3 ms·

It does have several additional attributes: 1. Since the normalized significand will always be 1.bbbb, the '1' bit is stripped from the significand representat

by dwaite 4y ago

It does have several additional attributes: 1. Since the normalized significand will always be 1.bbbb, the '1' bit is stripped from the significand representation, except: 2. To extend the range, the lowest 'zero' value of the exponent drops the leading '1'. This is referred to as the subnormal range 3. The highest exponent value, when the significand is zero, is used to represent positive and negative infinity 4. The highest exponent value with a non-zero significand is used to represent NaN 5. There are many different values usable for NaN by software, including a differentiation between 'quiet' NaNs and a (I believe implementation optional) 'signaling' variant, which will raise an interrupt when used. The idea is that these can be used to convey additional information, and that the signaling variant as well as the right interrupt handlers can be used to add additional functionality such as variable substitution. 6. Zero is signed

olliej 4y ago
Yes, I was giving a simplified description to convey how to translate what floating point is to something people are more familiar with. The technical details of how it handles _every_ case weren’t particularly relevant. However just to address 1,2 with some hilariousness (autocorrect wants this to be “hilarious mess” which may be more correct). Ieee754’s 80 bit format was the first widely deployed format, and was largely used by intel to get the other manufacturers to stop trying to reduce the functionality of ieee floating point because “it couldn’t be implemented, implemented efficiently, etc”. However because of that it has a quirk that was fixed for fp32,64,etc. FP80 uses an explicit bit for the leading 1. That means it can do 1.0 * 2 ^^ N, or 0.1 * 2 ^^ N it should hopefully be immediately obvious why this could be a problem :) Not only do the multiple representations for a single value result in sadness, it also gives us a variety of concepts like pseudo-denormals, pseudo normals, pseudo infinities, pseudo nans, etc all of which cause their own problems. Mercifully by default the only hardware fp80 implementation now (since 286 maybe?) defaults to just treating them as invalid and converts to Nan. But you can set a flag to make it treat them as it did originally.

by dwaite 4y ago

olliej 4y ago

Yes, I was giving a simplified description to convey how to translate what floating point is to something people are more familiar with. The technical details of how it handles _every_ case weren’t particularly relevant. However just to address 1,2 with some hilariousness (autocorrect wants this to be “hilarious mess” which may be more correct). Ieee754’s 80 bit format was the first widely deployed format, and was largely used by intel to get the other manufacturers to stop trying to reduce the functionality of ieee floating point because “it couldn’t be implemented, implemented efficiently, etc”. However because of that it has a quirk that was fixed for fp32,64,etc. FP80 uses an explicit bit for the leading 1. That means it can do 1.0 * 2 ^^ N, or 0.1 * 2 ^^ N it should hopefully be immediately obvious why this could be a problem :) Not only do the multiple representations for a single value result in sadness, it also gives us a variety of concepts like pseudo-denormals, pseudo normals, pseudo infinities, pseudo nans, etc all of which cause their own problems. Mercifully by default the only hardware fp80 implementation now (since 286 maybe?) defaults to just treating them as invalid and converts to Nan. But you can set a flag to make it treat them as it did originally.