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Fp-statusbits

!fp-statusbits->c2

Update the |X86ISA|::|C2| field of a fp-statusbits bit structure.

Signature
(!fp-statusbits->c2 c2 x) → new-x
Arguments: c2 — Guard (bitp c2).; x — Guard (fp-statusbits-p x).
Returns: new-x — Type (fp-statusbits-p new-x).

Definitions and Theorems

Function: !fp-statusbits->c2$inline

(defun !fp-statusbits->c2$inline (c2 x)
 (declare (xargs :guard (and (bitp c2) (fp-statusbits-p x))))
 (mbe
    :logic
    (b* ((c2 (mbe :logic (bfix c2) :exec c2))
         (x (fp-statusbits-fix x)))
      (part-install c2 x :width 1 :low 10))
    :exec (the (unsigned-byte 16)
               (logior (the (unsigned-byte 16)
                            (logand (the (unsigned-byte 16) x)
                                    (the (signed-byte 12) -1025)))
                       (the (unsigned-byte 11)
                            (ash (the (unsigned-byte 1) c2) 10))))))

Theorem: fp-statusbits-p-of-!fp-statusbits->c2

(defthm fp-statusbits-p-of-!fp-statusbits->c2
  (b* ((new-x (!fp-statusbits->c2$inline c2 x)))
    (fp-statusbits-p new-x))
  :rule-classes :rewrite)

Theorem: !fp-statusbits->c2$inline-of-bfix-c2

(defthm !fp-statusbits->c2$inline-of-bfix-c2
  (equal (!fp-statusbits->c2$inline (bfix c2) x)
         (!fp-statusbits->c2$inline c2 x)))

Theorem: !fp-statusbits->c2$inline-bit-equiv-congruence-on-c2

(defthm !fp-statusbits->c2$inline-bit-equiv-congruence-on-c2
  (implies (bit-equiv c2 c2-equiv)
           (equal (!fp-statusbits->c2$inline c2 x)
                  (!fp-statusbits->c2$inline c2-equiv x)))
  :rule-classes :congruence)

Theorem: !fp-statusbits->c2$inline-of-fp-statusbits-fix-x

(defthm !fp-statusbits->c2$inline-of-fp-statusbits-fix-x
  (equal (!fp-statusbits->c2$inline c2 (fp-statusbits-fix x))
         (!fp-statusbits->c2$inline c2 x)))

Theorem: !fp-statusbits->c2$inline-fp-statusbits-equiv-congruence-on-x

(defthm
      !fp-statusbits->c2$inline-fp-statusbits-equiv-congruence-on-x
  (implies (fp-statusbits-equiv x x-equiv)
           (equal (!fp-statusbits->c2$inline c2 x)
                  (!fp-statusbits->c2$inline c2 x-equiv)))
  :rule-classes :congruence)

Theorem: !fp-statusbits->c2-is-fp-statusbits

(defthm !fp-statusbits->c2-is-fp-statusbits
  (equal (!fp-statusbits->c2 c2 x)
         (change-fp-statusbits x :c2 c2)))

Theorem: fp-statusbits->c2-of-!fp-statusbits->c2

(defthm fp-statusbits->c2-of-!fp-statusbits->c2
  (b* ((?new-x (!fp-statusbits->c2$inline c2 x)))
    (equal (fp-statusbits->c2 new-x)
           (bfix c2))))

Theorem: !fp-statusbits->c2-equiv-under-mask

(defthm !fp-statusbits->c2-equiv-under-mask
  (b* ((?new-x (!fp-statusbits->c2$inline c2 x)))
    (fp-statusbits-equiv-under-mask new-x x -1025)))