From 52d2a5b0f47ad98a57ba18d5177e16bcc9a20bc0 Mon Sep 17 00:00:00 2001
From: Ahmet Inan <inan@aicodix.de>
Date: Mon, 12 Oct 2020 19:00:20 +0200
Subject: [PATCH] added amortized O(1) moving extrema

---
 README.md            |  7 +++++
 movext.hh            | 72 ++++++++++++++++++++++++++++++++++++++++++++
 tests/movext_test.cc | 57 +++++++++++++++++++++++++++++++++++
 3 files changed, 136 insertions(+)
 create mode 100644 movext.hh
 create mode 100644 tests/movext_test.cc

diff --git a/README.md b/README.md
index 56ae9aa..789b9e0 100644
--- a/README.md
+++ b/README.md
@@ -108,6 +108,13 @@ The [simple moving average](https://en.wikipedia.org/wiki/Moving_average#Simple_
 
 The sliding window accelerator uses a tree and only updates nodes that depend on the new input value for the pairwise reduction.
 
+### [movext.hh](movext.hh)
+
+[Amortized](https://en.wikipedia.org/wiki/Amortized_analysis) [O(1)](https://en.wikipedia.org/wiki/Computational_complexity_theory) moving [extrema](https://en.wikipedia.org/wiki/Maxima_and_minima) implementations of:
+
+* Moving Minimum
+* Moving Maximum
+
 ### [bip_buffer.hh](bip_buffer.hh)
 
 The [Bip buffer](https://en.wikipedia.org/wiki/Circular_buffer#Fixed-length-element_and_contiguous-block_circular_buffer) provides contiguous block access to the last N value stored in a circular buffer.
diff --git a/movext.hh b/movext.hh
new file mode 100644
index 0000000..4fffbd6
--- /dev/null
+++ b/movext.hh
@@ -0,0 +1,72 @@
+/*
+Moving Extrema
+
+Copyright 2020 Ahmet Inan <inan@aicodix.de>
+*/
+
+#pragma once
+
+#include "deque.hh"
+
+namespace DSP {
+
+template <typename TYPE, int NUM>
+class MovMin
+{
+	Deque<TYPE, NUM> window, dispenser, refill;
+public:
+	TYPE operator () (TYPE input)
+	{
+		if (window.full()) {
+			if (window.front() == dispenser.front())
+				dispenser.pop_front();
+			window.pop_front();
+		}
+		window.push_back(input);
+
+		while (!refill.empty() && input < refill.front())
+			refill.pop_front();
+		refill.push_front(input);
+
+		if (dispenser.empty()) {
+			while (!refill.empty()) {
+				dispenser.push_front(refill.front());
+				refill.pop_front();
+			}
+			return dispenser.front();
+		}
+		return dispenser.front() < refill.back() ? dispenser.front() : refill.back();
+	}
+};
+
+template <typename TYPE, int NUM>
+class MovMax
+{
+	Deque<TYPE, NUM> window, dispenser, refill;
+public:
+	TYPE operator () (TYPE input)
+	{
+		if (window.full()) {
+			if (window.front() == dispenser.front())
+				dispenser.pop_front();
+			window.pop_front();
+		}
+		window.push_back(input);
+
+		while (!refill.empty() && input > refill.front())
+			refill.pop_front();
+		refill.push_front(input);
+
+		if (dispenser.empty()) {
+			while (!refill.empty()) {
+				dispenser.push_front(refill.front());
+				refill.pop_front();
+			}
+			return dispenser.front();
+		}
+		return dispenser.front() > refill.back() ? dispenser.front() : refill.back();
+	}
+};
+
+}
+
diff --git a/tests/movext_test.cc b/tests/movext_test.cc
new file mode 100644
index 0000000..0f35baa
--- /dev/null
+++ b/tests/movext_test.cc
@@ -0,0 +1,57 @@
+/*
+Test for Moving Extrema
+
+Copyright 2020 Ahmet Inan <inan@aicodix.de>
+*/
+
+#include <iostream>
+#include <cassert>
+#include <random>
+#include <limits>
+#include "swa.hh"
+#include "movext.hh"
+
+template <int SIZE>
+void test()
+{
+	struct Min { int operator () (int a, int b) { return std::min(a, b); } };
+	DSP::SWA<int, Min, SIZE> ref_min(std::numeric_limits<int>::max());
+	DSP::MovMin<int, SIZE> dut_min;
+	struct Max { int operator () (int a, int b) { return std::max(a, b); } };
+	DSP::SWA<int, Max, SIZE> ref_max(std::numeric_limits<int>::min());
+	DSP::MovMax<int, SIZE> dut_max;
+	std::random_device ran;
+	std::default_random_engine gen(ran());
+	std::uniform_int_distribution<int> dis(std::numeric_limits<int>::min(), std::numeric_limits<int>::max());
+	for (int loop = 0; loop < 1000000; ++loop) {
+		int val = dis(gen);
+		assert(ref_min(val) == dut_min(val));
+		assert(ref_max(val) == dut_max(val));
+	}
+}
+
+int main()
+{
+	test<1>();
+	test<2>();
+	test<3>();
+	test<4>();
+	test<5>();
+	test<6>();
+	test<7>();
+	test<8>();
+	test<9>();
+	test<10>();
+	test<12>();
+	test<13>();
+	test<14>();
+	test<15>();
+	test<16>();
+	test<42>();
+	test<123>();
+	test<4567>();
+
+	std::cerr << "Moving extrema test passed!" << std::endl;
+	return 0;
+}
+