Function log2

include/half.hpp:1531–1551

Fixed point binary logarithm. This uses the BKM algorithm in L-mode. \param m mantissa in [1,2) as Q1.30 \param n number of iterations (at most 32) \return log2(\a m) as Q0.31

		/// \param n number of iterations (at most 32)
		/// \return log2(\a m) as Q0.31
		inline uint32 log2(uint32 m, unsigned int n = 32)
		{
			static const uint32 logs[] = {
				0x80000000, 0x4AE00D1D, 0x2934F098, 0x15C01A3A, 0x0B31FB7D, 0x05AEB4DD, 0x02DCF2D1, 0x016FE50B,
				0x00B84E23, 0x005C3E10, 0x002E24CA, 0x001713D6, 0x000B8A47, 0x0005C53B, 0x0002E2A3, 0x00017153,
				0x0000B8AA, 0x00005C55, 0x00002E2B, 0x00001715, 0x00000B8B, 0x000005C5, 0x000002E3, 0x00000171,
				0x000000B9, 0x0000005C, 0x0000002E, 0x00000017, 0x0000000C, 0x00000006, 0x00000003, 0x00000001 };
			if(m == 0x40000000)
				return 0;
			uint32 mx = 0x40000000, my = 0;
			for(unsigned int i=1; i<n; ++i)
			{
				uint32 mz = mx + (mx>>i);
				if(mz <= m)
				{
					mx = mz;
					my += logs[i];
				}
			}
			return my;
		}

		/// Fixed point sine and cosine.
		/// This uses the CORDIC algorithm in rotation mode.