X-Git-Url: http://repo.macrolet.net/gitweb/?a=blobdiff_plain;f=src%2Fcompiler%2Ffloat-tran.lisp;h=2ae1e3363ec58de9096748ceb3d67e29c500e760;hb=a189a69454ef7635149319ae213b337f17c50d20;hp=e42674749029bb350704a685184e67af2a26d8be;hpb=dec94b039e8ec90baf21463df839a6181de606f6;p=sbcl.git

diff --git a/src/compiler/float-tran.lisp b/src/compiler/float-tran.lisp
index e426747..2ae1e33 100644
--- a/src/compiler/float-tran.lisp
+++ b/src/compiler/float-tran.lisp
@@ -15,80 +15,144 @@
 
 ;;;; coercions
 
-(defknown %single-float (real) single-float (movable foldable flushable))
-(defknown %double-float (real) double-float (movable foldable flushable))
+(defknown %single-float (real) single-float
+    (movable foldable))
+(defknown %double-float (real) double-float
+    (movable foldable))
 
-(deftransform float ((n &optional f) (* &optional single-float) * :when :both)
+(deftransform float ((n f) (* single-float) *)
   '(%single-float n))
 
-(deftransform float ((n f) (* double-float) * :when :both)
+(deftransform float ((n f) (* double-float) *)
   '(%double-float n))
 
-(deftransform %single-float ((n) (single-float) * :when :both)
+(deftransform float ((n) *)
+  '(if (floatp n)
+       n
+       (%single-float n)))
+
+(deftransform %single-float ((n) (single-float) *)
   'n)
 
-(deftransform %double-float ((n) (double-float) * :when :both)
+(deftransform %double-float ((n) (double-float) *)
   'n)
 
 ;;; RANDOM
 (macrolet ((frob (fun type)
-	     `(deftransform random ((num &optional state)
-				    (,type &optional *) *
-				    :when :both)
-		"Use inline float operations."
-		'(,fun num (or state *random-state*)))))
+             `(deftransform random ((num &optional state)
+                                    (,type &optional *) *)
+                "Use inline float operations."
+                '(,fun num (or state *random-state*)))))
   (frob %random-single-float single-float)
   (frob %random-double-float double-float))
 
-;;; Mersenne Twister RNG
-;;;
-;;; FIXME: It's unpleasant to have RANDOM functionality scattered
-;;; through the code this way. It would be nice to move this into the
-;;; same file as the other RANDOM definitions.
+;;; Return an expression to generate an integer of N-BITS many random
+;;; bits, using the minimal number of random chunks possible.
+(defun generate-random-expr-for-power-of-2 (n-bits state)
+  (declare (type (integer 1 #.sb!vm:n-word-bits) n-bits))
+  (multiple-value-bind (n-chunk-bits chunk-expr)
+      (cond ((<= n-bits n-random-chunk-bits)
+             (values n-random-chunk-bits `(random-chunk ,state)))
+            ((<= n-bits (* 2 n-random-chunk-bits))
+             (values (* 2 n-random-chunk-bits) `(big-random-chunk ,state)))
+            (t
+             (error "Unexpectedly small N-RANDOM-CHUNK-BITS")))
+    (if (< n-bits n-chunk-bits)
+        `(logand ,(1- (ash 1 n-bits)) ,chunk-expr)
+        chunk-expr)))
+
+;;; This transform for compile-time constant word-sized integers
+;;; generates an accept-reject loop to achieve equidistribution of the
+;;; returned values. Several optimizations are done: If NUM is a power
+;;; of two no loop is needed. If the random chunk size is half the word
+;;; size only one chunk is used where sufficient. For values of NUM
+;;; where it is possible and results in faster code, the rejection
+;;; probability is reduced by accepting all values below the largest
+;;; multiple of the limit that fits into one or two chunks and and doing
+;;; a division to get the random value into the desired range.
 (deftransform random ((num &optional state)
-		      ((integer 1 #.(expt 2 32)) &optional *))
-  ;; FIXME: I almost conditionalized this as #!+sb-doc. Find some way
-  ;; of automatically finding #!+sb-doc in proximity to DEFTRANSFORM
-  ;; to let me scan for places that I made this mistake and didn't
-  ;; catch myself.
-  "use inline (UNSIGNED-BYTE 32) operations"
-  (let ((num-high (numeric-type-high (continuation-type num))))
-    (when (null num-high)
-      (give-up-ir1-transform))
-    (cond ((constant-continuation-p num)
-	   ;; Check the worst case sum absolute error for the random number
-	   ;; expectations.
-	   (let ((rem (rem (expt 2 32) num-high)))
-	     (unless (< (/ (* 2 rem (- num-high rem)) num-high (expt 2 32))
-			(expt 2 (- sb!kernel::random-integer-extra-bits)))
-	       (give-up-ir1-transform
-		"The random number expectations are inaccurate."))
-	     (if (= num-high (expt 2 32))
-		 '(random-chunk (or state *random-state*))
-		 #!-x86 '(rem (random-chunk (or state *random-state*)) num)
-		 #!+x86
-		 ;; Use multiplication, which is faster.
-		 '(values (sb!bignum::%multiply
-			   (random-chunk (or state *random-state*))
-			   num)))))
-	  ((> num-high random-fixnum-max)
-	   (give-up-ir1-transform
-	    "The range is too large to ensure an accurate result."))
-	  #!+x86
-	  ((< num-high (expt 2 32))
-	   '(values (sb!bignum::%multiply (random-chunk (or state
-							    *random-state*))
-		     num)))
-	  (t
-	   '(rem (random-chunk (or state *random-state*)) num)))))
+                      ((constant-arg (integer 1 #.(expt 2 sb!vm:n-word-bits)))
+                       &optional *)
+                      *
+                      :policy (and (> speed compilation-speed)
+                                   (> speed space)))
+  "optimize to inlined RANDOM-CHUNK operations"
+  (let ((num (lvar-value num)))
+    (if (= num 1)
+        0
+        (flet ((chunk-n-bits-and-expr (n-bits)
+                 (cond ((<= n-bits n-random-chunk-bits)
+                        (values n-random-chunk-bits
+                                '(random-chunk (or state *random-state*))))
+                       ((<= n-bits (* 2 n-random-chunk-bits))
+                        (values (* 2 n-random-chunk-bits)
+                                '(big-random-chunk (or state *random-state*))))
+                       (t
+                        (error "Unexpectedly small N-RANDOM-CHUNK-BITS")))))
+          (if (zerop (logand num (1- num)))
+              ;; NUM is a power of 2.
+              (let ((n-bits (integer-length (1- num))))
+                (multiple-value-bind (n-chunk-bits chunk-expr)
+                    (chunk-n-bits-and-expr n-bits)
+                  (if (< n-bits n-chunk-bits)
+                      `(logand ,(1- (ash 1 n-bits)) ,chunk-expr)
+                      chunk-expr)))
+              ;; Generate an accept-reject loop.
+              (let ((n-bits (integer-length num)))
+                (multiple-value-bind (n-chunk-bits chunk-expr)
+                    (chunk-n-bits-and-expr n-bits)
+                  (if (or (> (* num 3) (expt 2 n-chunk-bits))
+                          (logbitp (- n-bits 2) num))
+                      ;; Division can't help as the quotient is below 3,
+                      ;; or is too costly as the rejection probability
+                      ;; without it is already small (namely at most 1/4
+                      ;; with the given test, which is experimentally a
+                      ;; reasonable threshold and cheap to test for).
+                      `(loop
+                         (let ((bits ,(generate-random-expr-for-power-of-2
+                                       n-bits '(or state *random-state*))))
+                           (when (< bits num)
+                             (return bits))))
+                      (let ((d (truncate (expt 2 n-chunk-bits) num)))
+                        `(loop
+                           (let ((bits ,chunk-expr))
+                             (when (< bits ,(* num d))
+                               (return (values (truncate bits ,d)))))))))))))))
+
 
 ;;;; float accessors
 
 (defknown make-single-float ((signed-byte 32)) single-float
-  (movable foldable flushable))
+  (movable flushable))
 
 (defknown make-double-float ((signed-byte 32) (unsigned-byte 32)) double-float
-  (movable foldable flushable))
+  (movable flushable))
+
+#-sb-xc-host
+(deftransform make-single-float ((bits)
+                                 ((signed-byte 32)))
+  "Conditional constant folding"
+  (unless (constant-lvar-p bits)
+    (give-up-ir1-transform))
+  (let* ((bits  (lvar-value bits))
+         (float (make-single-float bits)))
+    (when (float-nan-p float)
+      (give-up-ir1-transform))
+    float))
+
+#-sb-xc-host
+(deftransform make-double-float ((hi lo)
+                                 ((signed-byte 32) (unsigned-byte 32)))
+  "Conditional constant folding"
+  (unless (and (constant-lvar-p hi)
+               (constant-lvar-p lo))
+    (give-up-ir1-transform))
+  (let* ((hi    (lvar-value hi))
+         (lo    (lvar-value lo))
+         (float (make-double-float hi lo)))
+    (when (float-nan-p float)
+      (give-up-ir1-transform))
+    float))
 
 (defknown single-float-bits (single-float) (signed-byte 32)
   (movable foldable flushable))
@@ -100,19 +164,19 @@
   (movable foldable flushable))
 
 (deftransform float-sign ((float &optional float2)
-			  (single-float &optional single-float) *)
+                          (single-float &optional single-float) *)
   (if float2
       (let ((temp (gensym)))
-	`(let ((,temp (abs float2)))
-	  (if (minusp (single-float-bits float)) (- ,temp) ,temp)))
+        `(let ((,temp (abs float2)))
+          (if (minusp (single-float-bits float)) (- ,temp) ,temp)))
       '(if (minusp (single-float-bits float)) -1f0 1f0)))
 
 (deftransform float-sign ((float &optional float2)
-			  (double-float &optional double-float) *)
+                          (double-float &optional double-float) *)
   (if float2
       (let ((temp (gensym)))
-	`(let ((,temp (abs float2)))
-	  (if (minusp (double-float-high-bits float)) (- ,temp) ,temp)))
+        `(let ((,temp (abs float2)))
+          (if (minusp (double-float-high-bits float)) (- ,temp) ,temp)))
       '(if (minusp (double-float-high-bits float)) -1d0 1d0)))
 
 ;;;; DECODE-FLOAT, INTEGER-DECODE-FLOAT, and SCALE-FLOAT
@@ -133,35 +197,35 @@
   (values double-float-significand double-float-int-exponent (integer -1 1))
   (movable foldable flushable))
 
-(defknown scale-single-float (single-float fixnum) single-float
+(defknown scale-single-float (single-float integer) single-float
   (movable foldable flushable))
 
-(defknown scale-double-float (double-float fixnum) double-float
+(defknown scale-double-float (double-float integer) double-float
   (movable foldable flushable))
 
-(deftransform decode-float ((x) (single-float) * :when :both)
+(deftransform decode-float ((x) (single-float) *)
   '(decode-single-float x))
 
-(deftransform decode-float ((x) (double-float) * :when :both)
+(deftransform decode-float ((x) (double-float) *)
   '(decode-double-float x))
 
-(deftransform integer-decode-float ((x) (single-float) * :when :both)
+(deftransform integer-decode-float ((x) (single-float) *)
   '(integer-decode-single-float x))
 
-(deftransform integer-decode-float ((x) (double-float) * :when :both)
+(deftransform integer-decode-float ((x) (double-float) *)
   '(integer-decode-double-float x))
 
-(deftransform scale-float ((f ex) (single-float *) * :when :both)
+(deftransform scale-float ((f ex) (single-float *) *)
   (if (and #!+x86 t #!-x86 nil
-	   (csubtypep (continuation-type ex)
-		      (specifier-type '(signed-byte 32))))
+           (csubtypep (lvar-type ex)
+                      (specifier-type '(signed-byte 32))))
       '(coerce (%scalbn (coerce f 'double-float) ex) 'single-float)
       '(scale-single-float f ex)))
 
-(deftransform scale-float ((f ex) (double-float *) * :when :both)
+(deftransform scale-float ((f ex) (double-float *) *)
   (if (and #!+x86 t #!-x86 nil
-	   (csubtypep (continuation-type ex)
-		      (specifier-type '(signed-byte 32))))
+           (csubtypep (lvar-type ex)
+                      (specifier-type '(signed-byte 32))))
       '(%scalbn f ex)
       '(scale-double-float f ex)))
 
@@ -207,74 +271,110 @@
 (defun scale-float-derive-type-aux (f ex same-arg)
   (declare (ignore same-arg))
   (flet ((scale-bound (x n)
-	   ;; We need to be a bit careful here and catch any overflows
-	   ;; that might occur. We can ignore underflows which become
-	   ;; zeros.
-	   (set-bound
-	    (handler-case
-	     (scale-float (type-bound-number x) n)
-	     (floating-point-overflow ()
-		nil))
-	    (consp x))))
+           ;; We need to be a bit careful here and catch any overflows
+           ;; that might occur. We can ignore underflows which become
+           ;; zeros.
+           (set-bound
+            (handler-case
+             (scale-float (type-bound-number x) n)
+             (floating-point-overflow ()
+                nil))
+            (consp x))))
     (when (and (numeric-type-p f) (numeric-type-p ex))
       (let ((f-lo (numeric-type-low f))
-	    (f-hi (numeric-type-high f))
-	    (ex-lo (numeric-type-low ex))
-	    (ex-hi (numeric-type-high ex))
-	    (new-lo nil)
-	    (new-hi nil))
-	(when (and f-hi ex-hi)
-	  (setf new-hi (scale-bound f-hi ex-hi)))
-	(when (and f-lo ex-lo)
-	  (setf new-lo (scale-bound f-lo ex-lo)))
-	(make-numeric-type :class (numeric-type-class f)
-			   :format (numeric-type-format f)
-			   :complexp :real
-			   :low new-lo
-			   :high new-hi)))))
+            (f-hi (numeric-type-high f))
+            (ex-lo (numeric-type-low ex))
+            (ex-hi (numeric-type-high ex))
+            (new-lo nil)
+            (new-hi nil))
+        (when f-hi
+          (if (< (float-sign (type-bound-number f-hi)) 0.0)
+              (when ex-lo
+                (setf new-hi (scale-bound f-hi ex-lo)))
+              (when ex-hi
+                (setf new-hi (scale-bound f-hi ex-hi)))))
+        (when f-lo
+          (if (< (float-sign (type-bound-number f-lo)) 0.0)
+              (when ex-hi
+                (setf new-lo (scale-bound f-lo ex-hi)))
+              (when ex-lo
+                (setf new-lo (scale-bound f-lo ex-lo)))))
+        (make-numeric-type :class (numeric-type-class f)
+                           :format (numeric-type-format f)
+                           :complexp :real
+                           :low new-lo
+                           :high new-hi)))))
 (defoptimizer (scale-single-float derive-type) ((f ex))
   (two-arg-derive-type f ex #'scale-float-derive-type-aux
-		       #'scale-single-float t))
+                       #'scale-single-float t))
 (defoptimizer (scale-double-float derive-type) ((f ex))
   (two-arg-derive-type f ex #'scale-float-derive-type-aux
-		       #'scale-double-float t))
+                       #'scale-double-float t))
 
 ;;; DEFOPTIMIZERs for %SINGLE-FLOAT and %DOUBLE-FLOAT. This makes the
 ;;; FLOAT function return the correct ranges if the input has some
 ;;; defined range. Quite useful if we want to convert some type of
 ;;; bounded integer into a float.
 (macrolet
-    ((frob (fun type)
+    ((frob (fun type most-negative most-positive)
        (let ((aux-name (symbolicate fun "-DERIVE-TYPE-AUX")))
-	 `(progn
-	   (defun ,aux-name (num)
-	     ;; When converting a number to a float, the limits are
-	     ;; the same.
-	     (let* ((lo (bound-func #'(lambda (x)
-					(coerce x ',type))
-				    (numeric-type-low num)))
-		    (hi (bound-func #'(lambda (x)
-					(coerce x ',type))
-				    (numeric-type-high num))))
-	       (specifier-type `(,',type ,(or lo '*) ,(or hi '*)))))
-
-	   (defoptimizer (,fun derive-type) ((num))
-	     (one-arg-derive-type num #',aux-name #',fun))))))
-  (frob %single-float single-float)
-  (frob %double-float double-float))
-) ; PROGN 
+         `(progn
+            (defun ,aux-name (num)
+              ;; When converting a number to a float, the limits are
+              ;; the same.
+              (let* ((lo (bound-func (lambda (x)
+                                       (if (< x ,most-negative)
+                                           ,most-negative
+                                           (coerce x ',type)))
+                                     (numeric-type-low num)
+                                     nil))
+                     (hi (bound-func (lambda (x)
+                                       (if (< ,most-positive x )
+                                           ,most-positive
+                                           (coerce x ',type)))
+                                     (numeric-type-high num)
+                                     nil)))
+                (specifier-type `(,',type ,(or lo '*) ,(or hi '*)))))
+
+            (defoptimizer (,fun derive-type) ((num))
+              (handler-case
+                  (one-arg-derive-type num #',aux-name #',fun)
+                (type-error ()
+                  nil)))))))
+  (frob %single-float single-float
+        most-negative-single-float most-positive-single-float)
+  (frob %double-float double-float
+        most-negative-double-float most-positive-double-float))
+) ; PROGN
 
 ;;;; float contagion
 
+(defun safe-ctype-for-single-coercion-p (x)
+  ;; See comment in SAFE-SINGLE-COERCION-P -- this deals with the same
+  ;; problem, but in the context of evaluated and compiled (+ <int> <single>)
+  ;; giving different result if we fail to check for this.
+  (or (not (csubtypep x (specifier-type 'integer)))
+      #!+x86
+      (csubtypep x (specifier-type `(integer ,most-negative-exactly-single-float-fixnum
+                                             ,most-positive-exactly-single-float-fixnum)))
+      #!-x86
+      (csubtypep x (specifier-type 'fixnum))))
+
 ;;; Do some stuff to recognize when the loser is doing mixed float and
 ;;; rational arithmetic, or different float types, and fix it up. If
 ;;; we don't, he won't even get so much as an efficiency note.
 (deftransform float-contagion-arg1 ((x y) * * :defun-only t :node node)
-  `(,(continuation-function-name (basic-combination-fun node))
-    (float x y) y))
+  (if (or (not (types-equal-or-intersect (lvar-type y) (specifier-type 'single-float)))
+          (safe-ctype-for-single-coercion-p (lvar-type x)))
+      `(,(lvar-fun-name (basic-combination-fun node))
+         (float x y) y)
+      (give-up-ir1-transform)))
 (deftransform float-contagion-arg2 ((x y) * * :defun-only t :node node)
-  `(,(continuation-function-name (basic-combination-fun node))
-    x (float y x)))
+  (if (or (not (types-equal-or-intersect (lvar-type x) (specifier-type 'single-float)))
+          (safe-ctype-for-single-coercion-p (lvar-type y)))
+      `(,(lvar-fun-name (basic-combination-fun node))
+         x (float y x))
+      (give-up-ir1-transform)))
 
 (dolist (x '(+ * / -))
   (%deftransform x '(function (rational float) *) #'float-contagion-arg1)
@@ -282,9 +382,76 @@
 
 (dolist (x '(= < > + * / -))
   (%deftransform x '(function (single-float double-float) *)
-		 #'float-contagion-arg1)
+                 #'float-contagion-arg1)
   (%deftransform x '(function (double-float single-float) *)
-		 #'float-contagion-arg2))
+                 #'float-contagion-arg2))
+
+(macrolet ((def (type &rest args)
+             `(deftransform * ((x y) (,type (constant-arg (member ,@args))) *
+                               ;; Beware the SNaN!
+                               :policy (zerop float-accuracy))
+                "optimize multiplication by one"
+                (let ((y (lvar-value y)))
+                  (if (minusp y)
+                      '(%negate x)
+                      'x)))))
+  (def single-float 1.0 -1.0)
+  (def double-float 1.0d0 -1.0d0))
+
+;;; Return the reciprocal of X if it can be represented exactly, NIL otherwise.
+(defun maybe-exact-reciprocal (x)
+  (unless (zerop x)
+    (handler-case
+        (multiple-value-bind (significand exponent sign)
+            (integer-decode-float x)
+          ;; only powers of 2 can be inverted exactly
+          (unless (zerop (logand significand (1- significand)))
+            (return-from maybe-exact-reciprocal nil))
+          (let ((expected   (/ sign significand (expt 2 exponent)))
+                (reciprocal (/ x)))
+            (multiple-value-bind (significand exponent sign)
+                (integer-decode-float reciprocal)
+              ;; Denorms can't be inverted safely.
+              (and (eql expected (* sign significand (expt 2 exponent)))
+                   reciprocal))))
+      (error () (return-from maybe-exact-reciprocal nil)))))
+
+;;; Replace constant division by multiplication with exact reciprocal,
+;;; if one exists.
+(macrolet ((def (type)
+             `(deftransform / ((x y) (,type (constant-arg ,type)) *
+                               :node node)
+                "convert to multiplication by reciprocal"
+                (let ((n (lvar-value y)))
+                  (if (policy node (zerop float-accuracy))
+                      `(* x ,(/ n))
+                      (let ((r (maybe-exact-reciprocal n)))
+                        (if r
+                            `(* x ,r)
+                            (give-up-ir1-transform
+                             "~S does not have an exact reciprocal"
+                             n))))))))
+  (def single-float)
+  (def double-float))
+
+;;; Optimize addition and subtraction of zero
+(macrolet ((def (op type &rest args)
+             `(deftransform ,op ((x y) (,type (constant-arg (member ,@args))) *
+                                 ;; Beware the SNaN!
+                                 :policy (zerop float-accuracy))
+                'x)))
+  ;; No signed zeros, thanks.
+  (def + single-float 0 0.0)
+  (def - single-float 0 0.0)
+  (def + double-float 0 0.0 0.0d0)
+  (def - double-float 0 0.0 0.0d0))
+
+;;; On most platforms (+ x x) is faster than (* x 2)
+(macrolet ((def (type &rest args)
+             `(deftransform * ((x y) (,type (constant-arg (member ,@args))))
+                '(+ x x))))
+  (def single-float 2 2.0)
+  (def double-float 2 2.0 2.0d0))
 
 ;;; Prevent ZEROP, PLUSP, and MINUSP from losing horribly. We can't in
 ;;; general float rational args to comparison, since Common Lisp
@@ -292,17 +459,17 @@
 ;;; do it for any rational that has a precise representation as a
 ;;; float (such as 0).
 (macrolet ((frob (op)
-	     `(deftransform ,op ((x y) (float rational) * :when :both)
-		"open-code FLOAT to RATIONAL comparison"
-		(unless (constant-continuation-p y)
-		  (give-up-ir1-transform
-		   "The RATIONAL value isn't known at compile time."))
-		(let ((val (continuation-value y)))
-		  (unless (eql (rational (float val)) val)
-		    (give-up-ir1-transform
-		     "~S doesn't have a precise float representation."
-		     val)))
-		`(,',op x (float y x)))))
+             `(deftransform ,op ((x y) (float rational) *)
+                "open-code FLOAT to RATIONAL comparison"
+                (unless (constant-lvar-p y)
+                  (give-up-ir1-transform
+                   "The RATIONAL value isn't known at compile time."))
+                (let ((val (lvar-value y)))
+                  (unless (eql (rational (float val)) val)
+                    (give-up-ir1-transform
+                     "~S doesn't have a precise float representation."
+                     val)))
+                `(,',op x (float y x)))))
   (frob <)
   (frob >)
   (frob =))
@@ -313,33 +480,33 @@
 ;;; appropriate domain.
 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
 (dolist (stuff '((asin (real -1.0 1.0))
-		 (acos (real -1.0 1.0))
-		 (acosh (real 1.0))
-		 (atanh (real -1.0 1.0))
-		 (sqrt (real 0.0))))
+                 (acos (real -1.0 1.0))
+                 (acosh (real 1.0))
+                 (atanh (real -1.0 1.0))
+                 (sqrt (real 0.0))))
   (destructuring-bind (name type) stuff
     (let ((type (specifier-type type)))
-      (setf (function-info-derive-type (function-info-or-lose name))
-	    (lambda (call)
-	      (declare (type combination call))
-	      (when (csubtypep (continuation-type
-				(first (combination-args call)))
-			       type)
-		(specifier-type 'float)))))))
+      (setf (fun-info-derive-type (fun-info-or-lose name))
+            (lambda (call)
+              (declare (type combination call))
+              (when (csubtypep (lvar-type
+                                (first (combination-args call)))
+                               type)
+                (specifier-type 'float)))))))
 
 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
 (defoptimizer (log derive-type) ((x &optional y))
-  (when (and (csubtypep (continuation-type x)
-			(specifier-type '(real 0.0)))
-	     (or (null y)
-		 (csubtypep (continuation-type y)
-			    (specifier-type '(real 0.0)))))
+  (when (and (csubtypep (lvar-type x)
+                        (specifier-type '(real 0.0)))
+             (or (null y)
+                 (csubtypep (lvar-type y)
+                            (specifier-type '(real 0.0)))))
     (specifier-type 'float)))
 
 ;;;; irrational transforms
 
 (defknown (%tan %sinh %asinh %atanh %log %logb %log10 %tan-quick)
-	  (double-float) double-float
+          (double-float) double-float
   (movable foldable flushable))
 
 (defknown (%sin %cos %tanh %sin-quick %cos-quick)
@@ -347,11 +514,13 @@
   (movable foldable flushable))
 
 (defknown (%asin %atan)
-  (double-float) (double-float #.(- (/ pi 2)) #.(/ pi 2))
+  (double-float)
+  (double-float #.(coerce (- (/ pi 2)) 'double-float)
+                #.(coerce (/ pi 2) 'double-float))
   (movable foldable flushable))
 
 (defknown (%acos)
-  (double-float) (double-float 0.0d0 #.pi)
+  (double-float) (double-float 0.0d0 #.(coerce pi 'double-float))
   (movable foldable flushable))
 
 (defknown (%cosh)
@@ -375,7 +544,9 @@
   (movable foldable flushable))
 
 (defknown (%atan2)
-  (double-float double-float) (double-float #.(- pi) #.pi)
+  (double-float double-float)
+  (double-float #.(coerce (- pi) 'double-float)
+                #.(coerce pi 'double-float))
   (movable foldable flushable))
 
 (defknown (%scalb)
@@ -390,75 +561,77 @@
   (double-float) double-float
   (movable foldable flushable))
 
-(dolist (stuff '((exp %exp *)
-		 (log %log float)
-		 (sqrt %sqrt float)
-		 (asin %asin float)
-		 (acos %acos float)
-		 (atan %atan *)
-		 (sinh %sinh *)
-		 (cosh %cosh *)
-		 (tanh %tanh *)
-		 (asinh %asinh *)
-		 (acosh %acosh float)
-		 (atanh %atanh float)))
-  (destructuring-bind (name prim rtype) stuff
-    (deftransform name ((x) '(single-float) rtype :eval-name t)
-      `(coerce (,prim (coerce x 'double-float)) 'single-float))
-    (deftransform name ((x) '(double-float) rtype :eval-name t :when :both)
-      `(,prim x))))
+(macrolet ((def (name prim rtype)
+             `(progn
+               (deftransform ,name ((x) (single-float) ,rtype)
+                 `(coerce (,',prim (coerce x 'double-float)) 'single-float))
+               (deftransform ,name ((x) (double-float) ,rtype)
+                 `(,',prim x)))))
+  (def exp %exp *)
+  (def log %log float)
+  (def sqrt %sqrt float)
+  (def asin %asin float)
+  (def acos %acos float)
+  (def atan %atan *)
+  (def sinh %sinh *)
+  (def cosh %cosh *)
+  (def tanh %tanh *)
+  (def asinh %asinh *)
+  (def acosh %acosh float)
+  (def atanh %atanh float))
 
 ;;; The argument range is limited on the x86 FP trig. functions. A
 ;;; post-test can detect a failure (and load a suitable result), but
 ;;; this test is avoided if possible.
-(dolist (stuff '((sin %sin %sin-quick)
-		 (cos %cos %cos-quick)
-		 (tan %tan %tan-quick)))
-  (destructuring-bind (name prim prim-quick) stuff
-    (declare (ignorable prim-quick))
-    (deftransform name ((x) '(single-float) '* :eval-name t)
-      #!+x86 (cond ((csubtypep (continuation-type x)
-			       (specifier-type '(single-float
-						 (#.(- (expt 2f0 64)))
-						 (#.(expt 2f0 64)))))
-		    `(coerce (,prim-quick (coerce x 'double-float))
-		    'single-float))
-		   (t
-		    (compiler-note
-		    "unable to avoid inline argument range check~@
-		      because the argument range (~S) was not within 2^64"
-		    (type-specifier (continuation-type x)))
-		    `(coerce (,prim (coerce x 'double-float)) 'single-float)))
-      #!-x86 `(coerce (,prim (coerce x 'double-float)) 'single-float))
-    (deftransform name ((x) '(double-float) '* :eval-name t :when :both)
-      #!+x86 (cond ((csubtypep (continuation-type x)
-			       (specifier-type '(double-float
-						 (#.(- (expt 2d0 64)))
-						 (#.(expt 2d0 64)))))
-		    `(,prim-quick x))
-		   (t
-		    (compiler-note
-		    "unable to avoid inline argument range check~@
-		   because the argument range (~S) was not within 2^64"
-		    (type-specifier (continuation-type x)))
-		    `(,prim x)))
-      #!-x86 `(,prim x))))
+(macrolet ((def (name prim prim-quick)
+             (declare (ignorable prim-quick))
+             `(progn
+                (deftransform ,name ((x) (single-float) *)
+                  #!+x86 (cond ((csubtypep (lvar-type x)
+                                           (specifier-type '(single-float
+                                                             (#.(- (expt 2f0 63)))
+                                                             (#.(expt 2f0 63)))))
+                                `(coerce (,',prim-quick (coerce x 'double-float))
+                                  'single-float))
+                               (t
+                                (compiler-notify
+                                 "unable to avoid inline argument range check~@
+                                  because the argument range (~S) was not within 2^63"
+                                 (type-specifier (lvar-type x)))
+                                `(coerce (,',prim (coerce x 'double-float)) 'single-float)))
+                  #!-x86 `(coerce (,',prim (coerce x 'double-float)) 'single-float))
+               (deftransform ,name ((x) (double-float) *)
+                 #!+x86 (cond ((csubtypep (lvar-type x)
+                                          (specifier-type '(double-float
+                                                            (#.(- (expt 2d0 63)))
+                                                            (#.(expt 2d0 63)))))
+                               `(,',prim-quick x))
+                              (t
+                               (compiler-notify
+                                "unable to avoid inline argument range check~@
+                                 because the argument range (~S) was not within 2^63"
+                                (type-specifier (lvar-type x)))
+                               `(,',prim x)))
+                 #!-x86 `(,',prim x)))))
+  (def sin %sin %sin-quick)
+  (def cos %cos %cos-quick)
+  (def tan %tan %tan-quick))
 
 (deftransform atan ((x y) (single-float single-float) *)
   `(coerce (%atan2 (coerce x 'double-float) (coerce y 'double-float))
     'single-float))
-(deftransform atan ((x y) (double-float double-float) * :when :both)
+(deftransform atan ((x y) (double-float double-float) *)
   `(%atan2 x y))
 
 (deftransform expt ((x y) ((single-float 0f0) single-float) *)
   `(coerce (%pow (coerce x 'double-float) (coerce y 'double-float))
     'single-float))
-(deftransform expt ((x y) ((double-float 0d0) double-float) * :when :both)
+(deftransform expt ((x y) ((double-float 0d0) double-float) *)
   `(%pow x y))
 (deftransform expt ((x y) ((single-float 0f0) (signed-byte 32)) *)
   `(coerce (%pow (coerce x 'double-float) (coerce y 'double-float))
     'single-float))
-(deftransform expt ((x y) ((double-float 0d0) (signed-byte 32)) * :when :both)
+(deftransform expt ((x y) ((double-float 0d0) (signed-byte 32)) *)
   `(%pow x (coerce y 'double-float)))
 
 ;;; ANSI says log with base zero returns zero.
@@ -467,23 +640,23 @@
 
 ;;; Handle some simple transformations.
 
-(deftransform abs ((x) ((complex double-float)) double-float :when :both)
+(deftransform abs ((x) ((complex double-float)) double-float)
   '(%hypot (realpart x) (imagpart x)))
 
 (deftransform abs ((x) ((complex single-float)) single-float)
   '(coerce (%hypot (coerce (realpart x) 'double-float)
-		   (coerce (imagpart x) 'double-float))
-	  'single-float))
+                   (coerce (imagpart x) 'double-float))
+          'single-float))
 
-(deftransform phase ((x) ((complex double-float)) double-float :when :both)
+(deftransform phase ((x) ((complex double-float)) double-float)
   '(%atan2 (imagpart x) (realpart x)))
 
 (deftransform phase ((x) ((complex single-float)) single-float)
   '(coerce (%atan2 (coerce (imagpart x) 'double-float)
-		   (coerce (realpart x) 'double-float))
-	  'single-float))
+                   (coerce (realpart x) 'double-float))
+          'single-float))
 
-(deftransform phase ((x) ((float)) float :when :both)
+(deftransform phase ((x) ((float)) float)
   '(if (minusp (float-sign x))
        (float pi x)
        (float 0 x)))
@@ -498,8 +671,8 @@
 (defun coerce-numeric-bound (bound type)
   (when bound
     (if (consp bound)
-	(list (coerce (car bound) type))
-	(coerce bound type))))
+        (list (coerce (car bound) type))
+        (coerce bound type))))
 
 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
 (progn
@@ -514,9 +687,9 @@
 (defun complex-float-type (arg)
   (declare (type numeric-type arg))
   (let* ((format (case (numeric-type-class arg)
-		   ((integer rational) 'single-float)
-		   (t (numeric-type-format arg))))
-	 (float-type (or format 'float)))
+                   ((integer rational) 'single-float)
+                   (t (numeric-type-format arg))))
+         (float-type (or format 'float)))
     (specifier-type `(complex ,float-type))))
 
 ;;; Compute a specifier like '(OR FLOAT (COMPLEX FLOAT)), except float
@@ -525,54 +698,66 @@
 (defun float-or-complex-float-type (arg &optional lo hi)
   (declare (type numeric-type arg))
   (let* ((format (case (numeric-type-class arg)
-		   ((integer rational) 'single-float)
-		   (t (numeric-type-format arg))))
-	 (float-type (or format 'float))
-	 (lo (coerce-numeric-bound lo float-type))
-	 (hi (coerce-numeric-bound hi float-type)))
+                   ((integer rational) 'single-float)
+                   (t (numeric-type-format arg))))
+         (float-type (or format 'float))
+         (lo (coerce-numeric-bound lo float-type))
+         (hi (coerce-numeric-bound hi float-type)))
     (specifier-type `(or (,float-type ,(or lo '*) ,(or hi '*))
-			 (complex ,float-type)))))
+                         (complex ,float-type)))))
+
+) ; PROGN
 
-;;; Test whether the numeric-type ARG is within in domain specified by
+(eval-when (:compile-toplevel :execute)
+  ;; So the problem with this hack is that it's actually broken.  If
+  ;; the host does not have long floats, then setting *R-D-F-F* to
+  ;; LONG-FLOAT doesn't actually buy us anything.  FIXME.
+  (setf *read-default-float-format*
+        #!+long-float 'long-float #!-long-float 'double-float))
+;;; Test whether the numeric-type ARG is within the domain specified by
 ;;; DOMAIN-LOW and DOMAIN-HIGH, consider negative and positive zero to
-;;; be distinct as for the :NEGATIVE-ZERO-IS-NOT-ZERO feature. With
-;;; the :NEGATIVE-ZERO-IS-NOT-ZERO feature this could be handled by
-;;; the numeric subtype code in type.lisp.
+;;; be distinct.
+#-sb-xc-host  ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
 (defun domain-subtypep (arg domain-low domain-high)
   (declare (type numeric-type arg)
-	   (type (or real null) domain-low domain-high))
+           (type (or real null) domain-low domain-high))
   (let* ((arg-lo (numeric-type-low arg))
-	 (arg-lo-val (type-bound-number arg-lo))
-	 (arg-hi (numeric-type-high arg))
-	 (arg-hi-val (type-bound-number arg-hi)))
+         (arg-lo-val (type-bound-number arg-lo))
+         (arg-hi (numeric-type-high arg))
+         (arg-hi-val (type-bound-number arg-hi)))
     ;; Check that the ARG bounds are correctly canonicalized.
     (when (and arg-lo (floatp arg-lo-val) (zerop arg-lo-val) (consp arg-lo)
-	       (minusp (float-sign arg-lo-val)))
-      (compiler-note "float zero bound ~S not correctly canonicalized?" arg-lo)
-      (setq arg-lo '(0l0) arg-lo-val 0l0))
+               (minusp (float-sign arg-lo-val)))
+      (compiler-notify "float zero bound ~S not correctly canonicalized?" arg-lo)
+      (setq arg-lo 0e0 arg-lo-val arg-lo))
     (when (and arg-hi (zerop arg-hi-val) (floatp arg-hi-val) (consp arg-hi)
-	       (plusp (float-sign arg-hi-val)))
-      (compiler-note "float zero bound ~S not correctly canonicalized?" arg-hi)
-      (setq arg-hi '(-0l0) arg-hi-val -0l0))
-    (and (or (null domain-low)
-	     (and arg-lo (>= arg-lo-val domain-low)
-		  (not (and (zerop domain-low) (floatp domain-low)
-			    (plusp (float-sign domain-low))
-			    (zerop arg-lo-val) (floatp arg-lo-val)
-			    (if (consp arg-lo)
-				(plusp (float-sign arg-lo-val))
-				(minusp (float-sign arg-lo-val)))))))
-	 (or (null domain-high)
-	     (and arg-hi (<= arg-hi-val domain-high)
-		  (not (and (zerop domain-high) (floatp domain-high)
-			    (minusp (float-sign domain-high))
-			    (zerop arg-hi-val) (floatp arg-hi-val)
-			    (if (consp arg-hi)
-				(minusp (float-sign arg-hi-val))
-				(plusp (float-sign arg-hi-val))))))))))
+               (plusp (float-sign arg-hi-val)))
+      (compiler-notify "float zero bound ~S not correctly canonicalized?" arg-hi)
+      (setq arg-hi (ecase *read-default-float-format*
+                     (double-float (load-time-value (make-unportable-float :double-float-negative-zero)))
+                     #!+long-float
+                     (long-float (load-time-value (make-unportable-float :long-float-negative-zero))))
+            arg-hi-val arg-hi))
+    (flet ((fp-neg-zero-p (f)           ; Is F -0.0?
+             (and (floatp f) (zerop f) (minusp (float-sign f))))
+           (fp-pos-zero-p (f)           ; Is F +0.0?
+             (and (floatp f) (zerop f) (plusp (float-sign f)))))
+      (and (or (null domain-low)
+               (and arg-lo (>= arg-lo-val domain-low)
+                    (not (and (fp-pos-zero-p domain-low)
+                              (fp-neg-zero-p arg-lo)))))
+           (or (null domain-high)
+               (and arg-hi (<= arg-hi-val domain-high)
+                    (not (and (fp-neg-zero-p domain-high)
+                              (fp-pos-zero-p arg-hi)))))))))
+(eval-when (:compile-toplevel :execute)
+  (setf *read-default-float-format* 'single-float))
+
+#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
+(progn
 
 ;;; Handle monotonic functions of a single variable whose domain is
-;;; possibly part of the real line. ARG is the variable, FCN is the
+;;; possibly part of the real line. ARG is the variable, FUN is the
 ;;; function, and DOMAIN is a specifier that gives the (real) domain
 ;;; of the function. If ARG is a subset of the DOMAIN, we compute the
 ;;; bounds directly. Otherwise, we compute the bounds for the
@@ -580,79 +765,76 @@
 ;;; result, which occurs for the parts of ARG not in the DOMAIN.
 ;;;
 ;;; Negative and positive zero are considered distinct within
-;;; DOMAIN-LOW and DOMAIN-HIGH, as for the :negative-zero-is-not-zero
-;;; feature.
+;;; DOMAIN-LOW and DOMAIN-HIGH.
 ;;;
 ;;; DEFAULT-LOW and DEFAULT-HIGH are the lower and upper bounds if we
-;;; can't compute the bounds using FCN.
-(defun elfun-derive-type-simple (arg fcn domain-low domain-high
-				     default-low default-high
-				     &optional (increasingp t))
+;;; can't compute the bounds using FUN.
+(defun elfun-derive-type-simple (arg fun domain-low domain-high
+                                     default-low default-high
+                                     &optional (increasingp t))
   (declare (type (or null real) domain-low domain-high))
   (etypecase arg
     (numeric-type
      (cond ((eq (numeric-type-complexp arg) :complex)
-	    (make-numeric-type :class (numeric-type-class arg)
-			       :format (numeric-type-format arg)
-			       :complexp :complex))
-	   ((numeric-type-real-p arg)
-	    ;; The argument is real, so let's find the intersection
-	    ;; between the argument and the domain of the function.
-	    ;; We compute the bounds on the intersection, and for
-	    ;; everything else, we return a complex number of the
-	    ;; appropriate type.
-	    (multiple-value-bind (intersection difference)
-		(interval-intersection/difference (numeric-type->interval arg)
-						  (make-interval
-						   :low domain-low
-						   :high domain-high))
-	      (cond
-		(intersection
-		 ;; Process the intersection.
-		 (let* ((low (interval-low intersection))
-			(high (interval-high intersection))
-			(res-lo (or (bound-func fcn (if increasingp low high))
-				    default-low))
-			(res-hi (or (bound-func fcn (if increasingp high low))
-				    default-high))
-			(format (case (numeric-type-class arg)
-				  ((integer rational) 'single-float)
-				  (t (numeric-type-format arg))))
-			(bound-type (or format 'float))
-			(result-type
-			 (make-numeric-type
-			  :class 'float
-			  :format format
-			  :low (coerce-numeric-bound res-lo bound-type)
-			  :high (coerce-numeric-bound res-hi bound-type))))
-		   ;; If the ARG is a subset of the domain, we don't
-		   ;; have to worry about the difference, because that
-		   ;; can't occur.
-		   (if (or (null difference)
-			   ;; Check whether the arg is within the domain.
-			   (domain-subtypep arg domain-low domain-high))
-		       result-type
-		       (list result-type
-			     (specifier-type `(complex ,bound-type))))))
-		(t
-		 ;; No intersection so the result must be purely complex.
-		 (complex-float-type arg)))))
-	   (t
-	    (float-or-complex-float-type arg default-low default-high))))))
+            (complex-float-type arg))
+           ((numeric-type-real-p arg)
+            ;; The argument is real, so let's find the intersection
+            ;; between the argument and the domain of the function.
+            ;; We compute the bounds on the intersection, and for
+            ;; everything else, we return a complex number of the
+            ;; appropriate type.
+            (multiple-value-bind (intersection difference)
+                (interval-intersection/difference (numeric-type->interval arg)
+                                                  (make-interval
+                                                   :low domain-low
+                                                   :high domain-high))
+              (cond
+                (intersection
+                 ;; Process the intersection.
+                 (let* ((low (interval-low intersection))
+                        (high (interval-high intersection))
+                        (res-lo (or (bound-func fun (if increasingp low high) nil)
+                                    default-low))
+                        (res-hi (or (bound-func fun (if increasingp high low) nil)
+                                    default-high))
+                        (format (case (numeric-type-class arg)
+                                  ((integer rational) 'single-float)
+                                  (t (numeric-type-format arg))))
+                        (bound-type (or format 'float))
+                        (result-type
+                         (make-numeric-type
+                          :class 'float
+                          :format format
+                          :low (coerce-numeric-bound res-lo bound-type)
+                          :high (coerce-numeric-bound res-hi bound-type))))
+                   ;; If the ARG is a subset of the domain, we don't
+                   ;; have to worry about the difference, because that
+                   ;; can't occur.
+                   (if (or (null difference)
+                           ;; Check whether the arg is within the domain.
+                           (domain-subtypep arg domain-low domain-high))
+                       result-type
+                       (list result-type
+                             (specifier-type `(complex ,bound-type))))))
+                (t
+                 ;; No intersection so the result must be purely complex.
+                 (complex-float-type arg)))))
+           (t
+            (float-or-complex-float-type arg default-low default-high))))))
 
 (macrolet
     ((frob (name domain-low domain-high def-low-bnd def-high-bnd
-		 &key (increasingp t))
+                 &key (increasingp t))
        (let ((num (gensym)))
-	 `(defoptimizer (,name derive-type) ((,num))
-	   (one-arg-derive-type
-	    ,num
-	    #'(lambda (arg)
-		(elfun-derive-type-simple arg #',name
-					  ,domain-low ,domain-high
-					  ,def-low-bnd ,def-high-bnd
-					  ,increasingp))
-	    #',name)))))
+         `(defoptimizer (,name derive-type) ((,num))
+           (one-arg-derive-type
+            ,num
+            (lambda (arg)
+              (elfun-derive-type-simple arg #',name
+                                        ,domain-low ,domain-high
+                                        ,def-low-bnd ,def-high-bnd
+                                        ,increasingp))
+            #',name)))))
   ;; These functions are easy because they are defined for the whole
   ;; real line.
   (frob exp nil nil 0 nil)
@@ -670,231 +852,242 @@
   (frob atanh -1d0 1d0 -1 1)
   ;; Kahan says that (sqrt -0.0) is -0.0, so use a specifier that
   ;; includes -0.0.
-  (frob sqrt -0d0 nil 0 nil))
+  (frob sqrt (load-time-value (make-unportable-float :double-float-negative-zero)) nil 0 nil))
 
 ;;; Compute bounds for (expt x y). This should be easy since (expt x
 ;;; y) = (exp (* y (log x))). However, computations done this way
 ;;; have too much roundoff. Thus we have to do it the hard way.
 (defun safe-expt (x y)
   (handler-case
-      (expt x y)
+      (when (< (abs y) 10000)
+        (expt x y))
     (error ()
       nil)))
 
 ;;; Handle the case when x >= 1.
 (defun interval-expt-> (x y)
   (case (sb!c::interval-range-info y 0d0)
-    ('+
+    (+
      ;; Y is positive and log X >= 0. The range of exp(y * log(x)) is
      ;; obviously non-negative. We just have to be careful for
      ;; infinite bounds (given by nil).
      (let ((lo (safe-expt (type-bound-number (sb!c::interval-low x))
-			  (type-bound-number (sb!c::interval-low y))))
-	   (hi (safe-expt (type-bound-number (sb!c::interval-high x))
-			  (type-bound-number (sb!c::interval-high y)))))
+                          (type-bound-number (sb!c::interval-low y))))
+           (hi (safe-expt (type-bound-number (sb!c::interval-high x))
+                          (type-bound-number (sb!c::interval-high y)))))
        (list (sb!c::make-interval :low (or lo 1) :high hi))))
-    ('-
+    (-
      ;; Y is negative and log x >= 0. The range of exp(y * log(x)) is
      ;; obviously [0, 1]. However, underflow (nil) means 0 is the
      ;; result.
      (let ((lo (safe-expt (type-bound-number (sb!c::interval-high x))
-			  (type-bound-number (sb!c::interval-low y))))
-	   (hi (safe-expt (type-bound-number (sb!c::interval-low x))
-			  (type-bound-number (sb!c::interval-high y)))))
+                          (type-bound-number (sb!c::interval-low y))))
+           (hi (safe-expt (type-bound-number (sb!c::interval-low x))
+                          (type-bound-number (sb!c::interval-high y)))))
        (list (sb!c::make-interval :low (or lo 0) :high (or hi 1)))))
     (t
      ;; Split the interval in half.
      (destructuring-bind (y- y+)
-	 (sb!c::interval-split 0 y t)
+         (sb!c::interval-split 0 y t)
        (list (interval-expt-> x y-)
-	     (interval-expt-> x y+))))))
+             (interval-expt-> x y+))))))
 
 ;;; Handle the case when x <= 1
 (defun interval-expt-< (x y)
   (case (sb!c::interval-range-info x 0d0)
-    ('+
+    (+
      ;; The case of 0 <= x <= 1 is easy
      (case (sb!c::interval-range-info y)
-       ('+
-	;; Y is positive and log X <= 0. The range of exp(y * log(x)) is
-	;; obviously [0, 1]. We just have to be careful for infinite bounds
-	;; (given by nil).
-	(let ((lo (safe-expt (type-bound-number (sb!c::interval-low x))
-			     (type-bound-number (sb!c::interval-high y))))
-	      (hi (safe-expt (type-bound-number (sb!c::interval-high x))
-			     (type-bound-number (sb!c::interval-low y)))))
-	  (list (sb!c::make-interval :low (or lo 0) :high (or hi 1)))))
-       ('-
-	;; Y is negative and log x <= 0. The range of exp(y * log(x)) is
-	;; obviously [1, inf].
-	(let ((hi (safe-expt (type-bound-number (sb!c::interval-low x))
-			     (type-bound-number (sb!c::interval-low y))))
-	      (lo (safe-expt (type-bound-number (sb!c::interval-high x))
-			     (type-bound-number (sb!c::interval-high y)))))
-	  (list (sb!c::make-interval :low (or lo 1) :high hi))))
+       (+
+        ;; Y is positive and log X <= 0. The range of exp(y * log(x)) is
+        ;; obviously [0, 1]. We just have to be careful for infinite bounds
+        ;; (given by nil).
+        (let ((lo (safe-expt (type-bound-number (sb!c::interval-low x))
+                             (type-bound-number (sb!c::interval-high y))))
+              (hi (safe-expt (type-bound-number (sb!c::interval-high x))
+                             (type-bound-number (sb!c::interval-low y)))))
+          (list (sb!c::make-interval :low (or lo 0) :high (or hi 1)))))
+       (-
+        ;; Y is negative and log x <= 0. The range of exp(y * log(x)) is
+        ;; obviously [1, inf].
+        (let ((hi (safe-expt (type-bound-number (sb!c::interval-low x))
+                             (type-bound-number (sb!c::interval-low y))))
+              (lo (safe-expt (type-bound-number (sb!c::interval-high x))
+                             (type-bound-number (sb!c::interval-high y)))))
+          (list (sb!c::make-interval :low (or lo 1) :high hi))))
        (t
-	;; Split the interval in half
-	(destructuring-bind (y- y+)
-	    (sb!c::interval-split 0 y t)
-	  (list (interval-expt-< x y-)
-		(interval-expt-< x y+))))))
-    ('-
+        ;; Split the interval in half
+        (destructuring-bind (y- y+)
+            (sb!c::interval-split 0 y t)
+          (list (interval-expt-< x y-)
+                (interval-expt-< x y+))))))
+    (-
      ;; The case where x <= 0. Y MUST be an INTEGER for this to work!
      ;; The calling function must insure this! For now we'll just
      ;; return the appropriate unbounded float type.
      (list (sb!c::make-interval :low nil :high nil)))
     (t
      (destructuring-bind (neg pos)
-	 (interval-split 0 x t t)
+         (interval-split 0 x t t)
        (list (interval-expt-< neg y)
-	     (interval-expt-< pos y))))))
+             (interval-expt-< pos y))))))
 
 ;;; Compute bounds for (expt x y).
 (defun interval-expt (x y)
   (case (interval-range-info x 1)
-    ('+
+    (+
      ;; X >= 1
-	 (interval-expt-> x y))
-    ('-
+         (interval-expt-> x y))
+    (-
      ;; X <= 1
      (interval-expt-< x y))
     (t
      (destructuring-bind (left right)
-	 (interval-split 1 x t t)
+         (interval-split 1 x t t)
        (list (interval-expt left y)
-	     (interval-expt right y))))))
+             (interval-expt right y))))))
 
 (defun fixup-interval-expt (bnd x-int y-int x-type y-type)
   (declare (ignore x-int))
   ;; Figure out what the return type should be, given the argument
   ;; types and bounds and the result type and bounds.
   (cond ((csubtypep x-type (specifier-type 'integer))
-	 ;; an integer to some power
-	 (case (numeric-type-class y-type)
-	   (integer
-	    ;; Positive integer to an integer power is either an
-	    ;; integer or a rational.
-	    (let ((lo (or (interval-low bnd) '*))
-		  (hi (or (interval-high bnd) '*)))
-	      (if (and (interval-low y-int)
-		       (>= (type-bound-number (interval-low y-int)) 0))
-		  (specifier-type `(integer ,lo ,hi))
-		  (specifier-type `(rational ,lo ,hi)))))
-	   (rational
-	    ;; Positive integer to rational power is either a rational
-	    ;; or a single-float.
-	    (let* ((lo (interval-low bnd))
-		   (hi (interval-high bnd))
-		   (int-lo (if lo
-			       (floor (type-bound-number lo))
-			       '*))
-		   (int-hi (if hi
-			       (ceiling (type-bound-number hi))
-			       '*))
-		   (f-lo (if lo
-			     (bound-func #'float lo)
-			     '*))
-		   (f-hi (if hi
-			     (bound-func #'float hi)
-			     '*)))
-	      (specifier-type `(or (rational ,int-lo ,int-hi)
-				(single-float ,f-lo, f-hi)))))
-	   (float
-	    ;; A positive integer to a float power is a float.
-	    (modified-numeric-type y-type
-				   :low (interval-low bnd)
-				   :high (interval-high bnd)))
-	   (t
-	    ;; A positive integer to a number is a number (for now).
-	    (specifier-type 'number))))
-	((csubtypep x-type (specifier-type 'rational))
-	 ;; a rational to some power
-	 (case (numeric-type-class y-type)
-	   (integer
-	    ;; A positive rational to an integer power is always a rational.
-	    (specifier-type `(rational ,(or (interval-low bnd) '*)
-				       ,(or (interval-high bnd) '*))))
-	   (rational
-	    ;; A positive rational to rational power is either a rational
-	    ;; or a single-float.
-	    (let* ((lo (interval-low bnd))
-		   (hi (interval-high bnd))
-		   (int-lo (if lo
-			       (floor (type-bound-number lo))
-			       '*))
-		   (int-hi (if hi
-			       (ceiling (type-bound-number hi))
-			       '*))
-		   (f-lo (if lo
-			     (bound-func #'float lo)
-			     '*))
-		   (f-hi (if hi
-			     (bound-func #'float hi)
-			     '*)))
-	      (specifier-type `(or (rational ,int-lo ,int-hi)
-				(single-float ,f-lo, f-hi)))))
-	   (float
-	    ;; A positive rational to a float power is a float.
-	    (modified-numeric-type y-type
-				   :low (interval-low bnd)
-				   :high (interval-high bnd)))
-	   (t
-	    ;; A positive rational to a number is a number (for now).
-	    (specifier-type 'number))))
-	((csubtypep x-type (specifier-type 'float))
-	 ;; a float to some power
-	 (case (numeric-type-class y-type)
-	   ((or integer rational)
-	    ;; A positive float to an integer or rational power is
-	    ;; always a float.
-	    (make-numeric-type
-	     :class 'float
-	     :format (numeric-type-format x-type)
-	     :low (interval-low bnd)
-	     :high (interval-high bnd)))
-	   (float
-	    ;; A positive float to a float power is a float of the
-	    ;; higher type.
-	    (make-numeric-type
-	     :class 'float
-	     :format (float-format-max (numeric-type-format x-type)
-				       (numeric-type-format y-type))
-	     :low (interval-low bnd)
-	     :high (interval-high bnd)))
-	   (t
-	    ;; A positive float to a number is a number (for now)
-	    (specifier-type 'number))))
-	(t
-	 ;; A number to some power is a number.
-	 (specifier-type 'number))))
+         ;; an integer to some power
+         (case (numeric-type-class y-type)
+           (integer
+            ;; Positive integer to an integer power is either an
+            ;; integer or a rational.
+            (let ((lo (or (interval-low bnd) '*))
+                  (hi (or (interval-high bnd) '*)))
+              (if (and (interval-low y-int)
+                       (>= (type-bound-number (interval-low y-int)) 0))
+                  (specifier-type `(integer ,lo ,hi))
+                  (specifier-type `(rational ,lo ,hi)))))
+           (rational
+            ;; Positive integer to rational power is either a rational
+            ;; or a single-float.
+            (let* ((lo (interval-low bnd))
+                   (hi (interval-high bnd))
+                   (int-lo (if lo
+                               (floor (type-bound-number lo))
+                               '*))
+                   (int-hi (if hi
+                               (ceiling (type-bound-number hi))
+                               '*))
+                   (f-lo (or (bound-func #'float lo nil)
+                             '*))
+                   (f-hi (or (bound-func #'float hi nil)
+                             '*)))
+              (specifier-type `(or (rational ,int-lo ,int-hi)
+                                (single-float ,f-lo, f-hi)))))
+           (float
+            ;; A positive integer to a float power is a float.
+            (let ((format (numeric-type-format y-type)))
+              (aver format)
+              (modified-numeric-type
+               y-type
+               :low (coerce-numeric-bound (interval-low bnd) format)
+               :high (coerce-numeric-bound (interval-high bnd) format))))
+           (t
+            ;; A positive integer to a number is a number (for now).
+            (specifier-type 'number))))
+        ((csubtypep x-type (specifier-type 'rational))
+         ;; a rational to some power
+         (case (numeric-type-class y-type)
+           (integer
+            ;; A positive rational to an integer power is always a rational.
+            (specifier-type `(rational ,(or (interval-low bnd) '*)
+                                       ,(or (interval-high bnd) '*))))
+           (rational
+            ;; A positive rational to rational power is either a rational
+            ;; or a single-float.
+            (let* ((lo (interval-low bnd))
+                   (hi (interval-high bnd))
+                   (int-lo (if lo
+                               (floor (type-bound-number lo))
+                               '*))
+                   (int-hi (if hi
+                               (ceiling (type-bound-number hi))
+                               '*))
+                   (f-lo (or (bound-func #'float lo nil)
+                             '*))
+                   (f-hi (or (bound-func #'float hi nil)
+                             '*)))
+              (specifier-type `(or (rational ,int-lo ,int-hi)
+                                (single-float ,f-lo, f-hi)))))
+           (float
+            ;; A positive rational to a float power is a float.
+            (let ((format (numeric-type-format y-type)))
+              (aver format)
+              (modified-numeric-type
+               y-type
+               :low (coerce-numeric-bound (interval-low bnd) format)
+               :high (coerce-numeric-bound (interval-high bnd) format))))
+           (t
+            ;; A positive rational to a number is a number (for now).
+            (specifier-type 'number))))
+        ((csubtypep x-type (specifier-type 'float))
+         ;; a float to some power
+         (case (numeric-type-class y-type)
+           ((or integer rational)
+            ;; A positive float to an integer or rational power is
+            ;; always a float.
+            (let ((format (numeric-type-format x-type)))
+              (aver format)
+              (make-numeric-type
+               :class 'float
+               :format format
+               :low (coerce-numeric-bound (interval-low bnd) format)
+               :high (coerce-numeric-bound (interval-high bnd) format))))
+           (float
+            ;; A positive float to a float power is a float of the
+            ;; higher type.
+            (let ((format (float-format-max (numeric-type-format x-type)
+                                            (numeric-type-format y-type))))
+              (aver format)
+              (make-numeric-type
+               :class 'float
+               :format format
+               :low (coerce-numeric-bound (interval-low bnd) format)
+               :high (coerce-numeric-bound (interval-high bnd) format))))
+           (t
+            ;; A positive float to a number is a number (for now)
+            (specifier-type 'number))))
+        (t
+         ;; A number to some power is a number.
+         (specifier-type 'number))))
 
 (defun merged-interval-expt (x y)
   (let* ((x-int (numeric-type->interval x))
-	 (y-int (numeric-type->interval y)))
+         (y-int (numeric-type->interval y)))
     (mapcar (lambda (type)
-	      (fixup-interval-expt type x-int y-int x y))
-	    (flatten-list (interval-expt x-int y-int)))))
+              (fixup-interval-expt type x-int y-int x y))
+            (flatten-list (interval-expt x-int y-int)))))
 
 (defun expt-derive-type-aux (x y same-arg)
   (declare (ignore same-arg))
   (cond ((or (not (numeric-type-real-p x))
-	     (not (numeric-type-real-p y)))
-	 ;; Use numeric contagion if either is not real.
-	 (numeric-contagion x y))
-	((csubtypep y (specifier-type 'integer))
-	 ;; A real raised to an integer power is well-defined.
-	 (merged-interval-expt x y))
-	(t
-	 ;; A real raised to a non-integral power can be a float or a
-	 ;; complex number.
-	 (cond ((or (csubtypep x (specifier-type '(rational 0)))
-		    (csubtypep x (specifier-type '(float (0d0)))))
-		;; But a positive real to any power is well-defined.
-		(merged-interval-expt x y))
-	       (t
-		;; a real to some power. The result could be a real
-		;; or a complex.
-		(float-or-complex-float-type (numeric-contagion x y)))))))
+             (not (numeric-type-real-p y)))
+         ;; Use numeric contagion if either is not real.
+         (numeric-contagion x y))
+        ((csubtypep y (specifier-type 'integer))
+         ;; A real raised to an integer power is well-defined.
+         (merged-interval-expt x y))
+        ;; A real raised to a non-integral power can be a float or a
+        ;; complex number.
+        ((or (csubtypep x (specifier-type '(rational 0)))
+             (csubtypep x (specifier-type '(float (0d0)))))
+         ;; But a positive real to any power is well-defined.
+         (merged-interval-expt x y))
+        ((and (csubtypep x (specifier-type 'rational))
+              (csubtypep y (specifier-type 'rational)))
+         ;; A rational to the power of a rational could be a rational
+         ;; or a possibly-complex single float
+         (specifier-type '(or rational single-float (complex single-float))))
+        (t
+         ;; a real to some power. The result could be a real or a
+         ;; complex.
+         (float-or-complex-float-type (numeric-contagion x y)))))
 
 (defoptimizer (expt derive-type) ((x y))
   (two-arg-derive-type x y #'expt-derive-type-aux #'expt))
@@ -906,13 +1099,13 @@
 
 (defun log-derive-type-aux-2 (x y same-arg)
   (let ((log-x (log-derive-type-aux-1 x))
-	(log-y (log-derive-type-aux-1 y))
-	(accumulated-list nil))
+        (log-y (log-derive-type-aux-1 y))
+        (accumulated-list nil))
     ;; LOG-X or LOG-Y might be union types. We need to run through
     ;; the union types ourselves because /-DERIVE-TYPE-AUX doesn't.
     (dolist (x-type (prepare-arg-for-derive-type log-x))
       (dolist (y-type (prepare-arg-for-derive-type log-y))
-	(push (/-derive-type-aux x-type y-type same-arg) accumulated-list)))
+        (push (/-derive-type-aux x-type y-type same-arg) accumulated-list)))
     (apply #'type-union (flatten-list accumulated-list))))
 
 (defoptimizer (log derive-type) ((x &optional y))
@@ -928,21 +1121,21 @@
   ;; The hard case with two args. We just return the max bounds.
   (let ((result-type (numeric-contagion y x)))
     (cond ((and (numeric-type-real-p x)
-		(numeric-type-real-p y))
-	   (let* (;; FIXME: This expression for FORMAT seems to
-		  ;; appear multiple times, and should be factored out.
-		  (format (case (numeric-type-class result-type)
-			    ((integer rational) 'single-float)
-			    (t (numeric-type-format result-type))))
-		  (bound-format (or format 'float)))
-	     (make-numeric-type :class 'float
-				:format format
-				:complexp :real
-				:low (coerce (- pi) bound-format)
-				:high (coerce pi bound-format))))
-	  (t
-	   ;; The result is a float or a complex number
-	   (float-or-complex-float-type result-type)))))
+                (numeric-type-real-p y))
+           (let* (;; FIXME: This expression for FORMAT seems to
+                  ;; appear multiple times, and should be factored out.
+                  (format (case (numeric-type-class result-type)
+                            ((integer rational) 'single-float)
+                            (t (numeric-type-format result-type))))
+                  (bound-format (or format 'float)))
+             (make-numeric-type :class 'float
+                                :format format
+                                :complexp :real
+                                :low (coerce (- pi) bound-format)
+                                :high (coerce pi bound-format))))
+          (t
+           ;; The result is a float or a complex number
+           (float-or-complex-float-type result-type)))))
 
 (defoptimizer (atan derive-type) ((y &optional x))
   (if x
@@ -962,47 +1155,47 @@
 
 (defun phase-derive-type-aux (arg)
   (let* ((format (case (numeric-type-class arg)
-		   ((integer rational) 'single-float)
-		   (t (numeric-type-format arg))))
-	 (bound-type (or format 'float)))
+                   ((integer rational) 'single-float)
+                   (t (numeric-type-format arg))))
+         (bound-type (or format 'float)))
     (cond ((numeric-type-real-p arg)
-	   (case (interval-range-info (numeric-type->interval arg) 0.0)
-	     ('+
-	      ;; The number is positive, so the phase is 0.
-	      (make-numeric-type :class 'float
-				 :format format
-				 :complexp :real
-				 :low (coerce 0 bound-type)
-				 :high (coerce 0 bound-type)))
-	     ('-
-	      ;; The number is always negative, so the phase is pi.
-	      (make-numeric-type :class 'float
-				 :format format
-				 :complexp :real
-				 :low (coerce pi bound-type)
-				 :high (coerce pi bound-type)))
-	     (t
-	      ;; We can't tell. The result is 0 or pi. Use a union
-	      ;; type for this.
-	      (list
-	       (make-numeric-type :class 'float
-				  :format format
-				  :complexp :real
-				  :low (coerce 0 bound-type)
-				  :high (coerce 0 bound-type))
-	       (make-numeric-type :class 'float
-				  :format format
-				  :complexp :real
-				  :low (coerce pi bound-type)
-				  :high (coerce pi bound-type))))))
-	  (t
-	   ;; We have a complex number. The answer is the range -pi
-	   ;; to pi. (-pi is included because we have -0.)
-	   (make-numeric-type :class 'float
-			      :format format
-			      :complexp :real
-			      :low (coerce (- pi) bound-type)
-			      :high (coerce pi bound-type))))))
+           (case (interval-range-info (numeric-type->interval arg) 0.0)
+             (+
+              ;; The number is positive, so the phase is 0.
+              (make-numeric-type :class 'float
+                                 :format format
+                                 :complexp :real
+                                 :low (coerce 0 bound-type)
+                                 :high (coerce 0 bound-type)))
+             (-
+              ;; The number is always negative, so the phase is pi.
+              (make-numeric-type :class 'float
+                                 :format format
+                                 :complexp :real
+                                 :low (coerce pi bound-type)
+                                 :high (coerce pi bound-type)))
+             (t
+              ;; We can't tell. The result is 0 or pi. Use a union
+              ;; type for this.
+              (list
+               (make-numeric-type :class 'float
+                                  :format format
+                                  :complexp :real
+                                  :low (coerce 0 bound-type)
+                                  :high (coerce 0 bound-type))
+               (make-numeric-type :class 'float
+                                  :format format
+                                  :complexp :real
+                                  :low (coerce pi bound-type)
+                                  :high (coerce pi bound-type))))))
+          (t
+           ;; We have a complex number. The answer is the range -pi
+           ;; to pi. (-pi is included because we have -0.)
+           (make-numeric-type :class 'float
+                              :format format
+                              :complexp :real
+                              :low (coerce (- pi) bound-type)
+                              :high (coerce pi bound-type))))))
 
 (defoptimizer (phase derive-type) ((num))
   (one-arg-derive-type num #'phase-derive-type-aux #'phase))
@@ -1018,68 +1211,69 @@
 ;;; should help a lot in optimized code.
 (defun realpart-derive-type-aux (type)
   (let ((class (numeric-type-class type))
-	(format (numeric-type-format type)))
+        (format (numeric-type-format type)))
     (cond ((numeric-type-real-p type)
-	   ;; The realpart of a real has the same type and range as
-	   ;; the input.
-	   (make-numeric-type :class class
-			      :format format
-			      :complexp :real
-			      :low (numeric-type-low type)
-			      :high (numeric-type-high type)))
-	  (t
-	   ;; We have a complex number. The result has the same type
-	   ;; as the real part, except that it's real, not complex,
-	   ;; obviously.
-	   (make-numeric-type :class class
-			      :format format
-			      :complexp :real
-			      :low (numeric-type-low type)
-			      :high (numeric-type-high type))))))
-#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
+           ;; The realpart of a real has the same type and range as
+           ;; the input.
+           (make-numeric-type :class class
+                              :format format
+                              :complexp :real
+                              :low (numeric-type-low type)
+                              :high (numeric-type-high type)))
+          (t
+           ;; We have a complex number. The result has the same type
+           ;; as the real part, except that it's real, not complex,
+           ;; obviously.
+           (make-numeric-type :class class
+                              :format format
+                              :complexp :real
+                              :low (numeric-type-low type)
+                              :high (numeric-type-high type))))))
+
 (defoptimizer (realpart derive-type) ((num))
   (one-arg-derive-type num #'realpart-derive-type-aux #'realpart))
+
 (defun imagpart-derive-type-aux (type)
   (let ((class (numeric-type-class type))
-	(format (numeric-type-format type)))
+        (format (numeric-type-format type)))
     (cond ((numeric-type-real-p type)
-	   ;; The imagpart of a real has the same type as the input,
-	   ;; except that it's zero.
-	   (let ((bound-format (or format class 'real)))
-	     (make-numeric-type :class class
-				:format format
-				:complexp :real
-				:low (coerce 0 bound-format)
-				:high (coerce 0 bound-format))))
-	  (t
-	   ;; We have a complex number. The result has the same type as
-	   ;; the imaginary part, except that it's real, not complex,
-	   ;; obviously.
-	   (make-numeric-type :class class
-			      :format format
-			      :complexp :real
-			      :low (numeric-type-low type)
-			      :high (numeric-type-high type))))))
-#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
+           ;; The imagpart of a real has the same type as the input,
+           ;; except that it's zero.
+           (let ((bound-format (or format class 'real)))
+             (make-numeric-type :class class
+                                :format format
+                                :complexp :real
+                                :low (coerce 0 bound-format)
+                                :high (coerce 0 bound-format))))
+          (t
+           ;; We have a complex number. The result has the same type as
+           ;; the imaginary part, except that it's real, not complex,
+           ;; obviously.
+           (make-numeric-type :class class
+                              :format format
+                              :complexp :real
+                              :low (numeric-type-low type)
+                              :high (numeric-type-high type))))))
+
 (defoptimizer (imagpart derive-type) ((num))
   (one-arg-derive-type num #'imagpart-derive-type-aux #'imagpart))
 
 (defun complex-derive-type-aux-1 (re-type)
   (if (numeric-type-p re-type)
       (make-numeric-type :class (numeric-type-class re-type)
-			 :format (numeric-type-format re-type)
-			 :complexp (if (csubtypep re-type
-						  (specifier-type 'rational))
-				       :real
-				       :complex)
-			 :low (numeric-type-low re-type)
-			 :high (numeric-type-high re-type))
+                         :format (numeric-type-format re-type)
+                         :complexp (if (csubtypep re-type
+                                                  (specifier-type 'rational))
+                                       :real
+                                       :complex)
+                         :low (numeric-type-low re-type)
+                         :high (numeric-type-high re-type))
       (specifier-type 'complex)))
 
 (defun complex-derive-type-aux-2 (re-type im-type same-arg)
   (declare (ignore same-arg))
   (if (and (numeric-type-p re-type)
-	   (numeric-type-p im-type))
+           (numeric-type-p im-type))
       ;; Need to check to make sure numeric-contagion returns the
       ;; right type for what we want here.
 
@@ -1089,17 +1283,17 @@
       ;; arguments are rational, we make it a union type of (or
       ;; rational (complex rational)).
       (let* ((element-type (numeric-contagion re-type im-type))
-	     (rat-result-p (csubtypep element-type
-				      (specifier-type 'rational))))
-	(if rat-result-p
-	    (type-union element-type
-			(specifier-type
-			 `(complex ,(numeric-type-class element-type))))
-	    (make-numeric-type :class (numeric-type-class element-type)
-			       :format (numeric-type-format element-type)
-			       :complexp (if rat-result-p
-					     :real
-					     :complex))))
+             (rat-result-p (csubtypep element-type
+                                      (specifier-type 'rational))))
+        (if rat-result-p
+            (type-union element-type
+                        (specifier-type
+                         `(complex ,(numeric-type-class element-type))))
+            (make-numeric-type :class (numeric-type-class element-type)
+                               :format (numeric-type-format element-type)
+                               :complexp (if rat-result-p
+                                             :real
+                                             :complex))))
       (specifier-type 'complex)))
 
 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
@@ -1111,71 +1305,131 @@
 ;;; Define some transforms for complex operations. We do this in lieu
 ;;; of complex operation VOPs.
 (macrolet ((frob (type)
-	     `(progn
-	       ;; negation
-	       (deftransform %negate ((z) ((complex ,type)) *)
-		 '(complex (%negate (realpart z)) (%negate (imagpart z))))
-	       ;; complex addition and subtraction
-	       (deftransform + ((w z) ((complex ,type) (complex ,type)) *)
-		 '(complex (+ (realpart w) (realpart z))
-			   (+ (imagpart w) (imagpart z))))
-	       (deftransform - ((w z) ((complex ,type) (complex ,type)) *)
-		 '(complex (- (realpart w) (realpart z))
-			   (- (imagpart w) (imagpart z))))
-	       ;; Add and subtract a complex and a real.
-	       (deftransform + ((w z) ((complex ,type) real) *)
-		 '(complex (+ (realpart w) z) (imagpart w)))
-	       (deftransform + ((z w) (real (complex ,type)) *)
-		 '(complex (+ (realpart w) z) (imagpart w)))
-	       ;; Add and subtract a real and a complex number.
-	       (deftransform - ((w z) ((complex ,type) real) *)
-		 '(complex (- (realpart w) z) (imagpart w)))
-	       (deftransform - ((z w) (real (complex ,type)) *)
-		 '(complex (- z (realpart w)) (- (imagpart w))))
-	       ;; Multiply and divide two complex numbers.
-	       (deftransform * ((x y) ((complex ,type) (complex ,type)) *)
-		 '(let* ((rx (realpart x))
-			 (ix (imagpart x))
-			 (ry (realpart y))
-			 (iy (imagpart y)))
-		    (complex (- (* rx ry) (* ix iy))
-			     (+ (* rx iy) (* ix ry)))))
-	       (deftransform / ((x y) ((complex ,type) (complex ,type)) *)
-		 '(let* ((rx (realpart x))
-			 (ix (imagpart x))
-			 (ry (realpart y))
-			 (iy (imagpart y)))
-		    (if (> (abs ry) (abs iy))
-			(let* ((r (/ iy ry))
-			       (dn (* ry (+ 1 (* r r)))))
-			  (complex (/ (+ rx (* ix r)) dn)
-				   (/ (- ix (* rx r)) dn)))
-			(let* ((r (/ ry iy))
-			       (dn (* iy (+ 1 (* r r)))))
-			  (complex (/ (+ (* rx r) ix) dn)
-				   (/ (- (* ix r) rx) dn))))))
-	       ;; Multiply a complex by a real or vice versa.
-	       (deftransform * ((w z) ((complex ,type) real) *)
-		 '(complex (* (realpart w) z) (* (imagpart w) z)))
-	       (deftransform * ((z w) (real (complex ,type)) *)
-		 '(complex (* (realpart w) z) (* (imagpart w) z)))
-	       ;; Divide a complex by a real.
-	       (deftransform / ((w z) ((complex ,type) real) *)
-		 '(complex (/ (realpart w) z) (/ (imagpart w) z)))
-	       ;; conjugate of complex number
-	       (deftransform conjugate ((z) ((complex ,type)) *)
-		 '(complex (realpart z) (- (imagpart z))))
-	       ;; CIS
-	       (deftransform cis ((z) ((,type)) *)
-		 '(complex (cos z) (sin z)))
-	       ;; comparison
-	       (deftransform = ((w z) ((complex ,type) (complex ,type)) *)
-		 '(and (= (realpart w) (realpart z))
-		       (= (imagpart w) (imagpart z))))
-	       (deftransform = ((w z) ((complex ,type) real) *)
-		 '(and (= (realpart w) z) (zerop (imagpart w))))
-	       (deftransform = ((w z) (real (complex ,type)) *)
-		 '(and (= (realpart z) w) (zerop (imagpart z)))))))
+             `(progn
+                (deftransform complex ((r) (,type))
+                  '(complex r ,(coerce 0 type)))
+                (deftransform complex ((r i) (,type (and real (not ,type))))
+                  '(complex r (truly-the ,type (coerce i ',type))))
+                (deftransform complex ((r i) ((and real (not ,type)) ,type))
+                  '(complex (truly-the ,type (coerce r ',type)) i))
+               ;; negation
+                #!-complex-float-vops
+               (deftransform %negate ((z) ((complex ,type)) *)
+                 '(complex (%negate (realpart z)) (%negate (imagpart z))))
+               ;; complex addition and subtraction
+               #!-complex-float-vops
+               (deftransform + ((w z) ((complex ,type) (complex ,type)) *)
+                 '(complex (+ (realpart w) (realpart z))
+                           (+ (imagpart w) (imagpart z))))
+               #!-complex-float-vops
+               (deftransform - ((w z) ((complex ,type) (complex ,type)) *)
+                 '(complex (- (realpart w) (realpart z))
+                           (- (imagpart w) (imagpart z))))
+               ;; Add and subtract a complex and a real.
+               #!-complex-float-vops
+               (deftransform + ((w z) ((complex ,type) real) *)
+                 `(complex (+ (realpart w) z)
+                           (+ (imagpart w) ,(coerce 0 ',type))))
+               #!-complex-float-vops
+               (deftransform + ((z w) (real (complex ,type)) *)
+                 `(complex (+ (realpart w) z)
+                           (+ (imagpart w) ,(coerce 0 ',type))))
+               ;; Add and subtract a real and a complex number.
+               #!-complex-float-vops
+               (deftransform - ((w z) ((complex ,type) real) *)
+                 `(complex (- (realpart w) z)
+                           (- (imagpart w) ,(coerce 0 ',type))))
+               #!-complex-float-vops
+               (deftransform - ((z w) (real (complex ,type)) *)
+                 `(complex (- z (realpart w))
+                           (- ,(coerce 0 ',type) (imagpart w))))
+               ;; Multiply and divide two complex numbers.
+               #!-complex-float-vops
+               (deftransform * ((x y) ((complex ,type) (complex ,type)) *)
+                 '(let* ((rx (realpart x))
+                         (ix (imagpart x))
+                         (ry (realpart y))
+                         (iy (imagpart y)))
+                    (complex (- (* rx ry) (* ix iy))
+                             (+ (* rx iy) (* ix ry)))))
+               (deftransform / ((x y) ((complex ,type) (complex ,type)) *)
+                 #!-complex-float-vops
+                 '(let* ((rx (realpart x))
+                         (ix (imagpart x))
+                         (ry (realpart y))
+                         (iy (imagpart y)))
+                    (if (> (abs ry) (abs iy))
+                        (let* ((r (/ iy ry))
+                               (dn (+ ry (* r iy))))
+                          (complex (/ (+ rx (* ix r)) dn)
+                                   (/ (- ix (* rx r)) dn)))
+                        (let* ((r (/ ry iy))
+                               (dn (+ iy (* r ry))))
+                          (complex (/ (+ (* rx r) ix) dn)
+                                   (/ (- (* ix r) rx) dn)))))
+                 #!+complex-float-vops
+                 `(let* ((cs (conjugate (sb!vm::swap-complex x)))
+                         (ry (realpart y))
+                         (iy (imagpart y)))
+                    (if (> (abs ry) (abs iy))
+                        (let* ((r (/ iy ry))
+                               (dn (+ ry (* r iy))))
+                          (/ (+ x (* cs r)) dn))
+                        (let* ((r (/ ry iy))
+                               (dn (+ iy (* r ry))))
+                          (/ (+ (* x r) cs) dn)))))
+               ;; Multiply a complex by a real or vice versa.
+               #!-complex-float-vops
+               (deftransform * ((w z) ((complex ,type) real) *)
+                 '(complex (* (realpart w) z) (* (imagpart w) z)))
+               #!-complex-float-vops
+               (deftransform * ((z w) (real (complex ,type)) *)
+                 '(complex (* (realpart w) z) (* (imagpart w) z)))
+               ;; Divide a complex by a real or vice versa.
+               #!-complex-float-vops
+               (deftransform / ((w z) ((complex ,type) real) *)
+                 '(complex (/ (realpart w) z) (/ (imagpart w) z)))
+               (deftransform / ((x y) (,type (complex ,type)) *)
+                 #!-complex-float-vops
+                 '(let* ((ry (realpart y))
+                         (iy (imagpart y)))
+                    (if (> (abs ry) (abs iy))
+                        (let* ((r (/ iy ry))
+                               (dn (+ ry (* r iy))))
+                          (complex (/ x dn)
+                                   (/ (- (* x r)) dn)))
+                        (let* ((r (/ ry iy))
+                               (dn (+ iy (* r ry))))
+                          (complex (/ (* x r) dn)
+                                   (/ (- x) dn)))))
+                 #!+complex-float-vops
+                 '(let* ((ry (realpart y))
+                         (iy (imagpart y)))
+                   (if (> (abs ry) (abs iy))
+                       (let* ((r (/ iy ry))
+                              (dn (+ ry (* r iy))))
+                         (/ (complex x (- (* x r))) dn))
+                       (let* ((r (/ ry iy))
+                              (dn (+ iy (* r ry))))
+                         (/ (complex (* x r) (- x)) dn)))))
+               ;; conjugate of complex number
+               #!-complex-float-vops
+               (deftransform conjugate ((z) ((complex ,type)) *)
+                 '(complex (realpart z) (- (imagpart z))))
+               ;; CIS
+               (deftransform cis ((z) ((,type)) *)
+                 '(complex (cos z) (sin z)))
+               ;; comparison
+               #!-complex-float-vops
+               (deftransform = ((w z) ((complex ,type) (complex ,type)) *)
+                 '(and (= (realpart w) (realpart z))
+                       (= (imagpart w) (imagpart z))))
+               #!-complex-float-vops
+               (deftransform = ((w z) ((complex ,type) real) *)
+                 '(and (= (realpart w) z) (zerop (imagpart w))))
+               #!-complex-float-vops
+               (deftransform = ((w z) (real (complex ,type)) *)
+                 '(and (= (realpart z) w) (zerop (imagpart z)))))))
 
   (frob single-float)
   (frob double-float))
@@ -1187,43 +1441,43 @@
 ;;; inputs are union types.
 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
 (progn
-(defun trig-derive-type-aux (arg domain fcn
-				 &optional def-lo def-hi (increasingp t))
+(defun trig-derive-type-aux (arg domain fun
+                                 &optional def-lo def-hi (increasingp t))
   (etypecase arg
     (numeric-type
      (cond ((eq (numeric-type-complexp arg) :complex)
-	    (make-numeric-type :class (numeric-type-class arg)
-			       :format (numeric-type-format arg)
-			       :complexp :complex))
-	   ((numeric-type-real-p arg)
-	    (let* ((format (case (numeric-type-class arg)
-			     ((integer rational) 'single-float)
-			     (t (numeric-type-format arg))))
-		   (bound-type (or format 'float)))
-	      ;; If the argument is a subset of the "principal" domain
-	      ;; of the function, we can compute the bounds because
-	      ;; the function is monotonic. We can't do this in
-	      ;; general for these periodic functions because we can't
-	      ;; (and don't want to) do the argument reduction in
-	      ;; exactly the same way as the functions themselves do
-	      ;; it.
-	      (if (csubtypep arg domain)
-		  (let ((res-lo (bound-func fcn (numeric-type-low arg)))
-			(res-hi (bound-func fcn (numeric-type-high arg))))
-		    (unless increasingp
-		      (rotatef res-lo res-hi))
-		    (make-numeric-type
-		     :class 'float
-		     :format format
-		     :low (coerce-numeric-bound res-lo bound-type)
-		     :high (coerce-numeric-bound res-hi bound-type)))
-		  (make-numeric-type
-		   :class 'float
-		   :format format
-		   :low (and def-lo (coerce def-lo bound-type))
-		   :high (and def-hi (coerce def-hi bound-type))))))
-	   (t
-	    (float-or-complex-float-type arg def-lo def-hi))))))
+            (make-numeric-type :class (numeric-type-class arg)
+                               :format (numeric-type-format arg)
+                               :complexp :complex))
+           ((numeric-type-real-p arg)
+            (let* ((format (case (numeric-type-class arg)
+                             ((integer rational) 'single-float)
+                             (t (numeric-type-format arg))))
+                   (bound-type (or format 'float)))
+              ;; If the argument is a subset of the "principal" domain
+              ;; of the function, we can compute the bounds because
+              ;; the function is monotonic. We can't do this in
+              ;; general for these periodic functions because we can't
+              ;; (and don't want to) do the argument reduction in
+              ;; exactly the same way as the functions themselves do
+              ;; it.
+              (if (csubtypep arg domain)
+                  (let ((res-lo (bound-func fun (numeric-type-low arg) nil))
+                        (res-hi (bound-func fun (numeric-type-high arg) nil)))
+                    (unless increasingp
+                      (rotatef res-lo res-hi))
+                    (make-numeric-type
+                     :class 'float
+                     :format format
+                     :low (coerce-numeric-bound res-lo bound-type)
+                     :high (coerce-numeric-bound res-hi bound-type)))
+                  (make-numeric-type
+                   :class 'float
+                   :format format
+                   :low (and def-lo (coerce def-lo bound-type))
+                   :high (and def-hi (coerce def-hi bound-type))))))
+           (t
+            (float-or-complex-float-type arg def-lo def-hi))))))
 
 (defoptimizer (sin derive-type) ((num))
   (one-arg-derive-type
@@ -1243,10 +1497,10 @@
    (lambda (arg)
      ;; Derive the bounds if the arg is in [0, pi].
      (trig-derive-type-aux arg
-			   (specifier-type `(float 0d0 ,pi))
-			   #'cos
-			   -1 1
-			   nil))
+                           (specifier-type `(float 0d0 ,pi))
+                           #'cos
+                           -1 1
+                           nil))
    #'cos))
 
 (defoptimizer (tan derive-type) ((num))
@@ -1255,68 +1509,172 @@
    (lambda (arg)
      ;; Derive the bounds if the arg is in [-pi/2, pi/2].
      (trig-derive-type-aux arg
-			   (specifier-type `(float ,(- (/ pi 2)) ,(/ pi 2)))
-			   #'tan
-			   nil nil))
+                           (specifier-type `(float ,(- (/ pi 2)) ,(/ pi 2)))
+                           #'tan
+                           nil nil))
    #'tan))
 
-;;; CONJUGATE always returns the same type as the input type.
-;;;
-;;; FIXME: ANSI allows any subtype of REAL for the components of COMPLEX.
-;;; So what if the input type is (COMPLEX (SINGLE-FLOAT 0 1))?
 (defoptimizer (conjugate derive-type) ((num))
-  (continuation-type num))
+  (one-arg-derive-type num
+    (lambda (arg)
+      (flet ((most-negative-bound (l h)
+               (and l h
+                    (if (< (type-bound-number l) (- (type-bound-number h)))
+                        l
+                        (set-bound (- (type-bound-number h)) (consp h)))))
+             (most-positive-bound (l h)
+               (and l h
+                    (if (> (type-bound-number h) (- (type-bound-number l)))
+                        h
+                        (set-bound (- (type-bound-number l)) (consp l))))))
+        (if (numeric-type-real-p arg)
+            (lvar-type num)
+            (let ((low (numeric-type-low arg))
+                  (high (numeric-type-high arg)))
+              (let ((new-low (most-negative-bound low high))
+                    (new-high (most-positive-bound low high)))
+              (modified-numeric-type arg :low new-low :high new-high))))))
+    #'conjugate))
 
 (defoptimizer (cis derive-type) ((num))
   (one-arg-derive-type num
-     #'(lambda (arg)
-	 (sb!c::specifier-type
-	  `(complex ,(or (numeric-type-format arg) 'float))))
-     #'cis))
+    (lambda (arg)
+      (sb!c::specifier-type
+       `(complex ,(or (numeric-type-format arg) 'float))))
+    #'cis))
 
 ) ; PROGN
 
 ;;;; TRUNCATE, FLOOR, CEILING, and ROUND
 
 (macrolet ((define-frobs (fun ufun)
-	     `(progn
-		(defknown ,ufun (real) integer (movable foldable flushable))
-		(deftransform ,fun ((x &optional by)
-				    (* &optional
-				       (constant-argument (member 1))))
-		  '(let ((res (,ufun x)))
-		     (values res (- x res)))))))
+             `(progn
+                (defknown ,ufun (real) integer (movable foldable flushable))
+                (deftransform ,fun ((x &optional by)
+                                    (* &optional
+                                       (constant-arg (member 1))))
+                  '(let ((res (,ufun x)))
+                     (values res (- x res)))))))
   (define-frobs truncate %unary-truncate)
   (define-frobs round %unary-round))
 
-;;; Convert (TRUNCATE x y) to the obvious implementation.  We only want
-;;; this when under certain conditions and let the generic TRUNCATE
-;;; handle the rest.  (Note: if Y = 1, the divide and multiply by Y
-;;; should be removed by other DEFTRANSFORMs.)
-(deftransform truncate ((x &optional y)
-                        (float &optional (or float integer)))
-  (let ((defaulted-y (if y 'y 1)))
-    `(let ((res (%unary-truncate (/ x ,defaulted-y))))
-       (values res (- x (* ,defaulted-y res))))))
+(deftransform %unary-truncate ((x) (single-float))
+  `(%unary-truncate/single-float x))
+(deftransform %unary-truncate ((x) (double-float))
+  `(%unary-truncate/double-float x))
+
+;;; Convert (TRUNCATE x y) to the obvious implementation.
+;;;
+;;; ...plus hair: Insert explicit coercions to appropriate float types: Python
+;;; is reluctant it generate explicit integer->float coercions due to
+;;; precision issues (see SAFE-SINGLE-COERCION-P &co), but this is not an
+;;; issue here as there is no DERIVE-TYPE optimizer on specialized versions of
+;;; %UNARY-TRUNCATE, so the derived type of TRUNCATE remains the best we can
+;;; do here -- which is fine. Also take care not to add unnecassary division
+;;; or multiplication by 1, since we are not able to always eliminate them,
+;;; depending on FLOAT-ACCURACY. Finally, leave out the secondary value when
+;;; we know it is unused: COERCE is not flushable.
+(macrolet ((def (type other-float-arg-types)
+             (let ((unary (symbolicate "%UNARY-TRUNCATE/" type))
+                   (coerce (symbolicate "%" type)))
+               `(deftransform truncate ((x &optional y)
+                                        (,type
+                                         &optional (or ,type ,@other-float-arg-types integer))
+                                        * :result result)
+                  (let* ((result-type (and result
+                                           (lvar-derived-type result)))
+                         (compute-all (and (values-type-p result-type)
+                                           (not (type-single-value-p result-type)))))
+                    (if (or (not y)
+                            (and (constant-lvar-p y) (= 1 (lvar-value y))))
+                        (if compute-all
+                            `(let ((res (,',unary x)))
+                               (values res (- x (,',coerce res))))
+                            `(let ((res (,',unary x)))
+                               ;; Dummy secondary value!
+                               (values res x)))
+                        (if compute-all
+                            `(let* ((f (,',coerce y))
+                                    (res (,',unary (/ x f))))
+                               (values res (- x (* f (,',coerce res)))))
+                            `(let* ((f (,',coerce y))
+                                    (res (,',unary (/ x f))))
+                               ;; Dummy secondary value!
+                               (values res x)))))))))
+  (def single-float ())
+  (def double-float (single-float)))
 
 (deftransform floor ((number &optional divisor)
                      (float &optional (or integer float)))
   (let ((defaulted-divisor (if divisor 'divisor 1)))
     `(multiple-value-bind (tru rem) (truncate number ,defaulted-divisor)
        (if (and (not (zerop rem))
-		(if (minusp ,defaulted-divisor)
-		    (plusp number)
-		    (minusp number)))
-	   (values (1- tru) (+ rem ,defaulted-divisor))
-	   (values tru rem)))))
+                (if (minusp ,defaulted-divisor)
+                    (plusp number)
+                    (minusp number)))
+           (values (1- tru) (+ rem ,defaulted-divisor))
+           (values tru rem)))))
 
 (deftransform ceiling ((number &optional divisor)
                        (float &optional (or integer float)))
   (let ((defaulted-divisor (if divisor 'divisor 1)))
     `(multiple-value-bind (tru rem) (truncate number ,defaulted-divisor)
        (if (and (not (zerop rem))
-		(if (minusp ,defaulted-divisor)
-		    (minusp number)
-		    (plusp number)))
-	   (values (1+ tru) (- rem ,defaulted-divisor))
-	   (values tru rem)))))
+                (if (minusp ,defaulted-divisor)
+                    (minusp number)
+                    (plusp number)))
+           (values (1+ tru) (- rem ,defaulted-divisor))
+           (values tru rem)))))
+
+(defknown %unary-ftruncate (real) float (movable foldable flushable))
+(defknown %unary-ftruncate/single (single-float) single-float
+  (movable foldable flushable))
+(defknown %unary-ftruncate/double (double-float) double-float
+  (movable foldable flushable))
+
+(defun %unary-ftruncate/single (x)
+  (declare (type single-float x))
+  (declare (optimize speed (safety 0)))
+  (let* ((bits (single-float-bits x))
+         (exp (ldb sb!vm:single-float-exponent-byte bits))
+         (biased (the single-float-exponent
+                   (- exp sb!vm:single-float-bias))))
+    (declare (type (signed-byte 32) bits))
+    (cond
+      ((= exp sb!vm:single-float-normal-exponent-max) x)
+      ((<= biased 0) (* x 0f0))
+      ((>= biased (float-digits x)) x)
+      (t
+       (let ((frac-bits (- (float-digits x) biased)))
+         (setf bits (logandc2 bits (- (ash 1 frac-bits) 1)))
+         (make-single-float bits))))))
+
+(defun %unary-ftruncate/double (x)
+  (declare (type double-float x))
+  (declare (optimize speed (safety 0)))
+  (let* ((high (double-float-high-bits x))
+         (low (double-float-low-bits x))
+         (exp (ldb sb!vm:double-float-exponent-byte high))
+         (biased (the double-float-exponent
+                   (- exp sb!vm:double-float-bias))))
+    (declare (type (signed-byte 32) high)
+             (type (unsigned-byte 32) low))
+    (cond
+      ((= exp sb!vm:double-float-normal-exponent-max) x)
+      ((<= biased 0) (* x 0d0))
+      ((>= biased (float-digits x)) x)
+      (t
+       (let ((frac-bits (- (float-digits x) biased)))
+         (cond ((< frac-bits 32)
+                (setf low (logandc2 low (- (ash 1 frac-bits) 1))))
+               (t
+                (setf low 0)
+                (setf high (logandc2 high (- (ash 1 (- frac-bits 32)) 1)))))
+         (make-double-float high low))))))
+
+(macrolet
+    ((def (float-type fun)
+         `(deftransform %unary-ftruncate ((x) (,float-type))
+            '(,fun x))))
+  (def single-float %unary-ftruncate/single)
+  (def double-float %unary-ftruncate/double))