diff --git a/module/language/cps/reify-primitives.scm b/module/language/cps/reify-primitives.scm
index 0823584d4..a473f954f 100644
--- a/module/language/cps/reify-primitives.scm
+++ b/module/language/cps/reify-primitives.scm
@@ -143,6 +143,14 @@
           ($ $continue k src ($ $primcall 'call-thunk/no-inline #f (proc))))
        (with-cps cps
          (setk label ($kargs names vars ($continue k src ($call proc ()))))))
+      (($ $kargs names vars
+          ($ $continue k src ($ $primcall 'mul/immediate b (a))))
+       (with-cps cps
+         (letv b*)
+         (letk kb ($kargs ('b) (b*)
+                    ($continue k src ($primcall 'mul #f (a b*)))))
+         (setk label ($kargs names vars
+                       ($continue kb src ($const b))))))
       (($ $kargs names vars ($ $continue k src ($ $primcall name param args)))
        (cond
         ((or (prim-instruction name) (branching-primitive? name))
diff --git a/module/language/cps/type-fold.scm b/module/language/cps/type-fold.scm
index 1e5800968..bf016ec83 100644
--- a/module/language/cps/type-fold.scm
+++ b/module/language/cps/type-fold.scm
@@ -161,6 +161,68 @@
 (define-branch-folder-alias s64-= =)
 
 
+
+
+;; Convert e.g. rsh to rsh/immediate.
+
+(define *primcall-macro-reducers* (make-hash-table))
+
+(define-syntax-rule (define-primcall-macro-reducer name f)
+  (hashq-set! *primcall-macro-reducers* 'name f))
+
+(define-syntax-rule (define-unary-primcall-macro-reducer (name cps k src
+                                                               arg type min max)
+                      body ...)
+  (define-primcall-macro-reducer name
+    (lambda (cps k src param arg type min max)
+      body ...)))
+
+(define-syntax-rule (define-binary-primcall-macro-reducer
+                      (name cps k src
+                            arg0 type0 min0 max0
+                            arg1 type1 min1 max1)
+                      body ...)
+  (define-primcall-macro-reducer name
+    (lambda (cps k src param arg0 type0 min0 max0 arg1 type1 min1 max1)
+      body ...)))
+
+(define-binary-primcall-macro-reducer (mul cps k src
+                                           arg0 type0 min0 max0
+                                           arg1 type1 min1 max1)
+  (cond
+   ((and (type<=? type0 &exact-integer) (= min0 max0))
+    (with-cps cps
+      (build-term
+        ($continue k src ($primcall 'mul/immediate min0 (arg1))))))
+   ((and (type<=? type1 &exact-integer) (= min1 max1))
+    (with-cps cps
+      (build-term
+        ($continue k src ($primcall 'mul/immediate min1 (arg0))))))
+   (else
+    (with-cps cps #f))))
+
+(define-binary-primcall-macro-reducer (lsh cps k src
+                                           arg0 type0 min0 max0
+                                           arg1 type1 min1 max1)
+  (cond
+   ((= min1 max1)
+    (with-cps cps
+      (build-term
+        ($continue k src ($primcall 'lsh/immediate min1 (arg0))))))
+   (else
+    (with-cps cps #f))))
+
+(define-binary-primcall-macro-reducer (rsh cps k src
+                                           arg0 type0 min0 max0
+                                           arg1 type1 min1 max1)
+  (cond
+   ((= min1 max1)
+    (with-cps cps
+      (build-term
+        ($continue k src ($primcall 'rsh/immediate min1 (arg0))))))
+   (else
+    (with-cps cps #f))))
+
 
 
 ;; Strength reduction.
@@ -170,14 +232,14 @@
 (define-syntax-rule (define-primcall-reducer name f)
   (hashq-set! *primcall-reducers* 'name f))
 
-(define-syntax-rule (define-unary-primcall-reducer (name cps k src
+(define-syntax-rule (define-unary-primcall-reducer (name cps k src param
                                                     arg type min max)
                       body ...)
   (define-primcall-reducer name
     (lambda (cps k src param arg type min max)
       body ...)))
 
-(define-syntax-rule (define-binary-primcall-reducer (name cps k src
+(define-syntax-rule (define-binary-primcall-reducer (name cps k src param
                                                      arg0 type0 min0 max0
                                                      arg1 type1 min1 max1)
                       body ...)
@@ -185,62 +247,42 @@
     (lambda (cps k src param arg0 type0 min0 max0 arg1 type1 min1 max1)
       body ...)))
 
-(define-binary-primcall-reducer (mul cps k src
-                                     arg0 type0 min0 max0
-                                     arg1 type1 min1 max1)
-  (define (fail) (with-cps cps #f))
-  (define (negate arg)
+(define-unary-primcall-reducer (mul/immediate cps k src constant
+                                              arg type min max)
+  (cond
+   ((not (type<=? type &number))
+    (with-cps cps #f))
+   ((eqv? constant -1)
+    ;; (* arg -1) -> (- 0 arg)
     (with-cps cps
       ($ (with-cps-constants ((zero 0))
            (build-term
              ($continue k src ($primcall 'sub #f (zero arg))))))))
-  (define (zero)
+   ((and (eqv? constant 0)
+         (type<=? type (logior &exact-integer &fraction)))
+    ;; (* arg 0) -> 0 if arg is exact
     (with-cps cps
       (build-term ($continue k src ($const 0)))))
-  (define (identity arg)
+   ((eqv? constant 1)
+    ;; (* arg 1) -> arg
     (with-cps cps
       (build-term ($continue k src ($values (arg))))))
-  (define (double arg)
+   ((eqv? constant 2)
+    ;; (* arg 2) -> (+ arg arg)
     (with-cps cps
       (build-term ($continue k src ($primcall 'add #f (arg arg))))))
-  (define (power-of-two constant arg)
+   ((and (type<=? type &exact-integer)
+         (positive? constant)
+         (zero? (logand constant (1- constant))))
+    ;; (* arg power-of-2) -> (lsh arg (log2 power-of-2))
     (let ((n (let lp ((bits 0) (constant constant))
                (if (= constant 1) bits (lp (1+ bits) (ash constant -1))))))
       (with-cps cps
         (build-term ($continue k src ($primcall 'lsh/immediate n (arg)))))))
-  (define (mul/constant constant constant-type arg arg-type)
-    (cond
-     ((not (or (type<=? constant-type &exact-integer)
-               (= constant-type arg-type)))
-      (fail))
-     ((eqv? constant -1)
-      ;; (* arg -1) -> (- 0 arg)
-      (negate arg))
-     ((eqv? constant 0)
-      ;; (* arg 0) -> 0 if arg is exact
-      (and (type<=? constant-type &exact-integer)
-           (type<=? arg-type (logior &exact-integer &fraction))
-           (zero)))
-     ((eqv? constant 1)
-      ;; (* arg 1) -> arg
-      (identity arg))
-     ((eqv? constant 2)
-      ;; (* arg 2) -> (+ arg arg)
-      (double arg))
-     ((and (type<=? (logior constant-type arg-type) &exact-integer)
-           (positive? constant)
-           (zero? (logand constant (1- constant))))
-      ;; (* arg power-of-2) -> (ash arg (log2 power-of-2))
-      (power-of-two constant arg))
-     (else
-      (fail))))
-  (cond
-   ((logtest (logior type0 type1) (lognot &number)) (fail))
-   ((= min0 max0) (mul/constant min0 type0 arg1 type1))
-   ((= min1 max1) (mul/constant min1 type1 arg0 type0))
-   (else (fail))))
+   (else
+    (with-cps cps #f))))
 
-(define-binary-primcall-reducer (logbit? cps k src
+(define-binary-primcall-reducer (logbit? cps k src param
                                          arg0 type0 min0 max0
                                          arg1 type1 min1 max1)
   ;; FIXME: Use an unboxed number for the mask instead of a fixnum.
@@ -252,8 +294,12 @@
               ($continue kmask src ($const (ash 1 min0)))))
           (with-cps cps
             ($ (with-cps-constants ((one 1))
+                 (letv n)
+                 (letk kn ($kargs ('n) (n)
+                            ($continue kmask src
+                              ($primcall 'lsh #f (one n)))))
                  (build-term
-                   ($continue kmask src ($primcall 'ash #f (one arg0)))))))))
+                   ($continue kn src ($primcall 'untag-fixnum #f (arg0)))))))))
     (with-cps cps
       (letv mask test)
       (letk kt ($kargs () ()
@@ -272,34 +318,33 @@
       ($ (compute-mask kmask src))))
   ;; Hairiness because we are converting from a primcall with unknown
   ;; arity to a branching primcall.
-  (let ((positive-fixnum-bits (- (* (target-word-size) 8) 3)))
-    (if (and (type<=? type0 &exact-integer)
-             (<= 0 min0 positive-fixnum-bits)
-             (<= 0 max0 positive-fixnum-bits))
-        (match (intmap-ref cps k)
-          (($ $kreceive arity kargs)
-           (match arity
-             (($ $arity (_) () (not #f) () #f)
-              (with-cps cps
-                (letv bool)
-                (let$ body (with-cps-constants ((nil '()))
-                             (build-term
-                               ($continue kargs src ($values (bool nil))))))
-                (letk kbool ($kargs (#f) (bool) ,body))
-                ($ (convert-to-logtest kbool))))
-             (_
-              (with-cps cps
-                (letv bool)
-                (letk kbool ($kargs (#f) (bool)
-                              ($continue k src ($primcall 'values #f (bool)))))
-                ($ (convert-to-logtest kbool))))))
-          (($ $ktail)
-           (with-cps cps
-             (letv bool)
-             (letk kbool ($kargs (#f) (bool)
-                           ($continue k src ($values (bool)))))
-             ($ (convert-to-logtest kbool)))))
-        (with-cps cps #f))))
+  (if (and (type<=? type0 &exact-integer)
+           (<= 0 min0 (target-most-positive-fixnum))
+           (<= 0 max0 (target-most-positive-fixnum)))
+      (match (intmap-ref cps k)
+        (($ $kreceive arity kargs)
+         (match arity
+           (($ $arity (_) () (not #f) () #f)
+            (with-cps cps
+              (letv bool)
+              (let$ body (with-cps-constants ((nil '()))
+                           (build-term
+                             ($continue kargs src ($values (bool nil))))))
+              (letk kbool ($kargs (#f) (bool) ,body))
+              ($ (convert-to-logtest kbool))))
+           (_
+            (with-cps cps
+              (letv bool)
+              (letk kbool ($kargs (#f) (bool)
+                            ($continue k src ($primcall 'values #f (bool)))))
+              ($ (convert-to-logtest kbool))))))
+        (($ $ktail)
+         (with-cps cps
+           (letv bool)
+           (letk kbool ($kargs (#f) (bool)
+                         ($continue k src ($values (bool)))))
+           ($ (convert-to-logtest kbool)))))
+      (with-cps cps #f)))
 
 
 
@@ -343,35 +388,43 @@
                    (setk label
                          ($kargs names vars
                            ($continue k* src ($primcall name param args))))))))))
+    (define (transform-primcall f cps label names vars k src name param args)
+      (and f
+           (match args
+             ((arg0)
+              (call-with-values (lambda () (lookup-pre-type types label arg0))
+                (lambda (type0 min0 max0)
+                  (call-with-values (lambda ()
+                                      (f cps k src param arg0 type0 min0 max0))
+                    (lambda (cps term)
+                      (and term
+                           (with-cps cps
+                             (setk label ($kargs names vars ,term)))))))))
+             ((arg0 arg1)
+              (call-with-values (lambda () (lookup-pre-type types label arg0))
+                (lambda (type0 min0 max0)
+                  (call-with-values (lambda () (lookup-pre-type types label arg1))
+                    (lambda (type1 min1 max1)
+                      (call-with-values (lambda ()
+                                          (f cps k src param arg0 type0 min0 max0
+                                             arg1 type1 min1 max1))
+                        (lambda (cps term)
+                          (and term
+                               (with-cps cps
+                                 (setk label ($kargs names vars ,term)))))))))))
+             (_ #f))))
     (define (reduce-primcall cps label names vars k src name param args)
-      (and=>
-       (hashq-ref *primcall-reducers* name)
-       (lambda (reducer)
-         (match args
-           ((arg0)
-            (call-with-values (lambda () (lookup-pre-type types label arg0))
-              (lambda (type0 min0 max0)
-                (call-with-values (lambda ()
-                                    (reducer cps k src param
-                                             arg0 type0 min0 max0))
-                  (lambda (cps term)
-                    (and term
-                         (with-cps cps
-                           (setk label ($kargs names vars ,term)))))))))
-           ((arg0 arg1)
-            (call-with-values (lambda () (lookup-pre-type types label arg0))
-              (lambda (type0 min0 max0)
-                (call-with-values (lambda () (lookup-pre-type types label arg1))
-                  (lambda (type1 min1 max1)
-                    (call-with-values (lambda ()
-                                        (reducer cps k src param
-                                                 arg0 type0 min0 max0
-                                                 arg1 type1 min1 max1))
-                      (lambda (cps term)
-                        (and term
-                             (with-cps cps
-                               (setk label ($kargs names vars ,term)))))))))))
-           (_ #f)))))
+      (cond
+       ((transform-primcall (hashq-ref *primcall-macro-reducers* name)
+                            cps label names vars k src name param args)
+        => (lambda (cps)
+             (match (intmap-ref cps label)
+               (($ $kargs names vars
+                   ($ $continue k src ($ $primcall name param args)))
+                (reduce-primcall cps label names vars k src name param args)))))
+       ((transform-primcall (hashq-ref *primcall-reducers* name)
+                            cps label names vars k src name param args))
+       (else cps)))
     (define (fold-unary-branch cps label names vars kf kt src name param arg)
       (and=>
        (hashq-ref *branch-folders* name)
@@ -412,11 +465,9 @@
          (match (intmap-ref cps k)
            (($ $kargs (_) (def))
             (or (fold-primcall cps label names vars k src name param args def)
-                (reduce-primcall cps label names vars k src name param args)
-                cps))
+                (reduce-primcall cps label names vars k src name param args)))
            (_
-            (or (reduce-primcall cps label names vars k src name param args)
-                cps))))
+            (reduce-primcall cps label names vars k src name param args))))
         (($ $branch kt ($ $primcall name param args))
          ;; We might be able to fold primcalls that branch.
          (match args