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Fp-statusbits

!fp-statusbits->es

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

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

Definitions and Theorems

Function: !fp-statusbits->es$inline

(defun !fp-statusbits->es$inline (es x)
 (declare (xargs :guard (and (bitp es) (fp-statusbits-p x))))
 (mbe
     :logic
     (b* ((es (mbe :logic (bfix es) :exec es))
          (x (fp-statusbits-fix x)))
       (part-install es x :width 1 :low 7))
     :exec (the (unsigned-byte 16)
                (logior (the (unsigned-byte 16)
                             (logand (the (unsigned-byte 16) x)
                                     (the (signed-byte 9) -129)))
                        (the (unsigned-byte 8)
                             (ash (the (unsigned-byte 1) es) 7))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !fp-statusbits->es-equiv-under-mask
  (b* ((?new-x (!fp-statusbits->es$inline es x)))
    (fp-statusbits-equiv-under-mask new-x x -129)))