(defoptimizer (random derive-type) ((bound &optional state))
(one-arg-derive-type bound #'random-derive-type-aux nil))
\f
-;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
-
-;;; Return the maximum number of bits an integer of the supplied type
-;;; can take up, or NIL if it is unbounded. The second (third) value
-;;; is T if the integer can be positive (negative) and NIL if not.
-;;; Zero counts as positive.
-(defun integer-type-length (type)
- (if (numeric-type-p type)
- (let ((min (numeric-type-low type))
- (max (numeric-type-high type)))
- (values (and min max (max (integer-length min) (integer-length max)))
- (or (null max) (not (minusp max)))
- (or (null min) (minusp min))))
- (values nil t t)))
-
-;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
-;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
-;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
-;;; versions in CMUCL, from which these functions copy liberally.
-
-(defun logand-derive-unsigned-low-bound (x y)
- (let ((a (numeric-type-low x))
- (b (numeric-type-high x))
- (c (numeric-type-low y))
- (d (numeric-type-high y)))
- (loop for m = (ash 1 (integer-length (lognor a c))) then (ash m -1)
- until (zerop m) do
- (unless (zerop (logand m (lognot a) (lognot c)))
- (let ((temp (logandc2 (logior a m) (1- m))))
- (when (<= temp b)
- (setf a temp)
- (loop-finish))
- (setf temp (logandc2 (logior c m) (1- m)))
- (when (<= temp d)
- (setf c temp)
- (loop-finish))))
- finally (return (logand a c)))))
-
-(defun logand-derive-unsigned-high-bound (x y)
- (let ((a (numeric-type-low x))
- (b (numeric-type-high x))
- (c (numeric-type-low y))
- (d (numeric-type-high y)))
- (loop for m = (ash 1 (integer-length (logxor b d))) then (ash m -1)
- until (zerop m) do
- (cond
- ((not (zerop (logand b (lognot d) m)))
- (let ((temp (logior (logandc2 b m) (1- m))))
- (when (>= temp a)
- (setf b temp)
- (loop-finish))))
- ((not (zerop (logand (lognot b) d m)))
- (let ((temp (logior (logandc2 d m) (1- m))))
- (when (>= temp c)
- (setf d temp)
- (loop-finish)))))
- finally (return (logand b d)))))
-
-(defun logand-derive-type-aux (x y &optional same-leaf)
- (when same-leaf
- (return-from logand-derive-type-aux x))
- (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
- (declare (ignore x-pos))
- (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
- (declare (ignore y-pos))
- (if (not x-neg)
- ;; X must be positive.
- (if (not y-neg)
- ;; They must both be positive.
- (cond ((and (null x-len) (null y-len))
- (specifier-type 'unsigned-byte))
- ((null x-len)
- (specifier-type `(unsigned-byte* ,y-len)))
- ((null y-len)
- (specifier-type `(unsigned-byte* ,x-len)))
- (t
- (let ((low (logand-derive-unsigned-low-bound x y))
- (high (logand-derive-unsigned-high-bound x y)))
- (specifier-type `(integer ,low ,high)))))
- ;; X is positive, but Y might be negative.
- (cond ((null x-len)
- (specifier-type 'unsigned-byte))
- (t
- (specifier-type `(unsigned-byte* ,x-len)))))
- ;; X might be negative.
- (if (not y-neg)
- ;; Y must be positive.
- (cond ((null y-len)
- (specifier-type 'unsigned-byte))
- (t (specifier-type `(unsigned-byte* ,y-len))))
- ;; Either might be negative.
- (if (and x-len y-len)
- ;; The result is bounded.
- (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
- ;; We can't tell squat about the result.
- (specifier-type 'integer)))))))
-
-(defun logior-derive-unsigned-low-bound (x y)
- (let ((a (numeric-type-low x))
- (b (numeric-type-high x))
- (c (numeric-type-low y))
- (d (numeric-type-high y)))
- (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
- until (zerop m) do
- (cond
- ((not (zerop (logandc2 (logand c m) a)))
- (let ((temp (logand (logior a m) (1+ (lognot m)))))
- (when (<= temp b)
- (setf a temp)
- (loop-finish))))
- ((not (zerop (logandc2 (logand a m) c)))
- (let ((temp (logand (logior c m) (1+ (lognot m)))))
- (when (<= temp d)
- (setf c temp)
- (loop-finish)))))
- finally (return (logior a c)))))
-
-(defun logior-derive-unsigned-high-bound (x y)
- (let ((a (numeric-type-low x))
- (b (numeric-type-high x))
- (c (numeric-type-low y))
- (d (numeric-type-high y)))
- (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
- until (zerop m) do
- (unless (zerop (logand b d m))
- (let ((temp (logior (- b m) (1- m))))
- (when (>= temp a)
- (setf b temp)
- (loop-finish))
- (setf temp (logior (- d m) (1- m)))
- (when (>= temp c)
- (setf d temp)
- (loop-finish))))
- finally (return (logior b d)))))
-
-(defun logior-derive-type-aux (x y &optional same-leaf)
- (when same-leaf
- (return-from logior-derive-type-aux x))
- (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
- (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
- (cond
- ((and (not x-neg) (not y-neg))
- ;; Both are positive.
- (if (and x-len y-len)
- (let ((low (logior-derive-unsigned-low-bound x y))
- (high (logior-derive-unsigned-high-bound x y)))
- (specifier-type `(integer ,low ,high)))
- (specifier-type `(unsigned-byte* *))))
- ((not x-pos)
- ;; X must be negative.
- (if (not y-pos)
- ;; Both are negative. The result is going to be negative
- ;; and be the same length or shorter than the smaller.
- (if (and x-len y-len)
- ;; It's bounded.
- (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
- ;; It's unbounded.
- (specifier-type '(integer * -1)))
- ;; X is negative, but we don't know about Y. The result
- ;; will be negative, but no more negative than X.
- (specifier-type
- `(integer ,(or (numeric-type-low x) '*)
- -1))))
- (t
- ;; X might be either positive or negative.
- (if (not y-pos)
- ;; But Y is negative. The result will be negative.
- (specifier-type
- `(integer ,(or (numeric-type-low y) '*)
- -1))
- ;; We don't know squat about either. It won't get any bigger.
- (if (and x-len y-len)
- ;; Bounded.
- (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
- ;; Unbounded.
- (specifier-type 'integer))))))))
-
-(defun logxor-derive-unsigned-low-bound (x y)
- (let ((a (numeric-type-low x))
- (b (numeric-type-high x))
- (c (numeric-type-low y))
- (d (numeric-type-high y)))
- (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
- until (zerop m) do
- (cond
- ((not (zerop (logandc2 (logand c m) a)))
- (let ((temp (logand (logior a m)
- (1+ (lognot m)))))
- (when (<= temp b)
- (setf a temp))))
- ((not (zerop (logandc2 (logand a m) c)))
- (let ((temp (logand (logior c m)
- (1+ (lognot m)))))
- (when (<= temp d)
- (setf c temp)))))
- finally (return (logxor a c)))))
-
-(defun logxor-derive-unsigned-high-bound (x y)
- (let ((a (numeric-type-low x))
- (b (numeric-type-high x))
- (c (numeric-type-low y))
- (d (numeric-type-high y)))
- (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
- until (zerop m) do
- (unless (zerop (logand b d m))
- (let ((temp (logior (- b m) (1- m))))
- (cond
- ((>= temp a) (setf b temp))
- (t (let ((temp (logior (- d m) (1- m))))
- (when (>= temp c)
- (setf d temp)))))))
- finally (return (logxor b d)))))
-
-(defun logxor-derive-type-aux (x y &optional same-leaf)
- (when same-leaf
- (return-from logxor-derive-type-aux (specifier-type '(eql 0))))
- (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
- (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
- (cond
- ((and (not x-neg) (not y-neg))
- ;; Both are positive
- (if (and x-len y-len)
- (let ((low (logxor-derive-unsigned-low-bound x y))
- (high (logxor-derive-unsigned-high-bound x y)))
- (specifier-type `(integer ,low ,high)))
- (specifier-type '(unsigned-byte* *))))
- ((and (not x-pos) (not y-pos))
- ;; Both are negative. The result will be positive, and as long
- ;; as the longer.
- (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
- (max x-len y-len)
- '*))))
- ((or (and (not x-pos) (not y-neg))
- (and (not y-pos) (not x-neg)))
- ;; Either X is negative and Y is positive or vice-versa. The
- ;; result will be negative.
- (specifier-type `(integer ,(if (and x-len y-len)
- (ash -1 (max x-len y-len))
- '*)
- -1)))
- ;; We can't tell what the sign of the result is going to be.
- ;; All we know is that we don't create new bits.
- ((and x-len y-len)
- (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
- (t
- (specifier-type 'integer))))))
-
-(macrolet ((deffrob (logfun)
- (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
- `(defoptimizer (,logfun derive-type) ((x y))
- (two-arg-derive-type x y #',fun-aux #',logfun)))))
- (deffrob logand)
- (deffrob logior)
- (deffrob logxor))
-
-(defoptimizer (logeqv derive-type) ((x y))
- (two-arg-derive-type x y (lambda (x y same-leaf)
- (lognot-derive-type-aux
- (logxor-derive-type-aux x y same-leaf)))
- #'logeqv))
-(defoptimizer (lognand derive-type) ((x y))
- (two-arg-derive-type x y (lambda (x y same-leaf)
- (lognot-derive-type-aux
- (logand-derive-type-aux x y same-leaf)))
- #'lognand))
-(defoptimizer (lognor derive-type) ((x y))
- (two-arg-derive-type x y (lambda (x y same-leaf)
- (lognot-derive-type-aux
- (logior-derive-type-aux x y same-leaf)))
- #'lognor))
-(defoptimizer (logandc1 derive-type) ((x y))
- (two-arg-derive-type x y (lambda (x y same-leaf)
- (if same-leaf
- (specifier-type '(eql 0))
- (logand-derive-type-aux
- (lognot-derive-type-aux x) y nil)))
- #'logandc1))
-(defoptimizer (logandc2 derive-type) ((x y))
- (two-arg-derive-type x y (lambda (x y same-leaf)
- (if same-leaf
- (specifier-type '(eql 0))
- (logand-derive-type-aux
- x (lognot-derive-type-aux y) nil)))
- #'logandc2))
-(defoptimizer (logorc1 derive-type) ((x y))
- (two-arg-derive-type x y (lambda (x y same-leaf)
- (if same-leaf
- (specifier-type '(eql -1))
- (logior-derive-type-aux
- (lognot-derive-type-aux x) y nil)))
- #'logorc1))
-(defoptimizer (logorc2 derive-type) ((x y))
- (two-arg-derive-type x y (lambda (x y same-leaf)
- (if same-leaf
- (specifier-type '(eql -1))
- (logior-derive-type-aux
- x (lognot-derive-type-aux y) nil)))
- #'logorc2))
-\f
;;;; miscellaneous derive-type methods
(defoptimizer (integer-length derive-type) ((x))
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