6 ms·
Nitpick: the 64 bit double type has a mantissa of 52 bits, but there's a 1 implied in front, so the precision is 53 bits.
by ant6n 11y ago
Nitpick: the 64 bit double type has a mantissa of 52 bits, but there's a 1 implied in front, so the precision is 53 bits.
- kazinator 11y agoImplied fixed material doesn't contribute precision. Otherwise we could pretend that there are twenty-four implied 1's and the precision is 76 bits. Because the implied 1 cannot be zero, it isn't a bit; it doesn't carry information. For instance if we define a four bit binary number type which has an implied 1, it can only represent values from 16 to 31. That's four bits of precision; the range is just displaced.
- ant6n 11y agoThe information of the first bit is implied via the exponent. Twenty four implied 1's would give you a precision of 76 bits, but you would restrict yourself to a very small subset of all possible numbers with that precision. EDIT: Let's put it another way. Assume you have 3 decimal digits of precision for a float. The first digit cannot be zero. Would you then claim that you don't have 3 digits of precision, but rather log(10x10x9,10) = 2.95.., because the first digit only carries 0.95.. digits of information?
- kazinator 11y agoStrictly speaking, the 2.95 is right; but there is justification in rounding it up to 3. There is much less justification for rounding up 2.0 to 3.
- deleted 11y ago[deleted]