From 3db12e8b236ac8f88db8eb4690d10e4a3b8dbcd4 Mon Sep 17 00:00:00 2001
From: matz <matz@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>
Date: Fri, 16 Jan 1998 12:13:05 +0000
Subject: Initial revision

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@2 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
---
 numeric.c | 1154 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 1154 insertions(+)
 create mode 100644 numeric.c

(limited to 'numeric.c')

diff --git a/numeric.c b/numeric.c
new file mode 100644
index 0000000000..242d13c14e
--- /dev/null
+++ b/numeric.c
@@ -0,0 +1,1154 @@
+/************************************************
+
+  numeric.c -
+
+  $Author$
+  $Date$
+  created at: Fri Aug 13 18:33:09 JST 1993
+
+  Copyright (C) 1993-1996 Yukihiro Matsumoto
+
+************************************************/
+
+#include "ruby.h"
+#include <math.h>
+#if defined (HAVE_STRING_H)
+#  include <string.h>
+#else
+#  include <strings.h>
+#endif
+
+static ID coerce;
+static ID to_i;
+
+VALUE cNumeric;
+VALUE cFloat;
+VALUE cInteger;
+VALUE cFixnum;
+
+VALUE eZeroDiv;
+
+ID rb_frame_last_func();
+VALUE float_new();
+double big2dbl();
+
+void
+num_zerodiv()
+{
+    Raise(eZeroDiv, "divided by 0");
+}
+
+static VALUE
+num_coerce(x, y)
+    VALUE x, y;
+{
+    return assoc_new(f_float(x,x),f_float(y,y));
+}
+
+VALUE
+num_coerce_bin(x, y)
+    VALUE x, y;
+{
+    VALUE ary;
+
+    ary = rb_funcall(y, coerce, 1, x);
+    if (TYPE(ary) != T_ARRAY || RARRAY(ary)->len != 2) {
+	TypeError("coerce must return [x, y]");
+    }
+
+    x = RARRAY(ary)->ptr[0];
+    y = RARRAY(ary)->ptr[1];
+
+    return rb_funcall(x, rb_frame_last_func(), 1, y);
+}
+
+static VALUE
+num_uplus(num)
+    VALUE num;
+{
+    return num;
+}
+
+static VALUE
+num_uminus(num)
+    VALUE num;
+{
+    VALUE ary, x, y;
+
+    ary = rb_funcall(num, coerce, 1, INT2FIX(0));
+    if (TYPE(ary) != T_ARRAY || RARRAY(ary)->len != 2) {
+	TypeError("coerce must return [x, y]");
+    }
+
+    x = RARRAY(ary)->ptr[0];
+    y = RARRAY(ary)->ptr[1];
+
+    return rb_funcall(x, '-', 1, y);
+}
+
+static VALUE
+num_divmod(x, y)
+    VALUE x, y;
+{
+    VALUE div, mod;
+
+    div = rb_funcall(x, '/', 1, y);
+    if (TYPE(div) == T_FLOAT) {
+	double d = floor(RFLOAT(div)->value);
+
+	if (RFLOAT(div)->value > d) {
+	    div = float_new(d);
+	}
+    }
+    mod = rb_funcall(x, '%', 1, y);
+    return assoc_new(div, mod);
+}
+
+static VALUE
+num_int_p(num)
+    VALUE num;
+{
+    return FALSE;
+}
+
+static VALUE
+num_chr(num)
+    VALUE num;
+{
+    char c;
+    int i = NUM2INT(num);
+
+    if (i < 0 || 0xff < i)
+	Fail("%d out of char range", i);
+    c = i;
+    return str_new(&c, 1);
+}
+
+static VALUE
+num_abs(num)
+    VALUE num;
+{
+    if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) {
+	return rb_funcall(num, rb_intern("-@"), 0);
+    }
+    return num;
+}
+
+VALUE
+float_new(d)
+    double d;
+{
+    NEWOBJ(flt, struct RFloat);
+    OBJSETUP(flt, cFloat, T_FLOAT);
+
+    flt->value = d;
+    return (VALUE)flt;
+}
+
+static VALUE
+flo_to_s(flt)
+    struct RFloat *flt;
+{
+    char buf[32];
+
+    sprintf(buf, "%g", flt->value);
+    if (strchr(buf, '.') == 0) {
+	int len = strlen(buf);
+	char *ind = strchr(buf, 'e');
+
+	if (ind) {
+	    memmove(ind+2, ind, len-(ind-buf)+1);
+	    ind[0] = '.';
+	    ind[1] = '0';
+	} else {
+	    strcat(buf, ".0");
+	}
+    }
+
+    return str_new2(buf);
+}
+
+static VALUE
+flo_coerce(x, y)
+    VALUE x, y;
+{
+    return assoc_new(f_float(x, y), x);
+}
+
+static VALUE
+flo_uminus(flt)
+    struct RFloat *flt;
+{
+    return float_new(-flt->value);
+}
+
+static VALUE
+flo_plus(x, y)
+    struct RFloat *x, *y;
+{
+    switch (TYPE(y)) {
+      case T_FIXNUM:
+	return float_new(x->value + (double)FIX2INT(y));
+      case T_BIGNUM:
+	return float_new(x->value + big2dbl(y));
+      case T_FLOAT:
+	return float_new(x->value + y->value);
+      case T_STRING:
+	return str_plus(obj_as_string(x), y);
+      default:
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+flo_minus(x, y)
+    struct RFloat *x, *y;
+{
+    switch (TYPE(y)) {
+      case T_FIXNUM:
+	return float_new(x->value - (double)FIX2INT(y));
+      case T_BIGNUM:
+	return float_new(x->value - big2dbl(y));
+      case T_FLOAT:
+	return float_new(x->value - y->value);
+      default:
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+flo_mul(x, y)
+    struct RFloat *x, *y;
+{
+    switch (TYPE(y)) {
+      case T_FIXNUM:
+	return float_new(x->value * (double)FIX2INT(y));
+      case T_BIGNUM:
+	return float_new(x->value * big2dbl(y));
+      case T_FLOAT:
+	return float_new(x->value * y->value);
+      case T_STRING:
+	return str_times(y, INT2FIX((int)x->value));
+      default:
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+flo_div(x, y)
+    struct RFloat *x, *y;
+{
+    int f_y;
+    double d;
+
+    switch (TYPE(y)) {
+      case T_FIXNUM:
+	f_y = FIX2INT(y);
+	if (f_y == 0) num_zerodiv();
+	return float_new(x->value / (double)f_y);
+      case T_BIGNUM:
+	d = big2dbl(y);
+	if (d == 0.0) num_zerodiv();
+	return float_new(x->value / d);
+      case T_FLOAT:
+	if (y->value == 0.0) num_zerodiv();
+	return float_new(x->value / y->value);
+      default:
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+flo_mod(x, y)
+    struct RFloat *x, *y;
+{
+    double value;
+
+    switch (TYPE(y)) {
+      case T_FIXNUM:
+	value = (double)FIX2INT(y);
+	break;
+      case T_BIGNUM:
+	value = big2dbl(y);
+	break;
+      case T_FLOAT:
+	value = y->value;
+	break;
+      default:
+	return num_coerce_bin(x, y);
+    }
+#ifdef HAVE_FMOD
+    value = fmod(x->value, value);
+#else
+    {
+	double value1 = x->value;
+	double value2;
+
+	modf(value1/value, &value2);
+	value = value1 - value2 * value;
+    }
+#endif
+
+    return float_new(value);
+}
+
+VALUE
+flo_pow(x, y)
+    struct RFloat *x, *y;
+{
+    switch (TYPE(y)) {
+      case T_FIXNUM:
+        return float_new(pow(x->value, (double)FIX2INT(y)));
+      case T_BIGNUM:
+	return float_new(pow(x->value, big2dbl(y)));
+      case T_FLOAT:
+        return float_new(pow(x->value, y->value));
+      default:
+        return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+num_eql(x, y)
+    VALUE x, y;
+{
+    if (TYPE(x) != TYPE(y)) return FALSE;
+
+    return rb_equal(x, y);
+}
+
+
+static VALUE
+num_equal(x, y)
+    VALUE x, y;
+{
+    return rb_equal(y, x);
+}
+
+static VALUE
+flo_eq(x, y)
+    struct RFloat *x, *y;
+{
+    switch (TYPE(y)) {
+      case T_FIXNUM:
+	if (x->value == FIX2INT(y)) return TRUE;
+	return FALSE;
+      case T_BIGNUM:
+	return (x->value == big2dbl(y))?TRUE:FALSE;
+      case T_FLOAT:
+	return (x->value == y->value)?TRUE:FALSE;
+      default:
+	return num_equal(x, y);
+    }
+}
+
+static VALUE
+flo_hash(num)
+    struct RFloat *num;
+{
+    double d;
+    char *c;
+    int i, hash;
+
+    d = num->value;
+    c = (char*)&d;
+    for (hash=0, i=0; i<sizeof(double);i++) {
+	hash += c[i] * 971;
+    }
+    if (hash < 0) hash = -hash;
+    return INT2FIX(hash);
+}
+
+static VALUE
+flo_cmp(x, y)
+    struct RFloat *x, *y;
+{
+    double a, b;
+
+    a = x->value;
+    switch (TYPE(y)) {
+      case T_FIXNUM:
+	b = (double)FIX2INT(y);
+	break;
+
+      case T_BIGNUM:
+	b = big2dbl(y);
+	break;
+
+      case T_FLOAT:
+	b = y->value;
+	break;
+
+      default:
+	return num_coerce_bin(x, y);
+    }
+    if (a == b) return INT2FIX(0);
+    if (a > b) return INT2FIX(1);
+    return INT2FIX(-1);
+}
+
+static VALUE
+flo_eql(x, y)
+    struct RFloat *x, *y;
+{
+    if (TYPE(y) == T_FLOAT) {
+	if (x->value == y->value) return TRUE;
+    }
+}
+
+static VALUE
+flo_to_i(num)
+    struct RFloat *num;
+{
+    double f = num->value;
+    int val;
+
+    if (!FIXABLE(f)) {
+	return dbl2big(f);
+    }
+    val = f;
+    return INT2FIX(val);
+}
+
+static VALUE
+flo_to_f(num)
+    VALUE num;
+{
+    return num;
+}
+
+static VALUE
+flo_abs(flt)
+    struct RFloat *flt;
+{
+    double val = fabs(flt->value);
+    return float_new(val);
+}
+
+static VALUE
+to_integer(val)
+    VALUE val;
+{
+    return rb_funcall(val, to_i, 0);
+}
+
+static VALUE
+fail_to_integer(val)
+    VALUE val;
+{
+    TypeError("failed to convert %s into Integer",
+	      rb_class2name(CLASS_OF(val)));
+}
+
+int
+num2int(val)
+    VALUE val;
+{
+    if (NIL_P(val)) return 0;
+
+    switch (TYPE(val)) {
+      case T_FIXNUM:
+	return FIX2INT(val);
+
+      case T_FLOAT:
+	if (RFLOAT(val)->value <= (double) LONG_MAX
+	    && RFLOAT(val)->value >= (double) LONG_MIN) {
+	    return (int)(RFLOAT(val)->value);
+	}
+	else {
+	    Fail("float %g out of rang of integer", RFLOAT(val)->value);
+	}
+
+      case T_BIGNUM:
+	return big2int(val);
+
+      default:
+	val = rb_rescue(to_integer, val, fail_to_integer, val);
+	return NUM2INT(val);
+    }
+}
+
+VALUE
+num2fix(val)
+    VALUE val;
+{
+    int v;
+
+    if (NIL_P(val)) return INT2FIX(0);
+    switch (TYPE(val)) {
+      case T_FIXNUM:
+	return val;
+
+      case T_FLOAT:
+      case T_BIGNUM:
+      default:
+	v = num2int(val);
+	if (!FIXABLE(v))
+	    Fail("integer %d out of range of Fixnum", v);
+	return INT2FIX(v);
+    }
+}
+
+static VALUE
+int_int_p(num)
+    VALUE num;
+{
+    return TRUE;
+}
+
+static VALUE
+int_succ(num)
+    VALUE num;
+{
+    return rb_funcall(num, '+', 1, INT2FIX(1));
+}
+
+static VALUE
+fix_uminus(num)
+    VALUE num;
+{
+    return int2inum(-FIX2INT(num));
+}
+
+VALUE
+fix2str(x, base)
+    VALUE x;
+    int base;
+{
+    char fmt[3], buf[12];
+
+    fmt[0] = '%'; fmt[2] = '\0';
+    if (base == 10) fmt[1] = 'd';
+    else if (base == 16) fmt[1] = 'x';
+    else if (base == 8) fmt[1] = 'o';
+    else Fatal("fixnum cannot treat base %d", base);
+
+    sprintf(buf, fmt, FIX2INT(x));
+    return str_new2(buf);
+}
+
+VALUE
+fix_to_s(in)
+    VALUE in;
+{
+    return fix2str(in, 10);
+}
+
+static VALUE
+fix_plus(x, y)
+    VALUE x;
+    struct RFloat *y;
+{
+    switch (TYPE(y)) {
+      case T_FIXNUM:
+	{
+	    int a, b, c;
+	    VALUE r;
+
+	    a = FIX2INT(x);
+	    b = FIX2INT(y);
+	    c = a + b;
+	    r = INT2FIX(c);
+
+	    if (FIX2INT(r) != c) {
+		r = big_plus(int2big(a), int2big(b));
+	    }
+	    return r;
+	}
+      case T_FLOAT:
+	return float_new((double)FIX2INT(x) + y->value);
+      default:
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+fix_minus(x, y)
+    VALUE x;
+    struct RFloat *y;
+{
+    switch (TYPE(y)) {
+      case T_FIXNUM:
+	{
+	    int a, b, c;
+	    VALUE r;
+
+	    a = FIX2INT(x);
+	    b = FIX2INT(y);
+	    c = a - b;
+	    r = INT2FIX(c);
+
+	    if (FIX2INT(r) != c) {
+		r = big_minus(int2big(a), int2big(b));
+	    }
+	    return r;
+	}
+      case T_FLOAT:
+	return float_new((double)FIX2INT(x) - y->value);
+      default:
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+fix_mul(x, y)
+    VALUE x;
+    struct RFloat *y;
+{
+    switch (TYPE(y)) {
+      case T_FIXNUM:
+	{
+	    int a, b, c;
+	    VALUE r;
+
+	    a = FIX2INT(x);
+	    if (a == 0) return x;
+
+	    b = FIX2INT(y);
+	    c = a * b;
+	    r = INT2FIX(c);
+
+	    if (FIX2INT(r) != c || c/a != b) {
+		r = big_mul(int2big(a), int2big(b));
+	    }
+	    return r;
+	}
+      case T_FLOAT:
+	return float_new((double)FIX2INT(x) * y->value);
+      default:
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+fix_div(x, y)
+    VALUE x;
+    struct RFloat *y;
+{
+    int i;
+
+    if (TYPE(y) == T_FIXNUM) {
+	i = FIX2INT(y);
+	if (i == 0) num_zerodiv();
+	i = FIX2INT(x)/i;
+	return INT2FIX(i);
+    }
+    return num_coerce_bin(x, y);
+}
+
+static VALUE
+fix_mod(x, y)
+    VALUE x, y;
+{
+    int i;
+
+    if (TYPE(y) == T_FIXNUM) {
+	i = FIX2INT(y);
+	if (i == 0) num_zerodiv();
+	i = FIX2INT(x)%i;
+	return INT2FIX(i);
+    }
+    return num_coerce_bin(x, y);
+}
+
+static VALUE
+fix_pow(x, y)
+    VALUE x, y;
+{
+    if (FIXNUM_P(y)) {
+	int a, b;
+
+	b = FIX2INT(y);
+	if (b == 0) return INT2FIX(1);
+	a = FIX2INT(x);
+	if (b > 0) {
+	    return big_pow(int2big(a), y);
+	}
+	return float_new(pow((double)a, (double)b));
+    }
+    else if (NIL_P(y)) {
+	return INT2FIX(1);
+    }
+    return num_coerce_bin(x, y);
+}
+
+static VALUE
+fix_equal(x, y)
+    VALUE x, y;
+{
+    if (FIXNUM_P(y)) {
+	return (FIX2INT(x) == FIX2INT(y))?TRUE:FALSE;
+    }
+    else {
+	return num_equal(x, y);
+    }
+}
+
+static VALUE
+fix_cmp(x, y)
+    VALUE x, y;
+{
+    if (FIXNUM_P(y)) {
+	int a = FIX2INT(x), b = FIX2INT(y);
+
+	if (a == b) return INT2FIX(0);
+	if (a > b) return INT2FIX(1);
+	return INT2FIX(-1);
+    }
+    else {
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+fix_gt(x, y)
+    VALUE x, y;
+{
+    if (FIXNUM_P(y)) {
+	int a = FIX2INT(x), b = FIX2INT(y);
+
+	if (a > b) return TRUE;
+	return FALSE;
+    }
+    else {
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+fix_ge(x, y)
+    VALUE x, y;
+{
+    if (FIXNUM_P(y)) {
+	int a = FIX2INT(x), b = FIX2INT(y);
+
+	if (a >= b) return TRUE;
+	return FALSE;
+    }
+    else {
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+fix_lt(x, y)
+    VALUE x, y;
+{
+    if (FIXNUM_P(y)) {
+	int a = FIX2INT(x), b = FIX2INT(y);
+
+	if (a < b) return TRUE;
+	return FALSE;
+    }
+    else {
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+fix_le(x, y)
+    VALUE x, y;
+{
+    if (FIXNUM_P(y)) {
+	int a = FIX2INT(x), b = FIX2INT(y);
+
+	if (a <= b) return TRUE;
+	return FALSE;
+    }
+    else {
+	return num_coerce_bin(x, y);
+    }
+}
+
+static VALUE
+fix_rev(num)
+    VALUE num;
+{
+    unsigned long val = FIX2UINT(num);
+
+    val = ~val;
+    return INT2FIX(val);
+}
+
+static VALUE
+fix_and(x, y)
+    VALUE x, y;
+{
+    long val;
+
+    if (TYPE(y) == T_BIGNUM) {
+	return big_and(y, x);
+    }
+    val = NUM2INT(x) & NUM2INT(y);
+    return int2inum(val);
+}
+
+static VALUE
+fix_or(x, y)
+    VALUE x, y;
+{
+    long val;
+
+    if (TYPE(y) == T_BIGNUM) {
+	return big_or(y, x);
+    }
+    val = NUM2INT(x) | NUM2INT(y);
+    return INT2FIX(val);
+}
+
+static VALUE
+fix_xor(x, y)
+    VALUE x, y;
+{
+    long val;
+
+    if (TYPE(y) == T_BIGNUM) {
+	return big_xor(y, x);
+    }
+    val = NUM2INT(x) ^ NUM2INT(y);
+    return INT2FIX(val);
+}
+
+static VALUE
+fix_lshift(x, y)
+    VALUE x, y;
+{
+    long val, width;
+
+    val = NUM2INT(x);
+    width = NUM2INT(y);
+    if (width > (sizeof(VALUE)*CHAR_BIT-1)
+	|| (unsigned)val>>(sizeof(VALUE)*CHAR_BIT-1-width) > 0) {
+	return big_lshift(int2big(val), y);
+    }
+    val = val << width;
+    return int2inum(val);
+}
+
+static VALUE
+fix_rshift(x, y)
+    VALUE x, y;
+{
+    long i, val;
+
+    i = NUM2INT(y);
+    if (y < 32) {
+	val = RSHIFT(FIX2INT(x), i);
+	return INT2FIX(val);
+    }
+
+    return INT2FIX(0);
+}
+
+static VALUE
+fix_aref(fix, idx)
+    VALUE fix, idx;
+{
+    unsigned long val = FIX2INT(fix);
+    int i = FIX2INT(idx);
+
+    if (i < 0 || sizeof(VALUE)*CHAR_BIT-1 < i)
+	return INT2FIX(0);
+    if (val & (1<<i))
+	return INT2FIX(1);
+    return INT2FIX(0);
+}
+
+static VALUE
+fix_to_i(num)
+    VALUE num;
+{
+    return num;
+}
+
+static VALUE
+fix_to_f(num)
+    VALUE num;
+{
+    double val;
+
+    val = (double)FIX2INT(num);
+
+    return float_new(val);
+}
+
+static VALUE
+fix_type(fix)
+    VALUE fix;
+{
+    return str_new2("Fixnum");
+}
+
+static VALUE
+fix_abs(fix)
+    VALUE fix;
+{
+    int i = FIX2INT(fix);
+
+    if (i < 0) i = -i;
+
+    return int2inum(i);
+}
+
+static VALUE
+fix_id2name(fix)
+    VALUE fix;
+{
+    char *name = rb_id2name(FIX2UINT(fix));
+    if (name) return str_new2(name);
+    return Qnil;
+}
+
+static VALUE
+fix_succ(fix)
+    VALUE fix;
+{
+    int i = FIX2INT(fix) + 1;
+
+    return int2inum(i);
+}
+
+static VALUE
+fix_size(fix)
+    VALUE fix;
+{
+    return INT2FIX(sizeof(VALUE));
+}
+
+VALUE
+num_upto(from, to)
+    VALUE from, to;
+{
+    VALUE i = from;
+
+    for (;;) {
+	if (RTEST(rb_funcall(i, '>', 1, to))) break;
+	rb_yield(i);
+	i = rb_funcall(i, '+', 1, INT2FIX(1));
+    }
+    return from;
+}
+
+static VALUE
+num_downto(from, to)
+    VALUE from, to;
+{
+    VALUE i = from;
+
+    for (;;) {
+	if (RTEST(rb_funcall(i, '<', 1, to))) break;
+	rb_yield(i);
+	i = rb_funcall(i, '-', 1, INT2FIX(1));
+    }
+    return from;
+}
+
+static VALUE
+num_step(from, to, step)
+    VALUE from, to, step;
+{
+    VALUE i = from;
+    ID cmp;
+
+    if (step == INT2FIX(0)) {
+	IndexError("step cannot be 0");
+    }
+
+    if (RTEST(rb_funcall(step, '>', 1, INT2FIX(0)))) {
+	cmp = '>';
+    }
+    else {
+	cmp = '<';
+    }
+    for (;;) {
+	if (RTEST(rb_funcall(i, cmp, 1, to))) break;
+	rb_yield(i);
+	i = rb_funcall(i, '+', 1, step);
+    }
+    return from;
+}
+
+static VALUE
+num_dotimes(num)
+    VALUE num;
+{
+    VALUE i = INT2FIX(0);
+
+    for (;;) {
+	if (!RTEST(rb_funcall(i, '<', 1, num))) break;
+	rb_yield(i);
+	i = rb_funcall(i, '+', 1, INT2FIX(1));
+    }
+    return num;
+}
+
+VALUE
+fix_upto(from, to)
+    VALUE from, to;
+{
+    int i, end;
+
+    if (!FIXNUM_P(to)) return num_upto(from, to);
+    end = FIX2INT(to);
+    for (i = FIX2INT(from); i <= end; i++) {
+	rb_yield(INT2FIX(i));
+    }
+
+    return from;
+}
+
+static VALUE
+fix_downto(from, to)
+    VALUE from, to;
+{
+    int i, end;
+
+    if (!FIXNUM_P(to)) return num_downto(from, to);
+    end = FIX2INT(to);
+    for (i=FIX2INT(from); i >= end; i--) {
+	rb_yield(INT2FIX(i));
+    }
+
+    return from;
+}
+
+static VALUE
+fix_step(from, to, step)
+    VALUE from, to, step;
+{
+    int i, end, diff;
+
+    if (!FIXNUM_P(to) || !FIXNUM_P(step))
+	return num_step(from, to, step);
+
+    end = FIX2INT(to);
+    diff = FIX2INT(step);
+
+    if (diff == 0) {
+	ArgError("step cannot be 0");
+    }
+    else if (diff > 0) {
+	for (i=FIX2INT(from); i <= end; i+=diff) {
+	    rb_yield(INT2FIX(i));
+	}
+    }
+    else {
+	for (i=FIX2INT(from); i >= end; i+=diff) {
+	    rb_yield(INT2FIX(i));
+	}
+    }
+    return from;
+}
+
+static VALUE
+fix_dotimes(num)
+    VALUE num;
+{
+    int i, end;
+
+    end = FIX2INT(num);
+    for (i=0; i<end; i++) {
+	rb_yield(INT2FIX(i));
+    }
+    return num;
+}
+
+extern VALUE mComparable;
+extern VALUE eException;
+
+void
+Init_Numeric()
+{
+    coerce = rb_intern("coerce");
+    to_i = rb_intern("to_i");
+
+    eZeroDiv = rb_define_class("ZeroDivisionError", eException);
+    cNumeric = rb_define_class("Numeric", cObject);
+
+    rb_include_module(cNumeric, mComparable);
+    rb_define_method(cNumeric, "coerce", num_coerce, 1);
+
+    rb_define_method(cNumeric, "+@", num_uplus, 0);
+    rb_define_method(cNumeric, "-@", num_uminus, 0);
+    rb_define_method(cNumeric, "eql?", num_eql, 1);
+    rb_define_method(cNumeric, "divmod", num_divmod, 1);
+    rb_define_method(cNumeric, "abs", num_abs, 0);
+
+    rb_define_method(cNumeric, "upto", num_upto, 1);
+    rb_define_method(cNumeric, "downto", num_downto, 1);
+    rb_define_method(cNumeric, "step", num_step, 2);
+    rb_define_method(cNumeric, "times", num_dotimes, 0);
+    rb_define_method(cNumeric, "integer?", num_int_p, 0);
+    rb_define_method(cNumeric, "chr", num_chr, 0);
+
+    cInteger = rb_define_class("Integer", cNumeric);
+    rb_define_method(cInteger, "integer?", int_int_p, 0);
+    rb_define_method(cInteger, "succ", int_succ, 0);
+
+    cFixnum = rb_define_class("Fixnum", cInteger);
+
+    rb_undef_method(CLASS_OF(cFixnum), "new");
+
+    rb_define_method(cFixnum, "to_s", fix_to_s, 0);
+    rb_define_method(cFixnum, "type", fix_type, 0);
+
+    rb_define_method(cFixnum, "id2name", fix_id2name, 0);
+
+    rb_define_method(cFixnum, "-@", fix_uminus, 0);
+    rb_define_method(cFixnum, "+", fix_plus, 1);
+    rb_define_method(cFixnum, "-", fix_minus, 1);
+    rb_define_method(cFixnum, "*", fix_mul, 1);
+    rb_define_method(cFixnum, "/", fix_div, 1);
+    rb_define_method(cFixnum, "%", fix_mod, 1);
+    rb_define_method(cFixnum, "**", fix_pow, 1);
+
+    rb_define_method(cFixnum, "abs", fix_abs, 0);
+
+    rb_define_method(cFixnum, "==", fix_equal, 1);
+    rb_define_method(cFixnum, "<=>", fix_cmp, 1);
+    rb_define_method(cFixnum, ">",  fix_gt, 1);
+    rb_define_method(cFixnum, ">=", fix_ge, 1);
+    rb_define_method(cFixnum, "<",  fix_lt, 1);
+    rb_define_method(cFixnum, "<=", fix_le, 1);
+
+    rb_define_method(cFixnum, "~", fix_rev, 0);
+    rb_define_method(cFixnum, "&", fix_and, 1);
+    rb_define_method(cFixnum, "|", fix_or,  1);
+    rb_define_method(cFixnum, "^", fix_xor, 1);
+    rb_define_method(cFixnum, "[]", fix_aref, 1);
+
+    rb_define_method(cFixnum, "<<", fix_lshift, 1);
+    rb_define_method(cFixnum, ">>", fix_rshift, 1);
+
+    rb_define_method(cFixnum, "to_i", fix_to_i, 0);
+    rb_define_method(cFixnum, "to_f", fix_to_f, 0);
+
+    rb_define_method(cFixnum, "succ", fix_succ, 0);
+    rb_define_method(cFixnum, "size", fix_size, 0);
+
+    rb_define_method(cFixnum, "upto", fix_upto, 1);
+    rb_define_method(cFixnum, "downto", fix_downto, 1);
+    rb_define_method(cFixnum, "step", fix_step, 2);
+    rb_define_method(cFixnum, "times", fix_dotimes, 0);
+
+    cFloat  = rb_define_class("Float", cNumeric);
+
+    rb_undef_method(CLASS_OF(cFloat), "new");
+
+    rb_define_method(cFloat, "to_s", flo_to_s, 0);
+    rb_define_method(cFloat, "coerce", flo_coerce, 1);
+    rb_define_method(cFloat, "-@", flo_uminus, 0);
+    rb_define_method(cFloat, "+", flo_plus, 1);
+    rb_define_method(cFloat, "-", flo_minus, 1);
+    rb_define_method(cFloat, "*", flo_mul, 1);
+    rb_define_method(cFloat, "/", flo_div, 1);
+    rb_define_method(cFloat, "%", flo_mod, 1);
+    rb_define_method(cFloat, "**", flo_pow, 1);
+    rb_define_method(cFloat, "==", flo_eq, 1);
+    rb_define_method(cFloat, "<=>", flo_cmp, 1);
+    rb_define_method(cFloat, "eql?", flo_eql, 1);
+    rb_define_method(cFloat, "hash", flo_hash, 0);
+    rb_define_method(cFloat, "to_i", flo_to_i, 0);
+    rb_define_method(cFloat, "to_f", flo_to_f, 0);
+    rb_define_method(cFloat, "abs", flo_abs, 0);
+}
-- 
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