		Search-engine friendly clone of the ACL2 documentation.

Fp-statusbits

!fp-statusbits->oe

Update the |X86ISA|::|OE| field of a fp-statusbits bit structure.

Signature
(!fp-statusbits->oe oe x) → new-x
Arguments: oe — Guard (bitp oe).; x — Guard (fp-statusbits-p x).
Returns: new-x — Type (fp-statusbits-p new-x).

Definitions and Theorems

Function: !fp-statusbits->oe$inline

(defun !fp-statusbits->oe$inline (oe x)
 (declare (xargs :guard (and (bitp oe) (fp-statusbits-p x))))
 (mbe
     :logic
     (b* ((oe (mbe :logic (bfix oe) :exec oe))
          (x (fp-statusbits-fix x)))
       (part-install oe x :width 1 :low 3))
     :exec (the (unsigned-byte 16)
                (logior (the (unsigned-byte 16)
                             (logand (the (unsigned-byte 16) x)
                                     (the (signed-byte 5) -9)))
                        (the (unsigned-byte 4)
                             (ash (the (unsigned-byte 1) oe) 3))))))

Theorem: fp-statusbits-p-of-!fp-statusbits->oe

(defthm fp-statusbits-p-of-!fp-statusbits->oe
  (b* ((new-x (!fp-statusbits->oe$inline oe x)))
    (fp-statusbits-p new-x))
  :rule-classes :rewrite)

Theorem: !fp-statusbits->oe$inline-of-bfix-oe

(defthm !fp-statusbits->oe$inline-of-bfix-oe
  (equal (!fp-statusbits->oe$inline (bfix oe) x)
         (!fp-statusbits->oe$inline oe x)))

Theorem: !fp-statusbits->oe$inline-bit-equiv-congruence-on-oe

(defthm !fp-statusbits->oe$inline-bit-equiv-congruence-on-oe
  (implies (bit-equiv oe oe-equiv)
           (equal (!fp-statusbits->oe$inline oe x)
                  (!fp-statusbits->oe$inline oe-equiv x)))
  :rule-classes :congruence)

Theorem: !fp-statusbits->oe$inline-of-fp-statusbits-fix-x

(defthm !fp-statusbits->oe$inline-of-fp-statusbits-fix-x
  (equal (!fp-statusbits->oe$inline oe (fp-statusbits-fix x))
         (!fp-statusbits->oe$inline oe x)))

Theorem: !fp-statusbits->oe$inline-fp-statusbits-equiv-congruence-on-x

(defthm
      !fp-statusbits->oe$inline-fp-statusbits-equiv-congruence-on-x
  (implies (fp-statusbits-equiv x x-equiv)
           (equal (!fp-statusbits->oe$inline oe x)
                  (!fp-statusbits->oe$inline oe x-equiv)))
  :rule-classes :congruence)

Theorem: !fp-statusbits->oe-is-fp-statusbits

(defthm !fp-statusbits->oe-is-fp-statusbits
  (equal (!fp-statusbits->oe oe x)
         (change-fp-statusbits x :oe oe)))

Theorem: fp-statusbits->oe-of-!fp-statusbits->oe

(defthm fp-statusbits->oe-of-!fp-statusbits->oe
  (b* ((?new-x (!fp-statusbits->oe$inline oe x)))
    (equal (fp-statusbits->oe new-x)
           (bfix oe))))

Theorem: !fp-statusbits->oe-equiv-under-mask

(defthm !fp-statusbits->oe-equiv-under-mask
  (b* ((?new-x (!fp-statusbits->oe$inline oe x)))
    (fp-statusbits-equiv-under-mask new-x x -9)))