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Mxcsrbits

!mxcsrbits->im

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

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

Definitions and Theorems

Function: !mxcsrbits->im$inline

(defun !mxcsrbits->im$inline (im x)
 (declare (xargs :guard (and (bitp im) (mxcsrbits-p x))))
 (mbe
     :logic
     (b* ((im (mbe :logic (bfix im) :exec im))
          (x (mxcsrbits-fix x)))
       (part-install im x :width 1 :low 7))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 9) -129)))
                        (the (unsigned-byte 8)
                             (ash (the (unsigned-byte 1) im) 7))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !mxcsrbits->im-is-mxcsrbits

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

Theorem: mxcsrbits->im-of-!mxcsrbits->im

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

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

(defthm !mxcsrbits->im-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->im$inline im x)))
    (mxcsrbits-equiv-under-mask new-x x -129)))