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Fp-statusbits

!fp-statusbits->b

Update the |ACL2|::|B| field of a fp-statusbits bit structure.

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

Definitions and Theorems

Function: !fp-statusbits->b$inline

(defun !fp-statusbits->b$inline (b x)
 (declare (xargs :guard (and (bitp b) (fp-statusbits-p x))))
 (mbe
     :logic
     (b* ((b (mbe :logic (bfix b) :exec b))
          (x (fp-statusbits-fix x)))
       (part-install b x :width 1 :low 15))
     :exec (the (unsigned-byte 16)
                (logior (the (unsigned-byte 16)
                             (logand (the (unsigned-byte 16) x)
                                     (the (signed-byte 17) -32769)))
                        (the (unsigned-byte 16)
                             (ash (the (unsigned-byte 1) b) 15))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !fp-statusbits->b-equiv-under-mask
  (b* ((?new-x (!fp-statusbits->b$inline b x)))
    (fp-statusbits-equiv-under-mask new-x x 32767)))