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120 lines (108 loc) · 3.46 KB
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/**
* Balanced Operations CNO in C++
*
* Performs operations that cancel out, resulting in no net effect.
* Demonstrates computational work that achieves equilibrium.
*
* CNO Properties:
* - Termination: All operations complete and return
* - Purity: Despite mutations, final state equals initial state
* - State Preservation: Net effect is zero
* - Observational Equivalence: Indistinguishable from nop.cpp
*
* Compilation:
* g++ -std=c++17 -O0 balanced_ops.cpp -o balanced_ops
* Note: Use -O0 to prevent optimizer from removing operations
*
* With optimizations:
* g++ -std=c++17 -O2 balanced_ops.cpp -o balanced_ops
* The optimizer may reduce this to a simple "return 0"
*/
#include <cstdint>
int main() {
// Use volatile to prevent compiler optimizations
// This ensures operations actually execute at runtime
volatile int x = 0;
volatile int y = 42;
// Balanced arithmetic operations
x = x + 100; // Add 100
x = x - 100; // Subtract 100 → net change: 0
// Balanced multiplication/division
x = x + 1; // Make x = 1 (avoid division by zero semantics)
x = x * 256; // Multiply by 256
x = x / 256; // Divide by 256 → back to 1
x = x - 1; // Back to 0
// XOR identity: x ⊕ x = 0
y = y ^ y; // Always results in 0
// Balanced bitwise operations
x = x | 0xFF; // Set all low bits
x = x & 0x00; // Clear all bits → 0
// Swap and swap back (using C++ std::swap semantics)
{
volatile int temp_x = x;
volatile int temp_y = y;
// Swap
x = temp_y;
y = temp_x;
// Swap back
temp_x = x;
temp_y = y;
x = temp_y;
y = temp_x;
}
// Increment/decrement cycle
for (int i = 0; i < 1000; ++i) {
x++;
}
for (int i = 0; i < 1000; ++i) {
x--;
}
// Final state: x = 0, y = 0
// Return 0 (success)
return 0;
}
/*
* Verification Notes:
* ==================
*
* Mathematical Properties:
* - Every operation has an inverse operation applied
* - Additive inverses: +n followed by -n
* - Multiplicative inverses: ×n followed by ÷n
* - XOR nilpotency: x ⊕ x = 0
* - Identity preservation: operations cancel algebraically
*
* Computational Work:
* - CPU cycles consumed
* - Memory reads/writes occur (volatile prevents caching)
* - Loop iterations execute
* - But: no observable output, no lasting state change
*
* Optimization Analysis:
* Without volatile:
* Compiler sees x and y are never read after operations
* Dead code elimination removes all operations
* Result: equivalent to nop.cpp
*
* With volatile:
* Compiler must preserve all operations
* Generates actual machine code for each operation
* But result is still CNO (no output, return 0)
*
* Philosophy:
* This demonstrates that "work" and "effect" are different.
* Significant computation can occur with zero net result.
* In physics terms: energy expended, entropy increased,
* but system state returned to initial configuration.
*
* C++ Specific Notes:
* - Uses C++11 range-for loops
* - Demonstrates volatile keyword (prevents optimization)
* - Shows RAII scope with temporary variables
* - Type safety via int and std::uint8_t considerations
*
* Contrast with C:
* - Same semantics as C version
* - Could use std::atomic for thread-safety (still CNO)
* - Could use constexpr for compile-time evaluation
*/