Well, in a sense the mantissa is 24 bits only 23 of which are stored (with the first one implied, unless the number is denormal, which we'd rather not exist at all when it comes to audio). In another sense the mantissa is 23 bits, because that's how many bits are actually allocated to store it. Depends on whether you think of values or bit patterns.I didn't say mantissa is 23 bits. Sure there is 1 bit that is omitted because it's always one. And sure mantissa is normalized.
Either way, the important part is that a single precision float can store unsigned integers of up to 24 bits exactly.. and for signed we can actually store the equivalent of 25-bit(!) 2s complement integers exactly (because the integer loses one bit to sign and we don't), so really a single-precision float is strictly one bit better than a signed 24-bit fixed point over the whole range (and obviously a whole lot better at lower signal amplitudes).
So.. just in order to be controversial I'm going to count both the signbit and the implied leading one as being part of the mantissa, so that I can claim it's 25 bits. In doing so I have managed to pack 25+8=33 bits into a 32bit word, so clearly we have managed about 3% compression and if we perform this conversion about 23 times recursively, we can compress any file to less than 50% of it's original size. Please discuss.
Statistics: Posted by mystran — Tue Apr 02, 2024 10:02 pm