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Aig-symbolic-arithmetic

Sv::aig-ash-ss

Signature
(sv::aig-ash-ss place n shamt) → sh
Arguments: place — Guard (posp place).; n — Guard (true-listp n).; shamt — Guard (true-listp shamt).
Returns: sh — Type (true-listp sh).

Definitions and Theorems

Function: aig-ash-ss

(defun sv::aig-ash-ss (place n shamt)
  (declare (xargs :guard (and (posp place)
                              (true-listp n)
                              (true-listp shamt))))
  (let ((__function__ 'sv::aig-ash-ss))
    (declare (ignorable __function__))
    (b* (((mv shdig shrst shend)
          (first/rest/end shamt))
         (place (lposfix place))
         ((when shend)
          (sv::aig-ite-bss shdig (sv::aig-logtail-ns 1 n)
                           (sv::aig-logapp-nss (1- place) nil n)))
         (rst (sv::aig-ash-ss (* 2 place) n shrst)))
      (sv::aig-ite-bss shdig
                       rst (sv::aig-logtail-ns place rst)))))

Theorem: true-listp-of-aig-ash-ss

(defthm sv::true-listp-of-aig-ash-ss
  (b* ((sh (sv::aig-ash-ss place n shamt)))
    (true-listp sh))
  :rule-classes :type-prescription)

Theorem: aig-ash-ss-correct

(defthm sv::aig-ash-ss-correct
  (b* ((sh (sv::aig-ash-ss place n shamt)))
    (and (equal (sv::aig-list->s sh env)
                (ash (sv::aig-list->s n env)
                     (+ -1 (pos-fix place)
                        (* (pos-fix place)
                           (sv::aig-list->s shamt env))))))))