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• A4vec-rsh

Aig-right-shift-ss

Signature

(aig-right-shift-ss place n shamt) → *

Arguments

place — Guard (posp place).

n — Guard (true-listp n).

shamt — Guard (true-listp shamt).

Definitions and Theorems

Function: aig-right-shift-ss

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

Theorem: aig-right-shift-ss-correct

(defthm aig-right-shift-ss-correct
  (implies (< (aig-list->s shamt env) 0)
           (equal (aig-list->s (aig-right-shift-ss place n shamt)
                               env)
                  (ash (aig-list->s n env)
                       (+ -1 (pos-fix place)
                          (* (pos-fix place)
                             (aig-list->s shamt env)))))))

Theorem: aig-right-shift-ss-of-pos-fix-place

(defthm aig-right-shift-ss-of-pos-fix-place
  (equal (aig-right-shift-ss (pos-fix place)
                             n shamt)
         (aig-right-shift-ss place n shamt)))

Theorem: aig-right-shift-ss-pos-equiv-congruence-on-place

(defthm aig-right-shift-ss-pos-equiv-congruence-on-place
  (implies (pos-equiv place place-equiv)
           (equal (aig-right-shift-ss place n shamt)
                  (aig-right-shift-ss place-equiv n shamt)))
  :rule-classes :congruence)

Theorem: aig-right-shift-ss-of-list-fix-n

(defthm aig-right-shift-ss-of-list-fix-n
  (equal (aig-right-shift-ss place (list-fix n)
                             shamt)
         (aig-right-shift-ss place n shamt)))

Theorem: aig-right-shift-ss-list-equiv-congruence-on-n

(defthm aig-right-shift-ss-list-equiv-congruence-on-n
  (implies (list-equiv n n-equiv)
           (equal (aig-right-shift-ss place n shamt)
                  (aig-right-shift-ss place n-equiv shamt)))
  :rule-classes :congruence)

Theorem: aig-right-shift-ss-of-list-fix-shamt

(defthm aig-right-shift-ss-of-list-fix-shamt
  (equal (aig-right-shift-ss place n (list-fix shamt))
         (aig-right-shift-ss place n shamt)))

Theorem: aig-right-shift-ss-list-equiv-congruence-on-shamt

(defthm aig-right-shift-ss-list-equiv-congruence-on-shamt
  (implies (list-equiv shamt shamt-equiv)
           (equal (aig-right-shift-ss place n shamt)
                  (aig-right-shift-ss place n shamt-equiv)))
  :rule-classes :congruence)