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• Mul-spec

Mul-spec-16

Signature

(mul-spec-16 dst src) → (mv * * *)

Definitions and Theorems

Function: mul-spec-16

(defun mul-spec-16 (dst src)
 (declare (type (unsigned-byte 16) dst)
          (type (unsigned-byte 16) src))
 (let ((__function__ 'mul-spec-16))
   (declare (ignorable __function__))
   (b*
    ((dst (mbe :logic (n-size 16 dst) :exec dst))
     (src (mbe :logic (n-size 16 src) :exec src))
     (product (the (unsigned-byte 32) (* dst src)))
     (product-high
          (mbe :logic (part-select product :low 16 :width 16)
               :exec (the (unsigned-byte 16)
                          (ash (the (unsigned-byte 32) product)
                               -16))))
     (product-low (mbe :logic (part-select product :low 0 :width 16)
                       :exec (the (unsigned-byte 16)
                                  (logand 65535 product)))))
    (mv product-high product-low product))))

Theorem: n16-mv-nth-0-mul-spec-16

(defthm n16-mv-nth-0-mul-spec-16
 (unsigned-byte-p 16 (mv-nth 0 (mul-spec-16 dst src)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 0 (mul-spec-16 dst src)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 0 (mul-spec-16 dst src)))
                   (< (mv-nth 0 (mul-spec-16 dst src))
                      65536))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: mv-nth-1-mul-spec-16

(defthm mv-nth-1-mul-spec-16
 (unsigned-byte-p 16 (mv-nth 1 (mul-spec-16 dst src)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 1 (mul-spec-16 dst src)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 1 (mul-spec-16 dst src)))
                   (< (mv-nth 1 (mul-spec-16 dst src))
                      65536))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: mv-nth-2-mul-spec-16

(defthm mv-nth-2-mul-spec-16
 (unsigned-byte-p 32 (mv-nth 2 (mul-spec-16 dst src)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 2 (mul-spec-16 dst src)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 2 (mul-spec-16 dst src)))
                   (< (mv-nth 2 (mul-spec-16 dst src))
                      4294967296))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))