		Search-engine friendly clone of the ACL2 documentation.

Fp-statusbits

!fp-statusbits->ze

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

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

Definitions and Theorems

Function: !fp-statusbits->ze$inline

(defun !fp-statusbits->ze$inline (ze x)
 (declare (xargs :guard (and (bitp ze) (fp-statusbits-p x))))
 (mbe
     :logic
     (b* ((ze (mbe :logic (bfix ze) :exec ze))
          (x (fp-statusbits-fix x)))
       (part-install ze x :width 1 :low 2))
     :exec (the (unsigned-byte 16)
                (logior (the (unsigned-byte 16)
                             (logand (the (unsigned-byte 16) x)
                                     (the (signed-byte 4) -5)))
                        (the (unsigned-byte 3)
                             (ash (the (unsigned-byte 1) ze) 2))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !fp-statusbits->ze-equiv-under-mask
  (b* ((?new-x (!fp-statusbits->ze$inline ze x)))
    (fp-statusbits-equiv-under-mask new-x x -5)))