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Mxcsrbits

!mxcsrbits->ftz

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

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

Definitions and Theorems

Function: !mxcsrbits->ftz$inline

(defun !mxcsrbits->ftz$inline (ftz x)
 (declare (xargs :guard (and (bitp ftz) (mxcsrbits-p x))))
 (mbe
     :logic
     (b* ((ftz (mbe :logic (bfix ftz) :exec ftz))
          (x (mxcsrbits-fix x)))
       (part-install ftz x :width 1 :low 15))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 17) -32769)))
                        (the (unsigned-byte 16)
                             (ash (the (unsigned-byte 1) ftz)
                                  15))))))

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

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

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

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

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

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

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

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

Theorem: !mxcsrbits->ftz-is-mxcsrbits

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

Theorem: mxcsrbits->ftz-of-!mxcsrbits->ftz

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

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

(defthm !mxcsrbits->ftz-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->ftz$inline ftz x)))
    (mxcsrbits-equiv-under-mask new-x x -32769)))