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Xcr0bits

!xcr0bits->sse-state

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

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

Definitions and Theorems

Function: !xcr0bits->sse-state$inline

(defun !xcr0bits->sse-state$inline (sse-state x)
 (declare (xargs :guard (and (bitp sse-state) (xcr0bits-p x))))
 (mbe :logic
      (b* ((sse-state (mbe :logic (bfix sse-state)
                           :exec sse-state))
           (x (xcr0bits-fix x)))
        (part-install sse-state x
                      :width 1
                      :low 1))
      :exec (the (unsigned-byte 64)
                 (logior (the (unsigned-byte 64)
                              (logand (the (unsigned-byte 64) x)
                                      (the (signed-byte 3) -3)))
                         (the (unsigned-byte 2)
                              (ash (the (unsigned-byte 1) sse-state)
                                   1))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !xcr0bits->sse-state-equiv-under-mask
  (b* ((?new-x (!xcr0bits->sse-state$inline sse-state x)))
    (xcr0bits-equiv-under-mask new-x x -3)))