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Mxcsrbits

!mxcsrbits->zm

Update the |X86ISA|::|ZM| field of a mxcsrbits bit structure.

Signature
(!mxcsrbits->zm zm x) → new-x
Arguments: zm — Guard (bitp zm).; x — Guard (mxcsrbits-p x).
Returns: new-x — Type (mxcsrbits-p new-x).

Definitions and Theorems

Function: !mxcsrbits->zm$inline

(defun !mxcsrbits->zm$inline (zm x)
 (declare (xargs :guard (and (bitp zm) (mxcsrbits-p x))))
 (mbe
     :logic
     (b* ((zm (mbe :logic (bfix zm) :exec zm))
          (x (mxcsrbits-fix x)))
       (part-install zm x :width 1 :low 9))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 11) -513)))
                        (the (unsigned-byte 10)
                             (ash (the (unsigned-byte 1) zm) 9))))))

Theorem: mxcsrbits-p-of-!mxcsrbits->zm

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

Theorem: !mxcsrbits->zm$inline-of-bfix-zm

(defthm !mxcsrbits->zm$inline-of-bfix-zm
  (equal (!mxcsrbits->zm$inline (bfix zm) x)
         (!mxcsrbits->zm$inline zm x)))

Theorem: !mxcsrbits->zm$inline-bit-equiv-congruence-on-zm

(defthm !mxcsrbits->zm$inline-bit-equiv-congruence-on-zm
  (implies (bit-equiv zm zm-equiv)
           (equal (!mxcsrbits->zm$inline zm x)
                  (!mxcsrbits->zm$inline zm-equiv x)))
  :rule-classes :congruence)

Theorem: !mxcsrbits->zm$inline-of-mxcsrbits-fix-x

(defthm !mxcsrbits->zm$inline-of-mxcsrbits-fix-x
  (equal (!mxcsrbits->zm$inline zm (mxcsrbits-fix x))
         (!mxcsrbits->zm$inline zm x)))

Theorem: !mxcsrbits->zm$inline-mxcsrbits-equiv-congruence-on-x

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

Theorem: !mxcsrbits->zm-is-mxcsrbits

(defthm !mxcsrbits->zm-is-mxcsrbits
  (equal (!mxcsrbits->zm zm x)
         (change-mxcsrbits x :zm zm)))

Theorem: mxcsrbits->zm-of-!mxcsrbits->zm

(defthm mxcsrbits->zm-of-!mxcsrbits->zm
  (b* ((?new-x (!mxcsrbits->zm$inline zm x)))
    (equal (mxcsrbits->zm new-x)
           (bfix zm))))

Theorem: !mxcsrbits->zm-equiv-under-mask

(defthm !mxcsrbits->zm-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->zm$inline zm x)))
    (mxcsrbits-equiv-under-mask new-x x -513)))