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• Integer-operations

Int-int-shiftl

Left shift of an int by an int [JLS14:4.2.2] [JLS14:15.19].

Signature

(int-int-shiftl operand-left operand-right) → result

Arguments

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

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

Returns

result — Type (int-valuep result).

Only the low 5 bits of the distance are used [JLS14:15.19].

Definitions and Theorems

Function: int-int-shiftl

(defun int-int-shiftl (operand-left operand-right)
  (declare (xargs :guard (and (int-valuep operand-left)
                              (int-valuep operand-right))))
  (b* ((x (int-value->int operand-left))
       (y (int-value->int operand-right)))
    (int-value (logext 32 (ash x (loghead 5 y))))))

Theorem: int-valuep-of-int-int-shiftl

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

Theorem: int-int-shiftl-of-int-value-fix-operand-left

(defthm int-int-shiftl-of-int-value-fix-operand-left
  (equal (int-int-shiftl (int-value-fix operand-left)
                         operand-right)
         (int-int-shiftl operand-left operand-right)))

Theorem: int-int-shiftl-int-value-equiv-congruence-on-operand-left

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

Theorem: int-int-shiftl-of-int-value-fix-operand-right

(defthm int-int-shiftl-of-int-value-fix-operand-right
  (equal (int-int-shiftl operand-left
                         (int-value-fix operand-right))
         (int-int-shiftl operand-left operand-right)))

Theorem: int-int-shiftl-int-value-equiv-congruence-on-operand-right

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