+
+// IsLittleEndian : true if and only if the binary is compiled on a little endian machine
+static inline const union { uint32_t i; char c[4]; } Le = { 0x01020304 };
+static inline const bool IsLittleEndian = (Le.c[0] == 4);
+
+
+// RunningAverage : a class to calculate a running average of a series of values.
+// For efficiency, all computations are done with integers.
+class RunningAverage {
+ public:
+
+ // Constructor
+ RunningAverage() {}
+
+ // Reset the running average to rational value p / q
+ void set(int64_t p, int64_t q)
+ { average = p * PERIOD * RESOLUTION / q; }
+
+ // Update average with value v
+ void update(int64_t v)
+ { average = RESOLUTION * v + (PERIOD - 1) * average / PERIOD; }
+
+ // Test if average is strictly greater than rational a / b
+ bool is_greater(int64_t a, int64_t b)
+ { return b * average > a * PERIOD * RESOLUTION ; }
+
+ private :
+ static constexpr int64_t PERIOD = 4096;
+ static constexpr int64_t RESOLUTION = 1024;
+ int64_t average;
+};
+
+template <typename T, std::size_t MaxSize>
+class ValueList {
+
+public:
+ std::size_t size() const { return size_; }
+ void resize(std::size_t newSize) { size_ = newSize; }
+ void push_back(const T& value) { values_[size_++] = value; }
+ T& operator[](std::size_t index) { return values_[index]; }
+ T* begin() { return values_; }
+ T* end() { return values_ + size_; }
+ const T& operator[](std::size_t index) const { return values_[index]; }
+ const T* begin() const { return values_; }
+ const T* end() const { return values_ + size_; }
+
+ void swap(ValueList& other) {
+ const std::size_t maxSize = std::max(size_, other.size_);
+ for (std::size_t i = 0; i < maxSize; ++i) {
+ std::swap(values_[i], other.values_[i]);
+ }
+ std::swap(size_, other.size_);
+ }
+
+private:
+ T values_[MaxSize];
+ std::size_t size_ = 0;
+};
+
+
+/// sigmoid(t, x0, y0, C, P, Q) implements a sigmoid-like function using only integers,
+/// with the following properties:
+///
+/// - sigmoid is centered in (x0, y0)
+/// - sigmoid has amplitude [-P/Q , P/Q] instead of [-1 , +1]
+/// - limit is (y0 - P/Q) when t tends to -infinity
+/// - limit is (y0 + P/Q) when t tends to +infinity
+/// - the slope can be adjusted using C > 0, smaller C giving a steeper sigmoid
+/// - the slope of the sigmoid when t = x0 is P/(Q*C)
+/// - sigmoid is increasing with t when P > 0 and Q > 0
+/// - to get a decreasing sigmoid, call with -t, or change sign of P
+/// - mean value of the sigmoid is y0
+///
+/// Use <https://www.desmos.com/calculator/jhh83sqq92> to draw the sigmoid
+
+inline int64_t sigmoid(int64_t t, int64_t x0,
+ int64_t y0,
+ int64_t C,
+ int64_t P,
+ int64_t Q)
+{
+ assert(C > 0);
+ return y0 + P * (t-x0) / (Q * (std::abs(t-x0) + C)) ;