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The only benefit Base10 has over Base2 is that it's more easily understandable by beginners. It's more complex to implement in hardware. It still has exactly t

The only benefit Base10 has over Base2 is that it's more easily understandable by beginners. It's more complex to implement in hardware. It still has exactly the same precision issues that must be taken into consideration. It still cannot represent everything exactly (1/3 in base 10 decimal. It gets truncated). Using base2 floating point is pretty much the same as using base2 integers.

KMag 12y ago
> The only benefit Base10 has over Base2 is that it's more easily understandable by beginners. Dr. William Kahan argues better than I can [1][2]. As far back as the 1970s, he tried to convince both Intel [3] and IBM [2] to implement base 10 floating point in hardware. First of all, in an ideal world, all software is written and reviewed by people have taken, aced, and remembered their discrete math courses. We don't live in that world. I work with a lot of bright people, but I've come to find that many of them have a model that's essentially floating point operations result in a value that's a low variance Gaussian distribution about the correct value. It's not uncommon for me to see things like doubles compared thusly: if (abs( floor(x) - floor(y) ) < 1e-30) ... Secondly, almost no financial or accounting rules or regulations are drafted by people with any knowledge of binary floating point semantics, so the semantics of IEEE 754-2008 decimal numbers more closely match financial rules and regulations. Thirdly, base 10 floating point numbers are less confusing for end users and result in fewer hacks such as the display hacks in Excel to prevent users from thinking floating point artifacts are bugs in Excel.[1] I think IEEE 754-1985 is a wonderful and well thought-out standard. However, the IEEE 754-2008 committee didn't add decimal floating points on a whim. There are very compelling use cases. [1] http://www.cs.berkeley.edu/~wkahan/ARITH_17.pdf [2] http://grouper.ieee.org/groups/754/email/msg01831.html (search for Yorktown Heights) [3] https://en.wikipedia.org/wiki/IEEE_754-1985#History Edit: It was a bit harsh to begin with "Incorrect." Sorry.

KMag 12y ago

> The only benefit Base10 has over Base2 is that it's more easily understandable by beginners. Dr. William Kahan argues better than I can [1][2]. As far back as the 1970s, he tried to convince both Intel [3] and IBM [2] to implement base 10 floating point in hardware. First of all, in an ideal world, all software is written and reviewed by people have taken, aced, and remembered their discrete math courses. We don't live in that world. I work with a lot of bright people, but I've come to find that many of them have a model that's essentially floating point operations result in a value that's a low variance Gaussian distribution about the correct value. It's not uncommon for me to see things like doubles compared thusly: if (abs( floor(x) - floor(y) ) < 1e-30) ... Secondly, almost no financial or accounting rules or regulations are drafted by people with any knowledge of binary floating point semantics, so the semantics of IEEE 754-2008 decimal numbers more closely match financial rules and regulations. Thirdly, base 10 floating point numbers are less confusing for end users and result in fewer hacks such as the display hacks in Excel to prevent users from thinking floating point artifacts are bugs in Excel.[1] I think IEEE 754-1985 is a wonderful and well thought-out standard. However, the IEEE 754-2008 committee didn't add decimal floating points on a whim. There are very compelling use cases. [1] http://www.cs.berkeley.edu/~wkahan/ARITH_17.pdf [2] http://grouper.ieee.org/groups/754/email/msg01831.html (search for Yorktown Heights) [3] https://en.wikipedia.org/wiki/IEEE_754-1985#History Edit: It was a bit harsh to begin with "Incorrect." Sorry.