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Structures

Cr8bits

An 4-bit unsigned bitstruct type.

This is a bitstruct type introduced by defbitstruct, represented as a unsigned 4-bit integer.

Fields

cr8-trpl — 4bits

Source: Intel Manual, Dec-23, Vol. 3A, Section 2.5

Definitions and Theorems

Function: cr8bits-p$inline

(defun cr8bits-p$inline (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p 4 x)
       :exec (and (natp x) (< x 16))))

Theorem: cr8bits-p-when-unsigned-byte-p

(defthm cr8bits-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 4 x)
           (cr8bits-p x)))

Theorem: unsigned-byte-p-when-cr8bits-p

(defthm unsigned-byte-p-when-cr8bits-p
  (implies (cr8bits-p x)
           (unsigned-byte-p 4 x)))

Theorem: cr8bits-p-compound-recognizer

(defthm cr8bits-p-compound-recognizer
  (implies (cr8bits-p x) (natp x))
  :rule-classes :compound-recognizer)

Function: cr8bits-fix$inline

(defun cr8bits-fix$inline (x)
  (declare (xargs :guard (cr8bits-p x)))
  (mbe :logic (loghead 4 x) :exec x))

Theorem: cr8bits-p-of-cr8bits-fix

(defthm cr8bits-p-of-cr8bits-fix
  (b* ((fty::fixed (cr8bits-fix$inline x)))
    (cr8bits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: cr8bits-fix-when-cr8bits-p

(defthm cr8bits-fix-when-cr8bits-p
  (implies (cr8bits-p x)
           (equal (cr8bits-fix x) x)))

Function: cr8bits-equiv$inline

(defun cr8bits-equiv$inline (x y)
  (declare (xargs :guard (and (cr8bits-p x) (cr8bits-p y))))
  (equal (cr8bits-fix x) (cr8bits-fix y)))

Theorem: cr8bits-equiv-is-an-equivalence

(defthm cr8bits-equiv-is-an-equivalence
  (and (booleanp (cr8bits-equiv x y))
       (cr8bits-equiv x x)
       (implies (cr8bits-equiv x y)
                (cr8bits-equiv y x))
       (implies (and (cr8bits-equiv x y)
                     (cr8bits-equiv y z))
                (cr8bits-equiv x z)))
  :rule-classes (:equivalence))

Theorem: cr8bits-equiv-implies-equal-cr8bits-fix-1

(defthm cr8bits-equiv-implies-equal-cr8bits-fix-1
  (implies (cr8bits-equiv x x-equiv)
           (equal (cr8bits-fix x)
                  (cr8bits-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: cr8bits-fix-under-cr8bits-equiv

(defthm cr8bits-fix-under-cr8bits-equiv
  (cr8bits-equiv (cr8bits-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Function: cr8bits$inline

(defun cr8bits$inline (cr8-trpl)
  (declare (xargs :guard (4bits-p cr8-trpl)))
  (b* ((cr8-trpl (mbe :logic (4bits-fix cr8-trpl)
                      :exec cr8-trpl)))
    cr8-trpl))

Theorem: cr8bits-p-of-cr8bits

(defthm cr8bits-p-of-cr8bits
  (b* ((cr8bits (cr8bits$inline cr8-trpl)))
    (cr8bits-p cr8bits))
  :rule-classes :rewrite)

Theorem: cr8bits$inline-of-4bits-fix-cr8-trpl

(defthm cr8bits$inline-of-4bits-fix-cr8-trpl
  (equal (cr8bits$inline (4bits-fix cr8-trpl))
         (cr8bits$inline cr8-trpl)))

Theorem: cr8bits$inline-4bits-equiv-congruence-on-cr8-trpl

(defthm cr8bits$inline-4bits-equiv-congruence-on-cr8-trpl
  (implies (4bits-equiv cr8-trpl cr8-trpl-equiv)
           (equal (cr8bits$inline cr8-trpl)
                  (cr8bits$inline cr8-trpl-equiv)))
  :rule-classes :congruence)

Function: cr8bits-equiv-under-mask$inline

(defun cr8bits-equiv-under-mask$inline (x x1 mask)
  (declare (xargs :guard (and (cr8bits-p x)
                              (cr8bits-p x1)
                              (integerp mask))))
  (fty::int-equiv-under-mask (cr8bits-fix x)
                             (cr8bits-fix x1)
                             mask))

Function: cr8bits->cr8-trpl$inline

(defun cr8bits->cr8-trpl$inline (x)
  (declare (xargs :guard (cr8bits-p x)))
  (mbe :logic
       (let ((x (cr8bits-fix x)))
         (part-select x :low 0 :width 4))
       :exec (the (unsigned-byte 4)
                  (logand (the (unsigned-byte 4) 15)
                          (the (unsigned-byte 4) x)))))

Theorem: 4bits-p-of-cr8bits->cr8-trpl

(defthm 4bits-p-of-cr8bits->cr8-trpl
  (b* ((cr8-trpl (cr8bits->cr8-trpl$inline x)))
    (4bits-p cr8-trpl))
  :rule-classes :rewrite)

Theorem: cr8bits->cr8-trpl$inline-of-cr8bits-fix-x

(defthm cr8bits->cr8-trpl$inline-of-cr8bits-fix-x
  (equal (cr8bits->cr8-trpl$inline (cr8bits-fix x))
         (cr8bits->cr8-trpl$inline x)))

Theorem: cr8bits->cr8-trpl$inline-cr8bits-equiv-congruence-on-x

(defthm cr8bits->cr8-trpl$inline-cr8bits-equiv-congruence-on-x
  (implies (cr8bits-equiv x x-equiv)
           (equal (cr8bits->cr8-trpl$inline x)
                  (cr8bits->cr8-trpl$inline x-equiv)))
  :rule-classes :congruence)

Theorem: cr8bits->cr8-trpl-of-cr8bits

(defthm cr8bits->cr8-trpl-of-cr8bits
  (equal (cr8bits->cr8-trpl (cr8bits cr8-trpl))
         (4bits-fix cr8-trpl)))

Theorem: cr8bits->cr8-trpl-of-write-with-mask

(defthm cr8bits->cr8-trpl-of-write-with-mask
 (implies
  (and
    (fty::bitstruct-read-over-write-hyps x cr8bits-equiv-under-mask)
    (cr8bits-equiv-under-mask x y fty::mask)
    (equal (logand (lognot fty::mask) 15)
           0))
  (equal (cr8bits->cr8-trpl x)
         (cr8bits->cr8-trpl y))))

Theorem: cr8bits-fix-in-terms-of-cr8bits

(defthm cr8bits-fix-in-terms-of-cr8bits
  (equal (cr8bits-fix x)
         (change-cr8bits x)))

Function: !cr8bits->cr8-trpl$inline

(defun !cr8bits->cr8-trpl$inline (cr8-trpl x)
  (declare (xargs :guard (and (4bits-p cr8-trpl) (cr8bits-p x))))
  (mbe :logic
       (b* ((cr8-trpl (mbe :logic (4bits-fix cr8-trpl)
                           :exec cr8-trpl))
            (x (cr8bits-fix x)))
         (part-install cr8-trpl x
                       :width 4
                       :low 0))
       :exec (the (unsigned-byte 4)
                  (logior (the (unsigned-byte 4)
                               (logand (the (unsigned-byte 4) x)
                                       (the (signed-byte 5) -16)))
                          (the (unsigned-byte 4) cr8-trpl)))))

Theorem: cr8bits-p-of-!cr8bits->cr8-trpl

(defthm cr8bits-p-of-!cr8bits->cr8-trpl
  (b* ((new-x (!cr8bits->cr8-trpl$inline cr8-trpl x)))
    (cr8bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr8bits->cr8-trpl$inline-of-4bits-fix-cr8-trpl

(defthm !cr8bits->cr8-trpl$inline-of-4bits-fix-cr8-trpl
  (equal (!cr8bits->cr8-trpl$inline (4bits-fix cr8-trpl)
                                    x)
         (!cr8bits->cr8-trpl$inline cr8-trpl x)))

Theorem: !cr8bits->cr8-trpl$inline-4bits-equiv-congruence-on-cr8-trpl

(defthm !cr8bits->cr8-trpl$inline-4bits-equiv-congruence-on-cr8-trpl
  (implies (4bits-equiv cr8-trpl cr8-trpl-equiv)
           (equal (!cr8bits->cr8-trpl$inline cr8-trpl x)
                  (!cr8bits->cr8-trpl$inline cr8-trpl-equiv x)))
  :rule-classes :congruence)

Theorem: !cr8bits->cr8-trpl$inline-of-cr8bits-fix-x

(defthm !cr8bits->cr8-trpl$inline-of-cr8bits-fix-x
  (equal (!cr8bits->cr8-trpl$inline cr8-trpl (cr8bits-fix x))
         (!cr8bits->cr8-trpl$inline cr8-trpl x)))

Theorem: !cr8bits->cr8-trpl$inline-cr8bits-equiv-congruence-on-x

(defthm !cr8bits->cr8-trpl$inline-cr8bits-equiv-congruence-on-x
  (implies (cr8bits-equiv x x-equiv)
           (equal (!cr8bits->cr8-trpl$inline cr8-trpl x)
                  (!cr8bits->cr8-trpl$inline cr8-trpl x-equiv)))
  :rule-classes :congruence)

Theorem: !cr8bits->cr8-trpl-is-cr8bits

(defthm !cr8bits->cr8-trpl-is-cr8bits
  (equal (!cr8bits->cr8-trpl cr8-trpl x)
         (change-cr8bits x :cr8-trpl cr8-trpl)))

Theorem: cr8bits->cr8-trpl-of-!cr8bits->cr8-trpl

(defthm cr8bits->cr8-trpl-of-!cr8bits->cr8-trpl
  (b* ((?new-x (!cr8bits->cr8-trpl$inline cr8-trpl x)))
    (equal (cr8bits->cr8-trpl new-x)
           (4bits-fix cr8-trpl))))

Theorem: !cr8bits->cr8-trpl-equiv-under-mask

(defthm !cr8bits->cr8-trpl-equiv-under-mask
  (b* ((?new-x (!cr8bits->cr8-trpl$inline cr8-trpl x)))
    (cr8bits-equiv-under-mask new-x x 0)))

Function: cr8bits-debug$inline

(defun cr8bits-debug$inline (x)
  (declare (xargs :guard (cr8bits-p x)))
  (b* (((cr8bits x)))
    (cons (cons 'cr8-trpl x.cr8-trpl) nil)))

Subtopics

!cr8bits->cr8-trpl: Update the |X86ISA|::|CR8-TRPL| field of a cr8bits bit structure.
Cr8bits->cr8-trpl: Access the |X86ISA|::|CR8-TRPL| field of a cr8bits bit structure.
Cr8bits-fix: Fixing function for cr8bits bit structures.
Cr8bits-p: Recognizer for cr8bits bit structures.