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• Sparseint-impl

Sparseint$-binary-bitop-offset

Signature

(sparseint$-binary-bitop-offset op x x.height y-offset y y.height) 
  → 
(mv binary-res height)

Arguments

op — Guard (integerp op).

x — Guard (sparseint$-p x).

x.height — Guard (natp x.height).

y-offset — Guard (natp y-offset).

y — Guard (sparseint$-p y).

y.height — Guard (natp y.height).

Returns

binary-res — Type (sparseint$-p binary-res).

height — Type (equal height (sparseint$-height binary-res)).

Definitions and Theorems

Function: sparseint$-binary-bitop-offset

(defun sparseint$-binary-bitop-offset
       (op x x.height y-offset y y.height)
 (declare (type (unsigned-byte 4) op))
 (declare (xargs :guard (and (integerp op)
                             (sparseint$-p x)
                             (natp x.height)
                             (natp y-offset)
                             (sparseint$-p y)
                             (natp y.height))))
 (declare
      (xargs :guard (and (sparseint$-height-correctp x)
                         (equal x.height (sparseint$-height x))
                         (sparseint$-height-correctp y)
                         (equal y.height (sparseint$-height y)))))
 (let ((__function__ 'sparseint$-binary-bitop-offset))
  (declare (ignorable __function__))
  (b* ((x.height (mbe :logic (sparseint$-height x)
                      :exec x.height))
       (y.height (mbe :logic (sparseint$-height y)
                      :exec y.height))
       (y-offset (lnfix y-offset)))
   (sparseint$-case
     x
     :leaf
     (sparseint$-case
          y
          :leaf
          (mv (sparseint$-leaf
                   (binary-bitop op x.val (logtail y-offset y.val)))
              0)
          :concat
          (sparseint$-binary-bitop-int (binary-bitop-swap op)
                                       y-offset y y.height x.val))
     :concat
     (sparseint$-case
          y :leaf
          (sparseint$-binary-bitop-int
               op
               0 x x.height (logtail y-offset y.val))
          :concat
          (b* ((y.msbs.height
                    (mbe :logic (sparseint$-height y.msbs)
                         :exec (- y.height (if y.lsbs-taller 2 1))))
               ((when (<= y.width y-offset))
                (sparseint$-binary-bitop-offset
                     op x x.height (- y-offset y.width)
                     y.msbs y.msbs.height))
               (x.lsbs.height
                    (mbe :logic (sparseint$-height x.lsbs)
                         :exec (- x.height (if x.msbs-taller 2 1))))
               ((mv lsbs-and lsbs-and.height)
                (sparseint$-binary-bitop-width
                     op x.width x.lsbs
                     x.lsbs.height y-offset y y.height))
               (x.msbs.height
                    (mbe :logic (sparseint$-height x.msbs)
                         :exec (- x.height (if x.lsbs-taller 2 1))))
               ((mv msbs-and msbs-and.height)
                (sparseint$-binary-bitop-offset
                     op x.msbs
                     x.msbs.height (+ x.width y-offset)
                     y y.height)))
            (sparseint$-concatenate-rebalance
                 x.width lsbs-and lsbs-and.height
                 msbs-and msbs-and.height)))))))

Theorem: sparseint$-p-of-sparseint$-binary-bitop-offset.binary-res

(defthm sparseint$-p-of-sparseint$-binary-bitop-offset.binary-res
  (b* (((mv ?binary-res ?height)
        (sparseint$-binary-bitop-offset
             op x x.height y-offset y y.height)))
    (sparseint$-p binary-res))
  :rule-classes :rewrite)

Theorem: return-type-of-sparseint$-binary-bitop-offset.height

(defthm return-type-of-sparseint$-binary-bitop-offset.height
  (b* (((mv ?binary-res ?height)
        (sparseint$-binary-bitop-offset
             op x x.height y-offset y y.height)))
    (equal height (sparseint$-height binary-res)))
  :rule-classes :rewrite)

Theorem: sparseint$-height-correctp-of-sparseint$-binary-bitop-offset

(defthm sparseint$-height-correctp-of-sparseint$-binary-bitop-offset
  (b* (((mv ?binary-res ?height)
        (sparseint$-binary-bitop-offset
             op x x.height y-offset y y.height)))
    (implies (and (sparseint$-height-correctp x)
                  (sparseint$-height-correctp y))
             (sparseint$-height-correctp binary-res))))

Theorem: sparseint$-val-of-sparseint$-binary-bitop-offset

(defthm sparseint$-val-of-sparseint$-binary-bitop-offset
  (b* (((mv ?binary-res ?height)
        (sparseint$-binary-bitop-offset
             op x x.height y-offset y y.height)))
    (equal (sparseint$-val binary-res)
           (binary-bitop op (sparseint$-val x)
                         (logtail y-offset (sparseint$-val y))))))

Theorem: sparseint$-binary-bitop-offset-of-ifix-op

(defthm sparseint$-binary-bitop-offset-of-ifix-op
 (equal
     (sparseint$-binary-bitop-offset (ifix op)
                                     x x.height y-offset y y.height)
     (sparseint$-binary-bitop-offset
          op x x.height y-offset y y.height)))

Theorem: sparseint$-binary-bitop-offset-int-equiv-congruence-on-op

(defthm sparseint$-binary-bitop-offset-int-equiv-congruence-on-op
 (implies
  (int-equiv op op-equiv)
  (equal
   (sparseint$-binary-bitop-offset
        op x x.height y-offset y y.height)
   (sparseint$-binary-bitop-offset op-equiv
                                   x x.height y-offset y y.height)))
 :rule-classes :congruence)

Theorem: sparseint$-binary-bitop-offset-of-sparseint$-fix-x

(defthm sparseint$-binary-bitop-offset-of-sparseint$-fix-x
  (equal
       (sparseint$-binary-bitop-offset op (sparseint$-fix x)
                                       x.height y-offset y y.height)
       (sparseint$-binary-bitop-offset
            op x x.height y-offset y y.height)))

Theorem: sparseint$-binary-bitop-offset-sparseint$-equiv-congruence-on-x

(defthm
    sparseint$-binary-bitop-offset-sparseint$-equiv-congruence-on-x
  (implies (sparseint$-equiv x x-equiv)
           (equal (sparseint$-binary-bitop-offset
                       op x x.height y-offset y y.height)
                  (sparseint$-binary-bitop-offset
                       op
                       x-equiv x.height y-offset y y.height)))
  :rule-classes :congruence)

Theorem: sparseint$-binary-bitop-offset-of-nfix-x.height

(defthm sparseint$-binary-bitop-offset-of-nfix-x.height
  (equal (sparseint$-binary-bitop-offset op x (nfix x.height)
                                         y-offset y y.height)
         (sparseint$-binary-bitop-offset
              op x x.height y-offset y y.height)))

Theorem: sparseint$-binary-bitop-offset-nat-equiv-congruence-on-x.height

(defthm
    sparseint$-binary-bitop-offset-nat-equiv-congruence-on-x.height
  (implies (nat-equiv x.height x.height-equiv)
           (equal (sparseint$-binary-bitop-offset
                       op x x.height y-offset y y.height)
                  (sparseint$-binary-bitop-offset
                       op
                       x x.height-equiv y-offset y y.height)))
  :rule-classes :congruence)

Theorem: sparseint$-binary-bitop-offset-of-nfix-y-offset

(defthm sparseint$-binary-bitop-offset-of-nfix-y-offset
  (equal
       (sparseint$-binary-bitop-offset op x x.height (nfix y-offset)
                                       y y.height)
       (sparseint$-binary-bitop-offset
            op x x.height y-offset y y.height)))

Theorem: sparseint$-binary-bitop-offset-nat-equiv-congruence-on-y-offset

(defthm
    sparseint$-binary-bitop-offset-nat-equiv-congruence-on-y-offset
  (implies (nat-equiv y-offset y-offset-equiv)
           (equal (sparseint$-binary-bitop-offset
                       op x x.height y-offset y y.height)
                  (sparseint$-binary-bitop-offset
                       op
                       x x.height y-offset-equiv y y.height)))
  :rule-classes :congruence)

Theorem: sparseint$-binary-bitop-offset-of-sparseint$-fix-y

(defthm sparseint$-binary-bitop-offset-of-sparseint$-fix-y
  (equal (sparseint$-binary-bitop-offset
              op
              x x.height y-offset (sparseint$-fix y)
              y.height)
         (sparseint$-binary-bitop-offset
              op x x.height y-offset y y.height)))

Theorem: sparseint$-binary-bitop-offset-sparseint$-equiv-congruence-on-y

(defthm
    sparseint$-binary-bitop-offset-sparseint$-equiv-congruence-on-y
  (implies (sparseint$-equiv y y-equiv)
           (equal (sparseint$-binary-bitop-offset
                       op x x.height y-offset y y.height)
                  (sparseint$-binary-bitop-offset
                       op
                       x x.height y-offset y-equiv y.height)))
  :rule-classes :congruence)

Theorem: sparseint$-binary-bitop-offset-of-nfix-y.height

(defthm sparseint$-binary-bitop-offset-of-nfix-y.height
  (equal (sparseint$-binary-bitop-offset
              op
              x x.height y-offset y (nfix y.height))
         (sparseint$-binary-bitop-offset
              op x x.height y-offset y y.height)))

Theorem: sparseint$-binary-bitop-offset-nat-equiv-congruence-on-y.height

(defthm
    sparseint$-binary-bitop-offset-nat-equiv-congruence-on-y.height
  (implies (nat-equiv y.height y.height-equiv)
           (equal (sparseint$-binary-bitop-offset
                       op x x.height y-offset y y.height)
                  (sparseint$-binary-bitop-offset
                       op
                       x x.height y-offset y y.height-equiv)))
  :rule-classes :congruence)