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Xcr0bits

!xcr0bits->bndcsr-state

Update the |X86ISA|::|BNDCSR-STATE| field of a xcr0bits bit structure.

Signature
(!xcr0bits->bndcsr-state bndcsr-state x) → new-x
Arguments: bndcsr-state — Guard (bitp bndcsr-state).; x — Guard (xcr0bits-p x).
Returns: new-x — Type (xcr0bits-p new-x).

Definitions and Theorems

Function: !xcr0bits->bndcsr-state$inline

(defun !xcr0bits->bndcsr-state$inline (bndcsr-state x)
 (declare (xargs :guard (and (bitp bndcsr-state)
                             (xcr0bits-p x))))
 (mbe
   :logic
   (b* ((bndcsr-state (mbe :logic (bfix bndcsr-state)
                           :exec bndcsr-state))
        (x (xcr0bits-fix x)))
     (part-install bndcsr-state x
                   :width 1
                   :low 4))
   :exec (the (unsigned-byte 64)
              (logior (the (unsigned-byte 64)
                           (logand (the (unsigned-byte 64) x)
                                   (the (signed-byte 6) -17)))
                      (the (unsigned-byte 5)
                           (ash (the (unsigned-byte 1) bndcsr-state)
                                4))))))

Theorem: xcr0bits-p-of-!xcr0bits->bndcsr-state

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

Theorem: !xcr0bits->bndcsr-state$inline-of-bfix-bndcsr-state

(defthm !xcr0bits->bndcsr-state$inline-of-bfix-bndcsr-state
  (equal (!xcr0bits->bndcsr-state$inline (bfix bndcsr-state)
                                         x)
         (!xcr0bits->bndcsr-state$inline bndcsr-state x)))

Theorem: !xcr0bits->bndcsr-state$inline-bit-equiv-congruence-on-bndcsr-state

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

Theorem: !xcr0bits->bndcsr-state$inline-of-xcr0bits-fix-x

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

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

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

Theorem: !xcr0bits->bndcsr-state-is-xcr0bits

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

Theorem: xcr0bits->bndcsr-state-of-!xcr0bits->bndcsr-state

(defthm xcr0bits->bndcsr-state-of-!xcr0bits->bndcsr-state
  (b* ((?new-x (!xcr0bits->bndcsr-state$inline bndcsr-state x)))
    (equal (xcr0bits->bndcsr-state new-x)
           (bfix bndcsr-state))))

Theorem: !xcr0bits->bndcsr-state-equiv-under-mask

(defthm !xcr0bits->bndcsr-state-equiv-under-mask
  (b* ((?new-x (!xcr0bits->bndcsr-state$inline bndcsr-state x)))
    (xcr0bits-equiv-under-mask new-x x -17)))