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• Primitive-narrowing-conversions

Long-to-short

Narrowing conversion from long to short [JLS14:5.1.3].

Signature

(long-to-short operand) → result

Arguments

operand — Guard (long-valuep operand).

Returns

result — Type (short-valuep result).

Definitions and Theorems

Function: long-to-short

(defun long-to-short (operand)
  (declare (xargs :guard (long-valuep operand)))
  (b* ((x (long-value->int operand)))
    (short-value (logext 16 x))))

Theorem: short-valuep-of-long-to-short

(defthm short-valuep-of-long-to-short
  (b* ((result (long-to-short operand)))
    (short-valuep result))
  :rule-classes :rewrite)

Theorem: long-to-short-of-long-value-fix-operand

(defthm long-to-short-of-long-value-fix-operand
  (equal (long-to-short (long-value-fix operand))
         (long-to-short operand)))

Theorem: long-to-short-long-value-equiv-congruence-on-operand

(defthm long-to-short-long-value-equiv-congruence-on-operand
  (implies (long-value-equiv operand operand-equiv)
           (equal (long-to-short operand)
                  (long-to-short operand-equiv)))
  :rule-classes :congruence)