214,216 @@ The performance profile of Thrust’s `exclusive_scan` is notable:
 ****************
 ** SCAN TESTS **
 ****************
-    [  16  35   8  21  46  26  19   0  42  43   9  45  49 ...  16   0 ]
+    [   2  43  36  34   6  47  28  21  20  47   9  14  36 ...  28   0 ]
 ==== cpu scan, power-of-two ====
-   elapsed time: 1.6805ms    (std::chrono Measured)
-    [   0  16  51  59  80 126 152 171 171 213 256 265 310 ... 102780293 102780309 ]
+   elapsed time: 1.6333ms    (std::chrono Measured)
+    [   0   2  45  81 115 121 168 196 217 237 284 293 307 ... 102726393 102726421 ]
 ==== cpu scan, non-power-of-two ====
-   elapsed time: 1.5015ms    (std::chrono Measured)
-    [   0  16  51  59  80 126 152 171 171 213 256 265 310 ... 102780200 102780221 ]
+   elapsed time: 1.4916ms    (std::chrono Measured)
+    [   0   2  45  81 115 121 168 196 217 237 284 293 307 ... 102726316 102726346 ]
     passed
 ==== naive scan, power-of-two ====
-   elapsed time: 0.376736ms    (CUDA Measured)
+   elapsed time: 0.335968ms    (CUDA Measured)
     passed
 ==== naive scan, non-power-of-two ====
-   elapsed time: 0.326432ms    (CUDA Measured)
+   elapsed time: 0.330656ms    (CUDA Measured)
     passed
 ==== work-efficient scan, power-of-two ====
-   elapsed time: 0.41936ms    (CUDA Measured)
+   elapsed time: 0.464192ms    (CUDA Measured)
     passed
 ==== work-efficient scan, non-power-of-two ====
-   elapsed time: 0.41024ms    (CUDA Measured)
+   elapsed time: 0.368544ms    (CUDA Measured)
+    passed
+==== work-efficient plus scan, power-of-two ====
+   elapsed time: 0.191456ms    (CUDA Measured)
+    passed
+==== work-efficient plus scan, non-power-of-two ====
+   elapsed time: 0.073984ms    (CUDA Measured)
     passed
 ==== thrust scan, power-of-two ====
-   elapsed time: 0.3416ms    (CUDA Measured)
+   elapsed time: 0.320512ms    (CUDA Measured)
     passed
 ==== thrust scan, non-power-of-two ====
-   elapsed time: 0.333088ms    (CUDA Measured)
+   elapsed time: 0.336736ms    (CUDA Measured)
     passed
 
 *****************************
 ** STREAM COMPACTION TESTS **
 *****************************
-    [   0   1   2   3   2   2   1   2   2   3   3   3   3 ...   2   0 ]
+    [   0   3   2   2   2   1   2   3   0   3   1   2   2 ...   2   0 ]
 ==== cpu compact without scan, power-of-two ====
-   elapsed time: 7.3473ms    (std::chrono Measured)
-    [   1   2   3   2   2   1   2   2   3   3   3   3   2 ...   3   2 ]
+   elapsed time: 7.1751ms    (std::chrono Measured)
+    [   3   2   2   2   1   2   3   3   1   2   2   2   3 ...   1   2 ]
     passed
 ==== cpu compact without scan, non-power-of-two ====
-   elapsed time: 7.2214ms    (std::chrono Measured)
-    [   1   2   3   2   2   1   2   2   3   3   3   3   2 ...   1   1 ]
+   elapsed time: 7.0687ms    (std::chrono Measured)
+    [   3   2   2   2   1   2   3   3   1   2   2   2   3 ...   3   2 ]
     passed
 ==== cpu compact with scan ====
-   elapsed time: 14.0601ms    (std::chrono Measured)
-    [   1   2   3   2   2   1   2   2   3   3   3   3   2 ...   3   2 ]
+   elapsed time: 14.5221ms    (std::chrono Measured)
+    [   3   2   2   2   1   2   3   3   1   2   2   2   3 ...   1   2 ]
     passed
 ==== work-efficient compact, power-of-two ====
-   elapsed time: 0.431744ms    (CUDA Measured)
+   elapsed time: 0.524ms    (CUDA Measured)
     passed
 ==== work-efficient compact, non-power-of-two ====
-   elapsed time: 0.576384ms    (CUDA Measured)
+   elapsed time: 0.521024ms    (CUDA Measured)
     passed
 Press any key to continue . . .
 ```
 
-#### Outputs of `tune_block_sizes.py`
+#### Outputs of `tune_parameters.py`
 
 ```text
 Naive scan, power-of-two
-Block size: 8, time: 6.231833506 ms
-Block size: 16, time: 3.173327995 ms
-Block size: 32, time: 1.6745983839999998 ms
-Block size: 64, time: 0.8986879886000001 ms
-Block size: 128, time: 0.5220288008999999 ms
-Block size: 256, time: 0.3854463994 ms
-Block size: 512, time: 0.4322271972999999 ms
-Block size: 1024, time: 0.4435839981 ms
-Optimal block size: 256, time: 0.3854463994 ms
+Block size: 8, time: 6.210713481 ms
+Block size: 16, time: 3.168515182 ms
+Block size: 32, time: 1.640864002 ms
+Block size: 64, time: 0.8767040014999999 ms
+Block size: 128, time: 0.5051392019 ms
+Block size: 256, time: 0.3497567982 ms
+Block size: 512, time: 0.3369727998 ms
+Block size: 1024, time: 0.3949791968 ms
+Optimal block size: 512, time: 0.3369727998 ms
 ========================================
 Naive scan, non-power-of-two
-Block size: 8, time: 6.219187259 ms
-Block size: 16, time: 3.18726716 ms
-Block size: 32, time: 1.658544017 ms
-Block size: 64, time: 0.8911647916 ms
-Block size: 128, time: 0.5024224044000001 ms
-Block size: 256, time: 0.3580832005 ms
-Block size: 512, time: 0.3581887961 ms
-Block size: 1024, time: 0.4385919958000001 ms
-Optimal block size: 256, time: 0.3580832005 ms
+Block size: 8, time: 6.208518411000001 ms
+Block size: 16, time: 3.1698239809999995 ms
+Block size: 32, time: 1.650400006 ms
+Block size: 64, time: 0.8862239956 ms
+Block size: 128, time: 0.5067872018 ms
+Block size: 256, time: 0.3504383981 ms
+Block size: 512, time: 0.346905601 ms
+Block size: 1024, time: 0.4155999988 ms
+Optimal block size: 512, time: 0.346905601 ms
 ========================================
 Work-efficient scan, power-of-two
-Block size: 8, time: 0.8682271958 ms
-Block size: 16, time: 0.6581280051999999 ms
-Block size: 32, time: 0.5843007983 ms
-Block size: 64, time: 0.511523199 ms
-Block size: 128, time: 0.47026240229999994 ms
-Block size: 256, time: 0.5074463992 ms
-Block size: 512, time: 0.48191359920000004 ms
-Block size: 1024, time: 0.4813536018 ms
-Optimal block size: 128, time: 0.47026240229999994 ms
+Block size: 8, time: 0.9049055992999999 ms
+Block size: 16, time: 0.7210080087999999 ms
+Block size: 32, time: 0.6597408055 ms
+Block size: 64, time: 0.5313376009999999 ms
+Block size: 128, time: 0.6298431963000001 ms
+Block size: 256, time: 0.6812607945 ms
+Block size: 512, time: 0.5833792001 ms
+Block size: 1024, time: 0.6668896109 ms
+Optimal block size: 64, time: 0.5313376009999999 ms
 ========================================
 Work-efficient scan, non-power-of-two
-Block size: 8, time: 0.8395776093 ms
-Block size: 16, time: 0.6402047992 ms
-Block size: 32, time: 0.5541888057000001 ms
-Block size: 64, time: 0.5040127992000001 ms
-Block size: 128, time: 0.4989087999 ms
-Block size: 256, time: 0.5251072078000001 ms
-Block size: 512, time: 0.48322560189999997 ms
-Block size: 1024, time: 0.49256000219999996 ms
-Optimal block size: 512, time: 0.48322560189999997 ms
+Block size: 8, time: 0.9357727944 ms
+Block size: 16, time: 0.7128639936000001 ms
+Block size: 32, time: 0.7185056090999999 ms
+Block size: 64, time: 0.5883967997000001 ms
+Block size: 128, time: 0.5995808003 ms
+Block size: 256, time: 0.6008256017000001 ms
+Block size: 512, time: 0.6760576010000001 ms
+Block size: 1024, time: 0.5939391851 ms
+Optimal block size: 64, time: 0.5883967997000001 ms
 ========================================
 Work-efficient compact, power-of-two
-Block size: 8, time: 1.4116608029999997 ms
-Block size: 16, time: 0.9503391928000001 ms
-Block size: 32, time: 0.7004479884 ms
-Block size: 64, time: 0.5998431921 ms
-Block size: 128, time: 0.5244000018 ms
-Block size: 256, time: 0.5620128065000001 ms
-Block size: 512, time: 0.7700480073 ms
-Block size: 1024, time: 0.6348639965 ms
-Optimal block size: 128, time: 0.5244000018 ms
+Block size: 8, time: 1.417711996 ms
+Block size: 16, time: 0.9495487984000001 ms
+Block size: 32, time: 0.7181632041999999 ms
+Block size: 64, time: 0.6332575947 ms
+Block size: 128, time: 0.6355327934999999 ms
+Block size: 256, time: 0.577478391 ms
+Block size: 512, time: 0.7434591980000002 ms
+Block size: 1024, time: 0.6726783932 ms
+Optimal block size: 256, time: 0.577478391 ms
 ========================================
 Work-efficient compact, non-power-of-two
-Block size: 8, time: 1.40685439 ms
-Block size: 16, time: 0.9263231993 ms
-Block size: 32, time: 0.7410848021000002 ms
-Block size: 64, time: 0.7034976004999999 ms
-Block size: 128, time: 0.7220223933 ms
-Block size: 256, time: 0.7788672031 ms
-Block size: 512, time: 0.7625663994 ms
-Block size: 1024, time: 0.7747167944 ms
-Optimal block size: 64, time: 0.7034976004999999 ms
+Block size: 8, time: 1.423475218 ms
+Block size: 16, time: 0.9857856036999998 ms
+Block size: 32, time: 0.8006624043 ms
+Block size: 64, time: 0.5751327993 ms
+Block size: 128, time: 0.6924479992 ms
+Block size: 256, time: 0.5636575996 ms
+Block size: 512, time: 0.6784191968000001 ms
+Block size: 1024, time: 0.6932192027999999 ms
+Optimal block size: 256, time: 0.5636575996 ms
+========================================
+Work-efficient plus scan, power-of-two
+Block size: 8, elements per thread: 1, time: 0.5458272011 ms
+Block size: 8, elements per thread: 2, time: 0.3792447983 ms
+Block size: 8, elements per thread: 4, time: 0.3159423963 ms
+Block size: 8, elements per thread: 8, time: 0.3622208059 ms
+Block size: 8, elements per thread: 16, time: 0.4684351951 ms
+Block size: 16, elements per thread: 1, time: 0.2957440004 ms
+Block size: 16, elements per thread: 2, time: 0.2765696033999999 ms
+Block size: 16, elements per thread: 4, time: 0.3591648042 ms
+Block size: 16, elements per thread: 8, time: 0.3541247966 ms
+Block size: 16, elements per thread: 16, time: 0.4408064038 ms
+Block size: 32, elements per thread: 1, time: 0.2547711969 ms
+Block size: 32, elements per thread: 2, time: 0.2487744019 ms
+Block size: 32, elements per thread: 4, time: 0.2829280005 ms
+Block size: 32, elements per thread: 8, time: 0.355180803 ms
+Block size: 32, elements per thread: 16, time: 0.4990495979999999 ms
+Block size: 64, elements per thread: 1, time: 0.21321919859999997 ms
+Block size: 64, elements per thread: 2, time: 0.23418560179999998 ms
+Block size: 64, elements per thread: 4, time: 0.26373759820000003 ms
+Block size: 64, elements per thread: 8, time: 0.3173408001 ms
+Block size: 64, elements per thread: 16, time: 0.45957120059999995 ms
+Block size: 128, elements per thread: 1, time: 0.2471552 ms
+Block size: 128, elements per thread: 2, time: 0.21002880040000002 ms
+Block size: 128, elements per thread: 4, time: 0.2764960006 ms
+Block size: 128, elements per thread: 8, time: 0.3514591991999999 ms
+Block size: 128, elements per thread: 16, time: 0.49059520079999996 ms
+Block size: 256, elements per thread: 1, time: 0.19113280039999997 ms
+Block size: 256, elements per thread: 2, time: 0.2154880017 ms
+Block size: 256, elements per thread: 4, time: 0.2787679984 ms
+Block size: 256, elements per thread: 8, time: 0.3731999963 ms
+Block size: 256, elements per thread: 16, time: 0.49939519470000004 ms
+Block size: 512, elements per thread: 1, time: 0.20608639850000002 ms
+Block size: 512, elements per thread: 2, time: 0.2563392014 ms
+Block size: 512, elements per thread: 4, time: 0.3583200006 ms
+Block size: 512, elements per thread: 8, time: 0.3594367981 ms
+Block size: 512, elements per thread: 16 - crashed
+Block size: 1024, elements per thread: 1, time: 0.234352003 ms
+Block size: 1024, elements per thread: 2, time: 0.25858239680000006 ms
+Block size: 1024, elements per thread: 4, time: 0.3363999992000001 ms
+Block size: 1024, elements per thread: 8 - crashed
+Block size: 1024, elements per thread: 16 - crashed
+Optimal config: block size 256, elements per thread 1, time: 0.19113280039999997 ms
+========================================
+Work-efficient plus scan, non-power-of-two
+Block size: 8, elements per thread: 1, time: 0.4914176017 ms
+Block size: 8, elements per thread: 2, time: 0.32388479719999996 ms
+Block size: 8, elements per thread: 4, time: 0.38091839839999997 ms
+Block size: 8, elements per thread: 8, time: 0.33217279899999996 ms
+Block size: 8, elements per thread: 16, time: 0.39384639860000004 ms
+Block size: 16, elements per thread: 1, time: 0.3107008011 ms
+Block size: 16, elements per thread: 2, time: 0.2454912007 ms
+Block size: 16, elements per thread: 4, time: 0.3092735976 ms
+Block size: 16, elements per thread: 8, time: 0.32160959829999997 ms
+Block size: 16, elements per thread: 16, time: 0.42109759750000003 ms
+Block size: 32, elements per thread: 1, time: 0.26428479559999996 ms
+Block size: 32, elements per thread: 2, time: 0.25905919679999995 ms
+Block size: 32, elements per thread: 4, time: 0.3214975982 ms
+Block size: 32, elements per thread: 8, time: 0.3603167982 ms
+Block size: 32, elements per thread: 16, time: 0.4624383956 ms
+Block size: 64, elements per thread: 1, time: 0.20346560030000002 ms
+Block size: 64, elements per thread: 2, time: 0.2914719998 ms
+Block size: 64, elements per thread: 4, time: 0.29802560209999995 ms
+Block size: 64, elements per thread: 8, time: 0.3288128018 ms
+Block size: 64, elements per thread: 16, time: 0.449561593 ms
+Block size: 128, elements per thread: 1, time: 0.20832960009999998 ms
+Block size: 128, elements per thread: 2, time: 0.24085119969999996 ms
+Block size: 128, elements per thread: 4, time: 0.2845311985 ms
+Block size: 128, elements per thread: 8, time: 0.3271040023 ms
+Block size: 128, elements per thread: 16, time: 0.46438719919999993 ms
+Block size: 256, elements per thread: 1, time: 0.1988800004 ms
+Block size: 256, elements per thread: 2, time: 0.24773760570000003 ms
+Block size: 256, elements per thread: 4, time: 0.3005983978 ms
+Block size: 256, elements per thread: 8, time: 0.3462976009 ms
+Block size: 256, elements per thread: 16, time: 0.48608960519999994 ms
+Block size: 512, elements per thread: 1, time: 0.2411488013 ms
+Block size: 512, elements per thread: 2, time: 0.2356735976 ms
+Block size: 512, elements per thread: 4, time: 0.31453439899999996 ms
+Block size: 512, elements per thread: 8, time: 0.36263679849999997 ms
+Block size: 512, elements per thread: 16 - crashed
+Block size: 1024, elements per thread: 1, time: 0.2502848000000001 ms
+Block size: 1024, elements per thread: 2, time: 0.25420480219999997 ms
+Block size: 1024, elements per thread: 4, time: 0.3396863997 ms
+Block size: 1024, elements per thread: 8 - crashed
+Block size: 1024, elements per thread: 16 - crashed
+Optimal config: block size 256, elements per thread 1, time: 0.1988800004 ms
 ```
diff --git a/img/performance-comparison-gpu-only.png b/img/performance-comparison-gpu-only.png
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diff --git a/scripts/helper.py b/scripts/helper.py
index 06b24fdf..858a9120 100644
--- a/scripts/helper.py
+++ b/scripts/helper.py
@@ -12,6 +12,7 @@ def measure_time(
     implementation: Literal["cpu", "naive", "efficient", "thrust"],
     input_size: int,
     block_size: int = -1,
+    elements_per_thread: int = -1,
 ) -> float:
     result = subprocess.run(
         [
@@ -20,6 +21,7 @@ def measure_time(
             implementation,
             str(input_size),
             str(block_size),
+            str(elements_per_thread),
         ],
         capture_output=True,
         cwd=ROOT_DIR,
diff --git a/scripts/measure_performance.py b/scripts/measure_performance.py
index 536cc6d3..602f0d50 100644
--- a/scripts/measure_performance.py
+++ b/scripts/measure_performance.py
@@ -24,7 +24,7 @@ def find_existing_entry(
                 return entry
         return None
 
-    for implementation in ["cpu", "naive", "efficient", "thrust"]:
+    for implementation in ["cpu", "naive", "efficient", "efficient_plus", "thrust"]:
         for exponent in range(4, 28):
             base_input_size = 1 << exponent
             for input_size in [base_input_size, base_input_size - 3]:
@@ -38,7 +38,7 @@ def find_existing_entry(
                     continue
 
                 time_sum = 0.0
-                time_count = 50
+                time_count = 20
                 for _ in range(time_count):
                     time_sum += measure_time("scan", implementation, input_size)
                 time = time_sum / time_count
diff --git a/scripts/performance.json b/scripts/performance.json
index ab35e794..bb266367 100644
--- a/scripts/performance.json
+++ b/scripts/performance.json
@@ -3,1152 +3,1440 @@
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 16,
-        "time": 0.00013399999751000004
+        "time": 0.00013499999770000005
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 13,
-        "time": 0.00013399999751000004
+        "time": 0.00012999999782500004
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 32,
-        "time": 0.00014399999769000005
+        "time": 0.00012499999687500004
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 29,
-        "time": 0.00012399999776000004
+        "time": 0.00014999999587500006
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 64,
-        "time": 0.00016799999795000006
+        "time": 0.00016499999695000008
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 61,
-        "time": 0.00014399999769000005
+        "time": 0.00014999999625000006
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 128,
-        "time": 0.00020399999919999996
+        "time": 0.00019499999835000004
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 125,
-        "time": 0.00019999999672000004
+        "time": 0.00021499999785000004
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 256,
-        "time": 0.00026600000066000017
+        "time": 0.00027500000065
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 253,
-        "time": 0.00026000000296000017
+        "time": 0.0002600000021
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 512,
-        "time": 0.00040800000540000027
+        "time": 0.00038000000780000003
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 509,
-        "time": 0.00043000000934000017
+        "time": 0.00037500000320000006
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 1024,
-        "time": 0.0005460000142200003
+        "time": 0.0005350000137000001
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 1021,
-        "time": 0.0005120000080000004
+        "time": 0.0004850000071000002
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 2048,
-        "time": 0.0009139999999599998
+        "time": 0.0009550000140000001
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 2045,
-        "time": 0.0009199999953
+        "time": 0.0010100000017500001
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 4096,
-        "time": 0.0018319999932
+        "time": 0.0017499999835000005
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 4093,
-        "time": 0.001818000007
+        "time": 0.0018949999810000003
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 8192,
-        "time": 0.0031719999760000004
+        "time": 0.0032299999740000003
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 8189,
-        "time": 0.0036460000050000008
+        "time": 0.0035950000285000006
     },
     {
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 16384,
-        "time": 0.006132000005399998
+        "time": 0.0069099999740000004
     },
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         "implementation": "cpu",
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-        "time": 0.006530000018599998
+        "time": 0.006765000031
     },
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-        "time": 0.013030000077999999
+        "time": 0.013600000004999998
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+        "time": 0.012445000145000001
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+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 4194304,
+        "time": 0.26313920025000004
+    },
+    {
+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 4194301,
+        "time": 0.24904000080000005
+    },
+    {
+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 8388608,
+        "time": 0.28106239965
+    },
+    {
+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 8388605,
+        "time": 0.2867519988000001
+    },
+    {
+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 16777216,
+        "time": 0.30306400055000005
+    },
+    {
+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 16777213,
+        "time": 0.30300320085
+    },
+    {
+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 33554432,
+        "time": 0.6449887960499999
+    },
+    {
+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 33554429,
+        "time": 0.6306928039499999
+    },
+    {
+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 67108864,
+        "time": 1.2027919950000001
+    },
+    {
+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 67108861,
+        "time": 1.2180655965
+    },
+    {
+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 134217728,
+        "time": 2.3920944094999994
+    },
+    {
+        "operation": "scan",
+        "implementation": "efficient_plus",
+        "input_size": 134217725,
+        "time": 2.396910416
     }
 ]
\ No newline at end of file
diff --git a/scripts/plot_performance.py b/scripts/plot_performance.py
index e11be0d2..3ded1b2e 100644
--- a/scripts/plot_performance.py
+++ b/scripts/plot_performance.py
@@ -47,14 +47,20 @@ def plot_and_save(
         fig.savefig(Path(__file__).parent.parent / "img" / filename)
 
     plot_and_save(
-        ["cpu", "naive", "efficient", "thrust"],
-        ["CPU", "GPU (naive)", "GPU (work-efficient)", "GPU (Thrust)"],
+        ["naive", "efficient", "efficient_plus", "thrust", "cpu"],
+        [
+            "GPU (naive)",
+            "GPU (efficient)",
+            "GPU (work-efficient plus)",
+            "GPU (Thrust)",
+            "CPU",
+        ],
         False,
         "performance.png",
     )
     plot_and_save(
-        ["naive", "efficient", "thrust"],
-        ["Naive", "Work-efficient", "Thrust"],
+        ["naive", "efficient", "efficient_plus", "thrust"],
+        ["Naive", "Work-efficient", "Work-efficient plus", "Thrust"],
         True,
         "performance-gpu-only.png",
     )
diff --git a/scripts/tune_block_sizes.py b/scripts/tune_block_sizes.py
deleted file mode 100644
index 1d86a198..00000000
--- a/scripts/tune_block_sizes.py
+++ /dev/null
@@ -1,48 +0,0 @@
-from helper import measure_time
-
-
-def tune_block_size(operation: str, implementation: str, input_size: int) -> None:
-    block_sizes = [8, 16, 32, 64, 128, 256, 512, 1024]
-    best_time = float("inf")
-    best_block_size = -1
-    for block_size in block_sizes:
-        time_sum = 0.0
-        time_count = 10
-        for _ in range(time_count):
-            time_sum += measure_time(operation, implementation, input_size, block_size)
-        time = time_sum / time_count
-        print(f"Block size: {block_size}, time: {time} ms")
-        if time < best_time:
-            best_time = time
-            best_block_size = block_size
-    print(f"Optimal block size: {best_block_size}, time: {best_time} ms")
-
-
-def print_divider() -> None:
-    print("=" * 40)
-
-
-def main():
-    input_size = 1 << 22
-
-    print("Naive scan, power-of-two")
-    tune_block_size("scan", "naive", input_size)
-    print_divider()
-    print("Naive scan, non-power-of-two")
-    tune_block_size("scan", "naive", input_size - 3)
-    print_divider()
-    print("Work-efficient scan, power-of-two")
-    tune_block_size("scan", "efficient", input_size)
-    print_divider()
-    print("Work-efficient scan, non-power-of-two")
-    tune_block_size("scan", "efficient", input_size - 3)
-    print_divider()
-    print("Work-efficient compact, power-of-two")
-    tune_block_size("compact", "efficient", input_size)
-    print_divider()
-    print("Work-efficient compact, non-power-of-two")
-    tune_block_size("compact", "efficient", input_size - 3)
-
-
-if __name__ == "__main__":
-    main()
diff --git a/scripts/tune_parameters.py b/scripts/tune_parameters.py
new file mode 100644
index 00000000..350b308b
--- /dev/null
+++ b/scripts/tune_parameters.py
@@ -0,0 +1,97 @@
+import subprocess
+
+from helper import measure_time
+
+
+def tune_block_size(operation: str, implementation: str, input_size: int) -> None:
+    block_sizes = [8, 16, 32, 64, 128, 256, 512, 1024]
+    best_time = float("inf")
+    best_block_size = -1
+    for block_size in block_sizes:
+        time_sum = 0.0
+        time_count = 10
+        for _ in range(time_count):
+            time_sum += measure_time(operation, implementation, input_size, block_size)
+        time = time_sum / time_count
+        print(f"Block size: {block_size}, time: {time} ms")
+        if time < best_time:
+            best_time = time
+            best_block_size = block_size
+    print(f"Optimal block size: {best_block_size}, time: {best_time} ms")
+
+
+def tune_efficient_plus(input_size: int) -> None:
+    block_sizes = [8, 16, 32, 64, 128, 256, 512, 1024]
+    elements_per_thread_values = [1, 2, 4, 8, 16]
+    best_time = float("inf")
+    best_config = (-1, -1)
+    for block_size in block_sizes:
+        for elements_per_thread in elements_per_thread_values:
+            time_sum = 0.0
+            time_count = 10
+            try:
+                for _ in range(time_count):
+                    time_sum += measure_time(
+                        "scan",
+                        "efficient_plus",
+                        input_size,
+                        block_size,
+                        elements_per_thread,
+                    )
+            except subprocess.CalledProcessError:
+                print(
+                    f"Block size: {block_size}, "
+                    f"elements per thread: {elements_per_thread} "
+                    "- crashed"
+                )
+                continue
+            time = time_sum / time_count
+            print(
+                f"Block size: {block_size}, "
+                f"elements per thread: {elements_per_thread}, "
+                f"time: {time} ms"
+            )
+            if time < best_time:
+                best_time = time
+                best_config = (block_size, elements_per_thread)
+    print(
+        f"Optimal config: block size {best_config[0]}, "
+        f"elements per thread {best_config[1]}, "
+        f"time: {best_time} ms"
+    )
+
+
+def print_divider() -> None:
+    print("=" * 40)
+
+
+def main():
+    input_size = 1 << 22
+
+    print("Naive scan, power-of-two")
+    tune_block_size("scan", "naive", input_size)
+    print_divider()
+    print("Naive scan, non-power-of-two")
+    tune_block_size("scan", "naive", input_size - 3)
+    print_divider()
+    print("Work-efficient scan, power-of-two")
+    tune_block_size("scan", "efficient", input_size)
+    print_divider()
+    print("Work-efficient scan, non-power-of-two")
+    tune_block_size("scan", "efficient", input_size - 3)
+    print_divider()
+    print("Work-efficient compact, power-of-two")
+    tune_block_size("compact", "efficient", input_size)
+    print_divider()
+    print("Work-efficient compact, non-power-of-two")
+    tune_block_size("compact", "efficient", input_size - 3)
+    print_divider()
+    print("Work-efficient plus scan, power-of-two")
+    tune_efficient_plus(input_size)
+    print_divider()
+    print("Work-efficient plus scan, non-power-of-two")
+    tune_efficient_plus(input_size - 3)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/src/main.cpp b/src/main.cpp
index 9df608c7..f4488f5c 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -10,6 +10,7 @@
 #include <stream_compaction/cpu.h>
 #include <stream_compaction/naive.h>
 #include <stream_compaction/efficient.h>
+#include <stream_compaction/efficient_plus.h>
 #include <stream_compaction/thrust.h>
 #include "testing_helpers.hpp"
 
@@ -81,6 +82,20 @@ int main(int argc, char* argv[]) {
     //printArray(NPOT, c, true);
     printCmpResult(NPOT, b, c);
 
+    zeroArray(SIZE, c);
+    printDesc("work-efficient plus scan, power-of-two");
+    StreamCompaction::EfficientPlus::scan(SIZE, c, a);
+    printElapsedTime(StreamCompaction::EfficientPlus::timer().getGpuElapsedTimeForPreviousOperation(), "(CUDA Measured)");
+    //printArray(SIZE, c, true);
+    printCmpResult(SIZE, b, c);
+
+    zeroArray(SIZE, c);
+    printDesc("work-efficient plus scan, non-power-of-two");
+    StreamCompaction::EfficientPlus::scan(NPOT, c, a);
+    printElapsedTime(StreamCompaction::EfficientPlus::timer().getGpuElapsedTimeForPreviousOperation(), "(CUDA Measured)");
+    //printArray(NPOT, c, true);
+    printCmpResult(NPOT, b, c);
+
     zeroArray(SIZE, c);
     printDesc("thrust scan, power-of-two");
     StreamCompaction::Thrust::scan(SIZE, c, a);
diff --git a/src/measure_time.cpp b/src/measure_time.cpp
index f6893c55..eec023d7 100644
--- a/src/measure_time.cpp
+++ b/src/measure_time.cpp
@@ -7,22 +7,25 @@
 
 #include <stream_compaction/cpu.h>
 #include <stream_compaction/efficient.h>
+#include <stream_compaction/efficient_plus.h>
 #include <stream_compaction/naive.h>
 #include <stream_compaction/thrust.h>
 
 int main(int argc, char *argv[]) {
     // argv[1]: scan/compact
-    // argv[2]: cpu/naive/efficient/thrust
+    // argv[2]: cpu/naive/efficient/efficient_plus/thrust
     // argv[3]: input size
     // argv[4]: block size
+    // argv[5]: elements per thread
 
-    if (argc != 5) {
+    if (argc != 6) {
         return -1;
     }
     const std::string operation(argv[1]);
     const std::string implementation(argv[2]);
     const int inputSize = std::stoi(argv[3]);
     const int blockSize = std::stoi(argv[4]);
+    const int elementsPerThread = std::stoi(argv[5]);
 
     std::vector<int> inputs(inputSize);
     std::vector<int> outputs(inputSize);
@@ -51,33 +54,57 @@ int main(int argc, char *argv[]) {
         timer = &StreamCompaction::Naive::timer();
     } else if (implementation == "efficient") {
         timer = &StreamCompaction::Efficient::timer();
+    } else if (implementation == "efficient_plus") {
+        timer = &StreamCompaction::EfficientPlus::timer();
     } else if (implementation == "thrust") {
         timer = &StreamCompaction::Thrust::timer();
     } else {
         return -1;
     }
 
-#define RUN_SCAN(scan)                                                                             \
-    do {                                                                                           \
-        if (blockSize >= 0) {                                                                      \
-            scan(inputSize, outputs.data(), inputs.data(), blockSize);                             \
-        } else {                                                                                   \
-            scan(inputSize, outputs.data(), inputs.data());                                        \
-        }                                                                                          \
-    } while (false)
-
     if (operation == "scan") {
         if (implementation == "cpu") {
-            if (blockSize >= 0) {
+            if (blockSize >= 0 || elementsPerThread >= 0) {
                 return -1;
             }
             StreamCompaction::CPU::scan(inputSize, outputs.data(), inputs.data());
         } else if (implementation == "naive") {
-            RUN_SCAN(StreamCompaction::Naive::scan);
+            if (elementsPerThread >= 0) {
+                return -1;
+            }
+            if (blockSize >= 0) {
+                StreamCompaction::Naive::scan(inputSize, outputs.data(), inputs.data(), blockSize);
+            } else {
+                StreamCompaction::Naive::scan(inputSize, outputs.data(), inputs.data());
+            }
         } else if (implementation == "efficient") {
-            RUN_SCAN(StreamCompaction::Efficient::scan);
-        } else if (implementation == "thrust") {
+            if (elementsPerThread >= 0) {
+                return -1;
+            }
             if (blockSize >= 0) {
+                StreamCompaction::Efficient::scan(inputSize, outputs.data(), inputs.data(),
+                                                  blockSize);
+            } else {
+                StreamCompaction::Efficient::scan(inputSize, outputs.data(), inputs.data());
+            }
+        } else if (implementation == "efficient_plus") {
+            if (blockSize >= 0) {
+                if (elementsPerThread >= 0) {
+                    StreamCompaction::EfficientPlus::scan(inputSize, outputs.data(), inputs.data(),
+                                                          blockSize, elementsPerThread);
+                } else {
+                    StreamCompaction::EfficientPlus::scan(inputSize, outputs.data(), inputs.data(),
+                                                          blockSize);
+                }
+            } else {
+                if (elementsPerThread >= 0) {
+                    return -1;
+                } else {
+                    StreamCompaction::EfficientPlus::scan(inputSize, outputs.data(), inputs.data());
+                }
+            }
+        } else if (implementation == "thrust") {
+            if (blockSize >= 0 || elementsPerThread >= 0) {
                 return -1;
             }
             StreamCompaction::Thrust::scan(inputSize, outputs.data(), inputs.data());
@@ -86,6 +113,9 @@ int main(int argc, char *argv[]) {
         }
     } else if (operation == "compact") {
         if (implementation == "efficient") {
+            if (elementsPerThread >= 0) {
+                return -1;
+            }
             if (blockSize >= 0) {
                 StreamCompaction::Efficient::compact(inputSize, outputs.data(), inputs.data(),
                                                      blockSize);
diff --git a/stream_compaction/CMakeLists.txt b/stream_compaction/CMakeLists.txt
index 19511caa..a79d894a 100644
--- a/stream_compaction/CMakeLists.txt
+++ b/stream_compaction/CMakeLists.txt
@@ -3,6 +3,7 @@ set(headers
     "cpu.h"
     "naive.h"
     "efficient.h"
+    "efficient_plus.h"
     "thrust.h"
     )
 
@@ -11,6 +12,7 @@ set(sources
     "cpu.cu"
     "naive.cu"
     "efficient.cu"
+    "efficient_plus.cu"
     "thrust.cu"
     )
 
diff --git a/stream_compaction/efficient.cu b/stream_compaction/efficient.cu
index 447b0a78..0ffc2587 100644
--- a/stream_compaction/efficient.cu
+++ b/stream_compaction/efficient.cu
@@ -77,6 +77,7 @@ namespace StreamCompaction {
             if (ceiledDataSize > dataSize) {
                 cudaMemset(dev_data + n, 0, ceiledDataSize - dataSize);
             }
+            cudaDeviceSynchronize();
 
             timer().startGpuTimer();
             scanImpl(ceiledN, dev_data, blockSize);
@@ -111,6 +112,7 @@ namespace StreamCompaction {
             cudaMalloc((void **)&dev_indices, ceiledDataSize);
             int *dev_oData;
             cudaMalloc((void **)&dev_oData, dataSize);
+            cudaDeviceSynchronize();
 
             timer().startGpuTimer();
             Common::kernMapToBoolean<<<gridSize, blockSize>>>(n, dev_bools, dev_iData);
diff --git a/stream_compaction/efficient.h b/stream_compaction/efficient.h
index 23a5bde4..8097e408 100644
--- a/stream_compaction/efficient.h
+++ b/stream_compaction/efficient.h
@@ -6,8 +6,8 @@ namespace StreamCompaction {
     namespace Efficient {
         StreamCompaction::Common::PerformanceTimer &timer();
 
-        void scan(int n, int *odata, const int *idata, const int blockSize = 128);
+        void scan(int n, int *odata, const int *idata, const int blockSize = 64);
 
-        int compact(int n, int *odata, const int *idata, const int blockSize = 128);
+        int compact(int n, int *odata, const int *idata, const int blockSize = 64);
     }
 }
diff --git a/stream_compaction/efficient_plus.cu b/stream_compaction/efficient_plus.cu
new file mode 100644
index 00000000..8eb88e62
--- /dev/null
+++ b/stream_compaction/efficient_plus.cu
@@ -0,0 +1,196 @@
+#include <cuda.h>
+#include <cuda_runtime.h>
+
+#include "common.h"
+#include "efficient_plus.h"
+
+namespace StreamCompaction {
+    namespace EfficientPlus {
+        using StreamCompaction::Common::PerformanceTimer;
+        PerformanceTimer &timer() {
+            static PerformanceTimer timer;
+            return timer;
+        }
+
+        __host__ __device__ unsigned conflictFreeIndex(unsigned index) {
+            // Number of banks: 32
+            unsigned offset = index / 32U;
+            offset += offset / 32U;
+            return index + offset;
+        }
+
+        __device__ int &conflictFreeGet(int *data, unsigned index) {
+            return data[conflictFreeIndex(index)];
+        }
+
+        template <unsigned ElementsPerThread>
+        __global__ void scanPerBlock(unsigned n, int *__restrict__ data, int *__restrict__ sums) {
+            unsigned tileSize = blockDim.x * ElementsPerThread * 2U;
+
+            extern __shared__ int sharedData[];
+            unsigned startSharedIndex = threadIdx.x * ElementsPerThread * 2U;
+            unsigned endSharedIndex = startSharedIndex + ElementsPerThread * 2U;
+            unsigned startGlobalIndex = blockIdx.x * tileSize + startSharedIndex;
+            unsigned endGlobalIndex = min(startGlobalIndex + ElementsPerThread * 2U, n);
+            {
+                // Copy data to shared memory.
+                unsigned sharedIndex = startSharedIndex;
+                unsigned globalIndex = startGlobalIndex;
+                for (; globalIndex < endGlobalIndex; ++sharedIndex, ++globalIndex) {
+                    conflictFreeGet(sharedData, sharedIndex) = data[globalIndex];
+                }
+                for (; sharedIndex < endSharedIndex; ++sharedIndex) {
+                    conflictFreeGet(sharedData, sharedIndex) = 0;
+                }
+            }
+            __syncthreads();
+
+            // Up-sweep
+            for (unsigned offset = 1U; offset < tileSize; offset *= 2U) {
+#pragma unroll
+                for (unsigned i = 0U; i < ElementsPerThread; ++i) {
+                    unsigned index = (threadIdx.x * ElementsPerThread + i + 1U) * offset * 2U - 1U;
+                    if (index < tileSize) {
+                        conflictFreeGet(sharedData, index) +=
+                            conflictFreeGet(sharedData, index - offset);
+                    }
+                }
+                __syncthreads();
+            }
+
+            if (threadIdx.x == 0U) {
+                int &lastElement = conflictFreeGet(sharedData, tileSize - 1U);
+                // Save the total sum of this block to the sums array.
+                if (sums != nullptr) {
+                    // sums may be nullptr for the last recursion.
+                    sums[blockIdx.x] = lastElement;
+                }
+                // Clear the last element before down-sweep.
+                lastElement = 0;
+            }
+            __syncthreads();
+
+            // Down-sweep
+            for (unsigned offset = tileSize / 2U; offset > 0U; offset /= 2U) {
+#pragma unroll
+                for (unsigned i = 0U; i < ElementsPerThread; ++i) {
+                    unsigned index = (threadIdx.x * ElementsPerThread + i + 1U) * offset * 2U - 1U;
+                    if (index < tileSize) {
+                        int &leftChild = conflictFreeGet(sharedData, index - offset);
+                        int &rightChild = conflictFreeGet(sharedData, index);
+                        int oldLeftChild = leftChild;
+                        leftChild = rightChild;
+                        rightChild += oldLeftChild;
+                    }
+                }
+                __syncthreads();
+            }
+
+            // Write results back to global memory.
+            {
+                unsigned sharedIndex = startSharedIndex;
+                unsigned globalIndex = startGlobalIndex;
+                for (; globalIndex < endGlobalIndex; ++sharedIndex, ++globalIndex) {
+                    data[globalIndex] = conflictFreeGet(sharedData, sharedIndex);
+                }
+            }
+        }
+
+        __global__ void addSums(unsigned n, int *__restrict__ data, const int *__restrict__ sums,
+                                unsigned elementsPerThread) {
+            unsigned startIndex = (blockIdx.x * blockDim.x + threadIdx.x) * elementsPerThread * 2U;
+            unsigned endIndex = min(startIndex + elementsPerThread * 2U, n);
+            int sum = sums[blockIdx.x];
+            for (unsigned index = startIndex; index < endIndex; ++index) {
+                data[index] += sum;
+            }
+        }
+
+        void scanImpl(unsigned n, int *data, unsigned blockSize, unsigned elementsPerThread,
+                      unsigned tileSize, unsigned sharedMemorySize, unsigned gridSize, int *sums) {
+#define DISPATCH(N) scanPerBlock<N><<<gridSize, blockSize, sharedMemorySize>>>(n, data, sums);
+            switch (elementsPerThread) {
+            case 1U:
+                DISPATCH(1U);
+                break;
+            case 2U:
+                DISPATCH(2U);
+                break;
+            case 4U:
+                DISPATCH(4U);
+                break;
+            case 8U:
+                DISPATCH(8U);
+                break;
+            case 16U:
+                DISPATCH(16U);
+                break;
+            default:
+                printf("Error: elementsPerThread %u is not supported!\n", elementsPerThread);
+                exit(1);
+            }
+#undef DISPATCH
+
+            checkCUDAErrorFn("scanPerBlock kernel failed!");
+            if (gridSize > 1U) {
+                unsigned nextGridSize = (gridSize + tileSize - 1U) / tileSize;
+                int *nextSums = nullptr;
+                if (nextGridSize > 1U) {
+                    nextSums = sums + gridSize;
+                }
+                scanImpl(gridSize, sums, blockSize, elementsPerThread, tileSize, sharedMemorySize,
+                         nextGridSize, nextSums);
+                addSums<<<gridSize, blockSize>>>(n, data, sums, elementsPerThread);
+                checkCUDAErrorFn("addSums kernel failed!");
+            }
+        }
+
+        void scan(int n, int *odata, const int *idata, const int blockSize,
+                  const int elementsPerThread) {
+            const auto dataSize = n * sizeof(int);
+
+            int *dev_data;
+            cudaMalloc((void **)&dev_data, dataSize);
+            checkCUDAErrorFn("cudaMalloc dev_data failed!");
+            cudaMemcpy(dev_data, idata, dataSize, cudaMemcpyHostToDevice);
+            checkCUDAErrorFn("cudaMemcpy to device failed!");
+
+            // Allocate GPU memory for sums beforehand.
+            unsigned tileSize = blockSize * elementsPerThread * 2U;
+            unsigned sharedMemorySize = (conflictFreeIndex(tileSize - 1U) + 1U) * sizeof(int);
+            unsigned gridSize = (n + tileSize - 1U) / tileSize;
+
+            unsigned totalSumCount = 0U;
+            {
+                unsigned gridSize = n;
+                while (true) {
+                    gridSize = (gridSize + tileSize - 1U) / tileSize;
+                    if (gridSize <= 1U) {
+                        break;
+                    }
+                    totalSumCount += gridSize;
+                }
+            }
+            int *dev_sums = nullptr;
+            if (totalSumCount > 0U) {
+                cudaMalloc((void **)&dev_sums, totalSumCount * sizeof(int));
+                checkCUDAErrorFn("cudaMalloc dev_sums failed!");
+            }
+
+            cudaDeviceSynchronize();
+            timer().startGpuTimer();
+            scanImpl(n, dev_data, blockSize, elementsPerThread, tileSize, sharedMemorySize,
+                     gridSize, dev_sums);
+            timer().endGpuTimer();
+
+            cudaMemcpy(odata, dev_data, dataSize, cudaMemcpyDeviceToHost);
+            checkCUDAErrorFn("cudaMemcpy to host failed!");
+            cudaFree(dev_data);
+            checkCUDAErrorFn("cudaFree failed!");
+            if (dev_sums != nullptr) {
+                cudaFree(dev_sums);
+                checkCUDAErrorFn("cudaFree failed!");
+            }
+        }
+    }
+}
diff --git a/stream_compaction/efficient_plus.h b/stream_compaction/efficient_plus.h
new file mode 100644
index 00000000..552fc645
--- /dev/null
+++ b/stream_compaction/efficient_plus.h
@@ -0,0 +1,12 @@
+#pragma once
+
+#include "common.h"
+
+namespace StreamCompaction {
+    namespace EfficientPlus {
+        StreamCompaction::Common::PerformanceTimer &timer();
+
+        void scan(int n, int *odata, const int *idata, const int blockSize = 256,
+                  const int elementsPerThread = 1);
+    }
+}
diff --git a/stream_compaction/naive.cu b/stream_compaction/naive.cu
index 9acd42d5..8b518ed1 100644
--- a/stream_compaction/naive.cu
+++ b/stream_compaction/naive.cu
@@ -40,6 +40,7 @@ namespace StreamCompaction {
             cudaMemcpy(dev_iData, idata, dataSize, cudaMemcpyHostToDevice);
             int *dev_oData;
             cudaMalloc((void **)&dev_oData, dataSize);
+            cudaDeviceSynchronize();
 
             timer().startGpuTimer();
             const int gridSize = (n + blockSize - 1) / blockSize;
diff --git a/stream_compaction/thrust.cu b/stream_compaction/thrust.cu
index 25f0a7c6..bcc61332 100644
--- a/stream_compaction/thrust.cu
+++ b/stream_compaction/thrust.cu
@@ -21,9 +21,12 @@ namespace StreamCompaction {
             thrust::host_vector<int> host_in(idata, idata + n);
             thrust::device_vector<int> dev_in = host_in;
             thrust::device_vector<int> dev_out(n);
+            cudaDeviceSynchronize();
+
             timer().startGpuTimer();
             thrust::exclusive_scan(dev_in.begin(), dev_in.end(), dev_out.begin());
             timer().endGpuTimer();
+
             thrust::copy(dev_out.begin(), dev_out.end(), odata);
         }
     }

From 7b0719c707b3113cd1c48539e9eda3ab63698eb7 Mon Sep 17 00:00:00 2001
From: Yunhao Qian <yunhaoqian@hotmail.com>
Date: Tue, 16 Sep 2025 23:58:19 -0400
Subject: [PATCH 12/12] Complete everything

---
 README.md                                 | 398 +++++++------
 img/efficient-plus-add-sums-ncu.png       | Bin 0 -> 355461 bytes
 img/efficient-plus-nsys.png               | Bin 0 -> 262213 bytes
 img/efficient-plus-scan-per-block-ncu.png | Bin 0 -> 335750 bytes
 img/performance-gpu-only.png              | Bin 50709 -> 62023 bytes
 img/performance.png                       | Bin 57469 -> 69446 bytes
 img/thrust-ncu.png                        | Bin 0 -> 332664 bytes
 img/thrust-nsys.png                       | Bin 0 -> 270770 bytes
 scripts/measure_performance.py            |   2 +-
 scripts/performance.json                  | 672 +++++++++++-----------
 src/main.cpp                              |  39 ++
 src/measure_time.cpp                      |  77 +--
 stream_compaction/CMakeLists.txt          |   4 +
 stream_compaction/cpu_sort.cu             |  24 +
 stream_compaction/cpu_sort.h              |  11 +
 stream_compaction/efficient.cu            |  14 +-
 stream_compaction/efficient.h             |  10 +-
 stream_compaction/efficient_plus.cu       | 121 ++--
 stream_compaction/efficient_plus.h        |   7 +-
 stream_compaction/naive.cu                |   7 +-
 stream_compaction/naive.h                 |   4 +-
 stream_compaction/radix_sort.cu           |  77 +++
 stream_compaction/radix_sort.h            |  11 +
 stream_compaction/thrust.cu               |  21 +-
 24 files changed, 879 insertions(+), 620 deletions(-)
 create mode 100644 img/efficient-plus-add-sums-ncu.png
 create mode 100644 img/efficient-plus-nsys.png
 create mode 100644 img/efficient-plus-scan-per-block-ncu.png
 create mode 100644 img/thrust-ncu.png
 create mode 100644 img/thrust-nsys.png
 create mode 100644 stream_compaction/cpu_sort.cu
 create mode 100644 stream_compaction/cpu_sort.h
 create mode 100644 stream_compaction/radix_sort.cu
 create mode 100644 stream_compaction/radix_sort.h

diff --git a/README.md b/README.md
index ec10e3fe..213e42a2 100644
--- a/README.md
+++ b/README.md
@@ -20,22 +20,26 @@ This project implements stream compaction and its building blocks (map, scan, sc
 - A CPU implementation of scan and stream compaction
 - GPU implementations of scan, using both naive and work-efficient methods
 - A GPU implementation of stream compaction based on the work-efficient scan
+- A carefully optimized work-efficient scan that leverages shared memory along with several additional optimizations
 - C++ and Python scripts used to automate performance measurement accurately and programmatically
 - Performance analysis comparing the different methods
+- More in-depth performance analysis conducted with Nsight
 
 ### Changes to `CMakeLists.txt`
 
-An additional executable,`measure_time.exe`, has been added to the project to support block size tuning, performance benchmarking, and profiling.
+- An additional executable,`measure_time.exe`, has been added to the project to support block size tuning, performance benchmarking, and profiling.
+- The files `cpu_sort.h`, `cpu_sort.cu`, `radix_sort.h`, `radix_sort.h` were introduced to implement Extra Credit 1.
+- The files `efficient_plus.h` and `efficient_plus.cu` were introduced to implement Extra Credit 2.
 
-### Changes to Function Signatures
+### Function Overloads
 
-To simplify block size tuning, I added an optional `blockSize` parameter to the following functions, each with a tuned default value:
+To make block size tuning easier, I added overloads of the following functions that accept an additional `blockSize` parameter. The original overloads remain unchanged and simply forward to the new versions with a tuned default value:
 
-- `Naive::scan(..., const int blockSize = 256)`
-- `Efficient::scan(..., const int blockSize = 64)`
-- `Efficient::compact(..., const int blockSize = 64)`
+- `Naive::scan(..., const int blockSize)`
+- `Efficient::scan(..., const int blockSize)`
+- `Efficient::compact(..., const int blockSize)`
 
-These parameters are used only by `measure_time.exe` and do not affect existing calls.
+These changes are only used by `measure_time.exe` and do not affect existing code paths.
 
 ## Part 1: CPU Scan & Stream Compaction
 
@@ -72,7 +76,7 @@ In [`common.h`](stream_compaction/common.h) and [`common.cu`](stream_compaction/
 - `kernMapToBoolean()` A CUDA kernel that maps each integer to 0 or 1, depending on whether the value is zero.
 - `kernScatter()`: A CUDA kernel that performs the scatter operation with vector addressing. Conditioned on a boolean array, it optionally stores elements at locations specified by an index array.
 
-In [`efficient.h](stream_compaction/efficient.h) and [`efficient.cu`](stream_compaction/efficient.cu):
+In [`efficient.h`](stream_compaction/efficient.h) and [`efficient.cu`](stream_compaction/efficient.cu):
 
 - `compact()`: Implements stream compaction on GPU using map (via `kernMapToBoolean()`) → scan (via `scanImpl()`) → scatter (via `kernScatter()`).
 
@@ -81,6 +85,7 @@ In [`efficient.h](stream_compaction/efficient.h) and [`efficient.cu`](stream_com
 In [`thrust.h`](stream_compaction/thrust.h) and [`thrust.cu`](stream_compaction/thrust.cu):
 
 - `scan()`: Wraps `thrust::exclusive_scan()`, adding timing instrumentation and exposing the same API as the other implementations.
+- Profiling revealed that beyond a certain input size, `thrust::exclusive_scan()` switches to an algorithm that allocates GPU memory internally. These allocations introduced significant variability in benchmarking, at times making Thrust appear slower than even the naive implementation. To address this, I created a reusable memory pool and invoked the overload of `exclusive_scan` that accepts an execution policy configured with that pool. This allows the benchmark to perform a warm-up run (which handles any necessary allocations) and then time the second run, which reuses the existing memory without additional allocations.
 
 ## Part 5: Why is My GPU Approach So Slow?
 
@@ -95,7 +100,16 @@ I believe Part 3.1 already incorporates the optimizations described in the instr
 
 ### Extra Credit 1: Radix Sort
 
-This part is not implemented.
+Radix sort is implemented in `radix_sort.cu`. It uses the `efficient_plus.cu` scan developed for extra credit 2, along with several other utility kernels. The algorithm processes the input data one bit at a time, from the least significant to the most significant.
+
+For each bit, the process is as follows:
+
+1. Extract Bits: The specific bit is extracted from each integer.
+2. Scan for Indices: A parallel scan is performed on these extracted bits to determine the correct destination index for each element.
+3. Count Deduction: The last element of the scanned output and the last element of the input are used to quickly deduce the counts of both zeros and ones.
+4. Stable Scatter: A stable scatter operation then moves the elements to their new, sorted positions based on the calculated indices, preserving the relative order of elements with the same bit value.
+
+After iterating through all the bits, the data is fully sorted. The correctness of the GPU implementation is verified in `main.cpp` by comparing its output against a baseline CPU sorting algorithm implemented in `cpu_sort.cu`. The results confirm that the implementation is accurate.
 
 ### Extra Credit 2: GPU Scan Using Shared Memory && Hardware Optimization
 
@@ -104,12 +118,13 @@ To improve the work-efficient implementation, I developed the work-efficient plu
 - Kernel fusing: The up-sweep and down-sweep phases are fused into a single kernel invocation. Although compacting indices no longer reduces the number of blocks, this approach minimizes divergence and is therefore retained.
 - Shared memory usage: Instead of operating directly on global memory, data is first copied into shared memory, scanned per block, and then copied back to global memory.
 - Recursive tiling: Since a block can only process a limited number of elements, the algorithm is made recursive.
-  - The array is partitioned into tiles, one per block.  
-  - In addition to performing the scan, each block writes its tile sum into a new array.  
+  - The array is partitioned into tiles, one per block.
+  - In addition to performing the scan, each block writes its tile sum into a new array.
   - An exclusive scan is recursively applied to this array of tile sums, and the results are then added back to the input data.
 - Avoiding shared memory bank conflicts: Shared memory indexing is padded following the method described in GPU Gems. This introduces only a small increase in memory usage.
 - Preallocating the recursion buffer: To avoid repeated allocation of temporary GPU buffers for tile sums, the recursion depth and total required storage are precomputed. A single contiguous GPU buffer is allocated and reused across all recursion levels.
 - Multiple elements per thread: As an experiment, I added support for processing multiple elements per thread, controlled by the compile-time template parameter `ElementsPerThread`. Different variants are dispatched at runtime, and loops over per-thread elements are unrolled with `#pragma unroll`. In practice, this optimization was not beneficial; the tuned configuration still uses one element per thread.
+- Shrinking block size in the final recursion: In the last recursion step, the input is often much smaller than the predefined block size. As a niche optimization, the block size can be reduced to the smallest power of two that accommodates the input, with shared memory usage adjusted accordingly. However, testing showed no measurable performance improvement from this change.
 
 ## Part 7: Write-up
 
@@ -142,15 +157,15 @@ From these experiments, the chosen defaults are:
 
 - Block size 256 for the naive scan
 - Block size 64 for the work-efficient scan and compaction
-- Block size 256 for the work-efficient plus (for extra credit 2) scan, with 1 element per thread
+- Block size 256 for the work-efficient plus (extra credit 2) scan, with 1 element per thread
 
 #### Performance Comparison
 
 To systematically collect execution time data across many configurations, I created a Python script, [`measure_performance.py`](scripts/measure_performance.py). This script relies on the previously described `measure_time.exe` to benchmark runtime across a range of input sizes and implementations. The procedure is as follows:
 
 - Input sizes are tested from $2^4$ up to $2^{27}$, using both exact powers of two and non-powers of two ($2^i - 3$ for each $i$) to capture different performance behaviors.
-- The number of elements processed per thread is selected from the set {1, 2, 4, 8, 16}.
-- Each configuration is executed 20 times, and the mean runtime is recorded.
+- The number of elements processed per thread is selected from the set `{1, 2, 4, 8, 16}`.
+- Each configuration is executed 10 times, and the mean runtime is recorded.
 - Results are stored in a JSON file ([`performance.json`](scripts/performance.json)).
 
 The JSON data is then processed by another script, [`plot_performance.py`](scripts/plot_performance.py), which generates the figures shown in this report.
@@ -188,25 +203,38 @@ Comparison of the two:
 - For $N < 2^{23}$, the so-called work-efficient implementation is actually slower than the naive version. This can be attributed to kernel launch overhead: the up-sweep and down-sweep phases double the number of kernel invocations. Although the total work is reduced, the benefit is negligible at these smaller sizes.
 - For larger $N$, the work-efficient method begins to outperform the naive implementation, and the gap widens quickly. This is because the work-efficient algorithm performs only $O(N)$ total operations, whereas the naive approach requires $O(N \log N)$.
 
-#### Work-Efficient Plus GPU Implementation (for Extra Credit 2)
+#### Work-Efficient Plus GPU Implementation (Extra Credit 2)
+
+- Outperforms both the naive and work-efficient versions even for very small $N$, likely due to requiring fewer kernel launches.
+- For larger inputs, achieves nearly an order of magnitude speedup over the previous two approaches, primarily from reduced global memory traffic and greater reliance on shared memory.
+- Despite these gains, Nsight analysis later shows that the implementation remains memory-bound.
+
+![Work-efficient plus Nsight Systems](img/efficient-plus-nsys.png)
+
+From the Nsight Systems timeline, execution begins with three `scanPerBlock` calls followed by three `addSums`. In the second and third recursion levels, the input size is so small that their runtimes are negligible. Nearly all of the execution time is spent in the first recursion level.
 
-- For small $N$, the performance is comparable to the naive and work-efficient implementations, without clear advantages. This is because each kernel must perform a full round trip from global memory → shared memory → global memory. When the amount of computation on shared memory is limited, this memory traffic dominates the runtime.  
-- For larger inputs ($N \geq 2^{20}$), the benefits of this implementation become evident due to the optimizations described earlier. It even outperforms Thrust at $2^{20} \leq N \leq 2^{25}$. However, I suspect Thrust’s performance in my environments are not representative (see below), so I do not claim that my implementation is more optimized than Thrust in general.
+![Work-efficient plus scanPerBlock Nsight Compute](img/efficient-plus-scan-per-block-ncu.png)
+
+![Work-efficient plus addSums Nsight Compute](img/efficient-plus-add-sums-ncu.png)
+
+In Nsight Compute, examining the first recursion’s `scanPerBlock` shows a moderate SM throughput of about 53%. The kernel is clearly memory-bound, with memory and DRAM throughput reaching 92%, indicating that global memory reads and writes still dominate execution time.
+
+In contrast, the first recursion's `addSums` achieves only 8% SM throughput, demonstrating that its performance is heavily constrained by global memory access. Under the current implementation, this behavior is expected and difficult to improve further without a major overhaul.
 
 #### Thrust GPU Implementation
 
-To better understand the behavior of `thrust::exclusive_scan()`, I profiled it using Nsight Systems. The results revealed only two CUDA kernel calls:
+Thrust’s `exclusive_scan()` delivers strong performance across all input sizes:
+
+- For small $N$, the runtime is comparable to the optimized work-efficient plus implementation.
+- For large $N$, Thrust is roughly 2x faster. However, it is essential to warm up once before timing, so that internal GPU buffer allocations are excluded; otherwise, the runtime exhibits a sudden step increase after roughly $N = 2^{19}$.
 
-- `DeviceScanInitKernel`, which is short-lived
-- `DeviceScanKernel`, which dominates execution time
+![Thrust Nsight Systems](img/thrust-nsys.png)
 
-This suggests that Thrust fuses the entire scan into just two kernels. While the internal algorithm is not directly visible, it is reasonable to assume that it leverages shared memory and optimized memory access patterns.
+From the timeline in Nsight Systems, execution begins with a lightweight `DeviceScanInitKernel`, followed by a single `DeviceScanKernel` that dominates the runtime. It is notable that the main computation is handled almost entirely within a single kernel launch.
 
-The performance profile of Thrust’s `exclusive_scan` is notable:
+![Thrust Nsight Compute](img/thrust-ncu.png)
 
-- Small sizes ($N \leq 2^{17}$): Runtime remains relatively flat across input sizes. Although slower than the CPU implementation, it is still much faster than the naive and work-efficient GPU versions, likely due to the minimal number of kernel launches.
-- Mid sizes ($2^{18} \leq N \leq 2^{23}$): Runtime unexpectedly spikes, at times even performing worse than the naive implementation. It seems unlikely that NVIDIA’s official library would be poorly optimized, especially since this anomaly does not appear for other people. I suspect the performance degradation is related to the measurement methodology: repeatedly allocating memory, copying data CPU → GPU, launching kernels, copying results GPU → CPU, and freeing memory. This atypical workflow may interact with the driver in unusual ways. This remains a hypothesis and warrants further investigation.
-- Large sizes ($N > 2^{23}$): Thrust significantly outperforms the naive and work-efficient GPU implementations, presumably because its internal use of shared memory and optimized access patterns scales effectively at large input sizes.
+In Nsight Compute, the `DeviceScanKernel` shows an SM throughput of 19%, lower than that of my work-efficient plus implementation, while memory and DRAM throughput remain similarly high at 93%. The high memory throughput reflects the inherent nature of the task. The lower SM throughput does not imply that Thrust’s implementation is less efficient. On the contrary, it likely reduces the total amount of computation through careful optimizations, with the lower SM utilization being a byproduct of that efficiency.
 
 #### Outputs of `cis5650_stream_compaction_test.exe`
 
@@ -214,216 +242,230 @@ The performance profile of Thrust’s `exclusive_scan` is notable:
 ****************
 ** SCAN TESTS **
 ****************
-    [   2  43  36  34   6  47  28  21  20  47   9  14  36 ...  28   0 ]
+    [  13  35   9   0  27   0   9  16  22   8  47  34  47 ...  12   0 ]
 ==== cpu scan, power-of-two ====
-   elapsed time: 1.6333ms    (std::chrono Measured)
-    [   0   2  45  81 115 121 168 196 217 237 284 293 307 ... 102726393 102726421 ]
+   elapsed time: 1.5831ms    (std::chrono Measured)
+    [   0  13  48  57  57  84  84  93 109 131 139 186 220 ... 102754952 102754964 ]
 ==== cpu scan, non-power-of-two ====
-   elapsed time: 1.4916ms    (std::chrono Measured)
-    [   0   2  45  81 115 121 168 196 217 237 284 293 307 ... 102726316 102726346 ]
+   elapsed time: 1.4894ms    (std::chrono Measured)
+    [   0  13  48  57  57  84  84  93 109 131 139 186 220 ... 102754881 102754896 ]
     passed
 ==== naive scan, power-of-two ====
-   elapsed time: 0.335968ms    (CUDA Measured)
+   elapsed time: 0.499936ms    (CUDA Measured)
     passed
 ==== naive scan, non-power-of-two ====
-   elapsed time: 0.330656ms    (CUDA Measured)
+   elapsed time: 0.336768ms    (CUDA Measured)
     passed
 ==== work-efficient scan, power-of-two ====
-   elapsed time: 0.464192ms    (CUDA Measured)
+   elapsed time: 0.865184ms    (CUDA Measured)
     passed
 ==== work-efficient scan, non-power-of-two ====
-   elapsed time: 0.368544ms    (CUDA Measured)
+   elapsed time: 0.569664ms    (CUDA Measured)
     passed
 ==== work-efficient plus scan, power-of-two ====
-   elapsed time: 0.191456ms    (CUDA Measured)
+   elapsed time: 0.472736ms    (CUDA Measured)
     passed
 ==== work-efficient plus scan, non-power-of-two ====
-   elapsed time: 0.073984ms    (CUDA Measured)
+   elapsed time: 0.07552ms    (CUDA Measured)
     passed
 ==== thrust scan, power-of-two ====
-   elapsed time: 0.320512ms    (CUDA Measured)
+   elapsed time: 0.277952ms    (CUDA Measured)
     passed
 ==== thrust scan, non-power-of-two ====
-   elapsed time: 0.336736ms    (CUDA Measured)
+   elapsed time: 0.04608ms    (CUDA Measured)
     passed
 
 *****************************
 ** STREAM COMPACTION TESTS **
 *****************************
-    [   0   3   2   2   2   1   2   3   0   3   1   2   2 ...   2   0 ]
+    [   1   3   1   0   1   0   1   0   0   0   1   0   1 ...   0   0 ]
 ==== cpu compact without scan, power-of-two ====
-   elapsed time: 7.1751ms    (std::chrono Measured)
-    [   3   2   2   2   1   2   3   3   1   2   2   2   3 ...   1   2 ]
+   elapsed time: 8.2601ms    (std::chrono Measured)
+    [   1   3   1   1   1   1   1   3   2   2   3   2   2 ...   1   2 ]
     passed
 ==== cpu compact without scan, non-power-of-two ====
-   elapsed time: 7.0687ms    (std::chrono Measured)
-    [   3   2   2   2   1   2   3   3   1   2   2   2   3 ...   3   2 ]
+   elapsed time: 8.5801ms    (std::chrono Measured)
+    [   1   3   1   1   1   1   1   3   2   2   3   2   2 ...   1   2 ]
     passed
 ==== cpu compact with scan ====
-   elapsed time: 14.5221ms    (std::chrono Measured)
-    [   3   2   2   2   1   2   3   3   1   2   2   2   3 ...   1   2 ]
+   elapsed time: 14.8527ms    (std::chrono Measured)
+    [   1   3   1   1   1   1   1   3   2   2   3   2   2 ...   1   2 ]
     passed
 ==== work-efficient compact, power-of-two ====
-   elapsed time: 0.524ms    (CUDA Measured)
+   elapsed time: 0.495744ms    (CUDA Measured)
     passed
 ==== work-efficient compact, non-power-of-two ====
-   elapsed time: 0.521024ms    (CUDA Measured)
+   elapsed time: 0.53136ms    (CUDA Measured)
+    passed
+
+*******************
+** SORTING TESTS **
+*******************
+    [ 4113 24235 21309 2900 15577 2400 30009 8016 29272 30408 23697 20184 22097 ... 4812   0 ]
+==== cpu sort, power-of-two ====
+   elapsed time: 189.038ms    (std::chrono Measured)
+==== gpu radix sort, power-of-two ====
+   elapsed time: 3.96045ms    (CUDA Measured)
+    passed
+==== cpu sort, non-power-of-two ====
+   elapsed time: 191.916ms    (std::chrono Measured)
+==== gpu radix sort, non-power-of-two ====
+   elapsed time: 4.00803ms    (CUDA Measured)
     passed
-Press any key to continue . . .
 ```
 
 #### Outputs of `tune_parameters.py`
 
 ```text
 Naive scan, power-of-two
-Block size: 8, time: 6.210713481 ms
-Block size: 16, time: 3.168515182 ms
-Block size: 32, time: 1.640864002 ms
-Block size: 64, time: 0.8767040014999999 ms
-Block size: 128, time: 0.5051392019 ms
-Block size: 256, time: 0.3497567982 ms
-Block size: 512, time: 0.3369727998 ms
-Block size: 1024, time: 0.3949791968 ms
-Optimal block size: 512, time: 0.3369727998 ms
+Block size: 8, time: 6.1931840430000005 ms
+Block size: 16, time: 3.160015989 ms
+Block size: 32, time: 1.6289984100000001 ms
+Block size: 64, time: 0.8754815995000002 ms
+Block size: 128, time: 0.5630367994000001 ms
+Block size: 256, time: 0.5268575905 ms
+Block size: 512, time: 0.5707488000000001 ms
+Block size: 1024, time: 0.4913184017000001 ms
+Optimal block size: 1024, time: 0.4913184017000001 ms
 ========================================
 Naive scan, non-power-of-two
-Block size: 8, time: 6.208518411000001 ms
-Block size: 16, time: 3.1698239809999995 ms
-Block size: 32, time: 1.650400006 ms
-Block size: 64, time: 0.8862239956 ms
-Block size: 128, time: 0.5067872018 ms
-Block size: 256, time: 0.3504383981 ms
-Block size: 512, time: 0.346905601 ms
-Block size: 1024, time: 0.4155999988 ms
-Optimal block size: 512, time: 0.346905601 ms
+Block size: 8, time: 6.197379209 ms
+Block size: 16, time: 3.1488416440000004 ms
+Block size: 32, time: 1.6155263910000002 ms
+Block size: 64, time: 0.8565600038000001 ms
+Block size: 128, time: 0.5647936076 ms
+Block size: 256, time: 0.45924159600000003 ms
+Block size: 512, time: 0.5508479952 ms
+Block size: 1024, time: 0.4998720078999999 ms
+Optimal block size: 256, time: 0.45924159600000003 ms
 ========================================
 Work-efficient scan, power-of-two
-Block size: 8, time: 0.9049055992999999 ms
-Block size: 16, time: 0.7210080087999999 ms
-Block size: 32, time: 0.6597408055 ms
-Block size: 64, time: 0.5313376009999999 ms
-Block size: 128, time: 0.6298431963000001 ms
-Block size: 256, time: 0.6812607945 ms
-Block size: 512, time: 0.5833792001 ms
-Block size: 1024, time: 0.6668896109 ms
-Optimal block size: 64, time: 0.5313376009999999 ms
+Block size: 8, time: 1.2334048075 ms
+Block size: 16, time: 0.9746495964999999 ms
+Block size: 32, time: 1.0865504112999997 ms
+Block size: 64, time: 0.7621375807999999 ms
+Block size: 128, time: 0.8848479986000001 ms
+Block size: 256, time: 0.7751007915 ms
+Block size: 512, time: 1.2780031998999999 ms
+Block size: 1024, time: 0.9169344123000001 ms
+Optimal block size: 64, time: 0.7621375807999999 ms
 ========================================
 Work-efficient scan, non-power-of-two
-Block size: 8, time: 0.9357727944 ms
-Block size: 16, time: 0.7128639936000001 ms
-Block size: 32, time: 0.7185056090999999 ms
-Block size: 64, time: 0.5883967997000001 ms
-Block size: 128, time: 0.5995808003 ms
-Block size: 256, time: 0.6008256017000001 ms
-Block size: 512, time: 0.6760576010000001 ms
-Block size: 1024, time: 0.5939391851 ms
-Optimal block size: 64, time: 0.5883967997000001 ms
+Block size: 8, time: 1.6846079939999998 ms
+Block size: 16, time: 1.1247648052 ms
+Block size: 32, time: 0.9946559961999999 ms
+Block size: 64, time: 1.1106271928 ms
+Block size: 128, time: 0.7899712115 ms
+Block size: 256, time: 0.8548672105999999 ms
+Block size: 512, time: 0.8211200056000001 ms
+Block size: 1024, time: 0.3766912013 ms
+Optimal block size: 1024, time: 0.3766912013 ms
 ========================================
 Work-efficient compact, power-of-two
-Block size: 8, time: 1.417711996 ms
-Block size: 16, time: 0.9495487984000001 ms
-Block size: 32, time: 0.7181632041999999 ms
-Block size: 64, time: 0.6332575947 ms
-Block size: 128, time: 0.6355327934999999 ms
-Block size: 256, time: 0.577478391 ms
-Block size: 512, time: 0.7434591980000002 ms
-Block size: 1024, time: 0.6726783932 ms
-Optimal block size: 256, time: 0.577478391 ms
+Block size: 8, time: 1.320752002 ms
+Block size: 16, time: 0.9775711956 ms
+Block size: 32, time: 0.9180895992 ms
+Block size: 64, time: 1.2212512094 ms
+Block size: 128, time: 0.8028352011 ms
+Block size: 256, time: 1.337366404 ms
+Block size: 512, time: 1.0536224006 ms
+Block size: 1024, time: 0.9021439969000001 ms
+Optimal block size: 128, time: 0.8028352011 ms
 ========================================
 Work-efficient compact, non-power-of-two
-Block size: 8, time: 1.423475218 ms
-Block size: 16, time: 0.9857856036999998 ms
-Block size: 32, time: 0.8006624043 ms
-Block size: 64, time: 0.5751327993 ms
-Block size: 128, time: 0.6924479992 ms
-Block size: 256, time: 0.5636575996 ms
-Block size: 512, time: 0.6784191968000001 ms
-Block size: 1024, time: 0.6932192027999999 ms
-Optimal block size: 256, time: 0.5636575996 ms
+Block size: 8, time: 1.819353578 ms
+Block size: 16, time: 1.3313984046000003 ms
+Block size: 32, time: 1.2955423931000003 ms
+Block size: 64, time: 1.0542688068000001 ms
+Block size: 128, time: 1.2601408064000004 ms
+Block size: 256, time: 1.2192768095 ms
+Block size: 512, time: 1.1920671929000002 ms
+Block size: 1024, time: 1.3155871931 ms
+Optimal block size: 64, time: 1.0542688068000001 ms
 ========================================
 Work-efficient plus scan, power-of-two
-Block size: 8, elements per thread: 1, time: 0.5458272011 ms
-Block size: 8, elements per thread: 2, time: 0.3792447983 ms
-Block size: 8, elements per thread: 4, time: 0.3159423963 ms
-Block size: 8, elements per thread: 8, time: 0.3622208059 ms
-Block size: 8, elements per thread: 16, time: 0.4684351951 ms
-Block size: 16, elements per thread: 1, time: 0.2957440004 ms
-Block size: 16, elements per thread: 2, time: 0.2765696033999999 ms
-Block size: 16, elements per thread: 4, time: 0.3591648042 ms
-Block size: 16, elements per thread: 8, time: 0.3541247966 ms
-Block size: 16, elements per thread: 16, time: 0.4408064038 ms
-Block size: 32, elements per thread: 1, time: 0.2547711969 ms
-Block size: 32, elements per thread: 2, time: 0.2487744019 ms
-Block size: 32, elements per thread: 4, time: 0.2829280005 ms
-Block size: 32, elements per thread: 8, time: 0.355180803 ms
-Block size: 32, elements per thread: 16, time: 0.4990495979999999 ms
-Block size: 64, elements per thread: 1, time: 0.21321919859999997 ms
-Block size: 64, elements per thread: 2, time: 0.23418560179999998 ms
-Block size: 64, elements per thread: 4, time: 0.26373759820000003 ms
-Block size: 64, elements per thread: 8, time: 0.3173408001 ms
-Block size: 64, elements per thread: 16, time: 0.45957120059999995 ms
-Block size: 128, elements per thread: 1, time: 0.2471552 ms
-Block size: 128, elements per thread: 2, time: 0.21002880040000002 ms
-Block size: 128, elements per thread: 4, time: 0.2764960006 ms
-Block size: 128, elements per thread: 8, time: 0.3514591991999999 ms
-Block size: 128, elements per thread: 16, time: 0.49059520079999996 ms
-Block size: 256, elements per thread: 1, time: 0.19113280039999997 ms
-Block size: 256, elements per thread: 2, time: 0.2154880017 ms
-Block size: 256, elements per thread: 4, time: 0.2787679984 ms
-Block size: 256, elements per thread: 8, time: 0.3731999963 ms
-Block size: 256, elements per thread: 16, time: 0.49939519470000004 ms
-Block size: 512, elements per thread: 1, time: 0.20608639850000002 ms
-Block size: 512, elements per thread: 2, time: 0.2563392014 ms
-Block size: 512, elements per thread: 4, time: 0.3583200006 ms
-Block size: 512, elements per thread: 8, time: 0.3594367981 ms
+Block size: 8, elements per thread: 1, time: 0.35677120390000006 ms
+Block size: 8, elements per thread: 2, time: 0.2461855993 ms
+Block size: 8, elements per thread: 4, time: 0.20586879839999997 ms
+Block size: 8, elements per thread: 8, time: 0.2564895988 ms
+Block size: 8, elements per thread: 16, time: 0.29693120419999997 ms
+Block size: 16, elements per thread: 1, time: 0.2679104015 ms
+Block size: 16, elements per thread: 2, time: 0.152214399 ms
+Block size: 16, elements per thread: 4, time: 0.199580802 ms
+Block size: 16, elements per thread: 8, time: 0.2125504002 ms
+Block size: 16, elements per thread: 16, time: 0.2828671993 ms
+Block size: 32, elements per thread: 1, time: 0.16852159649999998 ms
+Block size: 32, elements per thread: 2, time: 0.1681056015 ms
+Block size: 32, elements per thread: 4, time: 0.1758399994 ms
+Block size: 32, elements per thread: 8, time: 0.21814079869999997 ms
+Block size: 32, elements per thread: 16, time: 0.3729472012 ms
+Block size: 64, elements per thread: 1, time: 0.16515839977999996 ms
+Block size: 64, elements per thread: 2, time: 0.15373440083 ms
+Block size: 64, elements per thread: 4, time: 0.1847008006 ms
+Block size: 64, elements per thread: 8, time: 0.22609280039999996 ms
+Block size: 64, elements per thread: 16, time: 0.3613759995 ms
+Block size: 128, elements per thread: 1, time: 0.13827199933000003 ms
+Block size: 128, elements per thread: 2, time: 0.12009920111999998 ms
+Block size: 128, elements per thread: 4, time: 0.23142399940000002 ms
+Block size: 128, elements per thread: 8, time: 0.2426623969 ms
+Block size: 128, elements per thread: 16, time: 0.3689568042 ms
+Block size: 256, elements per thread: 1, time: 0.1315040014 ms
+Block size: 256, elements per thread: 2, time: 0.14512320169999998 ms
+Block size: 256, elements per thread: 4, time: 0.1842624008 ms
+Block size: 256, elements per thread: 8, time: 0.24464000160000002 ms
+Block size: 256, elements per thread: 16, time: 0.36462400240000004 ms
+Block size: 512, elements per thread: 1, time: 0.14869759980000002 ms
+Block size: 512, elements per thread: 2, time: 0.1295744002 ms
+Block size: 512, elements per thread: 4, time: 0.19439359899999997 ms
+Block size: 512, elements per thread: 8, time: 0.2625504031 ms
 Block size: 512, elements per thread: 16 - crashed
-Block size: 1024, elements per thread: 1, time: 0.234352003 ms
-Block size: 1024, elements per thread: 2, time: 0.25858239680000006 ms
-Block size: 1024, elements per thread: 4, time: 0.3363999992000001 ms
+Block size: 1024, elements per thread: 1, time: 0.12309759919999999 ms
+Block size: 1024, elements per thread: 2, time: 0.1486623989 ms
+Block size: 1024, elements per thread: 4, time: 0.2266975983 ms
 Block size: 1024, elements per thread: 8 - crashed
 Block size: 1024, elements per thread: 16 - crashed
-Optimal config: block size 256, elements per thread 1, time: 0.19113280039999997 ms
+Optimal config: block size 128, elements per thread 2, time: 0.12009920111999998 ms
 ========================================
 Work-efficient plus scan, non-power-of-two
-Block size: 8, elements per thread: 1, time: 0.4914176017 ms
-Block size: 8, elements per thread: 2, time: 0.32388479719999996 ms
-Block size: 8, elements per thread: 4, time: 0.38091839839999997 ms
-Block size: 8, elements per thread: 8, time: 0.33217279899999996 ms
-Block size: 8, elements per thread: 16, time: 0.39384639860000004 ms
-Block size: 16, elements per thread: 1, time: 0.3107008011 ms
-Block size: 16, elements per thread: 2, time: 0.2454912007 ms
-Block size: 16, elements per thread: 4, time: 0.3092735976 ms
-Block size: 16, elements per thread: 8, time: 0.32160959829999997 ms
-Block size: 16, elements per thread: 16, time: 0.42109759750000003 ms
-Block size: 32, elements per thread: 1, time: 0.26428479559999996 ms
-Block size: 32, elements per thread: 2, time: 0.25905919679999995 ms
-Block size: 32, elements per thread: 4, time: 0.3214975982 ms
-Block size: 32, elements per thread: 8, time: 0.3603167982 ms
-Block size: 32, elements per thread: 16, time: 0.4624383956 ms
-Block size: 64, elements per thread: 1, time: 0.20346560030000002 ms
-Block size: 64, elements per thread: 2, time: 0.2914719998 ms
-Block size: 64, elements per thread: 4, time: 0.29802560209999995 ms
-Block size: 64, elements per thread: 8, time: 0.3288128018 ms
-Block size: 64, elements per thread: 16, time: 0.449561593 ms
-Block size: 128, elements per thread: 1, time: 0.20832960009999998 ms
-Block size: 128, elements per thread: 2, time: 0.24085119969999996 ms
-Block size: 128, elements per thread: 4, time: 0.2845311985 ms
-Block size: 128, elements per thread: 8, time: 0.3271040023 ms
-Block size: 128, elements per thread: 16, time: 0.46438719919999993 ms
-Block size: 256, elements per thread: 1, time: 0.1988800004 ms
-Block size: 256, elements per thread: 2, time: 0.24773760570000003 ms
-Block size: 256, elements per thread: 4, time: 0.3005983978 ms
-Block size: 256, elements per thread: 8, time: 0.3462976009 ms
-Block size: 256, elements per thread: 16, time: 0.48608960519999994 ms
-Block size: 512, elements per thread: 1, time: 0.2411488013 ms
-Block size: 512, elements per thread: 2, time: 0.2356735976 ms
-Block size: 512, elements per thread: 4, time: 0.31453439899999996 ms
-Block size: 512, elements per thread: 8, time: 0.36263679849999997 ms
+Block size: 8, elements per thread: 1, time: 0.3583456037 ms
+Block size: 8, elements per thread: 2, time: 0.25230080190000004 ms
+Block size: 8, elements per thread: 4, time: 0.21565439989999996 ms
+Block size: 8, elements per thread: 8, time: 0.24966079579999997 ms
+Block size: 8, elements per thread: 16, time: 0.29572479430000004 ms
+Block size: 16, elements per thread: 1, time: 0.2169760003 ms
+Block size: 16, elements per thread: 2, time: 0.1610751987 ms
+Block size: 16, elements per thread: 4, time: 0.1980544014 ms
+Block size: 16, elements per thread: 8, time: 0.21126080009999998 ms
+Block size: 16, elements per thread: 16, time: 0.2852992027 ms
+Block size: 32, elements per thread: 1, time: 0.1461216008 ms
+Block size: 32, elements per thread: 2, time: 0.15881919949999998 ms
+Block size: 32, elements per thread: 4, time: 0.1823200002 ms
+Block size: 32, elements per thread: 8, time: 0.2195231989 ms
+Block size: 32, elements per thread: 16, time: 0.376639995 ms
+Block size: 64, elements per thread: 1, time: 0.15102400022 ms
+Block size: 64, elements per thread: 2, time: 0.13811200266 ms
+Block size: 64, elements per thread: 4, time: 0.1730176017 ms
+Block size: 64, elements per thread: 8, time: 0.217846398 ms
+Block size: 64, elements per thread: 16, time: 0.3569279999 ms
+Block size: 128, elements per thread: 1, time: 0.14728640024 ms
+Block size: 128, elements per thread: 2, time: 0.13456960240000002 ms
+Block size: 128, elements per thread: 4, time: 0.1838400023 ms
+Block size: 128, elements per thread: 8, time: 0.2354975983 ms
+Block size: 128, elements per thread: 16, time: 0.35950399940000005 ms
+Block size: 256, elements per thread: 1, time: 0.11884800039000001 ms
+Block size: 256, elements per thread: 2, time: 0.12683519940000001 ms
+Block size: 256, elements per thread: 4, time: 0.1796159998 ms
+Block size: 256, elements per thread: 8, time: 0.2481792004 ms
+Block size: 256, elements per thread: 16, time: 0.3609760016 ms
+Block size: 512, elements per thread: 1, time: 0.11134720002000001 ms
+Block size: 512, elements per thread: 2, time: 0.11812160169 ms
+Block size: 512, elements per thread: 4, time: 0.2151135998 ms
+Block size: 512, elements per thread: 8, time: 0.258998403 ms
 Block size: 512, elements per thread: 16 - crashed
-Block size: 1024, elements per thread: 1, time: 0.2502848000000001 ms
-Block size: 1024, elements per thread: 2, time: 0.25420480219999997 ms
-Block size: 1024, elements per thread: 4, time: 0.3396863997 ms
+Block size: 1024, elements per thread: 1, time: 0.11879039996999999 ms
+Block size: 1024, elements per thread: 2, time: 0.15765759950000002 ms
+Block size: 1024, elements per thread: 4, time: 0.22839040019999998 ms
 Block size: 1024, elements per thread: 8 - crashed
 Block size: 1024, elements per thread: 16 - crashed
-Optimal config: block size 256, elements per thread 1, time: 0.1988800004 ms
+Optimal config: block size 512, elements per thread 1, time: 0.11134720002000001 ms
 ```
diff --git a/img/efficient-plus-add-sums-ncu.png b/img/efficient-plus-add-sums-ncu.png
new file mode 100644
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diff --git a/img/performance.png b/img/performance.png
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literal 0
HcmV?d00001

diff --git a/scripts/measure_performance.py b/scripts/measure_performance.py
index 602f0d50..15320179 100644
--- a/scripts/measure_performance.py
+++ b/scripts/measure_performance.py
@@ -38,7 +38,7 @@ def find_existing_entry(
                     continue
 
                 time_sum = 0.0
-                time_count = 20
+                time_count = 10
                 for _ in range(time_count):
                     time_sum += measure_time("scan", implementation, input_size)
                 time = time_sum / time_count
diff --git a/scripts/performance.json b/scripts/performance.json
index bb266367..58da40b5 100644
--- a/scripts/performance.json
+++ b/scripts/performance.json
@@ -3,1440 +3,1440 @@
         "operation": "scan",
         "implementation": "cpu",
         "input_size": 16,
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+        "time": 0.00025000000105000004
     },
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         "operation": "scan",
         "implementation": "cpu",
         "input_size": 13,
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+        "time": 0.00013000000105000003
     },
     {
         "operation": "scan",
         "implementation": "cpu",
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+        "time": 0.00030000000560000004
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     {
         "operation": "scan",
         "implementation": "cpu",
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+        "time": 0.00024000000130000002
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         "implementation": "cpu",
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+        "time": 0.00014999999840000001
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         "implementation": "cpu",
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+        "time": 0.00030000000775000005
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         "operation": "scan",
         "implementation": "cpu",
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+        "time": 0.0003300000039
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         "implementation": "cpu",
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+        "time": 0.00029000000715
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+        "time": 0.0004299999958
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+        "implementation": "efficient_plus",
         "input_size": 16777213,
-        "time": 0.5767648011000001
+        "time": 0.1896639975
     },
     {
         "operation": "scan",
-        "implementation": "thrust",
+        "implementation": "efficient_plus",
         "input_size": 33554432,
-        "time": 0.7861919968500001
+        "time": 0.5722016038000001
     },
     {
         "operation": "scan",
-        "implementation": "thrust",
+        "implementation": "efficient_plus",
         "input_size": 33554429,
-        "time": 0.7637680054
+        "time": 0.5712223946
     },
     {
         "operation": "scan",
-        "implementation": "thrust",
+        "implementation": "efficient_plus",
         "input_size": 67108864,
-        "time": 1.2209151859999998
+        "time": 1.1539296169999997
     },
     {
         "operation": "scan",
-        "implementation": "thrust",
+        "implementation": "efficient_plus",
         "input_size": 67108861,
-        "time": 1.2257215975000002
+        "time": 1.154291202
     },
     {
         "operation": "scan",
-        "implementation": "thrust",
+        "implementation": "efficient_plus",
         "input_size": 134217728,
-        "time": 1.9061088024999997
+        "time": 2.316012813
     },
     {
         "operation": "scan",
-        "implementation": "thrust",
+        "implementation": "efficient_plus",
         "input_size": 134217725,
-        "time": 1.8970447955
+        "time": 2.3172320120000003
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 16,
-        "time": 0.25990239979999996
+        "time": 0.0278495999
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 13,
-        "time": 0.2816287994
+        "time": 0.031961599550000004
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 32,
-        "time": 0.2628847986499999
+        "time": 0.031990399940000004
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 29,
-        "time": 0.27383999914999996
+        "time": 0.04058240001
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 64,
-        "time": 0.25783039934999996
+        "time": 0.044662399990000004
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 61,
-        "time": 0.25985120084999996
+        "time": 0.027497600019999995
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 128,
-        "time": 0.2627199969999999
+        "time": 0.035180799670000006
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 125,
-        "time": 0.25792480265
+        "time": 0.03549760022
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 256,
-        "time": 0.26026559775
+        "time": 0.021094400069999998
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 253,
-        "time": 0.2638176002
+        "time": 0.047772799600000006
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 512,
-        "time": 0.26346879835000003
+        "time": 0.0302335998
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 509,
-        "time": 0.264231997
+        "time": 0.03101119957
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 1024,
-        "time": 0.28193119910000003
+        "time": 0.039052799709999995
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 1021,
-        "time": 0.28579680035
+        "time": 0.038742399610000006
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 2048,
-        "time": 0.28121440555
+        "time": 0.027734400139999997
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 2045,
-        "time": 0.27840639790000005
+        "time": 0.02224000002
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 4096,
-        "time": 0.27757759835
+        "time": 0.02301119956
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 4093,
-        "time": 0.26681919995000003
+        "time": 0.024169599829999992
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 8192,
-        "time": 0.27826560065000006
+        "time": 0.02102719992
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 8189,
-        "time": 0.27659839845
+        "time": 0.021628799839999997
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 16384,
-        "time": 0.27497759470000005
+        "time": 0.02471360044
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 16381,
-        "time": 0.29081280224999995
+        "time": 0.02351680009
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 32768,
-        "time": 0.28556479815
+        "time": 0.025039999949999996
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 32765,
-        "time": 0.30843520169999994
+        "time": 0.022559999680000005
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 65536,
-        "time": 0.34118079990000005
+        "time": 0.02583999989
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 65533,
-        "time": 0.34975359729999994
+        "time": 0.021139200219999998
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 131072,
-        "time": 0.3519711985999999
+        "time": 0.02293440011
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 131069,
-        "time": 0.3526464000499999
+        "time": 0.02241599989
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 262144,
-        "time": 0.34621759815
+        "time": 0.028640000340000006
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 262141,
-        "time": 0.35266239940000005
+        "time": 0.029644800180000003
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 524288,
-        "time": 0.33069600015
+        "time": 0.027737599989999993
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 524285,
-        "time": 0.34133920225000003
+        "time": 0.030038399440000002
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 1048576,
-        "time": 0.2523616
+        "time": 0.03103039991
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 1048573,
-        "time": 0.21884000154999997
+        "time": 0.03092800007
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 2097152,
-        "time": 0.24962719895000007
+        "time": 0.036678399890000005
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 2097149,
-        "time": 0.21965120135000005
+        "time": 0.03083839993
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 4194304,
-        "time": 0.26313920025000004
+        "time": 0.041769599909999997
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 4194301,
-        "time": 0.24904000080000005
+        "time": 0.043894399699999996
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 8388608,
-        "time": 0.28106239965
+        "time": 0.050057599689999996
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 8388605,
-        "time": 0.2867519988000001
+        "time": 0.050815999859999995
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 16777216,
-        "time": 0.30306400055000005
+        "time": 0.0800863996
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 16777213,
-        "time": 0.30300320085
+        "time": 0.09180160011999998
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 33554432,
-        "time": 0.6449887960499999
+        "time": 0.2736607999
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 33554429,
-        "time": 0.6306928039499999
+        "time": 0.27832959879999997
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 67108864,
-        "time": 1.2027919950000001
+        "time": 0.5728832066
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 67108861,
-        "time": 1.2180655965
+        "time": 0.5628224016
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 134217728,
-        "time": 2.3920944094999994
+        "time": 1.16590079
     },
     {
         "operation": "scan",
-        "implementation": "efficient_plus",
+        "implementation": "thrust",
         "input_size": 134217725,
-        "time": 2.396910416
+        "time": 1.150540817
     }
 ]
\ No newline at end of file
diff --git a/src/main.cpp b/src/main.cpp
index f4488f5c..c2df960b 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -8,9 +8,11 @@
 
 #include <cstdio>
 #include <stream_compaction/cpu.h>
+#include <stream_compaction/cpu_sort.h>
 #include <stream_compaction/naive.h>
 #include <stream_compaction/efficient.h>
 #include <stream_compaction/efficient_plus.h>
+#include <stream_compaction/radix_sort.h>
 #include <stream_compaction/thrust.h>
 #include "testing_helpers.hpp"
 
@@ -162,6 +164,43 @@ int main(int argc, char* argv[]) {
     //printArray(count, c, true);
     printCmpLenResult(count, expectedNPOT, b, c);
 
+    printf("\n");
+    printf("*******************\n");
+    printf("** SORTING TESTS **\n");
+    printf("*******************\n");
+
+    genArray(SIZE, a, SIZE);
+    a[SIZE - 1] = 0;
+    printArray(SIZE, a, true);
+
+    zeroArray(SIZE, b);
+    printDesc("cpu sort, power-of-two");
+    StreamCompaction::CPUSort::sort(SIZE, b, a);
+    printElapsedTime(StreamCompaction::CPUSort::timer().getCpuElapsedTimeForPreviousOperation(), "(std::chrono Measured)");
+    // printArray(SIZE, b, true);
+    // printCmpResult(SIZE, b, b);
+
+    zeroArray(SIZE, c);
+    printDesc("gpu radix sort, power-of-two");
+    StreamCompaction::RadixSort::sort(SIZE, c, a);
+    printElapsedTime(StreamCompaction::RadixSort::timer().getGpuElapsedTimeForPreviousOperation(), "(CUDA Measured)");
+    // printArray(SIZE, c, true);
+    printCmpResult(SIZE, b, c);
+
+    zeroArray(SIZE, b);
+    printDesc("cpu sort, non-power-of-two");
+    StreamCompaction::CPUSort::sort(NPOT, b, a);
+    printElapsedTime(StreamCompaction::CPUSort::timer().getCpuElapsedTimeForPreviousOperation(), "(std::chrono Measured)");
+    // printArray(NPOT, c, true);
+    // printCmpResult(NPOT, b, c);
+
+    zeroArray(SIZE, c);
+    printDesc("gpu radix sort, non-power-of-two");
+    StreamCompaction::RadixSort::sort(NPOT, c, a);
+    printElapsedTime(StreamCompaction::RadixSort::timer().getGpuElapsedTimeForPreviousOperation(), "(CUDA Measured)");
+    // printArray(NPOT, c, true);
+    printCmpResult(NPOT, b, c);
+
     system("pause"); // stop Win32 console from closing on exit
     delete[] a;
     delete[] b;
diff --git a/src/measure_time.cpp b/src/measure_time.cpp
index eec023d7..a2ab5e68 100644
--- a/src/measure_time.cpp
+++ b/src/measure_time.cpp
@@ -1,8 +1,10 @@
+#include <chrono>
 #include <iomanip>
 #include <iostream>
 #include <limits>
 #include <random>
 #include <string>
+#include <thread>
 #include <vector>
 
 #include <stream_compaction/cpu.h>
@@ -62,78 +64,43 @@ int main(int argc, char *argv[]) {
         return -1;
     }
 
+    // Some implementations (e.g., Thrust) allocates memory internally on the first run, so we run
+    // the operation twice and only measure the later one.
+#define REPEAT_TWICE(function, ...)                                                                \
+    do {                                                                                           \
+        function(inputSize, outputs.data(), inputs.data(), __VA_ARGS__);                           \
+        std::this_thread::sleep_for(std::chrono::milliseconds(10));                                \
+        function(inputSize, outputs.data(), inputs.data(), __VA_ARGS__);                           \
+    } while (false)
+
     if (operation == "scan") {
         if (implementation == "cpu") {
-            if (blockSize >= 0 || elementsPerThread >= 0) {
-                return -1;
-            }
-            StreamCompaction::CPU::scan(inputSize, outputs.data(), inputs.data());
+            REPEAT_TWICE(StreamCompaction::CPU::scan);
         } else if (implementation == "naive") {
-            if (elementsPerThread >= 0) {
-                return -1;
-            }
-            if (blockSize >= 0) {
-                StreamCompaction::Naive::scan(inputSize, outputs.data(), inputs.data(), blockSize);
-            } else {
-                StreamCompaction::Naive::scan(inputSize, outputs.data(), inputs.data());
-            }
+            REPEAT_TWICE(StreamCompaction::Naive::scan, blockSize);
         } else if (implementation == "efficient") {
-            if (elementsPerThread >= 0) {
-                return -1;
-            }
-            if (blockSize >= 0) {
-                StreamCompaction::Efficient::scan(inputSize, outputs.data(), inputs.data(),
-                                                  blockSize);
-            } else {
-                StreamCompaction::Efficient::scan(inputSize, outputs.data(), inputs.data());
-            }
+            REPEAT_TWICE(StreamCompaction::Efficient::scan, blockSize);
         } else if (implementation == "efficient_plus") {
-            if (blockSize >= 0) {
-                if (elementsPerThread >= 0) {
-                    StreamCompaction::EfficientPlus::scan(inputSize, outputs.data(), inputs.data(),
-                                                          blockSize, elementsPerThread);
-                } else {
-                    StreamCompaction::EfficientPlus::scan(inputSize, outputs.data(), inputs.data(),
-                                                          blockSize);
-                }
-            } else {
-                if (elementsPerThread >= 0) {
-                    return -1;
-                } else {
-                    StreamCompaction::EfficientPlus::scan(inputSize, outputs.data(), inputs.data());
-                }
-            }
+            REPEAT_TWICE(StreamCompaction::EfficientPlus::scan, blockSize, elementsPerThread);
         } else if (implementation == "thrust") {
-            if (blockSize >= 0 || elementsPerThread >= 0) {
-                return -1;
-            }
-            StreamCompaction::Thrust::scan(inputSize, outputs.data(), inputs.data());
+            REPEAT_TWICE(StreamCompaction::Thrust::scan);
         } else {
             return -1;
         }
     } else if (operation == "compact") {
-        if (implementation == "efficient") {
-            if (elementsPerThread >= 0) {
-                return -1;
-            }
-            if (blockSize >= 0) {
-                StreamCompaction::Efficient::compact(inputSize, outputs.data(), inputs.data(),
-                                                     blockSize);
-            } else {
-                StreamCompaction::Efficient::compact(inputSize, outputs.data(), inputs.data());
-            }
-        } else {
-            return -1;
-        }
+        REPEAT_TWICE(StreamCompaction::Efficient::compact, blockSize);
     } else {
         return -1;
     }
 
+#undef REPEAT_TWICE
+
     std::cout << std::setprecision(std::numeric_limits<float>::max_digits10);
     if (isGpu) {
-        std::cout << timer->getGpuElapsedTimeForPreviousOperation() << std::endl;
+        std::cout << timer->getGpuElapsedTimeForPreviousOperation();
     } else {
-        std::cout << timer->getCpuElapsedTimeForPreviousOperation() << std::endl;
+        std::cout << timer->getCpuElapsedTimeForPreviousOperation();
     }
+    std::cout << std::endl;
     return 0;
 }
diff --git a/stream_compaction/CMakeLists.txt b/stream_compaction/CMakeLists.txt
index a79d894a..16f92922 100644
--- a/stream_compaction/CMakeLists.txt
+++ b/stream_compaction/CMakeLists.txt
@@ -1,18 +1,22 @@
 set(headers
     "common.h"
     "cpu.h"
+    "cpu_sort.h"
     "naive.h"
     "efficient.h"
     "efficient_plus.h"
+    "radix_sort.h"
     "thrust.h"
     )
 
 set(sources
     "common.cu"
     "cpu.cu"
+    "cpu_sort.cu"
     "naive.cu"
     "efficient.cu"
     "efficient_plus.cu"
+    "radix_sort.cu"
     "thrust.cu"
     )
 
diff --git a/stream_compaction/cpu_sort.cu b/stream_compaction/cpu_sort.cu
new file mode 100644
index 00000000..62ec08d4
--- /dev/null
+++ b/stream_compaction/cpu_sort.cu
@@ -0,0 +1,24 @@
+#include <algorithm>
+
+#include <cuda.h>
+#include <cuda_runtime.h>
+
+#include "common.h"
+#include "cpu_sort.h"
+
+namespace StreamCompaction {
+    namespace CPUSort {
+        using StreamCompaction::Common::PerformanceTimer;
+        PerformanceTimer &timer() {
+            static PerformanceTimer timer;
+            return timer;
+        }
+
+        void sort(int n, int *odata, const int *idata) {
+            timer().startCpuTimer();
+            std::copy_n(idata, n, odata);
+            std::sort(odata, odata + n);
+            timer().endCpuTimer();
+        }
+    }
+}
diff --git a/stream_compaction/cpu_sort.h b/stream_compaction/cpu_sort.h
new file mode 100644
index 00000000..8879864a
--- /dev/null
+++ b/stream_compaction/cpu_sort.h
@@ -0,0 +1,11 @@
+#pragma once
+
+#include "common.h"
+
+namespace StreamCompaction {
+    namespace CPUSort {
+        StreamCompaction::Common::PerformanceTimer &timer();
+
+        void sort(int n, int *odata, const int *idata);
+    }
+}
diff --git a/stream_compaction/efficient.cu b/stream_compaction/efficient.cu
index 0ffc2587..2d425f8f 100644
--- a/stream_compaction/efficient.cu
+++ b/stream_compaction/efficient.cu
@@ -66,7 +66,12 @@ namespace StreamCompaction {
         /**
          * Performs prefix-sum (aka scan) on idata, storing the result into odata.
          */
-        void scan(int n, int *odata, const int *idata, const int blockSize) {
+        void scan(int n, int *odata, const int *idata, int blockSize) {
+            // Set default parameters.
+            if (blockSize <= 0) {
+                blockSize = 64;
+            }
+
             const auto dataSize = n * sizeof(int);
             const int ceiledN = 1 << ilog2ceil(n);
             const auto ceiledDataSize = ceiledN * sizeof(int);
@@ -96,7 +101,12 @@ namespace StreamCompaction {
          * @param idata  The array of elements to compact.
          * @returns      The number of elements remaining after compaction.
          */
-        int compact(int n, int *odata, const int *idata, const int blockSize) {
+        int compact(int n, int *odata, const int *idata, int blockSize) {
+            // Set default parameters.
+            if (blockSize <= 0) {
+                blockSize = 64;
+            }
+
             const auto dataSize = n * sizeof(int);
             const int ceiledN = 1 << ilog2ceil(n);
             const auto ceiledDataSize = ceiledN * sizeof(int);
diff --git a/stream_compaction/efficient.h b/stream_compaction/efficient.h
index 8097e408..eea99ff2 100644
--- a/stream_compaction/efficient.h
+++ b/stream_compaction/efficient.h
@@ -6,8 +6,14 @@ namespace StreamCompaction {
     namespace Efficient {
         StreamCompaction::Common::PerformanceTimer &timer();
 
-        void scan(int n, int *odata, const int *idata, const int blockSize = 64);
+        void scan(int n, int *odata, const int *idata, int blockSize);
 
-        int compact(int n, int *odata, const int *idata, const int blockSize = 64);
+        inline void scan(int n, int *odata, const int *idata) { scan(n, odata, idata, -1); }
+
+        int compact(int n, int *odata, const int *idata, int blockSize);
+
+        inline int compact(int n, int *odata, const int *idata) {
+            return compact(n, odata, idata, -1);
+        }
     }
 }
diff --git a/stream_compaction/efficient_plus.cu b/stream_compaction/efficient_plus.cu
index 8eb88e62..dd0322e6 100644
--- a/stream_compaction/efficient_plus.cu
+++ b/stream_compaction/efficient_plus.cu
@@ -96,41 +96,34 @@ namespace StreamCompaction {
             }
         }
 
-        __global__ void addSums(unsigned n, int *__restrict__ data, const int *__restrict__ sums,
-                                unsigned elementsPerThread) {
-            unsigned startIndex = (blockIdx.x * blockDim.x + threadIdx.x) * elementsPerThread * 2U;
-            unsigned endIndex = min(startIndex + elementsPerThread * 2U, n);
+        template <unsigned ElementsPerThread>
+        __global__ void addSums(unsigned n, int *__restrict__ data, const int *__restrict__ sums) {
+            unsigned startIndex = (blockIdx.x * blockDim.x + threadIdx.x) * ElementsPerThread * 2U;
+            unsigned endIndex = min(startIndex + ElementsPerThread * 2U, n);
             int sum = sums[blockIdx.x];
             for (unsigned index = startIndex; index < endIndex; ++index) {
                 data[index] += sum;
             }
         }
 
-        void scanImpl(unsigned n, int *data, unsigned blockSize, unsigned elementsPerThread,
-                      unsigned tileSize, unsigned sharedMemorySize, unsigned gridSize, int *sums) {
-#define DISPATCH(N) scanPerBlock<N><<<gridSize, blockSize, sharedMemorySize>>>(n, data, sums);
-            switch (elementsPerThread) {
-            case 1U:
-                DISPATCH(1U);
-                break;
-            case 2U:
-                DISPATCH(2U);
-                break;
-            case 4U:
-                DISPATCH(4U);
-                break;
-            case 8U:
-                DISPATCH(8U);
-                break;
-            case 16U:
-                DISPATCH(16U);
-                break;
-            default:
-                printf("Error: elementsPerThread %u is not supported!\n", elementsPerThread);
-                exit(1);
+        template <unsigned ElementsPerThread>
+        void scanImpl(unsigned n, int *data, unsigned blockSize, unsigned tileSize,
+                      unsigned gridSize, int *sums) {
+            unsigned actualBlockSize = blockSize;
+            if (gridSize == 1U) {
+                while (true) {
+                    unsigned nextBlockSize = actualBlockSize / 2U;
+                    if (nextBlockSize * ElementsPerThread * 2U < n) {
+                        break;
+                    }
+                    actualBlockSize = nextBlockSize;
+                }
             }
-#undef DISPATCH
-
+            unsigned sharedMemorySize =
+                (conflictFreeIndex(actualBlockSize * ElementsPerThread * 2U - 1U) + 1U) *
+                sizeof(int);
+            scanPerBlock<ElementsPerThread>
+                <<<gridSize, actualBlockSize, sharedMemorySize>>>(n, data, sums);
             checkCUDAErrorFn("scanPerBlock kernel failed!");
             if (gridSize > 1U) {
                 unsigned nextGridSize = (gridSize + tileSize - 1U) / tileSize;
@@ -138,15 +131,22 @@ namespace StreamCompaction {
                 if (nextGridSize > 1U) {
                     nextSums = sums + gridSize;
                 }
-                scanImpl(gridSize, sums, blockSize, elementsPerThread, tileSize, sharedMemorySize,
-                         nextGridSize, nextSums);
-                addSums<<<gridSize, blockSize>>>(n, data, sums, elementsPerThread);
+                scanImpl<ElementsPerThread>(gridSize, sums, blockSize, tileSize, nextGridSize,
+                                            nextSums);
+                addSums<ElementsPerThread><<<gridSize, blockSize>>>(n, data, sums);
                 checkCUDAErrorFn("addSums kernel failed!");
             }
         }
 
-        void scan(int n, int *odata, const int *idata, const int blockSize,
-                  const int elementsPerThread) {
+        void scan(int n, int *odata, const int *idata, int blockSize, int elementsPerThread) {
+            // Set default parameters.
+            if (blockSize <= 0) {
+                blockSize = 256;
+            }
+            if (elementsPerThread <= 0) {
+                elementsPerThread = 1;
+            }
+
             const auto dataSize = n * sizeof(int);
 
             int *dev_data;
@@ -157,7 +157,6 @@ namespace StreamCompaction {
 
             // Allocate GPU memory for sums beforehand.
             unsigned tileSize = blockSize * elementsPerThread * 2U;
-            unsigned sharedMemorySize = (conflictFreeIndex(tileSize - 1U) + 1U) * sizeof(int);
             unsigned gridSize = (n + tileSize - 1U) / tileSize;
 
             unsigned totalSumCount = 0U;
@@ -176,13 +175,29 @@ namespace StreamCompaction {
                 cudaMalloc((void **)&dev_sums, totalSumCount * sizeof(int));
                 checkCUDAErrorFn("cudaMalloc dev_sums failed!");
             }
-
             cudaDeviceSynchronize();
+
+#define DISPATCH(N)                                                                                \
+    case N:                                                                                        \
+        scanImpl<N>(n, dev_data, blockSize, tileSize, gridSize, dev_sums);                         \
+        break
+
             timer().startGpuTimer();
-            scanImpl(n, dev_data, blockSize, elementsPerThread, tileSize, sharedMemorySize,
-                     gridSize, dev_sums);
+
+            switch (elementsPerThread) {
+                DISPATCH(1);
+                DISPATCH(2);
+                DISPATCH(4);
+                DISPATCH(8);
+                DISPATCH(16);
+            default:
+                printf("Unsupported elementsPerThread: %d\n", elementsPerThread);
+                exit(1);
+            }
             timer().endGpuTimer();
 
+#undef DISPATCH
+
             cudaMemcpy(odata, dev_data, dataSize, cudaMemcpyDeviceToHost);
             checkCUDAErrorFn("cudaMemcpy to host failed!");
             cudaFree(dev_data);
@@ -192,5 +207,37 @@ namespace StreamCompaction {
                 checkCUDAErrorFn("cudaFree failed!");
             }
         }
+
+        void scanDeviceInPlace(int n, int *data) {
+            const unsigned blockSize = 256;
+            constexpr unsigned ElementsPerThread = 1;
+
+            unsigned tileSize = blockSize * ElementsPerThread * 2U;
+            unsigned gridSize = (n + tileSize - 1U) / tileSize;
+
+            unsigned totalSumCount = 0U;
+            {
+                unsigned gridSize = n;
+                while (true) {
+                    gridSize = (gridSize + tileSize - 1U) / tileSize;
+                    if (gridSize <= 1U) {
+                        break;
+                    }
+                    totalSumCount += gridSize;
+                }
+            }
+            int *dev_sums = nullptr;
+            if (totalSumCount > 0U) {
+                cudaMalloc((void **)&dev_sums, totalSumCount * sizeof(int));
+                checkCUDAErrorFn("cudaMalloc dev_sums failed!");
+            }
+
+            scanImpl<ElementsPerThread>(n, data, blockSize, tileSize, gridSize, dev_sums);
+
+            if (dev_sums != nullptr) {
+                cudaFree(dev_sums);
+                checkCUDAErrorFn("cudaFree failed!");
+            }
+        }
     }
 }
diff --git a/stream_compaction/efficient_plus.h b/stream_compaction/efficient_plus.h
index 552fc645..8d1486d8 100644
--- a/stream_compaction/efficient_plus.h
+++ b/stream_compaction/efficient_plus.h
@@ -6,7 +6,10 @@ namespace StreamCompaction {
     namespace EfficientPlus {
         StreamCompaction::Common::PerformanceTimer &timer();
 
-        void scan(int n, int *odata, const int *idata, const int blockSize = 256,
-                  const int elementsPerThread = 1);
+        void scan(int n, int *odata, const int *idata, int blockSize, int elementsPerThread);
+
+        inline void scan(int n, int *odata, const int *idata) { scan(n, odata, idata, -1, -1); }
+
+        void scanDeviceInPlace(int n, int *data);
     }
 }
diff --git a/stream_compaction/naive.cu b/stream_compaction/naive.cu
index 8b518ed1..dd6c17f6 100644
--- a/stream_compaction/naive.cu
+++ b/stream_compaction/naive.cu
@@ -32,7 +32,12 @@ namespace StreamCompaction {
         /**
          * Performs prefix-sum (aka scan) on idata, storing the result into odata.
          */
-        void scan(int n, int *odata, const int *idata, const int blockSize) {
+        void scan(int n, int *odata, const int *idata, int blockSize) {
+            // Set default parameters.
+            if (blockSize <= 0) {
+                blockSize = 256;
+            }
+
             const auto dataSize = n * sizeof(int);
 
             int *dev_iData;
diff --git a/stream_compaction/naive.h b/stream_compaction/naive.h
index 23042bcb..960103ae 100644
--- a/stream_compaction/naive.h
+++ b/stream_compaction/naive.h
@@ -6,6 +6,8 @@ namespace StreamCompaction {
     namespace Naive {
         StreamCompaction::Common::PerformanceTimer &timer();
 
-        void scan(int n, int *odata, const int *idata, const int blockSize = 256);
+        void scan(int n, int *odata, const int *idata, int blockSize);
+
+        inline void scan(int n, int *odata, const int *idata) { scan(n, odata, idata, -1); }
     }
 }
diff --git a/stream_compaction/radix_sort.cu b/stream_compaction/radix_sort.cu
new file mode 100644
index 00000000..9894372b
--- /dev/null
+++ b/stream_compaction/radix_sort.cu
@@ -0,0 +1,77 @@
+#include <cuda.h>
+#include <cuda_runtime.h>
+
+#include "common.h"
+#include "efficient_plus.h"
+#include "radix_sort.h"
+
+namespace StreamCompaction {
+    namespace RadixSort {
+        using StreamCompaction::Common::PerformanceTimer;
+        PerformanceTimer &timer() {
+            static PerformanceTimer timer;
+            return timer;
+        }
+
+        __global__ void kernExtractBit(int n, int mask, int *odata, const int *idata) {
+            int index = blockIdx.x * blockDim.x + threadIdx.x;
+            if (index >= n) {
+                return;
+            }
+            odata[index] = (idata[index] & mask) == 0 ? 0 : 1;
+        }
+
+        __global__ void kernScatter(int n, unsigned mask, int zeroCount, const int *positions,
+                                    const int *idata, int *odata) {
+            int index = blockIdx.x * blockDim.x + threadIdx.x;
+            if (index >= n) {
+                return;
+            }
+            bool isOne = (static_cast<unsigned>(idata[index]) & mask) != 0;
+            if (isOne) {
+                odata[zeroCount + positions[index]] = idata[index];
+            } else {
+                int zeros_before = index - positions[index];
+                odata[zeros_before] = idata[index];
+            }
+        }
+
+        void sort(int n, int *odata, const int *idata) {
+            const auto dataSize = n * sizeof(int);
+
+            int *dev_iData;
+            cudaMalloc((void **)&dev_iData, dataSize);
+            cudaMemcpy(dev_iData, idata, dataSize, cudaMemcpyHostToDevice);
+
+            int *dev_oData;
+            cudaMalloc((void **)&dev_oData, dataSize);
+
+            int *dev_positions;
+            cudaMalloc((void **)&dev_positions, dataSize);
+
+            timer().startGpuTimer();
+            const int blockSize = 256;
+            const int gridSize = (n + blockSize - 1) / blockSize;
+            for (int bit = 0; bit < 32; ++bit) {
+                const unsigned mask = 1u << bit;
+                kernExtractBit<<<gridSize, blockSize>>>(n, mask, dev_positions, dev_iData);
+                int lastBit;
+                cudaMemcpy(&lastBit, &dev_positions[n - 1], sizeof(int), cudaMemcpyDeviceToHost);
+                EfficientPlus::scanDeviceInPlace(n, dev_positions);
+                int oneCount;
+                cudaMemcpy(&oneCount, &dev_positions[n - 1], sizeof(int), cudaMemcpyDeviceToHost);
+                oneCount += lastBit;
+                int zeroCount = n - oneCount;
+                kernScatter<<<gridSize, blockSize>>>(n, mask, zeroCount, dev_positions, dev_iData,
+                                                     dev_oData);
+                std::swap(dev_iData, dev_oData);
+            }
+            timer().endGpuTimer();
+
+            cudaMemcpy(odata, dev_oData, dataSize, cudaMemcpyDeviceToHost);
+            cudaFree(dev_iData);
+            cudaFree(dev_oData);
+            cudaFree(dev_positions);
+        }
+    }
+}
diff --git a/stream_compaction/radix_sort.h b/stream_compaction/radix_sort.h
new file mode 100644
index 00000000..82c1d731
--- /dev/null
+++ b/stream_compaction/radix_sort.h
@@ -0,0 +1,11 @@
+#pragma once
+
+#include "common.h"
+
+namespace StreamCompaction {
+    namespace RadixSort {
+        StreamCompaction::Common::PerformanceTimer &timer();
+
+        void sort(int n, int *odata, const int *idata);
+    }
+}
diff --git a/stream_compaction/thrust.cu b/stream_compaction/thrust.cu
index bcc61332..b66f1c31 100644
--- a/stream_compaction/thrust.cu
+++ b/stream_compaction/thrust.cu
@@ -2,7 +2,11 @@
 #include <cuda_runtime.h>
 #include <thrust/device_vector.h>
 #include <thrust/host_vector.h>
+#include <thrust/mr/allocator.h>
+#include <thrust/mr/disjoint_pool.h>
 #include <thrust/scan.h>
+#include <thrust/system/cuda/execution_policy.h>
+#include <thrust/system/cuda/memory_resource.h>
 
 #include "common.h"
 #include "thrust.h"
@@ -14,20 +18,27 @@ namespace StreamCompaction {
             static PerformanceTimer timer;
             return timer;
         }
+
         /**
          * Performs prefix-sum (aka scan) on idata, storing the result into odata.
          */
         void scan(int n, int *odata, const int *idata) {
-            thrust::host_vector<int> host_in(idata, idata + n);
-            thrust::device_vector<int> dev_in = host_in;
-            thrust::device_vector<int> dev_out(n);
+            // Use a memory pool to reduce memory allocation overhead of Thrust operations.
+            static thrust::cuda::memory_resource upstream;
+            static thrust::mr::new_delete_resource bookkeeper;
+            static thrust::mr::disjoint_unsynchronized_pool_resource pool(&upstream, &bookkeeper);
+            thrust::mr::allocator<char, decltype(pool)> allocator(&pool);
+            const auto policy = thrust::cuda::par(allocator);
+
+            thrust::device_vector<int> dev_data(n);
+            thrust::copy_n(idata, n, dev_data.begin());
             cudaDeviceSynchronize();
 
             timer().startGpuTimer();
-            thrust::exclusive_scan(dev_in.begin(), dev_in.end(), dev_out.begin());
+            thrust::exclusive_scan(policy, dev_data.begin(), dev_data.end(), dev_data.begin());
             timer().endGpuTimer();
 
-            thrust::copy(dev_out.begin(), dev_out.end(), odata);
+            thrust::copy(dev_data.begin(), dev_data.end(), odata);
         }
     }
 }