#include <algorithm>

// Eliminate multiplication in comparison with 0
bool example1(T x) {
  T c = 5;
  return (x * c) > 0;
}

// Eliminate division after multiplication
T example2(T x) {
    T c1 = 14;
    T c2 = 7;
	return (x * 6) / 3;
}

// Eliminate negation
T example3(T x, T y) {
    return (-x) / (-y);
}

// Simplify comparisons that are always true or false
bool example4a(T x) {
	T c = 1;
	return x + c < x;
}

bool example4b(T x) {
	T c = 1;
	return x + c <= x;
}

bool example4c(T x) {
	T c = 1;
	return x + c > x;
}

bool example4d(T x) {
	T c = 1;
	return x + c >= x;
}

// Eliminate negation in comparisons
bool example5(T x, T y) {
  return (-x) == (-y);
}

// Reduce magnitude of constants
bool example6a(T x, T y) {
  T c = 5;
  return x + c > y;
}

bool example6b(T x, T y) {
  T c = 7;
  return x + c <= y;
}

// Eliminate constants in comparisons
bool example7a(T x, T y) {
  T c1 = 17, c2 = 23;
  return (x + c1) < c2;
}

bool example7b(T x, T y) {
  T c1 = 17, c2 = 23;
  return (x + c1) < (y + c2);
}

// Pointer arithmetic and type promotion
bool example8(float * a, T i) {
  float * e0 = a+i;
  float * e1 = a+(i+1);
  return e1 - e0 == 1;
}

// Value range calculations
T example9a(T x) {
    if (x > 0) {
 		T y = x + 5;
      	T z = y / 4;
  		return z;
    }
}

// Changing comparisons x<y to true or false if the ranges for x and y does not overlap
bool example9b(T x) {
    if (x > 0) {
 		T y = x + 5;
  		return x < y;
    }
}

// Changing min(x,y) or max(x,y) to x or y if the ranges do not overlap
T example9c(T x) {
    if (x > 0) {
 		T y = x + 5;
      	return std::min(x, y);
    }
}

// Changing abs(x) to x or -x if the range does not cross 0
T example9d(T x) {
    if (x > 0) {
      	return abs(x);
    }
}

// Changing x/c to x>>log2(c) if x>0 and the constant c is a power of 2
T example9e(T x) {
	T c = 8;
    if (x > 0) {
      	return x / c;
    }
}

// Loop analysis and optimization
T example10(T m) {
  int sum = 0;
  for (short T i = 0; i <= m; ++ i) {
    sum += i;
  }
  return sum;
}