GH-45201: [C++][Parquet] Improve performance of generating size statistics (#45202)

### Rationale for this change

We found out in #45085 that there is a non-trivial overhead when writing size statistics is enabled.

### What changes are included in this PR?

Dramatically reduce overhead by speeding up def/rep levels histogram updates.

Performance results on the author's machine:
```
------------------------------------------------------------------------------------------------------------------------------------------------
Benchmark                                                                                      Time             CPU   Iterations UserCounters...
------------------------------------------------------------------------------------------------------------------------------------------------
BM_WritePrimitiveColumn<SizeStatisticsLevel::None, ::arrow::Int64Type>                   8103053 ns      8098569 ns           86 bytes_per_second=1003.26Mi/s items_per_second=129.477M/s output_size=537.472k page_index_size=33
BM_WritePrimitiveColumn<SizeStatisticsLevel::ColumnChunk, ::arrow::Int64Type>            8153499 ns      8148492 ns           86 bytes_per_second=997.117Mi/s items_per_second=128.683M/s output_size=537.488k page_index_size=33
BM_WritePrimitiveColumn<SizeStatisticsLevel::PageAndColumnChunk, ::arrow::Int64Type>     8212560 ns      8207754 ns           83 bytes_per_second=989.918Mi/s items_per_second=127.754M/s output_size=537.502k page_index_size=47

BM_WritePrimitiveColumn<SizeStatisticsLevel::None, ::arrow::StringType>                 10405020 ns     10400775 ns           67 bytes_per_second=444.142Mi/s items_per_second=100.817M/s output_size=848.305k page_index_size=34
BM_WritePrimitiveColumn<SizeStatisticsLevel::ColumnChunk, ::arrow::StringType>          10464784 ns     10460778 ns           66 bytes_per_second=441.594Mi/s items_per_second=100.239M/s output_size=848.325k page_index_size=34
BM_WritePrimitiveColumn<SizeStatisticsLevel::PageAndColumnChunk, ::arrow::StringType>   10469832 ns     10465739 ns           67 bytes_per_second=441.385Mi/s items_per_second=100.191M/s output_size=848.344k page_index_size=48

BM_WriteListColumn<SizeStatisticsLevel::None, ::arrow::Int64Type>                       13004962 ns     12992678 ns           52 bytes_per_second=657.101Mi/s items_per_second=80.7052M/s output_size=617.464k page_index_size=34
BM_WriteListColumn<SizeStatisticsLevel::ColumnChunk, ::arrow::Int64Type>                13718352 ns     13705599 ns           50 bytes_per_second=622.921Mi/s items_per_second=76.5071M/s output_size=617.486k page_index_size=34
BM_WriteListColumn<SizeStatisticsLevel::PageAndColumnChunk, ::arrow::Int64Type>         13845553 ns     13832138 ns           52 bytes_per_second=617.222Mi/s items_per_second=75.8072M/s output_size=617.506k page_index_size=54

BM_WriteListColumn<SizeStatisticsLevel::None, ::arrow::StringType>                      15715263 ns     15702707 ns           44 bytes_per_second=320.449Mi/s items_per_second=66.7768M/s output_size=927.326k page_index_size=35
BM_WriteListColumn<SizeStatisticsLevel::ColumnChunk, ::arrow::StringType>               16507328 ns     16493800 ns           43 bytes_per_second=305.079Mi/s items_per_second=63.5739M/s output_size=927.352k page_index_size=35
BM_WriteListColumn<SizeStatisticsLevel::PageAndColumnChunk, ::arrow::StringType>        16575359 ns     16561311 ns           42 bytes_per_second=303.836Mi/s items_per_second=63.3148M/s output_size=927.377k page_index_size=55
```

Performance results without this PR:
```
------------------------------------------------------------------------------------------------------------------------------------------------
Benchmark                                                                                      Time             CPU   Iterations UserCounters...
------------------------------------------------------------------------------------------------------------------------------------------------
BM_WritePrimitiveColumn<SizeStatisticsLevel::None, ::arrow::Int64Type>                   8042576 ns      8037678 ns           87 bytes_per_second=1010.86Mi/s items_per_second=130.458M/s output_size=537.472k page_index_size=33
BM_WritePrimitiveColumn<SizeStatisticsLevel::ColumnChunk, ::arrow::Int64Type>            9576627 ns      9571279 ns           73 bytes_per_second=848.894Mi/s items_per_second=109.554M/s output_size=537.488k page_index_size=33
BM_WritePrimitiveColumn<SizeStatisticsLevel::PageAndColumnChunk, ::arrow::Int64Type>     9570204 ns      9563595 ns           73 bytes_per_second=849.576Mi/s items_per_second=109.642M/s output_size=537.502k page_index_size=47

BM_WritePrimitiveColumn<SizeStatisticsLevel::None, ::arrow::StringType>                 10165397 ns     10160868 ns           69 bytes_per_second=454.628Mi/s items_per_second=103.197M/s output_size=848.305k page_index_size=34
BM_WritePrimitiveColumn<SizeStatisticsLevel::ColumnChunk, ::arrow::StringType>          11662568 ns     11657396 ns           60 bytes_per_second=396.265Mi/s items_per_second=89.9494M/s output_size=848.325k page_index_size=34
BM_WritePrimitiveColumn<SizeStatisticsLevel::PageAndColumnChunk, ::arrow::StringType>   11657135 ns     11653063 ns           60 bytes_per_second=396.412Mi/s items_per_second=89.9829M/s output_size=848.344k page_index_size=48

BM_WriteListColumn<SizeStatisticsLevel::None, ::arrow::Int64Type>                       13182006 ns     13168704 ns           51 bytes_per_second=648.318Mi/s items_per_second=79.6264M/s output_size=617.464k page_index_size=34
BM_WriteListColumn<SizeStatisticsLevel::ColumnChunk, ::arrow::Int64Type>                16438205 ns     16421762 ns           43 bytes_per_second=519.89Mi/s items_per_second=63.8528M/s output_size=617.486k page_index_size=34
BM_WriteListColumn<SizeStatisticsLevel::PageAndColumnChunk, ::arrow::Int64Type>         16424615 ns     16409032 ns           42 bytes_per_second=520.293Mi/s items_per_second=63.9024M/s output_size=617.506k page_index_size=54

BM_WriteListColumn<SizeStatisticsLevel::None, ::arrow::StringType>                      15387808 ns     15373086 ns           46 bytes_per_second=327.32Mi/s items_per_second=68.2086M/s output_size=927.326k page_index_size=35
BM_WriteListColumn<SizeStatisticsLevel::ColumnChunk, ::arrow::StringType>               18319628 ns     18302938 ns           37 bytes_per_second=274.924Mi/s items_per_second=57.29M/s output_size=927.352k page_index_size=35
BM_WriteListColumn<SizeStatisticsLevel::PageAndColumnChunk, ::arrow::StringType>        18346665 ns     18329336 ns           37 bytes_per_second=274.528Mi/s items_per_second=57.2075M/s output_size=927.377k page_index_size=55
```

### Are these changes tested?

Tested by existing tests, validated by existing benchmarks.

### Are there any user-facing changes?

No.

* GitHub Issue: #45201

Authored-by: Antoine Pitrou <[email protected]>
Signed-off-by: Antoine Pitrou <[email protected]>

Author: pitrou

cpp/src/parquet/column_writer.cc

@@ -1468,42 +1468,43 @@ class TypedColumnWriterImpl : public ColumnWriterImpl, public TypedColumnWriter<
   // which case we call back to the dense write path)
   std::shared_ptr<::arrow::Array> preserved_dictionary_;
 
-  int64_t WriteLevels(int64_t num_values, const int16_t* def_levels,
+  int64_t WriteLevels(int64_t num_levels, const int16_t* def_levels,
                       const int16_t* rep_levels) {
+    // Update histograms now, to maximize cache efficiency.
+    UpdateLevelHistogram(num_levels, def_levels, rep_levels);
+
     int64_t values_to_write = 0;
     // If the field is required and non-repeated, there are no definition levels
     if (descr_->max_definition_level() > 0) {
-      for (int64_t i = 0; i < num_values; ++i) {
+      for (int64_t i = 0; i < num_levels; ++i) {
         if (def_levels[i] == descr_->max_definition_level()) {
           ++values_to_write;
         }
       }
 
-      WriteDefinitionLevels(num_values, def_levels);
+      WriteDefinitionLevels(num_levels, def_levels);
     } else {
       // Required field, write all values
-      values_to_write = num_values;
+      values_to_write = num_levels;
     }
 
     // Not present for non-repeated fields
     if (descr_->max_repetition_level() > 0) {
       // A row could include more than one value
       // Count the occasions where we start a new row
-      for (int64_t i = 0; i < num_values; ++i) {
+      for (int64_t i = 0; i < num_levels; ++i) {
         if (rep_levels[i] == 0) {
           rows_written_++;
           num_buffered_rows_++;
         }
       }
 
-      WriteRepetitionLevels(num_values, rep_levels);
+      WriteRepetitionLevels(num_levels, rep_levels);
     } else {
       // Each value is exactly one row
-      rows_written_ += num_values;
-      num_buffered_rows_ += num_values;
+      rows_written_ += num_levels;
+      num_buffered_rows_ += num_levels;
     }
-
-    UpdateLevelHistogram(num_values, def_levels, rep_levels);
     return values_to_write;
   }
 
@@ -1575,6 +1576,9 @@ class TypedColumnWriterImpl : public ColumnWriterImpl, public TypedColumnWriter<
 
   void WriteLevelsSpaced(int64_t num_levels, const int16_t* def_levels,
                          const int16_t* rep_levels) {
+    // Update histograms now, to maximize cache efficiency.
+    UpdateLevelHistogram(num_levels, def_levels, rep_levels);
+
     // If the field is required and non-repeated, there are no definition levels
     if (descr_->max_definition_level() > 0) {
       WriteDefinitionLevels(num_levels, def_levels);
@@ -1595,8 +1599,6 @@ class TypedColumnWriterImpl : public ColumnWriterImpl, public TypedColumnWriter<
       rows_written_ += num_levels;
       num_buffered_rows_ += num_levels;
     }
-
-    UpdateLevelHistogram(num_levels, def_levels, rep_levels);
   }
 
   void UpdateLevelHistogram(int64_t num_levels, const int16_t* def_levels,
@@ -1606,26 +1608,17 @@ class TypedColumnWriterImpl : public ColumnWriterImpl, public TypedColumnWriter<
     }
 
     auto add_levels = [](std::vector<int64_t>& level_histogram,
-                         ::arrow::util::span<const int16_t> levels) {
-      for (int16_t level : levels) {
-        ARROW_DCHECK_LT(level, static_cast<int16_t>(level_histogram.size()));
-        ++level_histogram[level];
-      }
+                         ::arrow::util::span<const int16_t> levels, int16_t max_level) {
+      ARROW_DCHECK_EQ(static_cast<size_t>(max_level) + 1, level_histogram.size());
+      ::parquet::UpdateLevelHistogram(levels, level_histogram);
     };
 
-    if (descr_->max_definition_level() > 0) {
-      add_levels(page_size_statistics_->definition_level_histogram,
-                 {def_levels, static_cast<size_t>(num_levels)});
-    } else {
-      page_size_statistics_->definition_level_histogram[0] += num_levels;
-    }
-
-    if (descr_->max_repetition_level() > 0) {
-      add_levels(page_size_statistics_->repetition_level_histogram,
-                 {rep_levels, static_cast<size_t>(num_levels)});
-    } else {
-      page_size_statistics_->repetition_level_histogram[0] += num_levels;
-    }
+    add_levels(page_size_statistics_->definition_level_histogram,
+               {def_levels, static_cast<size_t>(num_levels)},
+               descr_->max_definition_level());
+    add_levels(page_size_statistics_->repetition_level_histogram,
+               {rep_levels, static_cast<size_t>(num_levels)},
+               descr_->max_repetition_level());
   }
 
   // Update the unencoded data bytes for ByteArray only per the specification.

cpp/src/parquet/size_statistics.cc

@@ -18,13 +18,27 @@
 #include "parquet/size_statistics.h"
 
 #include <algorithm>
+#include <numeric>
+#include <ostream>
+#include <string_view>
 
 #include "arrow/util/logging.h"
 #include "parquet/exception.h"
 #include "parquet/schema.h"
 
 namespace parquet {
 
+namespace {
+
+void MergeLevelHistogram(::arrow::util::span<int64_t> histogram,
+                         ::arrow::util::span<const int64_t> other) {
+  ARROW_DCHECK_EQ(histogram.size(), other.size());
+  std::transform(histogram.begin(), histogram.end(), other.begin(), histogram.begin(),
+                 std::plus<>());
+}
+
+}  // namespace
+
 void SizeStatistics::Merge(const SizeStatistics& other) {
   if (repetition_level_histogram.size() != other.repetition_level_histogram.size()) {
     throw ParquetException("Repetition level histogram size mismatch");
@@ -36,12 +50,8 @@ void SizeStatistics::Merge(const SizeStatistics& other) {
       other.unencoded_byte_array_data_bytes.has_value()) {
     throw ParquetException("Unencoded byte array data bytes are not consistent");
   }
-  std::transform(repetition_level_histogram.begin(), repetition_level_histogram.end(),
-                 other.repetition_level_histogram.begin(),
-                 repetition_level_histogram.begin(), std::plus<>());
-  std::transform(definition_level_histogram.begin(), definition_level_histogram.end(),
-                 other.definition_level_histogram.begin(),
-                 definition_level_histogram.begin(), std::plus<>());
+  MergeLevelHistogram(repetition_level_histogram, other.repetition_level_histogram);
+  MergeLevelHistogram(definition_level_histogram, other.definition_level_histogram);
   if (unencoded_byte_array_data_bytes.has_value()) {
     unencoded_byte_array_data_bytes = unencoded_byte_array_data_bytes.value() +
                                       other.unencoded_byte_array_data_bytes.value();
@@ -91,4 +101,88 @@ std::unique_ptr<SizeStatistics> SizeStatistics::Make(const ColumnDescriptor* des
   return size_stats;
 }
 
+std::ostream& operator<<(std::ostream& os, const SizeStatistics& size_stats) {
+  constexpr std::string_view kComma = ", ";
+  os << "SizeStatistics{";
+  std::string_view sep = "";
+  if (size_stats.unencoded_byte_array_data_bytes.has_value()) {
+    os << "unencoded_byte_array_data_bytes="
+       << *size_stats.unencoded_byte_array_data_bytes;
+    sep = kComma;
+  }
+  auto print_histogram = [&](std::string_view name,
+                             const std::vector<int64_t>& histogram) {
+    if (!histogram.empty()) {
+      os << sep << name << "={";
+      sep = kComma;
+      std::string_view value_sep = "";
+      for (int64_t v : histogram) {
+        os << value_sep << v;
+        value_sep = kComma;
+      }
+      os << "}";
+    }
+  };
+  print_histogram("repetition_level_histogram", size_stats.repetition_level_histogram);
+  print_histogram("definition_level_histogram", size_stats.definition_level_histogram);
+  os << "}";
+  return os;
+}
+
+void UpdateLevelHistogram(::arrow::util::span<const int16_t> levels,
+                          ::arrow::util::span<int64_t> histogram) {
+  const int64_t num_levels = static_cast<int64_t>(levels.size());
+  DCHECK_GE(histogram.size(), 1);
+  const int16_t max_level = static_cast<int16_t>(histogram.size() - 1);
+  if (max_level == 0) {
+    histogram[0] += num_levels;
+    return;
+  }
+
+#ifndef NDEBUG
+  for (auto level : levels) {
+    ARROW_DCHECK_LE(level, max_level);
+  }
+#endif
+
+  if (max_level == 1) {
+    // Specialize the common case for non-repeated non-nested columns.
+    // Summing the levels gives us the number of 1s, and the number of 0s follows.
+    // We do repeated sums in the int16_t space, which the compiler is likely
+    // to vectorize efficiently.
+    constexpr int64_t kChunkSize = 1 << 14;  // to avoid int16_t overflows
+    int64_t hist1 = 0;
+    auto it = levels.begin();
+    while (it != levels.end()) {
+      const auto chunk_size = std::min<int64_t>(levels.end() - it, kChunkSize);
+      hist1 += std::accumulate(levels.begin(), levels.begin() + chunk_size, int16_t{0});
+      it += chunk_size;
+    }
+    histogram[0] += num_levels - hist1;
+    histogram[1] += hist1;
+    return;
+  }
+
+  // The generic implementation issues a series of histogram load-stores.
+  // However, it limits store-to-load dependencies by interleaving partial histogram
+  // updates.
+  constexpr int kUnroll = 4;
+  std::array<std::vector<int64_t>, kUnroll> partial_hist;
+  for (auto& hist : partial_hist) {
+    hist.assign(histogram.size(), 0);
+  }
+  int64_t i = 0;
+  for (; i <= num_levels - kUnroll; i += kUnroll) {
+    for (int j = 0; j < kUnroll; ++j) {
+      ++partial_hist[j][levels[i + j]];
+    }
+  }
+  for (; i < num_levels; ++i) {
+    ++partial_hist[0][levels[i]];
+  }
+  for (const auto& hist : partial_hist) {
+    MergeLevelHistogram(histogram, hist);
+  }
+}
+
 }  // namespace parquet

cpp/src/parquet/size_statistics.h

@@ -17,9 +17,12 @@
 
 #pragma once
 
+#include <cstdint>
+#include <iosfwd>
 #include <optional>
 #include <vector>
 
+#include "arrow/util/span.h"
 #include "parquet/platform.h"
 #include "parquet/type_fwd.h"
 
@@ -89,4 +92,11 @@ struct PARQUET_EXPORT SizeStatistics {
   static std::unique_ptr<SizeStatistics> Make(const ColumnDescriptor* descr);
 };
 
+PARQUET_EXPORT
+std::ostream& operator<<(std::ostream&, const SizeStatistics&);
+
+PARQUET_EXPORT
+void UpdateLevelHistogram(::arrow::util::span<const int16_t> levels,
+                          ::arrow::util::span<int64_t> histogram);
+
 }  // namespace parquet