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Floating-point-sqrt-specifications

Dp-sse-sqrt

Signature
(dp-sse-sqrt x mxcsr) → (mv * * *)

Definitions and Theorems

Function: dp-sse-sqrt

(defun dp-sse-sqrt (x mxcsr)
  (declare (type (unsigned-byte 64) x)
           (type (unsigned-byte 32) mxcsr))
  (let ((__function__ 'dp-sse-sqrt))
    (declare (ignorable __function__))
    (sse-sqrt x mxcsr 11 52)))

Theorem: n64p-result-dp-sse-sqrt

(defthm n64p-result-dp-sse-sqrt
 (unsigned-byte-p 64 (mv-nth 1 (dp-sse-sqrt x mxcsr)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 1 (dp-sse-sqrt x mxcsr)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 1 (dp-sse-sqrt x mxcsr)))
                   (< (mv-nth 1 (dp-sse-sqrt x mxcsr))
                      18446744073709551616))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: n32p-mxcsr-dp-sse-sqrt

(defthm n32p-mxcsr-dp-sse-sqrt
 (unsigned-byte-p 32 (mv-nth 2 (dp-sse-sqrt x mxcsr)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 2 (dp-sse-sqrt x mxcsr)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 2 (dp-sse-sqrt x mxcsr)))
                   (< (mv-nth 2 (dp-sse-sqrt x mxcsr))
                      4294967296))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))