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• Modr/m

!modr/m->mod

Update the |COMMON-LISP|::|MOD| field of a modr/m bit structure.

Signature

(!modr/m->mod mod x) → new-x

Arguments

mod — Guard (2bits-p mod).

x — Guard (modr/m-p x).

Returns

new-x — Type (modr/m-p new-x).

Definitions and Theorems

Function: !modr/m->mod$inline

(defun !modr/m->mod$inline (mod x)
 (declare (xargs :guard (and (2bits-p mod) (modr/m-p x))))
 (mbe
    :logic
    (b* ((mod (mbe :logic (2bits-fix mod) :exec mod))
         (x (modr/m-fix x)))
      (part-install mod x :width 2 :low 6))
    :exec (the (unsigned-byte 8)
               (logior (the (unsigned-byte 8)
                            (logand (the (unsigned-byte 8) x)
                                    (the (signed-byte 9) -193)))
                       (the (unsigned-byte 8)
                            (ash (the (unsigned-byte 2) mod) 6))))))

Theorem: modr/m-p-of-!modr/m->mod

(defthm modr/m-p-of-!modr/m->mod
  (b* ((new-x (!modr/m->mod$inline mod x)))
    (modr/m-p new-x))
  :rule-classes :rewrite)

Theorem: !modr/m->mod$inline-of-2bits-fix-mod

(defthm !modr/m->mod$inline-of-2bits-fix-mod
  (equal (!modr/m->mod$inline (2bits-fix mod) x)
         (!modr/m->mod$inline mod x)))

Theorem: !modr/m->mod$inline-2bits-equiv-congruence-on-mod

(defthm !modr/m->mod$inline-2bits-equiv-congruence-on-mod
  (implies (2bits-equiv mod mod-equiv)
           (equal (!modr/m->mod$inline mod x)
                  (!modr/m->mod$inline mod-equiv x)))
  :rule-classes :congruence)

Theorem: !modr/m->mod$inline-of-modr/m-fix-x

(defthm !modr/m->mod$inline-of-modr/m-fix-x
  (equal (!modr/m->mod$inline mod (modr/m-fix x))
         (!modr/m->mod$inline mod x)))

Theorem: !modr/m->mod$inline-modr/m-equiv-congruence-on-x

(defthm !modr/m->mod$inline-modr/m-equiv-congruence-on-x
  (implies (modr/m-equiv x x-equiv)
           (equal (!modr/m->mod$inline mod x)
                  (!modr/m->mod$inline mod x-equiv)))
  :rule-classes :congruence)

Theorem: !modr/m->mod-is-modr/m

(defthm !modr/m->mod-is-modr/m
  (equal (!modr/m->mod mod x)
         (change-modr/m x :mod mod)))

Theorem: modr/m->mod-of-!modr/m->mod

(defthm modr/m->mod-of-!modr/m->mod
  (b* ((?new-x (!modr/m->mod$inline mod x)))
    (equal (modr/m->mod new-x)
           (2bits-fix mod))))

Theorem: !modr/m->mod-equiv-under-mask

(defthm !modr/m->mod-equiv-under-mask
  (b* ((?new-x (!modr/m->mod$inline mod x)))
    (modr/m-equiv-under-mask new-x x 63)))