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Mxcsrbits

!mxcsrbits->pm

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

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

Definitions and Theorems

Function: !mxcsrbits->pm$inline

(defun !mxcsrbits->pm$inline (pm x)
 (declare (xargs :guard (and (bitp pm) (mxcsrbits-p x))))
 (mbe
    :logic
    (b* ((pm (mbe :logic (bfix pm) :exec pm))
         (x (mxcsrbits-fix x)))
      (part-install pm x :width 1 :low 12))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 14) -4097)))
                       (the (unsigned-byte 13)
                            (ash (the (unsigned-byte 1) pm) 12))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !mxcsrbits->pm-is-mxcsrbits

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

Theorem: mxcsrbits->pm-of-!mxcsrbits->pm

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

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

(defthm !mxcsrbits->pm-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->pm$inline pm x)))
    (mxcsrbits-equiv-under-mask new-x x -4097)))