Uniform access to IEEE floating point parameters?

[ornamentist]

Is there a place in the Coalton numeric typeclasses for uniform access to IEEE floating point parameters? I'm thinking of something like https://hackage.haskell.org/package/ieee-0.7/docs/Numeric-IEEE.html.

This would allow, for example uniform access to min-normal or max-finite for Single-Float, Double-Float and any other IEEE floating point types we might later support (e.g. float-16 or float-128).

I understand these values and related functions are available in the underlying Common Lisp standard library, so we can always access them via a (cl:foo...) function.

[eliaslfox]

I think so. Probably something like RealFloat :a => FloatIEEE :a. This would be a good place for the other lisp float deconstrucors too.

[ornamentist]

I needed something like this in a Coalton project so I used:

(define-class (Eq :a => IEEE :a)

    (infinity :a)

    (min-normal :a)

    (max-finite :a)

    (epsilon :a)

    (is-nan? (:a -> Boolean))

    (is-infinite? (:a -> Boolean)))

With a single float instance:

  (define-instance (IEEE Single-Float)

    (define infinity
      (Lisp Single-Float ()
        float-features:single-float-positive-infinity))

    (define min-normal
      1.17549435e-38)

    (define max-finite
      3.40282347e+38)

    (define epsilon
      (Lisp Single-Float ()
        cl:single-float-epsilon))

    (define (is-nan? x)
      (Lisp Boolean (x)
        (float-features:float-NaN-p x)))

    (define (is-infinite? x)
      (Lisp Boolean (x)
        (float-features:float-infinity-p x))))

And double float instance

 (define-instance (IEEE Double-Float)

    (define infinity
      (Lisp Double-Float ()
        float-features:double-float-positive-infinity))

    (define min-normal
      (the Double-Float 2.2250738585072014d-308))

    (define max-finite
      (the Double-Float 1.7976931348623157d+308))

    (define epsilon
      (Lisp Double-Float ()
        cl:double-float-epsilon))

    (define (is-nan? x)
      (Lisp Boolean (x)
        (float-features:float-NaN-p x)))

    (define (is-infinite? x)
      (Lisp Boolean (x)
        (float-features:float-infinity-p x))))

[stylewarning]

see also cl:most-positive-double-float and friends.

[ornamentist]

Excellent suggestion thanks.

[ornamentist]

Common Lisp supports four floating point formats: "short", "single", "double" and "long". I'm guessing the mapping of these to IEEE floats is compiler specific?

[ornamentist]

Maybe something like:

  (define-class (Eq :a => IEEE :a)
    "Defines the numerical limits of an IEEE floating point number."

    (infinity :a)

    (min-normal :a)

    (most-positive :a)

    (most-negative :a)

    (positive-epsilon :a)

    (nan? (:a -> Boolean))

    (infinite? (:a -> Boolean)))


  (define-instance (IEEE Single-Float)
    ;;"IEEE instance for Coalton (IEEE) single precision floats."

    (define infinity
      "Single precision floating point positive infinity."

      (Lisp Single-Float ()
        float-features:single-float-positive-infinity))

    (define min-normal
      "Single precision ..."

      (Lisp Single-Float ()
        cl:least-positive-normalized-single-float))

    (define most-positive
      "Most positive single precision floating point value."

      (Lisp Single-Float ()
        cl:most-positive-single-float))

    (define most-negative
      "Most negative single precision floating point value."

      (Lisp Single-Float ()
        cl:most-negative-single-float))

    (define epsilon
      "The smallest single precision floating point different from 1.0"

      (Lisp Single-Float ()
        cl:single-float-epsilon))

    (define (nan? x)
      "Is a single precision floating point value X a NaN?"

      (Lisp Boolean (x)
        (float-features:float-nan-p x)))

    (define (infinite? x)
      "Is a single precision floating point value X positive infinity?"

      (Lisp Boolean (x)
        (float-features:float-infinity-p x))))