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Mxcsrbits

Mxcsrbits->de

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

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

Definitions and Theorems

Function: mxcsrbits->de$inline

(defun mxcsrbits->de$inline (x)
 (declare (xargs :guard (mxcsrbits-p x)))
 (mbe
    :logic
    (let ((x (mxcsrbits-fix x)))
      (part-select x :low 1 :width 1))
    :exec (the (unsigned-byte 1)
               (logand (the (unsigned-byte 1) 1)
                       (the (unsigned-byte 31)
                            (ash (the (unsigned-byte 32) x) -1))))))

Theorem: bitp-of-mxcsrbits->de

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

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

(defthm mxcsrbits->de$inline-of-mxcsrbits-fix-x
  (equal (mxcsrbits->de$inline (mxcsrbits-fix x))
         (mxcsrbits->de$inline 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 x)
                  (mxcsrbits->de$inline x-equiv)))
  :rule-classes :congruence)

Theorem: mxcsrbits->de-of-mxcsrbits

(defthm mxcsrbits->de-of-mxcsrbits
 (equal
   (mxcsrbits->de (mxcsrbits ie de ze oe ue pe
                             daz im dm zm om um pm rc ftz reserved))
   (bfix de)))

Theorem: mxcsrbits->de-of-write-with-mask

(defthm mxcsrbits->de-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x mxcsrbits-equiv-under-mask)
                (mxcsrbits-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 2) 0))
           (equal (mxcsrbits->de x)
                  (mxcsrbits->de y))))