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Fp-statusbits

!fp-statusbits->sf

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

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

Definitions and Theorems

Function: !fp-statusbits->sf$inline

(defun !fp-statusbits->sf$inline (sf x)
 (declare (xargs :guard (and (bitp sf) (fp-statusbits-p x))))
 (mbe
     :logic
     (b* ((sf (mbe :logic (bfix sf) :exec sf))
          (x (fp-statusbits-fix x)))
       (part-install sf x :width 1 :low 6))
     :exec (the (unsigned-byte 16)
                (logior (the (unsigned-byte 16)
                             (logand (the (unsigned-byte 16) x)
                                     (the (signed-byte 8) -65)))
                        (the (unsigned-byte 7)
                             (ash (the (unsigned-byte 1) sf) 6))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !fp-statusbits->sf-equiv-under-mask
  (b* ((?new-x (!fp-statusbits->sf$inline sf x)))
    (fp-statusbits-equiv-under-mask new-x x -65)))