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Mxcsrbits

Mxcsrbits->um

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

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

Definitions and Theorems

Function: mxcsrbits->um$inline

(defun mxcsrbits->um$inline (x)
  (declare (xargs :guard (mxcsrbits-p x)))
  (mbe :logic
       (let ((x (mxcsrbits-fix x)))
         (part-select x :low 11 :width 1))
       :exec (the (unsigned-byte 1)
                  (logand (the (unsigned-byte 1) 1)
                          (the (unsigned-byte 21)
                               (ash (the (unsigned-byte 32) x)
                                    -11))))))

Theorem: bitp-of-mxcsrbits->um

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

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

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

Theorem: mxcsrbits->um$inline-mxcsrbits-equiv-congruence-on-x

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

Theorem: mxcsrbits->um-of-mxcsrbits

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

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

(defthm mxcsrbits->um-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) 2048)
                       0))
           (equal (mxcsrbits->um x)
                  (mxcsrbits->um y))))