diff --git a/complex.c b/complex.c
index 5b5f17edfa..1a851dd3b5 100644
--- a/complex.c
+++ b/complex.c
@@ -182,8 +182,12 @@ fun2(quo)
 inline static int
 f_negative_p(VALUE x)
 {
-    if (FIXNUM_P(x))
-	return FIXNUM_NEGATIVE_P(x);
+    if (RB_INTEGER_TYPE_P(x))
+        return INT_NEGATIVE_P(x);
+    else if (RB_FLOAT_TYPE_P(x))
+        return RFLOAT_VALUE(x) < 0.0;
+    else if (RB_TYPE_P(x, T_RATIONAL))
+        return INT_NEGATIVE_P(RRATIONAL(x)->num);
     return rb_num_negative_p(x);
 }
 
@@ -2045,8 +2049,8 @@ static VALUE
 numeric_arg(VALUE self)
 {
     if (f_positive_p(self))
-	return INT2FIX(0);
-    return rb_const_get(rb_mMath, id_PI);
+        return INT2FIX(0);
+    return DBL2NUM(M_PI);
 }
 
 /*
@@ -2062,6 +2066,8 @@ numeric_rect(VALUE self)
     return rb_assoc_new(self, INT2FIX(0));
 }
 
+static VALUE float_arg(VALUE self);
+
 /*
  * call-seq:
  *    num.polar  ->  array
@@ -2071,7 +2077,25 @@ numeric_rect(VALUE self)
 static VALUE
 numeric_polar(VALUE self)
 {
-    return rb_assoc_new(f_abs(self), f_arg(self));
+    VALUE abs, arg;
+
+    if (RB_INTEGER_TYPE_P(self)) {
+        abs = rb_int_abs(self);
+        arg = numeric_arg(self);
+    }
+    else if (RB_FLOAT_TYPE_P(self)) {
+        abs = rb_float_abs(self);
+        arg = float_arg(self);
+    }
+    else if (RB_TYPE_P(self, T_RATIONAL)) {
+        abs = rb_rational_abs(self);
+        arg = numeric_arg(self);
+    }
+    else {
+        abs = f_abs(self);
+        arg = f_arg(self);
+    }
+    return rb_assoc_new(abs, arg);
 }
 
 /*
diff --git a/internal.h b/internal.h
index acab0d31b7..a3ce94988f 100644
--- a/internal.h
+++ b/internal.h
@@ -1141,6 +1141,8 @@ void Init_newline(void);
 #define FIXNUM_NEGATIVE_P(num) ((SIGNED_VALUE)(num) < 0)
 #define FIXNUM_ZERO_P(num) ((num) == INT2FIX(0))
 
+#define INT_NEGATIVE_P(x) (FIXNUM_P(x) ? FIXNUM_NEGATIVE_P(x) : BIGNUM_NEGATIVE_P(x))
+
 #ifndef ROUND_DEFAULT
 # define ROUND_DEFAULT RUBY_NUM_ROUND_HALF_EVEN
 #endif
@@ -1181,6 +1183,7 @@ VALUE rb_int_and(VALUE x, VALUE y);
 VALUE rb_int_lshift(VALUE x, VALUE y);
 VALUE rb_int_div(VALUE x, VALUE y);
 VALUE rb_int_abs(VALUE num);
+VALUE rb_float_abs(VALUE flt);
 
 #if USE_FLONUM
 #define RUBY_BIT_ROTL(v, n) (((v) << (n)) | ((v) >> ((sizeof(v) * 8) - n)))
@@ -1373,6 +1376,7 @@ VALUE rb_rational_plus(VALUE self, VALUE other);
 VALUE rb_lcm(VALUE x, VALUE y);
 VALUE rb_rational_reciprocal(VALUE x);
 VALUE rb_cstr_to_rat(const char *, int);
+VALUE rb_rational_abs(VALUE self);
 
 /* re.c */
 VALUE rb_reg_compile(VALUE str, int options, const char *sourcefile, int sourceline);
diff --git a/numeric.c b/numeric.c
index 959626e28d..e7cb105b7d 100644
--- a/numeric.c
+++ b/numeric.c
@@ -1678,8 +1678,8 @@ flo_to_f(VALUE num)
  *
  */
 
-static VALUE
-flo_abs(VALUE flt)
+VALUE
+rb_float_abs(VALUE flt)
 {
     double val = fabs(RFLOAT_VALUE(flt));
     return DBL2NUM(val);
@@ -5406,8 +5406,8 @@ Init_Numeric(void)
     rb_define_method(rb_cFloat, "eql?", flo_eql, 1);
     rb_define_method(rb_cFloat, "hash", flo_hash, 0);
     rb_define_method(rb_cFloat, "to_f", flo_to_f, 0);
-    rb_define_method(rb_cFloat, "abs", flo_abs, 0);
-    rb_define_method(rb_cFloat, "magnitude", flo_abs, 0);
+    rb_define_method(rb_cFloat, "abs", rb_float_abs, 0);
+    rb_define_method(rb_cFloat, "magnitude", rb_float_abs, 0);
     rb_define_method(rb_cFloat, "zero?", flo_zero_p, 0);
 
     rb_define_method(rb_cFloat, "to_i", flo_to_i, 0);
diff --git a/rational.c b/rational.c
index d9ff5ce344..0a120368c3 100644
--- a/rational.c
+++ b/rational.c
@@ -28,7 +28,6 @@
 #define GMP_GCD_DIGITS 1
 
 #define INT_POSITIVE_P(x) (FIXNUM_P(x) ? FIXNUM_POSITIVE_P(x) : BIGNUM_POSITIVE_P(x))
-#define INT_NEGATIVE_P(x) (FIXNUM_P(x) ? FIXNUM_NEGATIVE_P(x) : BIGNUM_NEGATIVE_P(x))
 #define INT_ZERO_P(x) (FIXNUM_P(x) ? FIXNUM_ZERO_P(x) : rb_bigzero_p(x))
 
 VALUE rb_cRational;