3 ms·

In numerical analysis, "Hexadecimal float with an exponent" is not an obscure feature, it's a really nice one! If you want to communicate to somebody an exact n

In numerical analysis, "Hexadecimal float with an exponent" is not an obscure feature, it's a really nice one! If you want to communicate to somebody an exact number that your program has output, you need to either tell them the decimal number to enough digits + the number of digits (i.e., "Float32(0.1)", which is distinct from "Float64(0.1)"), or you can tell them the same number in full precision in binary, in which case the floating-point standard guarantees that that number is exactly correct and does not depend on how you interpret it. It's really nice for testing numerical code, especially with automated reproducible tests. Completely unambiguous, and I wish more languages had that (I saw the feature in Julia first).

piadodjanho 7y ago
Also, the printf can be used to display floating point in hexadecimal notation. The printf specifiers: %e Scientific notation 3.9265e+2 %a Hexadecimal floating point -0xc.90fep-2
jacobolus 7y ago
I wish Javascript, etc. had hexadecimal floats. It’s annoying to worry about whether different implementations might parse your numbers differently, worrying about whether you need to write down 15 or 17 decimal digits, ... Often the numbers (e.g. coefficients of some degree 10 polynomial approximation of a special function) are not intended to be human-readable anyway. Such values were typically computed in binary in the first place, and the only place they ever need to be decimal is when written into the code, where they will be immediately reconverted to binary numbers for use.
- microcolonel 7y ago
  I mean, it's not too difficult to add them. You can parse, shove your result into a data view, Uint32Array, or whatever, then turn that into a Float64Array.
  - jacobolus 7y ago
    Fair enough. You can also just base64-encode (or whatever) a big block of binary data. But having built-in support for hex floats would be nicer.
nestorD 7y ago
Note that you can uniquely identify all floats by printing them with printf(“%1.8e”): https://randomascii.wordpress.com/2013/02/07/float-precision-revisited-nine-digit-float-portability/ https://randomascii.wordpress.com/2013/02/07/float-precision...
- pascal_cuoq 7y ago
  As the parent already said, the nice thing about hexadecimal floating-point is that the standard MANDATES that you get exactly the float/double you have uniquely described. The assertion “you can uniquely identify all floats by printing them with printf("%1.8e")” on the other hand relies on the compiler using round-to-nearest for conversions between binary and decimal, which the standard does not mandate and which, even when the compiler documents the choice, is sophisticated enough that the compiler/printf/strtod may get it wrong for difficult inputs: https://www.exploringbinary.com/tag/bug/ https://www.exploringbinary.com/tag/bug/

piadodjanho 7y ago

Also, the printf can be used to display floating point in hexadecimal notation. The printf specifiers: %e Scientific notation 3.9265e+2 %a Hexadecimal floating point -0xc.90fep-2

jacobolus 7y ago

I wish Javascript, etc. had hexadecimal floats. It’s annoying to worry about whether different implementations might parse your numbers differently, worrying about whether you need to write down 15 or 17 decimal digits, ... Often the numbers (e.g. coefficients of some degree 10 polynomial approximation of a special function) are not intended to be human-readable anyway. Such values were typically computed in binary in the first place, and the only place they ever need to be decimal is when written into the code, where they will be immediately reconverted to binary numbers for use.

microcolonel 7y ago
I mean, it's not too difficult to add them. You can parse, shove your result into a data view, Uint32Array, or whatever, then turn that into a Float64Array.
- jacobolus 7y ago
  Fair enough. You can also just base64-encode (or whatever) a big block of binary data. But having built-in support for hex floats would be nicer.

nestorD 7y ago

Note that you can uniquely identify all floats by printing them with printf(“%1.8e”): https://randomascii.wordpress.com/2013/02/07/float-precision-revisited-nine-digit-float-portability/ https://randomascii.wordpress.com/2013/02/07/float-precision...

pascal_cuoq 7y ago
As the parent already said, the nice thing about hexadecimal floating-point is that the standard MANDATES that you get exactly the float/double you have uniquely described. The assertion “you can uniquely identify all floats by printing them with printf("%1.8e")” on the other hand relies on the compiler using round-to-nearest for conversions between binary and decimal, which the standard does not mandate and which, even when the compiler documents the choice, is sophisticated enough that the compiler/printf/strtod may get it wrong for difficult inputs: https://www.exploringbinary.com/tag/bug/ https://www.exploringbinary.com/tag/bug/