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Fp-statusbits

Fp-statusbits->top

Access the |ACL2|::|TOP| field of a fp-statusbits bit structure.

Signature
(fp-statusbits->top x) → top
Arguments: x — Guard (fp-statusbits-p x).
Returns: top — Type (3bits-p top).

Definitions and Theorems

Function: fp-statusbits->top$inline

(defun fp-statusbits->top$inline (x)
  (declare (xargs :guard (fp-statusbits-p x)))
  (mbe :logic
       (let ((x (fp-statusbits-fix x)))
         (part-select x :low 11 :width 3))
       :exec (the (unsigned-byte 3)
                  (logand (the (unsigned-byte 3) 7)
                          (the (unsigned-byte 5)
                               (ash (the (unsigned-byte 16) x)
                                    -11))))))

Theorem: 3bits-p-of-fp-statusbits->top

(defthm 3bits-p-of-fp-statusbits->top
  (b* ((top (fp-statusbits->top$inline x)))
    (3bits-p top))
  :rule-classes :rewrite)

Theorem: fp-statusbits->top$inline-of-fp-statusbits-fix-x

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

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

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

Theorem: fp-statusbits->top-of-fp-statusbits

(defthm fp-statusbits->top-of-fp-statusbits
 (equal (fp-statusbits->top
             (fp-statusbits ie
                            de ze oe ue pe sf es c0 c1 c2 top c3 b))
        (3bits-fix top)))

Theorem: fp-statusbits->top-of-write-with-mask

(defthm fp-statusbits->top-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x fp-statusbits-equiv-under-mask)
                (fp-statusbits-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 14336)
                       0))
           (equal (fp-statusbits->top x)
                  (fp-statusbits->top y))))