pow

std::pow does not run in constant time. Its runtime depends on the input values.

When the result is a subnormal number (very small, below DBL_MIN ≈ 2.2e-308), the CPU and math library must handle denormalized floating-point arithmetic, which is significantly slower:

• CPU penalty: subnormal operations can be 10-100x slower on some microarchitectures because the hardware fast path only handles normalized floats
• Library penalty: pow internally uses exp(y * log(x)), and both log and exp have slow paths for subnormal inputs/outputs

With x = 1e-300 and y = 1.1, the result is ~1e-330 which is subnormal, triggering both penalties.

This matters in scientific computing where values can span many orders of magnitude. The fix is to clamp inputs away from subnormal ranges, or use -ffast-math which may flush subnormals to zero (-ftz).

References:

• Wikipedia - Denormal Number
• Intel - Denormals Are Zeros