diff --git a/lib/scheme/division.scm b/lib/scheme/division.scm
index 24a0e065..0963f030 100644
--- a/lib/scheme/division.scm
+++ b/lib/scheme/division.scm
@@ -1,3 +1,19 @@
+;;;; division.scm -- portable R7RS (scheme division) implementation
+;;
+;; This code is written by Alex Shinn and placed in the
+;; Public Domain.  All warranties are disclaimed.
+;;
+;; This is basically the simplest possible implementation.  Note the
+;; code below assumes that either 1) exact ratios are supported and
+;; are handled correctly by floor, ceiling and round, or 2) that
+;; you're using a simple implementation with only fixnums and flonums.
+;; In the intermediate case where you have bignums but no ratios there
+;; will be a loss of precision for large values.
+;;
+;; In case 1) the calls to inexact->exact below are unecessary and can
+;; be removed.
+
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 
 ;; The builtin quotient and remainder implement truncation - the
 ;; fractional part is always discarded.
diff --git a/tests/division-tests.scm b/tests/division-tests.scm
new file mode 100644
index 00000000..5966c4c0
--- /dev/null
+++ b/tests/division-tests.scm
@@ -0,0 +1,387 @@
+
+(import (chibi test) (scheme division))
+
+(test-begin "division")
+
+;; These verify the basic rounding operators floor, ceiling, truncate
+;; and round, on which the other tests depend.
+
+(test-begin "rounding")
+
+(test 4.0 (floor 4.3))
+(test 5.0 (ceiling 4.3))
+(test 4.0 (truncate 4.3))
+(test 4.0 (round 4.3))
+(test -5.0 (floor -4.3))
+(test -4.0 (ceiling -4.3))
+(test -4.0 (truncate -4.3))
+(test -4.0 (round -4.3))
+(test 3.0 (floor 3.5)) 
+(test 4.0 (ceiling 3.5)) 
+(test 3.0 (truncate 3.5)) 
+(test 4.0 (round 3.5))
+(test -4.0 (floor -3.5)) 
+(test -3.0 (ceiling -3.5)) 
+(test -3.0 (truncate -3.5)) 
+(test -4.0 (round -3.5))
+(test 3 (floor (/ 1300000000000000000000 400000000000000000000)))
+(test 4 (ceiling (/ 1300000000000000000000 400000000000000000000)))
+(test 3 (truncate (/ 1300000000000000000000 400000000000000000000)))
+(test 3 (round (/ 1300000000000000000000 400000000000000000000)))
+(test -4 (floor (/ -1300000000000000000000 400000000000000000000)))
+(test -3 (ceiling (/ -1300000000000000000000 400000000000000000000)))
+(test -3 (truncate (/ -1300000000000000000000 400000000000000000000)))
+(test -3 (round (/ -1300000000000000000000 400000000000000000000)))
+(test 650000000000000000000 (floor (/ 1300000000000000000001 2)))
+(test 650000000000000000001 (ceiling (/ 1300000000000000000001 2)))
+(test 650000000000000000000 (truncate (/ 1300000000000000000001 2)))
+(test 650000000000000000000 (round (/ 1300000000000000000001 2)))
+(test 650000000000000000001 (floor (/ 1300000000000000000003 2)))
+(test 650000000000000000002 (ceiling (/ 1300000000000000000003 2)))
+(test 650000000000000000001 (truncate (/ 1300000000000000000003 2)))
+(test 650000000000000000002 (round (/ 1300000000000000000003 2)))
+(test -650000000000000000001 (floor (/ -1300000000000000000001 2)))
+(test -650000000000000000000 (ceiling (/ -1300000000000000000001 2)))
+(test -650000000000000000000 (truncate (/ -1300000000000000000001 2)))
+(test -650000000000000000000 (round (/ -1300000000000000000001 2)))
+(test -650000000000000000002 (floor (/ -1300000000000000000003 2)))
+(test -650000000000000000001 (ceiling (/ -1300000000000000000003 2)))
+(test -650000000000000000001 (truncate (/ -1300000000000000000003 2)))
+(test -650000000000000000002 (round (/ -1300000000000000000003 2)))
+(test 4 (round 7/2))
+(test 7 (round 7))
+
+(test-end)
+
+(test-begin "trivial zero divisor")
+
+;; All operators are the same when the quotient is zero.
+
+(test 0 (ceiling-quotient 0 4))
+(test 0 (ceiling-quotient 0 -4))
+
+(test 0 (ceiling-remainder 0 4))
+(test 0 (ceiling-remainder 0 -4))
+
+(test 0 (floor-quotient 0 4))
+(test 0 (floor-quotient 0 -4))
+
+(test 0 (floor-remainder 0 4))
+(test 0 (floor-remainder 0 -4))
+
+(test 0 (truncate-quotient 0 4))
+(test 0 (truncate-quotient 0 -4))
+
+(test 0 (truncate-remainder 0 4))
+(test 0 (truncate-remainder 0 -4))
+
+(test 0 (round-quotient 0 4))
+(test 0 (round-quotient 0 -4))
+
+(test 0 (round-remainder 0 4))
+(test 0 (round-remainder 0 -4))
+
+(test 0 (euclidean-quotient 0 4))
+(test 0 (euclidean-quotient 0 -4))
+
+(test 0 (euclidean-remainder 0 4))
+(test 0 (euclidean-remainder 0 -4))
+
+(test 0 (centered-quotient 0 4))
+(test 0 (centered-quotient 0 -4))
+
+(test 0 (centered-remainder 0 4))
+(test 0 (centered-remainder 0 -4))
+
+(test-end)
+
+(test-begin "trivial one dividend")
+
+;; The remainder is always zero when dividing by one.
+
+(test 13 (ceiling-quotient 13 1))
+(test -13 (ceiling-quotient -13 1))
+
+(test 0 (ceiling-remainder 13 1))
+(test 0 (ceiling-remainder -13 1))
+
+(test 13 (floor-quotient 13 1))
+(test -13 (floor-quotient -13 1))
+
+(test 0 (floor-remainder 13 1))
+(test 0 (floor-remainder -13 1))
+
+(test 13 (truncate-quotient 13 1))
+(test -13 (truncate-quotient -13 1))
+
+(test 0 (truncate-remainder 13 1))
+(test 0 (truncate-remainder -13 1))
+
+(test 13 (round-quotient 13 1))
+(test -13 (round-quotient -13 1))
+
+(test 0 (round-remainder 13 1))
+(test 0 (round-remainder -13 1))
+
+(test 13 (euclidean-quotient 13 1))
+(test -13 (euclidean-quotient -13 1))
+
+(test 0 (euclidean-remainder 13 1))
+(test 0 (euclidean-remainder -13 1))
+
+(test 13 (centered-quotient 13 1))
+(test -13 (centered-quotient -13 1))
+
+(test 0 (centered-remainder 13 1))
+(test 0 (centered-remainder -13 1))
+
+(test-end)
+
+(test-begin "fixnum division")
+
+;; Ceiling rounds towards positive infinity.
+
+(test 4 (ceiling-quotient 13 4))
+(test -3 (ceiling-quotient -13 4))
+(test -3 (ceiling-quotient 13 -4))
+(test 4 (ceiling-quotient -13 -4))
+
+(test -3 (ceiling-remainder 13 4))
+(test -1 (ceiling-remainder -13 4))
+(test 1 (ceiling-remainder 13 -4))
+(test 3 (ceiling-remainder -13 -4))
+
+;; Floor rounds towards negative infinity.
+
+(test 3 (floor-quotient 13 4))
+(test -4 (floor-quotient -13 4))
+(test -4 (floor-quotient 13 -4))
+(test 3 (floor-quotient -13 -4))
+
+(test 1 (floor-remainder 13 4))
+(test 3 (floor-remainder -13 4))
+(test -3 (floor-remainder 13 -4))
+(test -1 (floor-remainder -13 -4))
+
+;; Truncate rounds towards zero - the magnitudes never change
+;; regardless of the signs.
+
+(test 3 (truncate-quotient 13 4))
+(test -3 (truncate-quotient -13 4))
+(test -3 (truncate-quotient 13 -4))
+(test 3 (truncate-quotient -13 -4))
+
+(test 1 (truncate-remainder 13 4))
+(test -1 (truncate-remainder -13 4))
+(test 1 (truncate-remainder 13 -4))
+(test -1 (truncate-remainder -13 -4))
+
+;; Round rounds towards the nearest integer - it's equivalent to floor
+;; when signs are the same, and equivalent to ceiling when the signs
+;; differ.
+
+(test 3 (round-quotient 13 4))
+(test -3 (round-quotient -13 4))
+(test -3 (round-quotient 13 -4))
+(test 3 (round-quotient -13 -4))
+
+(test 1 (round-remainder 13 4))
+(test -1 (round-remainder -13 4))
+(test 1 (round-remainder 13 -4))
+(test -1 (round-remainder -13 -4))
+
+;; Euclidean rounds such that the remainder is always in the interval
+;; [0, divisor) - i.e. the remainder is always non-negative.  It's
+;; equivalent to floor if the divisor is negative, and ceiling
+;; otherwise.
+
+(test 3 (euclidean-quotient 13 4))
+(test -4 (euclidean-quotient -13 4))
+(test -3 (euclidean-quotient 13 -4))
+(test 4 (euclidean-quotient -13 -4))
+
+(test 1 (euclidean-remainder 13 4))
+(test 3 (euclidean-remainder -13 4))
+(test 1 (euclidean-remainder 13 -4))
+(test 3 (euclidean-remainder -13 -4))
+
+;; Centered differs from truncate only in the 0.5 remainder border
+;; case in the next test group.
+
+(test 3 (centered-quotient 13 4))
+(test -3 (centered-quotient -13 4))
+(test -3 (centered-quotient 13 -4))
+(test 3 (centered-quotient -13 -4))
+
+(test 1 (centered-remainder 13 4))
+(test -1 (centered-remainder -13 4))
+(test 1 (centered-remainder 13 -4))
+(test -1 (centered-remainder -13 -4))
+
+(test-end)
+
+(test-begin "one half remainder")
+
+;; Testing the 0.5 remainder border cases.  Ceiling, floor and
+;; truncate and euclidean don't change.
+
+(test 7 (ceiling-quotient 13 2))
+(test -6 (ceiling-quotient -13 2))
+(test -6 (ceiling-quotient 13 -2))
+(test 7 (ceiling-quotient -13 -2))
+
+(test -1 (ceiling-remainder 13 2))
+(test -1 (ceiling-remainder -13 2))
+(test 1 (ceiling-remainder 13 -2))
+(test 1 (ceiling-remainder -13 -2))
+
+(test 6 (floor-quotient 13 2))
+(test -7 (floor-quotient -13 2))
+(test -7 (floor-quotient 13 -2))
+(test 6 (floor-quotient -13 -2))
+
+(test 1 (floor-remainder 13 2))
+(test 1 (floor-remainder -13 2))
+(test -1 (floor-remainder 13 -2))
+(test -1 (floor-remainder -13 -2))
+
+(test 6 (truncate-quotient 13 2))
+(test -6 (truncate-quotient -13 2))
+(test -6 (truncate-quotient 13 -2))
+(test 6 (truncate-quotient -13 -2))
+
+(test 1 (truncate-remainder 13 2))
+(test -1 (truncate-remainder -13 2))
+(test 1 (truncate-remainder 13 -2))
+(test -1 (truncate-remainder -13 -2))
+
+(test 6 (euclidean-quotient 13 2))
+(test -7 (euclidean-quotient -13 2))
+(test -6 (euclidean-quotient 13 -2))
+(test 7 (euclidean-quotient -13 -2))
+
+(test 1 (euclidean-remainder 13 2))
+(test 1 (euclidean-remainder -13 2))
+(test 1 (euclidean-remainder 13 -2))
+(test 1 (euclidean-remainder -13 -2))
+
+;; For consistency with the default rounding mode specified by the
+;; IEEE floating point standard, round rounds to even when exactly
+;; half-way between two integers.
+
+(test 6 (round-quotient 13 2))
+(test -6 (round-quotient -13 2))
+(test -6 (round-quotient 13 -2))
+(test 6 (round-quotient -13 -2))
+
+(test 1 (round-remainder 13 2))
+(test -1 (round-remainder -13 2))
+(test 1 (round-remainder 13 -2))
+(test -1 (round-remainder -13 -2))
+
+;; Centered rounds up when exactly half-way between two integers.
+
+(test 7 (centered-quotient 13 2))
+(test -6 (centered-quotient -13 2))
+(test -7 (centered-quotient 13 -2))
+(test 6 (centered-quotient -13 -2))
+
+(test -1 (centered-remainder 13 2))
+(test -1 (centered-remainder -13 2))
+(test -1 (centered-remainder 13 -2))
+(test -1 (centered-remainder -13 -2))
+
+(test-end)
+
+(test-begin "bignum division")
+
+;; A repeat of the fixnum division tests above, using bignums to test
+;; bignum division.
+
+(test 4 (ceiling-quotient 1300000000000000000000 400000000000000000000))
+(test -3 (ceiling-quotient -1300000000000000000000 400000000000000000000))
+(test -3 (ceiling-quotient 1300000000000000000000 -400000000000000000000))
+(test 4 (ceiling-quotient -1300000000000000000000 -400000000000000000000))
+
+(test -300000000000000000000
+      (ceiling-remainder 1300000000000000000000 400000000000000000000))
+(test -100000000000000000000
+      (ceiling-remainder -1300000000000000000000 400000000000000000000))
+(test 100000000000000000000
+      (ceiling-remainder 1300000000000000000000 -400000000000000000000))
+(test 300000000000000000000
+      (ceiling-remainder -1300000000000000000000 -400000000000000000000))
+
+(test 3 (floor-quotient 1300000000000000000000 400000000000000000000))
+(test -4 (floor-quotient -1300000000000000000000 400000000000000000000))
+(test -4 (floor-quotient 1300000000000000000000 -400000000000000000000))
+(test 3 (floor-quotient -1300000000000000000000 -400000000000000000000))
+
+(test 100000000000000000000
+      (floor-remainder 1300000000000000000000 400000000000000000000))
+(test 300000000000000000000
+      (floor-remainder -1300000000000000000000 400000000000000000000))
+(test -300000000000000000000
+      (floor-remainder 1300000000000000000000 -400000000000000000000))
+(test -100000000000000000000
+      (floor-remainder -1300000000000000000000 -400000000000000000000))
+
+(test 3 (truncate-quotient 1300000000000000000000 400000000000000000000))
+(test -3 (truncate-quotient -1300000000000000000000 400000000000000000000))
+(test -3 (truncate-quotient 1300000000000000000000 -400000000000000000000))
+(test 3 (truncate-quotient -1300000000000000000000 -400000000000000000000))
+
+(test 100000000000000000000
+      (truncate-remainder 1300000000000000000000 400000000000000000000))
+(test -100000000000000000000
+      (truncate-remainder -1300000000000000000000 400000000000000000000))
+(test 100000000000000000000
+      (truncate-remainder 1300000000000000000000 -400000000000000000000))
+(test -100000000000000000000
+      (truncate-remainder -1300000000000000000000 -400000000000000000000))
+
+(test 3 (round-quotient 1300000000000000000000 400000000000000000000))
+(test -3 (round-quotient -1300000000000000000000 400000000000000000000))
+(test -3 (round-quotient 1300000000000000000000 -400000000000000000000))
+(test 3 (round-quotient -1300000000000000000000 -400000000000000000000))
+
+(test 100000000000000000000
+      (round-remainder 1300000000000000000000 400000000000000000000))
+(test -100000000000000000000
+      (round-remainder -1300000000000000000000 400000000000000000000))
+(test 100000000000000000000
+      (round-remainder 1300000000000000000000 -400000000000000000000))
+(test -100000000000000000000
+      (round-remainder -1300000000000000000000 -400000000000000000000))
+
+(test 3 (euclidean-quotient 1300000000000000000000 400000000000000000000))
+(test -4 (euclidean-quotient -1300000000000000000000 400000000000000000000))
+(test -3 (euclidean-quotient 1300000000000000000000 -400000000000000000000))
+(test 4 (euclidean-quotient -1300000000000000000000 -400000000000000000000))
+
+(test 100000000000000000000
+      (euclidean-remainder 1300000000000000000000 400000000000000000000))
+(test 300000000000000000000
+      (euclidean-remainder -1300000000000000000000 400000000000000000000))
+(test 100000000000000000000
+      (euclidean-remainder 1300000000000000000000 -400000000000000000000))
+(test 300000000000000000000
+      (euclidean-remainder -1300000000000000000000 -400000000000000000000))
+
+(test 3 (centered-quotient 1300000000000000000000 400000000000000000000))
+(test -3 (centered-quotient -1300000000000000000000 400000000000000000000))
+(test -3 (centered-quotient 1300000000000000000000 -400000000000000000000))
+(test 3 (centered-quotient -1300000000000000000000 -400000000000000000000))
+
+(test 100000000000000000000
+      (centered-remainder 1300000000000000000000 400000000000000000000))
+(test -100000000000000000000
+      (centered-remainder -1300000000000000000000 400000000000000000000))
+(test 100000000000000000000
+      (centered-remainder 1300000000000000000000 -400000000000000000000))
+(test -100000000000000000000
+      (centered-remainder -1300000000000000000000 -400000000000000000000))
+
+(test-end)
+
+(test-end)