It is not "floating point math" but "floating point math where the exponent is expressed as a power of 2" that is the problem.
That is, if the exponent is a power of 2 you can write 1/2, 1/4, 1/8 exactly but you can't write 1/3, 1/5, 1/10, etc.
If the exponent is base 10 then you can write 1/5, 1/10, 1/1000 and such exactly.
Note the mantissa and the exponent are both integers and so far as this problem is concerned it does not matter if these are written in binary or BCD or some other representation. There is some controversy about what is better, if you use a binary mantissa the math is a little faster and more accurate, if you use a decimal mantissa conversions to and from ASCII are quicker and ASCII conversions are a major part of real life math workloads.
I've long thought that this problem is one of a list of problems that many people encounter on the path to bending computers to their will and that some people decide that computer programming isn't for them because of this kind of problem. I think the kind of person who learns Python to put their outside-of-computing skills on wheels is particularly affected.
It is a "disruptive technology" problem because the person who is using IEEE floats heavily has accommodated to this problem and would not give up the slightest amount of performance. Decimal FP can be implemented in software but is slow in software. IBM has had hardware Decimal FP in their mainframes for a very long time and there is even an IEEE standard. (A company that has been using mainframes for a long time cut a check for the wrong amount because the abused the number system back in 1963 and thus learned their lesson a long time ago.)
The best hope I have is that the "social justice" people can be led to believe that unintuitive numerics keep underrepresented people out of the field and that they threaten Intel that they'll tear down their headquarters unless they catch up to where mainframes were 50 years ago. It could be a huge win for the industry and for the DEI office because employers would have to buy everyone a new computer and even white guys might think the DEI office was doing good work if it meant they got to replace their 5 year old corporate craptop. I mean, how is it that a few people with two fingers get to oppress all the rest of us with ten?
That is, if the exponent is a power of 2 you can write 1/2, 1/4, 1/8 exactly but you can't write 1/3, 1/5, 1/10, etc.
If the exponent is base 10 then you can write 1/5, 1/10, 1/1000 and such exactly.
Note the mantissa and the exponent are both integers and so far as this problem is concerned it does not matter if these are written in binary or BCD or some other representation. There is some controversy about what is better, if you use a binary mantissa the math is a little faster and more accurate, if you use a decimal mantissa conversions to and from ASCII are quicker and ASCII conversions are a major part of real life math workloads.
I've long thought that this problem is one of a list of problems that many people encounter on the path to bending computers to their will and that some people decide that computer programming isn't for them because of this kind of problem. I think the kind of person who learns Python to put their outside-of-computing skills on wheels is particularly affected.
It is a "disruptive technology" problem because the person who is using IEEE floats heavily has accommodated to this problem and would not give up the slightest amount of performance. Decimal FP can be implemented in software but is slow in software. IBM has had hardware Decimal FP in their mainframes for a very long time and there is even an IEEE standard. (A company that has been using mainframes for a long time cut a check for the wrong amount because the abused the number system back in 1963 and thus learned their lesson a long time ago.)
The best hope I have is that the "social justice" people can be led to believe that unintuitive numerics keep underrepresented people out of the field and that they threaten Intel that they'll tear down their headquarters unless they catch up to where mainframes were 50 years ago. It could be a huge win for the industry and for the DEI office because employers would have to buy everyone a new computer and even white guys might think the DEI office was doing good work if it meant they got to replace their 5 year old corporate craptop. I mean, how is it that a few people with two fingers get to oppress all the rest of us with ten?