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Fp-statusbits

!fp-statusbits->c0

Update the |X86ISA|::|C0| field of a fp-statusbits bit structure.

Signature
(!fp-statusbits->c0 c0 x) → new-x
Arguments: c0 — Guard (bitp c0).; x — Guard (fp-statusbits-p x).
Returns: new-x — Type (fp-statusbits-p new-x).

Definitions and Theorems

Function: !fp-statusbits->c0$inline

(defun !fp-statusbits->c0$inline (c0 x)
 (declare (xargs :guard (and (bitp c0) (fp-statusbits-p x))))
 (mbe
     :logic
     (b* ((c0 (mbe :logic (bfix c0) :exec c0))
          (x (fp-statusbits-fix x)))
       (part-install c0 x :width 1 :low 8))
     :exec (the (unsigned-byte 16)
                (logior (the (unsigned-byte 16)
                             (logand (the (unsigned-byte 16) x)
                                     (the (signed-byte 10) -257)))
                        (the (unsigned-byte 9)
                             (ash (the (unsigned-byte 1) c0) 8))))))

Theorem: fp-statusbits-p-of-!fp-statusbits->c0

(defthm fp-statusbits-p-of-!fp-statusbits->c0
  (b* ((new-x (!fp-statusbits->c0$inline c0 x)))
    (fp-statusbits-p new-x))
  :rule-classes :rewrite)

Theorem: !fp-statusbits->c0$inline-of-bfix-c0

(defthm !fp-statusbits->c0$inline-of-bfix-c0
  (equal (!fp-statusbits->c0$inline (bfix c0) x)
         (!fp-statusbits->c0$inline c0 x)))

Theorem: !fp-statusbits->c0$inline-bit-equiv-congruence-on-c0

(defthm !fp-statusbits->c0$inline-bit-equiv-congruence-on-c0
  (implies (bit-equiv c0 c0-equiv)
           (equal (!fp-statusbits->c0$inline c0 x)
                  (!fp-statusbits->c0$inline c0-equiv x)))
  :rule-classes :congruence)

Theorem: !fp-statusbits->c0$inline-of-fp-statusbits-fix-x

(defthm !fp-statusbits->c0$inline-of-fp-statusbits-fix-x
  (equal (!fp-statusbits->c0$inline c0 (fp-statusbits-fix x))
         (!fp-statusbits->c0$inline c0 x)))

Theorem: !fp-statusbits->c0$inline-fp-statusbits-equiv-congruence-on-x

(defthm
      !fp-statusbits->c0$inline-fp-statusbits-equiv-congruence-on-x
  (implies (fp-statusbits-equiv x x-equiv)
           (equal (!fp-statusbits->c0$inline c0 x)
                  (!fp-statusbits->c0$inline c0 x-equiv)))
  :rule-classes :congruence)

Theorem: !fp-statusbits->c0-is-fp-statusbits

(defthm !fp-statusbits->c0-is-fp-statusbits
  (equal (!fp-statusbits->c0 c0 x)
         (change-fp-statusbits x :c0 c0)))

Theorem: fp-statusbits->c0-of-!fp-statusbits->c0

(defthm fp-statusbits->c0-of-!fp-statusbits->c0
  (b* ((?new-x (!fp-statusbits->c0$inline c0 x)))
    (equal (fp-statusbits->c0 new-x)
           (bfix c0))))

Theorem: !fp-statusbits->c0-equiv-under-mask

(defthm !fp-statusbits->c0-equiv-under-mask
  (b* ((?new-x (!fp-statusbits->c0$inline c0 x)))
    (fp-statusbits-equiv-under-mask new-x x -257)))