fixed-sqrt v0.1.0

Integer square root for Q16.16 fixed-point values.

Application scenarios

• RMS, magnitude, and distance calculations on an MCU without an FPU.
• Sensor linearization that needs a square root.
• Control loops that must avoid floating point.

Contract

int32_t fixed_sqrt_q16(int32_t value);

• Input and output are Q16.16: the integer part is value >> 16.
• Negative inputs return 0.
• The result is the truncated integer square root.
• No allocation; no floating point; O(log n).

Parameters

• Input range is 0..INT32_MAX (about 32767.999 in Q16.16).
• The output of a valid input fits the Q16.16 range.

Memory and timing

• No state; one 64-bit loop with about 31 iterations.

Integration

int32_t rms = fixed_sqrt_q16((a * a + b * b) >> 16);

When not to use

• Values outside the Q16.16 range; use a wider type or scale first.
• A floating-point unit is available and the project allows floats.

Verification

make test covers exact squares, non-squares, zero, and negative input.

Behavior reference: libfixmath fix16_sqrt (MIT); this bitwise implementation is original.