Show HN: Floating point arithmetic types in C++ for any size and any base

Have nothing to say other than - neat!

For "any size" I was kind of expecting arbitrary sized mantissa/exponent, can be useful for emulating weird DACs, for example, 12-bit mantissa and 3-bit exponent[1].

[1] https://ajxs.me/blog/Yamaha_DX7_Technical_Analysis.html

Nice!

> TODO: (configurable) rounding support

What's the default rounding mode? Round to nearest even?

You might be interested in https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2024/p33... too, which is a recent paper for introducing reproducible floating point to C++.

Very small floating point types can be handy for exhaustive testing of floating point function templates, especially ones that take multiple arguments. Walking over all floating point values for a small type often finds most if not all corner cases that can manifest with a floating point type of any size.

Possibly could be combined with C23's _BitInt(N) for the template arguments? I think it's available in clang as a C++ extension.

edit: or I guess you could have your own Tmantissa and Texponent types as custom classes that correctly model _BitInt(N), they don't seem to be required to be builtin integral types.

Here is an example of the other end of the spectrum that I've used a couple of times: very simple fixpoints.

https://github.com/codr7/claes/blob/main/src/claes/f64.hpp

Consider dropping the specializations for the type traits, given that it's undefined behavior:

https://en.cppreference.com/w/cpp/types/is_fundamental

https://en.cppreference.com/w/cpp/types/is_floating_point

https://en.cppreference.com/w/cpp/types/is_arithmetic

https://en.cppreference.com/w/cpp/types/is_scalar

https://en.cppreference.com/w/cpp/types/is_object

Rounding: actually it just cuts off. I have not spent much time to think about how to specify and implement the different rounding modes. Maybe some day...

Thanks for the hint to the paper. I also faced these issues. Thus, I provided a constructor which accepts mantissa and exponent as values. Very handy for the unittests.

Actually you can specify the numeric limits of the mantissa and the exponent. They can be specified as template arguments[0]. So you could do:

      Float<uint8_t, // type of the mantissa
            uint8_t, // type of the exponent
            0,       // lowest possible value of the mantissa
            4095,    // highest possible value of the mantissa
            0,       // lowest possible value of the exponent
            7>       // highest possible value of the exponent

The Float then simulates an unsigned 12bit mantissa and a 3bit exponent. Sure it still takes 16 bytes. But you could create a union with bitfields where you shrink that even further.

[0] https://github.com/clemensmanert/fas/blob/58f9effbe6c13ab334...

Thank you :)

I don't get what you mean. I thought they specify how the type can be used?

Technically, you're not supposed to add your own specialisations to the `std` namespace

The cppreference page says:

> If the program adds specializations for std::is_fundamental or std::is_fundamental_v, the behavior is undefined.

This is an oversimplification. The actual rule is https://eel.is/c++draft/library#namespace.std-2 .

> the specialization meets the standard library requirements for the original template.

For is_fundamental<YourClassType> it means that is_fundamental<YourClassType>::value must be false, as YourClassType is not a fundamental type, as defined in https://eel.is/c++draft/basic.fundamental#17 .

Some traits are just not designed to be customization points.

Can you go in the other direction? Higher exponent and mantissa than regular float/double?

By cutting off do you mean that it correctly rounds towards zero? Maybe you can implement rounding to closest by just doing the calculation in a one digit wider mantissa with rounding to zero and observing the last digit, at least for an even base. It won't be rounding to even though, but for that a 2 digit wider mantissa is probably enough.

Rounding to nearest with an odd base doesn't seem to be as straightforwardly implementable from rounding to zero calculations at a higher precision.

Sure.

    Float<int64_t, int64_t>

Gives you a signed Mantissa with 64 bit and a signed Exponent with 64bit. Since there are numeric limits for int64_t available, Float knows the max and the min value.

You could get even bigger ranges for Float by implementing your own big integer type.

I remember that I tried that some time ago. Especially the multiplication was tough, but I can not recall where I gave up. When I find some time, I will pick it up again :)

In general this isn’t true (i guess it is in this specific context). For example I believe it’s totally expected to specialize std hash

It's copyrighted so I should not even look at it, and therefore not comment on it.

No LICENSE. Have you thought about adding one?

Why is std::is_object even specialized here? Isn't it always true regardless?

I’ve also done this with hash… though given the footguns scattered about, I wouldn’t be surprised if it broke the spec.

How does this compare to Boost.Multiprecision, which works well with Boost.Math?

https://www.boost.org/doc/libs/1_86_0/libs/multiprecision/do...

https://www.boost.org/doc/libs/1_86_0/libs/multiprecision/do...