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• Decoding-and-spec-utils

Rex-byte-from-vex-prefixes

Calculate a REX byte from a VEX prefix.

Signature

(rex-byte-from-vex-prefixes vex-prefixes) → rex-byte

Arguments

vex-prefixes — Guard (vex-prefixes-p vex-prefixes).

Returns

rex-byte — Type (unsigned-byte-p 8 rex-byte).

The VEX prefix (see Intel manual Volume 2 Section 2.3.5 of Dec 2023) provides an encoding of the REX byte. Since some of the functions in our model depend on the REX byte (e.g. x86-operand-from-modr/m-and-sib-bytes), here we introduce a function to build a REX byte from its encoding in the VEX prefix. We do that for both the 2-byte form and the 3-byte form of the VEX prefix; see vex->r, vex->x, vex->b, and vex->w. See Figure 2-9 in Intel manual Volume 2 of Dec 2023. Note that the R, X, B bits are encoded negated, while the W is encoded directly (not negated).

Definitions and Theorems

Function: rex-byte-from-vex-prefixes

(defun rex-byte-from-vex-prefixes (vex-prefixes)
  (declare (xargs :guard (vex-prefixes-p vex-prefixes)))
  (declare (xargs :guard (vex-prefixes-byte0-p vex-prefixes)))
  (let ((__function__ 'rex-byte-from-vex-prefixes))
    (declare (ignorable __function__))
    (b* ((vex.w (vex->w vex-prefixes))
         (vex.r (vex->r vex-prefixes))
         (vex.x (vex->x vex-prefixes))
         (vex.b (vex->b vex-prefixes))
         (rex-byte (+ 64 (if (= vex.w 0) 0 8)
                      (if (= vex.r 1) 0 4)
                      (if (= vex.x 1) 0 2)
                      (if (= vex.b 1) 0 1))))
      rex-byte)))

Theorem: return-type-of-rex-byte-from-vex-prefixes

(defthm return-type-of-rex-byte-from-vex-prefixes
  (b* ((rex-byte (rex-byte-from-vex-prefixes vex-prefixes)))
    (unsigned-byte-p 8 rex-byte))
  :rule-classes :rewrite)

Theorem: unsigned-byte-p-of-rex-byte-from-vex-prefixes

(defthm unsigned-byte-p-of-rex-byte-from-vex-prefixes
 (unsigned-byte-p 8
                  (rex-byte-from-vex-prefixes vex-prefixes))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (rex-byte-from-vex-prefixes vex-prefixes))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0
                       (rex-byte-from-vex-prefixes vex-prefixes))
                   (< (rex-byte-from-vex-prefixes vex-prefixes)
                      256))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))