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Imul-spec

Imul-spec-64

Signature
(imul-spec-64 dst src) → (mv * * * *)

Definitions and Theorems

Function: imul-spec-64

(defun imul-spec-64 (dst src)
 (declare (type (unsigned-byte 64) dst)
          (type (unsigned-byte 64) src))
 (let ((__function__ 'imul-spec-64))
  (declare (ignorable __function__))
  (b*
   ((dst-int (the (signed-byte 64) (ntoi 64 dst)))
    (src-int (the (signed-byte 64) (ntoi 64 src)))
    (product-int (the (signed-byte 128)
                      (* (the (signed-byte 64) dst-int)
                         (the (signed-byte 64) src-int))))
    (product (the (unsigned-byte 128)
                  (n-size 128 product-int)))
    (product-high
         (mbe :logic (part-select product :low 64 :width 64)
              :exec (the (unsigned-byte 64)
                         (ash (the (unsigned-byte 128) product)
                              -64))))
    (product-low
         (mbe :logic (part-select product :low 0 :width 64)
              :exec (the (unsigned-byte 64)
                         (logand 18446744073709551615 product))))
    (product-low-int (the (signed-byte 64)
                          (ntoi 64 product-low)))
    (cf-and-of
     (the
       (unsigned-byte 1)
       (bool->bit (not (equal (the (signed-byte 64) product-low-int)
                              (the (signed-byte 128)
                                   product-int)))))))
   (mv product-high
       product-low product cf-and-of))))

Theorem: n64-mv-nth-0-imul-spec-64

(defthm n64-mv-nth-0-imul-spec-64
 (unsigned-byte-p 64 (mv-nth 0 (imul-spec-64 dst src)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 0 (imul-spec-64 dst src)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 0 (imul-spec-64 dst src)))
                   (< (mv-nth 0 (imul-spec-64 dst src))
                      18446744073709551616))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: mv-nth-1-imul-spec-64

(defthm mv-nth-1-imul-spec-64
 (unsigned-byte-p 64 (mv-nth 1 (imul-spec-64 dst src)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 1 (imul-spec-64 dst src)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 1 (imul-spec-64 dst src)))
                   (< (mv-nth 1 (imul-spec-64 dst src))
                      18446744073709551616))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: mv-nth-2-imul-spec-64

(defthm mv-nth-2-imul-spec-64
 (unsigned-byte-p 128 (mv-nth 2 (imul-spec-64 dst src)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 2 (imul-spec-64 dst src)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 2 (imul-spec-64 dst src)))
                   (< (mv-nth 2 (imul-spec-64 dst src))
                      340282366920938463463374607431768211456))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: mv-nth-3-imul-spec-64

(defthm mv-nth-3-imul-spec-64
 (unsigned-byte-p 1 (mv-nth 3 (imul-spec-64 dst src)))
 :rule-classes
 (:rewrite
  (:type-prescription
     :corollary (bitp (mv-nth 3 (imul-spec-64 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-64 dst src)))
                   (< (mv-nth 3 (imul-spec-64 dst src)) 2))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))