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Floating-point-operations

Float-less

Less-than comparison < on floats [JLS14:4.2.4] [JLS14:15.20.1].

Signature
(float-less operand-left operand-right) → result
Arguments: operand-left — Guard (float-valuep operand-left).; operand-right — Guard (float-valuep operand-right).
Returns: result — Type (boolean-valuep result).

Definitions and Theorems

Function: float-less

(defun float-less (operand-left operand-right)
  (declare (xargs :guard (and (float-valuep operand-left)
                              (float-valuep operand-right))))
  (b* ((x (float-value->float operand-left))
       (y (float-value->float operand-right)))
    (boolean-value (float-less-abs x y))))

Theorem: boolean-valuep-of-float-less

(defthm boolean-valuep-of-float-less
  (b* ((result (float-less operand-left operand-right)))
    (boolean-valuep result))
  :rule-classes :rewrite)

Theorem: float-less-of-float-value-fix-operand-left

(defthm float-less-of-float-value-fix-operand-left
  (equal (float-less (float-value-fix operand-left)
                     operand-right)
         (float-less operand-left operand-right)))

Theorem: float-less-float-value-equiv-congruence-on-operand-left

(defthm float-less-float-value-equiv-congruence-on-operand-left
  (implies (float-value-equiv operand-left operand-left-equiv)
           (equal (float-less operand-left operand-right)
                  (float-less operand-left-equiv operand-right)))
  :rule-classes :congruence)

Theorem: float-less-of-float-value-fix-operand-right

(defthm float-less-of-float-value-fix-operand-right
  (equal (float-less operand-left
                     (float-value-fix operand-right))
         (float-less operand-left operand-right)))

Theorem: float-less-float-value-equiv-congruence-on-operand-right

(defthm float-less-float-value-equiv-congruence-on-operand-right
  (implies (float-value-equiv operand-right operand-right-equiv)
           (equal (float-less operand-left operand-right)
                  (float-less operand-left operand-right-equiv)))
  :rule-classes :congruence)