Application for Software Developer Position at Headlands Tech
Hello, I'm Tuğrul KÖK, applying for the Software Developer position at Headlands Tech. Recognizing that Headlands Tech operates in High Frequency Trading, I've prepared this demonstration to showcase my C++ programming capabilities and understanding of performance-critical systems.
In response to your coding challenge, I've implemented a C++ program that computes the square root of 42 using multiple optimization strategies. Rather than submitting a simple text file, I've deployed this as a live demonstration running on a custom POSIX socket server built from scratch using standard <sys/socket.h>, demonstrating both algorithmic proficiency and system programming skills.
Full Source Code & Documentation: GitHub Repository
Design Philosophy: While I recognize that std::sqrt is the standard for production code (often mapping to hardware instructions), I implemented these custom solutions to demonstrate algorithmic proficiency. This project highlights my ability to optimize across three layers of abstraction: Mathematical (deriving Newton-Raphson and Fast Inverse Square Root approximations), System-Level (direct usage of x86 SIMD Intrinsics), and Compiler-Level (leveraging constexpr and std::bit_cast for compile-time evaluation and type safety).
Technical Stack: C++20 POSIX Sockets x86 SIMD Nginx Reverse Proxy HTTPS
All methods compute √42. Results are calculated in real-time on the server:
The main implementation uses a unified smart function, with individual methods shown below for demonstration:
std::is_constant_evaluated() to detect compile-time evaluation and automatically routes to the optimal path.std::sqrt which compiles to hardware instructions (e.g., FSQRT on ARM). This provides equivalent behavior and precision across all architectures, ensuring consistency regardless of CPU type
// Unified "Best of Both Worlds" Function
constexpr float sqrt_smart(int x) {
// Path A: Compile-Time (The compiler does the math)
if (std::is_constant_evaluated()) {
return sqrt_constexpr(static_cast(x));
}
// Path B: Runtime (The Hardware does the math)
else {
#if HAS_INTRINSICS
// We can safely use intrinsics here because this block
// is ONLY entered at runtime!
return sqrt_intrinsics(x);
#else
// Path C: Standard library fallback
// Provides equivalent behavior on non-x86 architectures
// std::sqrt compiles to hardware instructions (e.g., FSQRT on ARM)
return std::sqrt(x);
#endif
}
}
// Example usage demonstrating compile-time evaluation
// Compile-time evaluation example (baked into binary)
static constexpr int val = 42;
static constexpr float res_smart_compile = sqrt_smart(val);
// Result is baked into the binary as a raw number. Zero CPU cost at runtime.
_mm_sqrt_ss instruction uses the CPU's floating-point unit, which is significantly faster than software implementations.std::sqrt on non-x86 architectures_mm_sqrt_ss)
// 1. Intrinsics Version
float sqrt_intrinsics(int x) {
if (x < 0) return -1.0f;
// check if intrinsics are available
#if HAS_INTRINSICS
// set the number
__m128 num = _mm_set_ss(static_cast(x));
// square root the number
__m128 result_vector = _mm_sqrt_ss(num);
// convert the result to a float
return _mm_cvtss_f32(result_vector);
#else
return std::sqrt(static_cast(x));
#endif
}
constexpr keyword allows the compiler to evaluate this at compile time when the input is known, eliminating runtime computation entirely.x_{n+1} = 0.5 * (x_n + a/x_n)constexpr enables compile-time evaluation
// 2. Constexpr Version
constexpr float sqrt_constexpr(float x) {
if (x < 0.0f) return -1.0f;
// newton-raphson method
float curr = x, prev = 0.0f;
while (curr != prev) {
prev = curr; // previous value
curr = 0.5f * (curr + x / curr); // new value
}
return curr; // return the final value
}
0x1fbd1df5 is derived from the IEEE 754 floating-point representation.std::sqrt is hardware-accelerated and precise, there are scenarios in low-latency systems (HFT, Monte Carlo simulations, graphics) where a small approximation error is acceptable for significant speed gains. The error margin is explicitly calculated and displayed above.std::bit_cast (C++20) for type-safe bit manipulation—avoids undefined behavior0x1fbd1df5 + (i >> 1) exploits floating-point bit patterns
// 3. Fast Square Root Approximation
float sqrt_fast(float x) {
if (x < 0.0f) return -1.0f;
// 1. Bit-level Manipulation (Initial Guess)
// Safely reinterpret float bits as int32 for manipulation
int32_t i = std::bit_cast(x);
// Apply the magic constant and bit-shift
i = 0x1fbd1df5 + (i >> 1);
// Reinterpret back to float
float y = std::bit_cast(i);
// 2. Newton-Raphson Refinement
// f(y) = y^2 - x = 0 => y' = 0.5 * (y + x/y)
y = 0.5f * (y + x / y);
return y;
}
std::bit_cast instead of C-style casting to ensure type safety and avoid undefined behavior