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Vl-arithclass-p

Vl-arithclass-max

(vl-arithclass-max x y &rest rst) computes the arithmetic class for a non self-determined operand, given the classes of the arguments.

See SystemVerilog-2012 Section 11.8.1, Expression Evaluation Rules. This function loosely corresponds to the case for non self-determined operands, where ``the following rules apply:

If any operand is real, the result is real.
If any operand is unsigned, the result is unsigned, regardless of the operator.
If all operands are signed, the result will be signed, regardless of operator, except when specified otherwise.''

These rules seem pretty incomplete because not all expressions fit nicely into these types: for instance what is the result from a mintypmax expression or a tagged union type or an unpacked type or that sort of thing. But at any rate we imagine a hierarchy, where:

signed < unsigned < shortreal < real < other

And the maximum class of an argument becomes the class for the operator. For example, if we're computing the type of a + b and a is a unsigned but b is a shortreal, then the sum should be a shortreal.

We assign the ``other'' class to anything that is valid but doesn't seem like a sensible arithmetic type. For instance, an unpacked structure or weird operator like a mintypmax.

We use the ``error'' class only for cases where we truly cannot determine the type of something because of an error (e.g., undeclared identifier, etc.)

Definitions and Theorems

Function: vl-arithclass-max-fn

(defun vl-arithclass-max-fn (x y)
  (declare (xargs :guard (and (vl-arithclass-p x)
                              (vl-arithclass-p y))))
  (b* ((x (vl-arithclass-fix x))
       (y (vl-arithclass-fix y)))
    (if (< (vl-arithclass-rank x)
           (vl-arithclass-rank y))
        y
      x)))

Theorem: vl-arithclass-p-of-vl-arithclass-max

(defthm vl-arithclass-p-of-vl-arithclass-max
  (vl-arithclass-p (vl-arithclass-max x y)))

Theorem: vl-arithclass-max-of-vl-arithclass-max

(defthm vl-arithclass-max-of-vl-arithclass-max
  (equal (vl-arithclass-max (vl-arithclass-max x y)
                            z)
         (vl-arithclass-max x (vl-arithclass-max y z))))

Theorem: vl-arithclass-max-fn-of-vl-arithclass-fix-x

(defthm vl-arithclass-max-fn-of-vl-arithclass-fix-x
  (equal (vl-arithclass-max-fn (vl-arithclass-fix x)
                               y)
         (vl-arithclass-max-fn x y)))

Theorem: vl-arithclass-max-fn-vl-arithclass-equiv-congruence-on-x

(defthm vl-arithclass-max-fn-vl-arithclass-equiv-congruence-on-x
  (implies (vl-arithclass-equiv x x-equiv)
           (equal (vl-arithclass-max-fn x y)
                  (vl-arithclass-max-fn x-equiv y)))
  :rule-classes :congruence)

Theorem: vl-arithclass-max-fn-of-vl-arithclass-fix-y

(defthm vl-arithclass-max-fn-of-vl-arithclass-fix-y
  (equal (vl-arithclass-max-fn x (vl-arithclass-fix y))
         (vl-arithclass-max-fn x y)))

Theorem: vl-arithclass-max-fn-vl-arithclass-equiv-congruence-on-y

(defthm vl-arithclass-max-fn-vl-arithclass-equiv-congruence-on-y
  (implies (vl-arithclass-equiv y y-equiv)
           (equal (vl-arithclass-max-fn x y)
                  (vl-arithclass-max-fn x y-equiv)))
  :rule-classes :congruence)

Subtopics

Vl-arithclass-rank: Rankings of vl-arithclass-ps used in vl-arithclass-max.