4 ms·
Erm, no, not in 754 floating point. The significand of a normalized number starts with an implied 1 to the left of the decimal point, which isn’t explicitly re
by labcomputer 2y ago
Erm, no, not in 754 floating point.
The significand of a normalized number starts with an implied 1 to the left of the decimal point, which isn’t explicitly represented. In other words, the significand represents the range [1, 2) for normalized numbers.
In fact, that’s reason we need subnormal numbers: they are numbers for which the implied first bit is not 1, so the significand represents the range [0, 1).
Subnormal numbers therefore do not have a fixed number of digits (precision). As subnormals approach zero, the precision gets smaller.
- librasteve 2y agofair point - I did reference this from a general article and it did not specify P754 - I guess this has an implied 1 and can save one bit of data path … but the definition of normalized is that the mantissa is shifted to be aligned to the binary point and not that is have a fixed number of digits since it will often be packed with trailing zeros
- labcomputer 2y ago> but the definition of normalized is that the mantissa is shifted to be aligned to the binary point And that’s the key point. A subnormal number does not have the significand/mantissa aligned to start with an (implied) 1. It has leading zeros. Thus the number of digits of a subnormal number is not fixed. 1.0000x10^0 has the same precision as 1.0000x10^-99. 1.0000x10^-99 does not have the same precision as 0.0010x10^-99. That is why the original poster wrote the subnormals have a not-fixed number of digits. But if you’re going to go around writing snarky “gotcha” comments, at least try to get your facts straight.
- deleted 2y ago[deleted]