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Rflag-specifications

General-cf-spec-fn

Signature
(general-cf-spec-fn result-nbits raw-result) → *

General CF Specification (Source: Intel Manuals, Vol. 1, Section 3.4.3.1):

Carry flag Set if an arithmetic operation generates a carry or a borrow out of the most-significant bit of the result; cleared otherwise. This flag indicates an overflow condition for unsigned-integer arithmetic. It is also used in multiple-precision arithmetic.

Definitions and Theorems

Function: general-cf-spec-fn$inline

(defun general-cf-spec-fn$inline (result-nbits raw-result)
  (declare (xargs :guard (and (natp result-nbits)
                              (natp raw-result))))
  (bool->bit (not (unsigned-byte-p result-nbits raw-result))))

Theorem: n01p-general-cf-spec-fn

(defthm n01p-general-cf-spec-fn
 (unsigned-byte-p 1
                  (general-cf-spec-fn result-nbits raw-result))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (general-cf-spec-fn result-nbits raw-result))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0
                       (general-cf-spec-fn result-nbits raw-result))
                   (< (general-cf-spec-fn result-nbits raw-result)
                      2))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))