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kmrns.h
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//
// Created by vout on 3/3/2018.
//
#ifndef KMLIB_RNS_H
#define KMLIB_RNS_H
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#if defined(__GNUC__) && defined(__aarch64__)
#define SIMDE_ENABLE_NATIVE_ALIASES
#include "../simde/x86/avx2.h"
#else
#include <x86intrin.h>
#endif
#include <vector>
namespace kmlib {
namespace internal {
template <unsigned BaseSize, unsigned Index, typename T>
struct SubPopcountMask {
static_assert(Index % BaseSize == 0, "");
static const T value =
(SubPopcountMask<BaseSize, Index - BaseSize, T>::value << BaseSize) |
1ULL;
};
template <unsigned BaseSize, typename T>
struct SubPopcountMask<BaseSize, 0, T> {
static const T value = 0;
};
template <unsigned BaseSize, typename T>
struct PopcountMask {
static const T value = SubPopcountMask<BaseSize, sizeof(T) * 8, T>::value;
};
template <unsigned BaseSize, typename T, unsigned Index = BaseSize / 2>
inline T PackToLowestBit(T value) {
if (Index == 0) {
return value;
}
value &= value >> Index;
return PackToLowestBit<BaseSize, T, Index / 2>(value);
}
using U = unsigned int;
using UL = unsigned long int;
using ULL = unsigned long long int;
#define CHECK_TYPE(T) \
static_assert(std::is_integral<T>::value, \
"only integral types are supported by popcount"); \
static_assert(sizeof(T) <= sizeof(ULL), \
"size bigger than unsigned long long not supported"); \
static_assert(!std::is_same<T, bool>::value, "bool type not supported")
template <typename T>
inline unsigned Popcount(T val) {
CHECK_TYPE(T);
return sizeof(T) <= sizeof(U)
? __builtin_popcount(val)
: sizeof(T) <= sizeof(UL)
? __builtin_popcountl(val)
: sizeof(T) <= sizeof(ULL) ? __builtin_popcountll(val) : 0;
}
template <typename T>
inline unsigned Ctz(T val) {
CHECK_TYPE(T);
return sizeof(T) <= sizeof(U)
? __builtin_ctz(val)
: sizeof(T) <= sizeof(UL)
? __builtin_ctzl(val)
: sizeof(T) <= sizeof(ULL) ? __builtin_ctzll(val) : 0;
}
template <typename Tx, typename Ty>
inline Tx Pdep(Tx x, Ty y) {
CHECK_TYPE(Tx);
return sizeof(Tx) <= sizeof(U)
? _pdep_u32(x, y)
: sizeof(Tx) <= sizeof(ULL) ? _pdep_u64(x, y) : 0;
}
#undef CHECK_TYPE
} // namespace internal
enum rnsmode { kRankOnly, kRandAndSelect };
template <unsigned BaseSize, unsigned AlphabetSize,
unsigned Mode = rnsmode::kRandAndSelect, typename TWord = uint64_t,
typename TInterval = uint32_t,
unsigned BasePerL2Interval = 65536 / BaseSize,
unsigned BasePerL1Interval = 1024 / BaseSize,
unsigned SelectSampleSize = 4096>
class RankAndSelect {
public:
static const unsigned kBitsPerByte = 8;
static const unsigned kBitsPerWord = sizeof(TWord) * kBitsPerByte;
static const unsigned kBitsPerBase = BaseSize;
static const unsigned kAlphabetSize = AlphabetSize;
static const unsigned kBasesPerL1 = BasePerL1Interval;
static const unsigned kBasesPerL2 = BasePerL2Interval;
static const unsigned kSelectSampleSize = SelectSampleSize;
static const unsigned kL1PerL2 = kBasesPerL2 / kBasesPerL1;
static const unsigned kBasesPerWord = kBitsPerWord / kBitsPerBase;
using size_type = int64_t;
using word_type = TWord;
static const size_type kNullID = static_cast<size_type>(-1);
RankAndSelect() {
for (unsigned i = kBitsPerBase == 1 ? 1 : 0; i < kAlphabetSize; ++i) {
xor_masks_[i] = 0;
for (unsigned j = 0; j < kBasesPerWord; ++j) {
xor_masks_[i] |= (word_type)i << (kBitsPerBase * j);
}
xor_masks_[i] = ~xor_masks_[i];
}
}
~RankAndSelect() = default;
void from_packed_array(const word_type *packed_array, size_type size) {
size_type num_l1 = DivCeiling(size, kBasesPerL1) + 1;
size_type num_l2 = DivCeiling(size, kBasesPerL2) + 1;
for (unsigned c = BaseSize == 1 ? 1 : 0; c < kAlphabetSize; ++c) {
const word_type *cur_word = packed_array;
size_type count = 0;
l2_occ_[c] = std::vector<size_type>(num_l2);
l1_occ_[c] = std::vector<uint16_t>(num_l1);
size_type size_rd = size - size % kBasesPerL1;
for (size_type i = 0; i < size_rd;
i += kBasesPerL1, cur_word += kBasesPerL1 / kBasesPerWord) {
if (i % kBasesPerL2 == 0) {
l2_occ_[c][i / kBasesPerL2] = count;
}
l1_occ_[c][i / kBasesPerL1] = count - l2_occ_[c][i / kBasesPerL2];
count += CountCharInWords(c, cur_word, kBasesPerL1 / kBasesPerWord);
}
for (size_type i = size_rd; i < size; i += kBasesPerWord, ++cur_word) {
if (i % kBasesPerL1 == 0) {
if (i % kBasesPerL2 == 0) {
l2_occ_[c][i / kBasesPerL2] = count;
}
l1_occ_[c][i / kBasesPerL1] = count - l2_occ_[c][i / kBasesPerL2];
}
count += CountCharInWord(c, *cur_word);
}
l2_occ_[c][num_l2 - 1] = count;
l1_occ_[c][num_l1 - 1] = count - l2_occ_[c][(num_l1 - 1) / kL1PerL2];
char_count_[c] = count;
if (Mode != rnsmode::kRankOnly) {
rank2itv_[c].reserve(DivCeiling(count, kSelectSampleSize) + 1);
for (size_type i = 0; i < num_l1; ++i) {
while (static_cast<size_type>(rank2itv_[c].size() *
kSelectSampleSize) < OccValue(c, i)) {
rank2itv_[c].push_back(i - 1);
}
}
rank2itv_[c].push_back(num_l1 - 1);
}
}
packed_array_ = packed_array;
this->size_ = size;
}
size_type rank(size_type pos) const {
static_assert(BaseSize == 1, "");
return InternalRank(1, pos);
}
size_type rank(uint8_t c, size_type pos) const {
static_assert(BaseSize != 1, "");
return InternalRank(c, pos);
}
size_type select(size_type ranking) const {
static_assert(BaseSize == 1, "");
return InternalSelect(1, ranking);
}
size_type select(uint8_t c, size_type ranking) const {
static_assert(BaseSize != 1, "");
return InternalSelect(c, ranking);
}
size_type pred(uint8_t c, size_type pos) const {
// the last c in [0...pos]
if (GetBaseAt(pos) == c) {
return pos;
}
return InternalSelect(c, InternalRank(c, pos) - 1);
}
size_type pred(size_type pos) const {
static_assert(BaseSize == 1, "");
return pred(1, pos);
}
size_type pred(uint8_t c, size_type pos, int step) const {
// the last c in [pos-step, pos], return pos-step-1 if not exist
size_type end = pos >= step ? pos - step : 0;
while (pos >= end) {
if (GetBaseAt(pos) == c) {
return pos;
}
--pos;
}
return pos;
}
size_type succ(uint8_t c, size_type pos) const {
// the first c in [pos...ReadLength]
if (GetBaseAt(pos) == c) {
return pos;
}
return InternalSelect(c, InternalRank(c, pos - 1));
}
size_type succ(size_type pos) const { return succ(1, pos); }
size_type succ(uint8_t c, size_type pos, int step) const {
// the first c in [pos, pos+step], return pos+step+1 if not exist
size_type end = pos + step;
if (end >= size_) end = size_;
while (pos <= end) {
if (GetBaseAt(pos) == c) {
return pos;
}
++pos;
}
return pos;
}
private:
unsigned CountCharInWord(uint8_t c, word_type x,
word_type mask = word_type(-1)) const {
if (BaseSize != 1) {
x ^= xor_masks_[c];
x = internal::PackToLowestBit<BaseSize>(x);
x &= kPopcntMask;
}
return internal::Popcount(x & mask);
}
unsigned CountCharInWords(uint8_t c, const word_type *ptr,
unsigned n_words) const {
unsigned count = 0;
for (unsigned i = 0; i < n_words; ++i) {
count += CountCharInWord(c, ptr[i]);
}
return count;
}
unsigned SelectInWord(uint8_t c, int num_c, word_type x) const {
if (BaseSize != 1) {
x ^= xor_masks_[c];
x = internal::PackToLowestBit<BaseSize>(x);
x &= kPopcntMask;
}
#if defined(__BMI2__) && defined(USE_BMI2)
return internal::Ctz(internal::Pdep(word_type(1) << (num_c - 1), x)) /
kBitsPerBase;
#else
unsigned trailing_zeros = 0;
while (num_c > 0) {
trailing_zeros = internal::Ctz(x);
x ^= TWord{1} << trailing_zeros;
--num_c;
}
return trailing_zeros / kBitsPerBase;
#endif
}
void PrefetchOcc(uint8_t c, int64_t i) const {
__builtin_prefetch(&l2_occ_[c][i / kL1PerL2], 0);
__builtin_prefetch(&l1_occ_[c][i], 0);
}
size_type OccValue(uint8_t c, size_type i) const {
return l2_occ_[c][i / kL1PerL2] + l1_occ_[c][i];
}
private:
size_type InternalRank(uint8_t c, size_type pos) const {
// the number of c's in [0...pos]
if (pos >= size_)
return kNullID;
else if (pos == size_ - 1)
return char_count_[c];
++pos;
size_type itv_idx = (pos + kBasesPerL1 / 2 - 1) / kBasesPerL1;
size_type sampled_pos = itv_idx * kBasesPerL1;
if (sampled_pos >= size_) {
sampled_pos -= kBasesPerL1;
itv_idx--;
}
PrefetchOcc(c, itv_idx);
if (sampled_pos > pos) {
return RankFwd(c, itv_idx, sampled_pos, sampled_pos - pos);
} else if (sampled_pos < pos) {
return RankBwd(c, itv_idx, sampled_pos, pos - sampled_pos);
} else {
return OccValue(c, itv_idx);
}
}
size_type InternalSelect(uint8_t c, size_type k) const {
static_assert(Mode != rnsmode::kRankOnly,
"cannot select on rank only struct");
// return the pos (0-based) of the kth (0-based) c
if (k > char_count_[c])
return kNullID;
else if (k == char_count_[c])
return size_;
// first locate which interval Select(c, k) falls
size_type interval_l = rank2itv_[c][k / kSelectSampleSize];
size_type interval_r = rank2itv_[c][DivCeiling(k, kSelectSampleSize)];
PrefetchOcc(c, interval_l);
while (interval_r > interval_l) {
size_type interval_m = (interval_r + interval_l + 1) / 2;
if (OccValue(c, interval_m) > k) {
interval_r = interval_m - 1;
} else {
interval_l = interval_m;
}
}
// refined select
__builtin_prefetch(packed_array_ +
interval_l * kBasesPerL1 / kBasesPerWord);
unsigned remain = k + 1 - OccValue(c, interval_l);
unsigned exceed = (interval_l + 1) * kBasesPerL1 >= size_
? kBasesPerL1
: (OccValue(c, interval_l + 1) - (k + 1));
if (remain <= exceed * 2) {
return SelectFwd(c, interval_l, remain);
} else {
return SelectBwd(c, interval_l, exceed);
}
}
size_type RankFwd(uint8_t c, TInterval itv, size_type sampled_pos,
unsigned n_bases) const {
unsigned n_words = n_bases / kBasesPerWord;
const word_type *p =
packed_array_ + sampled_pos / kBasesPerWord - n_words - 1;
__builtin_prefetch(p);
unsigned n_residual = n_bases % kBasesPerWord;
unsigned count = 0;
if (n_residual != 0) {
word_type mask =
1 + ~(1ULL << kBitsPerBase * (kBasesPerWord - n_residual));
count += CountCharInWord(c, p[0], mask);
}
count += CountCharInWords(c, p + 1, n_words);
return OccValue(c, itv) - count;
}
size_type RankBwd(uint8_t c, TInterval itv, size_type sampled_pos,
unsigned n_bases) const {
const word_type *p = packed_array_ + sampled_pos / kBasesPerWord;
__builtin_prefetch(p);
unsigned n_words = n_bases / kBasesPerWord;
unsigned n_residual = n_bases % kBasesPerWord;
unsigned count = 0;
count += CountCharInWords(c, p, n_words);
if (n_residual != 0) {
word_type mask = (1ULL << kBitsPerBase * n_residual) - 1;
count += CountCharInWord(c, p[n_words], mask);
}
return OccValue(c, itv) + count;
}
size_type SelectFwd(uint8_t c, TInterval itv, unsigned remain) const {
size_type pos = static_cast<size_type>(itv) * kBasesPerL1;
const word_type *begin = packed_array_ + pos / kBasesPerWord;
const word_type *p = begin;
for (unsigned popcnt; (popcnt = CountCharInWord(c, *p)) < remain;
remain -= popcnt, ++p)
;
return pos + (p - begin) * kBasesPerWord + SelectInWord(c, remain, *p);
}
size_type SelectBwd(uint8_t c, TInterval itv_l, unsigned exceed) const {
size_type pos = (static_cast<size_type>(itv_l) + 1) * kBasesPerL1;
const word_type *end = packed_array_ + pos / kBasesPerWord - 1;
const word_type *p = end;
unsigned popcnt;
for (; (popcnt = CountCharInWord(c, *p)) <= exceed; exceed -= popcnt, --p)
;
return pos - kBasesPerWord * (end - p) -
(kBasesPerWord - SelectInWord(c, popcnt - exceed, *p));
}
uint8_t GetBaseAt(size_type i) const {
return (packed_array_[i / kBasesPerWord] >>
(i % kBasesPerWord * kBitsPerBase)) &
((1 << kBitsPerBase) - 1);
}
template <typename T1, typename T2>
static T1 DivCeiling(T1 x, T2 y) {
return (x + y - 1) / y;
};
static const word_type kPopcntMask =
internal::PopcountMask<BaseSize, word_type>::value;
static const uint64_t kPopcntMask64 =
internal::PopcountMask<BaseSize, uint64_t>::value;
size_type size_{};
size_type char_count_[kAlphabetSize]{};
// main memory for the structure
const word_type *packed_array_;
// sampled structure for rank and select
// two level sampling for rank (occ value)
// call the function OccValue(c, i) to get the number of c's
// in packed_array_[0...i*kBasesPerL1-1]
// sampling for select
// rank_interval_lookup_[c][i]=j: the jth interval (0 based)
// contains the (i*kSelectSampleSize)th (0 based) c
// i.e. OccValue(c, j)<=i*kSelectSampleSize and OccValue(c,
// j+1)>i*kSelectSampleSize
std::vector<TInterval> rank2itv_[kAlphabetSize];
std::vector<uint16_t> l1_occ_[kAlphabetSize]; // level 1 OCC
std::vector<size_type> l2_occ_[kAlphabetSize]; // level 2 OCC
word_type xor_masks_[kAlphabetSize];
// e.g. if c = 0110(2), popcount_xorers_[c] = 1001 1001 1001 1001...(2),
// to make all c's in a word 1111
static_assert((1ull << kBitsPerBase) >= kAlphabetSize, "");
static_assert(kBitsPerWord % kBitsPerBase == 0, "");
static_assert(kBitsPerBase <= 8, "");
static_assert(kBasesPerL2 <= 65536, "");
};
} // namespace kmlib
#endif // KMLIB_RNS_H