Bitcoin Core  27.99.0 P2P Digital Currency
false_positives.h
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1 /**********************************************************************
2  * Copyright (c) 2020 Pieter Wuille, Greg Maxwell, Gleb Naumenko *
3  * Distributed under the MIT software license, see the accompanying *
5  **********************************************************************/
6
7 #ifndef _MINISKETCH_FALSE_POSITIVES_H_
8 #define _MINISKETCH_FALSE_POSITIVES_H_
9
10 #include "util.h"
11
12 #include "int_utils.h"
13
14 #include <stdint.h>
15
16 namespace {
17
19 uint64_t Log2Factorial(uint32_t x) {
21  static constexpr uint8_t T[32] = {
22  0, 4, 9, 13, 18, 22, 26, 30, 34, 37, 41, 45, 48, 52, 55, 58, 62, 65, 68,
23  71, 74, 77, 80, 82, 85, 88, 90, 93, 96, 98, 101, 103
24  };
25  int bits = CountBits(x, 32);
26  // Compute an (under)estimate of floor(106*log2(x)).
27  // This works by relying on floor(log2(x)) = countbits(x)-1, and adding
28  // precision using the top 6 bits of x (the highest one of which is always
29  // one).
30  unsigned l2_106 = 106 * (bits - 1) + T[((x << (32 - bits)) >> 26) & 31];
31  // Based on Stirling approximation for log2(x!):
32  // log2(x!) = log(x!) / log(2)
33  // = ((x + 1/2) * log(x) - x + log(2*pi)/2 + ...) / log(2)
34  // = (x + 1/2) * log2(x) - x/log(2) + log2(2*pi)/2 + ...
35  // = 1/2*(2*x+1)*log2(x) - (1/log(2))*x + log2(2*pi)/2 + ...
36  // = 1/212*(2*x+1)*(106*log2(x)) + (-1/log(2))*x + log2(2*pi)/2 + ...
37  // where 418079/88632748 is exactly 1/212
38  // -127870026/88632748 is slightly less than -1/log(2)
39  // 117504694/88632748 is less than log2(2*pi)/2
40  // A correction term is only needed for x < 3.
41  //
42  // See doc/log2_factorial.sage for how these constants were obtained.
43  return (418079 * (2 * uint64_t{x} + 1) * l2_106 - 127870026 * uint64_t{x} + 117504694 + 88632748 * (x < 3)) / 88632748;
44 }
45
49 uint64_t BaseFPBits(uint32_t bits, uint32_t capacity) {
50  // Correction table for low bits/capacities
51  static constexpr uint8_t ADD5[] = {1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12};
52  static constexpr uint8_t ADD6[] = {1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 10, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 20, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 24};
53  static constexpr uint8_t ADD7[] = {1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 7, 8, 9, 9, 9, 10, 11, 11, 12, 12, 13, 13, 15, 15, 15, 16, 17, 17, 18, 19, 20, 20};
54  static constexpr uint8_t ADD8[] = {1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 3, 4, 4, 5, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9};
55  static constexpr uint8_t ADD9[] = {1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 3, 4, 4, 4, 4};
56
57  if (capacity == 0) return 0;
58  uint64_t ret = 0;
59  if (bits < 32 && capacity >= (1U << bits)) {
60  ret = uint64_t{bits} * (capacity - (1U << bits) + 1);
61  capacity = (1U << bits) - 1;
62  }
63  ret += Log2Factorial(capacity);
64  switch (bits) {
65  case 2: return ret + (capacity <= 2 ? 0 : 1);
66  case 3: return ret + (capacity <= 2 ? 0 : (0x2a5 >> 2 * (capacity - 3)) & 3);
67  case 4: return ret + (capacity <= 3 ? 0 : (0xb6d91a449 >> 3 * (capacity - 4)) & 7);
68  case 5: return ret + (capacity <= 4 ? 0 : ADD5[capacity - 5]);
69  case 6: return ret + (capacity <= 4 ? 0 : capacity > 54 ? 25 : ADD6[capacity - 5]);
70  case 7: return ret + (capacity <= 4 ? 0 : capacity > 57 ? 21 : ADD7[capacity - 5]);
71  case 8: return ret + (capacity <= 9 ? 0 : capacity > 56 ? 10 : ADD8[capacity - 10]);
72  case 9: return ret + (capacity <= 11 ? 0 : capacity > 54 ? 5 : ADD9[capacity - 12]);
73  case 10: return ret + (capacity <= 21 ? 0 : capacity > 50 ? 2 : (0x1a6665545555041 >> 2 * (capacity - 22)) & 3);
74  case 11: return ret + (capacity <= 21 ? 0 : capacity > 45 ? 1 : (0x5b3dc1 >> (capacity - 22)) & 1);
75  case 12: return ret + (capacity <= 21 ? 0 : capacity > 57 ? 0 : (0xe65522041 >> (capacity - 22)) & 1);
76  case 13: return ret + (capacity <= 27 ? 0 : capacity > 55 ? 0 : (0x8904081 >> (capacity - 28)) & 1);
77  case 14: return ret + (capacity <= 47 ? 0 : capacity > 48 ? 0 : 1);
78  default: return ret;
79  }
80 }
81
82 size_t ComputeCapacity(uint32_t bits, size_t max_elements, uint32_t fpbits) {
83  if (bits == 0) return 0;
84  if (max_elements > 0xffffffff) return max_elements;
85  uint64_t base_fpbits = BaseFPBits(bits, static_cast<uint32_t>(max_elements));
86  // The fpbits provided by the base max_elements==capacity case are sufficient.
87  if (base_fpbits >= fpbits) return max_elements;
88  // Otherwise, increment capacity by ceil(fpbits / bits) beyond that.
89  return max_elements + (fpbits - base_fpbits + bits - 1) / bits;
90 }
91
92 size_t ComputeMaxElements(uint32_t bits, size_t capacity, uint32_t fpbits) {
93  if (bits == 0) return 0;
94  if (capacity > 0xffffffff) return capacity;
95  // Start with max_elements=capacity, and decrease max_elements until the corresponding capacity is capacity.
96  size_t max_elements = capacity;
97  while (true) {
98  size_t capacity_for_max_elements = ComputeCapacity(bits, max_elements, fpbits);
99  CHECK_SAFE(capacity_for_max_elements >= capacity);
100  if (capacity_for_max_elements <= capacity) return max_elements;
101  size_t adjust = capacity_for_max_elements - capacity;
102  // Decrementing max_elements by N will at most decrement the corresponding capacity by N.
103  // As the observed capacity is adjust too high, we can safely decrease max_elements by adjust.
104  // If that brings us into negative max_elements territory, no solution exists and we return 0.
105  if (max_elements < adjust) return 0;
106  max_elements -= adjust;
107  }
108 }
109
110 } // namespace
111
112 #endif
int ret
#define T(expected, seed, data)
static int CountBits(I val, int max)
Compute the smallest power of two that is larger than val.
Definition: int_utils.h:146
#define CHECK_SAFE(cond)
Check macro that does nothing in normal non-verify builds but crashes in verify builds.
Definition: util.h:50