Update the |X86ISA|::|IE| field of a fp-statusbits bit structure.
(!fp-statusbits->ie ie x) → new-x
Function:
(defun !fp-statusbits->ie$inline (ie x) (declare (xargs :guard (and (bitp ie) (fp-statusbits-p x)))) (mbe :logic (b* ((ie (mbe :logic (bfix ie) :exec ie)) (x (fp-statusbits-fix x))) (part-install ie x :width 1 :low 0)) :exec (the (unsigned-byte 16) (logior (the (unsigned-byte 16) (logand (the (unsigned-byte 16) x) (the (signed-byte 2) -2))) (the (unsigned-byte 1) ie)))))
Theorem:
(defthm fp-statusbits-p-of-!fp-statusbits->ie (b* ((new-x (!fp-statusbits->ie$inline ie x))) (fp-statusbits-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm !fp-statusbits->ie$inline-of-bfix-ie (equal (!fp-statusbits->ie$inline (bfix ie) x) (!fp-statusbits->ie$inline ie x)))
Theorem:
(defthm !fp-statusbits->ie$inline-bit-equiv-congruence-on-ie (implies (bit-equiv ie ie-equiv) (equal (!fp-statusbits->ie$inline ie x) (!fp-statusbits->ie$inline ie-equiv x))) :rule-classes :congruence)
Theorem:
(defthm !fp-statusbits->ie$inline-of-fp-statusbits-fix-x (equal (!fp-statusbits->ie$inline ie (fp-statusbits-fix x)) (!fp-statusbits->ie$inline ie x)))
Theorem:
(defthm !fp-statusbits->ie$inline-fp-statusbits-equiv-congruence-on-x (implies (fp-statusbits-equiv x x-equiv) (equal (!fp-statusbits->ie$inline ie x) (!fp-statusbits->ie$inline ie x-equiv))) :rule-classes :congruence)
Theorem:
(defthm !fp-statusbits->ie-is-fp-statusbits (equal (!fp-statusbits->ie ie x) (change-fp-statusbits x :ie ie)))
Theorem:
(defthm fp-statusbits->ie-of-!fp-statusbits->ie (b* ((?new-x (!fp-statusbits->ie$inline ie x))) (equal (fp-statusbits->ie new-x) (bfix ie))))
Theorem:
(defthm !fp-statusbits->ie-equiv-under-mask (b* ((?new-x (!fp-statusbits->ie$inline ie x))) (fp-statusbits-equiv-under-mask new-x x -2)))