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• Floating-point-operations

Float-sub

Subtraction - on floats [JLS14:4.2.4] [JLS14:15.18.2].

Signature

(float-sub operand-left operand-right) → result

Arguments

operand-left — Guard (float-valuep operand-left).

operand-right — Guard (float-valuep operand-right).

Returns

result — Type (float-valuep result).

Definitions and Theorems

Function: float-sub

(defun float-sub (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)))
    (float-value (float-sub-abs x y))))

Theorem: float-valuep-of-float-sub

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

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

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

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

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

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

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

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

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