Fix negation of SIMD-PACK types

[sbcl.git] / src / code / late-type.lisp

diff --git a/src/code/late-type.lisp b/src/code/late-type.lisp
index 799d6e9..04a93f2 100644 (file)
--- a/src/code/late-type.lisp
+++ b/src/code/late-type.lisp
@@ -30,18 +30,6 @@
 (define-condition parse-unknown-type (condition)
   ((specifier :reader parse-unknown-type-specifier :initarg :specifier)))
 
 (define-condition parse-unknown-type (condition)
   ((specifier :reader parse-unknown-type-specifier :initarg :specifier)))
 

-;;; FIXME: This really should go away. Alas, it doesn't seem to be so
-;;; simple to make it go away.. (See bug 123 in BUGS file.)
-(defvar *use-implementation-types* t ; actually initialized in cold init
-  #!+sb-doc
-  "*USE-IMPLEMENTATION-TYPES* is a semi-public flag which determines how
-   restrictive we are in determining type membership. If two types are the
-   same in the implementation, then we will consider them them the same when
-   this switch is on. When it is off, we try to be as restrictive as the
-   language allows, allowing us to detect more errors. Currently, this only
-   affects array types.")
-(!cold-init-forms (setq *use-implementation-types* t))
-

 ;;; These functions are used as method for types which need a complex
 ;;; subtypep method to handle some superclasses, but cover a subtree
 ;;; of the type graph (i.e. there is no simple way for any other type
 ;;; These functions are used as method for types which need a complex
 ;;; subtypep method to handle some superclasses, but cover a subtree
 ;;; of the type graph (i.e. there is no simple way for any other type

@@ -50,16 +38,16 @@
 ;;; chance to run, instead of immediately returning NIL, T.
 (defun delegate-complex-subtypep-arg2 (type1 type2)
   (let ((subtypep-arg1
 ;;; chance to run, instead of immediately returning NIL, T.
 (defun delegate-complex-subtypep-arg2 (type1 type2)
   (let ((subtypep-arg1

-        (type-class-complex-subtypep-arg1
-         (type-class-info type1))))
+         (type-class-complex-subtypep-arg1
+          (type-class-info type1))))

     (if subtypep-arg1
     (if subtypep-arg1

-       (funcall subtypep-arg1 type1 type2)
-       (values nil t))))
+        (funcall subtypep-arg1 type1 type2)
+        (values nil t))))

 (defun delegate-complex-intersection2 (type1 type2)
   (let ((method (type-class-complex-intersection2 (type-class-info type1))))
     (if (and method (not (eq method #'delegate-complex-intersection2)))
 (defun delegate-complex-intersection2 (type1 type2)
   (let ((method (type-class-complex-intersection2 (type-class-info type1))))
     (if (and method (not (eq method #'delegate-complex-intersection2)))

-       (funcall method type2 type1)
-       (hierarchical-intersection2 type1 type2))))
+        (funcall method type2 type1)
+        (hierarchical-intersection2 type1 type2))))

 
 ;;; This is used by !DEFINE-SUPERCLASSES to define the SUBTYPE-ARG1
 ;;; method. INFO is a list of conses
 
 ;;; This is used by !DEFINE-SUPERCLASSES to define the SUBTYPE-ARG1
 ;;; method. INFO is a list of conses

@@ -77,16 +65,16 @@
        ;; FIXME: This old CMU CL code probably deserves a comment
        ;; explaining to us mere mortals how it works...
        (and (sb!xc:typep type2 'classoid)
        ;; FIXME: This old CMU CL code probably deserves a comment
        ;; explaining to us mere mortals how it works...
        (and (sb!xc:typep type2 'classoid)

-           (dolist (x info nil)
-             (when (or (not (cdr x))
-                       (csubtypep type1 (specifier-type (cdr x))))
-               (return
-                (or (eq type2 (car x))
-                    (let ((inherits (layout-inherits
-                                     (classoid-layout (car x)))))
-                      (dotimes (i (length inherits) nil)
-                        (when (eq type2 (layout-classoid (svref inherits i)))
-                          (return t)))))))))
+            (dolist (x info nil)
+              (when (or (not (cdr x))
+                        (csubtypep type1 (specifier-type (cdr x))))
+                (return
+                 (or (eq type2 (car x))
+                     (let ((inherits (layout-inherits
+                                      (classoid-layout (car x)))))
+                       (dotimes (i (length inherits) nil)
+                         (when (eq type2 (layout-classoid (svref inherits i)))
+                           (return t)))))))))

        t)))
 
 ;;; This function takes a list of specs, each of the form
        t)))
 
 ;;; This function takes a list of specs, each of the form

@@ -105,19 +93,19 @@
   (with-unique-names (type-class info)
     `(,when
        (let ((,type-class (type-class-or-lose ',type-class-name))
   (with-unique-names (type-class info)
     `(,when
        (let ((,type-class (type-class-or-lose ',type-class-name))

-            (,info (mapcar (lambda (spec)
-                             (destructuring-bind
-                                 (super &optional guard)
-                                 spec
-                               (cons (find-classoid super) guard)))
-                           ',specs)))
-        (setf (type-class-complex-subtypep-arg1 ,type-class)
-              (lambda (type1 type2)
-                (!has-superclasses-complex-subtypep-arg1 type1 type2 ,info)))
-        (setf (type-class-complex-subtypep-arg2 ,type-class)
-              #'delegate-complex-subtypep-arg2)
-        (setf (type-class-complex-intersection2 ,type-class)
-              #'delegate-complex-intersection2)))))
+             (,info (mapcar (lambda (spec)
+                              (destructuring-bind
+                                  (super &optional guard)
+                                  spec
+                                (cons (find-classoid super) guard)))
+                            ',specs)))
+         (setf (type-class-complex-subtypep-arg1 ,type-class)
+               (lambda (type1 type2)
+                 (!has-superclasses-complex-subtypep-arg1 type1 type2 ,info)))
+         (setf (type-class-complex-subtypep-arg2 ,type-class)
+               #'delegate-complex-subtypep-arg2)
+         (setf (type-class-complex-intersection2 ,type-class)
+               #'delegate-complex-intersection2)))))

 \f
 ;;;; FUNCTION and VALUES types
 ;;;;
 \f
 ;;;; FUNCTION and VALUES types
 ;;;;

@@ -137,20 +125,20 @@
 
 ;;; the description of a &KEY argument
 (defstruct (key-info #-sb-xc-host (:pure t)
 
 ;;; the description of a &KEY argument
 (defstruct (key-info #-sb-xc-host (:pure t)

-                    (:copier nil))
+                     (:copier nil))

   ;; the key (not necessarily a keyword in ANSI Common Lisp)
   (name (missing-arg) :type symbol)
   ;; the type of the argument value
   (type (missing-arg) :type ctype))
 
 (!define-type-method (values :simple-subtypep :complex-subtypep-arg1)
   ;; the key (not necessarily a keyword in ANSI Common Lisp)
   (name (missing-arg) :type symbol)
   ;; the type of the argument value
   (type (missing-arg) :type ctype))
 
 (!define-type-method (values :simple-subtypep :complex-subtypep-arg1)

-                    (type1 type2)
+                     (type1 type2)

   (declare (ignore type2))
   ;; FIXME: should be TYPE-ERROR, here and in next method
   (error "SUBTYPEP is illegal on this type:~%  ~S" (type-specifier type1)))
 
 (!define-type-method (values :complex-subtypep-arg2)
   (declare (ignore type2))
   ;; FIXME: should be TYPE-ERROR, here and in next method
   (error "SUBTYPEP is illegal on this type:~%  ~S" (type-specifier type1)))
 
 (!define-type-method (values :complex-subtypep-arg2)

-                    (type1 type2)
+                     (type1 type2)

   (declare (ignore type1))
   (error "SUBTYPEP is illegal on this type:~%  ~S" (type-specifier type2)))
 
   (declare (ignore type1))
   (error "SUBTYPEP is illegal on this type:~%  ~S" (type-specifier type2)))
 

@@ -175,14 +163,14 @@
        (types2 list2 (cdr types2)))
       ((or (null types1) (null types2))
        (if (or types1 types2)
        (types2 list2 (cdr types2)))
       ((or (null types1) (null types2))
        (if (or types1 types2)

-          (values nil t)
-          (values t t)))
+           (values nil t)
+           (values t t)))

     (multiple-value-bind (val win)
     (multiple-value-bind (val win)

-       (type= (first types1) (first types2))
+        (type= (first types1) (first types2))

       (unless win
       (unless win

-       (return (values nil nil)))
+        (return (values nil nil)))

       (unless val
       (unless val

-       (return (values nil t))))))
+        (return (values nil t))))))

 
 (!define-type-method (values :simple-=) (type1 type2)
   (type=-args type1 type2))
 
 (!define-type-method (values :simple-=) (type1 type2)
   (type=-args type1 type2))

@@ -196,17 +184,17 @@
 (!cold-init-forms (setq *unparse-fun-type-simplify* nil))
 
 (!define-type-method (function :negate) (type)
 (!cold-init-forms (setq *unparse-fun-type-simplify* nil))
 
 (!define-type-method (function :negate) (type)

-  (error "NOT FUNCTION too confusing on ~S" (type-specifier type)))
+  (make-negation-type :type type))

 
 (!define-type-method (function :unparse) (type)
   (if *unparse-fun-type-simplify*
       'function
       (list 'function
 
 (!define-type-method (function :unparse) (type)
   (if *unparse-fun-type-simplify*
       'function
       (list 'function

-           (if (fun-type-wild-args type)
-               '*
-               (unparse-args-types type))
-           (type-specifier
-            (fun-type-returns type)))))
+            (if (fun-type-wild-args type)
+                '*
+                (unparse-args-types type))
+            (type-specifier
+             (fun-type-returns type)))))

 
 ;;; The meaning of this is a little confused. On the one hand, all
 ;;; function objects are represented the same way regardless of the
 
 ;;; The meaning of this is a little confused. On the one hand, all
 ;;; function objects are represented the same way regardless of the

@@ -232,13 +220,13 @@
                     (cond ((fun-type-keyp type2) (values nil nil))
                           ((not (fun-type-rest type2)) (values nil t))
                           ((not (null (fun-type-required type2)))
                     (cond ((fun-type-keyp type2) (values nil nil))
                           ((not (fun-type-rest type2)) (values nil t))
                           ((not (null (fun-type-required type2)))

-                          (values nil t))
+                           (values nil t))

                           (t (and/type (type= *universal-type*
                           (t (and/type (type= *universal-type*

-                                             (fun-type-rest type2))
+                                              (fun-type-rest type2))

                                        (every/type #'type=
                                        (every/type #'type=

-                                                  *universal-type*
+                                                   *universal-type*

                                                    (fun-type-optional
                                                    (fun-type-optional

-                                                   type2))))))
+                                                    type2))))))

                    ((not (and (fun-type-simple-p type1)
                               (fun-type-simple-p type2)))
                     (values nil nil))
                    ((not (and (fun-type-simple-p type1)
                               (fun-type-simple-p type2)))
                     (values nil nil))

@@ -248,11 +236,11 @@
                                  (values nil t))
                                 ((and (= min1 min2) (= max1 max2))
                                  (and/type (every-csubtypep
                                  (values nil t))
                                 ((and (= min1 min2) (= max1 max2))
                                  (and/type (every-csubtypep

-                                           (fun-type-required type1)
-                                           (fun-type-required type2))
+                                            (fun-type-required type1)
+                                            (fun-type-required type2))

                                            (every-csubtypep
                                            (every-csubtypep

-                                           (fun-type-optional type1)
-                                           (fun-type-optional type2))))
+                                            (fun-type-optional type1)
+                                            (fun-type-optional type2))))

                                 (t (every-csubtypep
                                     (concatenate 'list
                                                  (fun-type-required type1)
                                 (t (every-csubtypep
                                     (concatenate 'list
                                                  (fun-type-required type1)

@@ -307,6 +295,10 @@
     ((csubtypep type1 (specifier-type 'function)) nil)
     (t :call-other-method)))
 (!define-type-method (function :complex-union2) (type1 type2)
     ((csubtypep type1 (specifier-type 'function)) nil)
     (t :call-other-method)))
 (!define-type-method (function :complex-union2) (type1 type2)

+  (declare (ignore type2))
+  ;; TYPE2 is a FUNCTION type.  If TYPE1 is a classoid type naming
+  ;; FUNCTION, then it is the union of the two; otherwise, there is no
+  ;; special union.

   (cond
     ((type= type1 (specifier-type 'function)) type1)
     (t nil)))
   (cond
     ((type= type1 (specifier-type 'function)) type1)
     (t nil)))

@@ -348,7 +340,7 @@
     (when (args-type-optional type)
       (result '&optional)
       (dolist (arg (args-type-optional type))
     (when (args-type-optional type)
       (result '&optional)
       (dolist (arg (args-type-optional type))

-       (result (type-specifier arg))))
+        (result (type-specifier arg))))

 
     (when (args-type-rest type)
       (result '&rest)
 
     (when (args-type-rest type)
       (result '&rest)

@@ -357,8 +349,8 @@
     (when (args-type-keyp type)
       (result '&key)
       (dolist (key (args-type-keywords type))
     (when (args-type-keyp type)
       (result '&key)
       (dolist (key (args-type-keywords type))

-       (result (list (key-info-name key)
-                     (type-specifier (key-info-type key))))))
+        (result (list (key-info-name key)
+                      (type-specifier (key-info-type key))))))

 
     (when (args-type-allowp type)
       (result '&allow-other-keys))
 
     (when (args-type-allowp type)
       (result '&allow-other-keys))

@@ -366,19 +358,83 @@
     (result)))
 
 (!def-type-translator function (&optional (args '*) (result '*))
     (result)))
 
 (!def-type-translator function (&optional (args '*) (result '*))

-  (make-fun-type :args args
-                 :returns (coerce-to-values (values-specifier-type result))))
+  (let ((result (coerce-to-values (values-specifier-type result))))
+    (if (eq args '*)
+        (if (eq result *wild-type*)
+            (specifier-type 'function)
+            (make-fun-type :wild-args t :returns result))
+        (multiple-value-bind (required optional rest keyp keywords allowp)
+            (parse-args-types args)
+          (if (and (null required)
+                   (null optional)
+                   (eq rest *universal-type*)
+                   (not keyp))
+              (if (eq result *wild-type*)
+                  (specifier-type 'function)
+                  (make-fun-type :wild-args t :returns result))
+              (make-fun-type :required required
+                             :optional optional
+                             :rest rest
+                             :keyp keyp
+                             :keywords keywords
+                             :allowp allowp
+                             :returns result))))))

 
 (!def-type-translator values (&rest values)
 
 (!def-type-translator values (&rest values)

-  (make-values-type :args values))
+  (if (eq values '*)
+      *wild-type*
+      (multiple-value-bind (required optional rest keyp keywords allowp llk-p)
+          (parse-args-types values)
+        (declare (ignore keywords))
+        (cond (keyp
+               (error "&KEY appeared in a VALUES type specifier ~S."
+                      `(values ,@values)))
+              (llk-p
+               (make-values-type :required required
+                                 :optional optional
+                                 :rest rest
+                                 :allowp allowp))
+              (t
+               (make-short-values-type required))))))

 \f
 ;;;; VALUES types interfaces
 ;;;;
 ;;;; We provide a few special operations that can be meaningfully used
 ;;;; on VALUES types (as well as on any other type).
 
 \f
 ;;;; VALUES types interfaces
 ;;;;
 ;;;; We provide a few special operations that can be meaningfully used
 ;;;; on VALUES types (as well as on any other type).
 

+;;; Return the minimum number of values possibly matching VALUES type
+;;; TYPE.
+(defun values-type-min-value-count (type)
+  (etypecase type
+    (named-type
+     (ecase (named-type-name type)
+       ((t *) 0)
+       ((nil) 0)))
+    (values-type
+     (length (values-type-required type)))))
+
+;;; Return the maximum number of values possibly matching VALUES type
+;;; TYPE.
+(defun values-type-max-value-count (type)
+  (etypecase type
+    (named-type
+     (ecase (named-type-name type)
+       ((t *) call-arguments-limit)
+       ((nil) 0)))
+    (values-type
+     (if (values-type-rest type)
+         call-arguments-limit
+         (+ (length (values-type-optional type))
+            (length (values-type-required type)))))))
+
+(defun values-type-may-be-single-value-p (type)
+  (<= (values-type-min-value-count type)
+      1
+      (values-type-max-value-count type)))
+
+;;; VALUES type with a single value.

 (defun type-single-value-p (type)
 (defun type-single-value-p (type)

-  (and (values-type-p type)
+  (and (%values-type-p type)

        (not (values-type-rest type))
        (null (values-type-optional type))
        (singleton-p (values-type-required type))))
        (not (values-type-rest type))
        (null (values-type-optional type))
        (singleton-p (values-type-required type))))

@@ -395,10 +451,11 @@
          *empty-type*)
         ((not (values-type-p type))
          type)
          *empty-type*)
         ((not (values-type-p type))
          type)

-        (t (or (car (args-type-required type))
-               (car (args-type-optional type))
-               (args-type-rest type)
-               (specifier-type 'null)))))
+        ((car (args-type-required type)))
+        (t (type-union (specifier-type 'null)
+                       (or (car (args-type-optional type))
+                           (args-type-rest type)
+                           (specifier-type 'null))))))

 
 ;;; Return the minimum number of arguments that a function can be
 ;;; called with, and the maximum number or NIL. If not a function
 
 ;;; Return the minimum number of arguments that a function can be
 ;;; called with, and the maximum number or NIL. If not a function

@@ -407,11 +464,11 @@
   (declare (type ctype type))
   (if (and (fun-type-p type) (not (fun-type-wild-args type)))
       (let ((fixed (length (args-type-required type))))
   (declare (type ctype type))
   (if (and (fun-type-p type) (not (fun-type-wild-args type)))
       (let ((fixed (length (args-type-required type))))

-       (if (or (args-type-rest type)
-               (args-type-keyp type)
-               (args-type-allowp type))
-           (values fixed nil)
-           (values fixed (+ fixed (length (args-type-optional type))))))
+        (if (or (args-type-rest type)
+                (args-type-keyp type)
+                (args-type-allowp type))
+            (values fixed nil)
+            (values fixed (+ fixed (length (args-type-optional type))))))

       (values nil nil)))
 
 ;;; Determine whether TYPE corresponds to a definite number of values.
       (values nil nil)))
 
 ;;; Determine whether TYPE corresponds to a definite number of values.

@@ -421,13 +478,13 @@
 (defun values-types (type)
   (declare (type ctype type))
   (cond ((or (eq type *wild-type*) (eq type *empty-type*))
 (defun values-types (type)
   (declare (type ctype type))
   (cond ((or (eq type *wild-type*) (eq type *empty-type*))

-        (values nil :unknown))
-       ((or (args-type-optional type)
-            (args-type-rest type))
-        (values nil :unknown))
-       (t
-        (let ((req (args-type-required type)))
-          (values req (length req))))))
+         (values nil :unknown))
+        ((or (args-type-optional type)
+             (args-type-rest type))
+         (values nil :unknown))
+        (t
+         (let ((req (args-type-required type)))
+           (values req (length req))))))

 
 ;;; Return two values:
 ;;; 1. A list of all the positional (fixed and optional) types.
 
 ;;; Return two values:
 ;;; 1. A list of all the positional (fixed and optional) types.

@@ -491,16 +548,16 @@
   (declare (list types1 types2) (type ctype rest2) (type function operation))
   (let ((exact t))
     (values (mapcar (lambda (t1 t2)
   (declare (list types1 types2) (type ctype rest2) (type function operation))
   (let ((exact t))
     (values (mapcar (lambda (t1 t2)

-                     (multiple-value-bind (res win)
-                         (funcall operation t1 t2)
-                       (unless win
-                         (setq exact nil))
-                       res))
-                   types1
-                   (append types2
-                           (make-list (- (length types1) (length types2))
-                                      :initial-element rest2)))
-           exact)))
+                      (multiple-value-bind (res win)
+                          (funcall operation t1 t2)
+                        (unless win
+                          (setq exact nil))
+                        res))
+                    types1
+                    (append types2
+                            (make-list (- (length types1) (length types2))
+                                       :initial-element rest2)))
+            exact)))

 
 ;;; If TYPE isn't a values type, then make it into one.
 (defun-cached (%coerce-to-values
 
 ;;; If TYPE isn't a values type, then make it into one.
 (defun-cached (%coerce-to-values

@@ -569,7 +626,7 @@
 ;;; second value being true doesn't mean the result is exact.
 (defun args-type-op (type1 type2 operation nreq)
   (declare (type ctype type1 type2)
 ;;; second value being true doesn't mean the result is exact.
 (defun args-type-op (type1 type2 operation nreq)
   (declare (type ctype type1 type2)

-          (type function operation nreq))
+           (type function operation nreq))

   (when (eq type1 type2)
     (values type1 t))
   (multiple-value-bind (types1 rest1)
   (when (eq type1 type2)
     (values type1 t))
   (multiple-value-bind (types1 rest1)

@@ -598,6 +655,19 @@
                               :rest rest)
             exactp)))
 
                               :rest rest)
             exactp)))
 

+(defun compare-key-args (type1 type2)
+  (let ((keys1 (args-type-keywords type1))
+        (keys2 (args-type-keywords type2)))
+    (and (= (length keys1) (length keys2))
+         (eq (args-type-allowp type1)
+             (args-type-allowp type2))
+         (loop for key1 in keys1
+               for match = (find (key-info-name key1)
+                                 keys2 :key #'key-info-name)
+               always (and match
+                           (type= (key-info-type key1)
+                                  (key-info-type match)))))))
+

 (defun type=-args (type1 type2)
   (macrolet ((compare (comparator field)
                (let ((reader (symbolicate '#:args-type- field)))
 (defun type=-args (type1 type2)
   (macrolet ((compare (comparator field)
                (let ((reader (symbolicate '#:args-type- field)))

@@ -612,7 +682,7 @@
      (and/type (and/type (compare type=-list required)
                          (compare type=-list optional))
                (if (or (args-type-keyp type1) (args-type-keyp type2))
      (and/type (and/type (compare type=-list required)
                          (compare type=-list optional))
                (if (or (args-type-keyp type1) (args-type-keyp type2))

-                   (values nil nil)
+                   (values (compare-key-args type1 type2) t)

                    (values t t))))))
 
 ;;; Do a union or intersection operation on types that might be values
                    (values t t))))))
 
 ;;; Do a union or intersection operation on types that might be values

@@ -623,9 +693,9 @@
 ;;; The return convention seems to be analogous to
 ;;; TYPES-EQUAL-OR-INTERSECT. -- WHN 19990910.
 (defun-cached (values-type-union :hash-function type-cache-hash
 ;;; The return convention seems to be analogous to
 ;;; TYPES-EQUAL-OR-INTERSECT. -- WHN 19990910.
 (defun-cached (values-type-union :hash-function type-cache-hash

-                                :hash-bits 8
-                                :default nil
-                                :init-wrapper !cold-init-forms)
+                                 :hash-bits 8
+                                 :default nil
+                                 :init-wrapper !cold-init-forms)

     ((type1 eq) (type2 eq))
   (declare (type ctype type1 type2))
   (cond ((or (eq type1 *wild-type*) (eq type2 *wild-type*)) *wild-type*)
     ((type1 eq) (type2 eq))
   (declare (type ctype type1 type2))
   (cond ((or (eq type1 *wild-type*) (eq type2 *wild-type*)) *wild-type*)

@@ -635,9 +705,9 @@
          (values (values-type-op type1 type2 #'type-union #'min)))))
 
 (defun-cached (values-type-intersection :hash-function type-cache-hash
          (values (values-type-op type1 type2 #'type-union #'min)))))
 
 (defun-cached (values-type-intersection :hash-function type-cache-hash

-                                       :hash-bits 8
-                                       :default (values nil)
-                                       :init-wrapper !cold-init-forms)
+                                        :hash-bits 8
+                                        :default (values nil)
+                                        :init-wrapper !cold-init-forms)

     ((type1 eq) (type2 eq))
   (declare (type ctype type1 type2))
   (cond ((eq type1 *wild-type*)
     ((type1 eq) (type2 eq))
   (declare (type ctype type1 type2))
   (cond ((eq type1 *wild-type*)

@@ -665,21 +735,21 @@
 ;;; there isn't really any intersection.
 (defun values-types-equal-or-intersect (type1 type2)
   (cond ((or (eq type1 *empty-type*) (eq type2 *empty-type*))
 ;;; there isn't really any intersection.
 (defun values-types-equal-or-intersect (type1 type2)
   (cond ((or (eq type1 *empty-type*) (eq type2 *empty-type*))

-        (values t t))
+         (values t t))

         ((or (eq type1 *wild-type*) (eq type2 *wild-type*))
          (values t t))
         ((or (eq type1 *wild-type*) (eq type2 *wild-type*))
          (values t t))

-       (t
-        (let ((res (values-type-intersection type1 type2)))
-          (values (not (eq res *empty-type*))
-                  t)))))
+        (t
+         (let ((res (values-type-intersection type1 type2)))
+           (values (not (eq res *empty-type*))
+                   t)))))

 
 ;;; a SUBTYPEP-like operation that can be used on any types, including
 ;;; VALUES types
 (defun-cached (values-subtypep :hash-function type-cache-hash
 
 ;;; a SUBTYPEP-like operation that can be used on any types, including
 ;;; VALUES types
 (defun-cached (values-subtypep :hash-function type-cache-hash

-                              :hash-bits 8
-                              :values 2
-                              :default (values nil :empty)
-                              :init-wrapper !cold-init-forms)
+                               :hash-bits 8
+                               :values 2
+                               :default (values nil :empty)
+                               :init-wrapper !cold-init-forms)

     ((type1 eq) (type2 eq))
   (declare (type ctype type1 type2))
   (cond ((or (eq type2 *wild-type*) (eq type2 *universal-type*)
     ((type1 eq) (type2 eq))
   (declare (type ctype type1 type2))
   (cond ((or (eq type2 *wild-type*) (eq type2 *universal-type*)

@@ -718,23 +788,23 @@
 
 ;;; like SUBTYPEP, only works on CTYPE structures
 (defun-cached (csubtypep :hash-function type-cache-hash
 
 ;;; like SUBTYPEP, only works on CTYPE structures
 (defun-cached (csubtypep :hash-function type-cache-hash

-                        :hash-bits 8
-                        :values 2
-                        :default (values nil :empty)
-                        :init-wrapper !cold-init-forms)
-             ((type1 eq) (type2 eq))
+                         :hash-bits 8
+                         :values 2
+                         :default (values nil :empty)
+                         :init-wrapper !cold-init-forms)
+              ((type1 eq) (type2 eq))

   (declare (type ctype type1 type2))
   (cond ((or (eq type1 type2)
   (declare (type ctype type1 type2))
   (cond ((or (eq type1 type2)

-            (eq type1 *empty-type*)
-            (eq type2 *universal-type*))
-        (values t t))
+             (eq type1 *empty-type*)
+             (eq type2 *universal-type*))
+         (values t t))

         #+nil
         #+nil

-       ((eq type1 *universal-type*)
-        (values nil t))
-       (t
-        (!invoke-type-method :simple-subtypep :complex-subtypep-arg2
-                             type1 type2
-                             :complex-arg1 :complex-subtypep-arg1))))
+        ((eq type1 *universal-type*)
+         (values nil t))
+        (t
+         (!invoke-type-method :simple-subtypep :complex-subtypep-arg2
+                              type1 type2
+                              :complex-arg1 :complex-subtypep-arg1))))

 
 ;;; Just parse the type specifiers and call CSUBTYPE.
 (defun sb!xc:subtypep (type1 type2 &optional environment)
 
 ;;; Just parse the type specifiers and call CSUBTYPE.
 (defun sb!xc:subtypep (type1 type2 &optional environment)

@@ -750,11 +820,11 @@
 ;;; value indicates whether the first value is definitely correct.
 ;;; This should only fail in the presence of HAIRY types.
 (defun-cached (type= :hash-function type-cache-hash
 ;;; value indicates whether the first value is definitely correct.
 ;;; This should only fail in the presence of HAIRY types.
 (defun-cached (type= :hash-function type-cache-hash

-                    :hash-bits 8
-                    :values 2
-                    :default (values nil :empty)
-                    :init-wrapper !cold-init-forms)
-             ((type1 eq) (type2 eq))
+                     :hash-bits 8
+                     :values 2
+                     :default (values nil :empty)
+                     :init-wrapper !cold-init-forms)
+              ((type1 eq) (type2 eq))

   (declare (type ctype type1 type2))
   (if (eq type1 type2)
       (values t t)
   (declare (type ctype type1 type2))
   (if (eq type1 type2)
       (values t t)

@@ -767,8 +837,8 @@
   (declare (type ctype type1 type2))
   (multiple-value-bind (res win) (type= type1 type2)
     (if win
   (declare (type ctype type1 type2))
   (multiple-value-bind (res win) (type= type1 type2)
     (if win

-       (values (not res) t)
-       (values nil nil))))
+        (values (not res) t)
+        (values nil nil))))

 
 ;;; the type method dispatch case of TYPE-UNION2
 (defun %type-union2 (type1 type2)
 
 ;;; the type method dispatch case of TYPE-UNION2
 (defun %type-union2 (type1 type2)

@@ -779,12 +849,12 @@
   ;; %TYPE-INTERSECTION2, there seems to be no need to distinguish
   ;; between not finding a method and having a method return NIL.
   (flet ((1way (x y)
   ;; %TYPE-INTERSECTION2, there seems to be no need to distinguish
   ;; between not finding a method and having a method return NIL.
   (flet ((1way (x y)

-          (!invoke-type-method :simple-union2 :complex-union2
-                               x y
-                               :default nil)))
+           (!invoke-type-method :simple-union2 :complex-union2
+                                x y
+                                :default nil)))

     (declare (inline 1way))
     (or (1way type1 type2)
     (declare (inline 1way))
     (or (1way type1 type2)

-       (1way type2 type1))))
+        (1way type2 type1))))

 
 ;;; Find a type which includes both types. Any inexactness is
 ;;; represented by the fuzzy element types; we return a single value
 
 ;;; Find a type which includes both types. Any inexactness is
 ;;; represented by the fuzzy element types; we return a single value

@@ -792,27 +862,33 @@
 ;;; simplified into the canonical form, thus is not a UNION-TYPE
 ;;; unless we find no other way to represent the result.
 (defun-cached (type-union2 :hash-function type-cache-hash
 ;;; simplified into the canonical form, thus is not a UNION-TYPE
 ;;; unless we find no other way to represent the result.
 (defun-cached (type-union2 :hash-function type-cache-hash

-                          :hash-bits 8
-                          :init-wrapper !cold-init-forms)
-             ((type1 eq) (type2 eq))
+                           :hash-bits 8
+                           :init-wrapper !cold-init-forms)
+              ((type1 eq) (type2 eq))

   ;; KLUDGE: This was generated from TYPE-INTERSECTION2 by Ye Olde Cut And
   ;; Paste technique of programming. If it stays around (as opposed to
   ;; e.g. fading away in favor of some CLOS solution) the shared logic
   ;; should probably become shared code. -- WHN 2001-03-16
   (declare (type ctype type1 type2))
   ;; KLUDGE: This was generated from TYPE-INTERSECTION2 by Ye Olde Cut And
   ;; Paste technique of programming. If it stays around (as opposed to
   ;; e.g. fading away in favor of some CLOS solution) the shared logic
   ;; should probably become shared code. -- WHN 2001-03-16
   (declare (type ctype type1 type2))

-  (cond ((eq type1 type2)
-        type1)
-       ((csubtypep type1 type2) type2)
-       ((csubtypep type2 type1) type1)
-       ((or (union-type-p type1)
-            (union-type-p type2))
-        ;; Unions of UNION-TYPE should have the UNION-TYPE-TYPES
-        ;; values broken out and united separately. The full TYPE-UNION
-        ;; function knows how to do this, so let it handle it.
-        (type-union type1 type2))
-       (t
-        ;; the ordinary case: we dispatch to type methods
-        (%type-union2 type1 type2))))
+  (let ((t2 nil))
+    (cond ((eq type1 type2)
+           type1)
+          ;; CSUBTYPEP for array-types answers questions about the
+          ;; specialized type, yet for union we want to take the
+          ;; expressed type in account too.
+          ((and (not (and (array-type-p type1) (array-type-p type2)))
+                (or (setf t2 (csubtypep type1 type2))
+                    (csubtypep type2 type1)))
+           (if t2 type2 type1))
+         ((or (union-type-p type1)
+              (union-type-p type2))
+          ;; Unions of UNION-TYPE should have the UNION-TYPE-TYPES
+          ;; values broken out and united separately. The full TYPE-UNION
+          ;; function knows how to do this, so let it handle it.
+          (type-union type1 type2))
+         (t
+          ;; the ordinary case: we dispatch to type methods
+          (%type-union2 type1 type2)))))

 
 ;;; the type method dispatch case of TYPE-INTERSECTION2
 (defun %type-intersection2 (type1 type2)
 
 ;;; the type method dispatch case of TYPE-INTERSECTION2
 (defun %type-intersection2 (type1 type2)

@@ -833,43 +909,42 @@
   ;;
   ;; (Why yes, CLOS probably *would* be nicer..)
   (flet ((1way (x y)
   ;;
   ;; (Why yes, CLOS probably *would* be nicer..)
   (flet ((1way (x y)

-          (!invoke-type-method :simple-intersection2 :complex-intersection2
-                               x y
-                               :default :call-other-method)))
+           (!invoke-type-method :simple-intersection2 :complex-intersection2
+                                x y
+                                :default :call-other-method)))

     (declare (inline 1way))
     (let ((xy (1way type1 type2)))
       (or (and (not (eql xy :call-other-method)) xy)
     (declare (inline 1way))
     (let ((xy (1way type1 type2)))
       (or (and (not (eql xy :call-other-method)) xy)

-         (let ((yx (1way type2 type1)))
-           (or (and (not (eql yx :call-other-method)) yx)
-               (cond ((and (eql xy :call-other-method)
-                           (eql yx :call-other-method))
-                      *empty-type*)
-                     (t
-                      (aver (and (not xy) (not yx))) ; else handled above
-                      nil))))))))
+          (let ((yx (1way type2 type1)))
+            (or (and (not (eql yx :call-other-method)) yx)
+                (cond ((and (eql xy :call-other-method)
+                            (eql yx :call-other-method))
+                       *empty-type*)
+                      (t
+                       nil))))))))

 
 (defun-cached (type-intersection2 :hash-function type-cache-hash
 
 (defun-cached (type-intersection2 :hash-function type-cache-hash

-                                 :hash-bits 8
-                                 :values 1
-                                 :default nil
-                                 :init-wrapper !cold-init-forms)
-             ((type1 eq) (type2 eq))
+                                  :hash-bits 8
+                                  :values 1
+                                  :default nil
+                                  :init-wrapper !cold-init-forms)
+              ((type1 eq) (type2 eq))

   (declare (type ctype type1 type2))
   (cond ((eq type1 type2)
   (declare (type ctype type1 type2))
   (cond ((eq type1 type2)

-        ;; FIXME: For some reason, this doesn't catch e.g. type1 =
-        ;; type2 = (SPECIFIER-TYPE
-        ;; 'SOME-UNKNOWN-TYPE). Investigate. - CSR, 2002-04-10
-        type1)
-       ((or (intersection-type-p type1)
-            (intersection-type-p type2))
-        ;; Intersections of INTERSECTION-TYPE should have the
-        ;; INTERSECTION-TYPE-TYPES values broken out and intersected
-        ;; separately. The full TYPE-INTERSECTION function knows how
-        ;; to do that, so let it handle it.
-        (type-intersection type1 type2))
-       (t
-        ;; the ordinary case: we dispatch to type methods
-        (%type-intersection2 type1 type2))))
+         ;; FIXME: For some reason, this doesn't catch e.g. type1 =
+         ;; type2 = (SPECIFIER-TYPE
+         ;; 'SOME-UNKNOWN-TYPE). Investigate. - CSR, 2002-04-10
+         type1)
+        ((or (intersection-type-p type1)
+             (intersection-type-p type2))
+         ;; Intersections of INTERSECTION-TYPE should have the
+         ;; INTERSECTION-TYPE-TYPES values broken out and intersected
+         ;; separately. The full TYPE-INTERSECTION function knows how
+         ;; to do that, so let it handle it.
+         (type-intersection type1 type2))
+        (t
+         ;; the ordinary case: we dispatch to type methods
+         (%type-intersection2 type1 type2))))

 
 ;;; Return as restrictive and simple a type as we can discover that is
 ;;; no more restrictive than the intersection of TYPE1 and TYPE2. At
 
 ;;; Return as restrictive and simple a type as we can discover that is
 ;;; no more restrictive than the intersection of TYPE1 and TYPE2. At

@@ -877,8 +952,8 @@
 ;;; value (trying not to return a hairy type).
 (defun type-approx-intersection2 (type1 type2)
   (cond ((type-intersection2 type1 type2))
 ;;; value (trying not to return a hairy type).
 (defun type-approx-intersection2 (type1 type2)
   (cond ((type-intersection2 type1 type2))

-       ((hairy-type-p type1) type2)
-       (t type1)))
+        ((hairy-type-p type1) type2)
+        (t type1)))

 
 ;;; a test useful for checking whether a derived type matches a
 ;;; declared type
 
 ;;; a test useful for checking whether a derived type matches a
 ;;; declared type

@@ -893,13 +968,13 @@
   (if (or (eq type1 *empty-type*) (eq type2 *empty-type*))
       (values t t)
       (let ((intersection2 (type-intersection2 type1 type2)))
   (if (or (eq type1 *empty-type*) (eq type2 *empty-type*))
       (values t t)
       (let ((intersection2 (type-intersection2 type1 type2)))

-       (cond ((not intersection2)
-              (if (or (csubtypep *universal-type* type1)
-                      (csubtypep *universal-type* type2))
-                  (values t t)
-                  (values t nil)))
-             ((eq intersection2 *empty-type*) (values nil t))
-             (t (values t t))))))
+        (cond ((not intersection2)
+               (if (or (csubtypep *universal-type* type1)
+                       (csubtypep *universal-type* type2))
+                   (values t t)
+                   (values t nil)))
+              ((eq intersection2 *empty-type*) (values nil t))
+              (t (values t t))))))

 
 ;;; Return a Common Lisp type specifier corresponding to the TYPE
 ;;; object.
 
 ;;; Return a Common Lisp type specifier corresponding to the TYPE
 ;;; object.

@@ -908,16 +983,30 @@
   (funcall (type-class-unparse (type-class-info type)) type))
 
 (defun-cached (type-negation :hash-function (lambda (type)
   (funcall (type-class-unparse (type-class-info type)) type))
 
 (defun-cached (type-negation :hash-function (lambda (type)

-                                             (logand (type-hash-value type)
-                                                     #xff))
-                            :hash-bits 8
-                            :values 1
-                            :default nil
-                            :init-wrapper !cold-init-forms)
+                                              (logand (type-hash-value type)
+                                                      #xff))
+                             :hash-bits 8
+                             :values 1
+                             :default nil
+                             :init-wrapper !cold-init-forms)

               ((type eq))
   (declare (type ctype type))
   (funcall (type-class-negate (type-class-info type)) type))
 
               ((type eq))
   (declare (type ctype type))
   (funcall (type-class-negate (type-class-info type)) type))
 

+(defun-cached (type-singleton-p :hash-function (lambda (type)
+                                              (logand (type-hash-value type)
+                                                      #xff))
+                             :hash-bits 8
+                             :values 2
+                             :default (values nil t)
+                             :init-wrapper !cold-init-forms)
+              ((type eq))
+  (declare (type ctype type))
+  (let ((function (type-class-singleton-p (type-class-info type))))
+    (if function
+        (funcall function type)
+        (values nil nil))))
+

 ;;; (VALUES-SPECIFIER-TYPE and SPECIFIER-TYPE moved from here to
 ;;; early-type.lisp by WHN ca. 19990201.)
 
 ;;; (VALUES-SPECIFIER-TYPE and SPECIFIER-TYPE moved from here to
 ;;; early-type.lisp by WHN ca. 19990201.)
 

@@ -928,18 +1017,18 @@
   (dolist (spec specs)
     (let ((res (specifier-type spec)))
       (unless (unknown-type-p res)
   (dolist (spec specs)
     (let ((res (specifier-type spec)))
       (unless (unknown-type-p res)

-       (setf (info :type :builtin spec) res)
-       ;; KLUDGE: the three copies of this idiom in this file (and
-       ;; the one in class.lisp as at sbcl-0.7.4.1x) should be
-       ;; coalesced, or perhaps the error-detecting code that
-       ;; disallows redefinition of :PRIMITIVE types should be
-       ;; rewritten to use *TYPE-SYSTEM-FINALIZED* (rather than
-       ;; *TYPE-SYSTEM-INITIALIZED*). The effect of this is not to
-       ;; cause redefinition errors when precompute-types is called
-       ;; for a second time while building the target compiler using
-       ;; the cross-compiler. -- CSR, trying to explain why this
-       ;; isn't completely wrong, 2002-06-07
-       (setf (info :type :kind spec) #+sb-xc-host :defined #-sb-xc-host :primitive))))
+        (setf (info :type :builtin spec) res)
+        ;; KLUDGE: the three copies of this idiom in this file (and
+        ;; the one in class.lisp as at sbcl-0.7.4.1x) should be
+        ;; coalesced, or perhaps the error-detecting code that
+        ;; disallows redefinition of :PRIMITIVE types should be
+        ;; rewritten to use *TYPE-SYSTEM-FINALIZED* (rather than
+        ;; *TYPE-SYSTEM-INITIALIZED*). The effect of this is not to
+        ;; cause redefinition errors when precompute-types is called
+        ;; for a second time while building the target compiler using
+        ;; the cross-compiler. -- CSR, trying to explain why this
+        ;; isn't completely wrong, 2002-06-07
+        (setf (info :type :kind spec) #+sb-xc-host :defined #-sb-xc-host :primitive))))

   (values))
 \f
 ;;;; general TYPE-UNION and TYPE-INTERSECTION operations
   (values))
 \f
 ;;;; general TYPE-UNION and TYPE-INTERSECTION operations

@@ -953,30 +1042,30 @@
 ;;; component types, and with any SIMPLY2 simplifications applied.
 (macrolet
     ((def (name compound-type-p simplify2)
 ;;; component types, and with any SIMPLY2 simplifications applied.
 (macrolet
     ((def (name compound-type-p simplify2)

-        `(defun ,name (types)
-           (when types
-             (multiple-value-bind (first rest)
-                 (if (,compound-type-p (car types))
-                     (values (car (compound-type-types (car types)))
-                             (append (cdr (compound-type-types (car types)))
-                                     (cdr types)))
-                     (values (car types) (cdr types)))
-               (let ((rest (,name rest)) u)
-                 (dolist (r rest (cons first rest))
-                   (when (setq u (,simplify2 first r))
-                     (return (,name (nsubstitute u r rest)))))))))))
+         `(defun ,name (types)
+            (when types
+              (multiple-value-bind (first rest)
+                  (if (,compound-type-p (car types))
+                      (values (car (compound-type-types (car types)))
+                              (append (cdr (compound-type-types (car types)))
+                                      (cdr types)))
+                      (values (car types) (cdr types)))
+                (let ((rest (,name rest)) u)
+                  (dolist (r rest (cons first rest))
+                    (when (setq u (,simplify2 first r))
+                      (return (,name (nsubstitute u r rest)))))))))))

   (def simplify-intersections intersection-type-p type-intersection2)
   (def simplify-unions union-type-p type-union2))
   (def simplify-intersections intersection-type-p type-intersection2)
   (def simplify-unions union-type-p type-union2))

-                
+

 (defun maybe-distribute-one-union (union-type types)
   (let* ((intersection (apply #'type-intersection types))
 (defun maybe-distribute-one-union (union-type types)
   (let* ((intersection (apply #'type-intersection types))

-        (union (mapcar (lambda (x) (type-intersection x intersection))
-                       (union-type-types union-type))))
+         (union (mapcar (lambda (x) (type-intersection x intersection))
+                        (union-type-types union-type))))

     (if (notany (lambda (x) (or (hairy-type-p x)
     (if (notany (lambda (x) (or (hairy-type-p x)

-                               (intersection-type-p x)))
-               union)
-       union
-       nil)))
+                                (intersection-type-p x)))
+                union)
+        union
+        nil)))

 
 (defun type-intersection (&rest input-types)
   (%type-intersection input-types))
 
 (defun type-intersection (&rest input-types)
   (%type-intersection input-types))

@@ -995,23 +1084,23 @@
     ;; we try to generate a simple type by distributing the union; if
     ;; the type can't be made simple, we punt to HAIRY-TYPE.
     (if (and (cdr simplified-types) (some #'union-type-p simplified-types))
     ;; we try to generate a simple type by distributing the union; if
     ;; the type can't be made simple, we punt to HAIRY-TYPE.
     (if (and (cdr simplified-types) (some #'union-type-p simplified-types))

-       (let* ((first-union (find-if #'union-type-p simplified-types))
-              (other-types (coerce (remove first-union simplified-types)
-                                   'list))
-              (distributed (maybe-distribute-one-union first-union
-                                                       other-types)))
-         (if distributed
-             (apply #'type-union distributed)
-             (make-hairy-type
-              :specifier `(and ,@(map 'list
-                                      #'type-specifier
-                                      simplified-types)))))
-       (cond
-         ((null simplified-types) *universal-type*)
-         ((null (cdr simplified-types)) (car simplified-types))
-         (t (%make-intersection-type
-             (some #'type-enumerable simplified-types)
-             simplified-types))))))
+        (let* ((first-union (find-if #'union-type-p simplified-types))
+               (other-types (coerce (remove first-union simplified-types)
+                                    'list))
+               (distributed (maybe-distribute-one-union first-union
+                                                        other-types)))
+          (if distributed
+              (apply #'type-union distributed)
+              (make-hairy-type
+               :specifier `(and ,@(map 'list
+                                       #'type-specifier
+                                       simplified-types)))))
+        (cond
+          ((null simplified-types) *universal-type*)
+          ((null (cdr simplified-types)) (car simplified-types))
+          (t (%make-intersection-type
+              (some #'type-enumerable simplified-types)
+              simplified-types))))))

 
 (defun type-union (&rest input-types)
   (%type-union input-types))
 
 (defun type-union (&rest input-types)
   (%type-union input-types))

@@ -1024,49 +1113,78 @@
       ((null simplified-types) *empty-type*)
       ((null (cdr simplified-types)) (car simplified-types))
       (t (make-union-type
       ((null simplified-types) *empty-type*)
       ((null (cdr simplified-types)) (car simplified-types))
       (t (make-union-type

-         (every #'type-enumerable simplified-types)
-         simplified-types)))))
+          (every #'type-enumerable simplified-types)
+          simplified-types)))))

 \f
 ;;;; built-in types
 
 (!define-type-class named)
 
 \f
 ;;;; built-in types
 
 (!define-type-class named)
 

-(defvar *wild-type*)
-(defvar *empty-type*)
-(defvar *universal-type*)
-(defvar *universal-fun-type*)
-

 (!cold-init-forms
  (macrolet ((frob (name var)
 (!cold-init-forms
  (macrolet ((frob (name var)

-             `(progn
+              `(progn

                  (setq ,var (make-named-type :name ',name))
                  (setq ,var (make-named-type :name ',name))

-                (setf (info :type :kind ',name)
-                      #+sb-xc-host :defined #-sb-xc-host :primitive)
-                (setf (info :type :builtin ',name) ,var))))
+                 (setf (info :type :kind ',name)
+                       #+sb-xc-host :defined #-sb-xc-host :primitive)
+                 (setf (info :type :builtin ',name) ,var))))

    ;; KLUDGE: In ANSI, * isn't really the name of a type, it's just a
    ;; special symbol which can be stuck in some places where an
    ;; ordinary type can go, e.g. (ARRAY * 1) instead of (ARRAY T 1).
    ;; In SBCL it also used to denote universal VALUES type.
    (frob * *wild-type*)
    (frob nil *empty-type*)
    ;; KLUDGE: In ANSI, * isn't really the name of a type, it's just a
    ;; special symbol which can be stuck in some places where an
    ;; ordinary type can go, e.g. (ARRAY * 1) instead of (ARRAY T 1).
    ;; In SBCL it also used to denote universal VALUES type.
    (frob * *wild-type*)
    (frob nil *empty-type*)

-   (frob t *universal-type*))
+   (frob t *universal-type*)
+   ;; new in sbcl-0.9.5: these used to be CLASSOID types, but that
+   ;; view of them was incompatible with requirements on the MOP
+   ;; metaobject class hierarchy: the INSTANCE and
+   ;; FUNCALLABLE-INSTANCE types are disjoint (instances have
+   ;; instance-pointer-lowtag; funcallable-instances have
+   ;; fun-pointer-lowtag), while FUNCALLABLE-STANDARD-OBJECT is
+   ;; required to be a subclass of STANDARD-OBJECT.  -- CSR,
+   ;; 2005-09-09
+   (frob instance *instance-type*)
+   (frob funcallable-instance *funcallable-instance-type*)
+   ;; new in sbcl-1.0.3.3: necessary to act as a join point for the
+   ;; extended sequence hierarchy.  (Might be removed later if we use
+   ;; a dedicated FUNDAMENTAL-SEQUENCE class for this.)
+   (frob extended-sequence *extended-sequence-type*))

  (setf *universal-fun-type*
        (make-fun-type :wild-args t
  (setf *universal-fun-type*
        (make-fun-type :wild-args t

-                     :returns *wild-type*)))
+                      :returns *wild-type*)))

 
 (!define-type-method (named :simple-=) (type1 type2)
   ;;(aver (not (eq type1 *wild-type*))) ; * isn't really a type.
   (values (eq type1 type2) t))
 
 
 (!define-type-method (named :simple-=) (type1 type2)
   ;;(aver (not (eq type1 *wild-type*))) ; * isn't really a type.
   (values (eq type1 type2) t))
 

+(defun cons-type-might-be-empty-type (type)
+  (declare (type cons-type type))
+  (let ((car-type (cons-type-car-type type))
+        (cdr-type (cons-type-cdr-type type)))
+    (or
+     (if (cons-type-p car-type)
+         (cons-type-might-be-empty-type car-type)
+         (multiple-value-bind (yes surep)
+             (type= car-type *empty-type*)
+           (aver (not yes))
+           (not surep)))
+     (if (cons-type-p cdr-type)
+         (cons-type-might-be-empty-type cdr-type)
+         (multiple-value-bind (yes surep)
+             (type= cdr-type *empty-type*)
+           (aver (not yes))
+           (not surep))))))
+

 (!define-type-method (named :complex-=) (type1 type2)
   (cond
     ((and (eq type2 *empty-type*)
 (!define-type-method (named :complex-=) (type1 type2)
   (cond
     ((and (eq type2 *empty-type*)

-         (intersection-type-p type1)
-         ;; not allowed to be unsure on these... FIXME: keep the list
-         ;; of CL types that are intersection types once and only
-         ;; once.
-         (not (or (type= type1 (specifier-type 'ratio))
-                  (type= type1 (specifier-type 'keyword)))))
+          (or (and (intersection-type-p type1)
+                   ;; not allowed to be unsure on these... FIXME: keep
+                   ;; the list of CL types that are intersection types
+                   ;; once and only once.
+                   (not (or (type= type1 (specifier-type 'ratio))
+                            (type= type1 (specifier-type 'keyword)))))
+              (and (cons-type-p type1)
+                   (cons-type-might-be-empty-type type1))))

      ;; things like (AND (EQL 0) (SATISFIES ODDP)) or (AND FUNCTION
      ;; STREAM) can get here.  In general, we can't really tell
      ;; whether these are equal to NIL or not, so
      ;; things like (AND (EQL 0) (SATISFIES ODDP)) or (AND FUNCTION
      ;; STREAM) can get here.  In general, we can't really tell
      ;; whether these are equal to NIL or not, so

@@ -1077,7 +1195,10 @@
 
 (!define-type-method (named :simple-subtypep) (type1 type2)
   (aver (not (eq type1 *wild-type*))) ; * isn't really a type.
 
 (!define-type-method (named :simple-subtypep) (type1 type2)
   (aver (not (eq type1 *wild-type*))) ; * isn't really a type.

-  (values (or (eq type1 *empty-type*) (eq type2 *wild-type*)) t))
+  (aver (not (eq type1 type2)))
+  (values (or (eq type1 *empty-type*)
+              (eq type2 *wild-type*)
+              (eq type2 *universal-type*)) t))

 
 (!define-type-method (named :complex-subtypep-arg1) (type1 type2)
   ;; This AVER causes problems if we write accurate methods for the
 
 (!define-type-method (named :complex-subtypep-arg1) (type1 type2)
   ;; This AVER causes problems if we write accurate methods for the

@@ -1088,63 +1209,187 @@
   ;;
   ;; (aver (not (eq type1 *wild-type*))) ; * isn't really a type.
   (cond ((eq type1 *empty-type*)
   ;;
   ;; (aver (not (eq type1 *wild-type*))) ; * isn't really a type.
   (cond ((eq type1 *empty-type*)

-        t)
-       (;; When TYPE2 might be the universal type in disguise
-        (type-might-contain-other-types-p type2)
-        ;; Now that the UNION and HAIRY COMPLEX-SUBTYPEP-ARG2 methods
-        ;; can delegate to us (more or less as CALL-NEXT-METHOD) when
-        ;; they're uncertain, we can't just barf on COMPOUND-TYPE and
-        ;; HAIRY-TYPEs as we used to. Instead we deal with the
-        ;; problem (where at least part of the problem is cases like
-        ;;   (SUBTYPEP T '(SATISFIES FOO))
-        ;; or
-        ;;   (SUBTYPEP T '(AND (SATISFIES FOO) (SATISFIES BAR)))
-        ;; where the second type is a hairy type like SATISFIES, or
-        ;; is a compound type which might contain a hairy type) by
-        ;; returning uncertainty.
-        (values nil nil))
-       (t
-        ;; By elimination, TYPE1 is the universal type.
-        (aver (eq type1 *universal-type*))
-        ;; This case would have been picked off by the SIMPLE-SUBTYPEP
-        ;; method, and so shouldn't appear here.
-        (aver (not (eq type2 *universal-type*)))
-        ;; Since TYPE2 is not EQ *UNIVERSAL-TYPE* and is not the
-        ;; universal type in disguise, TYPE2 is not a superset of TYPE1.
-        (values nil t))))
+         t)
+        (;; When TYPE2 might be the universal type in disguise
+         (type-might-contain-other-types-p type2)
+         ;; Now that the UNION and HAIRY COMPLEX-SUBTYPEP-ARG2 methods
+         ;; can delegate to us (more or less as CALL-NEXT-METHOD) when
+         ;; they're uncertain, we can't just barf on COMPOUND-TYPE and
+         ;; HAIRY-TYPEs as we used to. Instead we deal with the
+         ;; problem (where at least part of the problem is cases like
+         ;;   (SUBTYPEP T '(SATISFIES FOO))
+         ;; or
+         ;;   (SUBTYPEP T '(AND (SATISFIES FOO) (SATISFIES BAR)))
+         ;; where the second type is a hairy type like SATISFIES, or
+         ;; is a compound type which might contain a hairy type) by
+         ;; returning uncertainty.
+         (values nil nil))
+        ((eq type1 *funcallable-instance-type*)
+         (values (eq type2 (specifier-type 'function)) t))
+        (t
+         ;; This case would have been picked off by the SIMPLE-SUBTYPEP
+         ;; method, and so shouldn't appear here.
+         (aver (not (named-type-p type2)))
+         ;; Since TYPE2 is not EQ *UNIVERSAL-TYPE* and is not another
+         ;; named type in disguise, TYPE2 is not a superset of TYPE1.
+         (values nil t))))

 
 (!define-type-method (named :complex-subtypep-arg2) (type1 type2)
   (aver (not (eq type2 *wild-type*))) ; * isn't really a type.
   (cond ((eq type2 *universal-type*)
 
 (!define-type-method (named :complex-subtypep-arg2) (type1 type2)
   (aver (not (eq type2 *wild-type*))) ; * isn't really a type.
   (cond ((eq type2 *universal-type*)

-        (values t t))
-       ((type-might-contain-other-types-p type1)
-        ;; those types can be *EMPTY-TYPE* or *UNIVERSAL-TYPE* in
-        ;; disguise.  So we'd better delegate.
-        (invoke-complex-subtypep-arg1-method type1 type2))
-       (t
-        ;; FIXME: This seems to rely on there only being 2 or 3
-        ;; NAMED-TYPE values, and the exclusion of various
-        ;; possibilities above. It would be good to explain it and/or
-        ;; rewrite it so that it's clearer.
-        (values (not (eq type2 *empty-type*)) t))))
+         (values t t))
+        ;; some CONS types can conceal danger
+        ((and (cons-type-p type1) (cons-type-might-be-empty-type type1))
+         (values nil nil))
+        ((type-might-contain-other-types-p type1)
+         ;; those types can be other types in disguise.  So we'd
+         ;; better delegate.
+         (invoke-complex-subtypep-arg1-method type1 type2))
+        ((and (or (eq type2 *instance-type*)
+                  (eq type2 *funcallable-instance-type*))
+              (member-type-p type1))
+         ;; member types can be subtypep INSTANCE and
+         ;; FUNCALLABLE-INSTANCE in surprising ways.
+         (invoke-complex-subtypep-arg1-method type1 type2))
+        ((and (eq type2 *extended-sequence-type*) (classoid-p type1))
+         (let* ((layout (classoid-layout type1))
+                (inherits (layout-inherits layout))
+                (sequencep (find (classoid-layout (find-classoid 'sequence))
+                                 inherits)))
+           (values (if sequencep t nil) t)))
+        ((and (eq type2 *instance-type*) (classoid-p type1))
+         (if (member type1 *non-instance-classoid-types* :key #'find-classoid)
+             (values nil t)
+             (let* ((layout (classoid-layout type1))
+                    (inherits (layout-inherits layout))
+                    (functionp (find (classoid-layout (find-classoid 'function))
+                                     inherits)))
+               (cond
+                 (functionp
+                  (values nil t))
+                 ((eq type1 (find-classoid 'function))
+                  (values nil t))
+                 ((or (structure-classoid-p type1)
+                      #+nil
+                      (condition-classoid-p type1))
+                  (values t t))
+                 (t (values nil nil))))))
+        ((and (eq type2 *funcallable-instance-type*) (classoid-p type1))
+         (if (member type1 *non-instance-classoid-types* :key #'find-classoid)
+             (values nil t)
+             (let* ((layout (classoid-layout type1))
+                    (inherits (layout-inherits layout))
+                    (functionp (find (classoid-layout (find-classoid 'function))
+                                     inherits)))
+               (values (if functionp t nil) t))))
+        (t
+         ;; FIXME: This seems to rely on there only being 4 or 5
+         ;; NAMED-TYPE values, and the exclusion of various
+         ;; possibilities above. It would be good to explain it and/or
+         ;; rewrite it so that it's clearer.
+         (values nil t))))

 
 (!define-type-method (named :complex-intersection2) (type1 type2)
   ;; FIXME: This assertion failed when I added it in sbcl-0.6.11.13.
   ;; Perhaps when bug 85 is fixed it can be reenabled.
   ;;(aver (not (eq type2 *wild-type*))) ; * isn't really a type.
 
 (!define-type-method (named :complex-intersection2) (type1 type2)
   ;; FIXME: This assertion failed when I added it in sbcl-0.6.11.13.
   ;; Perhaps when bug 85 is fixed it can be reenabled.
   ;;(aver (not (eq type2 *wild-type*))) ; * isn't really a type.

-  (hierarchical-intersection2 type1 type2))
+  (cond
+    ((eq type2 *extended-sequence-type*)
+     (typecase type1
+       (structure-classoid *empty-type*)
+       (classoid
+        (if (member type1 *non-instance-classoid-types* :key #'find-classoid)
+            *empty-type*
+            (if (find (classoid-layout (find-classoid 'sequence))
+                      (layout-inherits (classoid-layout type1)))
+                type1
+                nil)))
+       (t
+        (if (or (type-might-contain-other-types-p type1)
+                (member-type-p type1))
+            nil
+            *empty-type*))))
+    ((eq type2 *instance-type*)
+     (typecase type1
+       (structure-classoid type1)
+       (classoid
+        (if (and (not (member type1 *non-instance-classoid-types*
+                              :key #'find-classoid))
+                 (not (eq type1 (find-classoid 'function)))
+                 (not (find (classoid-layout (find-classoid 'function))
+                            (layout-inherits (classoid-layout type1)))))
+            nil
+            *empty-type*))
+       (t
+        (if (or (type-might-contain-other-types-p type1)
+                (member-type-p type1))
+            nil
+            *empty-type*))))
+    ((eq type2 *funcallable-instance-type*)
+     (typecase type1
+       (structure-classoid *empty-type*)
+       (classoid
+        (if (member type1 *non-instance-classoid-types* :key #'find-classoid)
+            *empty-type*
+            (if (find (classoid-layout (find-classoid 'function))
+                      (layout-inherits (classoid-layout type1)))
+                type1
+                (if (type= type1 (find-classoid 'function))
+                    type2
+                    nil))))
+       (fun-type nil)
+       (t
+        (if (or (type-might-contain-other-types-p type1)
+                (member-type-p type1))
+            nil
+            *empty-type*))))
+    (t (hierarchical-intersection2 type1 type2))))

 
 (!define-type-method (named :complex-union2) (type1 type2)
   ;; Perhaps when bug 85 is fixed this can be reenabled.
   ;;(aver (not (eq type2 *wild-type*))) ; * isn't really a type.
 
 (!define-type-method (named :complex-union2) (type1 type2)
   ;; Perhaps when bug 85 is fixed this can be reenabled.
   ;;(aver (not (eq type2 *wild-type*))) ; * isn't really a type.

-  (hierarchical-union2 type1 type2))
+  (cond
+    ((eq type2 *extended-sequence-type*)
+     (if (classoid-p type1)
+         (if (or (member type1 *non-instance-classoid-types*
+                         :key #'find-classoid)
+                 (not (find (classoid-layout (find-classoid 'sequence))
+                            (layout-inherits (classoid-layout type1)))))
+             nil
+             type2)
+         nil))
+    ((eq type2 *instance-type*)
+     (if (classoid-p type1)
+         (if (or (member type1 *non-instance-classoid-types*
+                         :key #'find-classoid)
+                 (find (classoid-layout (find-classoid 'function))
+                       (layout-inherits (classoid-layout type1))))
+             nil
+             type2)
+         nil))
+    ((eq type2 *funcallable-instance-type*)
+     (if (classoid-p type1)
+         (if (or (member type1 *non-instance-classoid-types*
+                         :key #'find-classoid)
+                 (not (find (classoid-layout (find-classoid 'function))
+                            (layout-inherits (classoid-layout type1)))))
+             nil
+             (if (eq type1 (specifier-type 'function))
+                 type1
+                 type2))
+         nil))
+    (t (hierarchical-union2 type1 type2))))

 
 (!define-type-method (named :negate) (x)
   (aver (not (eq x *wild-type*)))
   (cond
     ((eq x *universal-type*) *empty-type*)
     ((eq x *empty-type*) *universal-type*)
 
 (!define-type-method (named :negate) (x)
   (aver (not (eq x *wild-type*)))
   (cond
     ((eq x *universal-type*) *empty-type*)
     ((eq x *empty-type*) *universal-type*)

-    (t (bug "NAMED type not universal, wild or empty: ~S" x))))
+    ((or (eq x *instance-type*)
+         (eq x *funcallable-instance-type*)
+         (eq x *extended-sequence-type*))
+     (make-negation-type :type x))
+    (t (bug "NAMED type unexpected: ~S" x))))

 
 (!define-type-method (named :unparse) (x)
   (named-type-name x))
 
 (!define-type-method (named :unparse) (x)
   (named-type-name x))

@@ -1159,47 +1404,54 @@
 
 (!define-type-method (hairy :simple-subtypep) (type1 type2)
   (let ((hairy-spec1 (hairy-type-specifier type1))
 
 (!define-type-method (hairy :simple-subtypep) (type1 type2)
   (let ((hairy-spec1 (hairy-type-specifier type1))

-       (hairy-spec2 (hairy-type-specifier type2)))
+        (hairy-spec2 (hairy-type-specifier type2)))

     (cond ((equal-but-no-car-recursion hairy-spec1 hairy-spec2)
     (cond ((equal-but-no-car-recursion hairy-spec1 hairy-spec2)

-          (values t t))
-         (t
-          (values nil nil)))))
+           (values t t))
+          ((maybe-reparse-specifier! type1)
+           (csubtypep type1 type2))
+          ((maybe-reparse-specifier! type2)
+           (csubtypep type1 type2))
+          (t
+           (values nil nil)))))

 
 (!define-type-method (hairy :complex-subtypep-arg2) (type1 type2)
 
 (!define-type-method (hairy :complex-subtypep-arg2) (type1 type2)

-  (invoke-complex-subtypep-arg1-method type1 type2))
+  (if (maybe-reparse-specifier! type2)
+      (csubtypep type1 type2)
+      (let ((specifier (hairy-type-specifier type2)))
+        (cond ((and (consp specifier) (eql (car specifier) 'satisfies))
+               (case (cadr specifier)
+                 ((keywordp) (if (type= type1 (specifier-type 'symbol))
+                                 (values nil t)
+                                 (invoke-complex-subtypep-arg1-method type1 type2)))
+                 (t (invoke-complex-subtypep-arg1-method type1 type2))))
+              (t
+               (invoke-complex-subtypep-arg1-method type1 type2))))))

 
 (!define-type-method (hairy :complex-subtypep-arg1) (type1 type2)
 
 (!define-type-method (hairy :complex-subtypep-arg1) (type1 type2)

-  (declare (ignore type1 type2))
-  (values nil nil))
+  (if (maybe-reparse-specifier! type1)
+      (csubtypep type1 type2)
+      (values nil nil)))

 
 (!define-type-method (hairy :complex-=) (type1 type2)
 
 (!define-type-method (hairy :complex-=) (type1 type2)

-  (if (and (unknown-type-p type2)
-           (let* ((specifier2 (unknown-type-specifier type2))
-                  (name2 (if (consp specifier2)
-                             (car specifier2)
-                             specifier2)))
-             (info :type :kind name2)))
-      (let ((type2 (specifier-type (unknown-type-specifier type2))))
-        (if (unknown-type-p type2)
-            (values nil nil)
-            (type= type1 type2)))
-  (values nil nil)))
+  (if (maybe-reparse-specifier! type2)
+      (type= type1 type2)
+      (values nil nil)))

 
 

-(!define-type-method (hairy :simple-intersection2 :complex-intersection2) 
-                    (type1 type2)
+(!define-type-method (hairy :simple-intersection2 :complex-intersection2)
+                     (type1 type2)

   (if (type= type1 type2)
       type1
       nil))
 
   (if (type= type1 type2)
       type1
       nil))
 

-(!define-type-method (hairy :simple-union2) 
-                    (type1 type2)
+(!define-type-method (hairy :simple-union2)
+                     (type1 type2)

   (if (type= type1 type2)
       type1
       nil))
 
 (!define-type-method (hairy :simple-=) (type1 type2)
   (if (equal-but-no-car-recursion (hairy-type-specifier type1)
   (if (type= type1 type2)
       type1
       nil))
 
 (!define-type-method (hairy :simple-=) (type1 type2)
   (if (equal-but-no-car-recursion (hairy-type-specifier type1)

-                                 (hairy-type-specifier type2))
+                                  (hairy-type-specifier type2))

       (values t t)
       (values nil nil)))
 
       (values t t)
       (values nil nil)))
 

@@ -1210,10 +1462,10 @@
     (declare (ignore satisfies))
     (unless (symbolp predicate-name)
       (error 'simple-type-error
     (declare (ignore satisfies))
     (unless (symbolp predicate-name)
       (error 'simple-type-error

-            :datum predicate-name
-            :expected-type 'symbol
-            :format-control "The SATISFIES predicate name is not a symbol: ~S"
-            :format-arguments (list predicate-name))))
+             :datum predicate-name
+             :expected-type 'symbol
+             :format-control "The SATISFIES predicate name is not a symbol: ~S"
+             :format-arguments (list predicate-name))))

   ;; Create object.
   (make-hairy-type :specifier whole))
 \f
   ;; Create object.
   (make-hairy-type :specifier whole))
 \f

@@ -1223,19 +1475,21 @@
   (negation-type-type x))
 
 (!define-type-method (negation :unparse) (x)
   (negation-type-type x))
 
 (!define-type-method (negation :unparse) (x)

-  `(not ,(type-specifier (negation-type-type x))))
+  (if (type= (negation-type-type x) (specifier-type 'cons))
+      'atom
+      `(not ,(type-specifier (negation-type-type x)))))

 
 (!define-type-method (negation :simple-subtypep) (type1 type2)
   (csubtypep (negation-type-type type2) (negation-type-type type1)))
 
 (!define-type-method (negation :complex-subtypep-arg2) (type1 type2)
   (let* ((complement-type2 (negation-type-type type2))
 
 (!define-type-method (negation :simple-subtypep) (type1 type2)
   (csubtypep (negation-type-type type2) (negation-type-type type1)))
 
 (!define-type-method (negation :complex-subtypep-arg2) (type1 type2)
   (let* ((complement-type2 (negation-type-type type2))

-        (intersection2 (type-intersection2 type1
-                                           complement-type2)))
+         (intersection2 (type-intersection2 type1
+                                            complement-type2)))

     (if intersection2
     (if intersection2

-       ;; FIXME: if uncertain, maybe try arg1?
-       (type= intersection2 *empty-type*)
-       (invoke-complex-subtypep-arg1-method type1 type2))))
+        ;; FIXME: if uncertain, maybe try arg1?
+        (type= intersection2 *empty-type*)
+        (invoke-complex-subtypep-arg1-method type1 type2))))

 
 (!define-type-method (negation :complex-subtypep-arg1) (type1 type2)
   ;; "Incrementally extended heuristic algorithms tend inexorably toward the
 
 (!define-type-method (negation :complex-subtypep-arg1) (type1 type2)
   ;; "Incrementally extended heuristic algorithms tend inexorably toward the

@@ -1252,22 +1506,22 @@
     ;; maintenance might make it possible for it to end up in this
     ;; code.)
     (multiple-value-bind (equal certain)
     ;; maintenance might make it possible for it to end up in this
     ;; code.)
     (multiple-value-bind (equal certain)

-       (type= type2 *universal-type*)
+        (type= type2 *universal-type*)

       (unless certain
       (unless certain

-       (return (values nil nil)))
+        (return (values nil nil)))

       (when equal
       (when equal

-       (return (values t t))))
+        (return (values t t))))

     (let ((complement-type1 (negation-type-type type1)))
       ;; Do the special cases first, in order to give us a chance if
       ;; subtype/supertype relationships are hairy.
       (multiple-value-bind (equal certain)
     (let ((complement-type1 (negation-type-type type1)))
       ;; Do the special cases first, in order to give us a chance if
       ;; subtype/supertype relationships are hairy.
       (multiple-value-bind (equal certain)

-         (type= complement-type1 type2)
-       ;; If a = b, ~a is not a subtype of b (unless b=T, which was
-       ;; excluded above).
-       (unless certain
-         (return (values nil nil)))
-       (when equal
-         (return (values nil t))))
+          (type= complement-type1 type2)
+        ;; If a = b, ~a is not a subtype of b (unless b=T, which was
+        ;; excluded above).
+        (unless certain
+          (return (values nil nil)))
+        (when equal
+          (return (values nil t))))

       ;; KLUDGE: ANSI requires that the SUBTYPEP result between any
       ;; two built-in atomic type specifiers never be uncertain. This
       ;; is hard to do cleanly for the built-in types whose
       ;; KLUDGE: ANSI requires that the SUBTYPEP result between any
       ;; two built-in atomic type specifiers never be uncertain. This
       ;; is hard to do cleanly for the built-in types whose

@@ -1280,33 +1534,33 @@
       ;; representation in the type system could make it start
       ;; confidently returning incorrect results.) -- WHN 2002-03-08
       (unless (or (type-might-contain-other-types-p complement-type1)
       ;; representation in the type system could make it start
       ;; confidently returning incorrect results.) -- WHN 2002-03-08
       (unless (or (type-might-contain-other-types-p complement-type1)

-                 (type-might-contain-other-types-p type2))
-       ;; Because of the way our types which don't contain other
-       ;; types are disjoint subsets of the space of possible values,
-       ;; (SUBTYPEP '(NOT AA) 'B)=NIL when AA and B are simple (and B
-       ;; is not T, as checked above).
-       (return (values nil t)))
+                  (type-might-contain-other-types-p type2))
+        ;; Because of the way our types which don't contain other
+        ;; types are disjoint subsets of the space of possible values,
+        ;; (SUBTYPEP '(NOT AA) 'B)=NIL when AA and B are simple (and B
+        ;; is not T, as checked above).
+        (return (values nil t)))

       ;; The old (TYPE= TYPE1 TYPE2) branch would never be taken, as
       ;; TYPE1 and TYPE2 will only be equal if they're both NOT types,
       ;; and then the :SIMPLE-SUBTYPEP method would be used instead.
       ;; But a CSUBTYPEP relationship might still hold:
       (multiple-value-bind (equal certain)
       ;; The old (TYPE= TYPE1 TYPE2) branch would never be taken, as
       ;; TYPE1 and TYPE2 will only be equal if they're both NOT types,
       ;; and then the :SIMPLE-SUBTYPEP method would be used instead.
       ;; But a CSUBTYPEP relationship might still hold:
       (multiple-value-bind (equal certain)

-         (csubtypep complement-type1 type2)
-       ;; If a is a subtype of b, ~a is not a subtype of b (unless
-       ;; b=T, which was excluded above).
-       (unless certain
-         (return (values nil nil)))
-       (when equal
-         (return (values nil t))))
+          (csubtypep complement-type1 type2)
+        ;; If a is a subtype of b, ~a is not a subtype of b (unless
+        ;; b=T, which was excluded above).
+        (unless certain
+          (return (values nil nil)))
+        (when equal
+          (return (values nil t))))

       (multiple-value-bind (equal certain)
       (multiple-value-bind (equal certain)

-         (csubtypep type2 complement-type1)
-       ;; If b is a subtype of a, ~a is not a subtype of b.  (FIXME:
-       ;; That's not true if a=T. Do we know at this point that a is
-       ;; not T?)
-       (unless certain
-         (return (values nil nil)))
-       (when equal
-         (return (values nil t))))
+          (csubtypep type2 complement-type1)
+        ;; If b is a subtype of a, ~a is not a subtype of b.  (FIXME:
+        ;; That's not true if a=T. Do we know at this point that a is
+        ;; not T?)
+        (unless certain
+          (return (values nil nil)))
+        (when equal
+          (return (values nil t))))

       ;; old CSR comment ca. 0.7.2, now obsoleted by the SIMPLE-CTYPE?
       ;; KLUDGE case above: Other cases here would rely on being able
       ;; to catch all possible cases, which the fragility of this type
       ;; old CSR comment ca. 0.7.2, now obsoleted by the SIMPLE-CTYPE?
       ;; KLUDGE case above: Other cases here would rely on being able
       ;; to catch all possible cases, which the fragility of this type

@@ -1330,7 +1584,7 @@
 
 (!define-type-method (negation :simple-intersection2) (type1 type2)
   (let ((not1 (negation-type-type type1))
 
 (!define-type-method (negation :simple-intersection2) (type1 type2)
   (let ((not1 (negation-type-type type1))

-       (not2 (negation-type-type type2)))
+        (not2 (negation-type-type type2)))

     (cond
       ((csubtypep not1 not2) type2)
       ((csubtypep not2 not1) type1)
     (cond
       ((csubtypep not1 not2) type2)
       ((csubtypep not2 not1) type1)

@@ -1346,16 +1600,31 @@
        (aver (not (eq (type-union not1 not2) *universal-type*)))
        nil))))
 
        (aver (not (eq (type-union not1 not2) *universal-type*)))
        nil))))
 

+(defun maybe-complex-array-refinement (type1 type2)
+  (let* ((ntype (negation-type-type type2))
+         (ndims (array-type-dimensions ntype))
+         (ncomplexp (array-type-complexp ntype))
+         (nseltype (array-type-specialized-element-type ntype))
+         (neltype (array-type-element-type ntype)))
+    (if (and (eql ndims '*) (null ncomplexp)
+             (eql neltype *wild-type*) (eql nseltype *wild-type*))
+        (make-array-type :dimensions (array-type-dimensions type1)
+                         :complexp t
+                         :element-type (array-type-element-type type1)
+                         :specialized-element-type (array-type-specialized-element-type type1)))))
+

 (!define-type-method (negation :complex-intersection2) (type1 type2)
   (cond
     ((csubtypep type1 (negation-type-type type2)) *empty-type*)
     ((eq (type-intersection type1 (negation-type-type type2)) *empty-type*)
      type1)
 (!define-type-method (negation :complex-intersection2) (type1 type2)
   (cond
     ((csubtypep type1 (negation-type-type type2)) *empty-type*)
     ((eq (type-intersection type1 (negation-type-type type2)) *empty-type*)
      type1)

+    ((and (array-type-p type1) (array-type-p (negation-type-type type2)))
+     (maybe-complex-array-refinement type1 type2))

     (t nil)))
 
 (!define-type-method (negation :simple-union2) (type1 type2)
   (let ((not1 (negation-type-type type1))
     (t nil)))
 
 (!define-type-method (negation :simple-union2) (type1 type2)
   (let ((not1 (negation-type-type type1))

-       (not2 (negation-type-type type2)))
+        (not2 (negation-type-type type2)))

     (cond
       ((csubtypep not1 not2) type1)
       ((csubtypep not2 not1) type2)
     (cond
       ((csubtypep not1 not2) type1)
       ((csubtypep not2 not1) type2)

@@ -1389,8 +1658,8 @@
 (!define-type-method (number :simple-=) (type1 type2)
   (values
    (and (numeric-type-equal type1 type2)
 (!define-type-method (number :simple-=) (type1 type2)
   (values
    (and (numeric-type-equal type1 type2)

-       (equalp (numeric-type-low type1) (numeric-type-low type2))
-       (equalp (numeric-type-high type1) (numeric-type-high type2)))
+        (equalp (numeric-type-low type1) (numeric-type-low type2))
+        (equalp (numeric-type-high type1) (numeric-type-high type2)))

    t))
 
 (!define-type-method (number :negate) (type)
    t))
 
 (!define-type-method (number :negate) (type)

@@ -1398,78 +1667,88 @@
       (make-negation-type :type type)
       (type-union
        (make-negation-type
       (make-negation-type :type type)
       (type-union
        (make-negation-type

-       :type (modified-numeric-type type :low nil :high nil))
+        :type (modified-numeric-type type :low nil :high nil))

        (cond
        (cond

-        ((null (numeric-type-low type))
-         (modified-numeric-type
-          type
-          :low (let ((h (numeric-type-high type)))
-                 (if (consp h) (car h) (list h)))
-          :high nil))
-        ((null (numeric-type-high type))
-         (modified-numeric-type
-          type
-          :low nil
-          :high (let ((l (numeric-type-low type)))
-                  (if (consp l) (car l) (list l)))))
-        (t (type-union
-            (modified-numeric-type
-             type
-             :low nil
-             :high (let ((l (numeric-type-low type)))
-                     (if (consp l) (car l) (list l))))
-            (modified-numeric-type
-             type
-             :low (let ((h (numeric-type-high type)))
-                    (if (consp h) (car h) (list h)))
-             :high nil)))))))
+         ((null (numeric-type-low type))
+          (modified-numeric-type
+           type
+           :low (let ((h (numeric-type-high type)))
+                  (if (consp h) (car h) (list h)))
+           :high nil))
+         ((null (numeric-type-high type))
+          (modified-numeric-type
+           type
+           :low nil
+           :high (let ((l (numeric-type-low type)))
+                   (if (consp l) (car l) (list l)))))
+         (t (type-union
+             (modified-numeric-type
+              type
+              :low nil
+              :high (let ((l (numeric-type-low type)))
+                      (if (consp l) (car l) (list l))))
+             (modified-numeric-type
+              type
+              :low (let ((h (numeric-type-high type)))
+                     (if (consp h) (car h) (list h)))
+              :high nil)))))))

 
 (!define-type-method (number :unparse) (type)
   (let* ((complexp (numeric-type-complexp type))
 
 (!define-type-method (number :unparse) (type)
   (let* ((complexp (numeric-type-complexp type))

-        (low (numeric-type-low type))
-        (high (numeric-type-high type))
-        (base (case (numeric-type-class type)
-                (integer 'integer)
-                (rational 'rational)
-                (float (or (numeric-type-format type) 'float))
-                (t 'real))))
+         (low (numeric-type-low type))
+         (high (numeric-type-high type))
+         (base (case (numeric-type-class type)
+                 (integer 'integer)
+                 (rational 'rational)
+                 (float (or (numeric-type-format type) 'float))
+                 (t 'real))))

     (let ((base+bounds
     (let ((base+bounds

-          (cond ((and (eq base 'integer) high low)
-                 (let ((high-count (logcount high))
-                       (high-length (integer-length high)))
-                   (cond ((= low 0)
-                          (cond ((= high 0) '(integer 0 0))
-                                ((= high 1) 'bit)
-                                ((and (= high-count high-length)
-                                      (plusp high-length))
-                                 `(unsigned-byte ,high-length))
-                                (t
-                                 `(mod ,(1+ high)))))
-                         ((and (= low sb!xc:most-negative-fixnum)
-                               (= high sb!xc:most-positive-fixnum))
-                          'fixnum)
-                         ((and (= low (lognot high))
-                               (= high-count high-length)
-                               (> high-count 0))
-                          `(signed-byte ,(1+ high-length)))
-                         (t
-                          `(integer ,low ,high)))))
-                (high `(,base ,(or low '*) ,high))
-                (low
-                 (if (and (eq base 'integer) (= low 0))
-                     'unsigned-byte
-                     `(,base ,low)))
-                (t base))))
+           (cond ((and (eq base 'integer) high low)
+                  (let ((high-count (logcount high))
+                        (high-length (integer-length high)))
+                    (cond ((= low 0)
+                           (cond ((= high 0) '(integer 0 0))
+                                 ((= high 1) 'bit)
+                                 ((and (= high-count high-length)
+                                       (plusp high-length))
+                                  `(unsigned-byte ,high-length))
+                                 (t
+                                  `(mod ,(1+ high)))))
+                          ((and (= low sb!xc:most-negative-fixnum)
+                                (= high sb!xc:most-positive-fixnum))
+                           'fixnum)
+                          ((and (= low (lognot high))
+                                (= high-count high-length)
+                                (> high-count 0))
+                           `(signed-byte ,(1+ high-length)))
+                          (t
+                           `(integer ,low ,high)))))
+                 (high `(,base ,(or low '*) ,high))
+                 (low
+                  (if (and (eq base 'integer) (= low 0))
+                      'unsigned-byte
+                      `(,base ,low)))
+                 (t base))))

       (ecase complexp
       (ecase complexp

-       (:real
-        base+bounds)
-       (:complex
-        (if (eq base+bounds 'real)
-            'complex
-            `(complex ,base+bounds)))
-       ((nil)
-        (aver (eq base+bounds 'real))
-        'number)))))
+        (:real
+         base+bounds)
+        (:complex
+         (aver (neq base+bounds 'real))
+         `(complex ,base+bounds))
+        ((nil)
+         (aver (eq base+bounds 'real))
+         'number)))))
+
+(!define-type-method (number :singleton-p) (type)
+  (let ((low  (numeric-type-low  type))
+        (high (numeric-type-high type)))
+    (if (and low
+             (eql low high)
+             (eql (numeric-type-complexp type) :real)
+             (member (numeric-type-class type) '(integer rational
+                                                 #-sb-xc-host float)))
+        (values t (numeric-type-low type))
+        (values nil nil))))

 
 ;;; Return true if X is "less than or equal" to Y, taking open bounds
 ;;; into consideration. CLOSED is the predicate used to test the bound
 
 ;;; Return true if X is "less than or equal" to Y, taking open bounds
 ;;; into consideration. CLOSED is the predicate used to test the bound

@@ -1483,15 +1762,15 @@
 ;;; upper. Use NUMERIC-BOUND-TEST* for different kinds of bounds.
 (defmacro numeric-bound-test (x y closed open)
   `(cond ((not ,y) t)
 ;;; upper. Use NUMERIC-BOUND-TEST* for different kinds of bounds.
 (defmacro numeric-bound-test (x y closed open)
   `(cond ((not ,y) t)

-        ((not ,x) nil)
-        ((consp ,x)
-         (if (consp ,y)
-             (,closed (car ,x) (car ,y))
-             (,closed (car ,x) ,y)))
-        (t
-         (if (consp ,y)
-             (,open ,x (car ,y))
-             (,closed ,x ,y)))))
+         ((not ,x) nil)
+         ((consp ,x)
+          (if (consp ,y)
+              (,closed (car ,x) (car ,y))
+              (,closed (car ,x) ,y)))
+         (t
+          (if (consp ,y)
+              (,open ,x (car ,y))
+              (,closed ,x ,y)))))

 
 ;;; This is used to compare upper and lower bounds. This is different
 ;;; from the same-bound case:
 
 ;;; This is used to compare upper and lower bounds. This is different
 ;;; from the same-bound case:

@@ -1501,15 +1780,15 @@
 ;;;    causing us to use the OPEN test for those cases as well.
 (defmacro numeric-bound-test* (x y closed open)
   `(cond ((not ,y) t)
 ;;;    causing us to use the OPEN test for those cases as well.
 (defmacro numeric-bound-test* (x y closed open)
   `(cond ((not ,y) t)

-        ((not ,x) t)
-        ((consp ,x)
-         (if (consp ,y)
-             (,open (car ,x) (car ,y))
-             (,open (car ,x) ,y)))
-        (t
-         (if (consp ,y)
-             (,open ,x (car ,y))
-             (,closed ,x ,y)))))
+         ((not ,x) t)
+         ((consp ,x)
+          (if (consp ,y)
+              (,open (car ,x) (car ,y))
+              (,open (car ,x) ,y)))
+         (t
+          (if (consp ,y)
+              (,open ,x (car ,y))
+              (,closed ,x ,y)))))

 
 ;;; Return whichever of the numeric bounds X and Y is "maximal"
 ;;; according to the predicates CLOSED (e.g. >=) and OPEN (e.g. >).
 
 ;;; Return whichever of the numeric bounds X and Y is "maximal"
 ;;; according to the predicates CLOSED (e.g. >=) and OPEN (e.g. >).

@@ -1518,51 +1797,51 @@
 ;;; otherwise we return the other arg.
 (defmacro numeric-bound-max (x y closed open max-p)
   (once-only ((n-x x)
 ;;; otherwise we return the other arg.
 (defmacro numeric-bound-max (x y closed open max-p)
   (once-only ((n-x x)

-             (n-y y))
+              (n-y y))

     `(cond ((not ,n-x) ,(if max-p nil n-y))
     `(cond ((not ,n-x) ,(if max-p nil n-y))

-          ((not ,n-y) ,(if max-p nil n-x))
-          ((consp ,n-x)
-           (if (consp ,n-y)
-               (if (,closed (car ,n-x) (car ,n-y)) ,n-x ,n-y)
-               (if (,open (car ,n-x) ,n-y) ,n-x ,n-y)))
-          (t
-           (if (consp ,n-y)
-               (if (,open (car ,n-y) ,n-x) ,n-y ,n-x)
-               (if (,closed ,n-y ,n-x) ,n-y ,n-x))))))
+           ((not ,n-y) ,(if max-p nil n-x))
+           ((consp ,n-x)
+            (if (consp ,n-y)
+                (if (,closed (car ,n-x) (car ,n-y)) ,n-x ,n-y)
+                (if (,open (car ,n-x) ,n-y) ,n-x ,n-y)))
+           (t
+            (if (consp ,n-y)
+                (if (,open (car ,n-y) ,n-x) ,n-y ,n-x)
+                (if (,closed ,n-y ,n-x) ,n-y ,n-x))))))

 
 (!define-type-method (number :simple-subtypep) (type1 type2)
   (let ((class1 (numeric-type-class type1))
 
 (!define-type-method (number :simple-subtypep) (type1 type2)
   (let ((class1 (numeric-type-class type1))

-       (class2 (numeric-type-class type2))
-       (complexp2 (numeric-type-complexp type2))
-       (format2 (numeric-type-format type2))
-       (low1 (numeric-type-low type1))
-       (high1 (numeric-type-high type1))
-       (low2 (numeric-type-low type2))
-       (high2 (numeric-type-high type2)))
+        (class2 (numeric-type-class type2))
+        (complexp2 (numeric-type-complexp type2))
+        (format2 (numeric-type-format type2))
+        (low1 (numeric-type-low type1))
+        (high1 (numeric-type-high type1))
+        (low2 (numeric-type-low type2))
+        (high2 (numeric-type-high type2)))

     ;; If one is complex and the other isn't, they are disjoint.
     (cond ((not (or (eq (numeric-type-complexp type1) complexp2)
     ;; If one is complex and the other isn't, they are disjoint.
     (cond ((not (or (eq (numeric-type-complexp type1) complexp2)

-                   (null complexp2)))
-          (values nil t))
-         ;; If the classes are specified and different, the types are
-         ;; disjoint unless type2 is RATIONAL and type1 is INTEGER.
-         ;; [ or type1 is INTEGER and type2 is of the form (RATIONAL
-         ;; X X) for integral X, but this is dealt with in the
-         ;; canonicalization inside MAKE-NUMERIC-TYPE ]
-         ((not (or (eq class1 class2)
-                   (null class2)
-                   (and (eq class1 'integer) (eq class2 'rational))))
-          (values nil t))
-         ;; If the float formats are specified and different, the types
-         ;; are disjoint.
-         ((not (or (eq (numeric-type-format type1) format2)
-                   (null format2)))
-          (values nil t))
-         ;; Check the bounds.
-         ((and (numeric-bound-test low1 low2 >= >)
-               (numeric-bound-test high1 high2 <= <))
-          (values t t))
-         (t
-          (values nil t)))))
+                    (null complexp2)))
+           (values nil t))
+          ;; If the classes are specified and different, the types are
+          ;; disjoint unless type2 is RATIONAL and type1 is INTEGER.
+          ;; [ or type1 is INTEGER and type2 is of the form (RATIONAL
+          ;; X X) for integral X, but this is dealt with in the
+          ;; canonicalization inside MAKE-NUMERIC-TYPE ]
+          ((not (or (eq class1 class2)
+                    (null class2)
+                    (and (eq class1 'integer) (eq class2 'rational))))
+           (values nil t))
+          ;; If the float formats are specified and different, the types
+          ;; are disjoint.
+          ((not (or (eq (numeric-type-format type1) format2)
+                    (null format2)))
+           (values nil t))
+          ;; Check the bounds.
+          ((and (numeric-bound-test low1 low2 >= >)
+                (numeric-bound-test high1 high2 <= <))
+           (values t t))
+          (t
+           (values nil t)))))

 
 (!define-superclasses number ((number)) !cold-init-forms)
 
 
 (!define-superclasses number ((number)) !cold-init-forms)
 

@@ -1570,255 +1849,245 @@
 ;;; then return true, otherwise NIL.
 (defun numeric-types-adjacent (low high)
   (let ((low-bound (numeric-type-high low))
 ;;; then return true, otherwise NIL.
 (defun numeric-types-adjacent (low high)
   (let ((low-bound (numeric-type-high low))

-       (high-bound (numeric-type-low high)))
+        (high-bound (numeric-type-low high)))

     (cond ((not (and low-bound high-bound)) nil)
     (cond ((not (and low-bound high-bound)) nil)

-         ((and (consp low-bound) (consp high-bound)) nil)
-         ((consp low-bound)
-          (let ((low-value (car low-bound)))
-            (or (eql low-value high-bound)
-                (and (eql low-value
-                          (load-time-value (make-unportable-float
-                                            :single-float-negative-zero)))
-                     (eql high-bound 0f0))
-                (and (eql low-value 0f0)
-                     (eql high-bound
-                          (load-time-value (make-unportable-float
-                                            :single-float-negative-zero))))
-                (and (eql low-value
-                          (load-time-value (make-unportable-float
-                                            :double-float-negative-zero)))
-                     (eql high-bound 0d0))
-                (and (eql low-value 0d0)
-                     (eql high-bound
-                          (load-time-value (make-unportable-float
-                                            :double-float-negative-zero)))))))
-         ((consp high-bound)
-          (let ((high-value (car high-bound)))
-            (or (eql high-value low-bound)
-                (and (eql high-value
-                          (load-time-value (make-unportable-float
-                                            :single-float-negative-zero)))
-                     (eql low-bound 0f0))
-                (and (eql high-value 0f0)
-                     (eql low-bound
-                          (load-time-value (make-unportable-float
-                                            :single-float-negative-zero))))
-                (and (eql high-value
-                          (load-time-value (make-unportable-float
-                                            :double-float-negative-zero)))
-                     (eql low-bound 0d0))
-                (and (eql high-value 0d0)
-                     (eql low-bound
-                          (load-time-value (make-unportable-float
-                                            :double-float-negative-zero)))))))
-         ((and (eq (numeric-type-class low) 'integer)
-               (eq (numeric-type-class high) 'integer))
-          (eql (1+ low-bound) high-bound))
-         (t
-          nil))))
+          ((and (consp low-bound) (consp high-bound)) nil)
+          ((consp low-bound)
+           (let ((low-value (car low-bound)))
+             (or (eql low-value high-bound)
+                 (and (eql low-value
+                           (load-time-value (make-unportable-float
+                                             :single-float-negative-zero)))
+                      (eql high-bound 0f0))
+                 (and (eql low-value 0f0)
+                      (eql high-bound
+                           (load-time-value (make-unportable-float
+                                             :single-float-negative-zero))))
+                 (and (eql low-value
+                           (load-time-value (make-unportable-float
+                                             :double-float-negative-zero)))
+                      (eql high-bound 0d0))
+                 (and (eql low-value 0d0)
+                      (eql high-bound
+                           (load-time-value (make-unportable-float
+                                             :double-float-negative-zero)))))))
+          ((consp high-bound)
+           (let ((high-value (car high-bound)))
+             (or (eql high-value low-bound)
+                 (and (eql high-value
+                           (load-time-value (make-unportable-float
+                                             :single-float-negative-zero)))
+                      (eql low-bound 0f0))
+                 (and (eql high-value 0f0)
+                      (eql low-bound
+                           (load-time-value (make-unportable-float
+                                             :single-float-negative-zero))))
+                 (and (eql high-value
+                           (load-time-value (make-unportable-float
+                                             :double-float-negative-zero)))
+                      (eql low-bound 0d0))
+                 (and (eql high-value 0d0)
+                      (eql low-bound
+                           (load-time-value (make-unportable-float
+                                             :double-float-negative-zero)))))))
+          ((and (eq (numeric-type-class low) 'integer)
+                (eq (numeric-type-class high) 'integer))
+           (eql (1+ low-bound) high-bound))
+          (t
+           nil))))

 
 ;;; Return a numeric type that is a supertype for both TYPE1 and TYPE2.
 ;;;
 
 ;;; Return a numeric type that is a supertype for both TYPE1 and TYPE2.
 ;;;

-;;; Old comment, probably no longer applicable:
-;;;
-;;;   ### Note: we give up early to keep from dropping lots of
-;;;   information on the floor by returning overly general types.
+;;; Binding *APPROXIMATE-NUMERIC-UNIONS* to T allows merging non-adjacent
+;;; numeric types, eg (OR (INTEGER 0 12) (INTEGER 20 128)) => (INTEGER 0 128),
+;;; the compiler does this occasionally during type-derivation to avoid
+;;; creating absurdly complex unions of numeric types.
+(defvar *approximate-numeric-unions* nil)
+

 (!define-type-method (number :simple-union2) (type1 type2)
   (declare (type numeric-type type1 type2))
   (cond ((csubtypep type1 type2) type2)
 (!define-type-method (number :simple-union2) (type1 type2)
   (declare (type numeric-type type1 type2))
   (cond ((csubtypep type1 type2) type2)

-       ((csubtypep type2 type1) type1)
-       (t
-        (let ((class1 (numeric-type-class type1))
-              (format1 (numeric-type-format type1))
-              (complexp1 (numeric-type-complexp type1))
-              (class2 (numeric-type-class type2))
-              (format2 (numeric-type-format type2))
-              (complexp2 (numeric-type-complexp type2)))
-          (cond
-            ((and (eq class1 class2)
-                  (eq format1 format2)
-                  (eq complexp1 complexp2)
-                  (or (numeric-types-intersect type1 type2)
-                      (numeric-types-adjacent type1 type2)
-                      (numeric-types-adjacent type2 type1)))
-             (make-numeric-type
-              :class class1
-              :format format1
-              :complexp complexp1
-              :low (numeric-bound-max (numeric-type-low type1)
-                                      (numeric-type-low type2)
-                                      <= < t)
-              :high (numeric-bound-max (numeric-type-high type1)
-                                       (numeric-type-high type2)
-                                       >= > t)))
-            ;; FIXME: These two clauses are almost identical, and the
-            ;; consequents are in fact identical in every respect.
-            ((and (eq class1 'rational)
-                  (eq class2 'integer)
-                  (eq format1 format2)
-                  (eq complexp1 complexp2)
-                  (integerp (numeric-type-low type2))
-                  (integerp (numeric-type-high type2))
-                  (= (numeric-type-low type2) (numeric-type-high type2))
-                  (or (numeric-types-adjacent type1 type2)
-                      (numeric-types-adjacent type2 type1)))
-             (make-numeric-type
-              :class 'rational
-              :format format1
-              :complexp complexp1
-              :low (numeric-bound-max (numeric-type-low type1)
-                                      (numeric-type-low type2)
-                                      <= < t)
-              :high (numeric-bound-max (numeric-type-high type1)
-                                       (numeric-type-high type2)
-                                       >= > t)))
-            ((and (eq class1 'integer)
-                  (eq class2 'rational)
-                  (eq format1 format2)
-                  (eq complexp1 complexp2)
-                  (integerp (numeric-type-low type1))
-                  (integerp (numeric-type-high type1))
-                  (= (numeric-type-low type1) (numeric-type-high type1))
-                  (or (numeric-types-adjacent type1 type2)
-                      (numeric-types-adjacent type2 type1)))
-             (make-numeric-type
-              :class 'rational
-              :format format1
-              :complexp complexp1
-              :low (numeric-bound-max (numeric-type-low type1)
-                                      (numeric-type-low type2)
-                                      <= < t)
-              :high (numeric-bound-max (numeric-type-high type1)
-                                       (numeric-type-high type2)
-                                       >= > t)))
-            (t nil))))))
+        ((csubtypep type2 type1) type1)
+        (t
+         (let ((class1 (numeric-type-class type1))
+               (format1 (numeric-type-format type1))
+               (complexp1 (numeric-type-complexp type1))
+               (class2 (numeric-type-class type2))
+               (format2 (numeric-type-format type2))
+               (complexp2 (numeric-type-complexp type2)))
+           (cond
+             ((and (eq class1 class2)
+                   (eq format1 format2)
+                   (eq complexp1 complexp2)
+                   (or *approximate-numeric-unions*
+                       (numeric-types-intersect type1 type2)
+                       (numeric-types-adjacent type1 type2)
+                       (numeric-types-adjacent type2 type1)))
+              (make-numeric-type
+               :class class1
+               :format format1
+               :complexp complexp1
+               :low (numeric-bound-max (numeric-type-low type1)
+                                       (numeric-type-low type2)
+                                       <= < t)
+               :high (numeric-bound-max (numeric-type-high type1)
+                                        (numeric-type-high type2)
+                                        >= > t)))
+             ;; FIXME: These two clauses are almost identical, and the
+             ;; consequents are in fact identical in every respect.
+             ((and (eq class1 'rational)
+                   (eq class2 'integer)
+                   (eq format1 format2)
+                   (eq complexp1 complexp2)
+                   (integerp (numeric-type-low type2))
+                   (integerp (numeric-type-high type2))
+                   (= (numeric-type-low type2) (numeric-type-high type2))
+                   (or *approximate-numeric-unions*
+                       (numeric-types-adjacent type1 type2)
+                       (numeric-types-adjacent type2 type1)))
+              (make-numeric-type
+               :class 'rational
+               :format format1
+               :complexp complexp1
+               :low (numeric-bound-max (numeric-type-low type1)
+                                       (numeric-type-low type2)
+                                       <= < t)
+               :high (numeric-bound-max (numeric-type-high type1)
+                                        (numeric-type-high type2)
+                                        >= > t)))
+             ((and (eq class1 'integer)
+                   (eq class2 'rational)
+                   (eq format1 format2)
+                   (eq complexp1 complexp2)
+                   (integerp (numeric-type-low type1))
+                   (integerp (numeric-type-high type1))
+                   (= (numeric-type-low type1) (numeric-type-high type1))
+                   (or *approximate-numeric-unions*
+                       (numeric-types-adjacent type1 type2)
+                       (numeric-types-adjacent type2 type1)))
+              (make-numeric-type
+               :class 'rational
+               :format format1
+               :complexp complexp1
+               :low (numeric-bound-max (numeric-type-low type1)
+                                       (numeric-type-low type2)
+                                       <= < t)
+               :high (numeric-bound-max (numeric-type-high type1)
+                                        (numeric-type-high type2)
+                                        >= > t)))
+             (t nil))))))

 
 
 (!cold-init-forms
   (setf (info :type :kind 'number)
 
 
 (!cold-init-forms
   (setf (info :type :kind 'number)

-       #+sb-xc-host :defined #-sb-xc-host :primitive)
+        #+sb-xc-host :defined #-sb-xc-host :primitive)

   (setf (info :type :builtin 'number)
   (setf (info :type :builtin 'number)

-       (make-numeric-type :complexp nil)))
+        (make-numeric-type :complexp nil)))

 
 (!def-type-translator complex (&optional (typespec '*))
   (if (eq typespec '*)
 
 (!def-type-translator complex (&optional (typespec '*))
   (if (eq typespec '*)

-      (make-numeric-type :complexp :complex)
+      (specifier-type '(complex real))

       (labels ((not-numeric ()
       (labels ((not-numeric ()

-                (error "The component type for COMPLEX is not numeric: ~S"
-                       typespec))
-              (not-real ()
-                (error "The component type for COMPLEX is not real: ~S"
-                       typespec))
-              (complex1 (component-type)
-                (unless (numeric-type-p component-type)
-                  (not-numeric))
-                (when (eq (numeric-type-complexp component-type) :complex)
-                  (not-real))
-                (modified-numeric-type component-type :complexp :complex))
-              (complex-union (component)
-                (unless (numberp component)
-                  (not-numeric))
-                ;; KLUDGE: This TYPECASE more or less does
-                ;; (UPGRADED-COMPLEX-PART-TYPE (TYPE-OF COMPONENT)),
-                ;; (plus a small hack to treat (EQL COMPONENT 0) specially)
-                ;; but uses logic cut and pasted from the DEFUN of
-                ;; UPGRADED-COMPLEX-PART-TYPE. That's fragile, because
-                ;; changing the definition of UPGRADED-COMPLEX-PART-TYPE
-                ;; would tend to break the code here. Unfortunately,
-                ;; though, reusing UPGRADED-COMPLEX-PART-TYPE here
-                ;; would cause another kind of fragility, because
-                ;; ANSI's definition of TYPE-OF is so weak that e.g.
-                ;; (UPGRADED-COMPLEX-PART-TYPE (TYPE-OF 1/2)) could
-                ;; end up being (UPGRADED-COMPLEX-PART-TYPE 'REAL)
-                ;; instead of (UPGRADED-COMPLEX-PART-TYPE 'RATIONAL).
-                ;; So using TYPE-OF would mean that ANSI-conforming
-                ;; maintenance changes in TYPE-OF could break the code here.
-                ;; It's not clear how best to fix this. -- WHN 2002-01-21,
-                ;; trying to summarize CSR's concerns in his patch
-                (typecase component
-                  (complex (error "The component type for COMPLEX (EQL X) ~
-                                    is complex: ~S"
-                                  component))
-                  ((eql 0) (specifier-type nil)) ; as required by ANSI
-                  (single-float (specifier-type '(complex single-float)))
-                  (double-float (specifier-type '(complex double-float)))
-                  #!+long-float
-                  (long-float (specifier-type '(complex long-float)))
-                  (rational (specifier-type '(complex rational)))
-                  (t (specifier-type '(complex real))))))
-       (let ((ctype (specifier-type typespec)))
-         (typecase ctype
-           (numeric-type (complex1 ctype))
-           (union-type (apply #'type-union
-                              ;; FIXME: This code could suffer from
-                              ;; (admittedly very obscure) cases of
-                              ;; bug 145 e.g. when TYPE is
-                              ;;   (OR (AND INTEGER (SATISFIES ODDP))
-                              ;;       (AND FLOAT (SATISFIES FOO))
-                              ;; and not even report the problem very well.
-                              (mapcar #'complex1
-                                      (union-type-types ctype))))
-           ;; MEMBER-TYPE is almost the same as UNION-TYPE, but
-           ;; there's a gotcha: (COMPLEX (EQL 0)) is, according to
-           ;; ANSI, equal to type NIL, the empty set.
-           (member-type (apply #'type-union
-                               (mapcar #'complex-union
-                                       (member-type-members ctype))))
-           (t
-            (multiple-value-bind (subtypep certainly)
-                (csubtypep ctype (specifier-type 'real))
-              (if (and (not subtypep) certainly)
-                  (not-real)
-                  ;; ANSI just says that TYPESPEC is any subtype of
-                  ;; type REAL, not necessarily a NUMERIC-TYPE. In
-                  ;; particular, at this point TYPESPEC could legally be
-                  ;; an intersection type like (AND REAL (SATISFIES ODDP)),
-                  ;; in which case we fall through the logic above and
-                  ;; end up here, stumped.
-                  (bug "~@<(known bug #145): The type ~S is too hairy to be 
-                         used for a COMPLEX component.~:@>"
-                       typespec)))))))))
+                 (error "The component type for COMPLEX is not numeric: ~S"
+                        typespec))
+               (not-real ()
+                 (error "The component type for COMPLEX is not a subtype of REAL: ~S"
+                        typespec))
+               (complex1 (component-type)
+                 (unless (numeric-type-p component-type)
+                   (not-numeric))
+                 (when (eq (numeric-type-complexp component-type) :complex)
+                   (not-real))
+                 (if (csubtypep component-type (specifier-type '(eql 0)))
+                     *empty-type*
+                     (modified-numeric-type component-type
+                                            :complexp :complex)))
+               (do-complex (ctype)
+                 (cond
+                   ((eq ctype *empty-type*) *empty-type*)
+                   ((eq ctype *universal-type*) (not-real))
+                   ((typep ctype 'numeric-type) (complex1 ctype))
+                   ((typep ctype 'union-type)
+                    (apply #'type-union
+                           (mapcar #'do-complex (union-type-types ctype))))
+                   ((typep ctype 'member-type)
+                    (apply #'type-union
+                           (mapcar-member-type-members
+                            (lambda (x) (do-complex (ctype-of x)))
+                            ctype)))
+                   ((and (typep ctype 'intersection-type)
+                         ;; FIXME: This is very much a
+                         ;; not-quite-worst-effort, but we are required to do
+                         ;; something here because of our representation of
+                         ;; RATIO as (AND RATIONAL (NOT INTEGER)): we must
+                         ;; allow users to ask about (COMPLEX RATIO).  This
+                         ;; will of course fail to work right on such types
+                         ;; as (AND INTEGER (SATISFIES ZEROP))...
+                         (let ((numbers (remove-if-not
+                                         #'numeric-type-p
+                                         (intersection-type-types ctype))))
+                           (and (car numbers)
+                                (null (cdr numbers))
+                                (eq (numeric-type-complexp (car numbers)) :real)
+                                (complex1 (car numbers))))))
+                   (t
+                    (multiple-value-bind (subtypep certainly)
+                        (csubtypep ctype (specifier-type 'real))
+                      (if (and (not subtypep) certainly)
+                          (not-real)
+                          ;; ANSI just says that TYPESPEC is any subtype of
+                          ;; type REAL, not necessarily a NUMERIC-TYPE. In
+                          ;; particular, at this point TYPESPEC could legally
+                          ;; be a hairy type like (AND NUMBER (SATISFIES
+                          ;; REALP) (SATISFIES ZEROP)), in which case we fall
+                          ;; through the logic above and end up here,
+                          ;; stumped.
+                          (bug "~@<(known bug #145): The type ~S is too hairy to be ~
+used for a COMPLEX component.~:@>"
+                               typespec)))))))
+        (let ((ctype (specifier-type typespec)))
+          (do-complex ctype)))))

 
 ;;; If X is *, return NIL, otherwise return the bound, which must be a
 ;;; member of TYPE or a one-element list of a member of TYPE.
 #!-sb-fluid (declaim (inline canonicalized-bound))
 (defun canonicalized-bound (bound type)
   (cond ((eq bound '*) nil)
 
 ;;; If X is *, return NIL, otherwise return the bound, which must be a
 ;;; member of TYPE or a one-element list of a member of TYPE.
 #!-sb-fluid (declaim (inline canonicalized-bound))
 (defun canonicalized-bound (bound type)
   (cond ((eq bound '*) nil)

-       ((or (sb!xc:typep bound type)
-            (and (consp bound)
-                 (sb!xc:typep (car bound) type)
-                 (null (cdr bound))))
-         bound)
-       (t
-        (error "Bound is not ~S, a ~S or a list of a ~S: ~S"
-               '*
-               type
-               type
-               bound))))
+        ((or (sb!xc:typep bound type)
+             (and (consp bound)
+                  (sb!xc:typep (car bound) type)
+                  (null (cdr bound))))
+          bound)
+        (t
+         (error "Bound is not ~S, a ~S or a list of a ~S: ~S"
+                '*
+                type
+                type
+                bound))))

 
 (!def-type-translator integer (&optional (low '*) (high '*))
   (let* ((l (canonicalized-bound low 'integer))
 
 (!def-type-translator integer (&optional (low '*) (high '*))
   (let* ((l (canonicalized-bound low 'integer))

-        (lb (if (consp l) (1+ (car l)) l))
-        (h (canonicalized-bound high 'integer))
-        (hb (if (consp h) (1- (car h)) h)))
+         (lb (if (consp l) (1+ (car l)) l))
+         (h (canonicalized-bound high 'integer))
+         (hb (if (consp h) (1- (car h)) h)))

     (if (and hb lb (< hb lb))
     (if (and hb lb (< hb lb))

-       *empty-type*
+        *empty-type*

       (make-numeric-type :class 'integer
       (make-numeric-type :class 'integer

-                        :complexp :real
-                        :enumerable (not (null (and l h)))
-                        :low lb
-                        :high hb))))
+                         :complexp :real
+                         :enumerable (not (null (and l h)))
+                         :low lb
+                         :high hb))))

 
 (defmacro !def-bounded-type (type class format)
   `(!def-type-translator ,type (&optional (low '*) (high '*))
      (let ((lb (canonicalized-bound low ',type))
 
 (defmacro !def-bounded-type (type class format)
   `(!def-type-translator ,type (&optional (low '*) (high '*))
      (let ((lb (canonicalized-bound low ',type))

-          (hb (canonicalized-bound high ',type)))
+           (hb (canonicalized-bound high ',type)))

        (if (not (numeric-bound-test* lb hb <= <))
        (if (not (numeric-bound-test* lb hb <= <))

-          *empty-type*
-        (make-numeric-type :class ',class
-                           :format ',format
-                           :low lb
-                           :high hb)))))
+           *empty-type*
+         (make-numeric-type :class ',class
+                            :format ',format
+                            :low lb
+                            :high hb)))))

 
 (!def-bounded-type rational rational nil)
 
 
 (!def-bounded-type rational rational nil)
 

@@ -1848,39 +2117,93 @@
 ;;; FIXME: It's probably necessary to do something to fix the
 ;;; analogous problem with INTEGER and RATIONAL types. Perhaps
 ;;; bounded RATIONAL types should be represented as (OR RATIO INTEGER).
 ;;; FIXME: It's probably necessary to do something to fix the
 ;;; analogous problem with INTEGER and RATIONAL types. Perhaps
 ;;; bounded RATIONAL types should be represented as (OR RATIO INTEGER).

-(defun coerce-bound (bound type inner-coerce-bound-fun)
+(defun coerce-bound (bound type upperp inner-coerce-bound-fun)

   (declare (type function inner-coerce-bound-fun))
   (declare (type function inner-coerce-bound-fun))

-  (cond ((eql bound '*)
-        bound)
-       ((consp bound)
-        (destructuring-bind (inner-bound) bound
-          (list (funcall inner-coerce-bound-fun inner-bound type))))
-       (t
-        (funcall inner-coerce-bound-fun bound type))))
-(defun inner-coerce-real-bound (bound type)
-  (ecase type
-    (rational (rationalize bound))
-    (float (if (floatp bound)
-              bound
-              ;; Coerce to the widest float format available, to
-              ;; avoid unnecessary loss of precision:
-              (coerce bound 'long-float)))))
-(defun coerced-real-bound (bound type)
-  (coerce-bound bound type #'inner-coerce-real-bound))
-(defun coerced-float-bound (bound type)
-  (coerce-bound bound type #'coerce))
+  (if (eql bound '*)
+      bound
+      (funcall inner-coerce-bound-fun bound type upperp)))
+(defun inner-coerce-real-bound (bound type upperp)
+  #+sb-xc-host (declare (ignore upperp))
+  (let #+sb-xc-host ()
+       #-sb-xc-host
+       ((nl (load-time-value (symbol-value 'sb!xc:most-negative-long-float)))
+        (pl (load-time-value (symbol-value 'sb!xc:most-positive-long-float))))
+    (let ((nbound (if (consp bound) (car bound) bound))
+          (consp (consp bound)))
+      (ecase type
+        (rational
+         (if consp
+             (list (rational nbound))
+             (rational nbound)))
+        (float
+         (cond
+           ((floatp nbound) bound)
+           (t
+            ;; Coerce to the widest float format available, to avoid
+            ;; unnecessary loss of precision, but don't coerce
+            ;; unrepresentable numbers, except on the host where we
+            ;; shouldn't be making these types (but KLUDGE: can't even
+            ;; assert portably that we're not).
+            #-sb-xc-host
+            (ecase upperp
+              ((nil)
+               (when (< nbound nl) (return-from inner-coerce-real-bound nl)))
+              ((t)
+               (when (> nbound pl) (return-from inner-coerce-real-bound pl))))
+            (let ((result (coerce nbound 'long-float)))
+              (if consp (list result) result)))))))))
+(defun inner-coerce-float-bound (bound type upperp)
+  #+sb-xc-host (declare (ignore upperp))
+  (let #+sb-xc-host ()
+       #-sb-xc-host
+       ((nd (load-time-value (symbol-value 'sb!xc:most-negative-double-float)))
+        (pd (load-time-value (symbol-value 'sb!xc:most-positive-double-float)))
+        (ns (load-time-value (symbol-value 'sb!xc:most-negative-single-float)))
+        (ps (load-time-value
+             (symbol-value 'sb!xc:most-positive-single-float))))
+    (let ((nbound (if (consp bound) (car bound) bound))
+          (consp (consp bound)))
+      (ecase type
+        (single-float
+         (cond
+           ((typep nbound 'single-float) bound)
+           (t
+            #-sb-xc-host
+            (ecase upperp
+              ((nil)
+               (when (< nbound ns) (return-from inner-coerce-float-bound ns)))
+              ((t)
+               (when (> nbound ps) (return-from inner-coerce-float-bound ps))))
+            (let ((result (coerce nbound 'single-float)))
+              (if consp (list result) result)))))
+        (double-float
+         (cond
+           ((typep nbound 'double-float) bound)
+           (t
+            #-sb-xc-host
+            (ecase upperp
+              ((nil)
+               (when (< nbound nd) (return-from inner-coerce-float-bound nd)))
+              ((t)
+               (when (> nbound pd) (return-from inner-coerce-float-bound pd))))
+            (let ((result (coerce nbound 'double-float)))
+              (if consp (list result) result)))))))))
+(defun coerced-real-bound (bound type upperp)
+  (coerce-bound bound type upperp #'inner-coerce-real-bound))
+(defun coerced-float-bound (bound type upperp)
+  (coerce-bound bound type upperp #'inner-coerce-float-bound))

 (!def-type-translator real (&optional (low '*) (high '*))
 (!def-type-translator real (&optional (low '*) (high '*))

-  (specifier-type `(or (float ,(coerced-real-bound  low 'float)
-                             ,(coerced-real-bound high 'float))
-                      (rational ,(coerced-real-bound  low 'rational)
-                                ,(coerced-real-bound high 'rational)))))
+  (specifier-type `(or (float ,(coerced-real-bound  low 'float nil)
+                              ,(coerced-real-bound high 'float t))
+                       (rational ,(coerced-real-bound  low 'rational nil)
+                                 ,(coerced-real-bound high 'rational t)))))

 (!def-type-translator float (&optional (low '*) (high '*))
 (!def-type-translator float (&optional (low '*) (high '*))

-  (specifier-type 
-   `(or (single-float ,(coerced-float-bound  low 'single-float)
-                     ,(coerced-float-bound high 'single-float))
-       (double-float ,(coerced-float-bound  low 'double-float)
-                     ,(coerced-float-bound high 'double-float))
-       #!+long-float ,(error "stub: no long float support yet"))))
+  (specifier-type
+   `(or (single-float ,(coerced-float-bound  low 'single-float nil)
+                      ,(coerced-float-bound high 'single-float t))
+        (double-float ,(coerced-float-bound  low 'double-float nil)
+                      ,(coerced-float-bound high 'double-float t))
+        #!+long-float ,(error "stub: no long float support yet"))))

 
 (defmacro !define-float-format (f)
   `(!def-bounded-type ,f float ,f))
 
 (defmacro !define-float-format (f)
   `(!def-bounded-type ,f float ,f))

@@ -1893,43 +2216,43 @@
 (defun numeric-types-intersect (type1 type2)
   (declare (type numeric-type type1 type2))
   (let* ((class1 (numeric-type-class type1))
 (defun numeric-types-intersect (type1 type2)
   (declare (type numeric-type type1 type2))
   (let* ((class1 (numeric-type-class type1))

-        (class2 (numeric-type-class type2))
-        (complexp1 (numeric-type-complexp type1))
-        (complexp2 (numeric-type-complexp type2))
-        (format1 (numeric-type-format type1))
-        (format2 (numeric-type-format type2))
-        (low1 (numeric-type-low type1))
-        (high1 (numeric-type-high type1))
-        (low2 (numeric-type-low type2))
-        (high2 (numeric-type-high type2)))
+         (class2 (numeric-type-class type2))
+         (complexp1 (numeric-type-complexp type1))
+         (complexp2 (numeric-type-complexp type2))
+         (format1 (numeric-type-format type1))
+         (format2 (numeric-type-format type2))
+         (low1 (numeric-type-low type1))
+         (high1 (numeric-type-high type1))
+         (low2 (numeric-type-low type2))
+         (high2 (numeric-type-high type2)))

     ;; If one is complex and the other isn't, then they are disjoint.
     (cond ((not (or (eq complexp1 complexp2)
     ;; If one is complex and the other isn't, then they are disjoint.
     (cond ((not (or (eq complexp1 complexp2)

-                   (null complexp1) (null complexp2)))
-          nil)
-         ;; If either type is a float, then the other must either be
-         ;; specified to be a float or unspecified. Otherwise, they
-         ;; are disjoint.
-         ((and (eq class1 'float)
-               (not (member class2 '(float nil)))) nil)
-         ((and (eq class2 'float)
-               (not (member class1 '(float nil)))) nil)
-         ;; If the float formats are specified and different, the
-         ;; types are disjoint.
-         ((not (or (eq format1 format2) (null format1) (null format2)))
-          nil)
-         (t
-          ;; Check the bounds. This is a bit odd because we must
-          ;; always have the outer bound of the interval as the
-          ;; second arg.
-          (if (numeric-bound-test high1 high2 <= <)
-              (or (and (numeric-bound-test low1 low2 >= >)
-                       (numeric-bound-test* low1 high2 <= <))
-                  (and (numeric-bound-test low2 low1 >= >)
-                       (numeric-bound-test* low2 high1 <= <)))
-              (or (and (numeric-bound-test* low2 high1 <= <)
-                       (numeric-bound-test low2 low1 >= >))
-                  (and (numeric-bound-test high2 high1 <= <)
-                       (numeric-bound-test* high2 low1 >= >))))))))
+                    (null complexp1) (null complexp2)))
+           nil)
+          ;; If either type is a float, then the other must either be
+          ;; specified to be a float or unspecified. Otherwise, they
+          ;; are disjoint.
+          ((and (eq class1 'float)
+                (not (member class2 '(float nil)))) nil)
+          ((and (eq class2 'float)
+                (not (member class1 '(float nil)))) nil)
+          ;; If the float formats are specified and different, the
+          ;; types are disjoint.
+          ((not (or (eq format1 format2) (null format1) (null format2)))
+           nil)
+          (t
+           ;; Check the bounds. This is a bit odd because we must
+           ;; always have the outer bound of the interval as the
+           ;; second arg.
+           (if (numeric-bound-test high1 high2 <= <)
+               (or (and (numeric-bound-test low1 low2 >= >)
+                        (numeric-bound-test* low1 high2 <= <))
+                   (and (numeric-bound-test low2 low1 >= >)
+                        (numeric-bound-test* low2 high1 <= <)))
+               (or (and (numeric-bound-test* low2 high1 <= <)
+                        (numeric-bound-test low2 low1 >= >))
+                   (and (numeric-bound-test high2 high1 <= <)
+                        (numeric-bound-test* high2 low1 >= >))))))))

 
 ;;; Take the numeric bound X and convert it into something that can be
 ;;; used as a bound in a numeric type with the specified CLASS and
 
 ;;; Take the numeric bound X and convert it into something that can be
 ;;; used as a bound in a numeric type with the specified CLASS and

@@ -1954,15 +2277,25 @@
 (defun round-numeric-bound (x class format up-p)
   (if x
       (let ((cx (if (consp x) (car x) x)))
 (defun round-numeric-bound (x class format up-p)
   (if x
       (let ((cx (if (consp x) (car x) x)))

-       (ecase class
-         ((nil rational) x)
-         (integer
-          (if (and (consp x) (integerp cx))
-              (if up-p (1+ cx) (1- cx))
-              (if up-p (ceiling cx) (floor cx))))
-         (float
-          (let ((res (if format (coerce cx format) (float cx))))
-            (if (consp x) (list res) res)))))
+        (ecase class
+          ((nil rational) x)
+          (integer
+           (if (and (consp x) (integerp cx))
+               (if up-p (1+ cx) (1- cx))
+               (if up-p (ceiling cx) (floor cx))))
+          (float
+           (let ((res
+                  (cond
+                    ((and format (subtypep format 'double-float))
+                     (if (<= most-negative-double-float cx most-positive-double-float)
+                         (coerce cx format)
+                         nil))
+                    (t
+                     (if (<= most-negative-single-float cx most-positive-single-float)
+                         ;; FIXME: bug #389
+                         (coerce cx (or format 'single-float))
+                         nil)))))
+             (if (consp x) (list res) res)))))

       nil))
 
 ;;; Handle the case of type intersection on two numeric types. We use
       nil))
 
 ;;; Handle the case of type intersection on two numeric types. We use

@@ -1985,32 +2318,32 @@
   (declare (type numeric-type type1 type2))
   (if (numeric-types-intersect type1 type2)
       (let* ((class1 (numeric-type-class type1))
   (declare (type numeric-type type1 type2))
   (if (numeric-types-intersect type1 type2)
       (let* ((class1 (numeric-type-class type1))

-            (class2 (numeric-type-class type2))
-            (class (ecase class1
-                     ((nil) class2)
-                     ((integer float) class1)
-                     (rational (if (eq class2 'integer)
-                                      'integer
-                                      'rational))))
-            (format (or (numeric-type-format type1)
-                        (numeric-type-format type2))))
-       (make-numeric-type
-        :class class
-        :format format
-        :complexp (or (numeric-type-complexp type1)
-                      (numeric-type-complexp type2))
-        :low (numeric-bound-max
-              (round-numeric-bound (numeric-type-low type1)
-                                   class format t)
-              (round-numeric-bound (numeric-type-low type2)
-                                   class format t)
-              > >= nil)
-        :high (numeric-bound-max
-               (round-numeric-bound (numeric-type-high type1)
-                                    class format nil)
-               (round-numeric-bound (numeric-type-high type2)
-                                    class format nil)
-               < <= nil)))
+             (class2 (numeric-type-class type2))
+             (class (ecase class1
+                      ((nil) class2)
+                      ((integer float) class1)
+                      (rational (if (eq class2 'integer)
+                                       'integer
+                                       'rational))))
+             (format (or (numeric-type-format type1)
+                         (numeric-type-format type2))))
+        (make-numeric-type
+         :class class
+         :format format
+         :complexp (or (numeric-type-complexp type1)
+                       (numeric-type-complexp type2))
+         :low (numeric-bound-max
+               (round-numeric-bound (numeric-type-low type1)
+                                    class format t)
+               (round-numeric-bound (numeric-type-low type2)
+                                    class format t)
+               > >= nil)
+         :high (numeric-bound-max
+                (round-numeric-bound (numeric-type-high type1)
+                                     class format nil)
+                (round-numeric-bound (numeric-type-high type2)
+                                     class format nil)
+                < <= nil)))

       *empty-type*))
 
 ;;; Given two float formats, return the one with more precision. If
       *empty-type*))
 
 ;;; Given two float formats, return the one with more precision. If

@@ -2019,7 +2352,7 @@
   (when (and f1 f2)
     (dolist (f *float-formats* (error "bad float format: ~S" f1))
       (when (or (eq f f1) (eq f f2))
   (when (and f1 f2)
     (dolist (f *float-formats* (error "bad float format: ~S" f1))
       (when (or (eq f f1) (eq f f2))

-       (return f)))))
+        (return f)))))

 
 ;;; Return the result of an operation on TYPE1 and TYPE2 according to
 ;;; the rules of numeric contagion. This is always NUMBER, some float
 
 ;;; Return the result of an operation on TYPE1 and TYPE2 according to
 ;;; the rules of numeric contagion. This is always NUMBER, some float

@@ -2033,235 +2366,273 @@
 (defun numeric-contagion (type1 type2)
   (if (and (numeric-type-p type1) (numeric-type-p type2))
       (let ((class1 (numeric-type-class type1))
 (defun numeric-contagion (type1 type2)
   (if (and (numeric-type-p type1) (numeric-type-p type2))
       (let ((class1 (numeric-type-class type1))

-           (class2 (numeric-type-class type2))
-           (format1 (numeric-type-format type1))
-           (format2 (numeric-type-format type2))
-           (complexp1 (numeric-type-complexp type1))
-           (complexp2 (numeric-type-complexp type2)))
-       (cond ((or (null complexp1)
-                  (null complexp2))
-              (specifier-type 'number))
-             ((eq class1 'float)
-              (make-numeric-type
-               :class 'float
-               :format (ecase class2
-                         (float (float-format-max format1 format2))
-                         ((integer rational) format1)
-                         ((nil)
-                          ;; A double-float with any real number is a
-                          ;; double-float.
-                          #!-long-float
-                          (if (eq format1 'double-float)
-                            'double-float
-                            nil)
-                          ;; A long-float with any real number is a
-                          ;; long-float.
-                          #!+long-float
-                          (if (eq format1 'long-float)
-                            'long-float
-                            nil)))
-               :complexp (if (or (eq complexp1 :complex)
-                                 (eq complexp2 :complex))
-                             :complex
-                             :real)))
-             ((eq class2 'float) (numeric-contagion type2 type1))
-             ((and (eq complexp1 :real) (eq complexp2 :real))
-              (make-numeric-type
-               :class (and class1 class2 'rational)
-               :complexp :real))
-             (t
-              (specifier-type 'number))))
+            (class2 (numeric-type-class type2))
+            (format1 (numeric-type-format type1))
+            (format2 (numeric-type-format type2))
+            (complexp1 (numeric-type-complexp type1))
+            (complexp2 (numeric-type-complexp type2)))
+        (cond ((or (null complexp1)
+                   (null complexp2))
+               (specifier-type 'number))
+              ((eq class1 'float)
+               (make-numeric-type
+                :class 'float
+                :format (ecase class2
+                          (float (float-format-max format1 format2))
+                          ((integer rational) format1)
+                          ((nil)
+                           ;; A double-float with any real number is a
+                           ;; double-float.
+                           #!-long-float
+                           (if (eq format1 'double-float)
+                             'double-float
+                             nil)
+                           ;; A long-float with any real number is a
+                           ;; long-float.
+                           #!+long-float
+                           (if (eq format1 'long-float)
+                             'long-float
+                             nil)))
+                :complexp (if (or (eq complexp1 :complex)
+                                  (eq complexp2 :complex))
+                              :complex
+                              :real)))
+              ((eq class2 'float) (numeric-contagion type2 type1))
+              ((and (eq complexp1 :real) (eq complexp2 :real))
+               (make-numeric-type
+                :class (and class1 class2 'rational)
+                :complexp :real))
+              (t
+               (specifier-type 'number))))

       (specifier-type 'number)))
 \f
 ;;;; array types
 
 (!define-type-class array)
 
       (specifier-type 'number)))
 \f
 ;;;; array types
 
 (!define-type-class array)
 

-;;; What this does depends on the setting of the
-;;; *USE-IMPLEMENTATION-TYPES* switch. If true, return the specialized
-;;; element type, otherwise return the original element type.
-(defun specialized-element-type-maybe (type)
-  (declare (type array-type type))
-  (if *use-implementation-types*
-      (array-type-specialized-element-type type)
-      (array-type-element-type type)))
-

 (!define-type-method (array :simple-=) (type1 type2)
 (!define-type-method (array :simple-=) (type1 type2)

-  (if (or (unknown-type-p (array-type-element-type type1))
-         (unknown-type-p (array-type-element-type type2)))
-      (multiple-value-bind (equalp certainp)
-         (type= (array-type-element-type type1)
-                (array-type-element-type type2))
-       ;; by its nature, the call to TYPE= should never return NIL,
-       ;; T, as we don't know what the UNKNOWN-TYPE will grow up to
-       ;; be.  -- CSR, 2002-08-19
-       (aver (not (and (not equalp) certainp)))
-       (values equalp certainp))
-      (values (and (equal (array-type-dimensions type1)
-                         (array-type-dimensions type2))
-                  (eq (array-type-complexp type1)
-                      (array-type-complexp type2))
-                  (type= (specialized-element-type-maybe type1)
-                         (specialized-element-type-maybe type2)))
-             t)))
+  (cond ((not (and (equal (array-type-dimensions type1)
+                          (array-type-dimensions type2))
+                   (eq (array-type-complexp type1)
+                       (array-type-complexp type2))))
+         (values nil t))
+        ((or (unknown-type-p (array-type-element-type type1))
+             (unknown-type-p (array-type-element-type type2)))
+         (type= (array-type-element-type type1)
+                (array-type-element-type type2)))
+        (t
+         (values (type= (array-type-specialized-element-type type1)
+                        (array-type-specialized-element-type type2))
+                 t))))

 
 (!define-type-method (array :negate) (type)
   ;; FIXME (and hint to PFD): we're vulnerable here to attacks of the
   ;; form "are (AND ARRAY (NOT (ARRAY T))) and (OR (ARRAY BIT) (ARRAY
 
 (!define-type-method (array :negate) (type)
   ;; FIXME (and hint to PFD): we're vulnerable here to attacks of the
   ;; form "are (AND ARRAY (NOT (ARRAY T))) and (OR (ARRAY BIT) (ARRAY

-  ;; NIL) (ARRAY CHAR) ...) equivalent?  -- CSR, 2003-12-10
+  ;; NIL) (ARRAY CHAR) ...) equivalent?" -- CSR, 2003-12-10

   (make-negation-type :type type))
 
 (!define-type-method (array :unparse) (type)
   (let ((dims (array-type-dimensions type))
   (make-negation-type :type type))
 
 (!define-type-method (array :unparse) (type)
   (let ((dims (array-type-dimensions type))

-       (eltype (type-specifier (array-type-element-type type)))
-       (complexp (array-type-complexp type)))
+        (eltype (type-specifier (array-type-element-type type)))
+        (complexp (array-type-complexp type)))

     (cond ((eq dims '*)
     (cond ((eq dims '*)

-          (if (eq eltype '*)
-              (if complexp 'array 'simple-array)
-              (if complexp `(array ,eltype) `(simple-array ,eltype))))
-         ((= (length dims) 1)
-          (if complexp
-              (if (eq (car dims) '*)
-                  (case eltype
-                    (bit 'bit-vector)
-                    (base-char 'base-string)
-                    (* 'vector)
-                    (t `(vector ,eltype)))
-                  (case eltype
-                    (bit `(bit-vector ,(car dims)))
-                    (base-char `(base-string ,(car dims)))
-                    (t `(vector ,eltype ,(car dims)))))
-              (if (eq (car dims) '*)
-                  (case eltype
-                    (bit 'simple-bit-vector)
-                    (base-char 'simple-base-string)
-                    ((t) 'simple-vector)
-                    (t `(simple-array ,eltype (*))))
-                  (case eltype
-                    (bit `(simple-bit-vector ,(car dims)))
-                    (base-char `(simple-base-string ,(car dims)))
-                    ((t) `(simple-vector ,(car dims)))
-                    (t `(simple-array ,eltype ,dims))))))
-         (t
-          (if complexp
-              `(array ,eltype ,dims)
-              `(simple-array ,eltype ,dims))))))
+           (if (eq eltype '*)
+               (ecase complexp
+                 ((t) '(and array (not simple-array)))
+                 ((:maybe) 'array)
+                 ((nil) 'simple-array))
+               (ecase complexp
+                 ((t) `(and (array ,eltype) (not simple-array)))
+                 ((:maybe) `(array ,eltype))
+                 ((nil) `(simple-array ,eltype)))))
+          ((= (length dims) 1)
+           (if complexp
+               (let ((answer
+                      (if (eq (car dims) '*)
+                          (case eltype
+                            (bit 'bit-vector)
+                            ((base-char #!-sb-unicode character) 'base-string)
+                            (* 'vector)
+                            (t `(vector ,eltype)))
+                          (case eltype
+                            (bit `(bit-vector ,(car dims)))
+                            ((base-char #!-sb-unicode character)
+                             `(base-string ,(car dims)))
+                            (t `(vector ,eltype ,(car dims)))))))
+                 (if (eql complexp :maybe)
+                     answer
+                     `(and ,answer (not simple-array))))
+               (if (eq (car dims) '*)
+                   (case eltype
+                     (bit 'simple-bit-vector)
+                     ((base-char #!-sb-unicode character) 'simple-base-string)
+                     ((t) 'simple-vector)
+                     (t `(simple-array ,eltype (*))))
+                   (case eltype
+                     (bit `(simple-bit-vector ,(car dims)))
+                     ((base-char #!-sb-unicode character)
+                      `(simple-base-string ,(car dims)))
+                     ((t) `(simple-vector ,(car dims)))
+                     (t `(simple-array ,eltype ,dims))))))
+          (t
+           (ecase complexp
+             ((t) `(and (array ,eltype ,dims) (not simple-array)))
+             ((:maybe) `(array ,eltype ,dims))
+             ((nil) `(simple-array ,eltype ,dims)))))))

 
 (!define-type-method (array :simple-subtypep) (type1 type2)
   (let ((dims1 (array-type-dimensions type1))
 
 (!define-type-method (array :simple-subtypep) (type1 type2)
   (let ((dims1 (array-type-dimensions type1))

-       (dims2 (array-type-dimensions type2))
-       (complexp2 (array-type-complexp type2)))
+        (dims2 (array-type-dimensions type2))
+        (complexp2 (array-type-complexp type2)))

     (cond (;; not subtypep unless dimensions are compatible
     (cond (;; not subtypep unless dimensions are compatible

-          (not (or (eq dims2 '*)
-                   (and (not (eq dims1 '*))
-                        ;; (sbcl-0.6.4 has trouble figuring out that
-                        ;; DIMS1 and DIMS2 must be lists at this
-                        ;; point, and knowing that is important to
-                        ;; compiling EVERY efficiently.)
-                        (= (length (the list dims1))
-                           (length (the list dims2)))
-                        (every (lambda (x y)
-                                 (or (eq y '*) (eql x y)))
-                               (the list dims1)
-                               (the list dims2)))))
-          (values nil t))
-         ;; not subtypep unless complexness is compatible
-         ((not (or (eq complexp2 :maybe)
-                   (eq (array-type-complexp type1) complexp2)))
-          (values nil t))
-         ;; Since we didn't fail any of the tests above, we win
-         ;; if the TYPE2 element type is wild.
-         ((eq (array-type-element-type type2) *wild-type*)
-          (values t t))
-         (;; Since we didn't match any of the special cases above, we
-          ;; can't give a good answer unless both the element types
-          ;; have been defined.
-          (or (unknown-type-p (array-type-element-type type1))
-              (unknown-type-p (array-type-element-type type2)))
-          (values nil nil))
-         (;; Otherwise, the subtype relationship holds iff the
-          ;; types are equal, and they're equal iff the specialized
-          ;; element types are identical.
-          t
-          (values (type= (specialized-element-type-maybe type1)
-                         (specialized-element-type-maybe type2))
-                  t)))))
-
-;;; FIXME: is this dead?
+           (not (or (eq dims2 '*)
+                    (and (not (eq dims1 '*))
+                         ;; (sbcl-0.6.4 has trouble figuring out that
+                         ;; DIMS1 and DIMS2 must be lists at this
+                         ;; point, and knowing that is important to
+                         ;; compiling EVERY efficiently.)
+                         (= (length (the list dims1))
+                            (length (the list dims2)))
+                         (every (lambda (x y)
+                                  (or (eq y '*) (eql x y)))
+                                (the list dims1)
+                                (the list dims2)))))
+           (values nil t))
+          ;; not subtypep unless complexness is compatible
+          ((not (or (eq complexp2 :maybe)
+                    (eq (array-type-complexp type1) complexp2)))
+           (values nil t))
+          ;; Since we didn't fail any of the tests above, we win
+          ;; if the TYPE2 element type is wild.
+          ((eq (array-type-element-type type2) *wild-type*)
+           (values t t))
+          (;; Since we didn't match any of the special cases above, if
+           ;; either element type is unknown we can only give a good
+           ;; answer if they are the same.
+           (or (unknown-type-p (array-type-element-type type1))
+               (unknown-type-p (array-type-element-type type2)))
+           (if (type= (array-type-element-type type1)
+                      (array-type-element-type type2))
+               (values t t)
+               (values nil nil)))
+          (;; Otherwise, the subtype relationship holds iff the
+           ;; types are equal, and they're equal iff the specialized
+           ;; element types are identical.
+           t
+           (values (type= (array-type-specialized-element-type type1)
+                          (array-type-specialized-element-type type2))
+                   t)))))
+

 (!define-superclasses array
 (!define-superclasses array

-  ((base-string base-string)
-   (vector vector)
-   (array))
+  ((vector vector) (array))

   !cold-init-forms)
 
 (defun array-types-intersect (type1 type2)
   (declare (type array-type type1 type2))
   (let ((dims1 (array-type-dimensions type1))
   !cold-init-forms)
 
 (defun array-types-intersect (type1 type2)
   (declare (type array-type type1 type2))
   (let ((dims1 (array-type-dimensions type1))

-       (dims2 (array-type-dimensions type2))
-       (complexp1 (array-type-complexp type1))
-       (complexp2 (array-type-complexp type2)))
+        (dims2 (array-type-dimensions type2))
+        (complexp1 (array-type-complexp type1))
+        (complexp2 (array-type-complexp type2)))

     ;; See whether dimensions are compatible.
     (cond ((not (or (eq dims1 '*) (eq dims2 '*)
     ;; See whether dimensions are compatible.
     (cond ((not (or (eq dims1 '*) (eq dims2 '*)

-                   (and (= (length dims1) (length dims2))
-                        (every (lambda (x y)
-                                 (or (eq x '*) (eq y '*) (= x y)))
-                               dims1 dims2))))
-          (values nil t))
-         ;; See whether complexpness is compatible.
-         ((not (or (eq complexp1 :maybe)
-                   (eq complexp2 :maybe)
-                   (eq complexp1 complexp2)))
-          (values nil t))
-         ;; Old comment:
-         ;;
-         ;;   If either element type is wild, then they intersect.
-         ;;   Otherwise, the types must be identical.
-         ;;
-         ;; FIXME: There seems to have been a fair amount of
-         ;; confusion about the distinction between requested element
-         ;; type and specialized element type; here is one of
-         ;; them. If we request an array to hold objects of an
-         ;; unknown type, we can do no better than represent that
-         ;; type as an array specialized on wild-type.  We keep the
-         ;; requested element-type in the -ELEMENT-TYPE slot, and
-         ;; *WILD-TYPE* in the -SPECIALIZED-ELEMENT-TYPE.  So, here,
-         ;; we must test for the SPECIALIZED slot being *WILD-TYPE*,
-         ;; not just the ELEMENT-TYPE slot.  Maybe the return value
-         ;; in that specific case should be T, NIL?  Or maybe this
-         ;; function should really be called
-         ;; ARRAY-TYPES-COULD-POSSIBLY-INTERSECT?  In any case, this
-         ;; was responsible for bug #123, and this whole issue could
-         ;; do with a rethink and/or a rewrite.  -- CSR, 2002-08-21
-         ((or (eq (array-type-specialized-element-type type1) *wild-type*)
-              (eq (array-type-specialized-element-type type2) *wild-type*)
-              (type= (specialized-element-type-maybe type1)
-                     (specialized-element-type-maybe type2)))
-
-          (values t t))
-         (t
-          (values nil t)))))
+                    (and (= (length dims1) (length dims2))
+                         (every (lambda (x y)
+                                  (or (eq x '*) (eq y '*) (= x y)))
+                                dims1 dims2))))
+           (values nil t))
+          ;; See whether complexpness is compatible.
+          ((not (or (eq complexp1 :maybe)
+                    (eq complexp2 :maybe)
+                    (eq complexp1 complexp2)))
+           (values nil t))
+          ;; Old comment:
+          ;;
+          ;;   If either element type is wild, then they intersect.
+          ;;   Otherwise, the types must be identical.
+          ;;
+          ;; FIXME: There seems to have been a fair amount of
+          ;; confusion about the distinction between requested element
+          ;; type and specialized element type; here is one of
+          ;; them. If we request an array to hold objects of an
+          ;; unknown type, we can do no better than represent that
+          ;; type as an array specialized on wild-type.  We keep the
+          ;; requested element-type in the -ELEMENT-TYPE slot, and
+          ;; *WILD-TYPE* in the -SPECIALIZED-ELEMENT-TYPE.  So, here,
+          ;; we must test for the SPECIALIZED slot being *WILD-TYPE*,
+          ;; not just the ELEMENT-TYPE slot.  Maybe the return value
+          ;; in that specific case should be T, NIL?  Or maybe this
+          ;; function should really be called
+          ;; ARRAY-TYPES-COULD-POSSIBLY-INTERSECT?  In any case, this
+          ;; was responsible for bug #123, and this whole issue could
+          ;; do with a rethink and/or a rewrite.  -- CSR, 2002-08-21
+          ((or (eq (array-type-specialized-element-type type1) *wild-type*)
+               (eq (array-type-specialized-element-type type2) *wild-type*)
+               (type= (array-type-specialized-element-type type1)
+                      (array-type-specialized-element-type type2)))
+
+           (values t t))
+          (t
+           (values nil t)))))
+
+(!define-type-method (array :simple-union2) (type1 type2)
+   (let* ((dims1 (array-type-dimensions type1))
+          (dims2 (array-type-dimensions type2))
+          (complexp1 (array-type-complexp type1))
+          (complexp2 (array-type-complexp type2))
+          (eltype1 (array-type-element-type type1))
+          (eltype2 (array-type-element-type type2))
+          (stype1 (array-type-specialized-element-type type1))
+          (stype2 (array-type-specialized-element-type type2))
+          (wild1 (eq eltype1 *wild-type*))
+          (wild2 (eq eltype2 *wild-type*))
+          (e2 nil))
+     (when (or wild1 wild2
+               (and (or (setf e2 (csubtypep eltype1 eltype2))
+                        (csubtypep eltype2 eltype1))
+                    (type= stype1 stype2)))
+       (make-array-type
+        :dimensions (cond ((or (eq dims1 '*) (eq dims2 '*))
+                           '*)
+                          ((equal dims1 dims2)
+                           dims1)
+                          ((= (length dims1) (length dims2))
+                           (mapcar (lambda (x y) (if (eq x y) x '*))
+                                   dims1 dims2))
+                          (t
+                           '*))
+        :complexp (if (eq complexp1 complexp2) complexp1 :maybe)
+        :element-type (if (or wild2 e2) eltype2 eltype1)
+        :specialized-element-type (if wild2 stype2 stype1)))))

 
 (!define-type-method (array :simple-intersection2) (type1 type2)
   (declare (type array-type type1 type2))
   (if (array-types-intersect type1 type2)
       (let ((dims1 (array-type-dimensions type1))
 
 (!define-type-method (array :simple-intersection2) (type1 type2)
   (declare (type array-type type1 type2))
   (if (array-types-intersect type1 type2)
       (let ((dims1 (array-type-dimensions type1))

-           (dims2 (array-type-dimensions type2))
-           (complexp1 (array-type-complexp type1))
-           (complexp2 (array-type-complexp type2))
-           (eltype1 (array-type-element-type type1))
-           (eltype2 (array-type-element-type type2)))
-       (specialize-array-type
-        (make-array-type
-         :dimensions (cond ((eq dims1 '*) dims2)
-                           ((eq dims2 '*) dims1)
-                           (t
-                            (mapcar (lambda (x y) (if (eq x '*) y x))
-                                    dims1 dims2)))
-         :complexp (if (eq complexp1 :maybe) complexp2 complexp1)
-         :element-type (cond
-                         ((eq eltype1 *wild-type*) eltype2)
-                         ((eq eltype2 *wild-type*) eltype1)
-                         (t (type-intersection eltype1 eltype2))))))
+            (dims2 (array-type-dimensions type2))
+            (complexp1 (array-type-complexp type1))
+            (complexp2 (array-type-complexp type2))
+            (eltype1 (array-type-element-type type1))
+            (eltype2 (array-type-element-type type2))
+            (stype1 (array-type-specialized-element-type type1))
+            (stype2 (array-type-specialized-element-type type2)))
+        (flet ((intersect ()
+                 (make-array-type
+                  :dimensions (cond ((eq dims1 '*) dims2)
+                                    ((eq dims2 '*) dims1)
+                                    (t
+                                     (mapcar (lambda (x y) (if (eq x '*) y x))
+                                             dims1 dims2)))
+                  :complexp (if (eq complexp1 :maybe) complexp2 complexp1)
+                  :element-type (cond
+                                  ((eq eltype1 *wild-type*) eltype2)
+                                  ((eq eltype2 *wild-type*) eltype1)
+                                  (t (type-intersection eltype1 eltype2))))))
+          (if (or (eq stype1 *wild-type*) (eq stype2 *wild-type*))
+              (specialize-array-type (intersect))
+              (let ((type (intersect)))
+                (aver (type= stype1 stype2))
+                (setf (array-type-specialized-element-type type) stype1)
+                type))))

       *empty-type*))
 
 ;;; Check a supplied dimension list to determine whether it is legal,
       *empty-type*))
 
 ;;; Check a supplied dimension list to determine whether it is legal,

@@ -2280,10 +2651,10 @@
        (error "array type with too many dimensions: ~S" dims))
      (dolist (dim dims)
        (unless (eq dim '*)
        (error "array type with too many dimensions: ~S" dims))
      (dolist (dim dims)
        (unless (eq dim '*)

-        (unless (and (integerp dim)
-                     (>= dim 0)
-                     (< dim sb!xc:array-dimension-limit))
-          (error "bad dimension in array type: ~S" dim))))
+         (unless (and (integerp dim)
+                      (>= dim 0)
+                      (< dim sb!xc:array-dimension-limit))
+           (error "bad dimension in array type: ~S" dim))))

      dims)
     (t
      (error "Array dimensions is not a list, integer or *:~%  ~S" dims))))
      dims)
     (t
      (error "Array dimensions is not a list, integer or *:~%  ~S" dims))))

@@ -2293,40 +2664,29 @@
 (!define-type-class member)
 
 (!define-type-method (member :negate) (type)
 (!define-type-class member)
 
 (!define-type-method (member :negate) (type)

-  (let ((members (member-type-members type)))
-    (if (some #'floatp members)
-       (let (floats)
-         (dolist (pair `((0.0f0 . ,(load-time-value (make-unportable-float :single-float-negative-zero)))
-                         (0.0d0 . ,(load-time-value (make-unportable-float :double-float-negative-zero)))
-                         #!+long-float
-                         (0.0l0 . ,(load-time-value (make-unportable-float :long-float-negative-zero)))))
-           (when (member (car pair) members)
-             (aver (not (member (cdr pair) members)))
-             (push (cdr pair) floats)
-             (setf members (remove (car pair) members)))
-           (when (member (cdr pair) members)
-             (aver (not (member (car pair) members)))
-             (push (car pair) floats)
-             (setf members (remove (cdr pair) members))))
-         (apply #'type-intersection
-                (if (null members)
-                    *universal-type*
-                    (make-negation-type
-                     :type (make-member-type :members members)))
-                (mapcar
-                 (lambda (x)
-                   (let ((type (ctype-of x)))
-                     (type-union
-                      (make-negation-type
-                       :type (modified-numeric-type type
-                                                    :low nil :high nil))
-                      (modified-numeric-type type
-                                             :low nil :high (list x))
-                      (make-member-type :members (list x))
-                      (modified-numeric-type type
-                                             :low (list x) :high nil))))
-                 floats)))
-       (make-negation-type :type type))))
+  (let ((xset (member-type-xset type))
+        (fp-zeroes (member-type-fp-zeroes type)))
+    (if fp-zeroes
+        ;; Hairy case, which needs to do a bit of float type
+        ;; canonicalization.
+        (apply #'type-intersection
+               (if (xset-empty-p xset)
+                   *universal-type*
+                   (make-negation-type
+                    :type (make-member-type :xset xset)))
+               (mapcar
+                (lambda (x)
+                  (let* ((opposite (neg-fp-zero x))
+                         (type (ctype-of opposite)))
+                    (type-union
+                     (make-negation-type
+                      :type (modified-numeric-type type :low nil :high nil))
+                     (modified-numeric-type type :low nil :high (list opposite))
+                     (make-member-type :members (list opposite))
+                     (modified-numeric-type type :low (list opposite) :high nil))))
+                fp-zeroes))
+        ;; Easy case
+        (make-negation-type :type type))))

 
 (!define-type-method (member :unparse) (type)
   (let ((members (member-type-members type)))
 
 (!define-type-method (member :unparse) (type)
   (let ((members (member-type-members type)))

@@ -2335,90 +2695,113 @@
       ((type= type (specifier-type 'standard-char)) 'standard-char)
       (t `(member ,@members)))))
 
       ((type= type (specifier-type 'standard-char)) 'standard-char)
       (t `(member ,@members)))))
 

+(!define-type-method (member :singleton-p) (type)
+  (if (eql 1 (member-type-size type))
+      (values t (first (member-type-members type)))
+      (values nil nil)))
+

 (!define-type-method (member :simple-subtypep) (type1 type2)
 (!define-type-method (member :simple-subtypep) (type1 type2)

-  (values (subsetp (member-type-members type1) (member-type-members type2))
-         t))
+   (values (and (xset-subset-p (member-type-xset type1)
+                                 (member-type-xset type2))
+                (subsetp (member-type-fp-zeroes type1)
+                         (member-type-fp-zeroes type2)))
+           t))

 
 (!define-type-method (member :complex-subtypep-arg1) (type1 type2)
 
 (!define-type-method (member :complex-subtypep-arg1) (type1 type2)

-  (every/type (swapped-args-fun #'ctypep)
-             type2
-             (member-type-members type1)))
+  (block punt
+    (mapc-member-type-members
+     (lambda (elt)
+       (multiple-value-bind (ok surep) (ctypep elt type2)
+         (unless surep
+           (return-from punt (values nil nil)))
+         (unless ok
+           (return-from punt (values nil t)))))
+     type1)
+    (values t t)))

 
 ;;; We punt if the odd type is enumerable and intersects with the
 ;;; MEMBER type. If not enumerable, then it is definitely not a
 ;;; subtype of the MEMBER type.
 (!define-type-method (member :complex-subtypep-arg2) (type1 type2)
   (cond ((not (type-enumerable type1)) (values nil t))
 
 ;;; We punt if the odd type is enumerable and intersects with the
 ;;; MEMBER type. If not enumerable, then it is definitely not a
 ;;; subtype of the MEMBER type.
 (!define-type-method (member :complex-subtypep-arg2) (type1 type2)
   (cond ((not (type-enumerable type1)) (values nil t))

-       ((types-equal-or-intersect type1 type2)
-        (invoke-complex-subtypep-arg1-method type1 type2))
-       (t (values nil t))))
+        ((types-equal-or-intersect type1 type2)
+         (invoke-complex-subtypep-arg1-method type1 type2))
+        (t (values nil t))))

 
 (!define-type-method (member :simple-intersection2) (type1 type2)
 
 (!define-type-method (member :simple-intersection2) (type1 type2)

-  (let ((mem1 (member-type-members type1))
-       (mem2 (member-type-members type2)))
-    (cond ((subsetp mem1 mem2) type1)
-         ((subsetp mem2 mem1) type2)
-         (t
-          (let ((res (intersection mem1 mem2)))
-            (if res
-                (make-member-type :members res)
-                *empty-type*))))))
+  (make-member-type :xset (xset-intersection (member-type-xset type1)
+                                             (member-type-xset type2))
+                    :fp-zeroes (intersection (member-type-fp-zeroes type1)
+                                             (member-type-fp-zeroes type2))))

 
 (!define-type-method (member :complex-intersection2) (type1 type2)
   (block punt
 
 (!define-type-method (member :complex-intersection2) (type1 type2)
   (block punt

-    (collect ((members))
-      (let ((mem2 (member-type-members type2)))
-        (dolist (member mem2)
-         (multiple-value-bind (val win) (ctypep member type1)
-           (unless win
-             (return-from punt nil))
-           (when val (members member))))
-       (cond ((subsetp mem2 (members)) type2)
-             ((null (members)) *empty-type*)
-             (t
-              (make-member-type :members (members))))))))
+    (let ((xset (alloc-xset))
+          (fp-zeroes nil))
+      (mapc-member-type-members
+       (lambda (member)
+         (multiple-value-bind (ok sure) (ctypep member type1)
+           (unless sure
+             (return-from punt nil))
+           (when ok
+             (if (fp-zero-p member)
+                 (pushnew member fp-zeroes)
+                 (add-to-xset member xset)))))
+       type2)
+      (if (and (xset-empty-p xset) (not fp-zeroes))
+          *empty-type*
+          (make-member-type :xset xset :fp-zeroes fp-zeroes)))))

 
 ;;; We don't need a :COMPLEX-UNION2, since the only interesting case is
 ;;; a union type, and the member/union interaction is handled by the
 ;;; union type method.
 (!define-type-method (member :simple-union2) (type1 type2)
 
 ;;; We don't need a :COMPLEX-UNION2, since the only interesting case is
 ;;; a union type, and the member/union interaction is handled by the
 ;;; union type method.
 (!define-type-method (member :simple-union2) (type1 type2)

-  (let ((mem1 (member-type-members type1))
-       (mem2 (member-type-members type2)))
-    (cond ((subsetp mem1 mem2) type2)
-         ((subsetp mem2 mem1) type1)
-         (t
-          (make-member-type :members (union mem1 mem2))))))
+  (make-member-type :xset (xset-union (member-type-xset type1)
+                                      (member-type-xset type2))
+                    :fp-zeroes (union (member-type-fp-zeroes type1)
+                                      (member-type-fp-zeroes type2))))

 
 (!define-type-method (member :simple-=) (type1 type2)
 
 (!define-type-method (member :simple-=) (type1 type2)

-  (let ((mem1 (member-type-members type1))
-       (mem2 (member-type-members type2)))
-    (values (and (subsetp mem1 mem2)
-                (subsetp mem2 mem1))
-           t)))
+  (let ((xset1 (member-type-xset type1))
+        (xset2 (member-type-xset type2))
+        (l1 (member-type-fp-zeroes type1))
+        (l2 (member-type-fp-zeroes type2)))
+    (values (and (eql (xset-count xset1) (xset-count xset2))
+                 (xset-subset-p xset1 xset2)
+                 (xset-subset-p xset2 xset1)
+                 (subsetp l1 l2)
+                 (subsetp l2 l1))
+            t)))

 
 (!define-type-method (member :complex-=) (type1 type2)
   (if (type-enumerable type1)
       (multiple-value-bind (val win) (csubtypep type2 type1)
 
 (!define-type-method (member :complex-=) (type1 type2)
   (if (type-enumerable type1)
       (multiple-value-bind (val win) (csubtypep type2 type1)

-       (if (or val (not win))
-           (values nil nil)
-           (values nil t)))
+        (if (or val (not win))
+            (values nil nil)
+            (values nil t)))

       (values nil t)))
 
 (!def-type-translator member (&rest members)
   (if members
       (values nil t)))
 
 (!def-type-translator member (&rest members)
   (if members

-      (let (ms numbers)
-       (dolist (m (remove-duplicates members))
-         (typecase m
-           (float (if (zerop m)
-                      (push m ms)
-                      (push (ctype-of m) numbers)))
-           (number (push (ctype-of m) numbers))
-           (t (push m ms))))
-       (apply #'type-union
-              (if ms
-                  (make-member-type :members ms)
-                  *empty-type*)
-              (nreverse numbers)))
+      (let (ms numbers char-codes)
+        (dolist (m (remove-duplicates members))
+          (typecase m
+            (float (if (zerop m)
+                       (push m ms)
+                       (push (ctype-of m) numbers)))
+            (real (push (ctype-of m) numbers))
+           (character (push (sb!xc:char-code m) char-codes))
+            (t (push m ms))))
+        (apply #'type-union
+               (if ms
+                   (make-member-type :members ms)
+                   *empty-type*)
+              (if char-codes
+                  (make-character-set-type
+                   :pairs (mapcar (lambda (x) (cons x x))
+                                  (sort char-codes #'<)))
+                  *empty-type*)
+               (nreverse numbers)))

       *empty-type*))
 \f
 ;;;; intersection types
       *empty-type*))
 \f
 ;;;; intersection types

@@ -2444,21 +2827,21 @@
 
 (!define-type-method (intersection :negate) (type)
   (apply #'type-union
 
 (!define-type-method (intersection :negate) (type)
   (apply #'type-union

-        (mapcar #'type-negation (intersection-type-types type))))
+         (mapcar #'type-negation (intersection-type-types type))))

 
 ;;; A few intersection types have special names. The others just get
 ;;; mechanically unparsed.
 (!define-type-method (intersection :unparse) (type)
   (declare (type ctype type))
 
 ;;; A few intersection types have special names. The others just get
 ;;; mechanically unparsed.
 (!define-type-method (intersection :unparse) (type)
   (declare (type ctype type))

-  (or (find type '(ratio keyword) :key #'specifier-type :test #'type=)
+  (or (find type '(ratio keyword compiled-function) :key #'specifier-type :test #'type=)

       `(and ,@(mapcar #'type-specifier (intersection-type-types type)))))
 
 ;;; shared machinery for type equality: true if every type in the set
 ;;; TYPES1 matches a type in the set TYPES2 and vice versa
 (defun type=-set (types1 types2)
   (flet ((type<=-set (x y)
       `(and ,@(mapcar #'type-specifier (intersection-type-types type)))))
 
 ;;; shared machinery for type equality: true if every type in the set
 ;;; TYPES1 matches a type in the set TYPES2 and vice versa
 (defun type=-set (types1 types2)
   (flet ((type<=-set (x y)

-          (declare (type list x y))
-          (every/type (lambda (x y-element)
+           (declare (type list x y))
+           (every/type (lambda (x y-element)

                          (any/type #'type= y-element x))
                        x y)))
     (and/type (type<=-set types1 types2)
                          (any/type #'type= y-element x))
                        x y)))
     (and/type (type<=-set types1 types2)

@@ -2473,19 +2856,19 @@
 ;;; in this more obscure method?
 (!define-type-method (intersection :simple-=) (type1 type2)
   (type=-set (intersection-type-types type1)
 ;;; in this more obscure method?
 (!define-type-method (intersection :simple-=) (type1 type2)
   (type=-set (intersection-type-types type1)

-            (intersection-type-types type2)))
+             (intersection-type-types type2)))

 
 (defun %intersection-complex-subtypep-arg1 (type1 type2)
   (type= type1 (type-intersection type1 type2)))
 
 (defun %intersection-simple-subtypep (type1 type2)
   (every/type #'%intersection-complex-subtypep-arg1
 
 (defun %intersection-complex-subtypep-arg1 (type1 type2)
   (type= type1 (type-intersection type1 type2)))
 
 (defun %intersection-simple-subtypep (type1 type2)
   (every/type #'%intersection-complex-subtypep-arg1

-             type1
-             (intersection-type-types type2)))
+              type1
+              (intersection-type-types type2)))

 
 (!define-type-method (intersection :simple-subtypep) (type1 type2)
   (%intersection-simple-subtypep type1 type2))
 
 (!define-type-method (intersection :simple-subtypep) (type1 type2)
   (%intersection-simple-subtypep type1 type2))

-  
+

 (!define-type-method (intersection :complex-subtypep-arg1) (type1 type2)
   (%intersection-complex-subtypep-arg1 type1 type2))
 
 (!define-type-method (intersection :complex-subtypep-arg1) (type1 type2)
   (%intersection-complex-subtypep-arg1 type1 type2))
 

@@ -2503,70 +2886,71 @@
 ;;; reflect those symmetries in code in a way that ties them together
 ;;; more strongly than having two independent near-copies :-/
 (!define-type-method (intersection :simple-union2 :complex-union2)
 ;;; reflect those symmetries in code in a way that ties them together
 ;;; more strongly than having two independent near-copies :-/
 (!define-type-method (intersection :simple-union2 :complex-union2)

-                    (type1 type2)
+                     (type1 type2)

   ;; Within this method, type2 is guaranteed to be an intersection
   ;; type:
   (aver (intersection-type-p type2))
   ;; Make sure to call only the applicable methods...
   (cond ((and (intersection-type-p type1)
   ;; Within this method, type2 is guaranteed to be an intersection
   ;; type:
   (aver (intersection-type-p type2))
   ;; Make sure to call only the applicable methods...
   (cond ((and (intersection-type-p type1)

-             (%intersection-simple-subtypep type1 type2)) type2)
-       ((and (intersection-type-p type1)
-             (%intersection-simple-subtypep type2 type1)) type1)
-       ((and (not (intersection-type-p type1))
-             (%intersection-complex-subtypep-arg2 type1 type2))
-        type2)
-       ((and (not (intersection-type-p type1))
-             (%intersection-complex-subtypep-arg1 type2 type1))
-        type1)
-       ;; KLUDGE: This special (and somewhat hairy) magic is required
-       ;; to deal with the RATIONAL/INTEGER special case.  The UNION
-       ;; of (INTEGER * -1) and (AND (RATIONAL * -1/2) (NOT INTEGER))
-       ;; should be (RATIONAL * -1/2) -- CSR, 2003-02-28
-       ((and (csubtypep type2 (specifier-type 'ratio))
-             (numeric-type-p type1)
-             (csubtypep type1 (specifier-type 'integer))
-             (csubtypep type2
-                        (make-numeric-type
-                         :class 'rational
-                         :complexp nil
-                         :low (if (null (numeric-type-low type1))
-                                  nil
-                                  (list (1- (numeric-type-low type1))))
-                         :high (if (null (numeric-type-high type1))
-                                   nil
-                                   (list (1+ (numeric-type-high type1)))))))
-        (type-union type1
-                    (apply #'type-intersection
-                           (remove (specifier-type '(not integer))
-                                   (intersection-type-types type2)
-                                   :test #'type=))))
-       (t
-        (let ((accumulator *universal-type*))
-          (do ((t2s (intersection-type-types type2) (cdr t2s)))
-              ((null t2s) accumulator)
-            (let ((union (type-union type1 (car t2s))))
-              (when (union-type-p union)
-                ;; we have to give up here -- there are all sorts of
-                ;; ordering worries, but it's better than before.
-                ;; Doing exactly the same as in the UNION
-                ;; :SIMPLE/:COMPLEX-INTERSECTION2 method causes stack
-                ;; overflow with the mutual recursion never bottoming
-                ;; out.
-                (if (and (eq accumulator *universal-type*)
-                         (null (cdr t2s)))
-                    ;; KLUDGE: if we get here, we have a partially
-                    ;; simplified result.  While this isn't by any
-                    ;; means a universal simplification, including
-                    ;; this logic here means that we can get (OR
-                    ;; KEYWORD (NOT KEYWORD)) canonicalized to T.
-                    (return union)
-                    (return nil)))
-              (setf accumulator
-                    (type-intersection accumulator union))))))))
+              (%intersection-simple-subtypep type1 type2)) type2)
+        ((and (intersection-type-p type1)
+              (%intersection-simple-subtypep type2 type1)) type1)
+        ((and (not (intersection-type-p type1))
+              (%intersection-complex-subtypep-arg2 type1 type2))
+         type2)
+        ((and (not (intersection-type-p type1))
+              (%intersection-complex-subtypep-arg1 type2 type1))
+         type1)
+        ;; KLUDGE: This special (and somewhat hairy) magic is required
+        ;; to deal with the RATIONAL/INTEGER special case.  The UNION
+        ;; of (INTEGER * -1) and (AND (RATIONAL * -1/2) (NOT INTEGER))
+        ;; should be (RATIONAL * -1/2) -- CSR, 2003-02-28
+        ((and (csubtypep type2 (specifier-type 'ratio))
+              (numeric-type-p type1)
+              (csubtypep type1 (specifier-type 'integer))
+              (csubtypep type2
+                         (make-numeric-type
+                          :class 'rational
+                          :complexp nil
+                          :low (if (null (numeric-type-low type1))
+                                   nil
+                                   (list (1- (numeric-type-low type1))))
+                          :high (if (null (numeric-type-high type1))
+                                    nil
+                                    (list (1+ (numeric-type-high type1)))))))
+         (let* ((intersected (intersection-type-types type2))
+                (remaining   (remove (specifier-type '(not integer))
+                                     intersected
+                                     :test #'type=)))
+           (and (not (equal intersected remaining))
+                (type-union type1 (apply #'type-intersection remaining)))))
+        (t
+         (let ((accumulator *universal-type*))
+           (do ((t2s (intersection-type-types type2) (cdr t2s)))
+               ((null t2s) accumulator)
+             (let ((union (type-union type1 (car t2s))))
+               (when (union-type-p union)
+                 ;; we have to give up here -- there are all sorts of
+                 ;; ordering worries, but it's better than before.
+                 ;; Doing exactly the same as in the UNION
+                 ;; :SIMPLE/:COMPLEX-INTERSECTION2 method causes stack
+                 ;; overflow with the mutual recursion never bottoming
+                 ;; out.
+                 (if (and (eq accumulator *universal-type*)
+                          (null (cdr t2s)))
+                     ;; KLUDGE: if we get here, we have a partially
+                     ;; simplified result.  While this isn't by any
+                     ;; means a universal simplification, including
+                     ;; this logic here means that we can get (OR
+                     ;; KEYWORD (NOT KEYWORD)) canonicalized to T.
+                     (return union)
+                     (return nil)))
+               (setf accumulator
+                     (type-intersection accumulator union))))))))

 
 (!def-type-translator and (&whole whole &rest type-specifiers)
   (apply #'type-intersection
 
 (!def-type-translator and (&whole whole &rest type-specifiers)
   (apply #'type-intersection

-        (mapcar #'specifier-type type-specifiers)))
+         (mapcar #'specifier-type type-specifiers)))

 \f
 ;;;; union types
 
 \f
 ;;;; union types
 

@@ -2575,7 +2959,7 @@
 (!define-type-method (union :negate) (type)
   (declare (type ctype type))
   (apply #'type-intersection
 (!define-type-method (union :negate) (type)
   (declare (type ctype type))
   (apply #'type-intersection

-        (mapcar #'type-negation (union-type-types type))))
+         (mapcar #'type-negation (union-type-types type))))

 
 ;;; The LIST, FLOAT and REAL types have special names.  Other union
 ;;; types just get mechanically unparsed.
 
 ;;; The LIST, FLOAT and REAL types have special names.  Other union
 ;;; types just get mechanically unparsed.

@@ -2589,6 +2973,8 @@
     ((type= type (specifier-type 'bignum)) 'bignum)
     ((type= type (specifier-type 'simple-string)) 'simple-string)
     ((type= type (specifier-type 'string)) 'string)
     ((type= type (specifier-type 'bignum)) 'bignum)
     ((type= type (specifier-type 'simple-string)) 'simple-string)
     ((type= type (specifier-type 'string)) 'string)

+    ((type= type (specifier-type 'complex)) 'complex)
+    ((type= type (specifier-type 'standard-char)) 'standard-char)

     (t `(or ,@(mapcar #'type-specifier (union-type-types type))))))
 
 ;;; Two union types are equal if they are each subtypes of each
     (t `(or ,@(mapcar #'type-specifier (union-type-types type))))))
 
 ;;; Two union types are equal if they are each subtypes of each

@@ -2605,19 +2991,19 @@
   (multiple-value-bind (subtype certain?)
       (csubtypep type1 type2)
     (if subtype
   (multiple-value-bind (subtype certain?)
       (csubtypep type1 type2)
     (if subtype

-       (csubtypep type2 type1)
-       ;; we might as well become as certain as possible.
-       (if certain?
-           (values nil t)
-           (multiple-value-bind (subtype certain?)
-               (csubtypep type2 type1)
-             (declare (ignore subtype))
-             (values nil certain?))))))
+        (csubtypep type2 type1)
+        ;; we might as well become as certain as possible.
+        (if certain?
+            (values nil t)
+            (multiple-value-bind (subtype certain?)
+                (csubtypep type2 type1)
+              (declare (ignore subtype))
+              (values nil certain?))))))

 
 (!define-type-method (union :complex-=) (type1 type2)
   (declare (ignore type1))
 
 (!define-type-method (union :complex-=) (type1 type2)
   (declare (ignore type1))

-  (if (some #'type-might-contain-other-types-p 
-           (union-type-types type2))
+  (if (some #'type-might-contain-other-types-p
+            (union-type-types type2))

       (values nil nil)
       (values nil t)))
 
       (values nil nil)
       (values nil t)))
 

@@ -2625,68 +3011,68 @@
 ;;; every element of TYPE1 is a subtype of TYPE2.
 (defun union-simple-subtypep (type1 type2)
   (every/type (swapped-args-fun #'union-complex-subtypep-arg2)
 ;;; every element of TYPE1 is a subtype of TYPE2.
 (defun union-simple-subtypep (type1 type2)
   (every/type (swapped-args-fun #'union-complex-subtypep-arg2)

-             type2
-             (union-type-types type1)))
+              type2
+              (union-type-types type1)))

 
 (!define-type-method (union :simple-subtypep) (type1 type2)
   (union-simple-subtypep type1 type2))
 
 (!define-type-method (union :simple-subtypep) (type1 type2)
   (union-simple-subtypep type1 type2))

-  
+

 (defun union-complex-subtypep-arg1 (type1 type2)
   (every/type (swapped-args-fun #'csubtypep)
 (defun union-complex-subtypep-arg1 (type1 type2)
   (every/type (swapped-args-fun #'csubtypep)

-             type2
-             (union-type-types type1)))
+              type2
+              (union-type-types type1)))

 
 (!define-type-method (union :complex-subtypep-arg1) (type1 type2)
   (union-complex-subtypep-arg1 type1 type2))
 
 (defun union-complex-subtypep-arg2 (type1 type2)
 
 (!define-type-method (union :complex-subtypep-arg1) (type1 type2)
   (union-complex-subtypep-arg1 type1 type2))
 
 (defun union-complex-subtypep-arg2 (type1 type2)

+  ;; At this stage, we know that type2 is a union type and type1
+  ;; isn't. We might as well check this, though:
+  (aver (union-type-p type2))
+  (aver (not (union-type-p type1)))
+  ;; was: (any/type #'csubtypep type1 (union-type-types type2)), which
+  ;; turns out to be too restrictive, causing bug 91.
+  ;;
+  ;; the following reimplementation might look dodgy. It is dodgy. It
+  ;; depends on the union :complex-= method not doing very much work
+  ;; -- certainly, not using subtypep. Reasoning:
+  ;;
+  ;;     A is a subset of (B1 u B2)
+  ;; <=> A n (B1 u B2) = A
+  ;; <=> (A n B1) u (A n B2) = A
+  ;;
+  ;; But, we have to be careful not to delegate this type= to
+  ;; something that could invoke subtypep, which might get us back
+  ;; here -> stack explosion. We therefore ensure that the second type
+  ;; (which is the one that's dispatched on) is either a union type
+  ;; (where we've ensured that the complex-= method will not call
+  ;; subtypep) or something with no union types involved, in which
+  ;; case we'll never come back here.
+  ;;
+  ;; If we don't do this, then e.g.
+  ;; (SUBTYPEP '(MEMBER 3) '(OR (SATISFIES FOO) (SATISFIES BAR)))
+  ;; would loop infinitely, as the member :complex-= method is
+  ;; implemented in terms of subtypep.
+  ;;
+  ;; Ouch. - CSR, 2002-04-10

   (multiple-value-bind (sub-value sub-certain?)
   (multiple-value-bind (sub-value sub-certain?)

-      ;; was: (any/type #'csubtypep type1 (union-type-types type2)),
-      ;; which turns out to be too restrictive, causing bug 91.
-      ;;
-      ;; the following reimplementation might look dodgy.  It is
-      ;; dodgy. It depends on the union :complex-= method not doing
-      ;; very much work -- certainly, not using subtypep. Reasoning:
-      (progn
-       ;; At this stage, we know that type2 is a union type and type1
-       ;; isn't. We might as well check this, though:
-       (aver (union-type-p type2))
-       (aver (not (union-type-p type1)))
-       ;;     A is a subset of (B1 u B2)
-       ;; <=> A n (B1 u B2) = A
-       ;; <=> (A n B1) u (A n B2) = A
-       ;;
-       ;; But, we have to be careful not to delegate this type= to
-       ;; something that could invoke subtypep, which might get us
-       ;; back here -> stack explosion. We therefore ensure that the
-       ;; second type (which is the one that's dispatched on) is
-       ;; either a union type (where we've ensured that the complex-=
-       ;; method will not call subtypep) or something with no union
-       ;; types involved, in which case we'll never come back here.
-       ;;
-       ;; If we don't do this, then e.g.
-       ;; (SUBTYPEP '(MEMBER 3) '(OR (SATISFIES FOO) (SATISFIES BAR)))
-       ;; would loop infinitely, as the member :complex-= method is
-       ;; implemented in terms of subtypep.
-       ;;
-       ;; Ouch. - CSR, 2002-04-10
-       (type= type1
-              (apply #'type-union
-                     (mapcar (lambda (x) (type-intersection type1 x))
-                             (union-type-types type2)))))
+      (type= type1
+             (apply #'type-union
+                    (mapcar (lambda (x) (type-intersection type1 x))
+                            (union-type-types type2))))

     (if sub-certain?
     (if sub-certain?

-       (values sub-value sub-certain?)
-       ;; The ANY/TYPE expression above is a sufficient condition for
-       ;; subsetness, but not a necessary one, so we might get a more
-       ;; certain answer by this CALL-NEXT-METHOD-ish step when the
-       ;; ANY/TYPE expression is uncertain.
-       (invoke-complex-subtypep-arg1-method type1 type2))))
+        (values sub-value sub-certain?)
+        ;; The ANY/TYPE expression above is a sufficient condition for
+        ;; subsetness, but not a necessary one, so we might get a more
+        ;; certain answer by this CALL-NEXT-METHOD-ish step when the
+        ;; ANY/TYPE expression is uncertain.
+        (invoke-complex-subtypep-arg1-method type1 type2))))

 
 (!define-type-method (union :complex-subtypep-arg2) (type1 type2)
   (union-complex-subtypep-arg2 type1 type2))
 
 (!define-type-method (union :simple-intersection2 :complex-intersection2)
 
 (!define-type-method (union :complex-subtypep-arg2) (type1 type2)
   (union-complex-subtypep-arg2 type1 type2))
 
 (!define-type-method (union :simple-intersection2 :complex-intersection2)

-                    (type1 type2)
+                     (type1 type2)

   ;; The CSUBTYPEP clauses here let us simplify e.g.
   ;;   (TYPE-INTERSECTION2 (SPECIFIER-TYPE 'LIST)
   ;;                       (SPECIFIER-TYPE '(OR LIST VECTOR)))
   ;; The CSUBTYPEP clauses here let us simplify e.g.
   ;;   (TYPE-INTERSECTION2 (SPECIFIER-TYPE 'LIST)
   ;;                       (SPECIFIER-TYPE '(OR LIST VECTOR)))

@@ -2704,38 +3090,38 @@
   (aver (union-type-p type2))
   ;; Make sure to call only the applicable methods...
   (cond ((and (union-type-p type1)
   (aver (union-type-p type2))
   ;; Make sure to call only the applicable methods...
   (cond ((and (union-type-p type1)

-             (union-simple-subtypep type1 type2)) type1)
-       ((and (union-type-p type1)
-             (union-simple-subtypep type2 type1)) type2)
-       ((and (not (union-type-p type1))
-             (union-complex-subtypep-arg2 type1 type2))
-        type1)
-       ((and (not (union-type-p type1))
-             (union-complex-subtypep-arg1 type2 type1))
-        type2)
-       (t 
-        ;; KLUDGE: This code accumulates a sequence of TYPE-UNION2
-        ;; operations in a particular order, and gives up if any of
-        ;; the sub-unions turn out not to be simple. In other cases
-        ;; ca. sbcl-0.6.11.15, that approach to taking a union was a
-        ;; bad idea, since it can overlook simplifications which
-        ;; might occur if the terms were accumulated in a different
-        ;; order. It's possible that that will be a problem here too.
-        ;; However, I can't think of a good example to demonstrate
-        ;; it, and without an example to demonstrate it I can't write
-        ;; test cases, and without test cases I don't want to
-        ;; complicate the code to address what's still a hypothetical
-        ;; problem. So I punted. -- WHN 2001-03-20
-        (let ((accumulator *empty-type*))
-          (dolist (t2 (union-type-types type2) accumulator)
-            (setf accumulator
-                  (type-union accumulator
-                              (type-intersection type1 t2))))))))
+              (union-simple-subtypep type1 type2)) type1)
+        ((and (union-type-p type1)
+              (union-simple-subtypep type2 type1)) type2)
+        ((and (not (union-type-p type1))
+              (union-complex-subtypep-arg2 type1 type2))
+         type1)
+        ((and (not (union-type-p type1))
+              (union-complex-subtypep-arg1 type2 type1))
+         type2)
+        (t
+         ;; KLUDGE: This code accumulates a sequence of TYPE-UNION2
+         ;; operations in a particular order, and gives up if any of
+         ;; the sub-unions turn out not to be simple. In other cases
+         ;; ca. sbcl-0.6.11.15, that approach to taking a union was a
+         ;; bad idea, since it can overlook simplifications which
+         ;; might occur if the terms were accumulated in a different
+         ;; order. It's possible that that will be a problem here too.
+         ;; However, I can't think of a good example to demonstrate
+         ;; it, and without an example to demonstrate it I can't write
+         ;; test cases, and without test cases I don't want to
+         ;; complicate the code to address what's still a hypothetical
+         ;; problem. So I punted. -- WHN 2001-03-20
+         (let ((accumulator *empty-type*))
+           (dolist (t2 (union-type-types type2) accumulator)
+             (setf accumulator
+                   (type-union accumulator
+                               (type-intersection type1 t2))))))))

 
 (!def-type-translator or (&rest type-specifiers)
   (apply #'type-union
 
 (!def-type-translator or (&rest type-specifiers)
   (apply #'type-union

-        (mapcar #'specifier-type
-                type-specifiers)))
+         (mapcar #'specifier-type
+                 type-specifiers)))

 \f
 ;;;; CONS types
 
 \f
 ;;;; CONS types
 

@@ -2743,125 +3129,296 @@
 
 (!def-type-translator cons (&optional (car-type-spec '*) (cdr-type-spec '*))
   (let ((car-type (single-value-specifier-type car-type-spec))
 
 (!def-type-translator cons (&optional (car-type-spec '*) (cdr-type-spec '*))
   (let ((car-type (single-value-specifier-type car-type-spec))

-       (cdr-type (single-value-specifier-type cdr-type-spec)))
+        (cdr-type (single-value-specifier-type cdr-type-spec)))

     (make-cons-type car-type cdr-type)))
 
 (!define-type-method (cons :negate) (type)
   (if (and (eq (cons-type-car-type type) *universal-type*)
     (make-cons-type car-type cdr-type)))
 
 (!define-type-method (cons :negate) (type)
   (if (and (eq (cons-type-car-type type) *universal-type*)

-          (eq (cons-type-cdr-type type) *universal-type*))
+           (eq (cons-type-cdr-type type) *universal-type*))

       (make-negation-type :type type)
       (type-union
        (make-negation-type :type (specifier-type 'cons))
        (cond
       (make-negation-type :type type)
       (type-union
        (make-negation-type :type (specifier-type 'cons))
        (cond

-        ((and (not (eq (cons-type-car-type type) *universal-type*))
-              (not (eq (cons-type-cdr-type type) *universal-type*)))
-         (type-union
-          (make-cons-type
-           (type-negation (cons-type-car-type type))
-           *universal-type*)
-          (make-cons-type
-           *universal-type*
-           (type-negation (cons-type-cdr-type type)))))
-        ((not (eq (cons-type-car-type type) *universal-type*))
-         (make-cons-type
-          (type-negation (cons-type-car-type type))
-          *universal-type*))
-        ((not (eq (cons-type-cdr-type type) *universal-type*))
-         (make-cons-type
-          *universal-type*
-          (type-negation (cons-type-cdr-type type))))
-        (t (bug "Weird CONS type ~S" type))))))
+         ((and (not (eq (cons-type-car-type type) *universal-type*))
+               (not (eq (cons-type-cdr-type type) *universal-type*)))
+          (type-union
+           (make-cons-type
+            (type-negation (cons-type-car-type type))
+            *universal-type*)
+           (make-cons-type
+            *universal-type*
+            (type-negation (cons-type-cdr-type type)))))
+         ((not (eq (cons-type-car-type type) *universal-type*))
+          (make-cons-type
+           (type-negation (cons-type-car-type type))
+           *universal-type*))
+         ((not (eq (cons-type-cdr-type type) *universal-type*))
+          (make-cons-type
+           *universal-type*
+           (type-negation (cons-type-cdr-type type))))
+         (t (bug "Weird CONS type ~S" type))))))

 
 (!define-type-method (cons :unparse) (type)
   (let ((car-eltype (type-specifier (cons-type-car-type type)))
 
 (!define-type-method (cons :unparse) (type)
   (let ((car-eltype (type-specifier (cons-type-car-type type)))

-       (cdr-eltype (type-specifier (cons-type-cdr-type type))))
+        (cdr-eltype (type-specifier (cons-type-cdr-type type))))

     (if (and (member car-eltype '(t *))
     (if (and (member car-eltype '(t *))

-            (member cdr-eltype '(t *)))
-       'cons
-       `(cons ,car-eltype ,cdr-eltype))))
- 
+             (member cdr-eltype '(t *)))
+        'cons
+        `(cons ,car-eltype ,cdr-eltype))))
+

 (!define-type-method (cons :simple-=) (type1 type2)
   (declare (type cons-type type1 type2))
 (!define-type-method (cons :simple-=) (type1 type2)
   (declare (type cons-type type1 type2))

-  (and (type= (cons-type-car-type type1) (cons-type-car-type type2))
-       (type= (cons-type-cdr-type type1) (cons-type-cdr-type type2))))
- 
+  (multiple-value-bind (car-match car-win)
+      (type= (cons-type-car-type type1) (cons-type-car-type type2))
+    (multiple-value-bind (cdr-match cdr-win)
+        (type= (cons-type-cdr-type type1) (cons-type-cdr-type type2))
+      (cond ((and car-match cdr-match)
+             (aver (and car-win cdr-win))
+             (values t t))
+            (t
+             (values nil
+                     ;; FIXME: Ideally we would like to detect and handle
+                     ;;  (CONS UNKNOWN INTEGER) (CONS UNKNOWN SYMBOL) => NIL, T
+                     ;; but just returning a secondary true on (and car-win cdr-win)
+                     ;; unfortunately breaks other things. --NS 2006-08-16
+                     (and (or (and (not car-match) car-win)
+                              (and (not cdr-match) cdr-win))
+                          (not (and (cons-type-might-be-empty-type type1)
+                                    (cons-type-might-be-empty-type type2))))))))))
+

 (!define-type-method (cons :simple-subtypep) (type1 type2)
   (declare (type cons-type type1 type2))
   (multiple-value-bind (val-car win-car)
       (csubtypep (cons-type-car-type type1) (cons-type-car-type type2))
     (multiple-value-bind (val-cdr win-cdr)
 (!define-type-method (cons :simple-subtypep) (type1 type2)
   (declare (type cons-type type1 type2))
   (multiple-value-bind (val-car win-car)
       (csubtypep (cons-type-car-type type1) (cons-type-car-type type2))
     (multiple-value-bind (val-cdr win-cdr)

-       (csubtypep (cons-type-cdr-type type1) (cons-type-cdr-type type2))
+        (csubtypep (cons-type-cdr-type type1) (cons-type-cdr-type type2))

       (if (and val-car val-cdr)
       (if (and val-car val-cdr)

-         (values t (and win-car win-cdr))
-         (values nil (or win-car win-cdr))))))
- 
+          (values t (and win-car win-cdr))
+          (values nil (or (and (not val-car) win-car)
+                          (and (not val-cdr) win-cdr)))))))
+

 ;;; Give up if a precise type is not possible, to avoid returning
 ;;; overly general types.
 (!define-type-method (cons :simple-union2) (type1 type2)
   (declare (type cons-type type1 type2))
   (let ((car-type1 (cons-type-car-type type1))
 ;;; Give up if a precise type is not possible, to avoid returning
 ;;; overly general types.
 (!define-type-method (cons :simple-union2) (type1 type2)
   (declare (type cons-type type1 type2))
   (let ((car-type1 (cons-type-car-type type1))

-       (car-type2 (cons-type-car-type type2))
-       (cdr-type1 (cons-type-cdr-type type1))
-       (cdr-type2 (cons-type-cdr-type type2))
-       car-not1
-       car-not2)
+        (car-type2 (cons-type-car-type type2))
+        (cdr-type1 (cons-type-cdr-type type1))
+        (cdr-type2 (cons-type-cdr-type type2))
+        car-not1
+        car-not2)

     ;; UGH.  -- CSR, 2003-02-24
     (macrolet ((frob-car (car1 car2 cdr1 cdr2
     ;; UGH.  -- CSR, 2003-02-24
     (macrolet ((frob-car (car1 car2 cdr1 cdr2

-                         &optional (not1 nil not1p))
-                `(type-union
-                  (make-cons-type ,car1 (type-union ,cdr1 ,cdr2))
-                  (make-cons-type
-                   (type-intersection ,car2
-                    ,(if not1p
-                         not1
-                         `(type-negation ,car1)))
-                   ,cdr2))))
+                          &optional (not1 nil not1p))
+                 `(type-union
+                   (make-cons-type ,car1 (type-union ,cdr1 ,cdr2))
+                   (make-cons-type
+                    (type-intersection ,car2
+                     ,(if not1p
+                          not1
+                          `(type-negation ,car1)))
+                    ,cdr2))))

       (cond ((type= car-type1 car-type2)
       (cond ((type= car-type1 car-type2)

-            (make-cons-type car-type1
-                            (type-union cdr-type1 cdr-type2)))
-           ((type= cdr-type1 cdr-type2)
-            (make-cons-type (type-union car-type1 car-type2)
-                            cdr-type1))
-           ((csubtypep car-type1 car-type2)
-            (frob-car car-type1 car-type2 cdr-type1 cdr-type2))
-           ((csubtypep car-type2 car-type1)
-            (frob-car car-type2 car-type1 cdr-type2 cdr-type1))
-           ;; more general case of the above, but harder to compute
-           ((progn
-              (setf car-not1 (type-negation car-type1))
-              (not (csubtypep car-type2 car-not1)))
-            (frob-car car-type1 car-type2 cdr-type1 cdr-type2 car-not1))
-           ((progn
-              (setf car-not2 (type-negation car-type2))
-              (not (csubtypep car-type1 car-not2)))
-            (frob-car car-type2 car-type1 cdr-type2 cdr-type1 car-not2))
-           ;; Don't put these in -- consider the effect of taking the
-           ;; union of (CONS (INTEGER 0 2) (INTEGER 5 7)) and
-           ;; (CONS (INTEGER 0 3) (INTEGER 5 6)).
-           #+nil
-           ((csubtypep cdr-type1 cdr-type2)
-            (frob-cdr car-type1 car-type2 cdr-type1 cdr-type2))
-           #+nil
-           ((csubtypep cdr-type2 cdr-type1)
-            (frob-cdr car-type2 car-type1 cdr-type2 cdr-type1))))))
-           
+             (make-cons-type car-type1
+                             (type-union cdr-type1 cdr-type2)))
+            ((type= cdr-type1 cdr-type2)
+             (make-cons-type (type-union car-type1 car-type2)
+                             cdr-type1))
+            ((csubtypep car-type1 car-type2)
+             (frob-car car-type1 car-type2 cdr-type1 cdr-type2))
+            ((csubtypep car-type2 car-type1)
+             (frob-car car-type2 car-type1 cdr-type2 cdr-type1))
+            ;; more general case of the above, but harder to compute
+            ((progn
+               (setf car-not1 (type-negation car-type1))
+               (multiple-value-bind (yes win)
+                   (csubtypep car-type2 car-not1)
+                 (and (not yes) win)))
+             (frob-car car-type1 car-type2 cdr-type1 cdr-type2 car-not1))
+            ((progn
+               (setf car-not2 (type-negation car-type2))
+               (multiple-value-bind (yes win)
+                   (csubtypep car-type1 car-not2)
+                 (and (not yes) win)))
+             (frob-car car-type2 car-type1 cdr-type2 cdr-type1 car-not2))
+            ;; Don't put these in -- consider the effect of taking the
+            ;; union of (CONS (INTEGER 0 2) (INTEGER 5 7)) and
+            ;; (CONS (INTEGER 0 3) (INTEGER 5 6)).
+            #+nil
+            ((csubtypep cdr-type1 cdr-type2)
+             (frob-cdr car-type1 car-type2 cdr-type1 cdr-type2))
+            #+nil
+            ((csubtypep cdr-type2 cdr-type1)
+             (frob-cdr car-type2 car-type1 cdr-type2 cdr-type1))))))
+

 (!define-type-method (cons :simple-intersection2) (type1 type2)
   (declare (type cons-type type1 type2))
   (let ((car-int2 (type-intersection2 (cons-type-car-type type1)
 (!define-type-method (cons :simple-intersection2) (type1 type2)
   (declare (type cons-type type1 type2))
   (let ((car-int2 (type-intersection2 (cons-type-car-type type1)

-                                     (cons-type-car-type type2)))
-       (cdr-int2 (type-intersection2 (cons-type-cdr-type type1)
-                                     (cons-type-cdr-type type2))))
+                                      (cons-type-car-type type2)))
+        (cdr-int2 (type-intersection2 (cons-type-cdr-type type1)
+                                      (cons-type-cdr-type type2))))

     (cond
       ((and car-int2 cdr-int2) (make-cons-type car-int2 cdr-int2))
       (car-int2 (make-cons-type car-int2
     (cond
       ((and car-int2 cdr-int2) (make-cons-type car-int2 cdr-int2))
       (car-int2 (make-cons-type car-int2

-                               (type-intersection
-                                (cons-type-cdr-type type1)
-                                (cons-type-cdr-type type2))))
+                                (type-intersection
+                                 (cons-type-cdr-type type1)
+                                 (cons-type-cdr-type type2))))

       (cdr-int2 (make-cons-type
       (cdr-int2 (make-cons-type

-                (type-intersection (cons-type-car-type type1)
-                                   (cons-type-car-type type2))
-                cdr-int2)))))
-\f                               
+                 (type-intersection (cons-type-car-type type1)
+                                    (cons-type-car-type type2))
+                 cdr-int2)))))
+
+(!define-superclasses cons ((cons)) !cold-init-forms)
+\f
+;;;; CHARACTER-SET types
+
+(!define-type-class character-set)
+
+(!def-type-translator character-set
+    (&optional (pairs '((0 . #.(1- sb!xc:char-code-limit)))))
+  (make-character-set-type :pairs pairs))
+
+(!define-type-method (character-set :negate) (type)
+  (let ((pairs (character-set-type-pairs type)))
+    (if (and (= (length pairs) 1)
+             (= (caar pairs) 0)
+             (= (cdar pairs) (1- sb!xc:char-code-limit)))
+        (make-negation-type :type type)
+        (let ((not-character
+               (make-negation-type
+                :type (make-character-set-type
+                       :pairs '((0 . #.(1- sb!xc:char-code-limit)))))))
+          (type-union
+           not-character
+           (make-character-set-type
+            :pairs (let (not-pairs)
+                     (when (> (caar pairs) 0)
+                       (push (cons 0 (1- (caar pairs))) not-pairs))
+                     (do* ((tail pairs (cdr tail))
+                           (high1 (cdar tail) (cdar tail))
+                           (low2 (caadr tail) (caadr tail)))
+                          ((null (cdr tail))
+                           (when (< (cdar tail) (1- sb!xc:char-code-limit))
+                             (push (cons (1+ (cdar tail))
+                                         (1- sb!xc:char-code-limit))
+                                   not-pairs))
+                           (nreverse not-pairs))
+                       (push (cons (1+ high1) (1- low2)) not-pairs)))))))))
+
+(!define-type-method (character-set :unparse) (type)
+  (cond
+    ((type= type (specifier-type 'character)) 'character)
+    ((type= type (specifier-type 'base-char)) 'base-char)
+    ((type= type (specifier-type 'extended-char)) 'extended-char)
+    ((type= type (specifier-type 'standard-char)) 'standard-char)
+    (t
+     ;; Unparse into either MEMBER or CHARACTER-SET. We use MEMBER if there
+     ;; are at most as many characters than there are character code ranges.
+     (let* ((pairs (character-set-type-pairs type))
+            (count (length pairs))
+            (chars (loop named outer
+                         for (low . high) in pairs
+                         nconc (loop for code from low upto high
+                                     collect (sb!xc:code-char code)
+                                     when (minusp (decf count))
+                                     do (return-from outer t)))))
+       (if (eq chars t)
+           `(character-set ,pairs)
+           `(member ,@chars))))))
+
+(!define-type-method (character-set :singleton-p) (type)
+  (let* ((pairs (character-set-type-pairs type))
+         (pair  (first pairs)))
+    (if (and (typep pairs '(cons t null))
+             (eql (car pair) (cdr pair)))
+        (values t (code-char (car pair)))
+        (values nil nil))))
+
+(!define-type-method (character-set :simple-=) (type1 type2)
+  (let ((pairs1 (character-set-type-pairs type1))
+       (pairs2 (character-set-type-pairs type2)))
+    (values (equal pairs1 pairs2) t)))
+
+(!define-type-method (character-set :simple-subtypep) (type1 type2)
+  (values
+   (dolist (pair (character-set-type-pairs type1) t)
+     (unless (position pair (character-set-type-pairs type2)
+                      :test (lambda (x y) (and (>= (car x) (car y))
+                                               (<= (cdr x) (cdr y)))))
+       (return nil)))
+   t))
+
+(!define-type-method (character-set :simple-union2) (type1 type2)
+  ;; KLUDGE: the canonizing in the MAKE-CHARACTER-SET-TYPE function
+  ;; actually does the union for us.  It might be a little fragile to
+  ;; rely on it.
+  (make-character-set-type
+   :pairs (merge 'list
+                (copy-alist (character-set-type-pairs type1))
+                (copy-alist (character-set-type-pairs type2))
+                #'< :key #'car)))
+
+(!define-type-method (character-set :simple-intersection2) (type1 type2)
+  ;; KLUDGE: brute force.
+#|
+  (let (pairs)
+    (dolist (pair1 (character-set-type-pairs type1)
+            (make-character-set-type
+             :pairs (sort pairs #'< :key #'car)))
+      (dolist (pair2 (character-set-type-pairs type2))
+       (cond
+         ((<= (car pair1) (car pair2) (cdr pair1))
+          (push (cons (car pair2) (min (cdr pair1) (cdr pair2))) pairs))
+         ((<= (car pair2) (car pair1) (cdr pair2))
+          (push (cons (car pair1) (min (cdr pair1) (cdr pair2))) pairs))))))
+|#
+  (make-character-set-type
+   :pairs (intersect-type-pairs
+           (character-set-type-pairs type1)
+           (character-set-type-pairs type2))))
+
+;;;
+;;; Intersect two ordered lists of pairs
+;;; Each list is of the form ((start1 . end1) ... (startn . endn)),
+;;; where start1 <= end1 < start2 <= end2 < ... < startn <= endn.
+;;; Each pair represents the integer interval start..end.
+;;;
+(defun intersect-type-pairs (alist1 alist2)
+  (if (and alist1 alist2)
+      (let ((res nil)
+            (pair1 (pop alist1))
+            (pair2 (pop alist2)))
+        (loop
+         (when (> (car pair1) (car pair2))
+           (rotatef pair1 pair2)
+           (rotatef alist1 alist2))
+         (let ((pair1-cdr (cdr pair1)))
+           (cond
+            ((> (car pair2) pair1-cdr)
+             ;; No over lap -- discard pair1
+             (unless alist1 (return))
+             (setq pair1 (pop alist1)))
+            ((<= (cdr pair2) pair1-cdr)
+             (push (cons (car pair2) (cdr pair2)) res)
+             (cond
+              ((= (cdr pair2) pair1-cdr)
+               (unless alist1 (return))
+               (unless alist2 (return))
+               (setq pair1 (pop alist1)
+                     pair2 (pop alist2)))
+              (t ;; (< (cdr pair2) pair1-cdr)
+               (unless alist2 (return))
+               (setq pair1 (cons (1+ (cdr pair2)) pair1-cdr))
+               (setq pair2 (pop alist2)))))
+            (t ;; (> (cdr pair2) (cdr pair1))
+             (push (cons (car pair2) pair1-cdr) res)
+             (unless alist1 (return))
+             (setq pair2 (cons (1+ pair1-cdr) (cdr pair2)))
+             (setq pair1 (pop alist1))))))
+        (nreverse res))
+    nil))
+
+\f

 ;;; Return the type that describes all objects that are in X but not
 ;;; in Y. If we can't determine this type, then return NIL.
 ;;;
 ;;; Return the type that describes all objects that are in X but not
 ;;; in Y. If we can't determine this type, then return NIL.
 ;;;

@@ -2880,54 +3437,118 @@
 ;;; type without that particular element. This seems too hairy to be
 ;;; worthwhile, given its low utility.
 (defun type-difference (x y)
 ;;; type without that particular element. This seems too hairy to be
 ;;; worthwhile, given its low utility.
 (defun type-difference (x y)

-  (let ((x-types (if (union-type-p x) (union-type-types x) (list x)))
-       (y-types (if (union-type-p y) (union-type-types y) (list y))))
-    (collect ((res))
-      (dolist (x-type x-types)
-       (if (member-type-p x-type)
-           (collect ((members))
-             (dolist (mem (member-type-members x-type))
-               (multiple-value-bind (val win) (ctypep mem y)
-                 (unless win (return-from type-difference nil))
-                 (unless val
-                   (members mem))))
-             (when (members)
-               (res (make-member-type :members (members)))))
-           (dolist (y-type y-types (res x-type))
-             (multiple-value-bind (val win) (csubtypep x-type y-type)
-               (unless win (return-from type-difference nil))
-               (when val (return))
-               (when (types-equal-or-intersect x-type y-type)
-                 (return-from type-difference nil))))))
-      (let ((y-mem (find-if #'member-type-p y-types)))
-       (when y-mem
-         (let ((members (member-type-members y-mem)))
-           (dolist (x-type x-types)
-             (unless (member-type-p x-type)
-               (dolist (member members)
-                 (multiple-value-bind (val win) (ctypep member x-type)
-                   (when (or (not win) val)
-                     (return-from type-difference nil)))))))))
-      (apply #'type-union (res)))))
+  (if (and (numeric-type-p x) (numeric-type-p y))
+      ;; Numeric types are easy. Are there any others we should handle like this?
+      (type-intersection x (type-negation y))
+      (let ((x-types (if (union-type-p x) (union-type-types x) (list x)))
+            (y-types (if (union-type-p y) (union-type-types y) (list y))))
+        (collect ((res))
+          (dolist (x-type x-types)
+            (if (member-type-p x-type)
+                (let ((xset (alloc-xset))
+                      (fp-zeroes nil))
+                  (mapc-member-type-members
+                   (lambda (elt)
+                     (multiple-value-bind (ok sure) (ctypep elt y)
+                       (unless sure
+                         (return-from type-difference nil))
+                       (unless ok
+                         (if (fp-zero-p elt)
+                             (pushnew elt fp-zeroes)
+                             (add-to-xset elt xset)))))
+                   x-type)
+                  (unless (and (xset-empty-p xset) (not fp-zeroes))
+                    (res (make-member-type :xset xset :fp-zeroes fp-zeroes))))
+                (dolist (y-type y-types (res x-type))
+                  (multiple-value-bind (val win) (csubtypep x-type y-type)
+                    (unless win (return-from type-difference nil))
+                    (when val (return))
+                    (when (types-equal-or-intersect x-type y-type)
+                      (return-from type-difference nil))))))
+          (let ((y-mem (find-if #'member-type-p y-types)))
+            (when y-mem
+              (dolist (x-type x-types)
+                (unless (member-type-p x-type)
+                  (mapc-member-type-members
+                   (lambda (member)
+                     (multiple-value-bind (ok sure) (ctypep member x-type)
+                       (when (or (not sure) ok)
+                         (return-from type-difference nil))))
+                   y-mem)))))
+          (apply #'type-union (res))))))

 \f
 (!def-type-translator array (&optional (element-type '*)
 \f
 (!def-type-translator array (&optional (element-type '*)

-                                      (dimensions '*))
+                                       (dimensions '*))

   (specialize-array-type
    (make-array-type :dimensions (canonical-array-dimensions dimensions)
                     :complexp :maybe
   (specialize-array-type
    (make-array-type :dimensions (canonical-array-dimensions dimensions)
                     :complexp :maybe

-                   :element-type (if (eq element-type '*)
+                    :element-type (if (eq element-type '*)

                                       *wild-type*
                                       (specifier-type element-type)))))
 
 (!def-type-translator simple-array (&optional (element-type '*)
                                       *wild-type*
                                       (specifier-type element-type)))))
 
 (!def-type-translator simple-array (&optional (element-type '*)

-                                             (dimensions '*))
+                                              (dimensions '*))

   (specialize-array-type
    (make-array-type :dimensions (canonical-array-dimensions dimensions)
                     :complexp nil
   (specialize-array-type
    (make-array-type :dimensions (canonical-array-dimensions dimensions)
                     :complexp nil

-                   :element-type (if (eq element-type '*)
+                    :element-type (if (eq element-type '*)

                                       *wild-type*
                                       (specifier-type element-type)))))
 \f
                                       *wild-type*
                                       (specifier-type element-type)))))
 \f

+;;;; SIMD-PACK types
+#!+sb-simd-pack
+(progn
+  (!define-type-class simd-pack)
+
+  (!def-type-translator simd-pack (&optional (element-type-spec '*))
+     (if (eql element-type-spec '*)
+         (%make-simd-pack-type *simd-pack-element-types*)
+         (make-simd-pack-type (single-value-specifier-type element-type-spec))))
+
+  (!define-type-method (simd-pack :negate) (type)
+     (let ((remaining (set-difference *simd-pack-element-types*
+                                      (simd-pack-type-element-type type)))
+           (not-simd-pack (make-negation-type :type (specifier-type 'simd-pack))))
+       (if remaining
+           (type-union not-simd-pack (%make-simd-pack-type remaining))
+           not-simd-pack)))
+
+  (!define-type-method (simd-pack :unparse) (type)
+     (let ((eltypes (simd-pack-type-element-type type)))
+       (cond ((equal eltypes *simd-pack-element-types*)
+              'simd-pack)
+             ((= 1 (length eltypes))
+              `(simd-pack ,(first eltypes)))
+             (t
+              `(or ,@(mapcar (lambda (eltype)
+                               `(simd-pack ,eltype))
+                             eltypes))))))
+
+  (!define-type-method (simd-pack :simple-=) (type1 type2)
+     (declare (type simd-pack-type type1 type2))
+     (null (set-exclusive-or (simd-pack-type-element-type type1)
+                             (simd-pack-type-element-type type2))))
+
+  (!define-type-method (simd-pack :simple-subtypep) (type1 type2)
+     (declare (type simd-pack-type type1 type2))
+     (subsetp (simd-pack-type-element-type type1)
+              (simd-pack-type-element-type type2)))
+
+  (!define-type-method (simd-pack :simple-union2) (type1 type2)
+     (declare (type simd-pack-type type1 type2))
+     (%make-simd-pack-type (union (simd-pack-type-element-type type1)
+                                  (simd-pack-type-element-type type2))))
+
+  (!define-type-method (simd-pack :simple-intersection2) (type1 type2)
+     (declare (type simd-pack-type type1 type2))
+     (let ((intersection (intersection (simd-pack-type-element-type type1)
+                                       (simd-pack-type-element-type type2))))
+       (if intersection
+           (%make-simd-pack-type intersection)
+           *empty-type*)))
+
+  (!define-superclasses simd-pack ((simd-pack)) !cold-init-forms))
+\f

 ;;;; utilities shared between cross-compiler and target system
 
 ;;; Does the type derived from compilation of an actual function
 ;;;; utilities shared between cross-compiler and target system
 
 ;;; Does the type derived from compilation of an actual function

@@ -2935,53 +3556,57 @@
 (defun defined-ftype-matches-declared-ftype-p (defined-ftype declared-ftype)
   (declare (type ctype defined-ftype declared-ftype))
   (flet ((is-built-in-class-function-p (ctype)
 (defun defined-ftype-matches-declared-ftype-p (defined-ftype declared-ftype)
   (declare (type ctype defined-ftype declared-ftype))
   (flet ((is-built-in-class-function-p (ctype)

-          (and (built-in-classoid-p ctype)
-               (eq (built-in-classoid-name ctype) 'function))))
+           (and (built-in-classoid-p ctype)
+                (eq (built-in-classoid-name ctype) 'function))))

     (cond (;; DECLARED-FTYPE could certainly be #<BUILT-IN-CLASS FUNCTION>;
     (cond (;; DECLARED-FTYPE could certainly be #<BUILT-IN-CLASS FUNCTION>;

-          ;; that's what happens when we (DECLAIM (FTYPE FUNCTION FOO)).
-          (is-built-in-class-function-p declared-ftype)
-          ;; In that case, any definition satisfies the declaration.
-          t)
-         (;; It's not clear whether or how DEFINED-FTYPE might be
-          ;; #<BUILT-IN-CLASS FUNCTION>, but it's not obviously
-          ;; invalid, so let's handle that case too, just in case.
-          (is-built-in-class-function-p defined-ftype)
-          ;; No matter what DECLARED-FTYPE might be, we can't prove
-          ;; that an object of type FUNCTION doesn't satisfy it, so
-          ;; we return success no matter what.
-          t)
-         (;; Otherwise both of them must be FUN-TYPE objects.
-          t
-          ;; FIXME: For now we only check compatibility of the return
-          ;; type, not argument types, and we don't even check the
-          ;; return type very precisely (as per bug 94a). It would be
-          ;; good to do a better job. Perhaps to check the
-          ;; compatibility of the arguments, we should (1) redo
-          ;; VALUES-TYPES-EQUAL-OR-INTERSECT as
-          ;; ARGS-TYPES-EQUAL-OR-INTERSECT, and then (2) apply it to
-          ;; the ARGS-TYPE slices of the FUN-TYPEs. (ARGS-TYPE
-          ;; is a base class both of VALUES-TYPE and of FUN-TYPE.)
-          (values-types-equal-or-intersect
-           (fun-type-returns defined-ftype)
-           (fun-type-returns declared-ftype))))))
-          
+           ;; that's what happens when we (DECLAIM (FTYPE FUNCTION FOO)).
+           (is-built-in-class-function-p declared-ftype)
+           ;; In that case, any definition satisfies the declaration.
+           t)
+          (;; It's not clear whether or how DEFINED-FTYPE might be
+           ;; #<BUILT-IN-CLASS FUNCTION>, but it's not obviously
+           ;; invalid, so let's handle that case too, just in case.
+           (is-built-in-class-function-p defined-ftype)
+           ;; No matter what DECLARED-FTYPE might be, we can't prove
+           ;; that an object of type FUNCTION doesn't satisfy it, so
+           ;; we return success no matter what.
+           t)
+          (;; Otherwise both of them must be FUN-TYPE objects.
+           t
+           ;; FIXME: For now we only check compatibility of the return
+           ;; type, not argument types, and we don't even check the
+           ;; return type very precisely (as per bug 94a). It would be
+           ;; good to do a better job. Perhaps to check the
+           ;; compatibility of the arguments, we should (1) redo
+           ;; VALUES-TYPES-EQUAL-OR-INTERSECT as
+           ;; ARGS-TYPES-EQUAL-OR-INTERSECT, and then (2) apply it to
+           ;; the ARGS-TYPE slices of the FUN-TYPEs. (ARGS-TYPE
+           ;; is a base class both of VALUES-TYPE and of FUN-TYPE.)
+           (values-types-equal-or-intersect
+            (fun-type-returns defined-ftype)
+            (fun-type-returns declared-ftype))))))
+

 ;;; This messy case of CTYPE for NUMBER is shared between the
 ;;; cross-compiler and the target system.
 (defun ctype-of-number (x)
   (let ((num (if (complexp x) (realpart x) x)))
     (multiple-value-bind (complexp low high)
 ;;; This messy case of CTYPE for NUMBER is shared between the
 ;;; cross-compiler and the target system.
 (defun ctype-of-number (x)
   (let ((num (if (complexp x) (realpart x) x)))
     (multiple-value-bind (complexp low high)

-       (if (complexp x)
-           (let ((imag (imagpart x)))
-             (values :complex (min num imag) (max num imag)))
-           (values :real num num))
+        (if (complexp x)
+            (let ((imag (imagpart x)))
+              (values :complex (min num imag) (max num imag)))
+            (values :real num num))

       (make-numeric-type :class (etypecase num
       (make-numeric-type :class (etypecase num

-                                 (integer 'integer)
-                                 (rational 'rational)
-                                 (float 'float))
-                        :format (and (floatp num) (float-format-name num))
-                        :complexp complexp
-                        :low low
-                        :high high))))
+                                  (integer (if (complexp x)
+                                               (if (integerp (imagpart x))
+                                                   'integer
+                                                   'rational)
+                                               'integer))
+                                  (rational 'rational)
+                                  (float 'float))
+                         :format (and (floatp num) (float-format-name num))
+                         :complexp complexp
+                         :low low
+                         :high high))))

 \f
 (locally
   ;; Why SAFETY 0? To suppress the is-it-the-right-structure-type
 \f
 (locally
   ;; Why SAFETY 0? To suppress the is-it-the-right-structure-type