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• Primitive-narrowing-conversions

Short-to-byte

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

Signature

(short-to-byte operand) → result

Arguments

operand — Guard (short-valuep operand).

Returns

result — Type (byte-valuep result).

Definitions and Theorems

Function: short-to-byte

(defun short-to-byte (operand)
  (declare (xargs :guard (short-valuep operand)))
  (b* ((x (short-value->int operand)))
    (byte-value (logext 8 x))))

Theorem: byte-valuep-of-short-to-byte

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

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

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

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

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