		Search-engine friendly clone of the ACL2 documentation.

Imul-spec

Imul-spec-16

Signature
(imul-spec-16 dst src) → (mv * * * *)

Definitions and Theorems

Function: imul-spec-16

(defun imul-spec-16 (dst src)
 (declare (type (unsigned-byte 16) dst)
          (type (unsigned-byte 16) src))
 (let ((__function__ 'imul-spec-16))
  (declare (ignorable __function__))
  (b*
   ((dst-int (the (signed-byte 16) (ntoi 16 dst)))
    (src-int (the (signed-byte 16) (ntoi 16 src)))
    (product-int (the (signed-byte 32)
                      (* (the (signed-byte 16) dst-int)
                         (the (signed-byte 16) src-int))))
    (product (the (unsigned-byte 32)
                  (n-size 32 product-int)))
    (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))))
    (product-low-int (the (signed-byte 16)
                          (ntoi 16 product-low)))
    (cf-and-of
      (the (unsigned-byte 1)
           (bool->bit
                (not (equal (the (signed-byte 16) product-low-int)
                            (the (signed-byte 32) product-int)))))))
   (mv product-high
       product-low product cf-and-of))))

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

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

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

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

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

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

Theorem: mv-nth-3-imul-spec-16

(defthm mv-nth-3-imul-spec-16
 (unsigned-byte-p 1 (mv-nth 3 (imul-spec-16 dst src)))
 :rule-classes
 (:rewrite
  (:type-prescription
     :corollary (bitp (mv-nth 3 (imul-spec-16 dst src)))
     :hints
     (("Goal"
           :in-theory
           '(unsigned-byte-p integer-range-p natp bitp (:e expt)))))
  (:linear
   :corollary (and (<= 0 (mv-nth 3 (imul-spec-16 dst src)))
                   (< (mv-nth 3 (imul-spec-16 dst src)) 2))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))