Complex numbers

[scimind2460]

This RFC proposes FFI-compatible complex numbers to help scientific computing library authors use non-indirected complexes.

I apologise in advance to num-complex

Rendered

[joshtriplett]

Labeling this T-lang because the desire to make this FFI-compatible is a lang matter.

[clarfonthey]

It's worth pointing out another big issue with this is that the canonical a+bi is not actually the best representation of complex numbers in all cases, and so deciding on this is making a decision that might make life harder for external complex-numeric libraries out there.

In particular, while a+bi (orthogonal) representation is efficient for addition, r*(iθ).exp() is more efficient for multiplication, and depending on the equation you're using, it may be advantageous to switch between the two to reduce the number of arithmetic operations needed.

I'm not super compelled by the argument that C supports this, therefore the standard library needs to support this. I think that guaranteeing a std::ffi::Complex representation would be desirable, but there's no saying that we need to make this a canonical type in, say, std::num.

[tgross35]

It's worth pointing out another big issue with this is that the canonical a+bi is not actually the best representation of complex numbers in all cases, and so deciding on this is making a decision that might make life harder for external complex-numeric libraries out there.

In particular, while a+bi (orthogonal) representation is efficient for addition, r*(iθ).exp() is more efficient for multiplication, and depending on the equation you're using, it may be advantageous to switch between the two to reduce the number of arithmetic operations needed.

I think that polar form almost always is the more optimal form, at least in my experience. But the ABIs do use rectangular, e.g. from x86:

Arguments of complex T where T is one of the types float or double are treated as if they are implemented as:

struct complexT {
  T real;
  T imag;
};

so it makes sense that an interchange type matches that, and users can translate to/from a polar repr at the FFI boundary if needed. But this reasoning is definitely something to have in the RFC's rationale & alternatives.

[clarfonthey]

Right: I guess my main clarification here was that due to the polar-orthogonal discrepancy, it shouldn't be a canonical Rust type (e.g. std::num::Complex shouldn't be making a decision on which is more-canonical), but I do think that having extra FFI-compatibility types is reasonable and this shouldn't prevent us from adding std::ffi::Complex which is orthogonal.

[scimind2460]

Thanks everyone for the feedback! I have incorporated as much as I can into the RFC.
@clarfonthey I do think that the orthogonal representation is more "canonical", especially as it is the most commonly used one in crates.io and across languages. So I'm not sure if we can consider this an issue, especially as there are polar conversion methods in the RFC.

[scimind2460]

Will there be impls for fN: Mul<Complex<fN>>, fN: Add<Complex<fN>>, and the reverses of those? That would make it possible to write e.g. 1.0 + 2.0 * f32::i(). Seems like it should be either part of the RFC or a future possibility, or explicitly rejected.

It was there in an earlier draft, but I decided to relegate it to a future possibility. However, you can see that a related possibility such as the fn i(self) was discussed.

[scimind2460]

@tmandry I hope that all issues are sufficiently resolved?

[tmandry]

@rfcbot reviewed

View changes since this review

[lokyhark]

Just a remark about potential c32 and c64 aliases. I assume they refer to Complex<f32> and Complex<f64> respectively.

I like the idea that i32 is 32 bits, u64 is 64 bits etc. Using c32 for a type with a size of 64 bits may be confusing or at least, error prone for users.

For instance numpy use complex128 for Complex<64>. However it may be a bigger transition from well established complex number crates that rely on c32 = Complex<f32>.

Choosing the most appropriate one may require additional discussion.

[scimind2460]

I like the idea that i32 is 32 bits, u64 is 64 bits etc. Using c32 for a type with a size of 64 bits may be confusing or at least, error prone for users.

To be fair, one could also argue the other way, that it may be confusing for users who may think c64 is actually Complex<f64> instead of Complex<f32> due to them sharing the same number. It really is a matter of perspective.

We could theoretically discuss which one is better here, but I don't think this should block the RFC.

Thanks for raising the point @lokyhark!

[kennytm]

It really is a matter of perspective.

We could theoretically discuss which one is better here,

If one needs a discussion to determine whether c64 means Complex<f64> or Complex<f32> perhaps it's the best not to introduce such type alias to avoid ambiguity at all.

Also most prior art that provides such an alias uses complex128 to refer to Complex<f64>. I think num-complex is the only packages that uses "64" alone in a type name to refer to Complex<f64>.

Library	Named by total size	Named by component	Generic only
C	-	-	double _Complex
C++	-	-	std::complex<double>
Fortran	-	COMPLEX(8)	-
Haskell	-	-	Complex Double
D	-	cdouble	Complex!double
Go	complex128	-	-
numpy (Python)	complex128	cdouble	-
Mathematica	Complex128	ComplexReal64	-
swift-numerics (Swift)	-	-	Complex<Double>
num-complex (Rust)	-	Complex64	Complex<f64>

[scimind2460]

If one needs a discussion to determine whether c64 means Complex<f64> or Complex<f32> perhaps it's the best not to introduce such type alias to avoid ambiguity at all.

Yes, I agree. It would essentially be clear looking at the generic type.

Besides, we should have this discussion later, given that it's mentioned in the RFC as a future possibility.

[nikomatsakis]

@rfcbot reviewed

[scimind2460]

Thanks @nikomatsakis for the review!

By the way, is rfcbot bugged? It hasn't acknowledged the review yet.

[rust-rfcbot]

🔔 This is now entering its final comment period, as per the review above. 🔔

[traviscross]

@rfcbot reviewed

Thanks @scimind2460 for putting in the work on this.

[rust-rfcbot]

The final comment period, with a disposition to merge, as per the review above, is now complete.

As the automated representative of the governance process, I would like to thank the author for their work and everyone else who contributed.

[traviscross]

The lang and libs-api teams have decided to accept this RFC, and it's now been merged. Thanks to @scimind2460 for pushing this forward.

For further updates, see the tracking issue:

• Tracking issue for RFC 3892: Complex numbers. rust#154023