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Diffstat (limited to 'src/false_positives.h')
| -rw-r--r-- | src/false_positives.h | 110 |
1 files changed, 110 insertions, 0 deletions
diff --git a/src/false_positives.h b/src/false_positives.h new file mode 100644 index 0000000000..44ebb3e94c --- /dev/null +++ b/src/false_positives.h @@ -0,0 +1,110 @@ +/********************************************************************** + * Copyright (c) 2020 Pieter Wuille, Greg Maxwell, Gleb Naumenko * + * Distributed under the MIT software license, see the accompanying * + * file LICENSE or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef _MINISKETCH_FALSE_POSITIVES_H_ +#define _MINISKETCH_FALSE_POSITIVES_H_ + +#include "util.h" + +#include "int_utils.h" + +#include <stdint.h> + +namespace { + +/** Compute floor(log2(x!)), exactly up to x=57; an underestimate up to x=2^32-1. */ +uint64_t Log2Factorial(uint32_t x) { + //! Values of floor(106*log2(1 + i/32)) for i=0..31 + static constexpr uint8_t T[32] = { + 0, 4, 9, 13, 18, 22, 26, 30, 34, 37, 41, 45, 48, 52, 55, 58, 62, 65, 68, + 71, 74, 77, 80, 82, 85, 88, 90, 93, 96, 98, 101, 103 + }; + int bits = CountBits(x, 32); + // Compute an (under)estimate of floor(106*log2(x)). + // This works by relying on floor(log2(x)) = countbits(x)-1, and adding + // precision using the top 6 bits of x (the highest one of which is always + // one). + unsigned l2_106 = 106 * (bits - 1) + T[((x << (32 - bits)) >> 26) & 31]; + // Based on Stirling approximation for log2(x!): + // log2(x!) = log(x!) / log(2) + // = ((x + 1/2) * log(x) - x + log(2*pi)/2 + ...) / log(2) + // = (x + 1/2) * log2(x) - x/log(2) + log2(2*pi)/2 + ... + // = 1/2*(2*x+1)*log2(x) - (1/log(2))*x + log2(2*pi)/2 + ... + // = 1/212*(2*x+1)*(106*log2(x)) + (-1/log(2))*x + log2(2*pi)/2 + ... + // where 418079/88632748 is exactly 1/212 + // -127870026/88632748 is slightly less than -1/log(2) + // 117504694/88632748 is less than log2(2*pi)/2 + // A correction term is only needed for x < 3. + // + // See doc/log2_factorial.sage for how these constants were obtained. + return (418079 * (2 * uint64_t{x} + 1) * l2_106 - 127870026 * uint64_t{x} + 117504694 + 88632748 * (x < 3)) / 88632748; +} + +/** Compute floor(log2(2^(bits * capacity) / sum((2^bits - 1) choose k, k=0..capacity))), for bits>1 + * + * See doc/gen_basefpbits.sage for how the tables were obtained. */ +uint64_t BaseFPBits(uint32_t bits, uint32_t capacity) { + // Correction table for low bits/capacities + 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}; + 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}; + 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}; + 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}; + 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}; + + if (capacity == 0) return 0; + uint64_t ret = 0; + if (bits < 32 && capacity >= (1U << bits)) { + ret = uint64_t{bits} * (capacity - (1U << bits) + 1); + capacity = (1U << bits) - 1; + } + ret += Log2Factorial(capacity); + switch (bits) { + case 2: return ret + (capacity <= 2 ? 0 : 1); + case 3: return ret + (capacity <= 2 ? 0 : (0x2a5 >> 2 * (capacity - 3)) & 3); + case 4: return ret + (capacity <= 3 ? 0 : (0xb6d91a449 >> 3 * (capacity - 4)) & 7); + case 5: return ret + (capacity <= 4 ? 0 : ADD5[capacity - 5]); + case 6: return ret + (capacity <= 4 ? 0 : capacity > 54 ? 25 : ADD6[capacity - 5]); + case 7: return ret + (capacity <= 4 ? 0 : capacity > 57 ? 21 : ADD7[capacity - 5]); + case 8: return ret + (capacity <= 9 ? 0 : capacity > 56 ? 10 : ADD8[capacity - 10]); + case 9: return ret + (capacity <= 11 ? 0 : capacity > 54 ? 5 : ADD9[capacity - 12]); + case 10: return ret + (capacity <= 21 ? 0 : capacity > 50 ? 2 : (0x1a6665545555041 >> 2 * (capacity - 22)) & 3); + case 11: return ret + (capacity <= 21 ? 0 : capacity > 45 ? 1 : (0x5b3dc1 >> (capacity - 22)) & 1); + case 12: return ret + (capacity <= 21 ? 0 : capacity > 57 ? 0 : (0xe65522041 >> (capacity - 22)) & 1); + case 13: return ret + (capacity <= 27 ? 0 : capacity > 55 ? 0 : (0x8904081 >> (capacity - 28)) & 1); + case 14: return ret + (capacity <= 47 ? 0 : capacity > 48 ? 0 : 1); + default: return ret; + } +} + +size_t ComputeCapacity(uint32_t bits, size_t max_elements, uint32_t fpbits) { + if (bits == 0) return 0; + uint64_t base_fpbits = BaseFPBits(bits, max_elements); + // The fpbits provided by the base max_elements==capacity case are sufficient. + if (base_fpbits >= fpbits) return max_elements; + // Otherwise, increment capacity by ceil(fpbits / bits) beyond that. + return max_elements + (fpbits - base_fpbits + bits - 1) / bits; +} + +size_t ComputeMaxElements(uint32_t bits, size_t capacity, uint32_t fpbits) { + if (bits == 0) return 0; + // Start with max_elements=capacity, and decrease max_elements until the corresponding capacity is capacity. + size_t max_elements = capacity; + while (true) { + size_t capacity_for_max_elements = ComputeCapacity(bits, max_elements, fpbits); + CHECK_SAFE(capacity_for_max_elements >= capacity); + if (capacity_for_max_elements <= capacity) return max_elements; + size_t adjust = capacity_for_max_elements - capacity; + // Decrementing max_elements by N will at most decrement the corresponding capacity by N. + // As the observed capacity is adjust too high, we can safely decrease max_elements by adjust. + // If that brings us into negative max_elements territory, no solution exists and we return 0. + if (max_elements < adjust) return 0; + max_elements -= adjust; + } +} + +} // namespace + +#endif |