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Mxcsrbits

!mxcsrbits->um

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

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

Definitions and Theorems

Function: !mxcsrbits->um$inline

(defun !mxcsrbits->um$inline (um x)
 (declare (xargs :guard (and (bitp um) (mxcsrbits-p x))))
 (mbe
    :logic
    (b* ((um (mbe :logic (bfix um) :exec um))
         (x (mxcsrbits-fix x)))
      (part-install um x :width 1 :low 11))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 13) -2049)))
                       (the (unsigned-byte 12)
                            (ash (the (unsigned-byte 1) um) 11))))))

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

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

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

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

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

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

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

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

Theorem: !mxcsrbits->um-is-mxcsrbits

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

Theorem: mxcsrbits->um-of-!mxcsrbits->um

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

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

(defthm !mxcsrbits->um-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->um$inline um x)))
    (mxcsrbits-equiv-under-mask new-x x -2049)))