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Sib->index

Access the |X86ISA|::|INDEX| field of a sib bit structure.

Signature
(sib->index x) → index
Arguments: x — Guard (sib-p x).
Returns: index — Type (3bits-p index).

Definitions and Theorems

Function: sib->index$inline

(defun sib->index$inline (x)
 (declare (xargs :guard (sib-p x)))
 (mbe
     :logic
     (let ((x (sib-fix x)))
       (part-select x :low 3 :width 3))
     :exec (the (unsigned-byte 3)
                (logand (the (unsigned-byte 3) 7)
                        (the (unsigned-byte 5)
                             (ash (the (unsigned-byte 8) x) -3))))))

Theorem: 3bits-p-of-sib->index

(defthm 3bits-p-of-sib->index
  (b* ((index (sib->index$inline x)))
    (3bits-p index))
  :rule-classes :rewrite)

Theorem: sib->index$inline-of-sib-fix-x

(defthm sib->index$inline-of-sib-fix-x
  (equal (sib->index$inline (sib-fix x))
         (sib->index$inline x)))

Theorem: sib->index$inline-sib-equiv-congruence-on-x

(defthm sib->index$inline-sib-equiv-congruence-on-x
  (implies (sib-equiv x x-equiv)
           (equal (sib->index$inline x)
                  (sib->index$inline x-equiv)))
  :rule-classes :congruence)

Theorem: sib->index-of-sib

(defthm sib->index-of-sib
  (equal (sib->index (sib base index scale))
         (3bits-fix index)))

Theorem: sib->index-of-write-with-mask

(defthm sib->index-of-write-with-mask
 (implies
   (and (fty::bitstruct-read-over-write-hyps x sib-equiv-under-mask)
        (sib-equiv-under-mask x y fty::mask)
        (equal (logand (lognot fty::mask) 56)
               0))
   (equal (sib->index x) (sib->index y))))