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diff --git a/tests/arith.pure.lisp b/tests/arith.pure.lisp
index 00ff6af..6e13aea 100644
--- a/tests/arith.pure.lisp
+++ b/tests/arith.pure.lisp
@@ -69,17 +69,31 @@
 
 ;;; (CEILING x 2^k) was optimized incorrectly
 (loop for divisor in '(-4 4)
-   for ceiler = (compile nil `(lambda (x)
-                                (declare (fixnum x))
-                                (declare (optimize (speed 3)))
-                                (ceiling x ,divisor)))
-   do (loop for i from -5 to 5
-         for exact-q = (/ i divisor)
-         do (multiple-value-bind (q r)
-                (funcall ceiler i)
-              (assert (= (+ (* q divisor) r) i))
-              (assert (<= exact-q q))
-              (assert (< q (1+ exact-q))))))
+      for ceiler = (compile nil `(lambda (x)
+                                   (declare (fixnum x))
+                                   (declare (optimize (speed 3)))
+                                   (ceiling x ,divisor)))
+      do (loop for i from -5 to 5
+               for exact-q = (/ i divisor)
+               do (multiple-value-bind (q r)
+                      (funcall ceiler i)
+                    (assert (= (+ (* q divisor) r) i))
+                    (assert (<= exact-q q))
+                    (assert (< q (1+ exact-q))))))
+
+;;; (TRUNCATE x 2^k) was optimized incorrectly
+(loop for divisor in '(-4 4)
+      for truncater = (compile nil `(lambda (x)
+                                      (declare (fixnum x))
+                                      (declare (optimize (speed 3)))
+                                      (truncate x ,divisor)))
+      do (loop for i from -9 to 9
+               for exact-q = (/ i divisor)
+               do (multiple-value-bind (q r)
+                      (funcall truncater i)
+                    (assert (= (+ (* q divisor) r) i))
+                    (assert (<= (abs q) (abs exact-q)))
+                    (assert (< (abs exact-q) (1+ (abs q)))))))
 
 ;;; CEILING had a corner case, spotted by Paul Dietz
 (assert (= (ceiling most-negative-fixnum (1+ most-positive-fixnum)) -1))
@@ -110,9 +124,78 @@
   (assert (= (gcd 0 x) (abs x))))
 ;;; LCM returns a non-negative number
 (assert (= (lcm 4 -10) 20))
+(assert (= (lcm 0 0) 0))
 
 ;;; PPC bignum arithmetic bug:
 (multiple-value-bind (quo rem)
     (truncate 291351647815394962053040658028983955 10000000000000000000000000)
   (assert (= quo 29135164781))
   (assert (= rem 5394962053040658028983955)))
+
+;;; x86 LEA bug:
+(assert (= (funcall
+	    (compile nil '(lambda (x) (declare (bit x)) (+ x #xf0000000)))
+	    1)
+	   #xf0000001))
+
+;;; LOGBITP on bignums:
+(dolist (x '(((1+ most-positive-fixnum) 1 nil)
+	     ((1+ most-positive-fixnum) -1 t)
+	     ((1+ most-positive-fixnum) (1+ most-positive-fixnum) nil)
+	     ((1+ most-positive-fixnum) (1- most-negative-fixnum) t)
+	     (1 (ash most-negative-fixnum 1) nil)
+	     (29 most-negative-fixnum t)
+	     (30 (ash most-negative-fixnum 1) t)
+	     (31 (ash most-negative-fixnum 1) t)
+	     (64 (ash most-negative-fixnum 36) nil)
+	     (65 (ash most-negative-fixnum 36) t)))
+  (destructuring-bind (index int result) x
+    (assert (eq (eval `(logbitp ,index ,int)) result))))
+
+;;; off-by-1 type inference error for %DPB and %DEPOSIT-FIELD:
+(let ((f (compile nil '(lambda (b)
+                        (integer-length (dpb b (byte 4 28) -1005))))))
+  (assert (= (funcall f 1230070) 32)))
+(let ((f (compile nil '(lambda (b)
+                        (integer-length (deposit-field b (byte 4 28) -1005))))))
+  (assert (= (funcall f 1230070) 32)))
+
+;;; type inference leading to an internal compiler error:
+(let ((f (compile nil '(lambda (x)
+			(declare (type fixnum x))
+			(ldb (byte 0 0) x)))))
+  (assert (= (funcall f 1) 0))
+  (assert (= (funcall f most-positive-fixnum) 0))
+  (assert (= (funcall f -1) 0)))
+
+;;; Alpha bignum arithmetic bug:
+(assert (= (* 966082078641 419216044685) 404997107848943140073085))
+
+;;; Alpha smallnum arithmetic bug:
+(assert (= (ash -129876 -1026) -1))
+
+;;; Alpha middlenum (yes, really! Affecting numbers between 2^32 and
+;;; 2^64 :) arithmetic bug
+(let ((fn (compile nil '(LAMBDA (A B C D)
+          (DECLARE (TYPE (INTEGER -1621 -513) A)
+                   (TYPE (INTEGER -3 34163) B)
+                   (TYPE (INTEGER -9485132993 81272960) C)
+                   (TYPE (INTEGER -255340814 519943) D)
+                   (IGNORABLE A B C D)
+                   (OPTIMIZE (SPEED 3) (SAFETY 1) (DEBUG 1)))
+          (TRUNCATE C (MIN -100 4149605))))))
+  (assert (= (funcall fn -1332 5864 -6963328729 -43789079) 69633287)))
+
+;;; Here's another fantastic Alpha backend bug: the code to load
+;;; immediate 64-bit constants into a register was wrong.
+(let ((fn (compile nil '(LAMBDA (A B C D)
+          (DECLARE (TYPE (INTEGER -3563 2733564) A)
+                   (TYPE (INTEGER -548947 7159) B)
+                   (TYPE (INTEGER -19 0) C)
+                   (TYPE (INTEGER -2546009 0) D)
+                   (IGNORABLE A B C D)
+                   (OPTIMIZE (SPEED 3) (SAFETY 1) (DEBUG 1)))
+          (CASE A
+            ((89 125 16) (ASH A (MIN 18 -706)))
+            (T (DPB -3 (BYTE 30 30) -1)))))))
+  (assert (= (funcall fn 1227072 -529823 -18 -792831) -2147483649)))