// Copyright (c) 2019-2020, The Monero Project
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// Adapted from source by AShelly:
// Copyright (c) 2011 ashelly.myopenid.com, licenced under the MIT licence
// https://stackoverflow.com/questions/5527437/rolling-median-in-c-turlach-implementation
// https://stackoverflow.com/questions/1309263/rolling-median-algorithm-in-c
// https://ideone.com/XPbl6
#pragma once
#include <stdlib.h>
#include <stdint.h>
namespace epee
{
namespace misc_utils
{
template<typename Item>
struct rolling_median_t
{
private:
Item* data; //circular queue of values
int* pos; //index into `heap` for each value
int* heap; //max/median/min heap holding indexes into `data`.
int N; //allocated size.
int idx; //position in circular queue
int minCt; //count of items in min heap
int maxCt; //count of items in max heap
int sz; //count of items in heap
private:
//returns true if heap[i] < heap[j]
bool mmless(int i, int j) const
{
return data[heap[i]] < data[heap[j]];
}
//swaps items i&j in heap, maintains indexes
bool mmexchange(int i, int j)
{
const int t = heap[i];
heap[i] = heap[j];
heap[j] = t;
pos[heap[i]] = i;
pos[heap[j]] = j;
return 1;
}
//swaps items i&j if i<j; returns true if swapped
bool mmCmpExch(int i, int j)
{
return mmless(i, j) && mmexchange(i, j);
}
//maintains minheap property for all items below i.
void minSortDown(int i)
{
for (i *= 2; i <= minCt; i *= 2)
{
if (i < minCt && mmless(i + 1, i))
++i;
if (!mmCmpExch(i, i / 2))
break;
}
}
//maintains maxheap property for all items below i. (negative indexes)
void maxSortDown(int i)
{
for (i *= 2; i >= -maxCt; i *= 2)
{
if (i > -maxCt && mmless(i, i - 1))
--i;
if (!mmCmpExch(i / 2, i))
break;
}
}
//maintains minheap property for all items above i, including median
//returns true if median changed
bool minSortUp(int i)
{
while (i > 0 && mmCmpExch(i, i / 2))
i /= 2;
return i == 0;
}
//maintains maxheap property for all items above i, including median
//returns true if median changed
bool maxSortUp(int i)
{
while (i < 0 && mmCmpExch(i / 2, i))
i /= 2;
return i == 0;
}
protected:
rolling_median_t &operator=(const rolling_median_t&) = delete;
rolling_median_t(const rolling_median_t&) = delete;
public:
//creates new rolling_median_t: to calculate `nItems` running median.
rolling_median_t(size_t N): N(N)
{
int size = N * (sizeof(Item) + sizeof(int) * 2);
data = (Item*)malloc(size);
pos = (int*) (data + N);
heap = pos + N + (N / 2); //points to middle of storage.
clear();
}
rolling_median_t(rolling_median_t &&m)
{
free(data);
memcpy(this, &m, sizeof(rolling_median_t));
m.data = NULL;
}
rolling_median_t &operator=(rolling_median_t &&m)
{
free(data);
memcpy(this, &m, sizeof(rolling_median_t));
m.data = NULL;
return *this;
}
~rolling_median_t()
{
free(data);
}
void clear()
{
idx = 0;
minCt = 0;
maxCt = 0;
sz = 0;
int nItems = N;
while (nItems--) //set up initial heap fill pattern: median,max,min,max,...
{
pos[nItems] = ((nItems + 1) / 2) * ((nItems & 1) ? -1 : 1);
heap[pos[nItems]] = nItems;
}
}
int size() const
{
return sz;
}
//Inserts item, maintains median in O(lg nItems)
void insert(Item v)
{
int p = pos[idx];
Item old = data[idx];
data[idx] = v;
idx = (idx + 1) % N;
sz = std::min<int>(sz + 1, N);
if (p > 0) //new item is in minHeap
{
if (minCt < (N - 1) / 2)
{
++minCt;
}
else if (v > old)
{
minSortDown(p);
return;
}
if (minSortUp(p) && mmCmpExch(0, -1))
maxSortDown(-1);
}
else if (p < 0) //new item is in maxheap
{
if (maxCt < N / 2)
{
++maxCt;
}
else if (v < old)
{
maxSortDown(p);
return;
}
if (maxSortUp(p) && minCt && mmCmpExch(1, 0))
minSortDown(1);
}
else //new item is at median
{
if (maxCt && maxSortUp(-1))
maxSortDown(-1);
if (minCt && minSortUp(1))
minSortDown(1);
}
}
//returns median item (or average of 2 when item count is even)
Item median() const
{
Item v = data[heap[0]];
if (minCt < maxCt)
{
v = (v + data[heap[-1]]) / 2;
}
return v;
}
};
}
}
