(in-package :kira)
(defgeneric ternary-node-priority (generic-node)
(:method ((ternary-node-as-list list)) 0))
(define-persistent-class ternary-node ()
((label :initarg :label :accessor ternary-node-label)
(data :initform nil :initarg :data :accessor ternary-node-data)
(left :initform nil :initarg :left :accessor ternary-node-left)
(middle :initform nil :initarg :middle :accessor ternary-node-middle)
(right :initform nil :initarg :right :accessor ternary-node-right)
(priority :initform 0 :initarg :priority :accessor ternary-node-priority)))
(defconstant +max-priority+ (1- (ash 1 55)))
(defconstant +ternary-burst-threshold+ 64)
(defun ternary-search (key position node)
(let ((current-label (char key position)))
(cond ((listp node)
(loop for (entry-key . entry-key-association) in node
if (string-equal entry-key key :start2 position)
return entry-key-association))
((char-equal (ternary-node-label node) current-label)
(if (= (the array-index (1+ position)) (length key))
(ternary-node-data node)
(let ((middle (ternary-node-middle node)))
(ternary-search key (1+ position) middle))))
((char-greaterp current-label (ternary-node-label node))
(ternary-search key position (ternary-node-right node)))
((ternary-search key position (ternary-node-left node))))))
(defun get-term (key ternary-search-tree)
(ternary-search (string key) 0 ternary-search-tree))
(define-compiler-macro get-term (key ternary-search-tree)
`(ternary-search (string ,key) 0 ,ternary-search-tree))
(defun ternary-rotate-with-left (node)
(let ((left (ternary-node-left node)))
(with-accessors ((place ternary-node-right)) left
(setf (ternary-node-left node) place place node)
left)))
(defun ternary-rotate-with-right (node)
(let ((right (ternary-node-right node)))
(with-accessors ((place ternary-node-left)) right
(setf (ternary-node-right node) place place node)
right)))
(define-setf-expander get-term (key place &environment environment)
(multiple-value-bind (temps vals news writer reader) (get-setf-expansion place environment)
(unless (endp (cdr news)) (error "Multiple values aren't supported in ternary search trees."))
(with-gensyms (key-string node new-data)
(values `(,key-string ,@temps ,node)
`((string ,key) ,@vals ,reader)
`(,new-data)
`(prog1 ,new-data
(%ternary-insert ,key-string ,new-data 0 ,node)
(when (or (listp ,node) (not (eq ,node ,reader)))
(let ((,(car news) ,node)) ,writer)))
`(get-term ,key-string ,reader)))))
(defun nlabeled (split-key alist &aux (new-ternary-node-label (char split-key 0)))
"Destructively strip the leading character from each key in ALIST matching SPLIT-KEY."
(loop for entry in alist if (char-equal (char (car entry) 0) new-ternary-node-label)
collect entry into middle and do (setf (car entry) (subseq (car entry) 1))
finally (return (values new-ternary-node-label middle))))
(defun alist-insert (key data position alist)
(assert (< position (length key)) (key position) "Key ~S exhausted." key)
(loop for entry in alist if (string-equal (car entry) key :start2 position)
do (return-from alist-insert (progn (setf (cdr entry) data) alist))
finally (let ((alist-delta (list (cons (subseq key position) data))))
(setq alist (merge 'list alist alist-delta #'string-lessp :key #'car))
(let ((list-under-threshold-p (< (length alist) +ternary-burst-threshold+)))
(when list-under-threshold-p (return-from alist-insert alist))
(let* ((midpoint (floor (length alist) 2))
(split-key (car (nth midpoint alist))))
(multiple-value-bind (label middle) (nlabeled split-key alist)
(let* ((priority (1+ (the binary-fixnum (random +max-priority+))))
(alist (sort (set-difference alist middle) #'string-lessp :key #'car))
(right-position (position label alist :test #'string-lessp :key #'car))
(data (whereas ((empty (assoc "" middle :test #'string=))) (cdr empty)))
(right (when right-position (nthcdr right-position alist)))
(left (if right (ldiff alist right) alist)))
(deletef "" middle :key #'car :test #'string=)
(return (make-instance 'ternary-node
:label label :left left
:data data :priority priority
:middle middle :right right)))))))))
(defmacro set-if-changed (place new-value &environment environment)
(multiple-value-bind (temps vals news writer reader) (get-setf-expansion place environment)
(unless (endp (cdr news)) (error "Multiple values aren't supported in SET-IF-CHANGED."))
(with-gensyms (old-temp new-temp)
`(let* (,.(mapcar #'list temps vals) (,old-temp ,reader) (,new-temp ,new-value))
(if (eq ,new-temp ,old-temp) ,old-temp (let ((,(car news) ,new-temp)) ,writer))))))
(defmacro %ternary-insert (key data position place)
`(cond ((listp ,place) (setq ,place (alist-insert ,key ,data ,position ,place)))
(t (set-if-changed ,place (ternary-insert ,key ,data ,position ,place)))))
(defun ternary-key-label (key position)
(unless (< position (length key))
(error "Key ~S exhausted." key))
(char key position))
(defun ternary-insert (key data position node)
(let ((current-label (ternary-key-label key position)))
(with-slots* (priority left middle right label) node
(cond ((char-equal current-label label)
(if (= (the array-index (1+ position)) (length key))
(progn (setf (ternary-node-data node) data) node)
(progn (%ternary-insert key data (1+ position) middle)
(with-accessors ((middle-priority ternary-node-priority)) middle
(when (> middle-priority priority) (setq priority middle-priority))
node))))
((char-greaterp current-label label)
(%ternary-insert key data position right)
(let ((rotatep (> (ternary-node-priority right) priority)))
(if rotatep (ternary-rotate-with-right node) node)))
((%ternary-insert key data position left)
(let ((rotatep (> (ternary-node-priority left) priority)))
(if rotatep (ternary-rotate-with-left node) node)))))))
(defmacro delete-term (key place &environment environment)
(multiple-value-bind (temps vals news writer reader) (get-setf-expansion place environment)
(unless (endp (cdr news)) (error "Multiple values aren't supported in ternary search trees."))
(let ((temporary-bindings (mapcar #'list temps vals)) (new-place-store-variable (car news)))
(with-gensyms (key-temp place-temp)
`(let* ((,key-temp (string ,key))
,.temporary-bindings
(,place-temp ,reader))
(%ternary-delete ,key-temp 0 ,place-temp)
(when (or (listp ,place-temp) (not (eq ,place-temp ,reader)))
(let ((,new-place-store-variable ,place-temp)) ,writer))
,place-temp)))))
(defmacro %ternary-delete (key position place &aux (k `(subseq ,key ,position)))
`(cond ((listp ,place) (deletef ,k ,place :test #'string-equal :key #'car))
(t (set-if-changed ,place (ternary-delete ,key ,position ,place)))))
(defun ternary-delete (key position node)
(let ((current-label (ternary-key-label key position)))
(with-slots* (priority left middle right label) node
(if (char-equal current-label label)
(cond ((< (the array-index (1+ position)) (length key))
(let ((new-middle (%ternary-delete key (the array-index (1+ position)) middle)))
(when (eq (or (ternary-node-data node) new-middle) nil) (setq priority 0)))
(ternary-heapify-or-delete node))
((progn (setf (ternary-node-data node) nil) middle) node)
((progn (setq priority 0) (ternary-heapify-or-delete node))))
(prog1 node
(if (char-greaterp current-label label)
(%ternary-delete key position right)
(%ternary-delete key position left)))))))
(defun ternary-heapify-or-delete (node)
(with-slots* (priority left middle right data) node
(unless (or left middle right data) (return-from ternary-heapify-or-delete))
(with-accessors ((left-priority ternary-node-priority)) left
(with-accessors ((right-priority ternary-node-priority)) right
(cond ((>= priority (max right-priority left-priority)) node)
((> right-priority left-priority)
(let ((rotated-in-node (ternary-rotate-with-right node)))
(with-accessors ((left ternary-node-left)) rotated-in-node
(set-if-changed left (ternary-heapify-or-delete left)))
rotated-in-node))
((let ((rotated-in-node (ternary-rotate-with-left node)))
(with-accessors ((right ternary-node-right)) rotated-in-node
(set-if-changed right (ternary-heapify-or-delete right)))
rotated-in-node)))))))
(defun map-terms (function ternary-search-tree)
(cond ((typep ternary-search-tree 'ternary-node)
(map-terms function (ternary-node-left ternary-search-tree))
(whereas ((data (ternary-node-data ternary-search-tree)))
(funcall function data))
(map-terms function (ternary-node-middle ternary-search-tree))
(map-terms function (ternary-node-right ternary-search-tree))
ternary-search-tree)
((loop for entry in ternary-search-tree
do (funcall function (cdr entry))
finally (return ternary-search-tree)))))
(defmacro do-terms ((var ternary-search-tree &optional result-form) &body body)
`(block nil (map-terms #'(lambda (,var) (tagbody ,@body)) ,ternary-search-tree)
,result-form))
(defgeneric xvector-depth (xvector)
(:method ((null-xv null)) 0))
(defgeneric xvector-root (xvector)
(:method ((null-xv null)) nil))
(defgeneric xvector-max (xvector)
(:method ((null-xv null)) -1))
(define-persistent-class xvector ()
((depth :initform 0 :accessor xvector-depth)
(root :initform nil :accessor xvector-root)
(max :initform -1 :accessor xvector-max)))
(define-symbol-macro +base32hex+
"0123456789ABCDEFGHIJKLMNOPQRSTUV")
(defun key-depth (key)
(check-type key (integer 0 *) "a vector index")
(1- (max (ceiling (integer-length key) 5) 1)))
(defun make-string-key (key &optional (depth (key-depth key)))
(loop with string-key of-type simple-string = (make-string (1+ depth))
for position of-type fixnum downfrom (* 5 depth) downto 0 by 5
for val of-type (unsigned-byte 5) = (ldb (byte 5 position) key)
for i of-type array-index from 0 to (the array-index depth)
do (setf (schar string-key i) (schar +base32hex+ val))
finally (return string-key)))
(defun xvref (xvector key)
(unless xvector (return-from xvref))
(let* ((root (xvector-root xvector))
(depth (xvector-depth xvector))
(k (make-string-key key depth)))
(get-term k root)))
(define-setf-expander xvref (place key &environment environment)
(multiple-value-bind (temps vals news writer reader) (get-setf-expansion place environment)
(unless (endp (cdr news)) (error "Multiple values aren't supported by XVECTOR places."))
(with-gensyms (key-temp xvector new-data)
(values `(,key-temp ,@temps ,xvector)
`(,key ,@vals ,reader)
`(,new-data)
`(progn
(unless ,xvector
(setq ,xvector (make-instance 'xvector))
(let ((,(car news) ,xvector)) ,writer))
(%xvector-set ,xvector ,key-temp ,new-data))
`(xvref ,xvector ,key-temp)))))
(defun %xvector-set (xvector key data)
(loop with root = (xvector-root xvector)
with key-depth of-type fixnum = (key-depth key)
and root-priority = (ternary-node-priority root)
while (> key-depth (xvector-depth xvector))
do (setf (xvector-root xvector)
(make-instance
'ternary-node :label #\0 :middle (xvector-root xvector)
:priority (maxf root-priority (1+ (random +max-priority+))))
(xvector-depth xvector)
(1+ (xvector-depth xvector)))
finally (let ((string-key (make-string-key key (xvector-depth xvector))))
(setf (get-term string-key (xvector-root xvector)) data)
(unless (eq data nil) (maxf (xvector-max xvector) key))
(return data))))
(eval-always
(defconstant +bitmap-burst-threshold+ 64)
(defconstant +bitmap-bit-vector-size+ 14))
(eval-always
(defconstant +bitmap-quad-space-size+
(+ 2 +bitmap-bit-vector-size+)
"Upper two bits select QXR."))
(defmacro %set-bit (part bit-index)
`(let ((sub-index (ldb (byte +bitmap-bit-vector-size+ 0) ,bit-index)))
(declare (type (unsigned-byte ,+bitmap-bit-vector-size+) sub-index))
(prog1 ,part (setf (bit ,part sub-index) 1))))
(defstatic +quad-functions+
(vector (list #'qar #'(setf qar))
(list #'qbr #'(setf qbr))
(list #'qcr #'(setf qcr))
(list #'qdr #'(setf qdr))))
(defun %q-set-bit (quad bit-index)
(let ((part-index (ldb (byte 2 +bitmap-bit-vector-size+) bit-index)))
(destructuring-bind (reader writer) (svref +quad-functions+ part-index)
(flet ((make-bitmap-part () (make-bit-vector (expt 2 +bitmap-bit-vector-size+))))
(let ((part (or (funcall reader quad) (make-bitmap-part))))
(%set-bit part bit-index)
(funcall writer part quad))))))
(defun %xv-set-bit (bitmap i)
(let* ((item-index (ash i (- +bitmap-quad-space-size+)))
(existing-item (xvref bitmap item-index)))
(multiple-value-prog1 (values bitmap item-index)
(cond ((eql existing-item i))
((not existing-item) (setf (xvref bitmap item-index) i))
((typep existing-item 'quad) (%q-set-bit existing-item i))
((symbol-macrolet ((item-at-index (xvref bitmap item-index)))
(let ((quad (setq item-at-index (make-instance 'quad))))
(%q-set-bit quad existing-item) (%q-set-bit quad i))))))))
(defun %add-to-bitmap (bitmap i)
(cond ((typep bitmap 'xvector) (%xv-set-bit bitmap i))
(t (progn (pushnew i bitmap) (sortf bitmap #'<))
(when (< (length bitmap) +bitmap-burst-threshold+)
(return-from %add-to-bitmap bitmap))
(let ((new (make-instance 'xvector)))
(dolist (existing-bit-index bitmap new)
(%xv-set-bit new existing-bit-index))))))
(defmacro add-to-bitmap (place new-bit-index &environment environment)
(multiple-value-bind (temps vals news writer reader) (get-setf-expansion place environment)
(unless (endp (cdr news)) (error "Multiple values aren't supported in ADD-TO-BITMAP."))
(with-gensyms (bitmap new-bitmap)
`(let* (,.(mapcar #'list temps vals) (,bitmap ,reader))
(let ((,new-bitmap (%add-to-bitmap ,bitmap ,new-bit-index)))
(when (or (listp ,bitmap) (not (eq ,new-bitmap ,bitmap)))
(let ((,(car news) ,new-bitmap)) ,writer))
,new-bitmap)))))
(defun in-bitmap-p (bitmap i)
(cond ((listp bitmap) (if (member i bitmap) t nil))
((whereas ((item (xvref bitmap (ash i (- +bitmap-quad-space-size+)))))
(when (integerp item) (return-from in-bitmap-p (eql item i)))
(let* ((part-index (ldb (byte 2 +bitmap-bit-vector-size+) i))
(quad-reader-function (svref #(qar qbr qcr qdr) part-index))
(index-in-part (ldb (byte +bitmap-bit-vector-size+ 0) i))
(part (funcall quad-reader-function item)))
(declare (type (unsigned-byte 2) part-index))
(declare (type array-index index-in-part))
(and part (= (bit part index-in-part) 1)))))))