Integer log2 with 14-bit fractional part in C/C++

log2.cpp

#include <stdint.h>

int32_t log2_f14(int32_t x) {
	// We don't support zero or negative values, just return zero in that case
	if (x <= 0) {
		return 0;
	}

	// Compute the integer logarithm
	int32_t log2_int = 0;
	int32_t x_tmp = x;
	while (x_tmp > 1) {
		log2_int += 1;
		x_tmp >>= 1;
	}

	// Compute the fractional part; return if there is no fractional part
	x -= (int32_t(1) << log2_int);
	if (x <= 0) {
		return log2_int << 14;
	}

	// Scale the fractional part to a constant 14-bit dynamic range
	x <<= (31 - log2_int);
	x >>= 17;

	// Evaluate a polynomial of order 3 approximating the shape of the log
	// function on the fractional part
	int32_t res = 0;
	res = ((res * x) >> 14) + 2529;
	res = ((res * x) >> 14) - 9324;
	res = ((res * x) >> 14) + 23174;
	res = ((res * x) >> 14);
	return res + (log2_int << 14);
}