5 ms·

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

79 points by seg_fault 2y ago

Since there is so much interest on HN in floats lately and their software implementations, I wanted to show mine. It has no use and is just for teaching me floats and C++. Give me your thoughts.

a_t48 2y ago
Have nothing to say other than - neat!
- seg_fault 2y ago
  Thank you :)
fuhsnn 2y ago
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 https://ajxs.me/blog/Yamaha_DX7_Technical_Analysis.html
- badmintonbaseba 2y ago
  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.
- seg_fault 2y ago
  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/58f9effbe6c13ab334b05a956ec885edeac89fac/fas/float.hpp#L27 https://github.com/clemensmanert/fas/blob/58f9effbe6c13ab334...
  - Archit3ch 2y ago
    Can you go in the other direction? Higher exponent and mantissa than regular float/double?
    - seg_fault 2y ago
      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.
badmintonbaseba 2y ago
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/p3375r1.html 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.
- seg_fault 2y ago
  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.
  - badmintonbaseba 2y ago
    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.
    - seg_fault 2y ago
      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 :)
codr7 2y ago
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 https://github.com/codr7/claes/blob/main/src/claes/f64.hpp
listeria 2y ago
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_fundamental https://en.cppreference.com/w/cpp/types/is_floating_point 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_arithmetic https://en.cppreference.com/w/cpp/types/is_scalar https://en.cppreference.com/w/cpp/types/is_scalar https://en.cppreference.com/w/cpp/types/is_object https://en.cppreference.com/w/cpp/types/is_object
- seg_fault 2y ago
  I don't get what you mean. I thought they specify how the type can be used?
  - secondcoming 2y ago
    Technically, you're not supposed to add your own specialisations to the `std` namespace
    - pmalynin 2y ago
      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
      - tyleo 2y ago
        I’ve also done this with hash… though given the footguns scattered about, I wouldn’t be surprised if it broke the spec.
        Conscat 2y ago
        That is a completely intended way to use std::hash, along with a few other functions like std::tuple_size and std::tuple_element.
rurban 2y ago
It's copyrighted so I should not even look at it, and therefore not comment on it.
- recursive 2y ago
  And yet...
  - rurban 2y ago
    The API looks fine, well
- syockit 2y ago
  It's copyrighted, but nothing stops you from looking at it. It's akin to looking a t a mural painted at someone's house. You can also comment as long as you don't post snippets of the code (except for when fair use is applicable).
  - rurban 2y ago
    Legally yes, but in reality not. In most companies or projects legal tells me not to look at it all, esp. the FSF. I can look at the API, but not the implementation. That's why it's called https://en.wikipedia.org/wiki/Clean-room_design https://en.wikipedia.org/wiki/Clean-room_design.
- dahart 2y ago
  All creative works are copyrighted by default in the U.S. and any countries adhering to the Berne convention, unless copyrights are explicitly waived (which is not always an option). This is true regardless of what copyright notices exist, so by that standard you shouldn’t look at or comment on anything. ;) But, it’s legal to look at something copyrighted, you just can’t copy & distribute it. Just curious, did you mean that it lacks an open source license and you only look at open source, or was this just a joke that went sideways, or something else?
- seg_fault 2y ago
  Removed it.
skissane 2y ago
No LICENSE. Have you thought about adding one?
- seg_fault 2y ago
  Somebody wants to use it? :D I thought about something like where people can use it but have to make changed public. I am just curious, what should be changed. But I dont think there is actually a real world use case.
  - zokier 2y ago
    Sounds like you prefer copyleft licenses. I suggest MPL-2.0 or some variety of (L)GPL as they are the most well-known ones.
nly 2y ago
How does this compare to Boost.Multiprecision, which works well with Boost.Math? https://www.boost.org/doc/libs/1_86_0/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html https://www.boost.org/doc/libs/1_86_0/libs/multiprecision/do... https://www.boost.org/doc/libs/1_86_0/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html https://www.boost.org/doc/libs/1_86_0/libs/multiprecision/do...
- seg_fault 2y ago
  My type is a bit simpler. But I think the approach is the same. After all, boost's type has much more math functions implemented. I don't have exp, sqrt...
amelius 2y ago
Isn't this in libgmp already? https://gmplib.org/ https://gmplib.org/
- Archit3ch 2y ago
  GMP doesn't do arbitrary exponents.
  - amelius 2y ago
    Indeed, thanks.
    - Archit3ch 2y ago
      Slight correction, while the exponent is indeed fixed, it is larger than a f32/f64 exponent: https://gmplib.org/manual/Floating_002dpoint-Functions https://gmplib.org/manual/Floating_002dpoint-Functions However, this is not exposed in all GMP wrappers.
      - seg_fault 2y ago
        If I understand this correctly GMP has a flexible mantissa with no limitations during runtime. In fas you have to specify the sizes (of mantissa and exponent) during compile time. So the size of this type is fixed. Thus, there is no heap involved.
account42 2y ago
> std::numeric_limits<fas::Float<std::int16_t, std::int8_t>>::MAX() Surely you mean ::max()? > is_fundamental<int16_t, int16_t>::value et al. Besides the undefined behavior issue mentioned by others, none of these are syntactially correct. > #include "fas/stream.hpp> Ok then... > The Stl's std::numeric_limits is required the limits of the specified types for mantissa and exponent. Missing a word? Also, the STL [0] does not have std::numeric_limits, perhaps you mean the C++ standard library (or stdlib for short). [0] https://en.wikipedia.org/wiki/Standard_Template_Library https://en.wikipedia.org/wiki/Standard_Template_Library
ttoinou 2y ago
Waiting for someone to implement a mandelbrot zoom with that (:

79 points by seg_fault 2y ago

Since there is so much interest on HN in floats lately and their software implementations, I wanted to show mine. It has no use and is just for teaching me floats and C++. Give me your thoughts.

a_t48 2y ago

Have nothing to say other than - neat!

seg_fault 2y ago
Thank you :)

fuhsnn 2y ago

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 https://ajxs.me/blog/Yamaha_DX7_Technical_Analysis.html

badmintonbaseba 2y ago
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.
seg_fault 2y ago
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/58f9effbe6c13ab334b05a956ec885edeac89fac/fas/float.hpp#L27 https://github.com/clemensmanert/fas/blob/58f9effbe6c13ab334...
- Archit3ch 2y ago
  Can you go in the other direction? Higher exponent and mantissa than regular float/double?
  - seg_fault 2y ago
    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.

badmintonbaseba 2y ago

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/p3375r1.html 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.

seg_fault 2y ago
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.
- badmintonbaseba 2y ago
  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.
  - seg_fault 2y ago
    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 :)

codr7 2y ago

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

listeria 2y ago

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_fundamental https://en.cppreference.com/w/cpp/types/is_floating_point 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_arithmetic https://en.cppreference.com/w/cpp/types/is_scalar https://en.cppreference.com/w/cpp/types/is_scalar https://en.cppreference.com/w/cpp/types/is_object https://en.cppreference.com/w/cpp/types/is_object

seg_fault 2y ago
I don't get what you mean. I thought they specify how the type can be used?
- secondcoming 2y ago
  Technically, you're not supposed to add your own specialisations to the `std` namespace
  - pmalynin 2y ago
    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
    - tyleo 2y ago
      I’ve also done this with hash… though given the footguns scattered about, I wouldn’t be surprised if it broke the spec.
      - Conscat 2y ago
        That is a completely intended way to use std::hash, along with a few other functions like std::tuple_size and std::tuple_element.

rurban 2y ago

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

recursive 2y ago
And yet...
- rurban 2y ago
  The API looks fine, well
syockit 2y ago
It's copyrighted, but nothing stops you from looking at it. It's akin to looking a t a mural painted at someone's house. You can also comment as long as you don't post snippets of the code (except for when fair use is applicable).
- rurban 2y ago
  Legally yes, but in reality not. In most companies or projects legal tells me not to look at it all, esp. the FSF. I can look at the API, but not the implementation. That's why it's called https://en.wikipedia.org/wiki/Clean-room_design https://en.wikipedia.org/wiki/Clean-room_design.
dahart 2y ago
All creative works are copyrighted by default in the U.S. and any countries adhering to the Berne convention, unless copyrights are explicitly waived (which is not always an option). This is true regardless of what copyright notices exist, so by that standard you shouldn’t look at or comment on anything. ;) But, it’s legal to look at something copyrighted, you just can’t copy & distribute it. Just curious, did you mean that it lacks an open source license and you only look at open source, or was this just a joke that went sideways, or something else?
seg_fault 2y ago
Removed it.

skissane 2y ago

No LICENSE. Have you thought about adding one?

seg_fault 2y ago
Somebody wants to use it? :D I thought about something like where people can use it but have to make changed public. I am just curious, what should be changed. But I dont think there is actually a real world use case.
- zokier 2y ago
  Sounds like you prefer copyleft licenses. I suggest MPL-2.0 or some variety of (L)GPL as they are the most well-known ones.

nly 2y ago

How does this compare to Boost.Multiprecision, which works well with Boost.Math? https://www.boost.org/doc/libs/1_86_0/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_bin_float.html https://www.boost.org/doc/libs/1_86_0/libs/multiprecision/do... https://www.boost.org/doc/libs/1_86_0/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html https://www.boost.org/doc/libs/1_86_0/libs/multiprecision/do...

seg_fault 2y ago
My type is a bit simpler. But I think the approach is the same. After all, boost's type has much more math functions implemented. I don't have exp, sqrt...

amelius 2y ago

Isn't this in libgmp already? https://gmplib.org/ https://gmplib.org/

Archit3ch 2y ago
GMP doesn't do arbitrary exponents.
- amelius 2y ago
  Indeed, thanks.
  - Archit3ch 2y ago
    Slight correction, while the exponent is indeed fixed, it is larger than a f32/f64 exponent: https://gmplib.org/manual/Floating_002dpoint-Functions https://gmplib.org/manual/Floating_002dpoint-Functions However, this is not exposed in all GMP wrappers.
    - seg_fault 2y ago
      If I understand this correctly GMP has a flexible mantissa with no limitations during runtime. In fas you have to specify the sizes (of mantissa and exponent) during compile time. So the size of this type is fixed. Thus, there is no heap involved.

account42 2y ago

> std::numeric_limits<fas::Float<std::int16_t, std::int8_t>>::MAX() Surely you mean ::max()? > is_fundamental<int16_t, int16_t>::value et al. Besides the undefined behavior issue mentioned by others, none of these are syntactially correct. > #include "fas/stream.hpp> Ok then... > The Stl's std::numeric_limits is required the limits of the specified types for mantissa and exponent. Missing a word? Also, the STL [0] does not have std::numeric_limits, perhaps you mean the C++ standard library (or stdlib for short). [0] https://en.wikipedia.org/wiki/Standard_Template_Library https://en.wikipedia.org/wiki/Standard_Template_Library

ttoinou 2y ago

Waiting for someone to implement a mandelbrot zoom with that (: