Add `Floating` class #457

aijony · 2022-03-29T00:53:44Z

While I was waiting on #451, I actually wasn't too unhappy with having Floating being split into multiple segments. This would allow more flexible instances (e.g. square matrices via power series). We could also move (a)tan(h) to Floating if we wanted to remove Dividable from Trig. I put ** and logBase into Floating as well because giving them a multi parameter type class messes with stuff like logBase 2 2.0 - even though a power series of e^x or log x imply power series a^x or log_a x resp. One can also come up with a power series for sqrt, so I really haven't broken it up to allow all the mathematical edge-cases.

I'll be the first to admit this seems a bit advanced for a standard library, so I'm happy to make floating into a mega class when #451 gets sorted out. Either way, I'd love some input.

Fixes: #366

eliaslfox · 2022-03-29T02:13:06Z

library/arith.lisp

+
+(%define-floating-functions Single-Float cl:single-float)
+(%define-floating-functions Double-Float cl:double-float)
+(%define-floating-functions (Complex Single-Float) (cl:complex cl:single-float))


These should be (cl:or cl:single-float (cl:complex cl:single-float)).

See (typep #C(1 0) '(complex integer))

Those are only used to coerce pi at the moment, and actually it seems that coercing pi as either single-float or (complex single-float) work equally well. However, one cannot (coerce pi '(or single-float (complex single-foat)). However, if we don't coerce pi, it will sometimes decide it wants be a double-float.

Given the option of (coerce pi 'single-float) => 3.14... and (coerce pi '(complex single-float)) ;=> #C(3.14... 0) do think there is a best choice?

I think either is fine. I misunderstood the use case.

braised-babbage · 2022-03-30T00:28:23Z

I left a few questions about the granularity & specific details of the type constraints above.

I think it's worth distinguishing between two uses of typeclasses (perhaps there are others):

as syntactic sugar (e.g. letting us write (exp matrix) rather than (expm matrix))
as a substrate for generic programming (e.g. so we can write code that is agnostic to floating point precision, or which is also capable of working under interval arithmetic, automatic differentiation, etc).

This PR appears to be sensitive to both of these items, which is good. I would say that I would be surprised to see serious numeric code which is generic across substantially different domains (e.g. which works effectively for both complex double floats & real matrices), so I don't think it's worth sweating that part too much.

eliaslfox · 2022-03-30T00:33:05Z

@kilimanjaro If you had other comments, I don't think they saved.

braised-babbage · 2022-03-29T23:45:14Z

library/arith.lisp

+(coalton-toplevel
+  (define-class (Exponent :a)
+    "Exponential functions where exp is exponentiation of Euler's number and
+(exp (+ a b)) = (* (exp a) (exp b)) and (exp 0) = 1."


Should I take this to mean that :a is a member of some other typeclass (providing arithmetic and 0, 1)?

Yeah, I figured Num would imply commutative, but we could easily add it.

braised-babbage · 2022-03-29T23:46:30Z

library/arith.lisp

+(exp (+ a b)) = (* (exp a) (exp b)) and (exp 0) = 1."
+    (exp (:a -> :a)))
+
+  (define-class (Exponent :a => Logarithm :a)


Out of curiosity, do you have something in mind that would be an instance of Exponent but not Logarithm?

No specific examples, but if we end up splitting the class like this I think exp would be the most useful function. I guess for the cases were either ln(X) doesn't converge but e^X does - it could just throw an error (or in the case were the implementer is too lazy).

braised-babbage · 2022-03-29T23:48:18Z

library/arith.lisp

+    (atanh (:a -> :a)))
+
+  (define-class ((InvTrig :a) (Num :a) => Floating :a)
+    "Common floating point operations."


To be a bit pedantic here, I don't quite see what makes this a floating type. For example, one could imagine implementing all of these with fixed point arithmetic. Also, unless I'm missing something, it could even be satisfied by symbolic expressions (this is perhaps a silly thing to mention).

I'm happy if anyone has any better names. I just was trying to keep it somewhat friendly to Haskell-familiar users.

That makes sense. No real objections then.

braised-babbage · 2022-03-29T23:53:26Z

library/arith.lisp

+    "Logarithmic functions such that log is the inverse of exp."
+    (log (:a -> :a)))
+
+  (define-class ((Exponent :a) (Dividable :a :a) => Trig :a)


It's not clear why we need (Dividable :a :a). There's no comparable constraint placed on Exponent or Logarithm.

I'm not aware of a way to define tan without division, but I could be wrong. I could also move tan to Floating and remove Dividable.

a power series doesn't require division

I love it how my brain decided the only way to compute tan was sin/cos and just pretended tan didn't have a series representation.

when @kilimanjaro computes tan he uses a compass and ruler; i've seen it with my own two eyes

braised-babbage · 2022-03-29T23:58:50Z

library/arith.lisp

+    (cosh (:a -> :a))
+    (tanh (:a -> :a)))
+
+  (define-class ((Logarithm :a) (Trig :a) => InvTrig :a)


Similarly here; it's not clear why we need Logarithm. To me it sort of implies that these inverse trig functions can be defined in terms of log, which they can, but you need complex arithmetic for that, and also it's probably not how anybody would want to implement them.

Yeah, I was trying to instill some semblance of hierarchy, but I agree this one perhaps is just restrictive with no benefit.

braised-babbage · 2022-03-30T00:21:40Z

library/arith.lisp

+       (define (acosh x) (lisp ,coalton-type (x) (cl:acosh x)))
+       (define (atanh x) (lisp ,coalton-type (x) (cl:atanh x))))
+
+     (define-instance (Floating ,coalton-type)


Perhaps abs is worth adding here.

We already have abs for instances of Ord, but perhaps modulus or absolute? Or we could change abs for Ord to something like positive. However, I have code were I need Complex numbers as a vector space (for dot products), likewise I have been using norm on Complex numbers. But implementing linear algebra code is probably out of scope for this PR.

It strikes me as a bit odd that abs requires Ord, for the reason that you mentioned: one will end up defining a modulus or absolute or something for complex numbers. So if we do have the ability to move stuff around, I suggest dropping the Ord constraint.

yeah, abs in ord seems weird. I think haskell does it but I would be fine nixing it.

stylewarning self-assigned this Mar 29, 2022

eliaslfox reviewed Mar 29, 2022

View reviewed changes

braised-babbage reviewed Mar 30, 2022

View reviewed changes

Add floating

43b55ad

aijony mentioned this pull request Apr 2, 2022

Make / closed #480

Merged

This pull request was closed.

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

Add `Floating` class #457

Add `Floating` class #457

aijony commented Mar 29, 2022

eliaslfox Mar 29, 2022 •

edited

Loading

aijony Mar 31, 2022 •

edited

Loading

eliaslfox Mar 31, 2022

braised-babbage commented Mar 30, 2022

eliaslfox commented Mar 30, 2022

braised-babbage Mar 29, 2022

aijony Mar 30, 2022

braised-babbage Mar 29, 2022

aijony Mar 30, 2022

braised-babbage Mar 29, 2022

aijony Mar 30, 2022

braised-babbage Mar 31, 2022

braised-babbage Mar 29, 2022

aijony Mar 30, 2022 •

edited

Loading

stylewarning Mar 31, 2022

aijony Mar 31, 2022

stylewarning Mar 31, 2022

braised-babbage Mar 29, 2022

aijony Mar 30, 2022 •

edited

Loading

braised-babbage Mar 30, 2022

aijony Mar 30, 2022

braised-babbage Mar 31, 2022

stylewarning Mar 31, 2022

Add Floating class #457

Add Floating class #457

Conversation

aijony commented Mar 29, 2022

eliaslfox Mar 29, 2022 • edited Loading

Choose a reason for hiding this comment

aijony Mar 31, 2022 • edited Loading

Choose a reason for hiding this comment

Choose a reason for hiding this comment

braised-babbage commented Mar 30, 2022

eliaslfox commented Mar 30, 2022

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

aijony Mar 30, 2022 • edited Loading

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

aijony Mar 30, 2022 • edited Loading

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Add `Floating` class #457

Add `Floating` class #457

eliaslfox Mar 29, 2022 •

edited

Loading

aijony Mar 31, 2022 •

edited

Loading

aijony Mar 30, 2022 •

edited

Loading

aijony Mar 30, 2022 •

edited

Loading