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Mxcsrbits

!mxcsrbits->de

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

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

Definitions and Theorems

Function: !mxcsrbits->de$inline

(defun !mxcsrbits->de$inline (de x)
 (declare (xargs :guard (and (bitp de) (mxcsrbits-p x))))
 (mbe
     :logic
     (b* ((de (mbe :logic (bfix de) :exec de))
          (x (mxcsrbits-fix x)))
       (part-install de x :width 1 :low 1))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 3) -3)))
                        (the (unsigned-byte 2)
                             (ash (the (unsigned-byte 1) de) 1))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !mxcsrbits->de-is-mxcsrbits

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

Theorem: mxcsrbits->de-of-!mxcsrbits->de

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

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

(defthm !mxcsrbits->de-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->de$inline de x)))
    (mxcsrbits-equiv-under-mask new-x x -3)))