From f6288bf15a50fea6ef806e7326e963306bb8ccbb Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 5 Jun 2025 10:57:28 -0400 Subject: [PATCH 01/20] Outline of signed benchmarks --- doc/int128.adoc | 2 + doc/int128/i128_benchmarks.adoc | 244 ++++++++++++++++++++++++++++++++ doc/signed_plots.py | 224 +++++++++++++++++++++++++++++ doc/signed_plots_32bit.py | 153 ++++++++++++++++++++ 4 files changed, 623 insertions(+) create mode 100644 doc/int128/i128_benchmarks.adoc create mode 100644 doc/signed_plots.py create mode 100644 doc/signed_plots_32bit.py diff --git a/doc/int128.adoc b/doc/int128.adoc index 6fb83c3b..98231e60 100644 --- a/doc/int128.adoc +++ b/doc/int128.adoc @@ -39,6 +39,8 @@ include::int128/saturating.adoc[] include::int128/u128_benchmarks.adoc[] +include::int128/i128_benchmarks.adoc[] + include::int128/reference.adoc[] include::int128/copyright.adoc[] diff --git a/doc/int128/i128_benchmarks.adoc b/doc/int128/i128_benchmarks.adoc new file mode 100644 index 00000000..e986c8ef --- /dev/null +++ b/doc/int128/i128_benchmarks.adoc @@ -0,0 +1,244 @@ +//// +Copyright 2025 Matt Borland +Distributed under the Boost Software License, Version 1.0. +https://www.boost.org/LICENSE_1_0.txt +//// + +[#i128_benchmarks] += `int128_t` Benchmarks +:idprefix: i128_benchmarks_ + +== Methodology + +The benchmarks below represent the time in microseconds it takes to perform 20'000'000 operations between two values of random width (e.g. 2x1 words, 1x2 words, etc.). +On most platforms we use the builtin `\__int128` as the reference benchmark. +When this is unavailable (such as on 32-bit architectures) we us `boost::multiprecision::int128_t` (abbreviated as `boost::mp::int128_t`) as it is widely used, and known to be portable. +On MSVC platforms we use as reference `std::_Signed128` from the header `<__msvc_int128.hpp>` since this is bundled with their compiler. + +== Linux + +=== x86_64 + +[cols="1,1,1,1"] +|=== +| Operation | `std::_Signed128` | `int128_t` | `boost::mp::int128_t` + +| Comparisons | 2068491 | 2416378 | 3191439 +| Addition | 383258 | 180522 | 545521 +| Subtraction | 208155 | 192633 | 420573 +| Multiplication | 291075 | 241174 | 675361 +| Division | 3953939 | 4246753 | 4976285 +| Modulo | 4042166 | 3953441 | 4478923 +|=== + +//// +image::u128_graphs/linux/x64_benchmarks.png[x64 Benchmark Results, width=100%] +//// + +image::u128_graphs/linux/x64_relative_performance.png[x64 Relative Performance, width=100%] + +=== ARM64 + +[cols="1,1,1,1"] +|=== +| Operation | `std::_Signed128` | `int128_t` | `boost::mp::int128_t` + +| Comparisons | 2068491 | 2416378 | 3191439 +| Addition | 383258 | 180522 | 545521 +| Subtraction | 208155 | 192633 | 420573 +| Multiplication | 291075 | 241174 | 675361 +| Division | 3953939 | 4246753 | 4976285 +| Modulo | 4042166 | 3953441 | 4478923 +|=== + +//// +image::u128_graphs/linux/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] +//// + +image::u128_graphs/linux/ARM64_relative_performance.png[x64 Relative Performance, width=100%] + +=== S390x + +[cols="1,1,1,1"] +|=== +| Operation | `std::_Signed128` | `int128_t` | `boost::mp::int128_t` + +| Comparisons | 14415854 | 12658246 | 16561079 +| Addition | 1232397 | 1423451 | 2909066 +| Subtraction | 1239808 | 775766 | 2744664 +| Multiplication | 1928533 | 2600663 | 2384775 +| Division | 8102813 | 5759377 | 7828137 +| Modulo | 9072599 | 6648180 | 9172574 +|=== + +//// +image::u128_graphs/linux/s390x_benchmarks.png[s390x Benchmark Results, width=100%] +//// + +image::u128_graphs/linux/s390x_relative_performance.png[s390x Relative Performance, width=100%] + +=== PPC64LE + +[cols="1,1,1,1"] +|=== +| Operation | `std::_Signed128` | `int128_t` | `boost::mp::int128_t` + +| Comparisons | 5242604 | 4450958 | 5704848 +| Addition | 221776 | 193063 | 847504 +| Subtraction | 222894 | 175259 | 786659 +| Multiplication | 194494 | 192929 | 795187 +| Division | 4821119 | 4896360 | 5344637 +| Modulo | 4955570 | 4273487 | 5407877 +|=== + +//// +image::u128_graphs/linux/ppc64le_benchmarks.png[ppc64le Benchmark Results, width=100%] +//// + +image::u128_graphs/linux/ppc64le_relative_performance.png[ppc64le Relative Performance, width=100%] + + +=== x86_32 + +NOTE: This platform has no hardware type so we compare relative to `boost::mp::int128_t` + +[cols="1,1,1"] +|=== +| Operation | `int128_t` | `boost::mp::int128_t` + +| Comparisons | 9000979 | 8722814 +| Addition | 898718 | 9912175 +| Subtraction | 778881 | 9773677 +| Multiplication | 1778273 | 8678420 +| Division | 8496503 | 18133965 +| Modulo | 9081442 | 11257837 +|=== + +//// +image::u128_graphs/linux/x86_benchmarks.png[x86 Benchmark Results, width=100%] +//// + +image::u128_graphs/linux/x86_relative_performance.png[x86 Relative Performance, width=100%] + +=== ARM32 + +NOTE: This platform has no hardware type so we compare relative to `boost::mp::int128_t` + +[cols="1,1,1"] +|=== +| Operation | `int128_t` | `boost::mp::int128_t` + +| Comparisons | 5286033 | 4538707 +| Addition | 454715 | 5543856 +| Subtraction | 487190 | 6465126 +| Multiplication | 1471479 | 8246098 +| Division | 19868087 | 32820805 +| Modulo | 20332627 | 27238658 +|=== + +//// +image::u128_graphs/linux/ARM32_benchmarks.png[ARM32 Benchmark Results, width=100%] +//// + +image::u128_graphs/linux/ARM32_relative_performance.png[ARM32 Relative Performance, width=100%] + +== Windows + +=== ARM64 + +[cols="1,1,1,1"] +|=== +| Operation | `std::_Signed128` | `int128_t` | `boost::mp::int128_t` + +| Comparisons | 3424403 | 2062167 | 5026689 +| Addition | 123659 | 133084 | 587373 +| Subtraction | 171721 | 99453 | 330052 +| Multiplication | 329287 | 283443 | 972009 +| Division | 2044821 | 1825020 | 2190856 +| Modulo | 2176318 | 1897933 | 2227961 +|=== +//// +image::u128_graphs/windows/arm64_benchmarks.png[ARM64 Benchmark Results, width=100%] +//// + +image::u128_graphs/windows/arm64_relative_performance.png[ARM64 Relative Performance, width=100%] + +=== x86_32 + +[cols="1,1,1,1"] +|=== +| Operation | `std::_Signed128` | `int128_t` | `boost::mp::int128_t` + +| Comparisons | 4215438 | 3883846 | 2852442 +| Addition | 199945 | 208436 | 3242910 +| Subtraction | 1206168 | 210874 | 3851129 +| Multiplication | 2282869 | 2680359 | 5378001 +| Division | 5516964 | 4328917 | 6948267 +| Modulo | 4551146 | 4330152 | 6294325 +|=== +//// +image::u128_graphs/windows/x86_benchmarks.png[x86_32 Benchmark Results, width=100%] +//// + +image::u128_graphs/windows/x86_relative_performance.png[x86_32 Relative Performance, width=100%] + +=== x86_64 + +[cols="1,1,1,1"] +|=== +| Operation | `std::_Signed128` | `int128_t` | `boost::mp::int128_t` + +| Comparisons | 2060556 | 1921174 | 3009890 +| Addition | 261475 | 106545 | 2710279 +| Subtraction | 178724 | 124181 | 3059187 +| Multiplication | 146063 | 136115 | 3495634 +| Division | 1332838 | 1360295 | 4852899 +| Modulo | 1465138 | 1471169 | 3926336 +|=== +//// +image::u128_graphs/windows/x64_benchmarks.png[x64 Benchmark Results, width=100%] +//// + +image::u128_graphs/windows/x64_relative_performance.png[x64 Relative Performance, width=100%] + +== macOS + +=== ARM64 (Apple Silicon) + +[cols="1,1,1,1"] +|=== +| Operation | `unsigned __in128` | `int128_t` | `boost::mp::int128_t` + +| Comparisons | 131902 | 133564 | 134182 +| Addition | 20613 | 17912 | 40176 +| Subtraction | 20484 | 18237 | 40311 +| Multiplication | 20160 | 20580 | 43285 +| Division | 686521 | 699201 | 945928 +| Modulo | 777084 | 724648 | 953117 +|=== + +//// +image::u128_graphs/macos/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] +//// + +image::u128_graphs/macos/ARM64_relative_performance.png[ARM64 Relative Performance, width=100%] + +=== x86_64 + +[cols="1,1,1,1"] +|=== +| Operation | `unsigned __in128` | `int128_t` | `boost::mp::int128_t` + +| Comparisons | 131902 | 133564 | 134182 +| Addition | 20613 | 17912 | 40176 +| Subtraction | 20484 | 18237 | 40311 +| Multiplication | 20160 | 20580 | 43285 +| Division | 686521 | 699201 | 945928 +| Modulo | 777084 | 724648 | 953117 +|=== + +//// +image::u128_graphs/macos/x64_benchmarks.png[x64 Benchmark Results, width=100%] +//// + +image::u128_graphs/macos/x64_relative_performance.png[x64 Relative Performance, width=100%] diff --git a/doc/signed_plots.py b/doc/signed_plots.py new file mode 100644 index 00000000..91206ddf --- /dev/null +++ b/doc/signed_plots.py @@ -0,0 +1,224 @@ +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd + +""" +# ARM64 MSVC +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + 'std::_Unsigned128': [878929, 32788, 33627, 68120, 925583, 1104772], + 'uint128_t': [259725, 33723, 36799, 35334, 1020148, 1143344], + 'boost::mp::uint128_t': [1246502, 1437452, 1648131, 1459418, 2216648, 2089105] +} +""" + +""" +# x86 MSVC +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + 'std::_Unsigned128': [4215438, 199945, 1206168, 2282869, 5516964, 4551146], + 'uint128_t': [3883846, 208436, 210874, 2680359, 4328917, 4330152], + 'boost::mp::uint128_t': [2852442, 3242910, 3851129, 5378001, 6948267, 6294325] +} +""" + +""" +# x64 MSVC +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + 'std::_Unsigned128': [2060556, 261475, 178724, 146063, 1332838, 1465138], + 'uint128_t': [1921174, 106545, 124181, 136115, 1360295, 1471169], + 'boost::mp::uint128_t': [3009890, 2710279, 3059187, 3495634, 4852899, 3926336] +} +""" + +""" +# ARM64 macOS +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + 'unsigned __int128': [131902, 20613, 20484, 20160, 686521, 777084], + 'uint128_t': [133564, 17912, 18237, 20580, 699201, 724648], + 'boost::mp::uint128_t': [134182, 40176, 40311, 43285, 945928, 953117] +} +""" + +""" +# x64 macOS +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + 'unsigned __int128': [688225, 104921, 129150, 120363, 2333812, 2621949], + 'uint128_t': [712352, 124992, 102302, 119652, 1981469, 2219481], + 'boost::mp::uint128_t': [689146, 137819, 153484, 164100, 2784139, 2736682] +} +""" +""" +# Linux x64 +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + 'unsigned __int128': [2068491, 383258, 208155, 291075, 3953939, 4042166], + 'uint128_t': [2416378, 180522, 192633, 241174, 4246753, 3953441], + 'boost::mp::uint128_t': [3191439, 545521, 420573, 675361, 4976285, 4478923] +} +""" +""" +# Linux ARM64 +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + 'unsigned __int128': [3424403, 123659, 171721, 329287, 2044821, 2176318], + 'uint128_t': [2062167, 133084, 99453, 283443, 1825020, 1897933], + 'boost::mp::uint128_t': [5026689, 587373, 330052, 972009, 2190856, 2227961] +} +""" + +""" +# Linux S390x +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + 'unsigned __int128': [14415854, 1232397, 1239808, 1928533, 8102813, 9072599], + 'uint128_t': [12658246, 1423451, 775766, 2600663, 5759377, 6648180], + 'boost::mp::uint128_t': [16561079, 2909066, 2744664, 2384775, 7828137, 9172574] +} +""" + +# Linux ppc64le +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + 'unsigned __int128': [5242604, 221776, 222894, 194494, 4821119, 4955570], + 'uint128_t': [4450958, 193063, 175259, 192929, 4896360, 4273487], + 'boost::mp::uint128_t': [5704848, 847504, 786659, 795187, 5344637, 5407877] +} + +df = pd.DataFrame(data) + +# Function to determine color based on ranking +def get_colors_by_rank(row): + values = row[1:].values + ranks = np.argsort(values) + 1 + colors = [] + for rank in ranks: + if rank == 1: + colors.append('#90EE90') # Light Green - Best + elif rank == 2: + colors.append('#FFFFE0') # Light Yellow - Second + else: + colors.append('#FFB6C1') # Light Red - Third + return colors + +# Create figure with subplots +fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 10)) + +# Prepare data +operations = df['Operation'] +x = np.arange(len(operations)) +width = 0.25 + +# Get implementation names +implementations = df.columns[1:] + +# Plot 1: Regular scale bar chart with color coding +for i, (idx, row) in enumerate(df.iterrows()): + colors = get_colors_by_rank(row) + for j, impl in enumerate(implementations): + ax1.bar(x[i] + (j-1)*width, row[impl], width, + color=colors[j], edgecolor='black', linewidth=0.5, + label=impl if i == 0 else "") + +ax1.set_xlabel('Operations', fontsize=12) +ax1.set_ylabel('Time (nanoseconds)', fontsize=12) +ax1.set_title('GCC 14 - ppc64le Benchmark Results', fontsize=14, fontweight='bold') +ax1.set_xticks(x) +ax1.set_xticklabels(operations, rotation=45, ha='right') +ax1.legend(loc='upper left') +ax1.grid(axis='y', alpha=0.3) + +# Add value labels on bars +for i, (idx, row) in enumerate(df.iterrows()): + for j, impl in enumerate(implementations): + ax1.text(x[i] + (j-1)*width, row[impl], f'{row[impl]:,}', + ha='center', va='bottom', fontsize=8, rotation=90) + +# Plot 2: Log scale for better visualization +for i, impl in enumerate(implementations): + bars = ax2.bar(x + (i-1)*width, df[impl], width, label=impl, edgecolor='black', linewidth=0.5) + + # Color each bar based on its rank within operation + for j, bar in enumerate(bars): + operation_values = df.iloc[j, 1:].values + rank = np.argsort(operation_values).tolist().index(i) + 1 + if rank == 1: + bar.set_facecolor('#90EE90') + elif rank == 2: + bar.set_facecolor('#FFFFE0') + else: + bar.set_facecolor('#FFB6C1') + +ax2.set_xlabel('Operations', fontsize=12) +ax2.set_ylabel('Time (nanoseconds) - Log Scale', fontsize=12) +ax2.set_title('GCC 14 - ppc64le Benchmark Results (Log Scale)', fontsize=14, fontweight='bold') +ax2.set_yscale('log') +ax2.set_xticks(x) +ax2.set_xticklabels(operations, rotation=45, ha='right') +ax2.legend(loc='upper left') +ax2.grid(axis='y', alpha=0.3, which='both') + +plt.tight_layout() +plt.savefig('ppc64le_benchmarks.png', dpi=300, bbox_inches='tight') +plt.show() + +# Create a normalized performance chart +fig3, ax3 = plt.subplots(figsize=(10, 6)) + +# Normalize data relative to unsigned __int128 +normalized_df = df.copy() +for col in implementations: + normalized_df[col] = df[col] / df['unsigned __int128'] + +# Plot normalized bars +for i, impl in enumerate(implementations): + if impl == 'unsigned __int128': + continue # Skip since it's always 1.0 + bars = ax3.bar(x + (i-1.5)*width, normalized_df[impl], width, + label=impl, edgecolor='black', linewidth=0.5) + + # Add value labels + for j, bar in enumerate(bars): + height = bar.get_height() + ax3.text(bar.get_x() + bar.get_width()/2., height, + f'{height:.2f}x', ha='center', va='bottom', fontsize=9) + +# Add reference line at 1.0 +ax3.axhline(y=1.0, color='red', linestyle='--', alpha=0.5, label='unsigned __int128 baseline') + +ax3.set_xlabel('Operations', fontsize=12) +ax3.set_ylabel('Relative Performance (vs unsigned __int128)', fontsize=12) +ax3.set_title('Relative Performance Comparison - x64', fontsize=14, fontweight='bold') +ax3.set_xticks(x) +ax3.set_xticklabels(operations, rotation=45, ha='right') +ax3.legend() +ax3.grid(axis='y', alpha=0.3) + +# Add interpretation text +ax3.text(0.02, 0.98, 'Lower is better', transform=ax3.transAxes, + fontsize=10, verticalalignment='top', style='italic') + +plt.tight_layout() +plt.savefig('ppc64le_relative_performance.png', dpi=300, bbox_inches='tight') +plt.show() + +# Generate summary statistics +print("\nPerformance Summary (x64):") +print("-" * 50) +for impl in implementations: + if impl == 'unsigned __int128': + continue + avg_ratio = normalized_df[impl].mean() + print(f"{impl}: {avg_ratio:.2f}x average vs unsigned __int128") + +print("\nBest performer by operation:") +print("-" * 50) +for i, op in enumerate(operations): + row_data = df.iloc[i, 1:] + best_impl = row_data.idxmin() + best_time = row_data.min() + print(f"{op}: {best_impl} ({best_time:,} ns)") + diff --git a/doc/signed_plots_32bit.py b/doc/signed_plots_32bit.py new file mode 100644 index 00000000..4e98830e --- /dev/null +++ b/doc/signed_plots_32bit.py @@ -0,0 +1,153 @@ +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd + +""" +# Linux x86_32 +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + 'uint128_t': [9000979, 898718, 778881, 1778273, 8496503, 9081442], + 'boost::mp::uint128_t': [8722814, 9912175, 9773677, 8678420, 18133965, 11257837] +} +""" +# Linux ARM32 +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + 'uint128_t': [5286033, 454715, 487190, 1471479, 19868087, 20332627], + 'boost::mp::uint128_t': [4538707, 5543856, 6465126, 8246098, 32820805, 27238658] +} + +df = pd.DataFrame(data) + +# Function to determine color based on ranking +def get_colors_by_rank(row): + values = row[1:].values + ranks = np.argsort(values) + 1 + colors = [] + for rank in ranks: + if rank == 1: + colors.append('#90EE90') # Light Green - Best + elif rank == 2: + colors.append('#FFFFE0') # Light Yellow - Second + else: + colors.append('#FFB6C1') # Light Red - Third + return colors + +# Create figure with subplots +fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 10)) + +# Prepare data +operations = df['Operation'] +x = np.arange(len(operations)) +width = 0.25 + +# Get implementation names +implementations = df.columns[1:] + +# Plot 1: Regular scale bar chart with color coding +for i, (idx, row) in enumerate(df.iterrows()): + colors = get_colors_by_rank(row) + for j, impl in enumerate(implementations): + ax1.bar(x[i] + (j-1)*width, row[impl], width, + color=colors[j], edgecolor='black', linewidth=0.5, + label=impl if i == 0 else "") + +ax1.set_xlabel('Operations', fontsize=12) +ax1.set_ylabel('Time (nanoseconds)', fontsize=12) +ax1.set_title('GCC 14 - ARM32 Benchmark Results', fontsize=14, fontweight='bold') +ax1.set_xticks(x) +ax1.set_xticklabels(operations, rotation=45, ha='right') +ax1.legend(loc='upper left') +ax1.grid(axis='y', alpha=0.3) + +# Add value labels on bars +for i, (idx, row) in enumerate(df.iterrows()): + for j, impl in enumerate(implementations): + ax1.text(x[i] + (j-1)*width, row[impl], f'{row[impl]:,}', + ha='center', va='bottom', fontsize=8, rotation=90) + +# Plot 2: Log scale for better visualization +for i, impl in enumerate(implementations): + bars = ax2.bar(x + (i-1)*width, df[impl], width, label=impl, edgecolor='black', linewidth=0.5) + + # Color each bar based on its rank within operation + for j, bar in enumerate(bars): + operation_values = df.iloc[j, 1:].values + rank = np.argsort(operation_values).tolist().index(i) + 1 + if rank == 1: + bar.set_facecolor('#90EE90') + elif rank == 2: + bar.set_facecolor('#FFFFE0') + else: + bar.set_facecolor('#FFB6C1') + +ax2.set_xlabel('Operations', fontsize=12) +ax2.set_ylabel('Time (nanoseconds) - Log Scale', fontsize=12) +ax2.set_title('GCC 14 - ARM32 Benchmark Results (Log Scale)', fontsize=14, fontweight='bold') +ax2.set_yscale('log') +ax2.set_xticks(x) +ax2.set_xticklabels(operations, rotation=45, ha='right') +ax2.legend(loc='upper left') +ax2.grid(axis='y', alpha=0.3, which='both') + +plt.tight_layout() +plt.savefig('ARM32_benchmarks.png', dpi=300, bbox_inches='tight') +plt.show() + +# Create a normalized performance chart +fig3, ax3 = plt.subplots(figsize=(10, 6)) + +# Normalize data relative to boost::mp::uint128_t +normalized_df = df.copy() +for col in implementations: + normalized_df[col] = df[col] / df['boost::mp::uint128_t'] + +# Plot normalized bars +for i, impl in enumerate(implementations): + if impl == 'boost::mp::uint128_t': + continue # Skip since it's always 1.0 + bars = ax3.bar(x + (i-1.5)*width, normalized_df[impl], width, + label=impl, edgecolor='black', linewidth=0.5) + + # Add value labels + for j, bar in enumerate(bars): + height = bar.get_height() + ax3.text(bar.get_x() + bar.get_width()/2., height, + f'{height:.2f}x', ha='center', va='bottom', fontsize=9) + +# Add reference line at 1.0 +ax3.axhline(y=1.0, color='red', linestyle='--', alpha=0.5, label='boost::mp::uint128_t baseline') + +ax3.set_xlabel('Operations', fontsize=12) +ax3.set_ylabel('Relative Performance (vs boost::mp::uint128_t)', fontsize=12) +ax3.set_title('Relative Performance Comparison - ARM3232', fontsize=14, fontweight='bold') +ax3.set_xticks(x) +ax3.set_xticklabels(operations, rotation=45, ha='right') +ax3.legend() +ax3.grid(axis='y', alpha=0.3) + +# Add interpretation text +ax3.text(0.02, 0.98, 'Lower is better', transform=ax3.transAxes, + fontsize=10, verticalalignment='top', style='italic') + +plt.tight_layout() +plt.savefig('ARM32_relative_performance.png', dpi=300, bbox_inches='tight') +plt.show() + +# Generate summary statistics +print("\nPerformance Summary (x64):") +print("-" * 50) +for impl in implementations: + if impl == 'unsigned __int128': + continue + avg_ratio = normalized_df[impl].mean() + print(f"{impl}: {avg_ratio:.2f}x average vs unsigned __int128") + +print("\nBest performer by operation:") +print("-" * 50) +for i, op in enumerate(operations): + row_data = df.iloc[i, 1:] + best_impl = row_data.idxmin() + best_time = row_data.min() + print(f"{op}: {best_impl} ({best_time:,} ns)") + From 30682304134ff2c29947c59c77c77315a7571e7d Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 5 Jun 2025 11:02:28 -0400 Subject: [PATCH 02/20] Fix labels --- doc/int128/u128_benchmarks.adoc | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/doc/int128/u128_benchmarks.adoc b/doc/int128/u128_benchmarks.adoc index 4acfc990..174b3d08 100644 --- a/doc/int128/u128_benchmarks.adoc +++ b/doc/int128/u128_benchmarks.adoc @@ -21,7 +21,7 @@ On MSVC platforms we use as reference `std::_Unsigned128` from the header `<__ms [cols="1,1,1,1"] |=== -| Operation | `std::_Unsigned128` | `uint128_t` | `boost::mp::uint128_t` +| Operation | `unsigned __int128` | `uint128_t` | `boost::mp::uint128_t` | Comparisons | 2068491 | 2416378 | 3191439 | Addition | 383258 | 180522 | 545521 @@ -41,7 +41,7 @@ image::u128_graphs/linux/x64_relative_performance.png[x64 Relative Performance, [cols="1,1,1,1"] |=== -| Operation | `std::_Unsigned128` | `uint128_t` | `boost::mp::uint128_t` +| Operation | `unsigned __int128` | `uint128_t` | `boost::mp::uint128_t` | Comparisons | 2068491 | 2416378 | 3191439 | Addition | 383258 | 180522 | 545521 @@ -61,7 +61,7 @@ image::u128_graphs/linux/ARM64_relative_performance.png[x64 Relative Performance [cols="1,1,1,1"] |=== -| Operation | `std::_Unsigned128` | `uint128_t` | `boost::mp::uint128_t` +| Operation | `unsigned __int128` | `uint128_t` | `boost::mp::uint128_t` | Comparisons | 14415854 | 12658246 | 16561079 | Addition | 1232397 | 1423451 | 2909066 @@ -81,7 +81,7 @@ image::u128_graphs/linux/s390x_relative_performance.png[s390x Relative Performan [cols="1,1,1,1"] |=== -| Operation | `std::_Unsigned128` | `uint128_t` | `boost::mp::uint128_t` +| Operation | `unsigned __int128` | `uint128_t` | `boost::mp::uint128_t` | Comparisons | 5242604 | 4450958 | 5704848 | Addition | 221776 | 193063 | 847504 From cf33aa105cf5430fc363ded867b9b2848cd52b46 Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 5 Jun 2025 11:05:22 -0400 Subject: [PATCH 03/20] Add x64 signed data --- doc/i128_graphs/linux/x64_benchmarks.png | Bin 0 -> 366500 bytes .../linux/x64_relative_performance.png | Bin 0 -> 181427 bytes doc/int128/i128_benchmarks.adoc | 64 +++++------ doc/signed_plots.py | 106 +++--------------- 4 files changed, 46 insertions(+), 124 deletions(-) create mode 100644 doc/i128_graphs/linux/x64_benchmarks.png 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|=== -| Operation | `std::_Signed128` | `int128_t` | `boost::mp::int128_t` +| Operation | `__int128` | `int128_t` | `boost::mp::int128_t` -| Comparisons | 2068491 | 2416378 | 3191439 -| Addition | 383258 | 180522 | 545521 -| Subtraction | 208155 | 192633 | 420573 -| Multiplication | 291075 | 241174 | 675361 -| Division | 3953939 | 4246753 | 4976285 -| Modulo | 4042166 | 3953441 | 4478923 +| Comparisons | 2086545 | 1807917 | 6119951 +| Addition | 229772 | 249644 | 620566 +| Subtraction | 245300 | 172252 | 1522422 +| Multiplication | 403481 | 246659 | 898345 +| Division | 4315016 | 4369512 | 4767180 +| Modulo | 4303454 | 4686920 | 4855786 |=== //// -image::u128_graphs/linux/x64_benchmarks.png[x64 Benchmark Results, width=100%] +image::i128_graphs/linux/x64_benchmarks.png[x64 Benchmark Results, width=100%] //// -image::u128_graphs/linux/x64_relative_performance.png[x64 Relative Performance, width=100%] +image::i128_graphs/linux/x64_relative_performance.png[x64 Relative Performance, width=100%] === ARM64 [cols="1,1,1,1"] |=== -| Operation | `std::_Signed128` | `int128_t` | `boost::mp::int128_t` +| Operation | `__int128` | `int128_t` | `boost::mp::int128_t` | Comparisons | 2068491 | 2416378 | 3191439 | Addition | 383258 | 180522 | 545521 @@ -52,16 +52,16 @@ image::u128_graphs/linux/x64_relative_performance.png[x64 Relative Performance, |=== //// -image::u128_graphs/linux/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] +image::i128_graphs/linux/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] //// -image::u128_graphs/linux/ARM64_relative_performance.png[x64 Relative Performance, width=100%] +image::i128_graphs/linux/ARM64_relative_performance.png[x64 Relative Performance, width=100%] === S390x [cols="1,1,1,1"] |=== -| Operation | `std::_Signed128` | `int128_t` | `boost::mp::int128_t` +| Operation | `__int128` | `int128_t` | `boost::mp::int128_t` | Comparisons | 14415854 | 12658246 | 16561079 | Addition | 1232397 | 1423451 | 2909066 @@ -72,16 +72,16 @@ image::u128_graphs/linux/ARM64_relative_performance.png[x64 Relative Performance |=== //// -image::u128_graphs/linux/s390x_benchmarks.png[s390x Benchmark Results, width=100%] +image::i128_graphs/linux/s390x_benchmarks.png[s390x Benchmark Results, width=100%] //// -image::u128_graphs/linux/s390x_relative_performance.png[s390x Relative Performance, width=100%] +image::i128_graphs/linux/s390x_relative_performance.png[s390x Relative Performance, width=100%] === PPC64LE [cols="1,1,1,1"] |=== -| Operation | `std::_Signed128` | `int128_t` | `boost::mp::int128_t` +| Operation | `__int128` | `int128_t` | `boost::mp::int128_t` | Comparisons | 5242604 | 4450958 | 5704848 | Addition | 221776 | 193063 | 847504 @@ -92,10 +92,10 @@ image::u128_graphs/linux/s390x_relative_performance.png[s390x Relative Performan |=== //// -image::u128_graphs/linux/ppc64le_benchmarks.png[ppc64le Benchmark Results, width=100%] +image::i128_graphs/linux/ppc64le_benchmarks.png[ppc64le Benchmark Results, width=100%] //// -image::u128_graphs/linux/ppc64le_relative_performance.png[ppc64le Relative Performance, width=100%] +image::i128_graphs/linux/ppc64le_relative_performance.png[ppc64le Relative Performance, width=100%] === x86_32 @@ -115,10 +115,10 @@ NOTE: This platform has no hardware type so we compare relative to `boost::mp::i |=== //// -image::u128_graphs/linux/x86_benchmarks.png[x86 Benchmark Results, width=100%] +image::i128_graphs/linux/x86_benchmarks.png[x86 Benchmark Results, width=100%] //// -image::u128_graphs/linux/x86_relative_performance.png[x86 Relative Performance, width=100%] +image::i128_graphs/linux/x86_relative_performance.png[x86 Relative Performance, width=100%] === ARM32 @@ -137,10 +137,10 @@ NOTE: This platform has no hardware type so we compare relative to `boost::mp::i |=== //// -image::u128_graphs/linux/ARM32_benchmarks.png[ARM32 Benchmark Results, width=100%] +image::i128_graphs/linux/ARM32_benchmarks.png[ARM32 Benchmark Results, width=100%] //// -image::u128_graphs/linux/ARM32_relative_performance.png[ARM32 Relative Performance, width=100%] +image::i128_graphs/linux/ARM32_relative_performance.png[ARM32 Relative Performance, width=100%] == Windows @@ -158,10 +158,10 @@ image::u128_graphs/linux/ARM32_relative_performance.png[ARM32 Relative Performan | Modulo | 2176318 | 1897933 | 2227961 |=== //// -image::u128_graphs/windows/arm64_benchmarks.png[ARM64 Benchmark Results, width=100%] +image::i128_graphs/windows/arm64_benchmarks.png[ARM64 Benchmark Results, width=100%] //// -image::u128_graphs/windows/arm64_relative_performance.png[ARM64 Relative Performance, width=100%] +image::i128_graphs/windows/arm64_relative_performance.png[ARM64 Relative Performance, width=100%] === x86_32 @@ -177,10 +177,10 @@ image::u128_graphs/windows/arm64_relative_performance.png[ARM64 Relative Perform | Modulo | 4551146 | 4330152 | 6294325 |=== //// -image::u128_graphs/windows/x86_benchmarks.png[x86_32 Benchmark Results, width=100%] +image::i128_graphs/windows/x86_benchmarks.png[x86_32 Benchmark Results, width=100%] //// -image::u128_graphs/windows/x86_relative_performance.png[x86_32 Relative Performance, width=100%] +image::i128_graphs/windows/x86_relative_performance.png[x86_32 Relative Performance, width=100%] === x86_64 @@ -196,10 +196,10 @@ image::u128_graphs/windows/x86_relative_performance.png[x86_32 Relative Performa | Modulo | 1465138 | 1471169 | 3926336 |=== //// -image::u128_graphs/windows/x64_benchmarks.png[x64 Benchmark Results, width=100%] +image::i128_graphs/windows/x64_benchmarks.png[x64 Benchmark Results, width=100%] //// -image::u128_graphs/windows/x64_relative_performance.png[x64 Relative Performance, width=100%] +image::i128_graphs/windows/x64_relative_performance.png[x64 Relative Performance, width=100%] == macOS @@ -218,10 +218,10 @@ image::u128_graphs/windows/x64_relative_performance.png[x64 Relative Performance |=== //// -image::u128_graphs/macos/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] +image::i128_graphs/macos/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] //// -image::u128_graphs/macos/ARM64_relative_performance.png[ARM64 Relative Performance, width=100%] +image::i128_graphs/macos/ARM64_relative_performance.png[ARM64 Relative Performance, width=100%] === x86_64 @@ -238,7 +238,7 @@ image::u128_graphs/macos/ARM64_relative_performance.png[ARM64 Relative Performan |=== //// -image::u128_graphs/macos/x64_benchmarks.png[x64 Benchmark Results, width=100%] +image::i128_graphs/macos/x64_benchmarks.png[x64 Benchmark Results, width=100%] //// -image::u128_graphs/macos/x64_relative_performance.png[x64 Relative Performance, width=100%] +image::i128_graphs/macos/x64_relative_performance.png[x64 Relative Performance, width=100%] diff --git a/doc/signed_plots.py b/doc/signed_plots.py index 91206ddf..542ae59d 100644 --- a/doc/signed_plots.py +++ b/doc/signed_plots.py @@ -2,90 +2,12 @@ import numpy as np import pandas as pd -""" -# ARM64 MSVC -data = { - 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], - 'std::_Unsigned128': [878929, 32788, 33627, 68120, 925583, 1104772], - 'uint128_t': [259725, 33723, 36799, 35334, 1020148, 1143344], - 'boost::mp::uint128_t': [1246502, 1437452, 1648131, 1459418, 2216648, 2089105] -} -""" - -""" -# x86 MSVC -data = { - 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], - 'std::_Unsigned128': [4215438, 199945, 1206168, 2282869, 5516964, 4551146], - 'uint128_t': [3883846, 208436, 210874, 2680359, 4328917, 4330152], - 'boost::mp::uint128_t': [2852442, 3242910, 3851129, 5378001, 6948267, 6294325] -} -""" - -""" -# x64 MSVC -data = { - 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], - 'std::_Unsigned128': [2060556, 261475, 178724, 146063, 1332838, 1465138], - 'uint128_t': [1921174, 106545, 124181, 136115, 1360295, 1471169], - 'boost::mp::uint128_t': [3009890, 2710279, 3059187, 3495634, 4852899, 3926336] -} -""" - -""" -# ARM64 macOS -data = { - 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], - 'unsigned __int128': [131902, 20613, 20484, 20160, 686521, 777084], - 'uint128_t': [133564, 17912, 18237, 20580, 699201, 724648], - 'boost::mp::uint128_t': [134182, 40176, 40311, 43285, 945928, 953117] -} -""" - -""" -# x64 macOS -data = { - 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], - 'unsigned __int128': [688225, 104921, 129150, 120363, 2333812, 2621949], - 'uint128_t': [712352, 124992, 102302, 119652, 1981469, 2219481], - 'boost::mp::uint128_t': [689146, 137819, 153484, 164100, 2784139, 2736682] -} -""" -""" # Linux x64 data = { 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], - 'unsigned __int128': [2068491, 383258, 208155, 291075, 3953939, 4042166], - 'uint128_t': [2416378, 180522, 192633, 241174, 4246753, 3953441], - 'boost::mp::uint128_t': [3191439, 545521, 420573, 675361, 4976285, 4478923] -} -""" -""" -# Linux ARM64 -data = { - 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], - 'unsigned __int128': [3424403, 123659, 171721, 329287, 2044821, 2176318], - 'uint128_t': [2062167, 133084, 99453, 283443, 1825020, 1897933], - 'boost::mp::uint128_t': [5026689, 587373, 330052, 972009, 2190856, 2227961] -} -""" - -""" -# Linux S390x -data = { - 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], - 'unsigned __int128': [14415854, 1232397, 1239808, 1928533, 8102813, 9072599], - 'uint128_t': [12658246, 1423451, 775766, 2600663, 5759377, 6648180], - 'boost::mp::uint128_t': [16561079, 2909066, 2744664, 2384775, 7828137, 9172574] -} -""" - -# Linux ppc64le -data = { - 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], - 'unsigned __int128': [5242604, 221776, 222894, 194494, 4821119, 4955570], - 'uint128_t': [4450958, 193063, 175259, 192929, 4896360, 4273487], - 'boost::mp::uint128_t': [5704848, 847504, 786659, 795187, 5344637, 5407877] + '__int128': [2086545, 229772, 245300, 403481, 4315016, 4303454], + 'int128_t': [1807917, 249644, 172252, 246659, 4369512, 4686920], + 'boost::mp::int128_t': [6119951, 620566, 1522422, 898345, 4767180, 4855786] } df = pd.DataFrame(data) @@ -125,7 +47,7 @@ def get_colors_by_rank(row): ax1.set_xlabel('Operations', fontsize=12) ax1.set_ylabel('Time (nanoseconds)', fontsize=12) -ax1.set_title('GCC 14 - ppc64le Benchmark Results', fontsize=14, fontweight='bold') +ax1.set_title('GCC 14 - x64 Benchmark Results', fontsize=14, fontweight='bold') ax1.set_xticks(x) ax1.set_xticklabels(operations, rotation=45, ha='right') ax1.legend(loc='upper left') @@ -154,7 +76,7 @@ def get_colors_by_rank(row): ax2.set_xlabel('Operations', fontsize=12) ax2.set_ylabel('Time (nanoseconds) - Log Scale', fontsize=12) -ax2.set_title('GCC 14 - ppc64le Benchmark Results (Log Scale)', fontsize=14, fontweight='bold') +ax2.set_title('GCC 14 - x64 Benchmark Results (Log Scale)', fontsize=14, fontweight='bold') ax2.set_yscale('log') ax2.set_xticks(x) ax2.set_xticklabels(operations, rotation=45, ha='right') @@ -162,20 +84,20 @@ def get_colors_by_rank(row): ax2.grid(axis='y', alpha=0.3, which='both') plt.tight_layout() -plt.savefig('ppc64le_benchmarks.png', dpi=300, bbox_inches='tight') +plt.savefig('x64_benchmarks.png', dpi=300, bbox_inches='tight') plt.show() # Create a normalized performance chart fig3, ax3 = plt.subplots(figsize=(10, 6)) -# Normalize data relative to unsigned __int128 +# Normalize data relative to __int128 normalized_df = df.copy() for col in implementations: - normalized_df[col] = df[col] / df['unsigned __int128'] + normalized_df[col] = df[col] / df['__int128'] # Plot normalized bars for i, impl in enumerate(implementations): - if impl == 'unsigned __int128': + if impl == '__int128': continue # Skip since it's always 1.0 bars = ax3.bar(x + (i-1.5)*width, normalized_df[impl], width, label=impl, edgecolor='black', linewidth=0.5) @@ -187,10 +109,10 @@ def get_colors_by_rank(row): f'{height:.2f}x', ha='center', va='bottom', fontsize=9) # Add reference line at 1.0 -ax3.axhline(y=1.0, color='red', linestyle='--', alpha=0.5, label='unsigned __int128 baseline') +ax3.axhline(y=1.0, color='red', linestyle='--', alpha=0.5, label='__int128 baseline') ax3.set_xlabel('Operations', fontsize=12) -ax3.set_ylabel('Relative Performance (vs unsigned __int128)', fontsize=12) +ax3.set_ylabel('Relative Performance (vs __int128)', fontsize=12) ax3.set_title('Relative Performance Comparison - x64', fontsize=14, fontweight='bold') ax3.set_xticks(x) ax3.set_xticklabels(operations, rotation=45, ha='right') @@ -202,17 +124,17 @@ def get_colors_by_rank(row): fontsize=10, verticalalignment='top', style='italic') plt.tight_layout() -plt.savefig('ppc64le_relative_performance.png', dpi=300, bbox_inches='tight') +plt.savefig('x64_relative_performance.png', dpi=300, bbox_inches='tight') plt.show() # Generate summary statistics print("\nPerformance Summary (x64):") print("-" * 50) for impl in implementations: - if impl == 'unsigned __int128': + if impl == '__int128': continue avg_ratio = normalized_df[impl].mean() - print(f"{impl}: {avg_ratio:.2f}x average vs unsigned __int128") + print(f"{impl}: {avg_ratio:.2f}x average vs __int128") print("\nBest performer by operation:") print("-" * 50) From 3f0b6e745c09c580e980b35397e391a325df56eb Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 5 Jun 2025 11:15:43 -0400 Subject: [PATCH 04/20] Add size remark --- doc/int128/overview.adoc | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/doc/int128/overview.adoc b/doc/int128/overview.adoc index a49f3438..180dfac8 100644 --- a/doc/int128/overview.adoc +++ b/doc/int128/overview.adoc @@ -11,6 +11,7 @@ https://www.boost.org/LICENSE_1_0.txt == Description Boost.Int128 is a portable implementation of a signed, and an unsigned 128-bit integer and related functionality (e.g. bit counting). +Importantly, on all platforms, the `sizeof` the types provided in this library are 128-bits. The library is header-only, has no dependencies, and requires only C++14. @@ -26,7 +27,7 @@ Anywhere 128-bits are needed. == Supported Compilers Boost.Int128 is tested natively on Ubuntu (x86_64, s390x, and aarch64), macOS (x86_64, and Apple Silicon), and Windows (x32 and x64); -as well as emulated PPC64LE and STM32 using QEMU with the following compilers: +as well as emulated PPC64LE using QEMU with the following compilers: * GCC 5 and later * Clang 5 and later From 3b57150f56c0b6582143f5ad06e2b9c5a1ab57ce Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 5 Jun 2025 11:16:20 -0400 Subject: [PATCH 05/20] Add linux ARM64 data --- doc/i128_graphs/linux/ARM64_benchmarks.png | Bin 0 -> 366714 bytes .../linux/ARM64_relative_performance.png | Bin 0 -> 180316 bytes doc/int128/i128_benchmarks.adoc | 12 ++++++------ doc/signed_plots.py | 18 ++++++++++++++---- 4 files changed, 20 insertions(+), 10 deletions(-) create mode 100644 doc/i128_graphs/linux/ARM64_benchmarks.png create mode 100644 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291075 | 241174 | 675361 -| Division | 3953939 | 4246753 | 4976285 -| Modulo | 4042166 | 3953441 | 4478923 +| Comparisons | 3524205 | 2191692 | 5559916 +| Addition | 109691 | 126544 | 553814 +| Subtraction | 195129 | 196092 | 1024231 +| Multiplication | 286623 | 192214 | 924637 +| Division | 2350225 | 2163053 | 2718340 +| Modulo | 2345191 | 2167260 | 2380277 |=== //// diff --git a/doc/signed_plots.py b/doc/signed_plots.py index 542ae59d..205aaaca 100644 --- a/doc/signed_plots.py +++ b/doc/signed_plots.py @@ -2,6 +2,7 @@ import numpy as np import pandas as pd +""" # Linux x64 data = { 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], @@ -9,6 +10,15 @@ 'int128_t': [1807917, 249644, 172252, 246659, 4369512, 4686920], 'boost::mp::int128_t': [6119951, 620566, 1522422, 898345, 4767180, 4855786] } +""" + +# Linux ARM64 +data = { + 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], + '__int128': [3524205, 109691, 195129, 286623, 2350225, 2345191], + 'int128_t': [2191692, 126544, 196092, 192214, 2163053, 2167260], + 'boost::mp::int128_t': [5559916, 553814, 1024231, 924637, 2718340, 2380277] +} df = pd.DataFrame(data) @@ -47,7 +57,7 @@ def get_colors_by_rank(row): ax1.set_xlabel('Operations', fontsize=12) ax1.set_ylabel('Time (nanoseconds)', fontsize=12) -ax1.set_title('GCC 14 - x64 Benchmark Results', fontsize=14, fontweight='bold') +ax1.set_title('GCC 13 - ARM64 Benchmark Results', fontsize=14, fontweight='bold') ax1.set_xticks(x) ax1.set_xticklabels(operations, rotation=45, ha='right') ax1.legend(loc='upper left') @@ -76,7 +86,7 @@ def get_colors_by_rank(row): ax2.set_xlabel('Operations', fontsize=12) ax2.set_ylabel('Time (nanoseconds) - Log Scale', fontsize=12) -ax2.set_title('GCC 14 - x64 Benchmark Results (Log Scale)', fontsize=14, fontweight='bold') +ax2.set_title('GCC 13 - ARM64 Benchmark Results (Log Scale)', fontsize=14, fontweight='bold') ax2.set_yscale('log') ax2.set_xticks(x) ax2.set_xticklabels(operations, rotation=45, ha='right') @@ -84,7 +94,7 @@ def get_colors_by_rank(row): ax2.grid(axis='y', alpha=0.3, which='both') plt.tight_layout() -plt.savefig('x64_benchmarks.png', dpi=300, bbox_inches='tight') +plt.savefig('ARM64_benchmarks.png', dpi=300, bbox_inches='tight') plt.show() # Create a normalized performance chart @@ -124,7 +134,7 @@ def get_colors_by_rank(row): fontsize=10, verticalalignment='top', style='italic') plt.tight_layout() -plt.savefig('x64_relative_performance.png', dpi=300, bbox_inches='tight') +plt.savefig('ARM64_relative_performance.png', dpi=300, bbox_inches='tight') plt.show() # Generate summary statistics From 21d82f9e3062af10fafcc309bed6b39c0937e2e6 Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 5 Jun 2025 11:20:37 -0400 Subject: [PATCH 06/20] Add linux s390x data --- doc/i128_graphs/linux/s390x_benchmarks.png | Bin 0 -> 383364 bytes .../linux/s390x_relative_performance.png | Bin 0 -> 195228 bytes 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zb>bXzoY*4W(-f}#Gfc4=?OLksg1917rmIw207;||mFyPr-9XKef2lMN=Hle{b_)ZYhH~jSerHlXXU;nEsv0zf; XqknpYdV~=l{?^{1zdc>k_SF9aMx(#! literal 0 HcmV?d00001 diff --git a/doc/int128/i128_benchmarks.adoc b/doc/int128/i128_benchmarks.adoc index 8a3417fe..4c369662 100644 --- a/doc/int128/i128_benchmarks.adoc +++ b/doc/int128/i128_benchmarks.adoc @@ -106,12 +106,12 @@ NOTE: This platform has no hardware type so we compare relative to `boost::mp::i |=== | Operation | `int128_t` | `boost::mp::int128_t` -| Comparisons | 9000979 | 8722814 -| Addition | 898718 | 9912175 -| Subtraction | 778881 | 9773677 -| Multiplication | 1778273 | 8678420 -| Division | 8496503 | 18133965 -| Modulo | 9081442 | 11257837 +| Comparisons | 9530060 | 12168353 +| Addition | 785799 | 7777469 +| Subtraction | 778881 | 8214089 +| Multiplication | 1148024 | 9477355 +| Division | 10337258 | 22857709 +| Modulo | 10438037 | 14848256 |=== //// diff --git a/doc/signed_plots_32bit.py b/doc/signed_plots_32bit.py index 4e98830e..4167fadf 100644 --- a/doc/signed_plots_32bit.py +++ b/doc/signed_plots_32bit.py @@ -2,21 +2,14 @@ import numpy as np import pandas as pd -""" # Linux x86_32 data = { 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], - 'uint128_t': [9000979, 898718, 778881, 1778273, 8496503, 9081442], - 'boost::mp::uint128_t': [8722814, 9912175, 9773677, 8678420, 18133965, 11257837] -} -""" -# Linux ARM32 -data = { - 'Operation': ['Comparisons', 'Addition', 'Subtraction', 'Multiplication', 'Division', 'Modulo'], - 'uint128_t': [5286033, 454715, 487190, 1471479, 19868087, 20332627], - 'boost::mp::uint128_t': [4538707, 5543856, 6465126, 8246098, 32820805, 27238658] + 'int128_t': [9530060, 785799, 778881, 1148024, 10337258, 10438037], + 'boost::mp::int128_t': [12168353, 7777469, 8214089, 9477355, 22857709, 14848256] } + df = pd.DataFrame(data) # Function to determine color based on ranking @@ -54,7 +47,7 @@ def get_colors_by_rank(row): ax1.set_xlabel('Operations', fontsize=12) ax1.set_ylabel('Time (nanoseconds)', fontsize=12) -ax1.set_title('GCC 14 - ARM32 Benchmark Results', fontsize=14, fontweight='bold') +ax1.set_title('GCC 14 - x86_32 Benchmark Results', fontsize=14, fontweight='bold') ax1.set_xticks(x) ax1.set_xticklabels(operations, rotation=45, ha='right') ax1.legend(loc='upper left') @@ -83,7 +76,7 @@ def get_colors_by_rank(row): ax2.set_xlabel('Operations', fontsize=12) ax2.set_ylabel('Time (nanoseconds) - Log Scale', fontsize=12) -ax2.set_title('GCC 14 - ARM32 Benchmark Results (Log Scale)', fontsize=14, fontweight='bold') +ax2.set_title('GCC 14 - x86_32 Benchmark Results (Log Scale)', fontsize=14, fontweight='bold') ax2.set_yscale('log') ax2.set_xticks(x) ax2.set_xticklabels(operations, rotation=45, ha='right') @@ -91,20 +84,20 @@ def get_colors_by_rank(row): ax2.grid(axis='y', alpha=0.3, which='both') plt.tight_layout() -plt.savefig('ARM32_benchmarks.png', dpi=300, bbox_inches='tight') +plt.savefig('x86_benchmarks.png', dpi=300, bbox_inches='tight') plt.show() # Create a normalized performance chart fig3, ax3 = plt.subplots(figsize=(10, 6)) -# Normalize data relative to boost::mp::uint128_t +# Normalize data relative to boost::mp::int128_t normalized_df = df.copy() for col in implementations: - normalized_df[col] = df[col] / df['boost::mp::uint128_t'] + normalized_df[col] = df[col] / df['boost::mp::int128_t'] # Plot normalized bars for i, impl in enumerate(implementations): - if impl == 'boost::mp::uint128_t': + if impl == 'boost::mp::int128_t': continue # Skip since it's always 1.0 bars = ax3.bar(x + (i-1.5)*width, normalized_df[impl], width, label=impl, edgecolor='black', linewidth=0.5) @@ -116,11 +109,11 @@ def get_colors_by_rank(row): f'{height:.2f}x', ha='center', va='bottom', fontsize=9) # Add reference line at 1.0 -ax3.axhline(y=1.0, color='red', linestyle='--', alpha=0.5, label='boost::mp::uint128_t baseline') +ax3.axhline(y=1.0, color='red', linestyle='--', alpha=0.5, label='boost::mp::int128_t baseline') ax3.set_xlabel('Operations', fontsize=12) -ax3.set_ylabel('Relative Performance (vs boost::mp::uint128_t)', fontsize=12) -ax3.set_title('Relative Performance Comparison - ARM3232', fontsize=14, fontweight='bold') +ax3.set_ylabel('Relative Performance (vs boost::mp::int128_t)', fontsize=12) +ax3.set_title('Relative Performance Comparison - x86_32', fontsize=14, fontweight='bold') ax3.set_xticks(x) ax3.set_xticklabels(operations, rotation=45, ha='right') ax3.legend() @@ -131,17 +124,17 @@ def get_colors_by_rank(row): fontsize=10, verticalalignment='top', style='italic') plt.tight_layout() -plt.savefig('ARM32_relative_performance.png', dpi=300, bbox_inches='tight') +plt.savefig('x86_relative_performance.png', dpi=300, bbox_inches='tight') plt.show() # Generate summary statistics print("\nPerformance Summary (x64):") print("-" * 50) for impl in implementations: - if impl == 'unsigned __int128': + if impl == '__int128': continue avg_ratio = normalized_df[impl].mean() - print(f"{impl}: {avg_ratio:.2f}x average vs unsigned __int128") + print(f"{impl}: {avg_ratio:.2f}x average vs __int128") print("\nBest performer by operation:") print("-" * 50) From 6411a7dce4a09548969a99913fca377005777e72 Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 5 Jun 2025 11:50:07 -0400 Subject: [PATCH 09/20] Add linux ARM32 data --- doc/i128_graphs/linux/ARM32_benchmarks.png | Bin 0 -> 359560 bytes .../linux/ARM32_relative_performance.png | Bin 0 -> 183332 bytes doc/int128/i128_benchmarks.adoc | 12 ++++++------ doc/signed_plots_32bit.py | 18 +++++++++++++----- 4 files changed, 19 insertions(+), 11 deletions(-) create mode 100644 doc/i128_graphs/linux/ARM32_benchmarks.png create mode 100644 doc/i128_graphs/linux/ARM32_relative_performance.png diff --git a/doc/i128_graphs/linux/ARM32_benchmarks.png b/doc/i128_graphs/linux/ARM32_benchmarks.png new file mode 100644 index 0000000000000000000000000000000000000000..dc6a76173ba82d172d8505a58c6ebee402514a46 GIT binary patch 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z6H?ph3?e=rL4#kzV_8|q!n*LiWNg?$7?dVdLpOn{8EyC9uHCb5s`IBAW3eFbSc3#pCd9XY2r(D z3>Eo_IjN2@eA;vg1&Cs)$V_*Yo$$up)#zHEeAIsSVg4_5_ zF>!$g(mxRkk!&shw^6Pwhf-kmzxQf}R|&|^XRpD1`)1lZ{sYfQhIBS9Lo}l2H-Kal zF9q4%4;EX4kd1`E7Ag2b_$f`9Z~pw6AgFRO`NMLyagE}HxbvLt=dqHUR|u;X4AbOI zXzTXn;B#AtP5FlD#{^;-Q|(^a(!Q$WZF4#M4$+Lp93 zr({%(^ErC@j+SDQ#(hxRTL~hGV0&et8mC4&DH@4+ezxqzAettQ5ChJ$er!6?@{NwZ z+C(gX$x$+u^g@wCh^H2NlW&AODp}r541CDC3Jv zG$Ru37sr%8#@`mdy!r2cT>RF5+SlS&-2dsvj4!p&!MgZ;^5_2l&mR;YL47 Date: Thu, 5 Jun 2025 13:49:00 -0400 Subject: [PATCH 11/20] Change images dir --- doc/int128/i128_benchmarks.adoc | 45 +++++++++++++++++---------------- 1 file changed, 23 insertions(+), 22 deletions(-) diff --git a/doc/int128/i128_benchmarks.adoc b/doc/int128/i128_benchmarks.adoc index 64f69ea2..af843f5b 100644 --- a/doc/int128/i128_benchmarks.adoc +++ b/doc/int128/i128_benchmarks.adoc @@ -7,6 +7,7 @@ https://www.boost.org/LICENSE_1_0.txt [#i128_benchmarks] = `int128_t` Benchmarks :idprefix: i128_benchmarks_ +:imagesdir: i128_graphs == Methodology @@ -32,10 +33,10 @@ On MSVC platforms we use as reference `std::_Signed128` from the header `<__msvc |=== //// -image::i128_graphs/linux/x64_benchmarks.png[x64 Benchmark Results, width=100%] +image::linux/x64_benchmarks.png[x64 Benchmark Results, width=100%] //// -image::i128_graphs/linux/x64_relative_performance.png[x64 Relative Performance, width=100%] +image::linux/x64_relative_performance.png[x64 Relative Performance, width=100%] === ARM64 @@ -52,10 +53,10 @@ image::i128_graphs/linux/x64_relative_performance.png[x64 Relative Performance, |=== //// -image::i128_graphs/linux/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] +image::linux/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] //// -image::i128_graphs/linux/ARM64_relative_performance.png[x64 Relative Performance, width=100%] +image::linux/ARM64_relative_performance.png[x64 Relative Performance, width=100%] === S390x @@ -72,10 +73,10 @@ image::i128_graphs/linux/ARM64_relative_performance.png[x64 Relative Performance |=== //// -image::i128_graphs/linux/s390x_benchmarks.png[s390x Benchmark Results, width=100%] +image::linux/s390x_benchmarks.png[s390x Benchmark Results, width=100%] //// -image::i128_graphs/linux/s390x_relative_performance.png[s390x Relative Performance, width=100%] +image::linux/s390x_relative_performance.png[s390x Relative Performance, width=100%] === PPC64LE @@ -92,10 +93,10 @@ image::i128_graphs/linux/s390x_relative_performance.png[s390x Relative Performan |=== //// -image::i128_graphs/linux/ppc64le_benchmarks.png[ppc64le Benchmark Results, width=100%] +image::linux/ppc64le_benchmarks.png[ppc64le Benchmark Results, width=100%] //// -image::i128_graphs/linux/ppc64le_relative_performance.png[ppc64le Relative Performance, width=100%] +image::linux/ppc64le_relative_performance.png[ppc64le Relative Performance, width=100%] === x86_32 @@ -115,10 +116,10 @@ NOTE: This platform has no hardware type so we compare relative to `boost::mp::i |=== //// -image::i128_graphs/linux/x86_benchmarks.png[x86 Benchmark Results, width=100%] +image::linux/x86_benchmarks.png[x86 Benchmark Results, width=100%] //// -image::i128_graphs/linux/x86_relative_performance.png[x86 Relative Performance, width=100%] +image::linux/x86_relative_performance.png[x86 Relative Performance, width=100%] === ARM32 @@ -137,10 +138,10 @@ NOTE: This platform has no hardware type so we compare relative to `boost::mp::i |=== //// -image::i128_graphs/linux/ARM32_benchmarks.png[ARM32 Benchmark Results, width=100%] +image::linux/ARM32_benchmarks.png[ARM32 Benchmark Results, width=100%] //// -image::i128_graphs/linux/ARM32_relative_performance.png[ARM32 Relative Performance, width=100%] +image::linux/ARM32_relative_performance.png[ARM32 Relative Performance, width=100%] == Windows @@ -158,10 +159,10 @@ image::i128_graphs/linux/ARM32_relative_performance.png[ARM32 Relative Performan | Modulo | 2176318 | 1897933 | 2227961 |=== //// -image::i128_graphs/windows/arm64_benchmarks.png[ARM64 Benchmark Results, width=100%] +image::windows/arm64_benchmarks.png[ARM64 Benchmark Results, width=100%] //// -image::i128_graphs/windows/arm64_relative_performance.png[ARM64 Relative Performance, width=100%] +image::windows/arm64_relative_performance.png[ARM64 Relative Performance, width=100%] === x86_32 @@ -177,10 +178,10 @@ image::i128_graphs/windows/arm64_relative_performance.png[ARM64 Relative Perform | Modulo | 4551146 | 4330152 | 6294325 |=== //// -image::i128_graphs/windows/x86_benchmarks.png[x86_32 Benchmark Results, width=100%] +image::windows/x86_benchmarks.png[x86_32 Benchmark Results, width=100%] //// -image::i128_graphs/windows/x86_relative_performance.png[x86_32 Relative Performance, width=100%] +image::windows/x86_relative_performance.png[x86_32 Relative Performance, width=100%] === x86_64 @@ -196,10 +197,10 @@ image::i128_graphs/windows/x86_relative_performance.png[x86_32 Relative Performa | Modulo | 1465138 | 1471169 | 3926336 |=== //// -image::i128_graphs/windows/x64_benchmarks.png[x64 Benchmark Results, width=100%] +image::windows/x64_benchmarks.png[x64 Benchmark Results, width=100%] //// -image::i128_graphs/windows/x64_relative_performance.png[x64 Relative Performance, width=100%] +image::windows/x64_relative_performance.png[x64 Relative Performance, width=100%] == macOS @@ -218,10 +219,10 @@ image::i128_graphs/windows/x64_relative_performance.png[x64 Relative Performance |=== //// -image::i128_graphs/macos/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] +image::macos/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] //// -image::i128_graphs/macos/ARM64_relative_performance.png[ARM64 Relative Performance, width=100%] +image::macos/ARM64_relative_performance.png[ARM64 Relative Performance, width=100%] === x86_64 @@ -238,7 +239,7 @@ image::i128_graphs/macos/ARM64_relative_performance.png[ARM64 Relative Performan |=== //// -image::i128_graphs/macos/x64_benchmarks.png[x64 Benchmark Results, width=100%] +image::macos/x64_benchmarks.png[x64 Benchmark Results, width=100%] //// -image::i128_graphs/macos/x64_relative_performance.png[x64 Relative Performance, width=100%] +image::macos/x64_relative_performance.png[x64 Relative Performance, width=100%] From ba34bfd53fc879092f89326bec2ff93aa2f52bd4 Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 5 Jun 2025 13:50:05 -0400 Subject: [PATCH 12/20] Change unsigned images dir --- doc/int128/u128_benchmarks.adoc | 45 +++++++++++++++++---------------- 1 file changed, 23 insertions(+), 22 deletions(-) diff --git a/doc/int128/u128_benchmarks.adoc b/doc/int128/u128_benchmarks.adoc index 174b3d08..f163b4fc 100644 --- a/doc/int128/u128_benchmarks.adoc +++ b/doc/int128/u128_benchmarks.adoc @@ -7,6 +7,7 @@ https://www.boost.org/LICENSE_1_0.txt [#u128_benchmarks] = `uint128_t` Benchmarks :idprefix: u128_benchmarks_ +:imagesdir: u128_graphs == Methodology @@ -32,10 +33,10 @@ On MSVC platforms we use as reference `std::_Unsigned128` from the header `<__ms |=== //// -image::u128_graphs/linux/x64_benchmarks.png[x64 Benchmark Results, width=100%] +image::linux/x64_benchmarks.png[x64 Benchmark Results, width=100%] //// -image::u128_graphs/linux/x64_relative_performance.png[x64 Relative Performance, width=100%] +image::linux/x64_relative_performance.png[x64 Relative Performance, width=100%] === ARM64 @@ -52,10 +53,10 @@ image::u128_graphs/linux/x64_relative_performance.png[x64 Relative Performance, |=== //// -image::u128_graphs/linux/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] +image::linux/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] //// -image::u128_graphs/linux/ARM64_relative_performance.png[x64 Relative Performance, width=100%] +image::linux/ARM64_relative_performance.png[x64 Relative Performance, width=100%] === S390x @@ -72,10 +73,10 @@ image::u128_graphs/linux/ARM64_relative_performance.png[x64 Relative Performance |=== //// -image::u128_graphs/linux/s390x_benchmarks.png[s390x Benchmark Results, width=100%] +image::linux/s390x_benchmarks.png[s390x Benchmark Results, width=100%] //// -image::u128_graphs/linux/s390x_relative_performance.png[s390x Relative Performance, width=100%] +image::linux/s390x_relative_performance.png[s390x Relative Performance, width=100%] === PPC64LE @@ -92,10 +93,10 @@ image::u128_graphs/linux/s390x_relative_performance.png[s390x Relative Performan |=== //// -image::u128_graphs/linux/ppc64le_benchmarks.png[ppc64le Benchmark Results, width=100%] +image::linux/ppc64le_benchmarks.png[ppc64le Benchmark Results, width=100%] //// -image::u128_graphs/linux/ppc64le_relative_performance.png[ppc64le Relative Performance, width=100%] +image::linux/ppc64le_relative_performance.png[ppc64le Relative Performance, width=100%] === x86_32 @@ -115,10 +116,10 @@ NOTE: This platform has no hardware type so we compare relative to `boost::mp::u |=== //// -image::u128_graphs/linux/x86_benchmarks.png[x86 Benchmark Results, width=100%] +image::linux/x86_benchmarks.png[x86 Benchmark Results, width=100%] //// -image::u128_graphs/linux/x86_relative_performance.png[x86 Relative Performance, width=100%] +image::linux/x86_relative_performance.png[x86 Relative Performance, width=100%] === ARM32 @@ -137,10 +138,10 @@ NOTE: This platform has no hardware type so we compare relative to `boost::mp::u |=== //// -image::u128_graphs/linux/ARM32_benchmarks.png[ARM32 Benchmark Results, width=100%] +image::linux/ARM32_benchmarks.png[ARM32 Benchmark Results, width=100%] //// -image::u128_graphs/linux/ARM32_relative_performance.png[ARM32 Relative Performance, width=100%] +image::linux/ARM32_relative_performance.png[ARM32 Relative Performance, width=100%] == Windows @@ -158,10 +159,10 @@ image::u128_graphs/linux/ARM32_relative_performance.png[ARM32 Relative Performan | Modulo | 2176318 | 1897933 | 2227961 |=== //// -image::u128_graphs/windows/arm64_benchmarks.png[ARM64 Benchmark Results, width=100%] +image::windows/arm64_benchmarks.png[ARM64 Benchmark Results, width=100%] //// -image::u128_graphs/windows/arm64_relative_performance.png[ARM64 Relative Performance, width=100%] +image::windows/arm64_relative_performance.png[ARM64 Relative Performance, width=100%] === x86_32 @@ -177,10 +178,10 @@ image::u128_graphs/windows/arm64_relative_performance.png[ARM64 Relative Perform | Modulo | 4551146 | 4330152 | 6294325 |=== //// -image::u128_graphs/windows/x86_benchmarks.png[x86_32 Benchmark Results, width=100%] +image::windows/x86_benchmarks.png[x86_32 Benchmark Results, width=100%] //// -image::u128_graphs/windows/x86_relative_performance.png[x86_32 Relative Performance, width=100%] +image::windows/x86_relative_performance.png[x86_32 Relative Performance, width=100%] === x86_64 @@ -196,10 +197,10 @@ image::u128_graphs/windows/x86_relative_performance.png[x86_32 Relative Performa | Modulo | 1465138 | 1471169 | 3926336 |=== //// -image::u128_graphs/windows/x64_benchmarks.png[x64 Benchmark Results, width=100%] +image::windows/x64_benchmarks.png[x64 Benchmark Results, width=100%] //// -image::u128_graphs/windows/x64_relative_performance.png[x64 Relative Performance, width=100%] +image::windows/x64_relative_performance.png[x64 Relative Performance, width=100%] == macOS @@ -218,10 +219,10 @@ image::u128_graphs/windows/x64_relative_performance.png[x64 Relative Performance |=== //// -image::u128_graphs/macos/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] +image::macos/ARM64_benchmarks.png[ARM64 Benchmark Results, width=100%] //// -image::u128_graphs/macos/ARM64_relative_performance.png[ARM64 Relative Performance, width=100%] +image::macos/ARM64_relative_performance.png[ARM64 Relative Performance, width=100%] === x86_64 @@ -238,7 +239,7 @@ image::u128_graphs/macos/ARM64_relative_performance.png[ARM64 Relative Performan |=== //// -image::u128_graphs/macos/x64_benchmarks.png[x64 Benchmark Results, width=100%] +image::macos/x64_benchmarks.png[x64 Benchmark Results, width=100%] //// -image::u128_graphs/macos/x64_relative_performance.png[x64 Relative Performance, width=100%] +image::macos/x64_relative_performance.png[x64 Relative Performance, width=100%] From e71ea58da56a14c78af95e378ea6dbdea04ba3dd Mon Sep 17 00:00:00 2001 From: Matt Borland Date: Thu, 5 Jun 2025 14:22:08 -0400 Subject: [PATCH 13/20] Fix missing annotation for baseline and add x64 mac data --- .gitignore | 1 + doc/i128_graphs/linux/ARM64_benchmarks.png | Bin 366714 -> 373326 bytes .../linux/ARM64_relative_performance.png | Bin 180316 -> 187891 bytes doc/i128_graphs/linux/ppc64le_benchmarks.png | Bin 370216 -> 377340 bytes .../linux/ppc64le_relative_performance.png | Bin 186872 -> 193815 bytes doc/i128_graphs/linux/s390x_benchmarks.png | Bin 383364 -> 390831 bytes .../linux/s390x_relative_performance.png | Bin 195228 -> 203834 bytes doc/i128_graphs/linux/x64_benchmarks.png | Bin 366500 -> 372503 bytes .../linux/x64_relative_performance.png | Bin 181427 -> 188441 bytes doc/i128_graphs/macos/x64_benchmarks.png | Bin 0 -> 374866 bytes .../macos/x64_relative_performance.png | Bin 0 -> 183696 bytes doc/int128/i128_benchmarks.adoc | 16 ++++---- doc/int128/u128_benchmarks.adoc | 4 +- doc/signed_plots.py | 36 +++++++++++------- 14 files changed, 34 insertions(+), 23 deletions(-) create mode 100644 doc/i128_graphs/macos/x64_benchmarks.png create mode 100644 doc/i128_graphs/macos/x64_relative_performance.png diff --git a/.gitignore b/.gitignore index edfa67a6..5dd63832 100644 --- a/.gitignore +++ b/.gitignore @@ -32,3 +32,4 @@ *.app *.DS_Store +build/ diff --git a/doc/i128_graphs/linux/ARM64_benchmarks.png b/doc/i128_graphs/linux/ARM64_benchmarks.png index 69fe887e3deac8a8e004217796064dbf500cd8e1..5fde46526bc04e98694217d3ffd1d61bdb26aa9c 100644 GIT binary patch literal 373326 zcmeEu^;=YH`|p6oCRCJ?6i|_&L4S`JVT?_jP{x{sU)S*S>HM6KmFbp8NjPjh~8=0tG2ODGG(6xO+!d4Sp=4P-LG- zPQoLnKRSGbAHoiD4;|EPOdOmZ+Zm%2A3Hp=vT?97H@xU*Y-ew7^YjLe?7aSWsgGfvLpWyIVVdxqKHtayRy<4=ji$2Qy-|X 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