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Xcr0bits

!xcr0bits->fpu/mmx-state

Update the |X86ISA|::|FPU/MMX-STATE| field of a xcr0bits bit structure.

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

Definitions and Theorems

Function: !xcr0bits->fpu/mmx-state$inline

(defun !xcr0bits->fpu/mmx-state$inline (fpu/mmx-state x)
  (declare (xargs :guard (and (bitp fpu/mmx-state)
                              (xcr0bits-p x))))
  (mbe :logic
       (b* ((fpu/mmx-state (mbe :logic (bfix fpu/mmx-state)
                                :exec fpu/mmx-state))
            (x (xcr0bits-fix x)))
         (part-install fpu/mmx-state x
                       :width 1
                       :low 0))
       :exec (the (unsigned-byte 64)
                  (logior (the (unsigned-byte 64)
                               (logand (the (unsigned-byte 64) x)
                                       (the (signed-byte 2) -2)))
                          (the (unsigned-byte 1)
                               fpu/mmx-state)))))

Theorem: xcr0bits-p-of-!xcr0bits->fpu/mmx-state

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

Theorem: !xcr0bits->fpu/mmx-state$inline-of-bfix-fpu/mmx-state

(defthm !xcr0bits->fpu/mmx-state$inline-of-bfix-fpu/mmx-state
  (equal (!xcr0bits->fpu/mmx-state$inline (bfix fpu/mmx-state)
                                          x)
         (!xcr0bits->fpu/mmx-state$inline fpu/mmx-state x)))

Theorem: !xcr0bits->fpu/mmx-state$inline-bit-equiv-congruence-on-fpu/mmx-state

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

Theorem: !xcr0bits->fpu/mmx-state$inline-of-xcr0bits-fix-x

(defthm !xcr0bits->fpu/mmx-state$inline-of-xcr0bits-fix-x
 (equal
    (!xcr0bits->fpu/mmx-state$inline fpu/mmx-state (xcr0bits-fix x))
    (!xcr0bits->fpu/mmx-state$inline fpu/mmx-state x)))

Theorem: !xcr0bits->fpu/mmx-state$inline-xcr0bits-equiv-congruence-on-x

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

Theorem: !xcr0bits->fpu/mmx-state-is-xcr0bits

(defthm !xcr0bits->fpu/mmx-state-is-xcr0bits
  (equal (!xcr0bits->fpu/mmx-state fpu/mmx-state x)
         (change-xcr0bits x
                          :fpu/mmx-state fpu/mmx-state)))

Theorem: xcr0bits->fpu/mmx-state-of-!xcr0bits->fpu/mmx-state

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

Theorem: !xcr0bits->fpu/mmx-state-equiv-under-mask

(defthm !xcr0bits->fpu/mmx-state-equiv-under-mask
  (b* ((?new-x (!xcr0bits->fpu/mmx-state$inline fpu/mmx-state x)))
    (xcr0bits-equiv-under-mask new-x x -2)))