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Mxcsrbits

!mxcsrbits->daz

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

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

Definitions and Theorems

Function: !mxcsrbits->daz$inline

(defun !mxcsrbits->daz$inline (daz x)
 (declare (xargs :guard (and (bitp daz) (mxcsrbits-p x))))
 (mbe
    :logic
    (b* ((daz (mbe :logic (bfix daz) :exec daz))
         (x (mxcsrbits-fix x)))
      (part-install daz x :width 1 :low 6))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 8) -65)))
                       (the (unsigned-byte 7)
                            (ash (the (unsigned-byte 1) daz) 6))))))

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

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

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

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

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

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

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

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

Theorem: !mxcsrbits->daz$inline-mxcsrbits-equiv-congruence-on-x

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

Theorem: !mxcsrbits->daz-is-mxcsrbits

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

Theorem: mxcsrbits->daz-of-!mxcsrbits->daz

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

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

(defthm !mxcsrbits->daz-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->daz$inline daz x)))
    (mxcsrbits-equiv-under-mask new-x x -65)))