0.8.5.3:

[sbcl.git] / src / compiler / srctran.lisp

diff --git a/src/compiler/srctran.lisp b/src/compiler/srctran.lisp
index fc82d67..1fcfe78 100644 (file)
--- a/src/compiler/srctran.lisp
+++ b/src/compiler/srctran.lisp
@@ -1,6 +1,6 @@
 ;;;; This file contains macro-like source transformations which
 ;;;; convert uses of certain functions into the canonical form desired
 ;;;; This file contains macro-like source transformations which
 ;;;; convert uses of certain functions into the canonical form desired

-;;;; within the compiler. ### and other IR1 transforms and stuff.
+;;;; within the compiler. FIXME: and other IR1 transforms and stuff.

 
 ;;;; This software is part of the SBCL system. See the README file for
 ;;;; more information.
 
 ;;;; This software is part of the SBCL system. See the README file for
 ;;;; more information.

@@ -15,48 +15,44 @@
 
 ;;; Convert into an IF so that IF optimizations will eliminate redundant
 ;;; negations.
 
 ;;; Convert into an IF so that IF optimizations will eliminate redundant
 ;;; negations.

-(def-source-transform not (x) `(if ,x nil t))
-(def-source-transform null (x) `(if ,x nil t))
+(define-source-transform not (x) `(if ,x nil t))
+(define-source-transform null (x) `(if ,x nil t))

 
 

-;;; ENDP is just NULL with a LIST assertion.
-(def-source-transform endp (x) `(null (the list ,x)))
-;;; FIXME: Is THE LIST a strong enough assertion for ANSI's "should
-;;; return an error"? (THE LIST is optimized away when safety is low;
-;;; does that satisfy the spec?)
+;;; ENDP is just NULL with a LIST assertion. The assertion will be
+;;; optimized away when SAFETY optimization is low; hopefully that
+;;; is consistent with ANSI's "should return an error".
+(define-source-transform endp (x) `(null (the list ,x)))

 
 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
 ;;; returns the first value of its argument. Ditto for VALUES with one
 ;;; arg.
 
 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
 ;;; returns the first value of its argument. Ditto for VALUES with one
 ;;; arg.

-(def-source-transform identity (x) `(prog1 ,x))
-(def-source-transform values (x) `(prog1 ,x))
-
-;;; Bind the values and make a closure that returns them.
-(def-source-transform constantly (value &rest values)
-  (let ((temps (make-gensym-list (1+ (length values))))
-       (dum (gensym)))
-    `(let ,(loop for temp in temps and
-                value in (list* value values)
-                collect `(,temp ,value))
-       #'(lambda (&rest ,dum)
-          (declare (ignore ,dum))
-          (values ,@temps)))))
+(define-source-transform identity (x) `(prog1 ,x))
+(define-source-transform values (x) `(prog1 ,x))
+
+;;; Bind the value and make a closure that returns it.
+(define-source-transform constantly (value)
+  (with-unique-names (rest n-value)
+    `(let ((,n-value ,value))
+      (lambda (&rest ,rest)
+       (declare (ignore ,rest))
+       ,n-value))))

 
 ;;; If the function has a known number of arguments, then return a
 ;;; lambda with the appropriate fixed number of args. If the
 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
 ;;; MV optimization figure things out.
 
 ;;; If the function has a known number of arguments, then return a
 ;;; lambda with the appropriate fixed number of args. If the
 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
 ;;; MV optimization figure things out.

-(deftransform complement ((fun) * * :node node :when :both)
+(deftransform complement ((fun) * * :node node)

   "open code"
   (multiple-value-bind (min max)
   "open code"
   (multiple-value-bind (min max)

-      (function-type-nargs (continuation-type fun))
+      (fun-type-nargs (lvar-type fun))

     (cond
      ((and min (eql min max))
       (let ((dums (make-gensym-list min)))
        `#'(lambda ,dums (not (funcall fun ,@dums)))))
     (cond
      ((and min (eql min max))
       (let ((dums (make-gensym-list min)))
        `#'(lambda ,dums (not (funcall fun ,@dums)))))

-     ((let* ((cont (node-cont node))
-            (dest (continuation-dest cont)))
-       (and (combination-p dest)
-            (eq (combination-fun dest) cont)))
+     ((awhen (node-lvar node)
+        (let ((dest (lvar-dest it)))
+          (and (combination-p dest)
+               (eq (combination-fun dest) it))))

       '#'(lambda (&rest args)
           (not (apply fun args))))
      (t
       '#'(lambda (&rest args)
           (not (apply fun args))))
      (t

@@ -65,10 +61,9 @@
 \f
 ;;;; list hackery
 
 \f
 ;;;; list hackery
 

-;;; Translate CxxR into CAR/CDR combos.
-
+;;; Translate CxR into CAR/CDR combos.

 (defun source-transform-cxr (form)
 (defun source-transform-cxr (form)

-  (if (or (byte-compiling) (/= (length form) 2))
+  (if (/= (length form) 2)

       (values nil t)
       (let ((name (symbol-name (car form))))
        (do ((i (- (length name) 2) (1- i))
       (values nil t)
       (let ((name (symbol-name (car form))))
        (do ((i (- (length name) 2) (1- i))

@@ -79,55 +74,66 @@
                    ,res)))
            ((zerop i) res)))))
 
                    ,res)))
            ((zerop i) res)))))
 

-(do ((i 2 (1+ i))
-     (b '(1 0) (cons i b)))
-    ((= i 5))
-  (dotimes (j (ash 1 i))
-    (setf (info :function :source-transform
-               (intern (format nil "C~{~:[A~;D~]~}R"
-                               (mapcar #'(lambda (x) (logbitp x j)) b))))
-         #'source-transform-cxr)))
+;;; Make source transforms to turn CxR forms into combinations of CAR
+;;; and CDR. ANSI specifies that everything up to 4 A/D operations is
+;;; defined.
+(/show0 "about to set CxR source transforms")
+(loop for i of-type index from 2 upto 4 do
+      ;; Iterate over BUF = all names CxR where x = an I-element
+      ;; string of #\A or #\D characters.
+      (let ((buf (make-string (+ 2 i))))
+       (setf (aref buf 0) #\C
+             (aref buf (1+ i)) #\R)
+       (dotimes (j (ash 2 i))
+         (declare (type index j))
+         (dotimes (k i)
+           (declare (type index k))
+           (setf (aref buf (1+ k))
+                 (if (logbitp k j) #\A #\D)))
+         (setf (info :function :source-transform (intern buf))
+               #'source-transform-cxr))))
+(/show0 "done setting CxR source transforms")

 
 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
 ;;; favors it.
 
 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
 ;;; favors it.

-(def-source-transform first (x) `(car ,x))
-(def-source-transform rest (x) `(cdr ,x))
-(def-source-transform second (x) `(cadr ,x))
-(def-source-transform third (x) `(caddr ,x))
-(def-source-transform fourth (x) `(cadddr ,x))
-(def-source-transform fifth (x) `(nth 4 ,x))
-(def-source-transform sixth (x) `(nth 5 ,x))
-(def-source-transform seventh (x) `(nth 6 ,x))
-(def-source-transform eighth (x) `(nth 7 ,x))
-(def-source-transform ninth (x) `(nth 8 ,x))
-(def-source-transform tenth (x) `(nth 9 ,x))
+(define-source-transform first (x) `(car ,x))
+(define-source-transform rest (x) `(cdr ,x))
+(define-source-transform second (x) `(cadr ,x))
+(define-source-transform third (x) `(caddr ,x))
+(define-source-transform fourth (x) `(cadddr ,x))
+(define-source-transform fifth (x) `(nth 4 ,x))
+(define-source-transform sixth (x) `(nth 5 ,x))
+(define-source-transform seventh (x) `(nth 6 ,x))
+(define-source-transform eighth (x) `(nth 7 ,x))
+(define-source-transform ninth (x) `(nth 8 ,x))
+(define-source-transform tenth (x) `(nth 9 ,x))

 
 ;;; Translate RPLACx to LET and SETF.
 
 ;;; Translate RPLACx to LET and SETF.

-(def-source-transform rplaca (x y)
+(define-source-transform rplaca (x y)

   (once-only ((n-x x))
     `(progn
        (setf (car ,n-x) ,y)
        ,n-x)))
   (once-only ((n-x x))
     `(progn
        (setf (car ,n-x) ,y)
        ,n-x)))

-(def-source-transform rplacd (x y)
+(define-source-transform rplacd (x y)

   (once-only ((n-x x))
     `(progn
        (setf (cdr ,n-x) ,y)
        ,n-x)))
 
   (once-only ((n-x x))
     `(progn
        (setf (cdr ,n-x) ,y)
        ,n-x)))
 

-(def-source-transform nth (n l) `(car (nthcdr ,n ,l)))
+(define-source-transform nth (n l) `(car (nthcdr ,n ,l)))

 
 (defvar *default-nthcdr-open-code-limit* 6)
 (defvar *extreme-nthcdr-open-code-limit* 20)
 
 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
   "convert NTHCDR to CAxxR"
 
 (defvar *default-nthcdr-open-code-limit* 6)
 (defvar *extreme-nthcdr-open-code-limit* 20)
 
 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
   "convert NTHCDR to CAxxR"

-  (unless (constant-continuation-p n)
+  (unless (constant-lvar-p n)

     (give-up-ir1-transform))
     (give-up-ir1-transform))

-  (let ((n (continuation-value n)))
+  (let ((n (lvar-value n)))

     (when (> n
     (when (> n

-            (if (policy node (= speed 3) (= space 0))
+            (if (policy node (and (= speed 3) (= space 0)))

                 *extreme-nthcdr-open-code-limit*
                 *default-nthcdr-open-code-limit*))
       (give-up-ir1-transform))
                 *extreme-nthcdr-open-code-limit*
                 *default-nthcdr-open-code-limit*))
       (give-up-ir1-transform))

@@ -140,73 +146,72 @@
 \f
 ;;;; arithmetic and numerology
 
 \f
 ;;;; arithmetic and numerology
 

-(def-source-transform plusp (x) `(> ,x 0))
-(def-source-transform minusp (x) `(< ,x 0))
-(def-source-transform zerop (x) `(= ,x 0))
+(define-source-transform plusp (x) `(> ,x 0))
+(define-source-transform minusp (x) `(< ,x 0))
+(define-source-transform zerop (x) `(= ,x 0))

 
 

-(def-source-transform 1+ (x) `(+ ,x 1))
-(def-source-transform 1- (x) `(- ,x 1))
+(define-source-transform 1+ (x) `(+ ,x 1))
+(define-source-transform 1- (x) `(- ,x 1))

 
 

-(def-source-transform oddp (x) `(not (zerop (logand ,x 1))))
-(def-source-transform evenp (x) `(zerop (logand ,x 1)))
+(define-source-transform oddp (x) `(not (zerop (logand ,x 1))))
+(define-source-transform evenp (x) `(zerop (logand ,x 1)))

 
 ;;; Note that all the integer division functions are available for
 ;;; inline expansion.
 
 
 ;;; Note that all the integer division functions are available for
 ;;; inline expansion.
 

-;;; FIXME: DEF-FROB instead of FROB
-(macrolet ((frob (fun)
-            `(def-source-transform ,fun (x &optional (y nil y-p))
+(macrolet ((deffrob (fun)
+            `(define-source-transform ,fun (x &optional (y nil y-p))

                (declare (ignore y))
                (if y-p
                    (values nil t)
                    `(,',fun ,x 1)))))
                (declare (ignore y))
                (if y-p
                    (values nil t)
                    `(,',fun ,x 1)))))

-  (frob truncate)
-  (frob round)
-  #!+propagate-float-type
-  (frob floor)
-  #!+propagate-float-type
-  (frob ceiling))
-
-(def-source-transform lognand (x y) `(lognot (logand ,x ,y)))
-(def-source-transform lognor (x y) `(lognot (logior ,x ,y)))
-(def-source-transform logandc1 (x y) `(logand (lognot ,x) ,y))
-(def-source-transform logandc2 (x y) `(logand ,x (lognot ,y)))
-(def-source-transform logorc1 (x y) `(logior (lognot ,x) ,y))
-(def-source-transform logorc2 (x y) `(logior ,x (lognot ,y)))
-(def-source-transform logtest (x y) `(not (zerop (logand ,x ,y))))
-(def-source-transform logbitp (index integer)
-  `(not (zerop (logand (ash 1 ,index) ,integer))))
-(def-source-transform byte (size position) `(cons ,size ,position))
-(def-source-transform byte-size (spec) `(car ,spec))
-(def-source-transform byte-position (spec) `(cdr ,spec))
-(def-source-transform ldb-test (bytespec integer)
+  (deffrob truncate)
+  (deffrob round)
+  #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
+  (deffrob floor)
+  #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
+  (deffrob ceiling))
+
+(define-source-transform logtest (x y) `(not (zerop (logand ,x ,y))))
+
+(deftransform logbitp
+    ((index integer) (unsigned-byte (or (signed-byte #.sb!vm:n-word-bits)
+                                       (unsigned-byte #.sb!vm:n-word-bits))))
+  `(if (>= index #.sb!vm:n-word-bits)
+       (minusp integer)
+       (not (zerop (logand integer (ash 1 index))))))
+
+(define-source-transform byte (size position)
+  `(cons ,size ,position))
+(define-source-transform byte-size (spec) `(car ,spec))
+(define-source-transform byte-position (spec) `(cdr ,spec))
+(define-source-transform ldb-test (bytespec integer)

   `(not (zerop (mask-field ,bytespec ,integer))))
 
 ;;; With the ratio and complex accessors, we pick off the "identity"
 ;;; case, and use a primitive to handle the cell access case.
   `(not (zerop (mask-field ,bytespec ,integer))))
 
 ;;; With the ratio and complex accessors, we pick off the "identity"
 ;;; case, and use a primitive to handle the cell access case.

-(def-source-transform numerator (num)
+(define-source-transform numerator (num)

   (once-only ((n-num `(the rational ,num)))
     `(if (ratiop ,n-num)
         (%numerator ,n-num)
         ,n-num)))
   (once-only ((n-num `(the rational ,num)))
     `(if (ratiop ,n-num)
         (%numerator ,n-num)
         ,n-num)))

-(def-source-transform denominator (num)
+(define-source-transform denominator (num)

   (once-only ((n-num `(the rational ,num)))
     `(if (ratiop ,n-num)
         (%denominator ,n-num)
         1)))
 \f
   (once-only ((n-num `(the rational ,num)))
     `(if (ratiop ,n-num)
         (%denominator ,n-num)
         1)))
 \f

-;;;; Interval arithmetic for computing bounds
-;;;; (toy@rtp.ericsson.se)
+;;;; interval arithmetic for computing bounds

 ;;;;
 ;;;; This is a set of routines for operating on intervals. It
 ;;;; implements a simple interval arithmetic package. Although SBCL
 ;;;;
 ;;;; This is a set of routines for operating on intervals. It
 ;;;; implements a simple interval arithmetic package. Although SBCL

-;;;; has an interval type in numeric-type, we choose to use our own
+;;;; has an interval type in NUMERIC-TYPE, we choose to use our own

 ;;;; for two reasons:
 ;;;;
 ;;;; for two reasons:
 ;;;;

-;;;;   1. This package is simpler than numeric-type
+;;;;   1. This package is simpler than NUMERIC-TYPE.

 ;;;;
 ;;;;   2. It makes debugging much easier because you can just strip
 ;;;;
 ;;;;   2. It makes debugging much easier because you can just strip

-;;;;   out these routines and test them independently of SBCL. (a
+;;;;   out these routines and test them independently of SBCL. (This is a

 ;;;;   big win!)
 ;;;;
 ;;;; One disadvantage is a probable increase in consing because we
 ;;;;   big win!)
 ;;;;
 ;;;; One disadvantage is a probable increase in consing because we

@@ -214,27 +219,38 @@
 ;;;; numeric-type has everything we want to know. Reason 2 wins for
 ;;;; now.
 
 ;;;; numeric-type has everything we want to know. Reason 2 wins for
 ;;;; now.
 

-#-sb-xc-host ;(CROSS-FLOAT-INFINITY-KLUDGE, see base-target-features.lisp-expr)
-(progn
-#!+propagate-float-type
-(progn
+;;; Support operations that mimic real arithmetic comparison
+;;; operators, but imposing a total order on the floating points such
+;;; that negative zeros are strictly less than positive zeros.
+(macrolet ((def (name op)
+            `(defun ,name (x y)
+               (declare (real x y))
+               (if (and (floatp x) (floatp y) (zerop x) (zerop y))
+                   (,op (float-sign x) (float-sign y))
+                   (,op x y)))))
+  (def signed-zero->= >=)
+  (def signed-zero-> >)
+  (def signed-zero-= =)
+  (def signed-zero-< <)
+  (def signed-zero-<= <=))

 
 ;;; The basic interval type. It can handle open and closed intervals.
 ;;; A bound is open if it is a list containing a number, just like
 ;;; Lisp says. NIL means unbounded.
 
 ;;; The basic interval type. It can handle open and closed intervals.
 ;;; A bound is open if it is a list containing a number, just like
 ;;; Lisp says. NIL means unbounded.

-(defstruct (interval
-            (:constructor %make-interval))
+(defstruct (interval (:constructor %make-interval)
+                    (:copier nil))

   low high)
 
 (defun make-interval (&key low high)
   (labels ((normalize-bound (val)
   low high)
 
 (defun make-interval (&key low high)
   (labels ((normalize-bound (val)

-            (cond ((and (floatp val)
+            (cond #-sb-xc-host
+                   ((and (floatp val)

                         (float-infinity-p val))
                         (float-infinity-p val))

-                   ;; Handle infinities
+                   ;; Handle infinities.

                    nil)
                   ((or (numberp val)
                        (eq val nil))
                    nil)
                   ((or (numberp val)
                        (eq val nil))

-                   ;; Handle any closed bounds
+                   ;; Handle any closed bounds.

                    val)
                   ((listp val)
                    ;; We have an open bound. Normalize the numeric
                    val)
                   ((listp val)
                    ;; We have an open bound. Normalize the numeric

@@ -243,37 +259,33 @@
                    ;; bound is really unbounded, so drop the openness.
                    (let ((new-val (normalize-bound (first val))))
                      (when new-val
                    ;; bound is really unbounded, so drop the openness.
                    (let ((new-val (normalize-bound (first val))))
                      (when new-val

-                       ;; Bound exists, so keep it open still
+                       ;; The bound exists, so keep it open still.

                        (list new-val))))
                   (t
                        (list new-val))))
                   (t

-                   (error "Unknown bound type in make-interval!")))))
+                   (error "unknown bound type in MAKE-INTERVAL")))))

     (%make-interval :low (normalize-bound low)
                    :high (normalize-bound high))))
 
     (%make-interval :low (normalize-bound low)
                    :high (normalize-bound high))))
 

-#!-sb-fluid (declaim (inline bound-value set-bound))
-
-;;; Extract the numeric value of a bound. Return NIL, if X is NIL.
-(defun bound-value (x)
-  (if (consp x) (car x) x))
-

 ;;; Given a number X, create a form suitable as a bound for an
 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
 ;;; Given a number X, create a form suitable as a bound for an
 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.

+#!-sb-fluid (declaim (inline set-bound))

 (defun set-bound (x open-p)
   (if (and x open-p) (list x) x))
 
 ;;; Apply the function F to a bound X. If X is an open bound, then
 ;;; the result will be open. IF X is NIL, the result is NIL.
 (defun bound-func (f x)
 (defun set-bound (x open-p)
   (if (and x open-p) (list x) x))
 
 ;;; Apply the function F to a bound X. If X is an open bound, then
 ;;; the result will be open. IF X is NIL, the result is NIL.
 (defun bound-func (f x)

+  (declare (type function f))

   (and x
        (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
         ;; With these traps masked, we might get things like infinity
         ;; or negative infinity returned. Check for this and return
         ;; NIL to indicate unbounded.
   (and x
        (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
         ;; With these traps masked, we might get things like infinity
         ;; or negative infinity returned. Check for this and return
         ;; NIL to indicate unbounded.

-        (let ((y (funcall f (bound-value x))))
+        (let ((y (funcall f (type-bound-number x))))

           (if (and (floatp y)
                    (float-infinity-p y))
               nil
           (if (and (floatp y)
                    (float-infinity-p y))
               nil

-              (set-bound (funcall f (bound-value x)) (consp x)))))))
+              (set-bound (funcall f (type-bound-number x)) (consp x)))))))

 
 ;;; Apply a binary operator OP to two bounds X and Y. The result is
 ;;; NIL if either is NIL. Otherwise bound is computed and the result
 
 ;;; Apply a binary operator OP to two bounds X and Y. The result is
 ;;; NIL if either is NIL. Otherwise bound is computed and the result

@@ -283,19 +295,33 @@
 (defmacro bound-binop (op x y)
   `(and ,x ,y
        (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
 (defmacro bound-binop (op x y)
   `(and ,x ,y
        (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)

-        (set-bound (,op (bound-value ,x)
-                        (bound-value ,y))
+        (set-bound (,op (type-bound-number ,x)
+                        (type-bound-number ,y))

                    (or (consp ,x) (consp ,y))))))
 
                    (or (consp ,x) (consp ,y))))))
 

-;;; NUMERIC-TYPE->INTERVAL
-;;;

 ;;; Convert a numeric-type object to an interval object.
 ;;; Convert a numeric-type object to an interval object.

-

 (defun numeric-type->interval (x)
   (declare (type numeric-type x))
   (make-interval :low (numeric-type-low x)
                 :high (numeric-type-high x)))
 
 (defun numeric-type->interval (x)
   (declare (type numeric-type x))
   (make-interval :low (numeric-type-low x)
                 :high (numeric-type-high x)))
 

+(defun type-approximate-interval (type)
+  (declare (type ctype type))
+  (let ((types (prepare-arg-for-derive-type type))
+        (result nil))
+    (dolist (type types)
+      (let ((type (if (member-type-p type)
+                      (convert-member-type type)
+                      type)))
+        (unless (numeric-type-p type)
+          (return-from type-approximate-interval nil))
+        (let ((interval (numeric-type->interval type)))
+          (setq result
+                (if result
+                    (interval-approximate-union result interval)
+                    interval)))))
+    result))
+

 (defun copy-interval-limit (limit)
   (if (numberp limit)
       limit
 (defun copy-interval-limit (limit)
   (if (numberp limit)
       limit

@@ -306,8 +332,6 @@
   (make-interval :low (copy-interval-limit (interval-low x))
                 :high (copy-interval-limit (interval-high x))))
 
   (make-interval :low (copy-interval-limit (interval-low x))
                 :high (copy-interval-limit (interval-high x))))
 

-;;; INTERVAL-SPLIT
-;;;

 ;;; Given a point P contained in the interval X, split X into two
 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
 ;;; Given a point P contained in the interval X, split X into two
 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
 ;;; interval contains P. If CLOSE-UPPER is T, the right interval

@@ -320,99 +344,40 @@
        (make-interval :low (if close-upper (list p) p)
                       :high (copy-interval-limit (interval-high x)))))
 
        (make-interval :low (if close-upper (list p) p)
                       :high (copy-interval-limit (interval-high x)))))
 

-;;; INTERVAL-CLOSURE
-;;;

 ;;; Return the closure of the interval. That is, convert open bounds
 ;;; to closed bounds.
 (defun interval-closure (x)
   (declare (type interval x))
 ;;; Return the closure of the interval. That is, convert open bounds
 ;;; to closed bounds.
 (defun interval-closure (x)
   (declare (type interval x))

-  (make-interval :low (bound-value (interval-low x))
-                :high (bound-value (interval-high x))))
+  (make-interval :low (type-bound-number (interval-low x))
+                :high (type-bound-number (interval-high x))))

 
 

-(defun signed-zero->= (x y)
-  (declare (real x y))
-  (or (> x y)
-      (and (= x y)
-          (>= (float-sign (float x))
-              (float-sign (float y))))))
-
-;;; INTERVAL-RANGE-INFO
-;;;

 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
 ;;; '-. Otherwise return NIL.
 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
 ;;; '-. Otherwise return NIL.

-#+nil

 (defun interval-range-info (x &optional (point 0))
   (declare (type interval x))
   (let ((lo (interval-low x))
        (hi (interval-high x)))
 (defun interval-range-info (x &optional (point 0))
   (declare (type interval x))
   (let ((lo (interval-low x))
        (hi (interval-high x)))

-    (cond ((and lo (signed-zero->= (bound-value lo) point))
+    (cond ((and lo (signed-zero->= (type-bound-number lo) point))

           '+)
           '+)

-         ((and hi (signed-zero->= point (bound-value hi)))
+         ((and hi (signed-zero->= point (type-bound-number hi)))

           '-)
          (t
           nil))))
           '-)
          (t
           nil))))

-(defun interval-range-info (x &optional (point 0))
-  (declare (type interval x))
-  (labels ((signed->= (x y)
-            (if (and (zerop x) (zerop y) (floatp x) (floatp y))
-                (>= (float-sign x) (float-sign y))
-                (>= x y))))
-    (let ((lo (interval-low x))
-         (hi (interval-high x)))
-      (cond ((and lo (signed->= (bound-value lo) point))
-            '+)
-           ((and hi (signed->= point (bound-value hi)))
-            '-)
-           (t
-            nil)))))

 
 

-;;; INTERVAL-BOUNDED-P
-;;;

 ;;; Test to see whether the interval X is bounded. HOW determines the
 ;;; test, and should be either ABOVE, BELOW, or BOTH.
 (defun interval-bounded-p (x how)
   (declare (type interval x))
   (ecase how
 ;;; Test to see whether the interval X is bounded. HOW determines the
 ;;; test, and should be either ABOVE, BELOW, or BOTH.
 (defun interval-bounded-p (x how)
   (declare (type interval x))
   (ecase how

-    ('above
+    (above

      (interval-high x))
      (interval-high x))

-    ('below
+    (below

      (interval-low x))
      (interval-low x))

-    ('both
+    (both

      (and (interval-low x) (interval-high x)))))
 
      (and (interval-low x) (interval-high x)))))
 

-;;; Signed zero comparison functions. Use these functions if we need
-;;; to distinguish between signed zeroes.
-
-(defun signed-zero-< (x y)
-  (declare (real x y))
-  (or (< x y)
-      (and (= x y)
-          (< (float-sign (float x))
-             (float-sign (float y))))))
-(defun signed-zero-> (x y)
-  (declare (real x y))
-  (or (> x y)
-      (and (= x y)
-          (> (float-sign (float x))
-             (float-sign (float y))))))
-
-(defun signed-zero-= (x y)
-  (declare (real x y))
-  (and (= x y)
-       (= (float-sign (float x))
-         (float-sign (float y)))))
-
-(defun signed-zero-<= (x y)
-  (declare (real x y))
-  (or (< x y)
-      (and (= x y)
-          (<= (float-sign (float x))
-              (float-sign (float y))))))
-
-;;; INTERVAL-CONTAINS-P
-;;;
-;;; See whether the interval X contains the number P, taking into account
-;;; that the interval might not be closed.
+;;; See whether the interval X contains the number P, taking into
+;;; account that the interval might not be closed.

 (defun interval-contains-p (p x)
   (declare (type number p)
           (type interval x))
 (defun interval-contains-p (p x)
   (declare (type number p)
           (type interval x))

@@ -422,35 +387,33 @@
        (hi (interval-high x)))
     (cond ((and lo hi)
           ;; The interval is bounded
        (hi (interval-high x)))
     (cond ((and lo hi)
           ;; The interval is bounded

-          (if (and (signed-zero-<= (bound-value lo) p)
-                   (signed-zero-<= p (bound-value hi)))
+          (if (and (signed-zero-<= (type-bound-number lo) p)
+                   (signed-zero-<= p (type-bound-number hi)))

               ;; P is definitely in the closure of the interval.
               ;; We just need to check the end points now.
               ;; P is definitely in the closure of the interval.
               ;; We just need to check the end points now.

-              (cond ((signed-zero-= p (bound-value lo))
+              (cond ((signed-zero-= p (type-bound-number lo))

                      (numberp lo))
                      (numberp lo))

-                    ((signed-zero-= p (bound-value hi))
+                    ((signed-zero-= p (type-bound-number hi))

                      (numberp hi))
                     (t t))
               nil))
          (hi
           ;; Interval with upper bound
                      (numberp hi))
                     (t t))
               nil))
          (hi
           ;; Interval with upper bound

-          (if (signed-zero-< p (bound-value hi))
+          (if (signed-zero-< p (type-bound-number hi))

               t
               (and (numberp hi) (signed-zero-= p hi))))
          (lo
           ;; Interval with lower bound
               t
               (and (numberp hi) (signed-zero-= p hi))))
          (lo
           ;; Interval with lower bound

-          (if (signed-zero-> p (bound-value lo))
+          (if (signed-zero-> p (type-bound-number lo))

               t
               (and (numberp lo) (signed-zero-= p lo))))
          (t
           ;; Interval with no bounds
           t))))
 
               t
               (and (numberp lo) (signed-zero-= p lo))))
          (t
           ;; Interval with no bounds
           t))))
 

-;;; INTERVAL-INTERSECT-P
-;;;
-;;; Determine if two intervals X and Y intersect. Return T if so. If
-;;; CLOSED-INTERVALS-P is T, the treat the intervals as if they were
-;;; closed. Otherwise the intervals are treated as they are.
+;;; Determine whether two intervals X and Y intersect. Return T if so.
+;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
+;;; were closed. Otherwise the intervals are treated as they are.

 ;;;
 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
 ;;;
 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P

@@ -478,7 +441,7 @@
   (flet ((adjacent (lo hi)
           ;; Check to see whether lo and hi are adjacent. If either is
           ;; nil, they can't be adjacent.
   (flet ((adjacent (lo hi)
           ;; Check to see whether lo and hi are adjacent. If either is
           ;; nil, they can't be adjacent.

-          (when (and lo hi (= (bound-value lo) (bound-value hi)))
+          (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))

             ;; The bounds are equal. They are adjacent if one of
             ;; them is closed (a number). If both are open (consp),
             ;; then there is a number that lies between them.
             ;; The bounds are equal. They are adjacent if one of
             ;; them is closed (a number). If both are open (consp),
             ;; then there is a number that lies between them.

@@ -486,8 +449,6 @@
     (or (adjacent (interval-low y) (interval-high x))
        (adjacent (interval-low x) (interval-high y)))))
 
     (or (adjacent (interval-low y) (interval-high x))
        (adjacent (interval-low x) (interval-high y)))))
 

-;;; INTERVAL-INTERSECTION/DIFFERENCE
-;;;

 ;;; Compute the intersection and difference between two intervals.
 ;;; Two values are returned: the intersection and the difference.
 ;;;
 ;;; Compute the intersection and difference between two intervals.
 ;;; Two values are returned: the intersection and the difference.
 ;;;

@@ -514,14 +475,14 @@
               (list p)))
         (test-number (p int)
           ;; Test whether P is in the interval.
               (list p)))
         (test-number (p int)
           ;; Test whether P is in the interval.

-          (when (interval-contains-p (bound-value p)
+          (when (interval-contains-p (type-bound-number p)

                                      (interval-closure int))
             (let ((lo (interval-low int))
                   (hi (interval-high int)))
                                      (interval-closure int))
             (let ((lo (interval-low int))
                   (hi (interval-high int)))

-              ;; Check for endpoints
-              (cond ((and lo (= (bound-value p) (bound-value lo)))
+              ;; Check for endpoints.
+              (cond ((and lo (= (type-bound-number p) (type-bound-number lo)))

                      (not (and (consp p) (numberp lo))))
                      (not (and (consp p) (numberp lo))))

-                    ((and hi (= (bound-value p) (bound-value hi)))
+                    ((and hi (= (type-bound-number p) (type-bound-number hi)))

                      (not (and (numberp p) (consp hi))))
                     (t t)))))
         (test-lower-bound (p int)
                      (not (and (numberp p) (consp hi))))
                     (t t)))))
         (test-lower-bound (p int)

@@ -530,7 +491,7 @@
               (test-number p int)
               (not (interval-bounded-p int 'below))))
         (test-upper-bound (p int)
               (test-number p int)
               (not (interval-bounded-p int 'below))))
         (test-upper-bound (p int)

-          ;; P is an upper bound of an interval
+          ;; P is an upper bound of an interval.

           (if p
               (test-number p int)
               (not (interval-bounded-p int 'above)))))
           (if p
               (test-number p int)
               (not (interval-bounded-p int 'above)))))

@@ -550,13 +511,13 @@
                           (y-hi-in-x
                            (values y-hi (opposite-bound y-hi) x-hi)))
                   (values (make-interval :low lo :high hi)
                           (y-hi-in-x
                            (values y-hi (opposite-bound y-hi) x-hi)))
                   (values (make-interval :low lo :high hi)

-                          (list (make-interval :low left-lo :high left-hi)
-                                (make-interval :low right-lo :high right-hi))))))
+                          (list (make-interval :low left-lo
+                                               :high left-hi)
+                                (make-interval :low right-lo
+                                               :high right-hi))))))

              (t
               (values nil (list x y))))))))
 
              (t
               (values nil (list x y))))))))
 

-;;; INTERVAL-MERGE-PAIR
-;;;

 ;;; If intervals X and Y intersect, return a new interval that is the
 ;;; union of the two. If they do not intersect, return NIL.
 (defun interval-merge-pair (x y)
 ;;; If intervals X and Y intersect, return a new interval that is the
 ;;; union of the two. If they do not intersect, return NIL.
 (defun interval-merge-pair (x y)

@@ -566,15 +527,15 @@
   (when (or (interval-intersect-p x y)
            (interval-adjacent-p x y))
     (flet ((select-bound (x1 x2 min-op max-op)
   (when (or (interval-intersect-p x y)
            (interval-adjacent-p x y))
     (flet ((select-bound (x1 x2 min-op max-op)

-            (let ((x1-val (bound-value x1))
-                  (x2-val (bound-value x2)))
+            (let ((x1-val (type-bound-number x1))
+                  (x2-val (type-bound-number x2)))

               (cond ((and x1 x2)
                      ;; Both bounds are finite. Select the right one.
                      (cond ((funcall min-op x1-val x2-val)
               (cond ((and x1 x2)
                      ;; Both bounds are finite. Select the right one.
                      (cond ((funcall min-op x1-val x2-val)

-                            ;; x1 definitely better
+                            ;; x1 is definitely better.

                             x1)
                            ((funcall max-op x1-val x2-val)
                             x1)
                            ((funcall max-op x1-val x2-val)

-                            ;; x2 definitely better
+                            ;; x2 is definitely better.

                             x2)
                            (t
                             ;; Bounds are equal. Select either
                             x2)
                            (t
                             ;; Bounds are equal. Select either

@@ -592,37 +553,39 @@
        (make-interval :low (select-bound x-lo y-lo #'< #'>)
                       :high (select-bound x-hi y-hi #'> #'<))))))
 
        (make-interval :low (select-bound x-lo y-lo #'< #'>)
                       :high (select-bound x-hi y-hi #'> #'<))))))
 

-;;; Basic arithmetic operations on intervals. We probably should do
+;;; return the minimal interval, containing X and Y
+(defun interval-approximate-union (x y)
+  (cond ((interval-merge-pair x y))
+        ((interval-< x y)
+         (make-interval :low (copy-interval-limit (interval-low x))
+                        :high (copy-interval-limit (interval-high y))))
+        (t
+         (make-interval :low (copy-interval-limit (interval-low y))
+                        :high (copy-interval-limit (interval-high x))))))
+
+;;; basic arithmetic operations on intervals. We probably should do

 ;;; true interval arithmetic here, but it's complicated because we
 ;;; have float and integer types and bounds can be open or closed.
 
 ;;; true interval arithmetic here, but it's complicated because we
 ;;; have float and integer types and bounds can be open or closed.
 

-;;; INTERVAL-NEG
-;;;
-;;; The negative of an interval
+;;; the negative of an interval

 (defun interval-neg (x)
   (declare (type interval x))
   (make-interval :low (bound-func #'- (interval-high x))
                 :high (bound-func #'- (interval-low x))))
 
 (defun interval-neg (x)
   (declare (type interval x))
   (make-interval :low (bound-func #'- (interval-high x))
                 :high (bound-func #'- (interval-low x))))
 

-;;; INTERVAL-ADD
-;;;
-;;; Add two intervals
+;;; Add two intervals.

 (defun interval-add (x y)
   (declare (type interval x y))
   (make-interval :low (bound-binop + (interval-low x) (interval-low y))
                 :high (bound-binop + (interval-high x) (interval-high y))))
 
 (defun interval-add (x y)
   (declare (type interval x y))
   (make-interval :low (bound-binop + (interval-low x) (interval-low y))
                 :high (bound-binop + (interval-high x) (interval-high y))))
 

-;;; INTERVAL-SUB
-;;;
-;;; Subtract two intervals
+;;; Subtract two intervals.

 (defun interval-sub (x y)
   (declare (type interval x y))
   (make-interval :low (bound-binop - (interval-low x) (interval-high y))
                 :high (bound-binop - (interval-high x) (interval-low y))))
 
 (defun interval-sub (x y)
   (declare (type interval x y))
   (make-interval :low (bound-binop - (interval-low x) (interval-high y))
                 :high (bound-binop - (interval-high x) (interval-low y))))
 

-;;; INTERVAL-MUL
-;;;
-;;; Multiply two intervals
+;;; Multiply two intervals.

 (defun interval-mul (x y)
   (declare (type interval x y))
   (flet ((bound-mul (x y)
 (defun interval-mul (x y)
   (declare (type interval x y))
   (flet ((bound-mul (x y)

@@ -635,7 +598,7 @@
                  ;; is always a closed bound. But don't replace this
                  ;; with zero; we want the multiplication to produce
                  ;; the correct signed zero, if needed.
                  ;; is always a closed bound. But don't replace this
                  ;; with zero; we want the multiplication to produce
                  ;; the correct signed zero, if needed.

-                 (* (bound-value x) (bound-value y)))
+                 (* (type-bound-number x) (type-bound-number y)))

                 ((or (and (floatp x) (float-infinity-p x))
                      (and (floatp y) (float-infinity-p y)))
                  ;; Infinity times anything is infinity
                 ((or (and (floatp x) (float-infinity-p x))
                      (and (floatp y) (float-infinity-p y)))
                  ;; Infinity times anything is infinity

@@ -660,14 +623,13 @@
            ((eq y-range '-)
             (interval-neg (interval-mul x (interval-neg y))))
            ((and (eq x-range '+) (eq y-range '+))
            ((eq y-range '-)
             (interval-neg (interval-mul x (interval-neg y))))
            ((and (eq x-range '+) (eq y-range '+))

-            ;; If we are here, X and Y are both positive
-            (make-interval :low (bound-mul (interval-low x) (interval-low y))
-                           :high (bound-mul (interval-high x) (interval-high y))))
+            ;; If we are here, X and Y are both positive.
+            (make-interval
+             :low (bound-mul (interval-low x) (interval-low y))
+             :high (bound-mul (interval-high x) (interval-high y))))

            (t
            (t

-            (error "This shouldn't happen!"))))))
+            (bug "excluded case in INTERVAL-MUL"))))))

 
 

-;;; INTERVAL-DIV
-;;;

 ;;; Divide two intervals.
 (defun interval-div (top bot)
   (declare (type interval top bot))
 ;;; Divide two intervals.
 (defun interval-div (top bot)
   (declare (type interval top bot))

@@ -678,12 +640,12 @@
                  ;; we need to watch out for the sign of the result,
                  ;; to correctly handle signed zeros. We also need
                  ;; to watch out for positive or negative infinity.
                  ;; we need to watch out for the sign of the result,
                  ;; to correctly handle signed zeros. We also need
                  ;; to watch out for positive or negative infinity.

-                 (if (floatp (bound-value x))
+                 (if (floatp (type-bound-number x))

                      (if y-low-p
                      (if y-low-p

-                         (- (float-sign (bound-value x) 0.0))
-                         (float-sign (bound-value x) 0.0))
+                         (- (float-sign (type-bound-number x) 0.0))
+                         (float-sign (type-bound-number x) 0.0))

                      0))
                      0))

-                ((zerop (bound-value y))
+                ((zerop (type-bound-number y))

                  ;; Divide by zero means result is infinity
                  nil)
                 ((and (numberp x) (zerop x))
                  ;; Divide by zero means result is infinity
                  nil)
                 ((and (numberp x) (zerop x))

@@ -711,26 +673,24 @@
             ;; sign of the result.
             (interval-neg (interval-div (interval-neg top) bot)))
            ((and (eq top-range '+) (eq bot-range '+))
             ;; sign of the result.
             (interval-neg (interval-div (interval-neg top) bot)))
            ((and (eq top-range '+) (eq bot-range '+))

-            ;; The easy case
-            (make-interval :low (bound-div (interval-low top) (interval-high bot) t)
-                           :high (bound-div (interval-high top) (interval-low bot) nil)))
+            ;; the easy case
+            (make-interval
+             :low (bound-div (interval-low top) (interval-high bot) t)
+             :high (bound-div (interval-high top) (interval-low bot) nil)))

            (t
            (t

-            (error "This shouldn't happen!"))))))
+            (bug "excluded case in INTERVAL-DIV"))))))

 
 

-;;; INTERVAL-FUNC
-;;;

 ;;; Apply the function F to the interval X. If X = [a, b], then the
 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
 ;;; result makes sense. It will if F is monotonic increasing (or
 ;;; non-decreasing).
 (defun interval-func (f x)
 ;;; Apply the function F to the interval X. If X = [a, b], then the
 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
 ;;; result makes sense. It will if F is monotonic increasing (or
 ;;; non-decreasing).
 (defun interval-func (f x)

-  (declare (type interval x))
+  (declare (type function f)
+           (type interval x))

   (let ((lo (bound-func f (interval-low x)))
        (hi (bound-func f (interval-high x))))
     (make-interval :low lo :high hi)))
 
   (let ((lo (bound-func f (interval-low x)))
        (hi (bound-func f (interval-high x))))
     (make-interval :low lo :high hi)))
 

-;;; INTERVAL-<
-;;;

 ;;; Return T if X < Y. That is every number in the interval X is
 ;;; always less than any number in the interval Y.
 (defun interval-< (x y)
 ;;; Return T if X < Y. That is every number in the interval X is
 ;;; always less than any number in the interval Y.
 (defun interval-< (x y)

@@ -743,21 +703,19 @@
     ;; don't overlap.
     (let ((left (interval-high x))
          (right (interval-low y)))
     ;; don't overlap.
     (let ((left (interval-high x))
          (right (interval-low y)))

-      (cond ((> (bound-value left)
-               (bound-value right))
-            ;; Definitely overlap so result is NIL
+      (cond ((> (type-bound-number left)
+               (type-bound-number right))
+            ;; The intervals definitely overlap, so result is NIL.

             nil)
             nil)

-           ((< (bound-value left)
-               (bound-value right))
-            ;; Definitely don't touch, so result is T
+           ((< (type-bound-number left)
+               (type-bound-number right))
+            ;; The intervals definitely don't touch, so result is T.

             t)
            (t
             ;; Limits are equal. Check for open or closed bounds.
             ;; Don't overlap if one or the other are open.
             (or (consp left) (consp right)))))))
 
             t)
            (t
             ;; Limits are equal. Check for open or closed bounds.
             ;; Don't overlap if one or the other are open.
             (or (consp left) (consp right)))))))
 

-;;; INVTERVAL->=
-;;;

 ;;; Return T if X >= Y. That is, every number in the interval X is
 ;;; always greater than any number in the interval Y.
 (defun interval->= (x y)
 ;;; Return T if X >= Y. That is, every number in the interval X is
 ;;; always greater than any number in the interval Y.
 (defun interval->= (x y)

@@ -765,70 +723,66 @@
   ;; X >= Y if lower bound of X >= upper bound of Y
   (when (and (interval-bounded-p x 'below)
             (interval-bounded-p y 'above))
   ;; X >= Y if lower bound of X >= upper bound of Y
   (when (and (interval-bounded-p x 'below)
             (interval-bounded-p y 'above))

-    (>= (bound-value (interval-low x)) (bound-value (interval-high y)))))
+    (>= (type-bound-number (interval-low x))
+       (type-bound-number (interval-high y)))))

 
 

-;;; INTERVAL-ABS
-;;;
-;;; Return an interval that is the absolute value of X. Thus, if X =
-;;; [-1 10], the result is [0, 10].
+;;; Return an interval that is the absolute value of X. Thus, if
+;;; X = [-1 10], the result is [0, 10].

 (defun interval-abs (x)
   (declare (type interval x))
   (case (interval-range-info x)
 (defun interval-abs (x)
   (declare (type interval x))
   (case (interval-range-info x)

-    ('+
+    (+

      (copy-interval x))
      (copy-interval x))

-    ('-
+    (-

      (interval-neg x))
     (t
      (destructuring-bind (x- x+) (interval-split 0 x t t)
        (interval-merge-pair (interval-neg x-) x+)))))
 
      (interval-neg x))
     (t
      (destructuring-bind (x- x+) (interval-split 0 x t t)
        (interval-merge-pair (interval-neg x-) x+)))))
 

-;;; INTERVAL-SQR
-;;;

 ;;; Compute the square of an interval.
 (defun interval-sqr (x)
   (declare (type interval x))
 ;;; Compute the square of an interval.
 (defun interval-sqr (x)
   (declare (type interval x))

-  (interval-func #'(lambda (x) (* x x))
+  (interval-func (lambda (x) (* x x))

                 (interval-abs x)))
                 (interval-abs x)))

-)) ; end PROGN's

 \f
 \f

-;;;; numeric derive-type methods
+;;;; numeric DERIVE-TYPE methods
+
+;;; a utility for defining derive-type methods of integer operations. If
+;;; the types of both X and Y are integer types, then we compute a new
+;;; integer type with bounds determined Fun when applied to X and Y.
+;;; Otherwise, we use NUMERIC-CONTAGION.
+(defun derive-integer-type-aux (x y fun)
+  (declare (type function fun))
+  (if (and (numeric-type-p x) (numeric-type-p y)
+          (eq (numeric-type-class x) 'integer)
+          (eq (numeric-type-class y) 'integer)
+          (eq (numeric-type-complexp x) :real)
+          (eq (numeric-type-complexp y) :real))
+      (multiple-value-bind (low high) (funcall fun x y)
+       (make-numeric-type :class 'integer
+                          :complexp :real
+                          :low low
+                          :high high))
+      (numeric-contagion x y)))

 
 

-;;; Utility for defining derive-type methods of integer operations. If the
-;;; types of both X and Y are integer types, then we compute a new integer type
-;;; with bounds determined Fun when applied to X and Y. Otherwise, we use
-;;; Numeric-Contagion.

 (defun derive-integer-type (x y fun)
 (defun derive-integer-type (x y fun)

-  (declare (type continuation x y) (type function fun))
-  (let ((x (continuation-type x))
-       (y (continuation-type y)))
-    (if (and (numeric-type-p x) (numeric-type-p y)
-            (eq (numeric-type-class x) 'integer)
-            (eq (numeric-type-class y) 'integer)
-            (eq (numeric-type-complexp x) :real)
-            (eq (numeric-type-complexp y) :real))
-       (multiple-value-bind (low high) (funcall fun x y)
-         (make-numeric-type :class 'integer
-                            :complexp :real
-                            :low low
-                            :high high))
-       (numeric-contagion x y))))
-
-#!+(or propagate-float-type propagate-fun-type)
-(progn
+  (declare (type lvar x y) (type function fun))
+  (let ((x (lvar-type x))
+       (y (lvar-type y)))
+    (derive-integer-type-aux x y fun)))

 
 

-;; Simple utility to flatten a list
+;;; simple utility to flatten a list

 (defun flatten-list (x)
 (defun flatten-list (x)

-  (labels ((flatten-helper (x r);; 'r' is the stuff to the 'right'.
-            (cond ((null x) r)
-                  ((atom x)
-                   (cons x r))
-                  (t (flatten-helper (car x)
-                                     (flatten-helper (cdr x) r))))))
-    (flatten-helper x nil)))
-
-;;; Take some type of continuation and massage it so that we get a
-;;; list of the constituent types. If ARG is *EMPTY-TYPE*, return NIL
-;;; to indicate failure.
+  (labels ((flatten-and-append (tree list)
+            (cond ((null tree) list)
+                  ((atom tree) (cons tree list))
+                  (t (flatten-and-append
+                       (car tree) (flatten-and-append (cdr tree) list))))))
+    (flatten-and-append x nil)))
+
+;;; Take some type of lvar and massage it so that we get a list of the
+;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
+;;; failure.

 (defun prepare-arg-for-derive-type (arg)
   (flet ((listify (arg)
           (typecase arg
 (defun prepare-arg-for-derive-type (arg)
   (flet ((listify (arg)
           (typecase arg

@@ -857,19 +811,18 @@
          new-args)))))
 
 ;;; Convert from the standard type convention for which -0.0 and 0.0
          new-args)))))
 
 ;;; Convert from the standard type convention for which -0.0 and 0.0

-;;; and equal to an intermediate convention for which they are
+;;; are equal to an intermediate convention for which they are

 ;;; considered different which is more natural for some of the
 ;;; optimisers.
 ;;; considered different which is more natural for some of the
 ;;; optimisers.

-#!-negative-zero-is-not-zero

 (defun convert-numeric-type (type)
   (declare (type numeric-type type))
   ;;; Only convert real float interval delimiters types.
   (if (eq (numeric-type-complexp type) :real)
       (let* ((lo (numeric-type-low type))
 (defun convert-numeric-type (type)
   (declare (type numeric-type type))
   ;;; Only convert real float interval delimiters types.
   (if (eq (numeric-type-complexp type) :real)
       (let* ((lo (numeric-type-low type))

-            (lo-val (bound-value lo))
+            (lo-val (type-bound-number lo))

             (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
             (hi (numeric-type-high type))
             (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
             (hi (numeric-type-high type))

-            (hi-val (bound-value hi))
+            (hi-val (type-bound-number hi))

             (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
        (if (or lo-float-zero-p hi-float-zero-p)
            (make-numeric-type
             (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
        (if (or lo-float-zero-p hi-float-zero-p)
            (make-numeric-type

@@ -879,11 +832,11 @@
             :low (if lo-float-zero-p
                      (if (consp lo)
                          (list (float 0.0 lo-val))
             :low (if lo-float-zero-p
                      (if (consp lo)
                          (list (float 0.0 lo-val))

-                         (float -0.0 lo-val))
+                         (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))

                      lo)
             :high (if hi-float-zero-p
                       (if (consp hi)
                      lo)
             :high (if hi-float-zero-p
                       (if (consp hi)

-                          (list (float -0.0 hi-val))
+                          (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))

                           (float 0.0 hi-val))
                       hi))
            type))
                           (float 0.0 hi-val))
                       hi))
            type))

@@ -893,18 +846,17 @@
 ;;; Convert back from the intermediate convention for which -0.0 and
 ;;; 0.0 are considered different to the standard type convention for
 ;;; which and equal.
 ;;; Convert back from the intermediate convention for which -0.0 and
 ;;; 0.0 are considered different to the standard type convention for
 ;;; which and equal.

-#!-negative-zero-is-not-zero

 (defun convert-back-numeric-type (type)
   (declare (type numeric-type type))
   ;;; Only convert real float interval delimiters types.
   (if (eq (numeric-type-complexp type) :real)
       (let* ((lo (numeric-type-low type))
 (defun convert-back-numeric-type (type)
   (declare (type numeric-type type))
   ;;; Only convert real float interval delimiters types.
   (if (eq (numeric-type-complexp type) :real)
       (let* ((lo (numeric-type-low type))

-            (lo-val (bound-value lo))
+            (lo-val (type-bound-number lo))

             (lo-float-zero-p
              (and lo (floatp lo-val) (= lo-val 0.0)
                   (float-sign lo-val)))
             (hi (numeric-type-high type))
             (lo-float-zero-p
              (and lo (floatp lo-val) (= lo-val 0.0)
                   (float-sign lo-val)))
             (hi (numeric-type-high type))

-            (hi-val (bound-value hi))
+            (hi-val (type-bound-number hi))

             (hi-float-zero-p
              (and hi (floatp hi-val) (= hi-val 0.0)
                   (float-sign hi-val))))
             (hi-float-zero-p
              (and hi (floatp hi-val) (= hi-val 0.0)
                   (float-sign hi-val))))

@@ -912,8 +864,8 @@
          ;; (float +0.0 +0.0) => (member 0.0)
          ;; (float -0.0 -0.0) => (member -0.0)
          ((and lo-float-zero-p hi-float-zero-p)
          ;; (float +0.0 +0.0) => (member 0.0)
          ;; (float -0.0 -0.0) => (member -0.0)
          ((and lo-float-zero-p hi-float-zero-p)

-          ;; Shouldn't have exclusive bounds here.
-          (assert (and (not (consp lo)) (not (consp hi))))
+          ;; shouldn't have exclusive bounds here..
+          (aver (and (not (consp lo)) (not (consp hi))))

           (if (= lo-float-zero-p hi-float-zero-p)
               ;; (float +0.0 +0.0) => (member 0.0)
               ;; (float -0.0 -0.0) => (member -0.0)
           (if (= lo-float-zero-p hi-float-zero-p)
               ;; (float +0.0 +0.0) => (member 0.0)
               ;; (float -0.0 -0.0) => (member -0.0)

@@ -977,11 +929,10 @@
                                       :high (list (float 0.0 hi-val)))))))
          (t
           type)))
                                       :high (list (float 0.0 hi-val)))))))
          (t
           type)))

-      ;; Not real float.
+      ;; not real float

       type))
 
 ;;; Convert back a possible list of numeric types.
       type))
 
 ;;; Convert back a possible list of numeric types.

-#!-negative-zero-is-not-zero

 (defun convert-back-numeric-type-list (type-list)
   (typecase type-list
     (list
 (defun convert-back-numeric-type-list (type-list)
   (typecase type-list
     (list

@@ -1001,13 +952,17 @@
     (t
      type-list)))
 
     (t
      type-list)))
 

-;;; Make-Canonical-Union-Type
-;;;
+;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
+;;; belong in the kernel's type logic, invoked always, instead of in
+;;; the compiler, invoked only during some type optimizations. (In
+;;; fact, as of 0.pre8.100 or so they probably are, under
+;;; MAKE-MEMBER-TYPE, so probably this code can be deleted)
+

 ;;; Take a list of types and return a canonical type specifier,
 ;;; Take a list of types and return a canonical type specifier,

-;;; combining any members types together. If both positive and
-;;; negative members types are present they are converted to a float
-;;; type. X This would be far simpler if the type-union methods could
-;;; handle member/number unions.
+;;; combining any MEMBER types together. If both positive and negative
+;;; MEMBER types are present they are converted to a float type.
+;;; XXX This would be far simpler if the type-union methods could handle
+;;; member/number unions.

 (defun make-canonical-union-type (type-list)
   (let ((members '())
        (misc-types '()))
 (defun make-canonical-union-type (type-list)
   (let ((members '())
        (misc-types '()))

@@ -1016,101 +971,71 @@
          (setf members (union members (member-type-members type)))
          (push type misc-types)))
     #!+long-float
          (setf members (union members (member-type-members type)))
          (push type misc-types)))
     #!+long-float

-    (when (null (set-difference '(-0l0 0l0) members))
-      #!-negative-zero-is-not-zero
-      (push (specifier-type '(long-float 0l0 0l0)) misc-types)
-      #!+negative-zero-is-not-zero
-      (push (specifier-type '(long-float -0l0 0l0)) misc-types)
-      (setf members (set-difference members '(-0l0 0l0))))
-    (when (null (set-difference '(-0d0 0d0) members))
-      #!-negative-zero-is-not-zero
-      (push (specifier-type '(double-float 0d0 0d0)) misc-types)
-      #!+negative-zero-is-not-zero
-      (push (specifier-type '(double-float -0d0 0d0)) misc-types)
-      (setf members (set-difference members '(-0d0 0d0))))
-    (when (null (set-difference '(-0f0 0f0) members))
-      #!-negative-zero-is-not-zero
-      (push (specifier-type '(single-float 0f0 0f0)) misc-types)
-      #!+negative-zero-is-not-zero
-      (push (specifier-type '(single-float -0f0 0f0)) misc-types)
-      (setf members (set-difference members '(-0f0 0f0))))
-    (cond ((null members)
-          (let ((res (first misc-types)))
-            (dolist (type (rest misc-types))
-              (setq res (type-union res type)))
-            res))
-         ((null misc-types)
-          (make-member-type :members members))
-         (t
-          (let ((res (first misc-types)))
-            (dolist (type (rest misc-types))
-              (setq res (type-union res type)))
-            (dolist (type members)
-              (setq res (type-union
-                         res (make-member-type :members (list type)))))
-            res)))))
-
-;;; Convert-Member-Type
-;;;
+    (when (null (set-difference `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0) members))
+      (push (specifier-type '(long-float 0.0l0 0.0l0)) misc-types)
+      (setf members (set-difference members `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0))))
+    (when (null (set-difference `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0) members))
+      (push (specifier-type '(double-float 0.0d0 0.0d0)) misc-types)
+      (setf members (set-difference members `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0))))
+    (when (null (set-difference `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0) members))
+      (push (specifier-type '(single-float 0.0f0 0.0f0)) misc-types)
+      (setf members (set-difference members `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0))))
+    (if members
+       (apply #'type-union (make-member-type :members members) misc-types)
+       (apply #'type-union misc-types))))
+

 ;;; Convert a member type with a single member to a numeric type.
 (defun convert-member-type (arg)
   (let* ((members (member-type-members arg))
         (member (first members))
         (member-type (type-of member)))
 ;;; Convert a member type with a single member to a numeric type.
 (defun convert-member-type (arg)
   (let* ((members (member-type-members arg))
         (member (first members))
         (member-type (type-of member)))

-    (assert (not (rest members)))
-    (specifier-type `(,(if (subtypep member-type 'integer)
-                          'integer
-                          member-type)
-                     ,member ,member))))
+    (aver (not (rest members)))
+    (specifier-type (cond ((typep member 'integer)
+                           `(integer ,member ,member))
+                          ((memq member-type '(short-float single-float
+                                               double-float long-float))
+                           `(,member-type ,member ,member))
+                          (t
+                           member-type)))))

 
 

-;;; ONE-ARG-DERIVE-TYPE
-;;;

 ;;; This is used in defoptimizers for computing the resulting type of
 ;;; a function.
 ;;;
 ;;; This is used in defoptimizers for computing the resulting type of
 ;;; a function.
 ;;;

-;;; Given the continuation ARG, derive the resulting type using the
-;;; DERIVE-FCN. DERIVE-FCN takes exactly one argument which is some
-;;; "atomic" continuation type like numeric-type or member-type
-;;; (containing just one element). It should return the resulting
-;;; type, which can be a list of types.
+;;; Given the lvar ARG, derive the resulting type using the
+;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
+;;; "atomic" lvar type like numeric-type or member-type (containing
+;;; just one element). It should return the resulting type, which can
+;;; be a list of types.

 ;;;
 ;;;

-;;; For the case of member types, if a member-fcn is given it is
+;;; For the case of member types, if a MEMBER-FUN is given it is

 ;;; called to compute the result otherwise the member type is first
 ;;; called to compute the result otherwise the member type is first

-;;; converted to a numeric type and the derive-fcn is call.
-(defun one-arg-derive-type (arg derive-fcn member-fcn
+;;; converted to a numeric type and the DERIVE-FUN is called.
+(defun one-arg-derive-type (arg derive-fun member-fun

                                &optional (convert-type t))
                                &optional (convert-type t))

-  (declare (type function derive-fcn)
-          (type (or null function) member-fcn)
-          #!+negative-zero-is-not-zero (ignore convert-type))
-  (let ((arg-list (prepare-arg-for-derive-type (continuation-type arg))))
+  (declare (type function derive-fun)
+          (type (or null function) member-fun))
+  (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))

     (when arg-list
       (flet ((deriver (x)
               (typecase x
                 (member-type
     (when arg-list
       (flet ((deriver (x)
               (typecase x
                 (member-type

-                 (if member-fcn
+                 (if member-fun

                      (with-float-traps-masked
                          (:underflow :overflow :divide-by-zero)
                      (with-float-traps-masked
                          (:underflow :overflow :divide-by-zero)

-                       (make-member-type
-                        :members (list
-                                  (funcall member-fcn
-                                           (first (member-type-members x))))))
+                       (specifier-type
+                        `(eql ,(funcall member-fun
+                                        (first (member-type-members x))))))

                      ;; Otherwise convert to a numeric type.
                      (let ((result-type-list
                      ;; Otherwise convert to a numeric type.
                      (let ((result-type-list

-                            (funcall derive-fcn (convert-member-type x))))
-                       #!-negative-zero-is-not-zero
+                            (funcall derive-fun (convert-member-type x))))

                        (if convert-type
                            (convert-back-numeric-type-list result-type-list)
                        (if convert-type
                            (convert-back-numeric-type-list result-type-list)

-                           result-type-list)
-                       #!+negative-zero-is-not-zero
-                       result-type-list)))
+                           result-type-list))))

                 (numeric-type
                 (numeric-type

-                 #!-negative-zero-is-not-zero

                  (if convert-type
                      (convert-back-numeric-type-list
                  (if convert-type
                      (convert-back-numeric-type-list

-                      (funcall derive-fcn (convert-numeric-type x)))
-                     (funcall derive-fcn x))
-                 #!+negative-zero-is-not-zero
-                 (funcall derive-fcn x))
+                      (funcall derive-fun (convert-numeric-type x)))
+                     (funcall derive-fun x)))

                 (t
                  *universal-type*))))
        ;; Run down the list of args and derive the type of each one,
                 (t
                  *universal-type*))))
        ;; Run down the list of args and derive the type of each one,

@@ -1125,86 +1050,62 @@
              (make-canonical-union-type results)
              (first results)))))))
 
              (make-canonical-union-type results)
              (first results)))))))
 

-;;; TWO-ARG-DERIVE-TYPE
-;;;

 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes

-;;; two arguments. DERIVE-FCN takes 3 args in this case: the two
+;;; two arguments. DERIVE-FUN takes 3 args in this case: the two

 ;;; original args and a third which is T to indicate if the two args
 ;;; original args and a third which is T to indicate if the two args

-;;; really represent the same continuation. This is useful for
-;;; deriving the type of things like (* x x), which should always be
-;;; positive. If we didn't do this, we wouldn't be able to tell.
-(defun two-arg-derive-type (arg1 arg2 derive-fcn fcn
+;;; really represent the same lvar. This is useful for deriving the
+;;; type of things like (* x x), which should always be positive. If
+;;; we didn't do this, we wouldn't be able to tell.
+(defun two-arg-derive-type (arg1 arg2 derive-fun fun

                                 &optional (convert-type t))
                                 &optional (convert-type t))

-  #!+negative-zero-is-not-zero
-  (declare (ignore convert-type))
-  (flet (#!-negative-zero-is-not-zero
-        (deriver (x y same-arg)
+  (declare (type function derive-fun fun))
+  (flet ((deriver (x y same-arg)

           (cond ((and (member-type-p x) (member-type-p y))
                  (let* ((x (first (member-type-members x)))
                         (y (first (member-type-members y)))
           (cond ((and (member-type-p x) (member-type-p y))
                  (let* ((x (first (member-type-members x)))
                         (y (first (member-type-members y)))

-                        (result (with-float-traps-masked
-                                    (:underflow :overflow :divide-by-zero
-                                     :invalid)
-                                  (funcall fcn x y))))
-                   (cond ((null result))
+                        (result (ignore-errors
+                                   (with-float-traps-masked
+                                       (:underflow :overflow :divide-by-zero
+                                                   :invalid)
+                                     (funcall fun x y)))))
+                   (cond ((null result) *empty-type*)

                          ((and (floatp result) (float-nan-p result))
                          ((and (floatp result) (float-nan-p result))

-                          (make-numeric-type
-                           :class 'float
-                           :format (type-of result)
-                           :complexp :real))
+                          (make-numeric-type :class 'float
+                                             :format (type-of result)
+                                             :complexp :real))

                          (t
                          (t

-                          (make-member-type :members (list result))))))
+                          (specifier-type `(eql ,result))))))

                 ((and (member-type-p x) (numeric-type-p y))
                  (let* ((x (convert-member-type x))
                         (y (if convert-type (convert-numeric-type y) y))
                 ((and (member-type-p x) (numeric-type-p y))
                  (let* ((x (convert-member-type x))
                         (y (if convert-type (convert-numeric-type y) y))

-                        (result (funcall derive-fcn x y same-arg)))
+                        (result (funcall derive-fun x y same-arg)))

                    (if convert-type
                        (convert-back-numeric-type-list result)
                        result)))
                 ((and (numeric-type-p x) (member-type-p y))
                  (let* ((x (if convert-type (convert-numeric-type x) x))
                         (y (convert-member-type y))
                    (if convert-type
                        (convert-back-numeric-type-list result)
                        result)))
                 ((and (numeric-type-p x) (member-type-p y))
                  (let* ((x (if convert-type (convert-numeric-type x) x))
                         (y (convert-member-type y))

-                        (result (funcall derive-fcn x y same-arg)))
+                        (result (funcall derive-fun x y same-arg)))

                    (if convert-type
                        (convert-back-numeric-type-list result)
                        result)))
                 ((and (numeric-type-p x) (numeric-type-p y))
                  (let* ((x (if convert-type (convert-numeric-type x) x))
                         (y (if convert-type (convert-numeric-type y) y))
                    (if convert-type
                        (convert-back-numeric-type-list result)
                        result)))
                 ((and (numeric-type-p x) (numeric-type-p y))
                  (let* ((x (if convert-type (convert-numeric-type x) x))
                         (y (if convert-type (convert-numeric-type y) y))

-                        (result (funcall derive-fcn x y same-arg)))
+                        (result (funcall derive-fun x y same-arg)))

                    (if convert-type
                        (convert-back-numeric-type-list result)
                        result)))
                 (t
                    (if convert-type
                        (convert-back-numeric-type-list result)
                        result)))
                 (t

-                 *universal-type*)))
-        #!+negative-zero-is-not-zero
-        (deriver (x y same-arg)
-          (cond ((and (member-type-p x) (member-type-p y))
-                 (let* ((x (first (member-type-members x)))
-                        (y (first (member-type-members y)))
-                        (result (with-float-traps-masked
-                                    (:underflow :overflow :divide-by-zero)
-                                  (funcall fcn x y))))
-                   (if result
-                       (make-member-type :members (list result)))))
-                ((and (member-type-p x) (numeric-type-p y))
-                 (let ((x (convert-member-type x)))
-                   (funcall derive-fcn x y same-arg)))
-                ((and (numeric-type-p x) (member-type-p y))
-                 (let ((y (convert-member-type y)))
-                   (funcall derive-fcn x y same-arg)))
-                ((and (numeric-type-p x) (numeric-type-p y))
-                 (funcall derive-fcn x y same-arg))
-                (t

                  *universal-type*))))
     (let ((same-arg (same-leaf-ref-p arg1 arg2))
                  *universal-type*))))
     (let ((same-arg (same-leaf-ref-p arg1 arg2))

-         (a1 (prepare-arg-for-derive-type (continuation-type arg1)))
-         (a2 (prepare-arg-for-derive-type (continuation-type arg2))))
+         (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
+         (a2 (prepare-arg-for-derive-type (lvar-type arg2))))

       (when (and a1 a2)
        (let ((results nil))
          (if same-arg
       (when (and a1 a2)
        (let ((results nil))
          (if same-arg

-             ;; Since the args are the same continuation, just run
-             ;; down the lists.
+             ;; Since the args are the same LVARs, just run down the
+             ;; lists.

              (dolist (x a1)
                (let ((result (deriver x x same-arg)))
                  (if (listp result)
              (dolist (x a1)
                (let ((result (deriver x x same-arg)))
                  (if (listp result)

@@ -1221,10 +1122,8 @@
          (if (rest results)
              (make-canonical-union-type results)
              (first results)))))))
          (if (rest results)
              (make-canonical-union-type results)
              (first results)))))))

-
-) ; PROGN

 \f
 \f

-#!-propagate-float-type
+#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (progn
 (defoptimizer (+ derive-type) ((x y))
   (derive-integer-type
 (progn
 (defoptimizer (+ derive-type) ((x y))
   (derive-integer-type

@@ -1271,11 +1170,11 @@
                            nil))))))))
 
 (defoptimizer (/ derive-type) ((x y))
                            nil))))))))
 
 (defoptimizer (/ derive-type) ((x y))

-  (numeric-contagion (continuation-type x) (continuation-type y)))
+  (numeric-contagion (lvar-type x) (lvar-type y)))

 
 ) ; PROGN
 
 
 ) ; PROGN
 

-#!+propagate-float-type
+#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (progn
 (defun +-derive-type-aux (x y same-arg)
   (if (and (numeric-type-real-p x)
 (progn
 (defun +-derive-type-aux (x y same-arg)
   (if (and (numeric-type-real-p x)

@@ -1298,13 +1197,13 @@
        (make-numeric-type
         :class (if (and (eq (numeric-type-class x) 'integer)
                         (eq (numeric-type-class y) 'integer))
        (make-numeric-type
         :class (if (and (eq (numeric-type-class x) 'integer)
                         (eq (numeric-type-class y) 'integer))

-                   ;; The sum of integers is always an integer
+                   ;; The sum of integers is always an integer.

                    'integer
                    (numeric-type-class result-type))
         :format (numeric-type-format result-type)
         :low (interval-low result)
         :high (interval-high result)))
                    'integer
                    (numeric-type-class result-type))
         :format (numeric-type-format result-type)
         :low (interval-low result)
         :high (interval-high result)))

-      ;; General contagion
+      ;; general contagion

       (numeric-contagion x y)))
 
 (defoptimizer (+ derive-type) ((x y))
       (numeric-contagion x y)))
 
 (defoptimizer (+ derive-type) ((x y))

@@ -1314,7 +1213,7 @@
   (if (and (numeric-type-real-p x)
           (numeric-type-real-p y))
       (let ((result
   (if (and (numeric-type-real-p x)
           (numeric-type-real-p y))
       (let ((result

-            ;; (- x x) is always 0.
+            ;; (- X X) is always 0.

             (if same-arg
                 (make-interval :low 0 :high 0)
                 (interval-sub (numeric-type->interval x)
             (if same-arg
                 (make-interval :low 0 :high 0)
                 (interval-sub (numeric-type->interval x)

@@ -1331,13 +1230,13 @@
        (make-numeric-type
         :class (if (and (eq (numeric-type-class x) 'integer)
                         (eq (numeric-type-class y) 'integer))
        (make-numeric-type
         :class (if (and (eq (numeric-type-class x) 'integer)
                         (eq (numeric-type-class y) 'integer))

-                   ;; The difference of integers is always an integer
+                   ;; The difference of integers is always an integer.

                    'integer
                    (numeric-type-class result-type))
         :format (numeric-type-format result-type)
         :low (interval-low result)
         :high (interval-high result)))
                    'integer
                    (numeric-type-class result-type))
         :format (numeric-type-format result-type)
         :low (interval-low result)
         :high (interval-high result)))

-      ;; General contagion
+      ;; general contagion

       (numeric-contagion x y)))
 
 (defoptimizer (- derive-type) ((x y))
       (numeric-contagion x y)))
 
 (defoptimizer (- derive-type) ((x y))

@@ -1347,8 +1246,7 @@
   (if (and (numeric-type-real-p x)
           (numeric-type-real-p y))
       (let ((result
   (if (and (numeric-type-real-p x)
           (numeric-type-real-p y))
       (let ((result

-            ;; (* x x) is always positive, so take care to do it
-            ;; right.
+            ;; (* X X) is always positive, so take care to do it right.

             (if same-arg
                 (interval-sqr (numeric-type->interval x))
                 (interval-mul (numeric-type->interval x)
             (if same-arg
                 (interval-sqr (numeric-type->interval x))
                 (interval-mul (numeric-type->interval x)

@@ -1365,7 +1263,7 @@
        (make-numeric-type
         :class (if (and (eq (numeric-type-class x) 'integer)
                         (eq (numeric-type-class y) 'integer))
        (make-numeric-type
         :class (if (and (eq (numeric-type-class x) 'integer)
                         (eq (numeric-type-class y) 'integer))

-                   ;; The product of integers is always an integer
+                   ;; The product of integers is always an integer.

                    'integer
                    (numeric-type-class result-type))
         :format (numeric-type-format result-type)
                    'integer
                    (numeric-type-class result-type))
         :format (numeric-type-format result-type)

@@ -1380,7 +1278,7 @@
   (if (and (numeric-type-real-p x)
           (numeric-type-real-p y))
       (let ((result
   (if (and (numeric-type-real-p x)
           (numeric-type-real-p y))
       (let ((result

-            ;; (/ x x) is always 1, except if x can contain 0. In
+            ;; (/ X X) is always 1, except if X can contain 0. In

             ;; that case, we shouldn't optimize the division away
             ;; because we want 0/0 to signal an error.
             (if (and same-arg
             ;; that case, we shouldn't optimize the division away
             ;; because we want 0/0 to signal an error.
             (if (and same-arg

@@ -1409,68 +1307,53 @@
 
 ) ; PROGN
 
 
 ) ; PROGN
 

-;;; KLUDGE: All this ASH optimization is suppressed under CMU CL
-;;; because as of version 2.4.6 for Debian, CMU CL blows up on (ASH
-;;; 1000000000 -100000000000) (i.e. ASH of two bignums yielding zero)
-;;; and it's hard to avoid that calculation in here.
-#-(and cmu sb-xc-host)
-(progn
-#!-propagate-fun-type
-(defoptimizer (ash derive-type) ((n shift))
-  (or (let ((n-type (continuation-type n)))
-       (when (numeric-type-p n-type)
-         (let ((n-low (numeric-type-low n-type))
-               (n-high (numeric-type-high n-type)))
-           (if (constant-continuation-p shift)
-               (let ((shift (continuation-value shift)))
-                 (make-numeric-type :class 'integer
-                                    :complexp :real
-                                    :low (when n-low (ash n-low shift))
-                                    :high (when n-high (ash n-high shift))))
-               (let ((s-type (continuation-type shift)))
-                 (when (numeric-type-p s-type)
-                   (let ((s-low (numeric-type-low s-type))
-                         (s-high (numeric-type-high s-type)))
-                     (if (and s-low s-high (<= s-low 64) (<= s-high 64))
-                         (make-numeric-type :class 'integer
-                                            :complexp :real
-                                            :low (when n-low
-                                                   (min (ash n-low s-high)
-                                                        (ash n-low s-low)))
-                                            :high (when n-high
-                                                    (max (ash n-high s-high)
-                                                         (ash n-high s-low))))
-                         (make-numeric-type :class 'integer
-                                            :complexp :real)))))))))
-      *universal-type*))
-#!+propagate-fun-type

 (defun ash-derive-type-aux (n-type shift same-arg)
   (declare (ignore same-arg))
 (defun ash-derive-type-aux (n-type shift same-arg)
   (declare (ignore same-arg))

-  (or (and (csubtypep n-type (specifier-type 'integer))
-          (csubtypep shift (specifier-type 'integer))
-          (let ((n-low (numeric-type-low n-type))
-                (n-high (numeric-type-high n-type))
-                (s-low (numeric-type-low shift))
-                (s-high (numeric-type-high shift)))
-            ;; KLUDGE: The bare 64's here should be related to
-            ;; symbolic machine word size values somehow.
-            (if (and s-low s-high (<= s-low 64) (<= s-high 64))
-                (make-numeric-type :class 'integer :complexp :real
-                                   :low (when n-low
-                                          (min (ash n-low s-high)
-                                               (ash n-low s-low)))
-                                   :high (when n-high
-                                           (max (ash n-high s-high)
-                                                (ash n-high s-low))))
-                (make-numeric-type :class 'integer
-                                   :complexp :real))))
-      *universal-type*))
-#!+propagate-fun-type
+  ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
+  ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
+  ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
+  ;; two bignums yielding zero) and it's hard to avoid that
+  ;; calculation in here.
+  #+(and cmu sb-xc-host)
+  (when (and (or (typep (numeric-type-low n-type) 'bignum)
+                (typep (numeric-type-high n-type) 'bignum))
+            (or (typep (numeric-type-low shift) 'bignum)
+                (typep (numeric-type-high shift) 'bignum)))
+    (return-from ash-derive-type-aux *universal-type*))
+  (flet ((ash-outer (n s)
+          (when (and (fixnump s)
+                     (<= s 64)
+                     (> s sb!xc:most-negative-fixnum))
+            (ash n s)))
+         ;; KLUDGE: The bare 64's here should be related to
+         ;; symbolic machine word size values somehow.
+
+        (ash-inner (n s)
+          (if (and (fixnump s)
+                   (> s sb!xc:most-negative-fixnum))
+             (ash n (min s 64))
+             (if (minusp n) -1 0))))
+    (or (and (csubtypep n-type (specifier-type 'integer))
+            (csubtypep shift (specifier-type 'integer))
+            (let ((n-low (numeric-type-low n-type))
+                  (n-high (numeric-type-high n-type))
+                  (s-low (numeric-type-low shift))
+                  (s-high (numeric-type-high shift)))
+              (make-numeric-type :class 'integer  :complexp :real
+                                 :low (when n-low
+                                        (if (minusp n-low)
+                                           (ash-outer n-low s-high)
+                                           (ash-inner n-low s-low)))
+                                 :high (when n-high
+                                         (if (minusp n-high)
+                                            (ash-inner n-high s-low)
+                                            (ash-outer n-high s-high))))))
+       *universal-type*)))
+

 (defoptimizer (ash derive-type) ((n shift))
   (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
 (defoptimizer (ash derive-type) ((n shift))
   (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))

-) ; PROGN

 
 

-#!-propagate-float-type
+#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (macrolet ((frob (fun)
             `#'(lambda (type type2)
                  (declare (ignore type2))
 (macrolet ((frob (fun)
             `#'(lambda (type type2)
                  (declare (ignore type2))

@@ -1479,42 +1362,39 @@
                    (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
 
   (defoptimizer (%negate derive-type) ((num))
                    (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
 
   (defoptimizer (%negate derive-type) ((num))

-    (derive-integer-type num num (frob -)))
+    (derive-integer-type num num (frob -))))

 
 

-  (defoptimizer (lognot derive-type) ((int))
-    (derive-integer-type int int (frob lognot))))
+(defun lognot-derive-type-aux (int)
+  (derive-integer-type-aux int int
+                          (lambda (type type2)
+                            (declare (ignore type2))
+                            (let ((lo (numeric-type-low type))
+                                  (hi (numeric-type-high type)))
+                              (values (if hi (lognot hi) nil)
+                                      (if lo (lognot lo) nil)
+                                      (numeric-type-class type)
+                                      (numeric-type-format type))))))

 
 

-#!+propagate-float-type

 (defoptimizer (lognot derive-type) ((int))
 (defoptimizer (lognot derive-type) ((int))

-  (derive-integer-type int int
-                      #'(lambda (type type2)
-                          (declare (ignore type2))
-                          (let ((lo (numeric-type-low type))
-                                (hi (numeric-type-high type)))
-                            (values (if hi (lognot hi) nil)
-                                    (if lo (lognot lo) nil)
-                                    (numeric-type-class type)
-                                    (numeric-type-format type))))))
-
-#!+propagate-float-type
+  (lognot-derive-type-aux (lvar-type int)))
+
+#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (defoptimizer (%negate derive-type) ((num))
   (flet ((negate-bound (b)
 (defoptimizer (%negate derive-type) ((num))
   (flet ((negate-bound (b)

-          (set-bound (- (bound-value b)) (consp b))))
+           (and b
+               (set-bound (- (type-bound-number b))
+                          (consp b)))))

     (one-arg-derive-type num
     (one-arg-derive-type num

-                        #'(lambda (type)
-                            (let ((lo (numeric-type-low type))
-                                  (hi (numeric-type-high type))
-                                  (result (copy-numeric-type type)))
-                              (setf (numeric-type-low result)
-                                     (if hi (negate-bound hi) nil))
-                              (setf (numeric-type-high result)
-                                    (if lo (negate-bound lo) nil))
-                              result))
+                        (lambda (type)
+                          (modified-numeric-type
+                           type
+                           :low (negate-bound (numeric-type-high type))
+                           :high (negate-bound (numeric-type-low type))))

                         #'-)))
 
                         #'-)))
 

-#!-propagate-float-type
+#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (defoptimizer (abs derive-type) ((num))
 (defoptimizer (abs derive-type) ((num))

-  (let ((type (continuation-type num)))
+  (let ((type (lvar-type num)))

     (if (and (numeric-type-p type)
             (eq (numeric-type-class type) 'integer)
             (eq (numeric-type-complexp type) :real))
     (if (and (numeric-type-p type)
             (eq (numeric-type-class type) 'integer)
             (eq (numeric-type-complexp type) :real))

@@ -1532,7 +1412,7 @@
                                       nil)))
        (numeric-contagion type type))))
 
                                       nil)))
        (numeric-contagion type type))))
 

-#!+propagate-float-type
+#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (defun abs-derive-type-aux (type)
   (cond ((eq (numeric-type-complexp type) :complex)
         ;; The absolute value of a complex number is always a
 (defun abs-derive-type-aux (type)
   (cond ((eq (numeric-type-complexp type) :complex)
         ;; The absolute value of a complex number is always a

@@ -1561,14 +1441,14 @@
            :high (coerce-numeric-bound
                   (interval-high abs-bnd) bound-type))))))
 
            :high (coerce-numeric-bound
                   (interval-high abs-bnd) bound-type))))))
 

-#!+propagate-float-type
+#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (defoptimizer (abs derive-type) ((num))
   (one-arg-derive-type num #'abs-derive-type-aux #'abs))
 
 (defoptimizer (abs derive-type) ((num))
   (one-arg-derive-type num #'abs-derive-type-aux #'abs))
 

-#!-propagate-float-type
+#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (defoptimizer (truncate derive-type) ((number divisor))
 (defoptimizer (truncate derive-type) ((number divisor))

-  (let ((number-type (continuation-type number))
-       (divisor-type (continuation-type divisor))
+  (let ((number-type (lvar-type number))
+       (divisor-type (lvar-type divisor))

        (integer-type (specifier-type 'integer)))
     (if (and (numeric-type-p number-type)
             (csubtypep number-type integer-type)
        (integer-type (specifier-type 'integer)))
     (if (and (numeric-type-p number-type)
             (csubtypep number-type integer-type)

@@ -1585,9 +1465,7 @@
                                              divisor-low divisor-high))))
        *universal-type*)))
 
                                              divisor-low divisor-high))))
        *universal-type*)))
 

-#-sb-xc-host ;(CROSS-FLOAT-INFINITY-KLUDGE, see base-target-features.lisp-expr)
-(progn
-#!+propagate-float-type
+#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (progn
 
 (defun rem-result-type (number-type divisor-type)
 (progn
 
 (defun rem-result-type (number-type divisor-type)

@@ -1740,11 +1618,11 @@
 
 ;;; Define optimizers for FLOOR and CEILING.
 (macrolet
 
 ;;; Define optimizers for FLOOR and CEILING.
 (macrolet

-    ((frob-opt (name q-name r-name)
+    ((def (name q-name r-name)

        (let ((q-aux (symbolicate q-name "-AUX"))
             (r-aux (symbolicate r-name "-AUX")))
         `(progn
        (let ((q-aux (symbolicate q-name "-AUX"))
             (r-aux (symbolicate r-name "-AUX")))
         `(progn

-          ;; Compute type of quotient (first) result
+          ;; Compute type of quotient (first) result.

           (defun ,q-aux (number-type divisor-type)
             (let* ((number-interval
                     (numeric-type->interval number-type))
           (defun ,q-aux (number-type divisor-type)
             (let* ((number-interval
                     (numeric-type->interval number-type))

@@ -1754,7 +1632,7 @@
                                                 divisor-interval))))
               (specifier-type `(integer ,(or (interval-low quot) '*)
                                         ,(or (interval-high quot) '*)))))
                                                 divisor-interval))))
               (specifier-type `(integer ,(or (interval-low quot) '*)
                                         ,(or (interval-high quot) '*)))))

-          ;; Compute type of remainder
+          ;; Compute type of remainder.

           (defun ,r-aux (number-type divisor-type)
             (let* ((divisor-interval
                     (numeric-type->interval divisor-type))
           (defun ,r-aux (number-type divisor-type)
             (let* ((divisor-interval
                     (numeric-type->interval divisor-type))

@@ -1774,62 +1652,16 @@
                      (values nil nil)))
                 (when (member result-type '(float single-float double-float
                                             #!+long-float long-float))
                      (values nil nil)))
                 (when (member result-type '(float single-float double-float
                                             #!+long-float long-float))

-                  ;; Make sure the limits on the interval have
+                  ;; Make sure that the limits on the interval have

                   ;; the right type.
                   ;; the right type.

-                  (setf rem (interval-func #'(lambda (x)
-                                               (coerce x result-type))
+                  (setf rem (interval-func (lambda (x)
+                                             (coerce x result-type))

                                            rem)))
                 (make-numeric-type :class class
                                    :format format
                                    :low (interval-low rem)
                                    :high (interval-high rem)))))
                                            rem)))
                 (make-numeric-type :class class
                                    :format format
                                    :low (interval-low rem)
                                    :high (interval-high rem)))))

-          ;; The optimizer itself
-          (defoptimizer (,name derive-type) ((number divisor))
-            (flet ((derive-q (n d same-arg)
-                     (declare (ignore same-arg))
-                     (if (and (numeric-type-real-p n)
-                              (numeric-type-real-p d))
-                         (,q-aux n d)
-                         *empty-type*))
-                   (derive-r (n d same-arg)
-                     (declare (ignore same-arg))
-                     (if (and (numeric-type-real-p n)
-                              (numeric-type-real-p d))
-                         (,r-aux n d)
-                         *empty-type*)))
-              (let ((quot (two-arg-derive-type
-                           number divisor #'derive-q #',name))
-                    (rem (two-arg-derive-type
-                          number divisor #'derive-r #'mod)))
-                (when (and quot rem)
-                  (make-values-type :required (list quot rem))))))
-          ))))
-
-  ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
-  (frob-opt floor floor-quotient-bound floor-rem-bound)
-  (frob-opt ceiling ceiling-quotient-bound ceiling-rem-bound))
-
-;;; Define optimizers for FFLOOR and FCEILING
-(macrolet
-    ((frob-opt (name q-name r-name)
-       (let ((q-aux (symbolicate "F" q-name "-AUX"))
-            (r-aux (symbolicate r-name "-AUX")))
-        `(progn
-          ;; Compute type of quotient (first) result
-          (defun ,q-aux (number-type divisor-type)
-            (let* ((number-interval
-                    (numeric-type->interval number-type))
-                   (divisor-interval
-                    (numeric-type->interval divisor-type))
-                   (quot (,q-name (interval-div number-interval
-                                                divisor-interval)))
-                   (res-type (numeric-contagion number-type divisor-type)))
-              (make-numeric-type
-               :class (numeric-type-class res-type)
-               :format (numeric-type-format res-type)
-               :low  (interval-low quot)
-               :high (interval-high quot))))
-
+          ;; the optimizer itself

           (defoptimizer (,name derive-type) ((number divisor))
             (flet ((derive-q (n d same-arg)
                      (declare (ignore same-arg))
           (defoptimizer (,name derive-type) ((number divisor))
             (flet ((derive-q (n d same-arg)
                      (declare (ignore same-arg))

@@ -1850,12 +1682,55 @@
                 (when (and quot rem)
                   (make-values-type :required (list quot rem))))))))))
 
                 (when (and quot rem)
                   (make-values-type :required (list quot rem))))))))))
 

-  ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
-  (frob-opt ffloor floor-quotient-bound floor-rem-bound)
-  (frob-opt fceiling ceiling-quotient-bound ceiling-rem-bound))
+  (def floor floor-quotient-bound floor-rem-bound)
+  (def ceiling ceiling-quotient-bound ceiling-rem-bound))

 
 

-;;; Functions to compute the bounds on the quotient and remainder for
-;;; the FLOOR function.
+;;; Define optimizers for FFLOOR and FCEILING
+(macrolet ((def (name q-name r-name)
+            (let ((q-aux (symbolicate "F" q-name "-AUX"))
+                  (r-aux (symbolicate r-name "-AUX")))
+              `(progn
+                 ;; Compute type of quotient (first) result.
+                 (defun ,q-aux (number-type divisor-type)
+                   (let* ((number-interval
+                           (numeric-type->interval number-type))
+                          (divisor-interval
+                           (numeric-type->interval divisor-type))
+                          (quot (,q-name (interval-div number-interval
+                                                       divisor-interval)))
+                          (res-type (numeric-contagion number-type
+                                                       divisor-type)))
+                     (make-numeric-type
+                      :class (numeric-type-class res-type)
+                      :format (numeric-type-format res-type)
+                      :low  (interval-low quot)
+                      :high (interval-high quot))))
+
+                 (defoptimizer (,name derive-type) ((number divisor))
+                   (flet ((derive-q (n d same-arg)
+                            (declare (ignore same-arg))
+                            (if (and (numeric-type-real-p n)
+                                     (numeric-type-real-p d))
+                                (,q-aux n d)
+                                *empty-type*))
+                          (derive-r (n d same-arg)
+                            (declare (ignore same-arg))
+                            (if (and (numeric-type-real-p n)
+                                     (numeric-type-real-p d))
+                                (,r-aux n d)
+                                *empty-type*)))
+                     (let ((quot (two-arg-derive-type
+                                  number divisor #'derive-q #',name))
+                           (rem (two-arg-derive-type
+                                 number divisor #'derive-r #'mod)))
+                       (when (and quot rem)
+                         (make-values-type :required (list quot rem))))))))))
+
+  (def ffloor floor-quotient-bound floor-rem-bound)
+  (def fceiling ceiling-quotient-bound ceiling-rem-bound))
+
+;;; functions to compute the bounds on the quotient and remainder for
+;;; the FLOOR function

 (defun floor-quotient-bound (quot)
   ;; Take the floor of the quotient and then massage it into what we
   ;; need.
 (defun floor-quotient-bound (quot)
   ;; Take the floor of the quotient and then massage it into what we
   ;; need.

@@ -1864,9 +1739,9 @@
     ;; Take the floor of the lower bound. The result is always a
     ;; closed lower bound.
     (setf lo (if lo
     ;; Take the floor of the lower bound. The result is always a
     ;; closed lower bound.
     (setf lo (if lo

-                (floor (bound-value lo))
+                (floor (type-bound-number lo))

                 nil))
                 nil))

-    ;; For the upper bound, we need to be careful
+    ;; For the upper bound, we need to be careful.

     (setf hi
          (cond ((consp hi)
                 ;; An open bound. We need to be careful here because
     (setf hi
          (cond ((consp hi)
                 ;; An open bound. We need to be careful here because

@@ -1887,7 +1762,7 @@
   ;; correct sign for the remainder if we can.
   (case (interval-range-info div)
     (+
   ;; correct sign for the remainder if we can.
   (case (interval-range-info div)
     (+

-     ;; Divisor is always positive.
+     ;; The divisor is always positive.

      (let ((rem (interval-abs div)))
        (setf (interval-low rem) 0)
        (when (and (numberp (interval-high rem))
      (let ((rem (interval-abs div)))
        (setf (interval-low rem) 0)
        (when (and (numberp (interval-high rem))

@@ -1897,7 +1772,7 @@
         (setf (interval-high rem) (list (interval-high rem))))
        rem))
     (-
         (setf (interval-high rem) (list (interval-high rem))))
        rem))
     (-

-     ;; Divisor is always negative
+     ;; The divisor is always negative.

      (let ((rem (interval-neg (interval-abs div))))
        (setf (interval-high rem) 0)
        (when (numberp (interval-low rem))
      (let ((rem (interval-neg (interval-abs div))))
        (setf (interval-high rem) 0)
        (when (numberp (interval-low rem))

@@ -1905,11 +1780,10 @@
         (setf (interval-low rem) (list (interval-low rem))))
        rem))
     (otherwise
         (setf (interval-low rem) (list (interval-low rem))))
        rem))
     (otherwise

-     ;; The divisor can be positive or negative. All bets off.
-     ;; The magnitude of remainder is the maximum value of the
-     ;; divisor.
-     (let ((limit (bound-value (interval-high (interval-abs div)))))
-       ;; The bound never reaches the limit, so make the interval open
+     ;; The divisor can be positive or negative. All bets off. The
+     ;; magnitude of remainder is the maximum value of the divisor.
+     (let ((limit (type-bound-number (interval-high (interval-abs div)))))
+       ;; The bound never reaches the limit, so make the interval open.

        (make-interval :low (if limit
                               (list (- limit))
                               limit)
        (make-interval :low (if limit
                               (list (- limit))
                               limit)

@@ -1957,9 +1831,9 @@
     ;; Take the ceiling of the upper bound. The result is always a
     ;; closed upper bound.
     (setf hi (if hi
     ;; Take the ceiling of the upper bound. The result is always a
     ;; closed upper bound.
     (setf hi (if hi

-                (ceiling (bound-value hi))
+                (ceiling (type-bound-number hi))

                 nil))
                 nil))

-    ;; For the lower bound, we need to be careful
+    ;; For the lower bound, we need to be careful.

     (setf lo
          (cond ((consp lo)
                 ;; An open bound. We need to be careful here because
     (setf lo
          (cond ((consp lo)
                 ;; An open bound. We need to be careful here because

@@ -1978,7 +1852,6 @@
 (defun ceiling-rem-bound (div)
   ;; The remainder depends only on the divisor. Try to get the
   ;; correct sign for the remainder if we can.
 (defun ceiling-rem-bound (div)
   ;; The remainder depends only on the divisor. Try to get the
   ;; correct sign for the remainder if we can.

-

   (case (interval-range-info div)
     (+
      ;; Divisor is always positive. The remainder is negative.
   (case (interval-range-info div)
     (+
      ;; Divisor is always positive. The remainder is negative.

@@ -1999,11 +1872,10 @@
         (setf (interval-high rem) (list (interval-high rem))))
        rem))
     (otherwise
         (setf (interval-high rem) (list (interval-high rem))))
        rem))
     (otherwise

-     ;; The divisor can be positive or negative. All bets off.
-     ;; The magnitude of remainder is the maximum value of the
-     ;; divisor.
-     (let ((limit (bound-value (interval-high (interval-abs div)))))
-       ;; The bound never reaches the limit, so make the interval open
+     ;; The divisor can be positive or negative. All bets off. The
+     ;; magnitude of remainder is the maximum value of the divisor.
+     (let ((limit (type-bound-number (interval-high (interval-abs div)))))
+       ;; The bound never reaches the limit, so make the interval open.

        (make-interval :low (if limit
                               (list (- limit))
                               limit)
        (make-interval :low (if limit
                               (list (- limit))
                               limit)

@@ -2049,10 +1921,10 @@
   ;; it's the union of the two pieces.
   (case (interval-range-info quot)
     (+
   ;; it's the union of the two pieces.
   (case (interval-range-info quot)
     (+

-     ;; Just like floor
+     ;; just like FLOOR

      (floor-quotient-bound quot))
     (-
      (floor-quotient-bound quot))
     (-

-     ;; Just like ceiling
+     ;; just like CEILING

      (ceiling-quotient-bound quot))
     (otherwise
      ;; Split the interval into positive and negative pieces, compute
      (ceiling-quotient-bound quot))
     (otherwise
      ;; Split the interval into positive and negative pieces, compute

@@ -2062,9 +1934,9 @@
                            (floor-quotient-bound pos))))))
 
 (defun truncate-rem-bound (num div)
                            (floor-quotient-bound pos))))))
 
 (defun truncate-rem-bound (num div)

-  ;; This is significantly more complicated than floor or ceiling. We
+  ;; This is significantly more complicated than FLOOR or CEILING. We

   ;; need both the number and the divisor to determine the range. The
   ;; need both the number and the divisor to determine the range. The

-  ;; basic idea is to split the ranges of num and den into positive
+  ;; basic idea is to split the ranges of NUM and DEN into positive

   ;; and negative pieces and deal with each of the four possibilities
   ;; in turn.
   (case (interval-range-info num)
   ;; and negative pieces and deal with each of the four possibilities
   ;; in turn.
   (case (interval-range-info num)

@@ -2092,7 +1964,7 @@
      (destructuring-bind (neg pos) (interval-split 0 num t t)
        (interval-merge-pair (truncate-rem-bound neg div)
                            (truncate-rem-bound pos div))))))
      (destructuring-bind (neg pos) (interval-split 0 num t t)
        (interval-merge-pair (truncate-rem-bound neg div)
                            (truncate-rem-bound pos div))))))

-)) ; end PROGN's
+) ; PROGN

 
 ;;; Derive useful information about the range. Returns three values:
 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
 
 ;;; Derive useful information about the range. Returns three values:
 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.

@@ -2109,9 +1981,9 @@
 
 (defun integer-truncate-derive-type
        (number-low number-high divisor-low divisor-high)
 
 (defun integer-truncate-derive-type
        (number-low number-high divisor-low divisor-high)

-  ;; The result cannot be larger in magnitude than the number, but the sign
-  ;; might change. If we can determine the sign of either the number or
-  ;; the divisor, we can eliminate some of the cases.
+  ;; The result cannot be larger in magnitude than the number, but the
+  ;; sign might change. If we can determine the sign of either the
+  ;; number or the divisor, we can eliminate some of the cases.

   (multiple-value-bind (number-sign number-min number-max)
       (numeric-range-info number-low number-high)
     (multiple-value-bind (divisor-sign divisor-min divisor-max)
   (multiple-value-bind (number-sign number-min number-max)
       (numeric-range-info number-low number-high)
     (multiple-value-bind (divisor-sign divisor-min divisor-max)

@@ -2169,13 +2041,13 @@
             ;; anything about the result.
             `integer)))))
 
             ;; anything about the result.
             `integer)))))
 

-#!-propagate-float-type
+#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (defun integer-rem-derive-type
        (number-low number-high divisor-low divisor-high)
   (if (and divisor-low divisor-high)
 (defun integer-rem-derive-type
        (number-low number-high divisor-low divisor-high)
   (if (and divisor-low divisor-high)

-      ;; We know the range of the divisor, and the remainder must be smaller
-      ;; than the divisor. We can tell the sign of the remainer if we know
-      ;; the sign of the number.
+      ;; We know the range of the divisor, and the remainder must be
+      ;; smaller than the divisor. We can tell the sign of the
+      ;; remainer if we know the sign of the number.

       (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
        `(integer ,(if (or (null number-low)
                           (minusp number-low))
       (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
        `(integer ,(if (or (null number-low)
                           (minusp number-low))

@@ -2185,23 +2057,23 @@
                           (plusp number-high))
                       divisor-max
                       0)))
                           (plusp number-high))
                       divisor-max
                       0)))

-      ;; The divisor is potentially either very positive or very negative.
-      ;; Therefore, the remainer is unbounded, but we might be able to tell
-      ;; something about the sign from the number.
+      ;; The divisor is potentially either very positive or very
+      ;; negative. Therefore, the remainer is unbounded, but we might
+      ;; be able to tell something about the sign from the number.

       `(integer ,(if (and number-low (not (minusp number-low)))
       `(integer ,(if (and number-low (not (minusp number-low)))

-                    ;; The number we are dividing is positive. Therefore,
-                    ;; the remainder must be positive.
+                    ;; The number we are dividing is positive.
+                    ;; Therefore, the remainder must be positive.

                     0
                     '*)
                ,(if (and number-high (not (plusp number-high)))
                     0
                     '*)
                ,(if (and number-high (not (plusp number-high)))

-                    ;; The number we are dividing is negative. Therefore,
-                    ;; the remainder must be negative.
+                    ;; The number we are dividing is negative.
+                    ;; Therefore, the remainder must be negative.

                     0
                     '*))))
 
                     0
                     '*))))
 

-#!-propagate-float-type
+#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (defoptimizer (random derive-type) ((bound &optional state))
 (defoptimizer (random derive-type) ((bound &optional state))

-  (let ((type (continuation-type bound)))
+  (let ((type (lvar-type bound)))

     (when (numeric-type-p type)
       (let ((class (numeric-type-class type))
            (high (numeric-type-high type))
     (when (numeric-type-p type)
       (let ((class (numeric-type-class type))
            (high (numeric-type-high type))

@@ -2215,7 +2087,7 @@
                     ((or (consp high) (zerop high)) high)
                     (t `(,high))))))))
 
                     ((or (consp high) (zerop high)) high)
                     (t `(,high))))))))
 

-#!+propagate-float-type
+#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (defun random-derive-type-aux (type)
   (let ((class (numeric-type-class type))
        (high (numeric-type-high type))
 (defun random-derive-type-aux (type)
   (let ((class (numeric-type-class type))
        (high (numeric-type-high type))

@@ -2229,16 +2101,16 @@
                     ((or (consp high) (zerop high)) high)
                     (t `(,high))))))
 
                     ((or (consp high) (zerop high)) high)
                     (t `(,high))))))
 

-#!+propagate-float-type
+#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)

 (defoptimizer (random derive-type) ((bound &optional state))
   (one-arg-derive-type bound #'random-derive-type-aux nil))
 \f
 (defoptimizer (random derive-type) ((bound &optional state))
   (one-arg-derive-type bound #'random-derive-type-aux nil))
 \f

-;;;; logical derive-type methods
+;;;; 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.
+;;; 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))
 (defun integer-type-length (type)
   (if (numeric-type-p type)
       (let ((min (numeric-type-low type))

@@ -2248,121 +2120,6 @@
                (or (null min) (minusp min))))
       (values nil t t)))
 
                (or (null min) (minusp min))))
       (values nil t t)))
 

-#!-propagate-fun-type
-(progn
-(defoptimizer (logand derive-type) ((x y))
-  (multiple-value-bind (x-len x-pos x-neg)
-      (integer-type-length (continuation-type x))
-    (declare (ignore x-pos))
-    (multiple-value-bind (y-len y-pos y-neg)
-       (integer-type-length (continuation-type y))
-      (declare (ignore y-pos))
-      (if (not x-neg)
-         ;; X must be positive.
-         (if (not y-neg)
-             ;; The must both be positive.
-             (cond ((or (null x-len) (null y-len))
-                    (specifier-type 'unsigned-byte))
-                   ((or (zerop x-len) (zerop y-len))
-                    (specifier-type '(integer 0 0)))
-                   (t
-                    (specifier-type `(unsigned-byte ,(min x-len y-len)))))
-             ;; X is positive, but Y might be negative.
-             (cond ((null x-len)
-                    (specifier-type 'unsigned-byte))
-                   ((zerop x-len)
-                    (specifier-type '(integer 0 0)))
-                   (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))
-                   ((zerop y-len)
-                    (specifier-type '(integer 0 0)))
-                   (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)))))))
-
-(defoptimizer (logior derive-type) ((x y))
-  (multiple-value-bind (x-len x-pos x-neg)
-      (integer-type-length (continuation-type x))
-    (multiple-value-bind (y-len y-pos y-neg)
-       (integer-type-length (continuation-type y))
-      (cond
-       ((and (not x-neg) (not y-neg))
-       ;; Both are positive.
-       (specifier-type `(unsigned-byte ,(if (and x-len y-len)
-                                            (max x-len y-len)
-                                            '*))))
-       ((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 (continuation-type 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 (continuation-type 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))))))))
-
-(defoptimizer (logxor derive-type) ((x y))
-  (multiple-value-bind (x-len x-pos x-neg)
-      (integer-type-length (continuation-type x))
-    (multiple-value-bind (y-len y-pos y-neg)
-       (integer-type-length (continuation-type y))
-      (cond
-       ((or (and (not x-neg) (not y-neg))
-           (and (not x-pos) (not y-pos)))
-       ;; Either both are negative or both are positive. 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-neg) (not y-pos)))
-       ;; Either X is negative and Y is positive of vice-verca. 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))))))
-
-) ; PROGN
-
-#!+propagate-fun-type
-(progn

 (defun logand-derive-type-aux (x y &optional same-leaf)
   (declare (ignore same-leaf))
   (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
 (defun logand-derive-type-aux (x y &optional same-leaf)
   (declare (ignore same-leaf))
   (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)

@@ -2372,30 +2129,22 @@
       (if (not x-neg)
          ;; X must be positive.
          (if (not y-neg)
       (if (not x-neg)
          ;; X must be positive.
          (if (not y-neg)

-             ;; The must both be positive.
+             ;; They must both be positive.

              (cond ((or (null x-len) (null y-len))
                     (specifier-type 'unsigned-byte))
              (cond ((or (null x-len) (null y-len))
                     (specifier-type 'unsigned-byte))

-                   ((or (zerop x-len) (zerop y-len))
-                    (specifier-type '(integer 0 0)))

                    (t
                    (t

-                    (specifier-type `(unsigned-byte ,(min x-len y-len)))))
+                    (specifier-type `(unsigned-byte* ,(min x-len y-len)))))

              ;; X is positive, but Y might be negative.
              (cond ((null x-len)
                     (specifier-type 'unsigned-byte))
              ;; X is positive, but Y might be negative.
              (cond ((null x-len)
                     (specifier-type 'unsigned-byte))

-                   ((zerop x-len)
-                    (specifier-type '(integer 0 0)))

                    (t
                    (t

-                    (specifier-type `(unsigned-byte ,x-len)))))
+                    (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))
          ;; X might be negative.
          (if (not y-neg)
              ;; Y must be positive.
              (cond ((null y-len)
                     (specifier-type 'unsigned-byte))

-                   ((zerop y-len)
-                    (specifier-type '(integer 0 0)))
-                   (t
-                    (specifier-type
-                     `(unsigned-byte ,y-len))))
+                   (t (specifier-type `(unsigned-byte* ,y-len))))

              ;; Either might be negative.
              (if (and x-len y-len)
                  ;; The result is bounded.
              ;; Either might be negative.
              (if (and x-len y-len)
                  ;; The result is bounded.

@@ -2410,23 +2159,21 @@
       (cond
        ((and (not x-neg) (not y-neg))
        ;; Both are positive.
       (cond
        ((and (not x-neg) (not y-neg))
        ;; Both are positive.

-       (if (and x-len y-len (zerop x-len) (zerop y-len))
-           (specifier-type '(integer 0 0))
-           (specifier-type `(unsigned-byte ,(if (and x-len y-len)
-                                            (max x-len y-len)
-                                            '*)))))
+       (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
+                                             (max x-len y-len)
+                                             '*))))

        ((not x-pos)
        ;; X must be negative.
        (if (not y-pos)
        ((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.
+           ;; 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)))
            (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.
+           ;; 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))))
            (specifier-type
             `(integer ,(or (numeric-type-low x) '*)
                       -1))))

@@ -2451,43 +2198,78 @@
       (cond
        ((or (and (not x-neg) (not y-neg))
            (and (not x-pos) (not y-pos)))
       (cond
        ((or (and (not x-neg) (not y-neg))
            (and (not x-pos) (not y-pos)))

-       ;; Either both are negative or both are positive. The result will be
-       ;; positive, and as long as the longer.
-       (if (and x-len y-len (zerop x-len) (zerop y-len))
-           (specifier-type '(integer 0 0))
-           (specifier-type `(unsigned-byte ,(if (and x-len y-len)
-                                            (max x-len y-len)
-                                            '*)))))
+       ;; Either both are negative or both are positive. 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-neg) (not y-pos)))
        ((or (and (not x-pos) (not y-neg))
            (and (not y-neg) (not y-pos)))

-       ;; Either X is negative and Y is positive of vice-verca. The result
-       ;; will be negative.
+       ;; 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)))
        (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.
+       ;; 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))))))
 
        ((and x-len y-len)
        (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
        (t
        (specifier-type 'integer))))))
 

-(macrolet ((frob (logfcn)
-            (let ((fcn-aux (symbolicate logfcn "-DERIVE-TYPE-AUX")))
-            `(defoptimizer (,logfcn derive-type) ((x y))
-               (two-arg-derive-type x y #',fcn-aux #',logfcn)))))
-  ;; FIXME: DEF-FROB, not just FROB
-  (frob logand)
-  (frob logior)
-  (frob logxor))
+(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))
+
+;;; FIXME: could actually do stuff with SAME-LEAF
+(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)
+                            (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)
+                            (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)
+                            (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)
+                            (logior-derive-type-aux
+                             x (lognot-derive-type-aux y) nil))
+                      #'logorc2))
+\f
+;;;; miscellaneous derive-type methods

 
 (defoptimizer (integer-length derive-type) ((x))
 
 (defoptimizer (integer-length derive-type) ((x))

-  (let ((x-type (continuation-type x)))
-    (when (and (numeric-type-p x-type)
-               (csubtypep x-type (specifier-type 'integer)))
-      ;; If the X is of type (INTEGER LO HI), then the integer-length
-      ;; of X is (INTEGER (min lo hi) (max lo hi), basically.  Be
+  (let ((x-type (lvar-type x)))
+    (when (numeric-type-p x-type)
+      ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
+      ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically.  Be

       ;; careful about LO or HI being NIL, though.  Also, if 0 is
       ;; contained in X, the lower bound is obviously 0.
       (flet ((null-or-min (a b)
       ;; careful about LO or HI being NIL, though.  Also, if 0 is
       ;; contained in X, the lower bound is obviously 0.
       (flet ((null-or-min (a b)

@@ -2503,36 +2285,79 @@
           (when (ctypep 0 x-type)
             (setf min-len 0))
           (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
           (when (ctypep 0 x-type)
             (setf min-len 0))
           (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))

-) ; PROGN
-\f
-;;;; miscellaneous derive-type methods
+
+(defoptimizer (isqrt derive-type) ((x))
+  (let ((x-type (lvar-type x)))
+    (when (numeric-type-p x-type)
+      (let* ((lo (numeric-type-low x-type))
+             (hi (numeric-type-high x-type))
+             (lo-res (if lo (isqrt lo) '*))
+             (hi-res (if hi (isqrt hi) '*)))
+        (specifier-type `(integer ,lo-res ,hi-res))))))

 
 (defoptimizer (code-char derive-type) ((code))
   (specifier-type 'base-char))
 
 (defoptimizer (values derive-type) ((&rest values))
 
 (defoptimizer (code-char derive-type) ((code))
   (specifier-type 'base-char))
 
 (defoptimizer (values derive-type) ((&rest values))

-  (values-specifier-type
-   `(values ,@(mapcar #'(lambda (x)
-                         (type-specifier (continuation-type x)))
-                     values))))
+  (make-values-type :required (mapcar #'lvar-type values)))
+
+(defun signum-derive-type-aux (type)
+  (if (eq (numeric-type-complexp type) :complex)
+      (let* ((format (case (numeric-type-class type)
+                         ((integer rational) 'single-float)
+                         (t (numeric-type-format type))))
+               (bound-format (or format 'float)))
+          (make-numeric-type :class 'float
+                             :format format
+                             :complexp :complex
+                             :low (coerce -1 bound-format)
+                             :high (coerce 1 bound-format)))
+      (let* ((interval (numeric-type->interval type))
+            (range-info (interval-range-info interval))
+            (contains-0-p (interval-contains-p 0 interval))
+            (class (numeric-type-class type))
+            (format (numeric-type-format type))
+            (one (coerce 1 (or format class 'real)))
+            (zero (coerce 0 (or format class 'real)))
+            (minus-one (coerce -1 (or format class 'real)))
+            (plus (make-numeric-type :class class :format format
+                                     :low one :high one))
+            (minus (make-numeric-type :class class :format format
+                                      :low minus-one :high minus-one))
+            ;; KLUDGE: here we have a fairly horrible hack to deal
+            ;; with the schizophrenia in the type derivation engine.
+            ;; The problem is that the type derivers reinterpret
+            ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
+            ;; 0d0) within the derivation mechanism doesn't include
+            ;; -0d0.  Ugh.  So force it in here, instead.
+            (zero (make-numeric-type :class class :format format
+                                     :low (- zero) :high zero)))
+       (case range-info
+         (+ (if contains-0-p (type-union plus zero) plus))
+         (- (if contains-0-p (type-union minus zero) minus))
+         (t (type-union minus zero plus))))))
+
+(defoptimizer (signum derive-type) ((num))
+  (one-arg-derive-type num #'signum-derive-type-aux nil))

 \f
 ;;;; byte operations
 ;;;;
 \f
 ;;;; byte operations
 ;;;;

-;;;; We try to turn byte operations into simple logical operations. First, we
-;;;; convert byte specifiers into separate size and position arguments passed
-;;;; to internal %FOO functions. We then attempt to transform the %FOO
-;;;; functions into boolean operations when the size and position are constant
-;;;; and the operands are fixnums.
-
-(macrolet (;; Evaluate body with Size-Var and Pos-Var bound to expressions that
-          ;; evaluate to the Size and Position of the byte-specifier form
-          ;; Spec. We may wrap a let around the result of the body to bind
-          ;; some variables.
+;;;; We try to turn byte operations into simple logical operations.
+;;;; First, we convert byte specifiers into separate size and position
+;;;; arguments passed to internal %FOO functions. We then attempt to
+;;;; transform the %FOO functions into boolean operations when the
+;;;; size and position are constant and the operands are fixnums.
+
+(macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
+          ;; expressions that evaluate to the SIZE and POSITION of
+          ;; the byte-specifier form SPEC. We may wrap a let around
+          ;; the result of the body to bind some variables.

           ;;
           ;;

-          ;; If the spec is a Byte form, then bind the vars to the subforms.
-          ;; otherwise, evaluate Spec and use the Byte-Size and Byte-Position.
-          ;; The goal of this transformation is to avoid consing up byte
-          ;; specifiers and then immediately throwing them away.
+          ;; If the spec is a BYTE form, then bind the vars to the
+          ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
+          ;; and BYTE-POSITION. The goal of this transformation is to
+          ;; avoid consing up byte specifiers and then immediately
+          ;; throwing them away.

           (with-byte-specifier ((size-var pos-var spec) &body body)
             (once-only ((spec `(macroexpand ,spec))
                         (temp '(gensym)))
           (with-byte-specifier ((size-var pos-var spec) &body body)
             (once-only ((spec `(macroexpand ,spec))
                         (temp '(gensym)))

@@ -2547,35 +2372,35 @@
                          `(let ((,,temp ,,spec))
                             ,,@body))))))
 
                          `(let ((,,temp ,,spec))
                             ,,@body))))))
 

-  (def-source-transform ldb (spec int)
+  (define-source-transform ldb (spec int)

     (with-byte-specifier (size pos spec)
       `(%ldb ,size ,pos ,int)))
 
     (with-byte-specifier (size pos spec)
       `(%ldb ,size ,pos ,int)))
 

-  (def-source-transform dpb (newbyte spec int)
+  (define-source-transform dpb (newbyte spec int)

     (with-byte-specifier (size pos spec)
       `(%dpb ,newbyte ,size ,pos ,int)))
 
     (with-byte-specifier (size pos spec)
       `(%dpb ,newbyte ,size ,pos ,int)))
 

-  (def-source-transform mask-field (spec int)
+  (define-source-transform mask-field (spec int)

     (with-byte-specifier (size pos spec)
       `(%mask-field ,size ,pos ,int)))
 
     (with-byte-specifier (size pos spec)
       `(%mask-field ,size ,pos ,int)))
 

-  (def-source-transform deposit-field (newbyte spec int)
+  (define-source-transform deposit-field (newbyte spec int)

     (with-byte-specifier (size pos spec)
       `(%deposit-field ,newbyte ,size ,pos ,int))))
 
 (defoptimizer (%ldb derive-type) ((size posn num))
     (with-byte-specifier (size pos spec)
       `(%deposit-field ,newbyte ,size ,pos ,int))))
 
 (defoptimizer (%ldb derive-type) ((size posn num))

-  (let ((size (continuation-type size)))
+  (let ((size (lvar-type size)))

     (if (and (numeric-type-p size)
             (csubtypep size (specifier-type 'integer)))
        (let ((size-high (numeric-type-high size)))
     (if (and (numeric-type-p size)
             (csubtypep size (specifier-type 'integer)))
        (let ((size-high (numeric-type-high size)))

-         (if (and size-high (<= size-high sb!vm:word-bits))
-             (specifier-type `(unsigned-byte ,size-high))
+         (if (and size-high (<= size-high sb!vm:n-word-bits))
+             (specifier-type `(unsigned-byte* ,size-high))

              (specifier-type 'unsigned-byte)))
        *universal-type*)))
 
 (defoptimizer (%mask-field derive-type) ((size posn num))
              (specifier-type 'unsigned-byte)))
        *universal-type*)))
 
 (defoptimizer (%mask-field derive-type) ((size posn num))

-  (let ((size (continuation-type size))
-       (posn (continuation-type posn)))
+  (let ((size (lvar-type size))
+       (posn (lvar-type posn)))

     (if (and (numeric-type-p size)
             (csubtypep size (specifier-type 'integer))
             (numeric-type-p posn)
     (if (and (numeric-type-p size)
             (csubtypep size (specifier-type 'integer))
             (numeric-type-p posn)

@@ -2583,152 +2408,226 @@
        (let ((size-high (numeric-type-high size))
              (posn-high (numeric-type-high posn)))
          (if (and size-high posn-high
        (let ((size-high (numeric-type-high size))
              (posn-high (numeric-type-high posn)))
          (if (and size-high posn-high

-                  (<= (+ size-high posn-high) sb!vm:word-bits))
-             (specifier-type `(unsigned-byte ,(+ size-high posn-high)))
+                  (<= (+ size-high posn-high) sb!vm:n-word-bits))
+             (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))

              (specifier-type 'unsigned-byte)))
        *universal-type*)))
 
              (specifier-type 'unsigned-byte)))
        *universal-type*)))
 

+(defun %deposit-field-derive-type-aux (size posn int)
+  (let ((size (lvar-type size))
+       (posn (lvar-type posn))
+       (int (lvar-type int)))
+    (when (and (numeric-type-p size)
+               (numeric-type-p posn)
+               (numeric-type-p int))
+      (let ((size-high (numeric-type-high size))
+            (posn-high (numeric-type-high posn))
+            (high (numeric-type-high int))
+            (low (numeric-type-low int)))
+        (when (and size-high posn-high high low
+                  ;; KLUDGE: we need this cutoff here, otherwise we
+                  ;; will merrily derive the type of %DPB as
+                  ;; (UNSIGNED-BYTE 1073741822), and then attempt to
+                  ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
+                  ;; 1073741822))), with hilarious consequences.  We
+                  ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
+                  ;; over a reasonable amount of shifting, even on
+                  ;; the alpha/32 port, where N-WORD-BITS is 32 but
+                  ;; machine integers are 64-bits.  -- CSR,
+                  ;; 2003-09-12
+                   (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
+          (let ((raw-bit-count (max (integer-length high)
+                                    (integer-length low)
+                                    (+ size-high posn-high))))
+            (specifier-type
+             (if (minusp low)
+                 `(signed-byte ,(1+ raw-bit-count))
+                 `(unsigned-byte* ,raw-bit-count)))))))))
+

 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
 (defoptimizer (%dpb derive-type) ((newbyte size posn int))

-  (let ((size (continuation-type size))
-       (posn (continuation-type posn))
-       (int (continuation-type int)))
-    (if (and (numeric-type-p size)
-            (csubtypep size (specifier-type 'integer))
-            (numeric-type-p posn)
-            (csubtypep posn (specifier-type 'integer))
-            (numeric-type-p int)
-            (csubtypep int (specifier-type 'integer)))
-       (let ((size-high (numeric-type-high size))
-             (posn-high (numeric-type-high posn))
-             (high (numeric-type-high int))
-             (low (numeric-type-low int)))
-         (if (and size-high posn-high high low
-                  (<= (+ size-high posn-high) sb!vm:word-bits))
-             (specifier-type
-              (list (if (minusp low) 'signed-byte 'unsigned-byte)
-                    (max (integer-length high)
-                         (integer-length low)
-                         (+ size-high posn-high))))
-             *universal-type*))
-       *universal-type*)))
+  (%deposit-field-derive-type-aux size posn int))

 
 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
 
 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))

-  (let ((size (continuation-type size))
-       (posn (continuation-type posn))
-       (int (continuation-type int)))
-    (if (and (numeric-type-p size)
-            (csubtypep size (specifier-type 'integer))
-            (numeric-type-p posn)
-            (csubtypep posn (specifier-type 'integer))
-            (numeric-type-p int)
-            (csubtypep int (specifier-type 'integer)))
-       (let ((size-high (numeric-type-high size))
-             (posn-high (numeric-type-high posn))
-             (high (numeric-type-high int))
-             (low (numeric-type-low int)))
-         (if (and size-high posn-high high low
-                  (<= (+ size-high posn-high) sb!vm:word-bits))
-             (specifier-type
-              (list (if (minusp low) 'signed-byte 'unsigned-byte)
-                    (max (integer-length high)
-                         (integer-length low)
-                         (+ size-high posn-high))))
-             *universal-type*))
-       *universal-type*)))
+  (%deposit-field-derive-type-aux size posn int))

 
 (deftransform %ldb ((size posn int)
                    (fixnum fixnum integer)
 
 (deftransform %ldb ((size posn int)
                    (fixnum fixnum integer)

-                   (unsigned-byte #.sb!vm:word-bits))
-  "convert to inline logical ops"
+                   (unsigned-byte #.sb!vm:n-word-bits))
+  "convert to inline logical operations"

   `(logand (ash int (- posn))
   `(logand (ash int (- posn))

-          (ash ,(1- (ash 1 sb!vm:word-bits))
-               (- size ,sb!vm:word-bits))))
+          (ash ,(1- (ash 1 sb!vm:n-word-bits))
+               (- size ,sb!vm:n-word-bits))))

 
 (deftransform %mask-field ((size posn int)
                           (fixnum fixnum integer)
 
 (deftransform %mask-field ((size posn int)
                           (fixnum fixnum integer)

-                          (unsigned-byte #.sb!vm:word-bits))
-  "convert to inline logical ops"
+                          (unsigned-byte #.sb!vm:n-word-bits))
+  "convert to inline logical operations"

   `(logand int
   `(logand int

-          (ash (ash ,(1- (ash 1 sb!vm:word-bits))
-                    (- size ,sb!vm:word-bits))
+          (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
+                    (- size ,sb!vm:n-word-bits))

                posn)))
 
 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
 ;;;   (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
                posn)))
 
 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
 ;;;   (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))

-;;; as the result type, as that would allow result types
-;;; that cover the range -2^(n-1) .. 1-2^n, instead of allowing result types
-;;; of (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
+;;; as the result type, as that would allow result types that cover
+;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
+;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).

 
 (deftransform %dpb ((new size posn int)
                    *
 
 (deftransform %dpb ((new size posn int)
                    *

-                   (unsigned-byte #.sb!vm:word-bits))
-  "convert to inline logical ops"
+                   (unsigned-byte #.sb!vm:n-word-bits))
+  "convert to inline logical operations"

   `(let ((mask (ldb (byte size 0) -1)))
      (logior (ash (logand new mask) posn)
             (logand int (lognot (ash mask posn))))))
 
 (deftransform %dpb ((new size posn int)
                    *
   `(let ((mask (ldb (byte size 0) -1)))
      (logior (ash (logand new mask) posn)
             (logand int (lognot (ash mask posn))))))
 
 (deftransform %dpb ((new size posn int)
                    *

-                   (signed-byte #.sb!vm:word-bits))
-  "convert to inline logical ops"
+                   (signed-byte #.sb!vm:n-word-bits))
+  "convert to inline logical operations"

   `(let ((mask (ldb (byte size 0) -1)))
      (logior (ash (logand new mask) posn)
             (logand int (lognot (ash mask posn))))))
 
 (deftransform %deposit-field ((new size posn int)
                              *
   `(let ((mask (ldb (byte size 0) -1)))
      (logior (ash (logand new mask) posn)
             (logand int (lognot (ash mask posn))))))
 
 (deftransform %deposit-field ((new size posn int)
                              *

-                             (unsigned-byte #.sb!vm:word-bits))
-  "convert to inline logical ops"
+                             (unsigned-byte #.sb!vm:n-word-bits))
+  "convert to inline logical operations"

   `(let ((mask (ash (ldb (byte size 0) -1) posn)))
      (logior (logand new mask)
             (logand int (lognot mask)))))
 
 (deftransform %deposit-field ((new size posn int)
                              *
   `(let ((mask (ash (ldb (byte size 0) -1) posn)))
      (logior (logand new mask)
             (logand int (lognot mask)))))
 
 (deftransform %deposit-field ((new size posn int)
                              *

-                             (signed-byte #.sb!vm:word-bits))
-  "convert to inline logical ops"
+                             (signed-byte #.sb!vm:n-word-bits))
+  "convert to inline logical operations"

   `(let ((mask (ash (ldb (byte size 0) -1) posn)))
      (logior (logand new mask)
             (logand int (lognot mask)))))
 \f
   `(let ((mask (ash (ldb (byte size 0) -1) posn)))
      (logior (logand new mask)
             (logand int (lognot mask)))))
 \f

+;;; Modular functions
+
+;;; (ldb (byte s 0) (foo                 x  y ...)) =
+;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
+;;;
+;;; and similar for other arguments.
+
+;;; Try to recursively cut all uses of LVAR to WIDTH bits.
+;;;
+;;; For good functions, we just recursively cut arguments; their
+;;; "goodness" means that the result will not increase (in the
+;;; (unsigned-byte +infinity) sense). An ordinary modular function is
+;;; replaced with the version, cutting its result to WIDTH or more
+;;; bits. For most functions (e.g. for +) we cut all arguments; for
+;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
+;;; arguments (maybe to a different width) and returning the name of a
+;;; modular version, if it exists, or NIL. If we have changed
+;;; anything, we need to flush old derived types, because they have
+;;; nothing in common with the new code.
+(defun cut-to-width (lvar width)
+  (declare (type lvar lvar) (type (integer 0) width))
+  (labels ((reoptimize-node (node name)
+             (setf (node-derived-type node)
+                   (fun-type-returns
+                    (info :function :type name)))
+             (setf (lvar-%derived-type (node-lvar node)) nil)
+             (setf (node-reoptimize node) t)
+             (setf (block-reoptimize (node-block node)) t)
+             (setf (component-reoptimize (node-component node)) t))
+           (cut-node (node &aux did-something)
+             (when (and (not (block-delete-p (node-block node)))
+                        (combination-p node)
+                        (fun-info-p (basic-combination-kind node)))
+               (let* ((fun-ref (lvar-use (combination-fun node)))
+                      (fun-name (leaf-source-name (ref-leaf fun-ref)))
+                      (modular-fun (find-modular-version fun-name width)))
+                 (when (and modular-fun
+                            (not (and (eq fun-name 'logand)
+                                      (csubtypep
+                                       (single-value-type (node-derived-type node))
+                                       (specifier-type `(unsigned-byte ,width))))))
+                   (binding* ((name (etypecase modular-fun
+                                      ((eql :good) fun-name)
+                                      (modular-fun-info
+                                       (modular-fun-info-name modular-fun))
+                                      (function
+                                       (funcall modular-fun node width)))
+                                :exit-if-null))
+                     (unless (eql modular-fun :good)
+                       (setq did-something t)
+                       (change-ref-leaf
+                        fun-ref
+                        (find-free-fun name "in a strange place"))
+                       (setf (combination-kind node) :full))
+                     (unless (functionp modular-fun)
+                       (dolist (arg (basic-combination-args node))
+                         (when (cut-lvar arg)
+                           (setq did-something t))))
+                     (when did-something
+                       (reoptimize-node node name))
+                     did-something)))))
+           (cut-lvar (lvar &aux did-something)
+             (do-uses (node lvar)
+               (when (cut-node node)
+                 (setq did-something t)))
+             did-something))
+    (cut-lvar lvar)))
+
+(defoptimizer (logand optimizer) ((x y) node)
+  (let ((result-type (single-value-type (node-derived-type node))))
+    (when (numeric-type-p result-type)
+      (let ((low (numeric-type-low result-type))
+            (high (numeric-type-high result-type)))
+        (when (and (numberp low)
+                   (numberp high)
+                   (>= low 0))
+          (let ((width (integer-length high)))
+            (when (some (lambda (x) (<= width x))
+                        *modular-funs-widths*)
+              ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
+              (cut-to-width x width)
+              (cut-to-width y width)
+              nil ; After fixing above, replace with T.
+              )))))))
+\f

 ;;; miscellanous numeric transforms
 
 ;;; If a constant appears as the first arg, swap the args.
 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
 ;;; miscellanous numeric transforms
 
 ;;; If a constant appears as the first arg, swap the args.
 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)

-  (if (and (constant-continuation-p x)
-          (not (constant-continuation-p y)))
-      `(,(continuation-function-name (basic-combination-fun node))
+  (if (and (constant-lvar-p x)
+          (not (constant-lvar-p y)))
+      `(,(lvar-fun-name (basic-combination-fun node))

        y
        y

-       ,(continuation-value x))
+       ,(lvar-value x))

       (give-up-ir1-transform)))
 
 (dolist (x '(= char= + * logior logand logxor))
   (%deftransform x '(function * *) #'commutative-arg-swap
       (give-up-ir1-transform)))
 
 (dolist (x '(= char= + * logior logand logxor))
   (%deftransform x '(function * *) #'commutative-arg-swap

-                "place constant arg last."))
+                "place constant arg last"))

 
 ;;; Handle the case of a constant BOOLE-CODE.
 
 ;;; Handle the case of a constant BOOLE-CODE.

-(deftransform boole ((op x y) * * :when :both)
-  "convert to inline logical ops"
-  (unless (constant-continuation-p op)
+(deftransform boole ((op x y) * *)
+  "convert to inline logical operations"
+  (unless (constant-lvar-p op)

     (give-up-ir1-transform "BOOLE code is not a constant."))
     (give-up-ir1-transform "BOOLE code is not a constant."))

-  (let ((control (continuation-value op)))
+  (let ((control (lvar-value op)))

     (case control
     (case control

-      (#.boole-clr 0)
-      (#.boole-set -1)
-      (#.boole-1 'x)
-      (#.boole-2 'y)
-      (#.boole-c1 '(lognot x))
-      (#.boole-c2 '(lognot y))
-      (#.boole-and '(logand x y))
-      (#.boole-ior '(logior x y))
-      (#.boole-xor '(logxor x y))
-      (#.boole-eqv '(logeqv x y))
-      (#.boole-nand '(lognand x y))
-      (#.boole-nor '(lognor x y))
-      (#.boole-andc1 '(logandc1 x y))
-      (#.boole-andc2 '(logandc2 x y))
-      (#.boole-orc1 '(logorc1 x y))
-      (#.boole-orc2 '(logorc2 x y))
+      (#.sb!xc:boole-clr 0)
+      (#.sb!xc:boole-set -1)
+      (#.sb!xc:boole-1 'x)
+      (#.sb!xc:boole-2 'y)
+      (#.sb!xc:boole-c1 '(lognot x))
+      (#.sb!xc:boole-c2 '(lognot y))
+      (#.sb!xc:boole-and '(logand x y))
+      (#.sb!xc:boole-ior '(logior x y))
+      (#.sb!xc:boole-xor '(logxor x y))
+      (#.sb!xc:boole-eqv '(logeqv x y))
+      (#.sb!xc:boole-nand '(lognand x y))
+      (#.sb!xc:boole-nor '(lognor x y))
+      (#.sb!xc:boole-andc1 '(logandc1 x y))
+      (#.sb!xc:boole-andc2 '(logandc2 x y))
+      (#.sb!xc:boole-orc1 '(logorc1 x y))
+      (#.sb!xc:boole-orc2 '(logorc2 x y))

       (t
        (abort-ir1-transform "~S is an illegal control arg to BOOLE."
                            control)))))
       (t
        (abort-ir1-transform "~S is an illegal control arg to BOOLE."
                            control)))))

@@ -2736,11 +2635,11 @@
 ;;;; converting special case multiply/divide to shifts
 
 ;;; If arg is a constant power of two, turn * into a shift.
 ;;;; converting special case multiply/divide to shifts
 
 ;;; If arg is a constant power of two, turn * into a shift.

-(deftransform * ((x y) (integer integer) * :when :both)
+(deftransform * ((x y) (integer integer) *)

   "convert x*2^k to shift"
   "convert x*2^k to shift"

-  (unless (constant-continuation-p y)
+  (unless (constant-lvar-p y)

     (give-up-ir1-transform))
     (give-up-ir1-transform))

-  (let* ((y (continuation-value y))
+  (let* ((y (lvar-value y))

         (y-abs (abs y))
         (len (1- (integer-length y-abs))))
     (unless (= y-abs (ash 1 len))
         (y-abs (abs y))
         (len (1- (integer-length y-abs))))
     (unless (= y-abs (ash 1 len))

@@ -2749,71 +2648,26 @@
        `(- (ash x ,len))
        `(ash x ,len))))
 
        `(- (ash x ,len))
        `(ash x ,len))))
 

-;;; If both arguments and the result are (unsigned-byte 32), try to come up
-;;; with a ``better'' multiplication using multiplier recoding. There are two
-;;; different ways the multiplier can be recoded. The more obvious is to shift
-;;; X by the correct amount for each bit set in Y and to sum the results. But
-;;; if there is a string of bits that are all set, you can add X shifted by
-;;; one more then the bit position of the first set bit and subtract X shifted
-;;; by the bit position of the last set bit. We can't use this second method
-;;; when the high order bit is bit 31 because shifting by 32 doesn't work
-;;; too well.
-(deftransform * ((x y)
-                ((unsigned-byte 32) (unsigned-byte 32))
-                (unsigned-byte 32))
-  "recode as shift and add"
-  (unless (constant-continuation-p y)
-    (give-up-ir1-transform))
-  (let ((y (continuation-value y))
-       (result nil)
-       (first-one nil))
-    (labels ((tub32 (x) `(truly-the (unsigned-byte 32) ,x))
-            (add (next-factor)
-              (setf result
-                    (tub32
-                     (if result
-                         `(+ ,result ,(tub32 next-factor))
-                         next-factor)))))
-      (declare (inline add))
-      (dotimes (bitpos 32)
-       (if first-one
-           (when (not (logbitp bitpos y))
-             (add (if (= (1+ first-one) bitpos)
-                      ;; There is only a single bit in the string.
-                      `(ash x ,first-one)
-                      ;; There are at least two.
-                      `(- ,(tub32 `(ash x ,bitpos))
-                          ,(tub32 `(ash x ,first-one)))))
-             (setf first-one nil))
-           (when (logbitp bitpos y)
-             (setf first-one bitpos))))
-      (when first-one
-       (cond ((= first-one 31))
-             ((= first-one 30)
-              (add '(ash x 30)))
-             (t
-              (add `(- ,(tub32 '(ash x 31)) ,(tub32 `(ash x ,first-one))))))
-       (add '(ash x 31))))
-    (or result 0)))
-
-;;; If arg is a constant power of two, turn FLOOR into a shift and mask.
-;;; If CEILING, add in (1- (ABS Y)) and then do FLOOR.
+;;; If arg is a constant power of two, turn FLOOR into a shift and
+;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
+;;; remainder.

 (flet ((frob (y ceil-p)
 (flet ((frob (y ceil-p)

-        (unless (constant-continuation-p y)
+        (unless (constant-lvar-p y)

           (give-up-ir1-transform))
           (give-up-ir1-transform))

-        (let* ((y (continuation-value y))
+        (let* ((y (lvar-value y))

                (y-abs (abs y))
                (len (1- (integer-length y-abs))))
           (unless (= y-abs (ash 1 len))
             (give-up-ir1-transform))
           (let ((shift (- len))
                (y-abs (abs y))
                (len (1- (integer-length y-abs))))
           (unless (= y-abs (ash 1 len))
             (give-up-ir1-transform))
           (let ((shift (- len))

-                (mask (1- y-abs)))
-            `(let ,(when ceil-p `((x (+ x ,(1- y-abs)))))
+                (mask (1- y-abs))
+                 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
+            `(let ((x (+ x ,delta)))

                ,(if (minusp y)
                     `(values (ash (- x) ,shift)
                ,(if (minusp y)
                     `(values (ash (- x) ,shift)

-                             (- (logand (- x) ,mask)))
+                             (- (- (logand (- x) ,mask)) ,delta))

                     `(values (ash x ,shift)
                     `(values (ash x ,shift)

-                             (logand x ,mask))))))))
+                             (- (logand x ,mask) ,delta))))))))

   (deftransform floor ((x y) (integer integer) *)
     "convert division by 2^k to shift"
     (frob y nil))
   (deftransform floor ((x y) (integer integer) *)
     "convert division by 2^k to shift"
     (frob y nil))

@@ -2822,11 +2676,11 @@
     (frob y t)))
 
 ;;; Do the same for MOD.
     (frob y t)))
 
 ;;; Do the same for MOD.

-(deftransform mod ((x y) (integer integer) * :when :both)
+(deftransform mod ((x y) (integer integer) *)

   "convert remainder mod 2^k to LOGAND"
   "convert remainder mod 2^k to LOGAND"

-  (unless (constant-continuation-p y)
+  (unless (constant-lvar-p y)

     (give-up-ir1-transform))
     (give-up-ir1-transform))

-  (let* ((y (continuation-value y))
+  (let* ((y (lvar-value y))

         (y-abs (abs y))
         (len (1- (integer-length y-abs))))
     (unless (= y-abs (ash 1 len))
         (y-abs (abs y))
         (len (1- (integer-length y-abs))))
     (unless (= y-abs (ash 1 len))

@@ -2839,9 +2693,9 @@
 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
 (deftransform truncate ((x y) (integer integer))
   "convert division by 2^k to shift"
 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
 (deftransform truncate ((x y) (integer integer))
   "convert division by 2^k to shift"

-  (unless (constant-continuation-p y)
+  (unless (constant-lvar-p y)

     (give-up-ir1-transform))
     (give-up-ir1-transform))

-  (let* ((y (continuation-value y))
+  (let* ((y (lvar-value y))

         (y-abs (abs y))
         (len (1- (integer-length y-abs))))
     (unless (= y-abs (ash 1 len))
         (y-abs (abs y))
         (len (1- (integer-length y-abs))))
     (unless (= y-abs (ash 1 len))

@@ -2854,16 +2708,16 @@
                        `(- (ash (- x) ,shift)))
                   (- (logand (- x) ,mask)))
           (values ,(if (minusp y)
                        `(- (ash (- x) ,shift)))
                   (- (logand (- x) ,mask)))
           (values ,(if (minusp y)

-                       `(- (ash (- x) ,shift))
+                       `(ash (- ,mask x) ,shift)

                        `(ash x ,shift))
                   (logand x ,mask))))))
 
 ;;; And the same for REM.
                        `(ash x ,shift))
                   (logand x ,mask))))))
 
 ;;; And the same for REM.

-(deftransform rem ((x y) (integer integer) * :when :both)
+(deftransform rem ((x y) (integer integer) *)

   "convert remainder mod 2^k to LOGAND"
   "convert remainder mod 2^k to LOGAND"

-  (unless (constant-continuation-p y)
+  (unless (constant-lvar-p y)

     (give-up-ir1-transform))
     (give-up-ir1-transform))

-  (let* ((y (continuation-value y))
+  (let* ((y (lvar-value y))

         (y-abs (abs y))
         (len (1- (integer-length y-abs))))
     (unless (= y-abs (ash 1 len))
         (y-abs (abs y))
         (len (1- (integer-length y-abs))))
     (unless (= y-abs (ash 1 len))

@@ -2874,50 +2728,57 @@
           (logand x ,mask)))))
 \f
 ;;;; arithmetic and logical identity operation elimination
           (logand x ,mask)))))
 \f
 ;;;; arithmetic and logical identity operation elimination

-;;;;
-;;;; Flush calls to various arith functions that convert to the identity
-;;;; function or a constant.
-
-(dolist (stuff '((ash 0 x)
-                (logand -1 x)
-                (logand 0 0)
-                (logior 0 x)
-                (logior -1 -1)
-                (logxor -1 (lognot x))
-                (logxor 0 x)))
-  (destructuring-bind (name identity result) stuff
-    (deftransform name ((x y) `(* (constant-argument (member ,identity))) '*
-                       :eval-name t :when :both)
-      "fold identity operations"
-      result)))
+
+;;; Flush calls to various arith functions that convert to the
+;;; identity function or a constant.
+(macrolet ((def (name identity result)
+             `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
+                "fold identity operations"
+                ',result)))
+  (def ash 0 x)
+  (def logand -1 x)
+  (def logand 0 0)
+  (def logior 0 x)
+  (def logior -1 -1)
+  (def logxor -1 (lognot x))
+  (def logxor 0 x))
+
+(deftransform logand ((x y) (* (constant-arg t)) *)
+  "fold identity operation"
+  (let ((y (lvar-value y)))
+    (unless (and (plusp y)
+                 (= y (1- (ash 1 (integer-length y)))))
+      (give-up-ir1-transform))
+    (unless (csubtypep (lvar-type x)
+                       (specifier-type `(integer 0 ,y)))
+      (give-up-ir1-transform))
+    'x))

 
 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
 ;;; (* 0 -4.0) is -0.0.
 
 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
 ;;; (* 0 -4.0) is -0.0.

-(deftransform - ((x y) ((constant-argument (member 0)) rational) *
-                :when :both)
+(deftransform - ((x y) ((constant-arg (member 0)) rational) *)

   "convert (- 0 x) to negate"
   '(%negate y))
   "convert (- 0 x) to negate"
   '(%negate y))

-(deftransform * ((x y) (rational (constant-argument (member 0))) *
-                :when :both)
-  "convert (* x 0) to 0."
+(deftransform * ((x y) (rational (constant-arg (member 0))) *)
+  "convert (* x 0) to 0"

   0)
 
   0)
 

-;;; Return T if in an arithmetic op including continuations X and Y, the
-;;; result type is not affected by the type of X. That is, Y is at least as
-;;; contagious as X.
+;;; Return T if in an arithmetic op including lvars X and Y, the
+;;; result type is not affected by the type of X. That is, Y is at
+;;; least as contagious as X.

 #+nil
 (defun not-more-contagious (x y)
   (declare (type continuation x y))
 #+nil
 (defun not-more-contagious (x y)
   (declare (type continuation x y))

-  (let ((x (continuation-type x))
-       (y (continuation-type y)))
+  (let ((x (lvar-type x))
+       (y (lvar-type y)))

     (values (type= (numeric-contagion x y)
                   (numeric-contagion y y)))))
 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
     (values (type= (numeric-contagion x y)
                   (numeric-contagion y y)))))
 ;;; Patched version by Raymond Toy. dtc: Should be safer although it

-;;; needs more work as valid transforms are missed; some cases are
+;;; XXX needs more work as valid transforms are missed; some cases are

 ;;; specific to particular transform functions so the use of this
 ;;; function may need a re-think.
 (defun not-more-contagious (x y)
 ;;; specific to particular transform functions so the use of this
 ;;; function may need a re-think.
 (defun not-more-contagious (x y)

-  (declare (type continuation x y))
+  (declare (type lvar x y))

   (flet ((simple-numeric-type (num)
           (and (numeric-type-p num)
                ;; Return non-NIL if NUM is integer, rational, or a float
   (flet ((simple-numeric-type (num)
           (and (numeric-type-p num)
                ;; Return non-NIL if NUM is integer, rational, or a float

@@ -2929,8 +2790,8 @@
                   (numeric-type-format num))
                  (t
                   nil)))))
                   (numeric-type-format num))
                  (t
                   nil)))))

-    (let ((x (continuation-type x))
-         (y (continuation-type y)))
+    (let ((x (lvar-type x))
+         (y (lvar-type y)))

       (if (and (simple-numeric-type x)
               (simple-numeric-type y))
          (values (type= (numeric-contagion x y)
       (if (and (simple-numeric-type x)
               (simple-numeric-type y))
          (values (type= (numeric-contagion x y)

@@ -2938,11 +2799,11 @@
 
 ;;; Fold (+ x 0).
 ;;;
 
 ;;; Fold (+ x 0).
 ;;;

-;;;    If y is not constant, not zerop, or is contagious, or a
-;;; positive float +0.0 then give up.
-(deftransform + ((x y) (t (constant-argument t)) * :when :both)
+;;; If y is not constant, not zerop, or is contagious, or a positive
+;;; float +0.0 then give up.
+(deftransform + ((x y) (t (constant-arg t)) *)

   "fold zero arg"
   "fold zero arg"

-  (let ((val (continuation-value y)))
+  (let ((val (lvar-value y)))

     (unless (and (zerop val)
                 (not (and (floatp val) (plusp (float-sign val))))
                 (not-more-contagious y x))
     (unless (and (zerop val)
                 (not (and (floatp val) (plusp (float-sign val))))
                 (not-more-contagious y x))

@@ -2951,11 +2812,11 @@
 
 ;;; Fold (- x 0).
 ;;;
 
 ;;; Fold (- x 0).
 ;;;

-;;;    If y is not constant, not zerop, or is contagious, or a
-;;; negative float -0.0 then give up.
-(deftransform - ((x y) (t (constant-argument t)) * :when :both)
+;;; If y is not constant, not zerop, or is contagious, or a negative
+;;; float -0.0 then give up.
+(deftransform - ((x y) (t (constant-arg t)) *)

   "fold zero arg"
   "fold zero arg"

-  (let ((val (continuation-value y)))
+  (let ((val (lvar-value y)))

     (unless (and (zerop val)
                 (not (and (floatp val) (minusp (float-sign val))))
                 (not-more-contagious y x))
     (unless (and (zerop val)
                 (not (and (floatp val) (minusp (float-sign val))))
                 (not-more-contagious y x))

@@ -2963,31 +2824,42 @@
   'x)
 
 ;;; Fold (OP x +/-1)
   'x)
 
 ;;; Fold (OP x +/-1)

-(dolist (stuff '((* x (%negate x))
-                (/ x (%negate x))
-                (expt x (/ 1 x))))
-  (destructuring-bind (name result minus-result) stuff
-    (deftransform name ((x y) '(t (constant-argument real)) '* :eval-name t
-                       :when :both)
-      "fold identity operations"
-      (let ((val (continuation-value y)))
-       (unless (and (= (abs val) 1)
-                    (not-more-contagious y x))
-         (give-up-ir1-transform))
-       (if (minusp val) minus-result result)))))
+(macrolet ((def (name result minus-result)
+             `(deftransform ,name ((x y) (t (constant-arg real)) *)
+                "fold identity operations"
+                (let ((val (lvar-value y)))
+                  (unless (and (= (abs val) 1)
+                               (not-more-contagious y x))
+                    (give-up-ir1-transform))
+                  (if (minusp val) ',minus-result ',result)))))
+  (def * x (%negate x))
+  (def / x (%negate x))
+  (def expt x (/ 1 x)))

 
 ;;; Fold (expt x n) into multiplications for small integral values of
 ;;; N; convert (expt x 1/2) to sqrt.
 
 ;;; Fold (expt x n) into multiplications for small integral values of
 ;;; N; convert (expt x 1/2) to sqrt.

-(deftransform expt ((x y) (t (constant-argument real)) *)
+(deftransform expt ((x y) (t (constant-arg real)) *)

   "recode as multiplication or sqrt"
   "recode as multiplication or sqrt"

-  (let ((val (continuation-value y)))
+  (let ((val (lvar-value y)))

     ;; If Y would cause the result to be promoted to the same type as
     ;; Y, we give up. If not, then the result will be the same type
     ;; as X, so we can replace the exponentiation with simple
     ;; multiplication and division for small integral powers.
     (unless (not-more-contagious y x)
       (give-up-ir1-transform))
     ;; If Y would cause the result to be promoted to the same type as
     ;; Y, we give up. If not, then the result will be the same type
     ;; as X, so we can replace the exponentiation with simple
     ;; multiplication and division for small integral powers.
     (unless (not-more-contagious y x)
       (give-up-ir1-transform))

-    (cond ((zerop val) '(float 1 x))
+    (cond ((zerop val)
+           (let ((x-type (lvar-type x)))
+             (cond ((csubtypep x-type (specifier-type '(or rational
+                                                        (complex rational))))
+                    '1)
+                   ((csubtypep x-type (specifier-type 'real))
+                    `(if (rationalp x)
+                         1
+                         (float 1 x)))
+                   ((csubtypep x-type (specifier-type 'complex))
+                    ;; both parts are float
+                    `(1+ (* x ,val)))
+                   (t (give-up-ir1-transform)))))

          ((= val 2) '(* x x))
          ((= val -2) '(/ (* x x)))
          ((= val 3) '(* x x x))
          ((= val 2) '(* x x))
          ((= val -2) '(/ (* x x)))
          ((= val 3) '(* x x x))

@@ -2999,18 +2871,24 @@
 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
 ;;; transformations?
 ;;; Perhaps we should have to prove that the denominator is nonzero before
 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
 ;;; transformations?
 ;;; Perhaps we should have to prove that the denominator is nonzero before

-;;; doing them? (Also the DOLIST over macro calls is weird. Perhaps
-;;; just FROB?) -- WHN 19990917
-(dolist (name '(ash /))
-  (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
-                     :eval-name t :when :both)
-    "fold zero arg"
-    0))
-(dolist (name '(truncate round floor ceiling))
-  (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
-                     :eval-name t :when :both)
-    "fold zero arg"
-    '(values 0 0)))
+;;; doing them?  -- WHN 19990917
+(macrolet ((def (name)
+             `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
+                                   *)
+                "fold zero arg"
+                0)))
+  (def ash)
+  (def /))
+
+(macrolet ((def (name)
+             `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
+                                   *)
+                "fold zero arg"
+                '(values 0 0))))
+  (def truncate)
+  (def round)
+  (def floor)
+  (def ceiling))

 \f
 ;;;; character operations
 
 \f
 ;;;; character operations
 

@@ -3042,62 +2920,68 @@
 \f
 ;;;; equality predicate transforms
 
 \f
 ;;;; equality predicate transforms
 

-;;; Return true if X and Y are continuations whose only use is a reference
-;;; to the same leaf, and the value of the leaf cannot change.
+;;; Return true if X and Y are lvars whose only use is a
+;;; reference to the same leaf, and the value of the leaf cannot
+;;; change.

 (defun same-leaf-ref-p (x y)
 (defun same-leaf-ref-p (x y)

-  (declare (type continuation x y))
-  (let ((x-use (continuation-use x))
-       (y-use (continuation-use y)))
+  (declare (type lvar x y))
+  (let ((x-use (principal-lvar-use x))
+       (y-use (principal-lvar-use y)))

     (and (ref-p x-use)
         (ref-p y-use)
         (eq (ref-leaf x-use) (ref-leaf y-use))
         (constant-reference-p x-use))))
 
     (and (ref-p x-use)
         (ref-p y-use)
         (eq (ref-leaf x-use) (ref-leaf y-use))
         (constant-reference-p x-use))))
 

-;;; If X and Y are the same leaf, then the result is true. Otherwise, if
-;;; there is no intersection between the types of the arguments, then the
-;;; result is definitely false.
-(deftransform simple-equality-transform ((x y) * * :defun-only t
-                                        :when :both)
+;;; If X and Y are the same leaf, then the result is true. Otherwise,
+;;; if there is no intersection between the types of the arguments,
+;;; then the result is definitely false.
+(deftransform simple-equality-transform ((x y) * *
+                                        :defun-only t)

   (cond ((same-leaf-ref-p x y)
   (cond ((same-leaf-ref-p x y)

-        't)
-       ((not (types-intersect (continuation-type x) (continuation-type y)))
-        'nil)
+        t)
+       ((not (types-equal-or-intersect (lvar-type x)
+                                       (lvar-type y)))
+        nil)

        (t
         (give-up-ir1-transform))))
 
        (t
         (give-up-ir1-transform))))
 

-(dolist (x '(eq char= equal))
-  (%deftransform x '(function * *) #'simple-equality-transform))
-
-;;; Similar to SIMPLE-EQUALITY-PREDICATE, except that we also try to convert
-;;; to a type-specific predicate or EQ:
-;;; -- If both args are characters, convert to CHAR=. This is better than just
-;;;    converting to EQ, since CHAR= may have special compilation strategies
-;;;    for non-standard representations, etc.
-;;; -- If either arg is definitely not a number, then we can compare with EQ.
-;;; -- Otherwise, we try to put the arg we know more about second. If X is
-;;;    constant then we put it second. If X is a subtype of Y, we put it
-;;;    second. These rules make it easier for the back end to match these
-;;;    interesting cases.
-;;; -- If Y is a fixnum, then we quietly pass because the back end can handle
-;;;    that case, otherwise give an efficency note.
-(deftransform eql ((x y) * * :when :both)
+(macrolet ((def (x)
+             `(%deftransform ',x '(function * *) #'simple-equality-transform)))
+  (def eq)
+  (def char=)
+  (def equal))
+
+;;; This is similar to SIMPLE-EQUALITY-PREDICATE, except that we also
+;;; try to convert to a type-specific predicate or EQ:
+;;; -- If both args are characters, convert to CHAR=. This is better than
+;;;    just converting to EQ, since CHAR= may have special compilation
+;;;    strategies for non-standard representations, etc.
+;;; -- If either arg is definitely not a number, then we can compare
+;;;    with EQ.
+;;; -- Otherwise, we try to put the arg we know more about second. If X
+;;;    is constant then we put it second. If X is a subtype of Y, we put
+;;;    it second. These rules make it easier for the back end to match
+;;;    these interesting cases.
+;;; -- If Y is a fixnum, then we quietly pass because the back end can
+;;;    handle that case, otherwise give an efficiency note.
+(deftransform eql ((x y) * *)

   "convert to simpler equality predicate"
   "convert to simpler equality predicate"

-  (let ((x-type (continuation-type x))
-       (y-type (continuation-type y))
+  (let ((x-type (lvar-type x))
+       (y-type (lvar-type y))

        (char-type (specifier-type 'character))
        (number-type (specifier-type 'number)))
     (cond ((same-leaf-ref-p x y)
        (char-type (specifier-type 'character))
        (number-type (specifier-type 'number)))
     (cond ((same-leaf-ref-p x y)

-          't)
-         ((not (types-intersect x-type y-type))
-          'nil)
+          t)
+         ((not (types-equal-or-intersect x-type y-type))
+          nil)

          ((and (csubtypep x-type char-type)
                (csubtypep y-type char-type))
           '(char= x y))
          ((and (csubtypep x-type char-type)
                (csubtypep y-type char-type))
           '(char= x y))

-         ((or (not (types-intersect x-type number-type))
-              (not (types-intersect y-type number-type)))
+         ((or (not (types-equal-or-intersect x-type number-type))
+              (not (types-equal-or-intersect y-type number-type)))

           '(eq x y))
           '(eq x y))

-         ((and (not (constant-continuation-p y))
-               (or (constant-continuation-p x)
+         ((and (not (constant-lvar-p y))
+               (or (constant-lvar-p x)

                    (and (csubtypep x-type y-type)
                         (not (csubtypep y-type x-type)))))
           '(eql y x))
                    (and (csubtypep x-type y-type)
                         (not (csubtypep y-type x-type)))))
           '(eql y x))

@@ -3106,10 +2990,10 @@
 
 ;;; Convert to EQL if both args are rational and complexp is specified
 ;;; and the same for both.
 
 ;;; Convert to EQL if both args are rational and complexp is specified
 ;;; and the same for both.

-(deftransform = ((x y) * * :when :both)
+(deftransform = ((x y) * *)

   "open code"
   "open code"

-  (let ((x-type (continuation-type x))
-       (y-type (continuation-type y)))
+  (let ((x-type (lvar-type x))
+       (y-type (lvar-type y)))

     (if (and (csubtypep x-type (specifier-type 'number))
             (csubtypep y-type (specifier-type 'number)))
        (cond ((or (and (csubtypep x-type (specifier-type 'float))
     (if (and (csubtypep x-type (specifier-type 'number))
             (csubtypep y-type (specifier-type 'number)))
        (cond ((or (and (csubtypep x-type (specifier-type 'float))

@@ -3121,10 +3005,12 @@
               (give-up-ir1-transform))
              ((or (and (csubtypep x-type (specifier-type 'rational))
                        (csubtypep y-type (specifier-type 'rational)))
               (give-up-ir1-transform))
              ((or (and (csubtypep x-type (specifier-type 'rational))
                        (csubtypep y-type (specifier-type 'rational)))

-                  (and (csubtypep x-type (specifier-type '(complex rational)))
-                       (csubtypep y-type (specifier-type '(complex rational)))))
-              ;; They are both rationals and complexp is the same. Convert
-              ;; to EQL.
+                  (and (csubtypep x-type
+                                  (specifier-type '(complex rational)))
+                       (csubtypep y-type
+                                  (specifier-type '(complex rational)))))
+              ;; They are both rationals and complexp is the same.
+              ;; Convert to EQL.

               '(eql x y))
              (t
               (give-up-ir1-transform
               '(eql x y))
              (t
               (give-up-ir1-transform

@@ -3132,69 +3018,57 @@
        (give-up-ir1-transform
         "The operands might not be the same type."))))
 
        (give-up-ir1-transform
         "The operands might not be the same type."))))
 

-;;; If Cont's type is a numeric type, then return the type, otherwise
+;;; If LVAR's type is a numeric type, then return the type, otherwise

 ;;; GIVE-UP-IR1-TRANSFORM.
 ;;; GIVE-UP-IR1-TRANSFORM.

-(defun numeric-type-or-lose (cont)
-  (declare (type continuation cont))
-  (let ((res (continuation-type cont)))
+(defun numeric-type-or-lose (lvar)
+  (declare (type lvar lvar))
+  (let ((res (lvar-type lvar)))

     (unless (numeric-type-p res) (give-up-ir1-transform))
     res))
 
     (unless (numeric-type-p res) (give-up-ir1-transform))
     res))
 

-;;; See whether we can statically determine (< X Y) using type information.
-;;; If X's high bound is < Y's low, then X < Y. Similarly, if X's low is >=
-;;; to Y's high, the X >= Y (so return NIL). If not, at least make sure any
-;;; constant arg is second.
-;;;
-;;; KLUDGE: Why should constant argument be second? It would be nice to find
-;;; out and explain. -- WHN 19990917
-#!-propagate-float-type
-(defun ir1-transform-< (x y first second inverse)
-  (if (same-leaf-ref-p x y)
-      'nil
-      (let* ((x-type (numeric-type-or-lose x))
-            (x-lo (numeric-type-low x-type))
-            (x-hi (numeric-type-high x-type))
-            (y-type (numeric-type-or-lose y))
-            (y-lo (numeric-type-low y-type))
-            (y-hi (numeric-type-high y-type)))
-       (cond ((and x-hi y-lo (< x-hi y-lo))
-              't)
-             ((and y-hi x-lo (>= x-lo y-hi))
-              'nil)
-             ((and (constant-continuation-p first)
-                   (not (constant-continuation-p second)))
-              `(,inverse y x))
-             (t
-              (give-up-ir1-transform))))))
-#!+propagate-float-type
-(defun ir1-transform-< (x y first second inverse)
-  (if (same-leaf-ref-p x y)
-      'nil
-      (let ((xi (numeric-type->interval (numeric-type-or-lose x)))
-           (yi (numeric-type->interval (numeric-type-or-lose y))))
-       (cond ((interval-< xi yi)
-              't)
-             ((interval->= xi yi)
-              'nil)
-             ((and (constant-continuation-p first)
-                   (not (constant-continuation-p second)))
-              `(,inverse y x))
-             (t
-              (give-up-ir1-transform))))))
-
-(deftransform < ((x y) (integer integer) * :when :both)
-  (ir1-transform-< x y x y '>))
-
-(deftransform > ((x y) (integer integer) * :when :both)
-  (ir1-transform-< y x x y '<))
-
-#!+propagate-float-type
-(deftransform < ((x y) (float float) * :when :both)
-  (ir1-transform-< x y x y '>))
-
-#!+propagate-float-type
-(deftransform > ((x y) (float float) * :when :both)
-  (ir1-transform-< y x x y '<))
+;;; See whether we can statically determine (< X Y) using type
+;;; information. If X's high bound is < Y's low, then X < Y.
+;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
+;;; NIL). If not, at least make sure any constant arg is second.
+(macrolet ((def (name inverse reflexive-p surely-true surely-false)
+             `(deftransform ,name ((x y))
+                (if (same-leaf-ref-p x y)
+                    ,reflexive-p
+                    (let ((ix (or (type-approximate-interval (lvar-type x))
+                                  (give-up-ir1-transform)))
+                          (iy (or (type-approximate-interval (lvar-type y))
+                                  (give-up-ir1-transform))))
+                      (cond (,surely-true
+                             t)
+                            (,surely-false
+                             nil)
+                            ((and (constant-lvar-p x)
+                                  (not (constant-lvar-p y)))
+                             `(,',inverse y x))
+                            (t
+                             (give-up-ir1-transform))))))))
+  (def < > nil (interval-< ix iy) (interval->= ix iy))
+  (def > < nil (interval-< iy ix) (interval->= iy ix))
+  (def <= >= t (interval->= iy ix) (interval-< iy ix))
+  (def >= <= t (interval->= ix iy) (interval-< ix iy)))
+
+(defun ir1-transform-char< (x y first second inverse)
+  (cond
+    ((same-leaf-ref-p x y) nil)
+    ;; If we had interval representation of character types, as we
+    ;; might eventually have to to support 2^21 characters, then here
+    ;; we could do some compile-time computation as in transforms for
+    ;; < above. -- CSR, 2003-07-01
+    ((and (constant-lvar-p first)
+         (not (constant-lvar-p second)))
+     `(,inverse y x))
+    (t (give-up-ir1-transform))))
+
+(deftransform char< ((x y) (character character) *)
+  (ir1-transform-char< x y x y 'char>))
+
+(deftransform char> ((x y) (character character) *)
+  (ir1-transform-char< y x x y 'char<))

 \f
 ;;;; converting N-arg comparisons
 ;;;;
 \f
 ;;;; converting N-arg comparisons
 ;;;;

@@ -3211,11 +3085,11 @@
 ;;; negated test as appropriate. If it is a degenerate one-arg call,
 ;;; then we transform to code that returns true. Otherwise, we bind
 ;;; all the arguments and expand into a bunch of IFs.
 ;;; negated test as appropriate. If it is a degenerate one-arg call,
 ;;; then we transform to code that returns true. Otherwise, we bind
 ;;; all the arguments and expand into a bunch of IFs.

-(declaim (ftype (function (symbol list boolean) *) multi-compare))
-(defun multi-compare (predicate args not-p)
+(declaim (ftype (function (symbol list boolean t) *) multi-compare))
+(defun multi-compare (predicate args not-p type)

   (let ((nargs (length args)))
     (cond ((< nargs 1) (values nil t))
   (let ((nargs (length args)))
     (cond ((< nargs 1) (values nil t))

-         ((= nargs 1) `(progn ,@args t))
+         ((= nargs 1) `(progn (the ,type ,@args) t))

          ((= nargs 2)
           (if not-p
               `(if (,predicate ,(first args) ,(second args)) nil t)
          ((= nargs 2)
           (if not-p
               `(if (,predicate ,(first args) ,(second args)) nil t)

@@ -3225,163 +3099,183 @@
                 (last nil current)
                 (current (gensym) (gensym))
                 (vars (list current) (cons current vars))
                 (last nil current)
                 (current (gensym) (gensym))
                 (vars (list current) (cons current vars))

-                (result 't (if not-p
-                               `(if (,predicate ,current ,last)
-                                    nil ,result)
-                               `(if (,predicate ,current ,last)
-                                    ,result nil))))
+                (result t (if not-p
+                              `(if (,predicate ,current ,last)
+                                   nil ,result)
+                              `(if (,predicate ,current ,last)
+                                   ,result nil))))

               ((zerop i)
               ((zerop i)

-               `((lambda ,vars ,result) . ,args)))))))
-
-(def-source-transform = (&rest args) (multi-compare '= args nil))
-(def-source-transform < (&rest args) (multi-compare '< args nil))
-(def-source-transform > (&rest args) (multi-compare '> args nil))
-(def-source-transform <= (&rest args) (multi-compare '> args t))
-(def-source-transform >= (&rest args) (multi-compare '< args t))
-
-(def-source-transform char= (&rest args) (multi-compare 'char= args nil))
-(def-source-transform char< (&rest args) (multi-compare 'char< args nil))
-(def-source-transform char> (&rest args) (multi-compare 'char> args nil))
-(def-source-transform char<= (&rest args) (multi-compare 'char> args t))
-(def-source-transform char>= (&rest args) (multi-compare 'char< args t))
-
-(def-source-transform char-equal (&rest args) (multi-compare 'char-equal args nil))
-(def-source-transform char-lessp (&rest args) (multi-compare 'char-lessp args nil))
-(def-source-transform char-greaterp (&rest args) (multi-compare 'char-greaterp args nil))
-(def-source-transform char-not-greaterp (&rest args) (multi-compare 'char-greaterp args t))
-(def-source-transform char-not-lessp (&rest args) (multi-compare 'char-lessp args t))
+               `((lambda ,vars (declare (type ,type ,@vars)) ,result)
+                  ,@args)))))))
+
+(define-source-transform = (&rest args) (multi-compare '= args nil 'number))
+(define-source-transform < (&rest args) (multi-compare '< args nil 'real))
+(define-source-transform > (&rest args) (multi-compare '> args nil 'real))
+(define-source-transform <= (&rest args) (multi-compare '> args t 'real))
+(define-source-transform >= (&rest args) (multi-compare '< args t 'real))
+
+(define-source-transform char= (&rest args) (multi-compare 'char= args nil
+                                                           'character))
+(define-source-transform char< (&rest args) (multi-compare 'char< args nil
+                                                           'character))
+(define-source-transform char> (&rest args) (multi-compare 'char> args nil
+                                                           'character))
+(define-source-transform char<= (&rest args) (multi-compare 'char> args t
+                                                            'character))
+(define-source-transform char>= (&rest args) (multi-compare 'char< args t
+                                                            'character))
+
+(define-source-transform char-equal (&rest args)
+  (multi-compare 'char-equal args nil 'character))
+(define-source-transform char-lessp (&rest args)
+  (multi-compare 'char-lessp args nil 'character))
+(define-source-transform char-greaterp (&rest args)
+  (multi-compare 'char-greaterp args nil 'character))
+(define-source-transform char-not-greaterp (&rest args)
+  (multi-compare 'char-greaterp args t 'character))
+(define-source-transform char-not-lessp (&rest args)
+  (multi-compare 'char-lessp args t 'character))

 
 ;;; This function does source transformation of N-arg inequality
 
 ;;; This function does source transformation of N-arg inequality

-;;; functions such as /=. This is similar to Multi-Compare in the <3
+;;; functions such as /=. This is similar to MULTI-COMPARE in the <3

 ;;; arg cases. If there are more than two args, then we expand into
 ;;; the appropriate n^2 comparisons only when speed is important.
 ;;; arg cases. If there are more than two args, then we expand into
 ;;; the appropriate n^2 comparisons only when speed is important.

-(declaim (ftype (function (symbol list) *) multi-not-equal))
-(defun multi-not-equal (predicate args)
+(declaim (ftype (function (symbol list t) *) multi-not-equal))
+(defun multi-not-equal (predicate args type)

   (let ((nargs (length args)))
     (cond ((< nargs 1) (values nil t))
   (let ((nargs (length args)))
     (cond ((< nargs 1) (values nil t))

-         ((= nargs 1) `(progn ,@args t))
+         ((= nargs 1) `(progn (the ,type ,@args) t))

          ((= nargs 2)
           `(if (,predicate ,(first args) ,(second args)) nil t))
          ((= nargs 2)
           `(if (,predicate ,(first args) ,(second args)) nil t))

-         ((not (policy nil (>= speed space) (>= speed cspeed)))
+         ((not (policy *lexenv*
+                       (and (>= speed space)
+                            (>= speed compilation-speed))))

           (values nil t))
          (t
           (let ((vars (make-gensym-list nargs)))
             (do ((var vars next)
                  (next (cdr vars) (cdr next))
           (values nil t))
          (t
           (let ((vars (make-gensym-list nargs)))
             (do ((var vars next)
                  (next (cdr vars) (cdr next))

-                 (result 't))
+                 (result t))

                 ((null next)
                 ((null next)

-                 `((lambda ,vars ,result) . ,args))
+                 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
+                    ,@args))

               (let ((v1 (first var)))
                 (dolist (v2 next)
                   (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
 
               (let ((v1 (first var)))
                 (dolist (v2 next)
                   (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
 

-(def-source-transform /= (&rest args) (multi-not-equal '= args))
-(def-source-transform char/= (&rest args) (multi-not-equal 'char= args))
-(def-source-transform char-not-equal (&rest args) (multi-not-equal 'char-equal args))
+(define-source-transform /= (&rest args)
+  (multi-not-equal '= args 'number))
+(define-source-transform char/= (&rest args)
+  (multi-not-equal 'char= args 'character))
+(define-source-transform char-not-equal (&rest args)
+  (multi-not-equal 'char-equal args 'character))

 
 ;;; Expand MAX and MIN into the obvious comparisons.
 
 ;;; Expand MAX and MIN into the obvious comparisons.

-(def-source-transform max (arg &rest more-args)
-  (if (null more-args)
-      `(values ,arg)
-      (once-only ((arg1 arg)
-                 (arg2 `(max ,@more-args)))
-       `(if (> ,arg1 ,arg2)
-            ,arg1 ,arg2))))
-(def-source-transform min (arg &rest more-args)
-  (if (null more-args)
-      `(values ,arg)
-      (once-only ((arg1 arg)
-                 (arg2 `(min ,@more-args)))
-       `(if (< ,arg1 ,arg2)
-            ,arg1 ,arg2))))
+(define-source-transform max (arg0 &rest rest)
+  (once-only ((arg0 arg0))
+    (if (null rest)
+       `(values (the real ,arg0))
+       `(let ((maxrest (max ,@rest)))
+         (if (> ,arg0 maxrest) ,arg0 maxrest)))))
+(define-source-transform min (arg0 &rest rest)
+  (once-only ((arg0 arg0))
+    (if (null rest)
+       `(values (the real ,arg0))
+       `(let ((minrest (min ,@rest)))
+         (if (< ,arg0 minrest) ,arg0 minrest)))))

 \f
 ;;;; converting N-arg arithmetic functions
 ;;;;
 ;;;; N-arg arithmetic and logic functions are associated into two-arg
 ;;;; versions, and degenerate cases are flushed.
 
 \f
 ;;;; converting N-arg arithmetic functions
 ;;;;
 ;;;; N-arg arithmetic and logic functions are associated into two-arg
 ;;;; versions, and degenerate cases are flushed.
 

-;;; Left-associate First-Arg and More-Args using Function.
-(declaim (ftype (function (symbol t list) list) associate-arguments))
-(defun associate-arguments (function first-arg more-args)
+;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
+(declaim (ftype (function (symbol t list) list) associate-args))
+(defun associate-args (function first-arg more-args)

   (let ((next (rest more-args))
        (arg (first more-args)))
     (if (null next)
        `(,function ,first-arg ,arg)
   (let ((next (rest more-args))
        (arg (first more-args)))
     (if (null next)
        `(,function ,first-arg ,arg)

-       (associate-arguments function `(,function ,first-arg ,arg) next))))
+       (associate-args function `(,function ,first-arg ,arg) next))))

 
 ;;; Do source transformations for transitive functions such as +.
 ;;; One-arg cases are replaced with the arg and zero arg cases with
 
 ;;; Do source transformations for transitive functions such as +.
 ;;; One-arg cases are replaced with the arg and zero arg cases with

-;;; the identity. If Leaf-Fun is true, then replace two-arg calls with
-;;; a call to that function.
-(defun source-transform-transitive (fun args identity &optional leaf-fun)
-  (declare (symbol fun leaf-fun) (list args))
+;;; the identity.  ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
+;;; ensure (with THE) that the argument in one-argument calls is.
+(defun source-transform-transitive (fun args identity
+                                   &optional one-arg-result-type)
+  (declare (symbol fun) (list args))

   (case (length args)
     (0 identity)
   (case (length args)
     (0 identity)

-    (1 `(values ,(first args)))
-    (2 (if leaf-fun
-          `(,leaf-fun ,(first args) ,(second args))
-          (values nil t)))
+    (1 (if one-arg-result-type
+          `(values (the ,one-arg-result-type ,(first args)))
+          `(values ,(first args))))
+    (2 (values nil t))

     (t
     (t

-     (associate-arguments fun (first args) (rest args)))))
-
-(def-source-transform + (&rest args) (source-transform-transitive '+ args 0))
-(def-source-transform * (&rest args) (source-transform-transitive '* args 1))
-(def-source-transform logior (&rest args) (source-transform-transitive 'logior args 0))
-(def-source-transform logxor (&rest args) (source-transform-transitive 'logxor args 0))
-(def-source-transform logand (&rest args) (source-transform-transitive 'logand args -1))
-
-(def-source-transform logeqv (&rest args)
-  (if (evenp (length args))
-      `(lognot (logxor ,@args))
-      `(logxor ,@args)))
+     (associate-args fun (first args) (rest args)))))
+
+(define-source-transform + (&rest args)
+  (source-transform-transitive '+ args 0 'number))
+(define-source-transform * (&rest args)
+  (source-transform-transitive '* args 1 'number))
+(define-source-transform logior (&rest args)
+  (source-transform-transitive 'logior args 0 'integer))
+(define-source-transform logxor (&rest args)
+  (source-transform-transitive 'logxor args 0 'integer))
+(define-source-transform logand (&rest args)
+  (source-transform-transitive 'logand args -1 'integer))
+(define-source-transform logeqv (&rest args)
+  (source-transform-transitive 'logeqv args -1 'integer))

 
 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
 ;;; because when they are given one argument, they return its absolute
 ;;; value.
 
 
 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
 ;;; because when they are given one argument, they return its absolute
 ;;; value.
 

-(def-source-transform gcd (&rest args)
+(define-source-transform gcd (&rest args)

   (case (length args)
     (0 0)
     (1 `(abs (the integer ,(first args))))
     (2 (values nil t))
   (case (length args)
     (0 0)
     (1 `(abs (the integer ,(first args))))
     (2 (values nil t))

-    (t (associate-arguments 'gcd (first args) (rest args)))))
+    (t (associate-args 'gcd (first args) (rest args)))))

 
 

-(def-source-transform lcm (&rest args)
+(define-source-transform lcm (&rest args)

   (case (length args)
     (0 1)
     (1 `(abs (the integer ,(first args))))
     (2 (values nil t))
   (case (length args)
     (0 1)
     (1 `(abs (the integer ,(first args))))
     (2 (values nil t))

-    (t (associate-arguments 'lcm (first args) (rest args)))))
+    (t (associate-args 'lcm (first args) (rest args)))))

 
 ;;; Do source transformations for intransitive n-arg functions such as
 ;;; /. With one arg, we form the inverse. With two args we pass.
 ;;; Otherwise we associate into two-arg calls.
 
 ;;; Do source transformations for intransitive n-arg functions such as
 ;;; /. With one arg, we form the inverse. With two args we pass.
 ;;; Otherwise we associate into two-arg calls.

-(declaim (ftype (function (symbol list t) list) source-transform-intransitive))
+(declaim (ftype (function (symbol list t)
+                          (values list &optional (member nil t)))
+                source-transform-intransitive))

 (defun source-transform-intransitive (function args inverse)
   (case (length args)
     ((0 2) (values nil t))
     (1 `(,@inverse ,(first args)))
 (defun source-transform-intransitive (function args inverse)
   (case (length args)
     ((0 2) (values nil t))
     (1 `(,@inverse ,(first args)))

-    (t (associate-arguments function (first args) (rest args)))))
+    (t (associate-args function (first args) (rest args)))))

 
 

-(def-source-transform - (&rest args)
+(define-source-transform - (&rest args)

   (source-transform-intransitive '- args '(%negate)))
   (source-transform-intransitive '- args '(%negate)))

-(def-source-transform / (&rest args)
+(define-source-transform / (&rest args)

   (source-transform-intransitive '/ args '(/ 1)))
 \f
   (source-transform-intransitive '/ args '(/ 1)))
 \f

-;;;; APPLY
+;;;; transforming APPLY

 
 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
 ;;; only needs to understand one kind of variable-argument call. It is
 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
 
 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
 ;;; only needs to understand one kind of variable-argument call. It is
 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.

-(def-source-transform apply (fun arg &rest more-args)
+(define-source-transform apply (fun arg &rest more-args)

   (let ((args (cons arg more-args)))
     `(multiple-value-call ,fun
   (let ((args (cons arg more-args)))
     `(multiple-value-call ,fun

-       ,@(mapcar #'(lambda (x)
-                    `(values ,x))
+       ,@(mapcar (lambda (x)
+                  `(values ,x))

                 (butlast args))
        (values-list ,(car (last args))))))
 \f
                 (butlast args))
        (values-list ,(car (last args))))))
 \f

-;;;; FORMAT
+;;;; transforming FORMAT

 ;;;;
 ;;;; If the control string is a compile-time constant, then replace it
 ;;;; with a use of the FORMATTER macro so that the control string is
 ;;;;
 ;;;; If the control string is a compile-time constant, then replace it
 ;;;; with a use of the FORMATTER macro so that the control string is

@@ -3389,14 +3283,57 @@
 ;;;; or T and the control string is a function (i.e. FORMATTER), then
 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
 
 ;;;; or T and the control string is a function (i.e. FORMATTER), then
 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
 

+;;; for compile-time argument count checking.
+;;;
+;;; FIXME I: this is currently called from DEFTRANSFORMs, the vast
+;;; majority of which are not going to transform the code, but instead
+;;; are going to GIVE-UP-IR1-TRANSFORM unconditionally.  It would be
+;;; nice to make this explicit, maybe by implementing a new
+;;; "optimizer" (say, DEFOPTIMIZER CONSISTENCY-CHECK).
+;;;
+;;; FIXME II: In some cases, type information could be correlated; for
+;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
+;;; of a corresponding argument is known and does not intersect the
+;;; list type, a warning could be signalled.
+(defun check-format-args (string args fun)
+  (declare (type string string))
+  (unless (typep string 'simple-string)
+    (setq string (coerce string 'simple-string)))
+  (multiple-value-bind (min max)
+      (handler-case (sb!format:%compiler-walk-format-string string args)
+       (sb!format:format-error (c)
+         (compiler-warn "~A" c)))
+    (when min
+      (let ((nargs (length args)))
+       (cond
+         ((< nargs min)
+          (compiler-warn "Too few arguments (~D) to ~S ~S: ~
+                           requires at least ~D."
+                         nargs fun string min))
+         ((> nargs max)
+          (;; to get warned about probably bogus code at
+           ;; cross-compile time.
+           #+sb-xc-host compiler-warn
+           ;; ANSI saith that too many arguments doesn't cause a
+           ;; run-time error.
+           #-sb-xc-host compiler-style-warn
+           "Too many arguments (~D) to ~S ~S: uses at most ~D."
+           nargs fun string max)))))))
+
+(defoptimizer (format optimizer) ((dest control &rest args))
+  (when (constant-lvar-p control)
+    (let ((x (lvar-value control)))
+      (when (stringp x)
+       (check-format-args x args 'format)))))
+

 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
                      :policy (> speed space))
 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
                      :policy (> speed space))

-  (unless (constant-continuation-p control)
+  (unless (constant-lvar-p control)

     (give-up-ir1-transform "The control string is not a constant."))
   (let ((arg-names (make-gensym-list (length args))))
     `(lambda (dest control ,@arg-names)
        (declare (ignore control))
     (give-up-ir1-transform "The control string is not a constant."))
   (let ((arg-names (make-gensym-list (length args))))
     `(lambda (dest control ,@arg-names)
        (declare (ignore control))

-       (format dest (formatter ,(continuation-value control)) ,@arg-names))))
+       (format dest (formatter ,(lvar-value control)) ,@arg-names))))

 
 (deftransform format ((stream control &rest args) (stream function &rest t) *
                      :policy (> speed space))
 
 (deftransform format ((stream control &rest args) (stream function &rest t) *
                      :policy (> speed space))

@@ -3412,3 +3349,339 @@
        (declare (ignore tee))
        (funcall control *standard-output* ,@arg-names)
        nil)))
        (declare (ignore tee))
        (funcall control *standard-output* ,@arg-names)
        nil)))

+
+(macrolet
+    ((def (name)
+        `(defoptimizer (,name optimizer) ((control &rest args))
+           (when (constant-lvar-p control)
+             (let ((x (lvar-value control)))
+               (when (stringp x)
+                 (check-format-args x args ',name)))))))
+  (def error)
+  (def warn)
+  #+sb-xc-host ; Only we should be using these
+  (progn
+    (def style-warn)
+    (def compiler-abort)
+    (def compiler-error)
+    (def compiler-warn)
+    (def compiler-style-warn)
+    (def compiler-notify)
+    (def maybe-compiler-notify)
+    (def bug)))
+
+(defoptimizer (cerror optimizer) ((report control &rest args))
+  (when (and (constant-lvar-p control)
+            (constant-lvar-p report))
+    (let ((x (lvar-value control))
+         (y (lvar-value report)))
+      (when (and (stringp x) (stringp y))
+       (multiple-value-bind (min1 max1)
+           (handler-case
+               (sb!format:%compiler-walk-format-string x args)
+             (sb!format:format-error (c)
+               (compiler-warn "~A" c)))
+         (when min1
+           (multiple-value-bind (min2 max2)
+               (handler-case
+                   (sb!format:%compiler-walk-format-string y args)
+                 (sb!format:format-error (c)
+                   (compiler-warn "~A" c)))
+             (when min2
+               (let ((nargs (length args)))
+                 (cond
+                   ((< nargs (min min1 min2))
+                    (compiler-warn "Too few arguments (~D) to ~S ~S ~S: ~
+                                     requires at least ~D."
+                                   nargs 'cerror y x (min min1 min2)))
+                   ((> nargs (max max1 max2))
+                    (;; to get warned about probably bogus code at
+                     ;; cross-compile time.
+                     #+sb-xc-host compiler-warn
+                     ;; ANSI saith that too many arguments doesn't cause a
+                     ;; run-time error.
+                     #-sb-xc-host compiler-style-warn
+                     "Too many arguments (~D) to ~S ~S ~S: uses at most ~D."
+                     nargs 'cerror y x (max max1 max2)))))))))))))
+
+(defoptimizer (coerce derive-type) ((value type))
+  (cond
+    ((constant-lvar-p type)
+     ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
+     ;; but dealing with the niggle that complex canonicalization gets
+     ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
+     ;; type COMPLEX.
+     (let* ((specifier (lvar-value type))
+           (result-typeoid (careful-specifier-type specifier)))
+       (cond
+        ((null result-typeoid) nil)
+        ((csubtypep result-typeoid (specifier-type 'number))
+         ;; the difficult case: we have to cope with ANSI 12.1.5.3
+         ;; Rule of Canonical Representation for Complex Rationals,
+         ;; which is a truly nasty delivery to field.
+         (cond
+           ((csubtypep result-typeoid (specifier-type 'real))
+            ;; cleverness required here: it would be nice to deduce
+            ;; that something of type (INTEGER 2 3) coerced to type
+            ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
+            ;; FLOAT gets its own clause because it's implemented as
+            ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
+            ;; logic below.
+            result-typeoid)
+           ((and (numeric-type-p result-typeoid)
+                 (eq (numeric-type-complexp result-typeoid) :real))
+            ;; FIXME: is this clause (a) necessary or (b) useful?
+            result-typeoid)
+           ((or (csubtypep result-typeoid
+                           (specifier-type '(complex single-float)))
+                (csubtypep result-typeoid
+                           (specifier-type '(complex double-float)))
+                #!+long-float
+                (csubtypep result-typeoid
+                           (specifier-type '(complex long-float))))
+            ;; float complex types are never canonicalized.
+            result-typeoid)
+           (t
+            ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
+            ;; probably just a COMPLEX or equivalent.  So, in that
+            ;; case, we will return a complex or an object of the
+            ;; provided type if it's rational:
+            (type-union result-typeoid
+                        (type-intersection (lvar-type value)
+                                           (specifier-type 'rational))))))
+        (t result-typeoid))))
+    (t
+     ;; OK, the result-type argument isn't constant.  However, there
+     ;; are common uses where we can still do better than just
+     ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
+     ;; where Y is of a known type.  See messages on cmucl-imp
+     ;; 2001-02-14 and sbcl-devel 2002-12-12.  We only worry here
+     ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
+     ;; the basis that it's unlikely that other uses are both
+     ;; time-critical and get to this branch of the COND (non-constant
+     ;; second argument to COERCE).  -- CSR, 2002-12-16
+     (let ((value-type (lvar-type value))
+          (type-type (lvar-type type)))
+       (labels
+          ((good-cons-type-p (cons-type)
+             ;; Make sure the cons-type we're looking at is something
+             ;; we're prepared to handle which is basically something
+             ;; that array-element-type can return.
+             (or (and (member-type-p cons-type)
+                      (null (rest (member-type-members cons-type)))
+                      (null (first (member-type-members cons-type))))
+                 (let ((car-type (cons-type-car-type cons-type)))
+                   (and (member-type-p car-type)
+                        (null (rest (member-type-members car-type)))
+                        (or (symbolp (first (member-type-members car-type)))
+                            (numberp (first (member-type-members car-type)))
+                            (and (listp (first (member-type-members
+                                                car-type)))
+                                 (numberp (first (first (member-type-members
+                                                         car-type))))))
+                        (good-cons-type-p (cons-type-cdr-type cons-type))))))
+           (unconsify-type (good-cons-type)
+             ;; Convert the "printed" respresentation of a cons
+             ;; specifier into a type specifier.  That is, the
+             ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
+             ;; NULL)) is converted to (SIGNED-BYTE 16).
+             (cond ((or (null good-cons-type)
+                        (eq good-cons-type 'null))
+                    nil)
+                   ((and (eq (first good-cons-type) 'cons)
+                         (eq (first (second good-cons-type)) 'member))
+                    `(,(second (second good-cons-type))
+                      ,@(unconsify-type (caddr good-cons-type))))))
+           (coerceable-p (c-type)
+             ;; Can the value be coerced to the given type?  Coerce is
+             ;; complicated, so we don't handle every possible case
+             ;; here---just the most common and easiest cases:
+             ;;
+             ;; * Any REAL can be coerced to a FLOAT type.
+             ;; * Any NUMBER can be coerced to a (COMPLEX
+             ;;   SINGLE/DOUBLE-FLOAT).
+             ;;
+             ;; FIXME I: we should also be able to deal with characters
+             ;; here.
+             ;;
+             ;; FIXME II: I'm not sure that anything is necessary
+             ;; here, at least while COMPLEX is not a specialized
+             ;; array element type in the system.  Reasoning: if
+             ;; something cannot be coerced to the requested type, an
+             ;; error will be raised (and so any downstream compiled
+             ;; code on the assumption of the returned type is
+             ;; unreachable).  If something can, then it will be of
+             ;; the requested type, because (by assumption) COMPLEX
+             ;; (and other difficult types like (COMPLEX INTEGER)
+             ;; aren't specialized types.
+             (let ((coerced-type c-type))
+               (or (and (subtypep coerced-type 'float)
+                        (csubtypep value-type (specifier-type 'real)))
+                   (and (subtypep coerced-type
+                                  '(or (complex single-float)
+                                       (complex double-float)))
+                        (csubtypep value-type (specifier-type 'number))))))
+           (process-types (type)
+             ;; FIXME: This needs some work because we should be able
+             ;; to derive the resulting type better than just the
+             ;; type arg of coerce.  That is, if X is (INTEGER 10
+             ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
+             ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
+             ;; double-float.
+             (cond ((member-type-p type)
+                    (let ((members (member-type-members type)))
+                      (if (every #'coerceable-p members)
+                          (specifier-type `(or ,@members))
+                          *universal-type*)))
+                   ((and (cons-type-p type)
+                         (good-cons-type-p type))
+                    (let ((c-type (unconsify-type (type-specifier type))))
+                      (if (coerceable-p c-type)
+                          (specifier-type c-type)
+                          *universal-type*)))
+                   (t
+                    *universal-type*))))
+        (cond ((union-type-p type-type)
+               (apply #'type-union (mapcar #'process-types
+                                           (union-type-types type-type))))
+              ((or (member-type-p type-type)
+                   (cons-type-p type-type))
+               (process-types type-type))
+              (t
+               *universal-type*)))))))
+
+(defoptimizer (compile derive-type) ((nameoid function))
+  (when (csubtypep (lvar-type nameoid)
+                  (specifier-type 'null))
+    (values-specifier-type '(values function boolean boolean))))
+
+;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
+;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
+;;; optimizer, above).
+(defoptimizer (array-element-type derive-type) ((array))
+  (let ((array-type (lvar-type array)))
+    (labels ((consify (list)
+              (if (endp list)
+                  '(eql nil)
+                  `(cons (eql ,(car list)) ,(consify (rest list)))))
+            (get-element-type (a)
+              (let ((element-type
+                    (type-specifier (array-type-specialized-element-type a))))
+                (cond ((eq element-type '*)
+                       (specifier-type 'type-specifier))
+                     ((symbolp element-type)
+                       (make-member-type :members (list element-type)))
+                      ((consp element-type)
+                       (specifier-type (consify element-type)))
+                      (t
+                       (error "can't understand type ~S~%" element-type))))))
+      (cond ((array-type-p array-type)
+            (get-element-type array-type))
+           ((union-type-p array-type)
+             (apply #'type-union
+                    (mapcar #'get-element-type (union-type-types array-type))))
+           (t
+            *universal-type*)))))
+
+(define-source-transform sb!impl::sort-vector (vector start end predicate key)
+  `(macrolet ((%index (x) `(truly-the index ,x))
+             (%parent (i) `(ash ,i -1))
+             (%left (i) `(%index (ash ,i 1)))
+             (%right (i) `(%index (1+ (ash ,i 1))))
+             (%heapify (i)
+              `(do* ((i ,i)
+                     (left (%left i) (%left i)))
+                ((> left current-heap-size))
+                (declare (type index i left))
+                (let* ((i-elt (%elt i))
+                       (i-key (funcall keyfun i-elt))
+                       (left-elt (%elt left))
+                       (left-key (funcall keyfun left-elt)))
+                  (multiple-value-bind (large large-elt large-key)
+                      (if (funcall ,',predicate i-key left-key)
+                          (values left left-elt left-key)
+                          (values i i-elt i-key))
+                    (let ((right (%right i)))
+                      (multiple-value-bind (largest largest-elt)
+                          (if (> right current-heap-size)
+                              (values large large-elt)
+                              (let* ((right-elt (%elt right))
+                                     (right-key (funcall keyfun right-elt)))
+                                (if (funcall ,',predicate large-key right-key)
+                                    (values right right-elt)
+                                    (values large large-elt))))
+                        (cond ((= largest i)
+                               (return))
+                              (t
+                               (setf (%elt i) largest-elt
+                                     (%elt largest) i-elt
+                                     i largest)))))))))
+             (%sort-vector (keyfun &optional (vtype 'vector))
+              `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had trouble getting
+                          ;; type inference to propagate all the way
+                          ;; through this tangled mess of
+                          ;; inlining. The TRULY-THE here works
+                          ;; around that. -- WHN
+                          (%elt (i)
+                           `(aref (truly-the ,',vtype ,',',vector)
+                             (%index (+ (%index ,i) start-1)))))
+                (let ((start-1 (1- ,',start)) ; Heaps prefer 1-based addressing.
+                      (current-heap-size (- ,',end ,',start))
+                      (keyfun ,keyfun))
+                  (declare (type (integer -1 #.(1- most-positive-fixnum))
+                                 start-1))
+                  (declare (type index current-heap-size))
+                  (declare (type function keyfun))
+                  (loop for i of-type index
+                        from (ash current-heap-size -1) downto 1 do
+                        (%heapify i))
+                  (loop
+                   (when (< current-heap-size 2)
+                     (return))
+                   (rotatef (%elt 1) (%elt current-heap-size))
+                   (decf current-heap-size)
+                   (%heapify 1))))))
+    (if (typep ,vector 'simple-vector)
+       ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
+       ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
+       (if (null ,key)
+           ;; Special-casing the KEY=NIL case lets us avoid some
+           ;; function calls.
+           (%sort-vector #'identity simple-vector)
+           (%sort-vector ,key simple-vector))
+       ;; It's hard to anticipate many speed-critical applications for
+       ;; sorting vector types other than (VECTOR T), so we just lump
+       ;; them all together in one slow dynamically typed mess.
+       (locally
+         (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
+         (%sort-vector (or ,key #'identity))))))
+\f
+;;;; debuggers' little helpers
+
+;;; for debugging when transforms are behaving mysteriously,
+;;; e.g. when debugging a problem with an ASH transform
+;;;   (defun foo (&optional s)
+;;;     (sb-c::/report-lvar s "S outside WHEN")
+;;;     (when (and (integerp s) (> s 3))
+;;;       (sb-c::/report-lvar s "S inside WHEN")
+;;;       (let ((bound (ash 1 (1- s))))
+;;;         (sb-c::/report-lvar bound "BOUND")
+;;;         (let ((x (- bound))
+;;;              (y (1- bound)))
+;;;          (sb-c::/report-lvar x "X")
+;;;           (sb-c::/report-lvar x "Y"))
+;;;         `(integer ,(- bound) ,(1- bound)))))
+;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
+;;; and the function doesn't do anything at all.)
+#!+sb-show
+(progn
+  (defknown /report-lvar (t t) null)
+  (deftransform /report-lvar ((x message) (t t))
+    (format t "~%/in /REPORT-LVAR~%")
+    (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
+    (when (constant-lvar-p x)
+      (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
+    (format t "/MESSAGE=~S~%" (lvar-value message))
+    (give-up-ir1-transform "not a real transform"))
+  (defun /report-lvar (x message)
+    (declare (ignore x message))))