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Xcr0bits

!xcr0bits->res4

Update the |X86ISA|::|RES4| field of a xcr0bits bit structure.

Signature
(!xcr0bits->res4 res4 x) → new-x
Arguments: res4 — Guard (45bits-p res4).; x — Guard (xcr0bits-p x).
Returns: new-x — Type (xcr0bits-p new-x).

Definitions and Theorems

Function: !xcr0bits->res4$inline

(defun !xcr0bits->res4$inline (res4 x)
  (declare (xargs :guard (and (45bits-p res4) (xcr0bits-p x))))
  (mbe :logic
       (b* ((res4 (mbe :logic (45bits-fix res4)
                       :exec res4))
            (x (xcr0bits-fix x)))
         (part-install res4 x :width 45 :low 19))
       :exec (the (unsigned-byte 64)
                  (logior (the (unsigned-byte 64)
                               (logand (the (unsigned-byte 64) x)
                                       (the (signed-byte 65)
                                            -18446744073709027329)))
                          (the (unsigned-byte 64)
                               (ash (the (unsigned-byte 45) res4)
                                    19))))))

Theorem: xcr0bits-p-of-!xcr0bits->res4

(defthm xcr0bits-p-of-!xcr0bits->res4
  (b* ((new-x (!xcr0bits->res4$inline res4 x)))
    (xcr0bits-p new-x))
  :rule-classes :rewrite)

Theorem: !xcr0bits->res4$inline-of-45bits-fix-res4

(defthm !xcr0bits->res4$inline-of-45bits-fix-res4
  (equal (!xcr0bits->res4$inline (45bits-fix res4)
                                 x)
         (!xcr0bits->res4$inline res4 x)))

Theorem: !xcr0bits->res4$inline-45bits-equiv-congruence-on-res4

(defthm !xcr0bits->res4$inline-45bits-equiv-congruence-on-res4
  (implies (45bits-equiv res4 res4-equiv)
           (equal (!xcr0bits->res4$inline res4 x)
                  (!xcr0bits->res4$inline res4-equiv x)))
  :rule-classes :congruence)

Theorem: !xcr0bits->res4$inline-of-xcr0bits-fix-x

(defthm !xcr0bits->res4$inline-of-xcr0bits-fix-x
  (equal (!xcr0bits->res4$inline res4 (xcr0bits-fix x))
         (!xcr0bits->res4$inline res4 x)))

Theorem: !xcr0bits->res4$inline-xcr0bits-equiv-congruence-on-x

(defthm !xcr0bits->res4$inline-xcr0bits-equiv-congruence-on-x
  (implies (xcr0bits-equiv x x-equiv)
           (equal (!xcr0bits->res4$inline res4 x)
                  (!xcr0bits->res4$inline res4 x-equiv)))
  :rule-classes :congruence)

Theorem: !xcr0bits->res4-is-xcr0bits

(defthm !xcr0bits->res4-is-xcr0bits
  (equal (!xcr0bits->res4 res4 x)
         (change-xcr0bits x :res4 res4)))

Theorem: xcr0bits->res4-of-!xcr0bits->res4

(defthm xcr0bits->res4-of-!xcr0bits->res4
  (b* ((?new-x (!xcr0bits->res4$inline res4 x)))
    (equal (xcr0bits->res4 new-x)
           (45bits-fix res4))))

Theorem: !xcr0bits->res4-equiv-under-mask

(defthm !xcr0bits->res4-equiv-under-mask
  (b* ((?new-x (!xcr0bits->res4$inline res4 x)))
    (xcr0bits-equiv-under-mask new-x x 524287)))