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Mxcsrbits

Mxcsrbits->rc

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

Signature
(mxcsrbits->rc x) → rc
Arguments: x — Guard (mxcsrbits-p x).
Returns: rc — Type (2bits-p rc).

Definitions and Theorems

Function: mxcsrbits->rc$inline

(defun mxcsrbits->rc$inline (x)
  (declare (xargs :guard (mxcsrbits-p x)))
  (mbe :logic
       (let ((x (mxcsrbits-fix x)))
         (part-select x :low 13 :width 2))
       :exec (the (unsigned-byte 2)
                  (logand (the (unsigned-byte 2) 3)
                          (the (unsigned-byte 19)
                               (ash (the (unsigned-byte 32) x)
                                    -13))))))

Theorem: 2bits-p-of-mxcsrbits->rc

(defthm 2bits-p-of-mxcsrbits->rc
  (b* ((rc (mxcsrbits->rc$inline x)))
    (2bits-p rc))
  :rule-classes :rewrite)

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

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

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

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

Theorem: mxcsrbits->rc-of-mxcsrbits

(defthm mxcsrbits->rc-of-mxcsrbits
 (equal
   (mxcsrbits->rc (mxcsrbits ie de ze oe ue pe
                             daz im dm zm om um pm rc ftz reserved))
   (2bits-fix rc)))

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

(defthm mxcsrbits->rc-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) 24576)
                       0))
           (equal (mxcsrbits->rc x)
                  (mxcsrbits->rc y))))