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Xcr0bits

!xcr0bits->res2

Update the |X86ISA|::|RES2| field of a xcr0bits bit structure.

Signature
(!xcr0bits->res2 res2 x) → new-x
Arguments: res2 — Guard (7bits-p res2).; x — Guard (xcr0bits-p x).
Returns: new-x — Type (xcr0bits-p new-x).

Definitions and Theorems

Function: !xcr0bits->res2$inline

(defun !xcr0bits->res2$inline (res2 x)
 (declare (xargs :guard (and (7bits-p res2) (xcr0bits-p x))))
 (mbe
    :logic
    (b* ((res2 (mbe :logic (7bits-fix res2)
                    :exec res2))
         (x (xcr0bits-fix x)))
      (part-install res2 x :width 7 :low 10))
    :exec (the (unsigned-byte 64)
               (logior (the (unsigned-byte 64)
                            (logand (the (unsigned-byte 64) x)
                                    (the (signed-byte 18) -130049)))
                       (the (unsigned-byte 17)
                            (ash (the (unsigned-byte 7) res2)
                                 10))))))

Theorem: xcr0bits-p-of-!xcr0bits->res2

(defthm xcr0bits-p-of-!xcr0bits->res2
  (b* ((new-x (!xcr0bits->res2$inline res2 x)))
    (xcr0bits-p new-x))
  :rule-classes :rewrite)

Theorem: !xcr0bits->res2$inline-of-7bits-fix-res2

(defthm !xcr0bits->res2$inline-of-7bits-fix-res2
  (equal (!xcr0bits->res2$inline (7bits-fix res2)
                                 x)
         (!xcr0bits->res2$inline res2 x)))

Theorem: !xcr0bits->res2$inline-7bits-equiv-congruence-on-res2

(defthm !xcr0bits->res2$inline-7bits-equiv-congruence-on-res2
  (implies (7bits-equiv res2 res2-equiv)
           (equal (!xcr0bits->res2$inline res2 x)
                  (!xcr0bits->res2$inline res2-equiv x)))
  :rule-classes :congruence)

Theorem: !xcr0bits->res2$inline-of-xcr0bits-fix-x

(defthm !xcr0bits->res2$inline-of-xcr0bits-fix-x
  (equal (!xcr0bits->res2$inline res2 (xcr0bits-fix x))
         (!xcr0bits->res2$inline res2 x)))

Theorem: !xcr0bits->res2$inline-xcr0bits-equiv-congruence-on-x

(defthm !xcr0bits->res2$inline-xcr0bits-equiv-congruence-on-x
  (implies (xcr0bits-equiv x x-equiv)
           (equal (!xcr0bits->res2$inline res2 x)
                  (!xcr0bits->res2$inline res2 x-equiv)))
  :rule-classes :congruence)

Theorem: !xcr0bits->res2-is-xcr0bits

(defthm !xcr0bits->res2-is-xcr0bits
  (equal (!xcr0bits->res2 res2 x)
         (change-xcr0bits x :res2 res2)))

Theorem: xcr0bits->res2-of-!xcr0bits->res2

(defthm xcr0bits->res2-of-!xcr0bits->res2
  (b* ((?new-x (!xcr0bits->res2$inline res2 x)))
    (equal (xcr0bits->res2 new-x)
           (7bits-fix res2))))

Theorem: !xcr0bits->res2-equiv-under-mask

(defthm !xcr0bits->res2-equiv-under-mask
  (b* ((?new-x (!xcr0bits->res2$inline res2 x)))
    (xcr0bits-equiv-under-mask new-x x -130049)))