diff --git a/eval.c b/eval.c
index aedd5356..47ba5042 100644
--- a/eval.c
+++ b/eval.c
@@ -1142,6 +1142,13 @@ sexp sexp_register_optimization (sexp ctx sexp_api_params(self, n), sexp f, sexp
 #define maybe_convert_bignum(z)
 #endif
 
+#if SEXP_USE_RATIOS
+#define maybe_convert_ratio(z) \
+  else if (sexp_ratiop(z)) d = sexp_ratio_to_double(z);
+#else
+#define maybe_convert_ratio(z)
+#endif
+
 #define define_math_op(name, cname)                                     \
   static sexp name (sexp ctx sexp_api_params(self, n), sexp z) {        \
     double d;                                                           \
@@ -1149,6 +1156,7 @@ sexp sexp_register_optimization (sexp ctx sexp_api_params(self, n), sexp f, sexp
       d = sexp_flonum_value(z);                                         \
     else if (sexp_fixnump(z))                                           \
       d = (double)sexp_unbox_fixnum(z);                                 \
+    maybe_convert_ratio(z)                                              \
     maybe_convert_bignum(z)                                             \
     else                                                                \
       return sexp_type_exception(ctx, self, SEXP_NUMBER, z);            \
@@ -1243,6 +1251,17 @@ static sexp sexp_expt_op (sexp ctx sexp_api_params(self, n), sexp x, sexp e) {
   return res;
 }
 
+#if SEXP_USE_RATIOS
+static sexp sexp_ratio_numerator_op (sexp ctx sexp_api_params(self, n), sexp rat) {
+  sexp_assert_type(ctx, sexp_ratiop, SEXP_RATIO, rat);
+  return sexp_ratio_numerator(rat);
+}
+static sexp sexp_ratio_denominator_op (sexp ctx sexp_api_params(self, n), sexp rat) {
+  sexp_assert_type(ctx, sexp_ratiop, SEXP_RATIO, rat);
+  return sexp_ratio_denominator(rat);
+}
+#endif
+
 static sexp sexp_string_cmp_op (sexp ctx sexp_api_params(self, n), sexp str1, sexp str2, sexp ci) {
   sexp_sint_t len1, len2, len, diff;
   sexp_assert_type(ctx, sexp_stringp, SEXP_STRING, str1);
@@ -1785,6 +1804,9 @@ sexp sexp_load_standard_env (sexp ctx, sexp e, sexp version) {
 #endif
 #if SEXP_USE_AUTO_FORCE
   sexp_push(ctx, tmp, sym=sexp_intern(ctx, "auto-force", -1));
+#endif
+#if SEXP_USE_RATIOS
+  sexp_push(ctx, tmp, sym=sexp_intern(ctx, "ratios", -1));
 #endif
   sexp_push(ctx, tmp, sym=sexp_intern(ctx, "chibi", -1));
   sexp_env_define(ctx, e, sym=sexp_intern(ctx, "*features*", -1), tmp);
diff --git a/include/chibi/bignum.h b/include/chibi/bignum.h
index 9c6ede07..03b416d4 100644
--- a/include/chibi/bignum.h
+++ b/include/chibi/bignum.h
@@ -1,6 +1,6 @@
-/*  bignum.h -- header for bignum utilities              */
-/*  Copyright (c) 2009 Alex Shinn.  All rights reserved. */
-/*  BSD-style license: http://synthcode.com/license.txt  */
+/*  bignum.h -- header for bignum utilities                   */
+/*  Copyright (c) 2009-2011 Alex Shinn.  All rights reserved. */
+/*  BSD-style license: http://synthcode.com/license.txt       */
 
 #ifndef SEXP_BIGNUM_H
 #define SEXP_BIGNUM_H
@@ -38,6 +38,11 @@ sexp sexp_mul (sexp ctx, sexp a, sexp b);
 sexp sexp_div (sexp ctx, sexp a, sexp b);
 sexp sexp_quotient (sexp ctx, sexp a, sexp b);
 sexp sexp_remainder (sexp ctx, sexp a, sexp b);
+#if SEXP_USE_RATIOS
+double sexp_ratio_to_double (sexp rat);
+sexp sexp_make_ratio (sexp ctx, sexp num, sexp den);
+sexp sexp_ratio_normalize (sexp ctx, sexp rat, sexp in);
+#endif
 
 #endif  /* ! SEXP_BIGNUM_H */
 
diff --git a/include/chibi/features.h b/include/chibi/features.h
index 716e7431..08bc157c 100644
--- a/include/chibi/features.h
+++ b/include/chibi/features.h
@@ -117,6 +117,13 @@
 /*   in opt/bignum.c. */
 /* #define SEXP_USE_BIGNUMS 0 */
 
+/* uncomment this if you don't want exact ratio support */
+/*   Ratios are part of the bignum library and imply bignums. */
+/* #define SEXP_USE_RATIOS 0 */
+
+/* uncomment this if you don't want imaginary number support */
+/* #define SEXP_USE_COMPLEX 0 */
+
 /* uncomment this if you don't want 1## style approximate digits */
 /* #define SEXP_USE_PLACEHOLDER_DIGITS 0 */
 
@@ -354,6 +361,19 @@
 #define SEXP_USE_EXTENDED_FCALL ! SEXP_USE_NO_FEATURES
 #endif
 
+#ifndef SEXP_USE_RATIOS
+#define SEXP_USE_RATIOS ! SEXP_USE_NO_FEATURES
+#endif
+
+/* #ifndef SEXP_USE_COMPLEX */
+/* #define SEXP_USE_COMPLEX ! SEXP_USE_NO_FEATURES */
+/* #endif */
+#define SEXP_USE_COMPLEX 0
+
+#ifndef SEXP_USE_BIGNUMS
+#define SEXP_USE_BIGNUMS (SEXP_USE_RATIOS || SEXP_USE_COMPLEX)
+#endif
+
 #ifndef SEXP_USE_FLONUMS
 #define SEXP_USE_FLONUMS ! SEXP_USE_NO_FEATURES
 #endif
@@ -378,10 +398,6 @@
 #define SEXP_PLACEHOLDER_DIGIT '#'
 #endif
 
-#ifndef SEXP_USE_BIGNUMS
-#define SEXP_USE_BIGNUMS ! SEXP_USE_NO_FEATURES
-#endif
-
 #ifndef SEXP_USE_MATH
 #define SEXP_USE_MATH SEXP_USE_FLONUMS && ! SEXP_USE_NO_FEATURES
 #endif
diff --git a/include/chibi/sexp.h b/include/chibi/sexp.h
index 65add36e..480280b1 100755
--- a/include/chibi/sexp.h
+++ b/include/chibi/sexp.h
@@ -103,6 +103,8 @@ enum sexp_types {
   SEXP_VECTOR,
   SEXP_FLONUM,
   SEXP_BIGNUM,
+  SEXP_RATIO,
+  SEXP_COMPLEX,
   SEXP_IPORT,
   SEXP_OPORT,
   SEXP_EXCEPTION,
@@ -300,6 +302,12 @@ struct sexp_struct {
       sexp_uint_t length;
       sexp_uint_t data[];
     } bignum;
+    struct {
+      sexp numerator, denominator;
+    } ratio;
+    struct {
+      sexp real, imag;
+    } complex;
     struct {
       sexp_uint_t length;
       void *value;
@@ -553,6 +561,8 @@ sexp sexp_make_flonum(sexp ctx, double f);
 #define sexp_iportp(x)      (sexp_check_tag(x, SEXP_IPORT))
 #define sexp_oportp(x)      (sexp_check_tag(x, SEXP_OPORT))
 #define sexp_bignump(x)     (sexp_check_tag(x, SEXP_BIGNUM))
+#define sexp_ratiop(x)      (sexp_check_tag(x, SEXP_RATIO))
+#define sexp_complexp(x)    (sexp_check_tag(x, SEXP_COMPLEX))
 #define sexp_cpointerp(x)   (sexp_check_tag(x, SEXP_CPOINTER))
 #define sexp_exceptionp(x)  (sexp_check_tag(x, SEXP_EXCEPTION))
 #define sexp_procedurep(x)  (sexp_check_tag(x, SEXP_PROCEDURE))
@@ -646,6 +656,18 @@ SEXP_API sexp sexp_make_unsigned_integer(sexp ctx, sexp_luint_t x);
 #define sexp_numberp(x) sexp_exact_integerp(x)
 #endif
 
+#define sexp_exact_negativep(x) (sexp_fixnump(x) ? (sexp_unbox_fixnum(x) < 0) \
+                                 : (SEXP_USE_BIGNUMS && sexp_bignump(x)) \
+                                 && (sexp_bignum_sign(x) < 0))
+#define sexp_negativep(x) (sexp_exact_negativep(x) ||                   \
+                           (sexp_flonump(x) && sexp_flonum_value(x) < 0))
+
+#define sexp_negate(x)                                  \
+  if (sexp_bignump(x))                                  \
+    sexp_bignum_sign(x) = -sexp_bignum_sign(x);         \
+  else if (sexp_fixnump(x))                             \
+    x = sexp_fx_neg(x);
+
 #if SEXP_USE_FLONUMS || SEXP_USE_BIGNUMS
 #define sexp_uint_value(x) ((sexp_uint_t)(sexp_fixnump(x) ? sexp_unbox_fixnum(x) : sexp_bignum_data(x)[0]))
 #define sexp_sint_value(x) ((sexp_sint_t)(sexp_fixnump(x) ? sexp_unbox_fixnum(x) : sexp_bignum_sign(x)*sexp_bignum_data(x)[0]))
@@ -723,6 +745,12 @@ SEXP_API sexp sexp_make_unsigned_integer(sexp ctx, sexp_luint_t x);
 #define sexp_port_offset(p)     (sexp_pred_field(p, port, sexp_portp, offset))
 #define sexp_port_flags(p)      (sexp_pred_field(p, port, sexp_portp, flags))
 
+#define sexp_ratio_numerator(q)   (sexp_pred_field(q, ratio, sexp_ratiop, numerator))
+#define sexp_ratio_denominator(q) (sexp_pred_field(q, ratio, sexp_ratiop, denominator))
+
+#define sexp_complex_real(q)   (sexp_pred_field(q, complex, sexp_complexp, real))
+#define sexp_complex_imag(q)   (sexp_pred_field(q, complex, sexp_complexp, imag))
+
 #define sexp_exception_kind(x)      (sexp_field(x, exception, SEXP_EXCEPTION, kind))
 #define sexp_exception_message(x)   (sexp_field(x, exception, SEXP_EXCEPTION, message))
 #define sexp_exception_irritants(x) (sexp_field(x, exception, SEXP_EXCEPTION, irritants))
diff --git a/lib/init.scm b/lib/init.scm
index f8984e4b..8ff79c19 100644
--- a/lib/init.scm
+++ b/lib/init.scm
@@ -350,6 +350,26 @@
 
 ;; string utils
 
+(define (digit-char n)
+  (if (<= n 9)
+      (integer->char (+ n (char->integer #\0)))
+      (integer->char (+ (- n 10) (char->integer #\A)))))
+(define (digit-value ch)
+  (if (char-numeric? ch)
+      (- (char->integer ch) (char->integer #\0))
+      (and (<= 65 (char->integer (char-upcase ch)) 70)
+           (- (char->integer (char-upcase ch)) 55))))
+
+(define (number->string num . o)
+  (if (if (null? o) #t (eq? 10 (car o)))
+      (call-with-output-string (lambda (out) (write num out)))
+      (let lp ((n (abs num)) (d (car o)) (res '()))
+        (if (> n 0)
+            (lp (quotient n d) d (cons (digit-char (remainder n d)) res))
+            (if (null? res)
+                "0"
+                (list->string (if (negative? num) (cons #\- res) res)))))))
+
 (define (symbol->string sym)
   (call-with-output-string (lambda (out) (write sym out))))
 
@@ -413,93 +433,6 @@
 (define (find pred ls)
   (cond ((find-tail pred ls) => car) (else #f)))
 
-;; math utils
-
-(define (number? x) (if (fixnum? x) #t (if (bignum? x) #t (flonum? x))))
-(define complex? number?)
-(define rational? number?)
-(define real? number?)
-(define (exact? x) (if (fixnum? x) #t (bignum? x)))
-(define inexact? flonum?)
-(define (exact-integer? x) (if (fixnum? x) #t (bignum? x)))
-(define (integer? x)
-  (if (exact-integer? x) #t (and (flonum? x) (= x (truncate x)))))
-
-(define (exact-integer-sqrt x)
-  (let ((res (sqrt x)))
-    (if (exact? res)
-        (values res 0)
-        (let ((res (inexact->exact (truncate res))))
-          (values res (- x (* res res)))))))
-
-(define (zero? x) (= x 0))
-(define (positive? x) (> x 0))
-(define (negative? x) (< x 0))
-(define (even? n) (= (remainder n 2) 0))
-(define (odd? n) (= (remainder n 2) 1))
-
-(define (abs x) (if (< x 0) (- x) x))
-
-(define (numerator x)
-  (if (integer? x) x (numerator (* x 10))))
-(define (denominator x)
-  (if (exact? x)
-      1
-      (let lp ((x x) (r 1.0)) (if (integer? x) r (lp (* x 10) (* r 10))))))
-
-(define (modulo a b)
-  (let ((res (remainder a b)))
-    (if (< b 0)
-        (if (<= res 0) res (+ res b))
-        (if (>= res 0) res (+ res b)))))
-
-(define (gcd a b)
-  (if (= b 0)
-      (abs a)
-      (gcd b (remainder a b))))
-
-(define (lcm a b)
-  (abs (quotient (* a b) (gcd a b))))
-
-(define (max x . rest)
-  (let lp ((hi x) (ls rest))
-    (if (null? ls)
-        hi
-        (lp (if (> (car ls) hi) (car ls) hi) (cdr ls)))))
-
-(define (min x . rest)
-  (let lp ((lo x) (ls rest))
-    (if (null? ls)
-        lo
-        (lp (if (< (car ls) lo) (car ls) lo) (cdr ls)))))
-
-(define (real-part z) z)
-(define (imag-part z) 0.0)
-(define magnitude abs)
-(define (angle z) (if (< z 0) 3.141592653589793 0))
-
-(define (atan x . o) (if (null? o) (atan1 x) (atan1 (/ x (car o)))))
-
-(define (digit-char n)
-  (if (<= n 9)
-      (integer->char (+ n (char->integer #\0)))
-      (integer->char (+ (- n 10) (char->integer #\A)))))
-(define (digit-value ch)
-  (if (char-numeric? ch)
-      (- (char->integer ch) (char->integer #\0))
-      (and (<= 65 (char->integer (char-upcase ch)) 70)
-           (- (char->integer (char-upcase ch)) 55))))
-
-(define (number->string num . o)
-  (if (if (null? o) #t (eq? 10 (car o)))
-      (call-with-output-string (lambda (out) (write num out)))
-      (let lp ((n (abs num)) (d (car o)) (res '()))
-        (if (> n 0)
-            (lp (quotient n d) d (cons (digit-char (remainder n d)) res))
-            (if (null? res)
-                "0"
-                (list->string (if (negative? num) (cons #\- res) res)))))))
-
 ;; vector utils
 
 (define (list->vector ls)
@@ -955,6 +888,86 @@
        result)))
   (define (force x) (if (procedure? x) (x) x))))
 
+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+;; math utils
+
+(cond-expand
+ (ratios
+  (define (exact? x) (if (fixnum? x) #t (if (bignum? x) #t (ratio? x))))
+  (define (numerator x)
+    (if (ratio? x)
+        (ratio-numerator x)
+        (if (integer? x) x (numerator (* x 10)))))
+  (define (denominator x)
+    (if (exact? x)
+        (if (ratio? x) (ratio-denominator x) 1)
+        (let lp ((x x) (r 1.0)) (if (integer? x) r (lp (* x 10) (* r 10)))))))
+ (else
+  (define (exact? x) (if (fixnum? x) #t (bignum? x)))
+  (define (numerator x)
+    (if (integer? x) x (numerator (* x 10))))
+  (define (denominator x)
+    (if (exact? x)
+        1
+        (let lp ((x x) (r 1.0)) (if (integer? x) r (lp (* x 10) (* r 10))))))))
+
+(define inexact? flonum?)
+(define (exact-integer? x) (if (fixnum? x) #t (bignum? x)))
+(define (integer? x)
+  (if (exact-integer? x) #t (and (flonum? x) (= x (truncate x)))))
+(define (number? x) (if (inexact? x) #t (exact? x)))
+(define complex? number?)
+(define rational? number?)
+(define real? number?)
+
+(define (exact-integer-sqrt x)
+  (let ((res (sqrt x)))
+    (if (exact? res)
+        (values res 0)
+        (let ((res (inexact->exact (truncate res))))
+          (values res (- x (* res res)))))))
+
+(define (zero? x) (= x 0))
+(define (positive? x) (> x 0))
+(define (negative? x) (< x 0))
+(define (even? n) (= (remainder n 2) 0))
+(define (odd? n) (= (remainder n 2) 1))
+
+(define (abs x) (if (< x 0) (- x) x))
+
+(define (modulo a b)
+  (let ((res (remainder a b)))
+    (if (< b 0)
+        (if (<= res 0) res (+ res b))
+        (if (>= res 0) res (+ res b)))))
+
+(define (gcd a b)
+  (if (= b 0)
+      (abs a)
+      (gcd b (remainder a b))))
+
+(define (lcm a b)
+  (abs (quotient (* a b) (gcd a b))))
+
+(define (max x . rest)
+  (let lp ((hi x) (ls rest))
+    (if (null? ls)
+        hi
+        (lp (if (> (car ls) hi) (car ls) hi) (cdr ls)))))
+
+(define (min x . rest)
+  (let lp ((lo x) (ls rest))
+    (if (null? ls)
+        lo
+        (lp (if (< (car ls) lo) (car ls) lo) (cdr ls)))))
+
+(define (real-part z) z)
+(define (imag-part z) 0.0)
+(define magnitude abs)
+(define (angle z) (if (< z 0) 3.141592653589793 0))
+
+(define (atan x . o) (if (null? o) (atan1 x) (atan1 (/ x (car o)))))
+
 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 ;; string cursors
 
diff --git a/opcodes.c b/opcodes.c
index dc2937dc..6f812e4e 100644
--- a/opcodes.c
+++ b/opcodes.c
@@ -82,6 +82,11 @@ _FN1(_I(SEXP_BOOLEAN), _I(SEXP_OBJECT), "flonum?", 0, sexp_flonump_op),
 _OP(SEXP_OPC_TYPE_PREDICATE, SEXP_OP_TYPEP,  1, 0, _I(SEXP_BOOLEAN), _I(SEXP_OBJECT), SEXP_FALSE, SEXP_FALSE, 0, "flonum?", _I(SEXP_FLONUM), 0),
 #endif
 _OP(SEXP_OPC_TYPE_PREDICATE, SEXP_OP_TYPEP,  1, 0, _I(SEXP_BOOLEAN), _I(SEXP_OBJECT), SEXP_FALSE, SEXP_FALSE, 0, "bignum?", _I(SEXP_BIGNUM), 0),
+#if SEXP_USE_RATIOS
+_OP(SEXP_OPC_TYPE_PREDICATE, SEXP_OP_TYPEP,  1, 0, _I(SEXP_BOOLEAN), _I(SEXP_OBJECT), SEXP_FALSE, SEXP_FALSE, 0, "ratio?", _I(SEXP_RATIO), 0),
+_FN1(_I(SEXP_FIXNUM), _I(SEXP_RATIO), "ratio-numerator", 0, sexp_ratio_numerator_op),
+_FN1(_I(SEXP_FIXNUM), _I(SEXP_RATIO), "ratio-denominator", 0, sexp_ratio_denominator_op),
+#endif
 _OP(SEXP_OPC_TYPE_PREDICATE, SEXP_OP_TYPEP,  1, 0, _I(SEXP_BOOLEAN), _I(SEXP_OBJECT), SEXP_FALSE, SEXP_FALSE, 0, "closure?", _I(SEXP_PROCEDURE), 0),
 _OP(SEXP_OPC_TYPE_PREDICATE, SEXP_OP_TYPEP,  1, 0, _I(SEXP_BOOLEAN), _I(SEXP_OBJECT), SEXP_FALSE, SEXP_FALSE, 0, "opcode?", _I(SEXP_OPCODE), 0),
 _OP(SEXP_OPC_TYPE_PREDICATE, SEXP_OP_TYPEP,  1, 0, _I(SEXP_BOOLEAN), _I(SEXP_OBJECT), SEXP_FALSE, SEXP_FALSE, 0, "input-port?", _I(SEXP_IPORT), 0),
diff --git a/opt/bignum.c b/opt/bignum.c
index f68f4821..b347706d 100644
--- a/opt/bignum.c
+++ b/opt/bignum.c
@@ -1,15 +1,9 @@
 /*  bignum.c -- bignum support                                */
-/*  Copyright (c) 2009-2010 Alex Shinn.  All rights reserved. */
+/*  Copyright (c) 2009-2011 Alex Shinn.  All rights reserved. */
 /*  BSD-style license: http://synthcode.com/license.txt       */
 
 #define SEXP_INIT_BIGNUM_SIZE 2
 
-#define sexp_negate(x)                                  \
-  if (sexp_bignump(x))                                  \
-    sexp_bignum_sign(x) = -sexp_bignum_sign(x);         \
-  else if (sexp_fixnump(x))                            \
-    x = sexp_fx_neg(x);
-
 sexp sexp_make_bignum (sexp ctx, sexp_uint_t len) {
   sexp_uint_t size = sexp_sizeof(bignum) + len*sizeof(sexp_uint_t);
   sexp res = sexp_alloc_tagged(ctx, size, SEXP_BIGNUM);
@@ -229,6 +223,13 @@ sexp sexp_read_bignum (sexp ctx, sexp in, sexp_uint_t init,
       if (c!='.') sexp_push_char(ctx, c, in); /* push the e back */
       res = sexp_read_float_tail(ctx, in, sexp_bignum_to_double(res), (sign==-1));
     }
+#if SEXP_USE_RATIOS
+  } else if (c=='/') {
+    res = sexp_bignum_normalize(res);
+    res = sexp_make_ratio(ctx, res, SEXP_ONE);
+    sexp_ratio_denominator(res) = sexp_read_number(ctx, in, 10);
+    res = sexp_ratio_normalize(ctx, res, in);
+#endif
   } else if ((c!=EOF) && ! is_separator(c)) {
     res = sexp_read_error(ctx, "invalid numeric syntax",
                           sexp_make_character(c), in);
@@ -458,13 +459,71 @@ sexp sexp_bignum_expt (sexp ctx, sexp a, sexp b) {
   return sexp_bignum_normalize(res);
 }
 
+/************************ ratios ******************************/
+
+#if SEXP_USE_RATIOS
+
+double sexp_ratio_to_double (sexp rat) {
+  sexp num = sexp_ratio_numerator(rat), den = sexp_ratio_denominator(rat);
+  return (sexp_bignump(num) ? sexp_bignum_to_double(num)
+          : sexp_fixnum_to_double(num))
+    / (sexp_bignump(den) ? sexp_bignum_to_double(den)
+       : sexp_fixnum_to_double(den));
+}
+
+sexp sexp_ratio_add (sexp ctx, sexp a, sexp b) {
+  sexp_gc_var3(res, num, den);
+  sexp_gc_preserve3(ctx, res, num, den);
+  num = sexp_mul(ctx, sexp_ratio_numerator(a), sexp_ratio_denominator(b));
+  den = sexp_mul(ctx, sexp_ratio_numerator(b), sexp_ratio_denominator(a));
+  num = sexp_add(ctx, num, den);
+  den = sexp_mul(ctx, sexp_ratio_denominator(a), sexp_ratio_denominator(b));
+  res = sexp_make_ratio(ctx, num, den);
+  sexp_gc_release3(ctx);
+  return sexp_ratio_normalize(ctx, res, SEXP_FALSE);
+}
+
+sexp sexp_ratio_mul (sexp ctx, sexp a, sexp b) {
+  sexp_gc_var3(res, num, den);
+  sexp_gc_preserve3(ctx, res, num, den);
+  num = sexp_mul(ctx, sexp_ratio_numerator(a), sexp_ratio_numerator(b));
+  den = sexp_mul(ctx, sexp_ratio_denominator(a), sexp_ratio_denominator(b));
+  res = sexp_make_ratio(ctx, num, den);
+  sexp_gc_release3(ctx);
+  return sexp_ratio_normalize(ctx, res, SEXP_FALSE);
+}
+
+sexp sexp_ratio_div (sexp ctx, sexp a, sexp b) {
+  sexp_gc_var3(res, num, den);
+  sexp_gc_preserve3(ctx, res, num, den);
+  num = sexp_mul(ctx, sexp_ratio_numerator(a), sexp_ratio_denominator(b));
+  den = sexp_mul(ctx, sexp_ratio_denominator(a), sexp_ratio_numerator(b));
+  res = sexp_make_ratio(ctx, num, den);
+  sexp_gc_release3(ctx);
+  return sexp_ratio_normalize(ctx, res, SEXP_FALSE);
+}
+
+sexp sexp_ratio_compare (sexp ctx, sexp a, sexp b) {
+  sexp_gc_var2(a2, b2);
+  sexp_gc_preserve2(ctx, a2, b2);
+  a2 = sexp_mul(ctx, sexp_ratio_numerator(a), sexp_ratio_denominator(b));
+  b2 = sexp_mul(ctx, sexp_ratio_numerator(b), sexp_ratio_denominator(a));
+  a2 = sexp_compare(ctx, a2, b2);
+  sexp_gc_release2(ctx);
+  return a2;
+}
+
+#endif
+
 /****************** generic arithmetic ************************/
 
 enum sexp_number_types {
   SEXP_NUM_NOT = 0,
   SEXP_NUM_FIX,
   SEXP_NUM_FLO,
-  SEXP_NUM_BIG
+  SEXP_NUM_BIG,
+  SEXP_NUM_RAT,
+  SEXP_NUM_CPX,
 };
 
 enum sexp_number_combs {
@@ -472,22 +531,68 @@ enum sexp_number_combs {
   SEXP_NUM_NOT_FIX,
   SEXP_NUM_NOT_FLO,
   SEXP_NUM_NOT_BIG,
+#if SEXP_USE_RATIOS
+  SEXP_NUM_NOT_RAT,
+#endif
+#if SEXP_USE_COMPLEX
+  SEXP_NUM_NOT_CPX,
+#endif
   SEXP_NUM_FIX_NOT,
   SEXP_NUM_FIX_FIX,
   SEXP_NUM_FIX_FLO,
   SEXP_NUM_FIX_BIG,
+#if SEXP_USE_RATIOS
+  SEXP_NUM_FIX_RAT,
+#endif
+#if SEXP_USE_COMPLEX
+  SEXP_NUM_FIX_CPX,
+#endif
   SEXP_NUM_FLO_NOT,
   SEXP_NUM_FLO_FIX,
   SEXP_NUM_FLO_FLO,
   SEXP_NUM_FLO_BIG,
+#if SEXP_USE_RATIOS
+  SEXP_NUM_FLO_RAT,
+#endif
+#if SEXP_USE_COMPLEX
+  SEXP_NUM_FLO_CPX,
+#endif
   SEXP_NUM_BIG_NOT,
   SEXP_NUM_BIG_FIX,
   SEXP_NUM_BIG_FLO,
-  SEXP_NUM_BIG_BIG
+  SEXP_NUM_BIG_BIG,
+#if SEXP_USE_RATIOS
+  SEXP_NUM_BIG_RAT,
+#endif
+#if SEXP_USE_COMPLEX
+  SEXP_NUM_BIG_CPX,
+#endif
+#if SEXP_USE_RATIOS
+  SEXP_NUM_RAT_NOT,
+  SEXP_NUM_RAT_FIX,
+  SEXP_NUM_RAT_FLO,
+  SEXP_NUM_RAT_BIG,
+  SEXP_NUM_RAT_RAT,
+#if SEXP_USE_COMPLEX
+  SEXP_NUM_RAT_CPX,
+#endif
+#endif
+#if SEXP_USE_COMPLEX
+  SEXP_NUM_CPX_NOT,
+  SEXP_NUM_CPX_FIX,
+  SEXP_NUM_CPX_FLO,
+  SEXP_NUM_CPX_BIG,
+#if SEXP_USE_RATIOS
+  SEXP_NUM_CPX_RAT,
+#endif
+  SEXP_NUM_CPX_CPX,
+#endif
 };
 
 static int sexp_number_types[] =
-  {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0};
+  {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 4, 5, 0, 0};
+
+#define SEXP_NUM_NUMBER_TYPES (4 + SEXP_USE_RATIOS + SEXP_USE_COMPLEX)
 
 static int sexp_number_type (sexp a) {
   return sexp_pointerp(a) ? sexp_number_types[sexp_pointer_tag(a)&15]
@@ -500,10 +605,15 @@ static int sexp_number_type (sexp a) {
 sexp sexp_add (sexp ctx, sexp a, sexp b) {
   int at=sexp_number_type(a), bt=sexp_number_type(b), t;
   sexp r=SEXP_VOID;
+  sexp_gc_var1(tmp);
+  sexp_gc_preserve1(ctx, tmp);
   if (at > bt) {r=a; a=b; b=r; t=at; at=bt; bt=t;}
-  switch ((at << 2) + bt) {
+  switch ((at * SEXP_NUM_NUMBER_TYPES) + bt) {
   case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
   case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_NOT_RAT:
+#endif
     r = sexp_type_exception(ctx, NULL, SEXP_NUMBER, a);
     break;
   case SEXP_NUM_FIX_FIX:
@@ -524,21 +634,40 @@ sexp sexp_add (sexp ctx, sexp a, sexp b) {
   case SEXP_NUM_BIG_BIG:
     r = sexp_bignum_normalize(sexp_bignum_add(ctx, NULL, b, a));
     break;
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_FLO_RAT:
+    r = sexp_make_flonum(ctx, sexp_flonum_value(a) + sexp_ratio_to_double(b));
+    break;
+  case SEXP_NUM_FIX_RAT:
+  case SEXP_NUM_BIG_RAT:
+    a = tmp = sexp_make_ratio(ctx, a, SEXP_ONE);
+    /* ... FALLTHROUGH ... */
+  case SEXP_NUM_RAT_RAT:
+    r = sexp_ratio_add(ctx, a, b);
+    break;
+#endif
   }
+  sexp_gc_release1(ctx);
   return r;
 }
 
 sexp sexp_sub (sexp ctx, sexp a, sexp b) {
-  int at=sexp_number_type(a), bt=sexp_number_type(b);
+  int at=sexp_number_type(a), bt=sexp_number_type(b), negatep=0;
   sexp r=SEXP_VOID;
-  sexp_gc_var1(tmp);
-  sexp_gc_preserve1(ctx, tmp);
-  switch ((at << 2) + bt) {
+  sexp_gc_var2(tmp1, tmp2);
+  sexp_gc_preserve2(ctx, tmp1, tmp2);
+  switch ((at * SEXP_NUM_NUMBER_TYPES) + bt) {
   case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
   case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_NOT_RAT:
+#endif
     r = sexp_type_exception(ctx, NULL, SEXP_NUMBER, a);
     break;
   case SEXP_NUM_FIX_NOT: case SEXP_NUM_FLO_NOT: case SEXP_NUM_BIG_NOT:
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_RAT_NOT:
+#endif
     r = sexp_type_exception(ctx, NULL, SEXP_NUMBER, b);
     break;
   case SEXP_NUM_FIX_FIX:
@@ -548,8 +677,8 @@ sexp sexp_sub (sexp ctx, sexp a, sexp b) {
     r = sexp_make_flonum(ctx, sexp_fixnum_to_double(a)-sexp_flonum_value(b));
     break;
   case SEXP_NUM_FIX_BIG:
-    tmp = sexp_fixnum_to_bignum(ctx, a);
-    r = sexp_bignum_sub(ctx, NULL, b, tmp);
+    tmp1 = sexp_fixnum_to_bignum(ctx, a);
+    r = sexp_bignum_sub(ctx, NULL, b, tmp1);
     sexp_negate(r);
     r = sexp_bignum_normalize(r);
     break;
@@ -563,8 +692,8 @@ sexp sexp_sub (sexp ctx, sexp a, sexp b) {
     r = sexp_make_flonum(ctx, sexp_flonum_value(a) - sexp_bignum_to_double(b));
     break;
   case SEXP_NUM_BIG_FIX:
-    tmp = sexp_fixnum_to_bignum(ctx, b);
-    r = sexp_bignum_normalize(sexp_bignum_sub(ctx, NULL, a, tmp));
+    tmp1 = sexp_fixnum_to_bignum(ctx, b);
+    r = sexp_bignum_normalize(sexp_bignum_sub(ctx, NULL, a, tmp1));
     break;
   case SEXP_NUM_BIG_FLO:
     r = sexp_make_flonum(ctx, sexp_bignum_to_double(a) - sexp_flonum_value(b));
@@ -572,18 +701,52 @@ sexp sexp_sub (sexp ctx, sexp a, sexp b) {
   case SEXP_NUM_BIG_BIG:
     r = sexp_bignum_normalize(sexp_bignum_sub(ctx, NULL, a, b));
     break;
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_FLO_RAT:
+    r = sexp_make_flonum(ctx, sexp_flonum_value(a) - sexp_ratio_to_double(b));
+    break;
+  case SEXP_NUM_RAT_FLO:
+    r = sexp_make_flonum(ctx, sexp_ratio_to_double(b) - sexp_flonum_value(a));
+    break;
+  case SEXP_NUM_RAT_FIX:
+  case SEXP_NUM_RAT_BIG:
+    tmp1 = a; a = b; b = tmp1;
+    negatep = 1;
+    /* ... FALLTHROUGH ... */
+  case SEXP_NUM_FIX_RAT:
+  case SEXP_NUM_BIG_RAT:
+    a = tmp1 = sexp_make_ratio(ctx, a, SEXP_ONE);
+    /* ... FALLTHROUGH ... */
+  case SEXP_NUM_RAT_RAT:
+    tmp2 = sexp_make_ratio(ctx, sexp_ratio_numerator(b), sexp_ratio_denominator(b));
+    sexp_negate(sexp_ratio_numerator(tmp2));
+    r = sexp_ratio_add(ctx, a, tmp2);
+    if (negatep) {
+      if (sexp_ratiop(r)) {
+        sexp_negate(sexp_ratio_numerator(r));
+      } else {
+        sexp_negate(r);
+      }
+    }
+    break;
+#endif
   }
-  sexp_gc_release1(ctx);
+  sexp_gc_release2(ctx);
   return r;
 }
 
 sexp sexp_mul (sexp ctx, sexp a, sexp b) {
   int at=sexp_number_type(a), bt=sexp_number_type(b), t;
   sexp r=SEXP_VOID;
+  sexp_gc_var1(tmp);
+  sexp_gc_preserve1(ctx, tmp);
   if (at > bt) {r=a; a=b; b=r; t=at; at=bt; bt=t;}
-  switch ((at << 2) + bt) {
+  switch ((at * SEXP_NUM_NUMBER_TYPES) + bt) {
   case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
   case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_NOT_RAT:
+#endif
     r = sexp_type_exception(ctx, NULL, SEXP_NUMBER, a);
     break;
   case SEXP_NUM_FIX_FIX:
@@ -605,7 +768,20 @@ sexp sexp_mul (sexp ctx, sexp a, sexp b) {
   case SEXP_NUM_BIG_BIG:
     r = sexp_bignum_mul(ctx, NULL, a, b);
     break;
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_FLO_RAT:
+    r = sexp_make_flonum(ctx, sexp_flonum_value(a) * sexp_ratio_to_double(b));
+    break;
+  case SEXP_NUM_FIX_RAT:
+  case SEXP_NUM_BIG_RAT:
+    a = tmp = sexp_make_ratio(ctx, a, SEXP_ONE);
+    /* ... FALLTHROUGH ... */
+  case SEXP_NUM_RAT_RAT:
+    r = sexp_ratio_mul(ctx, a, b);
+    break;
+#endif
   }
+  sexp_gc_release1(ctx);
   return r;
 }
 
@@ -615,12 +791,18 @@ sexp sexp_div (sexp ctx, sexp a, sexp b) {
   sexp r=SEXP_VOID;
   sexp_gc_var2(tmp, rem);
   sexp_gc_preserve2(ctx, tmp, rem);
-  switch ((at << 2) + bt) {
+  switch ((at * SEXP_NUM_NUMBER_TYPES) + bt) {
   case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
   case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_NOT_RAT:
+#endif
     r = sexp_type_exception(ctx, NULL, SEXP_NUMBER, a);
     break;
   case SEXP_NUM_FIX_NOT: case SEXP_NUM_FLO_NOT: case SEXP_NUM_BIG_NOT:
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_RAT_NOT:
+#endif
     r = sexp_type_exception(ctx, NULL, SEXP_NUMBER, b);
     break;
   case SEXP_NUM_FIX_FIX:
@@ -657,6 +839,25 @@ sexp sexp_div (sexp ctx, sexp a, sexp b) {
   case SEXP_NUM_BIG_FLO:
     r = sexp_make_flonum(ctx, sexp_bignum_to_double(a) / sexp_flonum_value(b));
     break;
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_FLO_RAT:
+    r = sexp_make_flonum(ctx, sexp_flonum_value(a) / sexp_ratio_to_double(b));
+    break;
+  case SEXP_NUM_RAT_FLO:
+    r = sexp_make_flonum(ctx, sexp_ratio_to_double(b) / sexp_flonum_value(a));
+    break;
+  case SEXP_NUM_RAT_FIX:
+  case SEXP_NUM_RAT_BIG:
+    b = tmp = sexp_make_ratio(ctx, b, SEXP_ONE);
+  case SEXP_NUM_FIX_RAT:
+  case SEXP_NUM_BIG_RAT:
+    if (!sexp_ratiop(a))
+      a = tmp = sexp_make_ratio(ctx, a, SEXP_ONE);
+    /* ... FALLTHROUGH ... */
+  case SEXP_NUM_RAT_RAT:
+    r = sexp_ratio_div(ctx, a, b);
+    break;
+#endif
   }
   sexp_gc_release2(ctx);
   return r;
@@ -667,7 +868,7 @@ sexp sexp_quotient (sexp ctx, sexp a, sexp b) {
   sexp r=SEXP_VOID;
   sexp_gc_var1(tmp);
   sexp_gc_preserve1(ctx, tmp);
-  switch ((at << 2) + bt) {
+  switch ((at * SEXP_NUM_NUMBER_TYPES) + bt) {
   case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
   case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
     r = sexp_type_exception(ctx, NULL, SEXP_FIXNUM, a);
@@ -676,9 +877,16 @@ sexp sexp_quotient (sexp ctx, sexp a, sexp b) {
     r = sexp_type_exception(ctx, NULL, SEXP_FIXNUM, b);
     break;
   case SEXP_NUM_FLO_FIX: case SEXP_NUM_FLO_FLO: case SEXP_NUM_FLO_BIG:
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_FLO_RAT: case SEXP_NUM_RAT_FIX: case SEXP_NUM_RAT_FLO:
+  case SEXP_NUM_RAT_BIG: case SEXP_NUM_RAT_RAT:
+#endif
     r = sexp_type_exception(ctx, NULL, SEXP_FIXNUM, a);
     break;
   case SEXP_NUM_FIX_FLO: case SEXP_NUM_BIG_FLO:
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_FIX_RAT: case SEXP_NUM_BIG_RAT:
+#endif
     r = sexp_type_exception(ctx, NULL, SEXP_FIXNUM, b);
     break;
   case SEXP_NUM_FIX_FIX:
@@ -703,7 +911,7 @@ sexp sexp_remainder (sexp ctx, sexp a, sexp b) {
   sexp r=SEXP_VOID;
   sexp_gc_var1(tmp);
   sexp_gc_preserve1(ctx, tmp);
-  switch ((at << 2) + bt) {
+  switch ((at * SEXP_NUM_NUMBER_TYPES) + bt) {
   case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
   case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
     r = sexp_type_exception(ctx, NULL, SEXP_FIXNUM, a);
@@ -712,9 +920,16 @@ sexp sexp_remainder (sexp ctx, sexp a, sexp b) {
     r = sexp_type_exception(ctx, NULL, SEXP_FIXNUM, b);
     break;
   case SEXP_NUM_FLO_FIX: case SEXP_NUM_FLO_FLO: case SEXP_NUM_FLO_BIG:
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_FLO_RAT: case SEXP_NUM_RAT_FIX: case SEXP_NUM_RAT_FLO:
+  case SEXP_NUM_RAT_BIG: case SEXP_NUM_RAT_RAT:
+#endif
     r = sexp_type_exception(ctx, NULL, SEXP_FIXNUM, a);
     break;
   case SEXP_NUM_FIX_FLO: case SEXP_NUM_BIG_FLO:
+#if SEXP_USE_RATIOS
+  case SEXP_NUM_FIX_RAT: case SEXP_NUM_BIG_RAT:
+#endif
     r = sexp_type_exception(ctx, NULL, SEXP_FIXNUM, b);
     break;
   case SEXP_NUM_FIX_FIX:
@@ -738,11 +953,13 @@ sexp sexp_compare (sexp ctx, sexp a, sexp b) {
   int at=sexp_number_type(a), bt=sexp_number_type(b);
   sexp r=SEXP_VOID;
   double f;
+  sexp_gc_var1(tmp);
+  sexp_gc_preserve1(ctx, tmp);
   if (at > bt) {
     r = sexp_compare(ctx, b, a);
     sexp_negate(r);
   } else {
-    switch ((at << 2) + bt) {
+    switch ((at * SEXP_NUM_NUMBER_TYPES) + bt) {
     case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
     case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
       r = sexp_type_exception(ctx, NULL, SEXP_NUMBER, a);
@@ -768,8 +985,20 @@ sexp sexp_compare (sexp ctx, sexp a, sexp b) {
     case SEXP_NUM_BIG_BIG:
       r = sexp_make_fixnum(sexp_bignum_compare(a, b));
       break;
+#if SEXP_USE_RATIOS
+    case SEXP_NUM_FLO_RAT:
+      r = sexp_make_fixnum((sexp_sint_t)(sexp_flonum_value(a) - sexp_ratio_to_double(b)));
+      break;
+    case SEXP_NUM_FIX_RAT:
+    case SEXP_NUM_BIG_RAT:
+      a = tmp = sexp_make_ratio(ctx, a, SEXP_ONE);
+      /* ... FALLTHROUGH ... */
+    case SEXP_NUM_RAT_RAT:
+      r = sexp_ratio_compare(ctx, a, b);
+      break;
+#endif
     }
   }
+  sexp_gc_release1(ctx);
   return r;
 }
-
diff --git a/sexp.c b/sexp.c
index 2a8f8a6f..c1209c01 100644
--- a/sexp.c
+++ b/sexp.c
@@ -97,6 +97,8 @@ static struct sexp_type_struct _sexp_type_specs[] = {
   {SEXP_VECTOR, sexp_offsetof(vector, data), 0, 0, sexp_offsetof(vector, length), 1, sexp_sizeof(vector), sexp_offsetof(vector, length), sizeof(sexp), 0, 0, 0, 0, 0, 0, "vector", SEXP_FALSE, SEXP_FALSE, NULL},
   {SEXP_FLONUM, 0, 0, 0, 0, 0, sexp_sizeof(flonum), 0, 0, 0, 0, 0, 0, 0, 0, "real", SEXP_FALSE, SEXP_FALSE, NULL},
   {SEXP_BIGNUM, 0, 0, 0, 0, 0, sexp_sizeof(bignum), sexp_offsetof(bignum, length), sizeof(sexp_uint_t), 0, 0, 0, 0, 0, 0, "bignum", SEXP_FALSE, SEXP_FALSE, NULL},
+  {SEXP_RATIO, sexp_offsetof(ratio, numerator), 2, 2, 0, 0, sexp_sizeof(ratio), 0, 0, 0, 0, 0, 0, 0, 0, "ratio", SEXP_FALSE, SEXP_FALSE, NULL},
+  {SEXP_COMPLEX, sexp_offsetof(complex, real), 2, 2, 0, 0, sexp_sizeof(complex), 0, 0, 0, 0, 0, 0, 0, 0, "complex", SEXP_FALSE, SEXP_FALSE, NULL},
   {SEXP_IPORT, sexp_offsetof(port, name), 2, 2, 0, 0, sexp_sizeof(port), 0, 0, 0, 0, 0, 0, 0, 0, "input-port", SEXP_FALSE, SEXP_FALSE, SEXP_FINALIZE_PORT},
   {SEXP_OPORT, sexp_offsetof(port, name), 2, 2, 0, 0, sexp_sizeof(port), 0, 0, 0, 0, 0, 0, 0, 0, "output-port", SEXP_FALSE, SEXP_FALSE, SEXP_FINALIZE_PORT},
   {SEXP_EXCEPTION, sexp_offsetof(exception, kind), 6, 6, 0, 0, sexp_sizeof(exception), 0, 0, 0, 0, 0, 0, 0, 0, "exception", SEXP_FALSE, SEXP_FALSE, NULL},
@@ -1371,6 +1373,22 @@ sexp sexp_write_one (sexp ctx, sexp obj, sexp out) {
     case SEXP_BIGNUM:
       sexp_write_bignum(ctx, obj, out, 10);
       break;
+#endif
+#if SEXP_USE_RATIOS
+    case SEXP_RATIO:
+      sexp_write(ctx, sexp_ratio_numerator(obj), out);
+      sexp_write_char(ctx, '/', out);
+      sexp_write(ctx, sexp_ratio_denominator(obj), out);
+      break;
+#endif
+#if SEXP_USE_COMPLEX
+    case SEXP_COMPLEX:
+      sexp_write(ctx, sexp_complex_real(obj), out);
+      if (!sexp_negativep(sexp_complex_imag(obj)))
+        sexp_write_char(ctx, '+', out);
+      sexp_write(ctx, sexp_complex_imag(obj), out);
+      sexp_write_char(ctx, 'i', out);
+      break;
 #endif
     case SEXP_OPCODE:
       sexp_write_string(ctx, "#<opcode ", out);
@@ -1460,7 +1478,9 @@ sexp sexp_write_one (sexp ctx, sexp obj, sexp out) {
     case (sexp_uint_t) SEXP_VOID:
       sexp_write_string(ctx, "#<undef>", out); break;
     default:
-      sexp_write_string(ctx, "#<invalid immediate>", out);
+      sexp_write_string(ctx, "#<invalid immediate: ", out);
+      sexp_write(ctx, sexp_make_fixnum(obj), out);
+      sexp_write_char(ctx, '>', out);
     }
   }
   return SEXP_VOID;
@@ -1603,13 +1623,52 @@ sexp sexp_read_float_tail (sexp ctx, sexp in, double whole, int negp) {
 #endif
 }
 
+#if SEXP_USE_RATIOS
+sexp sexp_make_ratio (sexp ctx, sexp num, sexp den) {
+  sexp res = sexp_alloc_type(ctx, ratio, SEXP_RATIO);
+  sexp_ratio_numerator(res) = num;
+  sexp_ratio_denominator(res) = den;
+  return res;
+}
+
+sexp sexp_ratio_normalize (sexp ctx, sexp rat, sexp in) {
+  sexp tmp;
+  sexp_gc_var2(num, den);
+  sexp_gc_preserve2(ctx, num, den);
+  num = sexp_ratio_numerator(rat), den = sexp_ratio_denominator(rat);
+  if (den == SEXP_ZERO)
+    return sexp_read_error(ctx, "zero denominator in ratio", rat, in);
+  else if (num == SEXP_ZERO)
+    return SEXP_ZERO;
+  while (den != SEXP_ZERO) {
+    tmp = sexp_remainder(ctx, num, den);
+    if (sexp_exceptionp(tmp)) {
+      sexp_gc_release2(ctx);
+      return tmp;
+    }
+    num = den, den = tmp;
+  }
+  sexp_ratio_denominator(rat)
+    = den = sexp_quotient(ctx, sexp_ratio_denominator(rat), num);
+  sexp_ratio_numerator(rat)
+    = sexp_quotient(ctx, sexp_ratio_numerator(rat), num);
+  if (sexp_exact_negativep(sexp_ratio_denominator(rat))) {
+    sexp_negate(sexp_ratio_numerator(rat));
+    sexp_negate(sexp_ratio_denominator(rat));
+  }
+  sexp_gc_release2(ctx);
+  return (sexp_ratio_denominator(rat) == SEXP_ONE) ? sexp_ratio_numerator(rat)
+    : rat;
+}
+#endif
+
 sexp sexp_read_number (sexp ctx, sexp in, int base) {
-  sexp den;
-  sexp_uint_t res = 0, tmp;
+  sexp_sint_t val = 0, tmp;
   int c, digit, negativep = 0;
 #if SEXP_USE_PLACEHOLDER_DIGITS
   double whole = 0.0, scale = 0.1;
 #endif
+  sexp_gc_var2(res, den);
 
   c = sexp_read_char(ctx, in);
   if (c == '-') {
@@ -1621,19 +1680,19 @@ sexp sexp_read_number (sexp ctx, sexp in, int base) {
     digit = digit_value(c);
     if ((digit < 0) || (digit >= base))
       break;
-    tmp = res * base + digit;
+    tmp = val * base + digit;
 #if SEXP_USE_BIGNUMS
-    if ((tmp < res) || (tmp > SEXP_MAX_FIXNUM)) {
+    if ((tmp < val) || (tmp > SEXP_MAX_FIXNUM)) {
       sexp_push_char(ctx, c, in);
-      return sexp_read_bignum(ctx, in, res, (negativep ? -1 : 1), base);
+      return sexp_read_bignum(ctx, in, val, (negativep ? -1 : 1), base);
     }
 #endif
-    res = tmp;
+    val = tmp;
   }
 
 #if SEXP_USE_PLACEHOLDER_DIGITS
   if (sexp_placeholder_digit_p(c)) {
-    whole = res;
+    whole = val;
     for ( ; sexp_placeholder_digit_p(c); c=sexp_read_char(ctx, in))
       whole = whole*10 + sexp_placeholder_digit_value(base);
     if ((c=='.' || c=='e' || c=='E') && (base != 10))
@@ -1658,14 +1717,22 @@ sexp sexp_read_number (sexp ctx, sexp in, int base) {
     if (base != 10)
       return sexp_read_error(ctx, "found non-base 10 float", SEXP_NULL, in);
     if (c!='.') sexp_push_char(ctx, c, in);
-    return sexp_read_float_tail(ctx, in, res, negativep);
+    return sexp_read_float_tail(ctx, in, val, negativep);
   } else if (c=='/') {
+    sexp_gc_preserve2(ctx, res, den);
     den = sexp_read_number(ctx, in, base);
-    if (! sexp_fixnump(den))
+    if (! (sexp_fixnump(den) || sexp_bignump(den)))
       return (sexp_exceptionp(den)
               ? den : sexp_read_error(ctx, "invalid rational syntax", den, in));
-    return sexp_make_flonum(ctx, (double)(negativep ? -res : res)
-                            / (double)sexp_unbox_fixnum(den));
+#if SEXP_USE_RATIOS
+    res = sexp_make_ratio(ctx, sexp_make_fixnum(negativep ? -val : val), den);
+    res = sexp_ratio_normalize(ctx, res, in);
+#else
+    res = sexp_make_flonum(ctx, (double)(negativep ? -val : val)
+                           / (double)sexp_unbox_fixnum(den));
+#endif
+    sexp_gc_release2(ctx);
+    return res;
   } else {
     if ((c!=EOF) && ! is_separator(c))
       return sexp_read_error(ctx, "invalid numeric syntax",
@@ -1673,7 +1740,7 @@ sexp sexp_read_number (sexp ctx, sexp in, int base) {
     sexp_push_char(ctx, c, in);
   }
 
-  return sexp_make_fixnum(negativep ? -res : res);
+  return sexp_make_fixnum(negativep ? -val : val);
 }
 
 #if SEXP_USE_UTF8_STRINGS
@@ -1978,6 +2045,16 @@ sexp sexp_read_raw (sexp ctx, sexp in) {
             else
               sexp_bignum_sign(res) = -sexp_bignum_sign(res);
           } else
+#endif
+#if SEXP_USE_RATIOS
+          if (sexp_ratiop(res)) {
+            sexp_negate(sexp_ratio_numerator(res));
+          } else
+#endif
+#if SEXP_USE_COMPLEX
+          if (sexp_complexp(res)) {
+            sexp_negate(sexp_complex_real(res));
+          } else
 #endif
             res = sexp_fx_mul(res, SEXP_NEG_ONE);
       }
diff --git a/vm.c b/vm.c
index a8c1e083..79f40145 100644
--- a/vm.c
+++ b/vm.c
@@ -1620,6 +1620,10 @@ sexp sexp_apply (sexp ctx, sexp proc, sexp args) {
 #if SEXP_USE_BIGNUMS
     else if (sexp_bignump(_ARG1))
       _ARG1 = sexp_make_flonum(ctx, sexp_bignum_to_double(_ARG1));
+#endif
+#if SEXP_USE_RATIOS
+    else if (sexp_ratiop(_ARG1))
+      _ARG1 = sexp_make_flonum(ctx, sexp_ratio_to_double(_ARG1));
 #endif
     else if (! sexp_flonump(_ARG1))
       sexp_raise("exact->inexact: not a number", sexp_list1(ctx, _ARG1));