tinygraph · daniel-j-h · Aug 7, 2021
diff --git a/tinygraph/tinygraph-align.c b/tinygraph/tinygraph-align.c
@@ -0,0 +1,18 @@
+#define _POSIX_C_SOURCE 200809L
+#include <stdlib.h>
+
+
+void* tinygraph_align_malloc(size_t alignment, size_t size) {
+  void *p;
+
+  if (posix_memalign(&p, alignment, size) != 0) {
+    return NULL;
+  }
+
+  return p;
+}
+
+
+void tinygraph_align_free(void *p) {
+  free(p);
+}
diff --git a/tinygraph/tinygraph-align.h b/tinygraph/tinygraph-align.h
@@ -0,0 +1,17 @@
+#ifndef TINYGRAPH_ALIGN_H
+#define TINYGRAPH_ALIGN_H
+
+#include <stdint.h>
+
+#include "tinygraph-utils.h"
+
+
+#define TINYGRAPH_ALIGN(x) __attribute__((aligned(x)))
+
+TINYGRAPH_WARN_UNUSED
+void* tinygraph_align_malloc(size_t alignment, size_t size);
+
+void tinygraph_align_free(void *p);
+
+
+#endif
diff --git a/tinygraph/tinygraph-bitset.c b/tinygraph/tinygraph-bitset.c
@@ -107,10 +107,19 @@ bool tinygraph_bitset_get_at(tinygraph_bitset *bitset, uint64_t i) {
 
 
 uint64_t tinygraph_bitset_get_size(tinygraph_bitset_s bitset) {
+  TINYGRAPH_ASSERT(bitset);
+
   return bitset->size;
 }
 
 
+uint64_t* tinygraph_bitset_get_data(tinygraph_bitset_s bitset) {
+  TINYGRAPH_ASSERT(bitset);
+
+  return bitset->blocks;
+}
+
+
 void tinygraph_bitset_clear(tinygraph_bitset_s bitset) {
   TINYGRAPH_ASSERT(bitset);
 

diff --git a/tinygraph/tinygraph-bitset.h b/tinygraph/tinygraph-bitset.h
@@ -33,6 +33,9 @@ bool tinygraph_bitset_get_at(tinygraph_bitset_s bitset, uint64_t i);
 TINYGRAPH_WARN_UNUSED
 uint64_t tinygraph_bitset_get_size(tinygraph_bitset_s bitset);
 
+TINYGRAPH_WARN_UNUSED
+uint64_t* tinygraph_bitset_get_data(tinygraph_bitset_s bitset);
+
 void tinygraph_bitset_clear(tinygraph_bitset_s bitset);
 
 void tinygraph_bitset_not(tinygraph_bitset_s bitset);

diff --git a/tinygraph/tinygraph-poppy.c b/tinygraph/tinygraph-poppy.c
@@ -0,0 +1,138 @@
+#include <math.h>
+#include <string.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <stdio.h>
+
+#include "tinygraph-bits.h"
+#include "tinygraph-align.h"
+#include "tinygraph-poppy.h"
+
+
+typedef struct tinygraph_poppy_rank {
+  uint64_t *level0;
+  uint64_t level0_len;
+
+  tinygraph_bitset_s bitset_view;
+} tinygraph_poppy_rank;
+
+
+tinygraph_poppy_rank* tinygraph_poppy_rank_construct(tinygraph_bitset_s bitset) {
+  TINYGRAPH_ASSERT(bitset);
+
+  tinygraph_poppy_rank *out = malloc(sizeof(tinygraph_poppy_rank));
+
+  if (!out) {
+    return NULL;
+  }
+
+  // It's important that we align the index structures at
+  // the cache line boundary, which is 64 bytes nowadays
+  const uint32_t cacheline = 64;
+
+  const uint64_t *bits = tinygraph_bitset_get_data(bitset);
+  const uint64_t nbits = tinygraph_bitset_get_size(bitset);
+
+  // 512 bits basic blocks for now
+  const uint64_t level0_len = nbits / 512;
+
+  if (level0_len == 0) {
+    *out = (tinygraph_poppy_rank){
+      .level0 = NULL,
+      .level0_len = 0,
+      .bitset_view = bitset,
+    };
+
+    return out;
+  }
+
+  // TODO: implement optimizations to get 12.5% down to 3.2%
+  // At the moment we only implement Fig. 3 from the paper
+
+  uint64_t *level0 = tinygraph_align_malloc(cacheline, level0_len);
+
+  if (!level0) {
+    free(out);
+
+    return NULL;
+  }
+
+  memset(level0, 0, level0_len);
+
+  uint64_t csum = 0;
+
+  for (uint64_t i = 0; i < level0_len; ++i) {
+    csum += tinygraph_bits_count(bits[i * 8 + 0]);
+    csum += tinygraph_bits_count(bits[i * 8 + 1]);
+    csum += tinygraph_bits_count(bits[i * 8 + 2]);
+    csum += tinygraph_bits_count(bits[i * 8 + 3]);
+    csum += tinygraph_bits_count(bits[i * 8 + 4]);
+    csum += tinygraph_bits_count(bits[i * 8 + 5]);
+    csum += tinygraph_bits_count(bits[i * 8 + 6]);
+    csum += tinygraph_bits_count(bits[i * 8 + 7]);
+
+    level0[i] = csum;
+  }
+
+  *out = (tinygraph_poppy_rank){
+    .level0 = level0,
+    .level0_len = level0_len,
+    .bitset_view = bitset,
+  };
+
+  return out;
+}
+
+
+void tinygraph_poppy_rank_destruct(tinygraph_poppy_rank *rank) {
+  if (!rank) {
+    return;
+  }
+
+  TINYGRAPH_ASSERT(rank->level0);
+
+  tinygraph_align_free(rank->level0);
+
+  rank->level0 = NULL;
+
+  free(rank);
+}
+
+
+uint64_t tinygraph_poppy_rank_get(tinygraph_poppy_rank_s rank, uint64_t n) {
+  TINYGRAPH_ASSERT(rank);
+  TINYGRAPH_ASSERT(n < tinygraph_bitset_get_size(rank->bitset_view));
+
+  const uint64_t block = n / 512;
+
+  TINYGRAPH_ASSERT(block <= rank->level0_len);
+
+  // pre-computed cumulative sums from index
+  const uint64_t leftof = block > 0 ? rank->level0[block - 1] : 0;
+
+  // bits within last block we need to count
+  const uint64_t *bits = tinygraph_bitset_get_data(rank->bitset_view);
+
+  uint64_t count = 0;
+
+  for (uint64_t i = block * 8; i < block * 8 + ((n % 512) / 64); ++i) {
+    count += tinygraph_bits_count(bits[i]);
+  }
+
+  count += tinygraph_bits_rank(bits[block * 8 + ((n % 512) / 64)], (n % 512) % 64);
+
+  return leftof + count;
+}
+
+
+void tinygraph_poppy_rank_print_internal(tinygraph_poppy_rank_s rank) {
+  TINYGRAPH_ASSERT(rank);
+
+  fprintf(stderr, "poppy rank internals\n");
+
+  for (uint64_t i = 0; i < rank->level0_len; ++i) {
+    fprintf(stderr, " %ju", (uintmax_t)rank->level0[i]);
+  }
+
+  fprintf(stderr, "\n");
+}
diff --git a/tinygraph/tinygraph-poppy.h b/tinygraph/tinygraph-poppy.h
@@ -0,0 +1,35 @@
+#ifndef TINYGRAPH_POPPY_H
+#define TINYGRAPH_POPPY_H
+
+#include "tinygraph-bitset.h"
+#include "tinygraph-utils.h"
+
+/*
+ * The Poppy Rank/Select data structures from the paper
+ *
+ *  "Space-Efficient, High-Performance Rank & Select
+ *   Structures on Uncompressed Bit Sequences"
+ *
+ * with space-overhead 3.2% (rank) and 0.39% (select)
+ *
+ * See
+ * - https://www.cs.cmu.edu/~dga/papers/zhou-sea2013.pdf
+ */
+
+
+typedef struct tinygraph_poppy_rank* tinygraph_poppy_rank_s;
+
+
+TINYGRAPH_WARN_UNUSED
+tinygraph_poppy_rank_s tinygraph_poppy_rank_construct(tinygraph_bitset_s bitset);
+
+void tinygraph_poppy_rank_destruct(tinygraph_poppy_rank_s rank);
+
+TINYGRAPH_WARN_UNUSED
+uint64_t tinygraph_poppy_rank_get(tinygraph_poppy_rank_s rank, uint64_t n);
+
+void tinygraph_poppy_rank_print_internal(tinygraph_poppy_rank_s rank);
+
+
+
+#endif
diff --git a/tinygraph/tinygraph-tests.c b/tinygraph/tinygraph-tests.c
@@ -13,6 +13,7 @@
 #include "tinygraph-zigzag.h"
 #include "tinygraph-zorder.h"
 #include "tinygraph-bits.h"
+#include "tinygraph-poppy.h"
 #include "tinygraph-eliasfano.h"
 
 
@@ -569,8 +570,6 @@ void test18() {
 
   tinygraph_bitset_s bits = tinygraph_eliasfano_encode(data, 5);
 
-  tinygraph_bitset_print_internal(bits);
-
   tinygraph_bitset_destruct(bits);
 }
 
@@ -647,6 +646,30 @@ void test21() {
 }
 
 
+void test22() {
+  tinygraph_bitset_s bits = tinygraph_bitset_construct(1098);
+
+  tinygraph_bitset_set_at(bits, 0);
+  tinygraph_bitset_set_at(bits, 512);
+  tinygraph_bitset_set_at(bits, 1097);
+
+  tinygraph_bitset_print_internal(bits);
+
+  tinygraph_poppy_rank_s rank = tinygraph_poppy_rank_construct(bits);
+
+  tinygraph_poppy_rank_print_internal(rank);
+
+  fprintf(stderr, "%ju\n", tinygraph_poppy_rank_get(rank, 0));
+  fprintf(stderr, "%ju\n", tinygraph_poppy_rank_get(rank, 1));
+  fprintf(stderr, "%ju\n", tinygraph_poppy_rank_get(rank, 511));
+  fprintf(stderr, "%ju\n", tinygraph_poppy_rank_get(rank, 512));
+  fprintf(stderr, "%ju\n", tinygraph_poppy_rank_get(rank, 513));
+  fprintf(stderr, "%ju\n", tinygraph_poppy_rank_get(rank, 1095));
+  fprintf(stderr, "%ju\n", tinygraph_poppy_rank_get(rank, 1096));
+  fprintf(stderr, "%ju\n", tinygraph_poppy_rank_get(rank, 1097));
+}
+
+
 int main() {
   test1();
   test2();
@@ -669,4 +692,5 @@ int main() {
   test19();
   test20();
   test21();
+  test22();
 }