		Search-engine friendly clone of the ACL2 documentation.

Mxcsrbits

Mxcsrbits->ftz

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

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

Definitions and Theorems

Function: mxcsrbits->ftz$inline

(defun mxcsrbits->ftz$inline (x)
  (declare (xargs :guard (mxcsrbits-p x)))
  (mbe :logic
       (let ((x (mxcsrbits-fix x)))
         (part-select x :low 15 :width 1))
       :exec (the (unsigned-byte 1)
                  (logand (the (unsigned-byte 1) 1)
                          (the (unsigned-byte 17)
                               (ash (the (unsigned-byte 32) x)
                                    -15))))))

Theorem: bitp-of-mxcsrbits->ftz

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

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

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

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

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

Theorem: mxcsrbits->ftz-of-mxcsrbits

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

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

(defthm mxcsrbits->ftz-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) 32768)
                       0))
           (equal (mxcsrbits->ftz x)
                  (mxcsrbits->ftz y))))