--- /dev/null
+/**********************************************************************
+
+ numeric.c -
+
+ $Author: yugui $
+ created at: Fri Aug 13 18:33:09 JST 1993
+
+ Copyright (C) 1993-2007 Yukihiro Matsumoto
+
+**********************************************************************/
+
+#include "ruby/ruby.h"
+#include "ruby/encoding.h"
+#include <ctype.h>
+#include <math.h>
+#include <stdio.h>
+
+#if defined(__FreeBSD__) && __FreeBSD__ < 4
+#include <floatingpoint.h>
+#endif
+
+#ifdef HAVE_FLOAT_H
+#include <float.h>
+#endif
+
+#ifdef HAVE_IEEEFP_H
+#include <ieeefp.h>
+#endif
+
+/* use IEEE 64bit values if not defined */
+#ifndef FLT_RADIX
+#define FLT_RADIX 2
+#endif
+#ifndef FLT_ROUNDS
+#define FLT_ROUNDS 1
+#endif
+#ifndef DBL_MIN
+#define DBL_MIN 2.2250738585072014e-308
+#endif
+#ifndef DBL_MAX
+#define DBL_MAX 1.7976931348623157e+308
+#endif
+#ifndef DBL_MIN_EXP
+#define DBL_MIN_EXP (-1021)
+#endif
+#ifndef DBL_MAX_EXP
+#define DBL_MAX_EXP 1024
+#endif
+#ifndef DBL_MIN_10_EXP
+#define DBL_MIN_10_EXP (-307)
+#endif
+#ifndef DBL_MAX_10_EXP
+#define DBL_MAX_10_EXP 308
+#endif
+#ifndef DBL_DIG
+#define DBL_DIG 15
+#endif
+#ifndef DBL_MANT_DIG
+#define DBL_MANT_DIG 53
+#endif
+#ifndef DBL_EPSILON
+#define DBL_EPSILON 2.2204460492503131e-16
+#endif
+
+#ifndef HAVE_ROUND
+double
+round(double x)
+{
+ double f;
+
+ if (x > 0.0) {
+ f = floor(x);
+ x = f + (x - f >= 0.5);
+ }
+ else if (x < 0.0) {
+ f = ceil(x);
+ x = f - (f - x >= 0.5);
+ }
+ return x;
+}
+#elif defined(__BEOS__)
+/* appears to be a bug in the BeOS headers */
+double round(double x);
+#endif
+
+static ID id_coerce, id_to_i, id_eq;
+
+VALUE rb_cNumeric;
+VALUE rb_cFloat;
+VALUE rb_cInteger;
+VALUE rb_cFixnum;
+
+VALUE rb_eZeroDivError;
+VALUE rb_eFloatDomainError;
+
+void
+rb_num_zerodiv(void)
+{
+ rb_raise(rb_eZeroDivError, "divided by 0");
+}
+
+
+/*
+ * call-seq:
+ * num.coerce(numeric) => array
+ *
+ * If <i>aNumeric</i> is the same type as <i>num</i>, returns an array
+ * containing <i>aNumeric</i> and <i>num</i>. Otherwise, returns an
+ * array with both <i>aNumeric</i> and <i>num</i> represented as
+ * <code>Float</code> objects. This coercion mechanism is used by
+ * Ruby to handle mixed-type numeric operations: it is intended to
+ * find a compatible common type between the two operands of the operator.
+ *
+ * 1.coerce(2.5) #=> [2.5, 1.0]
+ * 1.2.coerce(3) #=> [3.0, 1.2]
+ * 1.coerce(2) #=> [2, 1]
+ */
+
+static VALUE
+num_coerce(VALUE x, VALUE y)
+{
+ if (CLASS_OF(x) == CLASS_OF(y))
+ return rb_assoc_new(y, x);
+ x = rb_Float(x);
+ y = rb_Float(y);
+ return rb_assoc_new(y, x);
+}
+
+static VALUE
+coerce_body(VALUE *x)
+{
+ return rb_funcall(x[1], id_coerce, 1, x[0]);
+}
+
+static VALUE
+coerce_rescue(VALUE *x)
+{
+ volatile VALUE v = rb_inspect(x[1]);
+
+ rb_raise(rb_eTypeError, "%s can't be coerced into %s",
+ rb_special_const_p(x[1])?
+ RSTRING_PTR(v):
+ rb_obj_classname(x[1]),
+ rb_obj_classname(x[0]));
+ return Qnil; /* dummy */
+}
+
+static int
+do_coerce(VALUE *x, VALUE *y, int err)
+{
+ VALUE ary;
+ VALUE a[2];
+
+ a[0] = *x; a[1] = *y;
+
+ ary = rb_rescue(coerce_body, (VALUE)a, err?coerce_rescue:0, (VALUE)a);
+ if (TYPE(ary) != T_ARRAY || RARRAY_LEN(ary) != 2) {
+ if (err) {
+ rb_raise(rb_eTypeError, "coerce must return [x, y]");
+ }
+ return Qfalse;
+ }
+
+ *x = RARRAY_PTR(ary)[0];
+ *y = RARRAY_PTR(ary)[1];
+ return Qtrue;
+}
+
+VALUE
+rb_num_coerce_bin(VALUE x, VALUE y, ID func)
+{
+ do_coerce(&x, &y, Qtrue);
+ return rb_funcall(x, func, 1, y);
+}
+
+VALUE
+rb_num_coerce_cmp(VALUE x, VALUE y, ID func)
+{
+ if (do_coerce(&x, &y, Qfalse))
+ return rb_funcall(x, func, 1, y);
+ return Qnil;
+}
+
+VALUE
+rb_num_coerce_relop(VALUE x, VALUE y, ID func)
+{
+ VALUE c, x0 = x, y0 = y;
+
+ if (!do_coerce(&x, &y, Qfalse) ||
+ NIL_P(c = rb_funcall(x, func, 1, y))) {
+ rb_cmperr(x0, y0);
+ return Qnil; /* not reached */
+ }
+ return c;
+}
+
+/*
+ * Trap attempts to add methods to <code>Numeric</code> objects. Always
+ * raises a <code>TypeError</code>
+ */
+
+static VALUE
+num_sadded(VALUE x, VALUE name)
+{
+ const char *nstr = rb_id2name(rb_to_id(name));
+ /* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */
+ /* Numerics should be values; singleton_methods should not be added to them */
+ rb_remove_method(rb_singleton_class(x), nstr);
+ rb_raise(rb_eTypeError,
+ "can't define singleton method \"%s\" for %s",
+ nstr,
+ rb_obj_classname(x));
+ return Qnil; /* not reached */
+}
+
+/* :nodoc: */
+static VALUE
+num_init_copy(VALUE x, VALUE y)
+{
+ /* Numerics are immutable values, which should not be copied */
+ rb_raise(rb_eTypeError, "can't copy %s", rb_obj_classname(x));
+ return Qnil; /* not reached */
+}
+
+/*
+ * call-seq:
+ * +num => num
+ *
+ * Unary Plus---Returns the receiver's value.
+ */
+
+static VALUE
+num_uplus(VALUE num)
+{
+ return num;
+}
+
+/*
+ * call-seq:
+ * -num => numeric
+ *
+ * Unary Minus---Returns the receiver's value, negated.
+ */
+
+static VALUE
+num_uminus(VALUE num)
+{
+ VALUE zero;
+
+ zero = INT2FIX(0);
+ do_coerce(&zero, &num, Qtrue);
+
+ return rb_funcall(zero, '-', 1, num);
+}
+
+/*
+ * call-seq:
+ * num.quo(numeric) => result
+ *
+ * Returns most exact division (rational for integers, float for floats).
+ */
+
+static VALUE
+num_quo(VALUE x, VALUE y)
+{
+ return rb_funcall(rb_rational_raw1(x), '/', 1, y);
+}
+
+
+/*
+ * call-seq:
+ * num.fdiv(numeric) => float
+ *
+ * Returns float division.
+ */
+
+static VALUE
+num_fdiv(VALUE x, VALUE y)
+{
+ return rb_funcall(rb_Float(x), '/', 1, y);
+}
+
+
+static VALUE num_floor(VALUE num);
+
+/*
+ * call-seq:
+ * num.div(numeric) => integer
+ *
+ * Uses <code>/</code> to perform division, then converts the result to
+ * an integer. <code>Numeric</code> does not define the <code>/</code>
+ * operator; this is left to subclasses.
+ */
+
+static VALUE
+num_div(VALUE x, VALUE y)
+{
+ if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv();
+ return num_floor(rb_funcall(x, '/', 1, y));
+}
+
+
+/*
+ * call-seq:
+ * num.divmod( aNumeric ) -> anArray
+ *
+ * Returns an array containing the quotient and modulus obtained by
+ * dividing <i>num</i> by <i>aNumeric</i>. If <code>q, r =
+ * x.divmod(y)</code>, then
+ *
+ * q = floor(float(x)/float(y))
+ * x = q*y + r
+ *
+ * The quotient is rounded toward -infinity, as shown in the following table:
+ *
+ * a | b | a.divmod(b) | a/b | a.modulo(b) | a.remainder(b)
+ * ------+-----+---------------+---------+-------------+---------------
+ * 13 | 4 | 3, 1 | 3 | 1 | 1
+ * ------+-----+---------------+---------+-------------+---------------
+ * 13 | -4 | -4, -3 | -3 | -3 | 1
+ * ------+-----+---------------+---------+-------------+---------------
+ * -13 | 4 | -4, 3 | -4 | 3 | -1
+ * ------+-----+---------------+---------+-------------+---------------
+ * -13 | -4 | 3, -1 | 3 | -1 | -1
+ * ------+-----+---------------+---------+-------------+---------------
+ * 11.5 | 4 | 2, 3.5 | 2.875 | 3.5 | 3.5
+ * ------+-----+---------------+---------+-------------+---------------
+ * 11.5 | -4 | -3, -0.5 | -2.875 | -0.5 | 3.5
+ * ------+-----+---------------+---------+-------------+---------------
+ * -11.5 | 4 | -3, 0.5 | -2.875 | 0.5 | -3.5
+ * ------+-----+---------------+---------+-------------+---------------
+ * -11.5 | -4 | 2, -3.5 | 2.875 | -3.5 | -3.5
+ *
+ *
+ * Examples
+ *
+ * 11.divmod(3) #=> [3, 2]
+ * 11.divmod(-3) #=> [-4, -1]
+ * 11.divmod(3.5) #=> [3, 0.5]
+ * (-11).divmod(3.5) #=> [-4, 3.0]
+ * (11.5).divmod(3.5) #=> [3, 1.0]
+ */
+
+static VALUE
+num_divmod(VALUE x, VALUE y)
+{
+ return rb_assoc_new(num_div(x, y), rb_funcall(x, '%', 1, y));
+}
+
+/*
+ * call-seq:
+ * num.modulo(numeric) => result
+ *
+ * Equivalent to
+ * <i>num</i>.<code>divmod(</code><i>aNumeric</i><code>)[1]</code>.
+ */
+
+static VALUE
+num_modulo(VALUE x, VALUE y)
+{
+ return rb_funcall(x, '%', 1, y);
+}
+
+/*
+ * call-seq:
+ * num.remainder(numeric) => result
+ *
+ * If <i>num</i> and <i>numeric</i> have different signs, returns
+ * <em>mod</em>-<i>numeric</i>; otherwise, returns <em>mod</em>. In
+ * both cases <em>mod</em> is the value
+ * <i>num</i>.<code>modulo(</code><i>numeric</i><code>)</code>. The
+ * differences between <code>remainder</code> and modulo
+ * (<code>%</code>) are shown in the table under <code>Numeric#divmod</code>.
+ */
+
+static VALUE
+num_remainder(VALUE x, VALUE y)
+{
+ VALUE z = rb_funcall(x, '%', 1, y);
+
+ if ((!rb_equal(z, INT2FIX(0))) &&
+ ((RTEST(rb_funcall(x, '<', 1, INT2FIX(0))) &&
+ RTEST(rb_funcall(y, '>', 1, INT2FIX(0)))) ||
+ (RTEST(rb_funcall(x, '>', 1, INT2FIX(0))) &&
+ RTEST(rb_funcall(y, '<', 1, INT2FIX(0)))))) {
+ return rb_funcall(z, '-', 1, y);
+ }
+ return z;
+}
+
+/*
+ * call-seq:
+ * num.real? -> true or false
+ *
+ * Returns <code>true</code> if <i>num</i> is a <code>Real</code>
+ * (i.e. non <code>Complex</code>).
+ */
+
+static VALUE
+num_real_p(VALUE num)
+{
+ return Qtrue;
+}
+
+/*
+ * call-seq:
+ * num.integer? -> true or false
+ *
+ * Returns <code>true</code> if <i>num</i> is an <code>Integer</code>
+ * (including <code>Fixnum</code> and <code>Bignum</code>).
+ */
+
+static VALUE
+num_int_p(VALUE num)
+{
+ return Qfalse;
+}
+
+/*
+ * call-seq:
+ * num.abs => num or numeric
+ *
+ * Returns the absolute value of <i>num</i>.
+ *
+ * 12.abs #=> 12
+ * (-34.56).abs #=> 34.56
+ * -34.56.abs #=> 34.56
+ */
+
+static VALUE
+num_abs(VALUE num)
+{
+ if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) {
+ return rb_funcall(num, rb_intern("-@"), 0);
+ }
+ return num;
+}
+
+
+/*
+ * call-seq:
+ * num.zero? => true or false
+ *
+ * Returns <code>true</code> if <i>num</i> has a zero value.
+ */
+
+static VALUE
+num_zero_p(VALUE num)
+{
+ if (rb_equal(num, INT2FIX(0))) {
+ return Qtrue;
+ }
+ return Qfalse;
+}
+
+
+/*
+ * call-seq:
+ * num.nonzero? => num or nil
+ *
+ * Returns <i>num</i> if <i>num</i> is not zero, <code>nil</code>
+ * otherwise. This behavior is useful when chaining comparisons:
+ *
+ * a = %w( z Bb bB bb BB a aA Aa AA A )
+ * b = a.sort {|a,b| (a.downcase <=> b.downcase).nonzero? || a <=> b }
+ * b #=> ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"]
+ */
+
+static VALUE
+num_nonzero_p(VALUE num)
+{
+ if (RTEST(rb_funcall(num, rb_intern("zero?"), 0, 0))) {
+ return Qnil;
+ }
+ return num;
+}
+
+/*
+ * call-seq:
+ * num.to_int => integer
+ *
+ * Invokes the child class's <code>to_i</code> method to convert
+ * <i>num</i> to an integer.
+ */
+
+static VALUE
+num_to_int(VALUE num)
+{
+ return rb_funcall(num, id_to_i, 0, 0);
+}
+
+
+/********************************************************************
+ *
+ * Document-class: Float
+ *
+ * <code>Float</code> objects represent real numbers using the native
+ * architecture's double-precision floating point representation.
+ */
+
+VALUE
+rb_float_new(double d)
+{
+ NEWOBJ(flt, struct RFloat);
+ OBJSETUP(flt, rb_cFloat, T_FLOAT);
+
+ flt->float_value = d;
+ return (VALUE)flt;
+}
+
+/*
+ * call-seq:
+ * flt.to_s => string
+ *
+ * Returns a string containing a representation of self. As well as a
+ * fixed or exponential form of the number, the call may return
+ * ``<code>NaN</code>'', ``<code>Infinity</code>'', and
+ * ``<code>-Infinity</code>''.
+ */
+
+static VALUE
+flo_to_s(VALUE flt)
+{
+ char buf[32];
+ double value = RFLOAT_VALUE(flt);
+ char *p, *e;
+
+ if (isinf(value))
+ return rb_usascii_str_new2(value < 0 ? "-Infinity" : "Infinity");
+ else if(isnan(value))
+ return rb_usascii_str_new2("NaN");
+
+ snprintf(buf, sizeof(buf), "%#.15g", value); /* ensure to print decimal point */
+ if (!(e = strchr(buf, 'e'))) {
+ e = buf + strlen(buf);
+ }
+ if (!ISDIGIT(e[-1])) { /* reformat if ended with decimal point (ex 111111111111111.) */
+ snprintf(buf, sizeof(buf), "%#.14e", value);
+ if (!(e = strchr(buf, 'e'))) {
+ e = buf + strlen(buf);
+ }
+ }
+ p = e;
+ while (p[-1]=='0' && ISDIGIT(p[-2]))
+ p--;
+ memmove(p, e, strlen(e)+1);
+ return rb_usascii_str_new2(buf);
+}
+
+/*
+ * MISSING: documentation
+ */
+
+static VALUE
+flo_coerce(VALUE x, VALUE y)
+{
+ return rb_assoc_new(rb_Float(y), x);
+}
+
+/*
+ * call-seq:
+ * -float => float
+ *
+ * Returns float, negated.
+ */
+
+static VALUE
+flo_uminus(VALUE flt)
+{
+ return DBL2NUM(-RFLOAT_VALUE(flt));
+}
+
+/*
+ * call-seq:
+ * float + other => float
+ *
+ * Returns a new float which is the sum of <code>float</code>
+ * and <code>other</code>.
+ */
+
+static VALUE
+flo_plus(VALUE x, VALUE y)
+{
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
+ case T_BIGNUM:
+ return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
+ case T_FLOAT:
+ return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
+ default:
+ return rb_num_coerce_bin(x, y, '+');
+ }
+}
+
+/*
+ * call-seq:
+ * float + other => float
+ *
+ * Returns a new float which is the difference of <code>float</code>
+ * and <code>other</code>.
+ */
+
+static VALUE
+flo_minus(VALUE x, VALUE y)
+{
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
+ case T_BIGNUM:
+ return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
+ case T_FLOAT:
+ return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
+ default:
+ return rb_num_coerce_bin(x, y, '-');
+ }
+}
+
+/*
+ * call-seq:
+ * float * other => float
+ *
+ * Returns a new float which is the product of <code>float</code>
+ * and <code>other</code>.
+ */
+
+static VALUE
+flo_mul(VALUE x, VALUE y)
+{
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
+ case T_BIGNUM:
+ return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
+ case T_FLOAT:
+ return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y));
+ default:
+ return rb_num_coerce_bin(x, y, '*');
+ }
+}
+
+/*
+ * call-seq:
+ * float / other => float
+ *
+ * Returns a new float which is the result of dividing
+ * <code>float</code> by <code>other</code>.
+ */
+
+static VALUE
+flo_div(VALUE x, VALUE y)
+{
+ long f_y;
+ double d;
+
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ f_y = FIX2LONG(y);
+ return DBL2NUM(RFLOAT_VALUE(x) / (double)f_y);
+ case T_BIGNUM:
+ d = rb_big2dbl(y);
+ return DBL2NUM(RFLOAT_VALUE(x) / d);
+ case T_FLOAT:
+ return DBL2NUM(RFLOAT_VALUE(x) / RFLOAT_VALUE(y));
+ default:
+ return rb_num_coerce_bin(x, y, '/');
+ }
+}
+
+static VALUE
+flo_quo(VALUE x, VALUE y)
+{
+ return rb_funcall(x, '/', 1, y);
+}
+
+static void
+flodivmod(double x, double y, double *divp, double *modp)
+{
+ double div, mod;
+
+#ifdef HAVE_FMOD
+ mod = fmod(x, y);
+#else
+ {
+ double z;
+
+ modf(x/y, &z);
+ mod = x - z * y;
+ }
+#endif
+ if (isinf(x) && !isinf(y) && !isnan(y))
+ div = x;
+ else
+ div = (x - mod) / y;
+ if (y*mod < 0) {
+ mod += y;
+ div -= 1.0;
+ }
+ if (modp) *modp = mod;
+ if (divp) *divp = div;
+}
+
+
+/*
+ * call-seq:
+ * flt % other => float
+ * flt.modulo(other) => float
+ *
+ * Return the modulo after division of <code>flt</code> by <code>other</code>.
+ *
+ * 6543.21.modulo(137) #=> 104.21
+ * 6543.21.modulo(137.24) #=> 92.9299999999996
+ */
+
+static VALUE
+flo_mod(VALUE x, VALUE y)
+{
+ double fy, mod;
+
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ fy = (double)FIX2LONG(y);
+ break;
+ case T_BIGNUM:
+ fy = rb_big2dbl(y);
+ break;
+ case T_FLOAT:
+ fy = RFLOAT_VALUE(y);
+ break;
+ default:
+ return rb_num_coerce_bin(x, y, '%');
+ }
+ flodivmod(RFLOAT_VALUE(x), fy, 0, &mod);
+ return DBL2NUM(mod);
+}
+
+static VALUE
+dbl2ival(double d)
+{
+ if (FIXABLE(d)) {
+ d = round(d);
+ return LONG2FIX((long)d);
+ }
+ else if (isnan(d) || isinf(d)) {
+ /* special case: cannot return integer value */
+ return rb_float_new(d);
+ }
+ else {
+ return rb_dbl2big(d);
+ }
+}
+
+/*
+ * call-seq:
+ * flt.divmod(numeric) => array
+ *
+ * See <code>Numeric#divmod</code>.
+ */
+
+static VALUE
+flo_divmod(VALUE x, VALUE y)
+{
+ double fy, div, mod;
+ volatile VALUE a, b;
+
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ fy = (double)FIX2LONG(y);
+ break;
+ case T_BIGNUM:
+ fy = rb_big2dbl(y);
+ break;
+ case T_FLOAT:
+ fy = RFLOAT_VALUE(y);
+ break;
+ default:
+ return rb_num_coerce_bin(x, y, rb_intern("divmod"));
+ }
+ flodivmod(RFLOAT_VALUE(x), fy, &div, &mod);
+ a = dbl2ival(div);
+ b = DBL2NUM(mod);
+ return rb_assoc_new(a, b);
+}
+
+/*
+ * call-seq:
+ *
+ * flt ** other => float
+ *
+ * Raises <code>float</code> the <code>other</code> power.
+ */
+
+static VALUE
+flo_pow(VALUE x, VALUE y)
+{
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ return DBL2NUM(pow(RFLOAT_VALUE(x), (double)FIX2LONG(y)));
+ case T_BIGNUM:
+ return DBL2NUM(pow(RFLOAT_VALUE(x), rb_big2dbl(y)));
+ case T_FLOAT:
+ return DBL2NUM(pow(RFLOAT_VALUE(x), RFLOAT_VALUE(y)));
+ default:
+ return rb_num_coerce_bin(x, y, rb_intern("**"));
+ }
+}
+
+/*
+ * call-seq:
+ * num.eql?(numeric) => true or false
+ *
+ * Returns <code>true</code> if <i>num</i> and <i>numeric</i> are the
+ * same type and have equal values.
+ *
+ * 1 == 1.0 #=> true
+ * 1.eql?(1.0) #=> false
+ * (1.0).eql?(1.0) #=> true
+ */
+
+static VALUE
+num_eql(VALUE x, VALUE y)
+{
+ if (TYPE(x) != TYPE(y)) return Qfalse;
+
+ return rb_equal(x, y);
+}
+
+/*
+ * call-seq:
+ * num <=> other -> 0 or nil
+ *
+ * Returns zero if <i>num</i> equals <i>other</i>, <code>nil</code>
+ * otherwise.
+ */
+
+static VALUE
+num_cmp(VALUE x, VALUE y)
+{
+ if (x == y) return INT2FIX(0);
+ return Qnil;
+}
+
+static VALUE
+num_equal(VALUE x, VALUE y)
+{
+ if (x == y) return Qtrue;
+ return rb_funcall(y, id_eq, 1, x);
+}
+
+/*
+ * call-seq:
+ * flt == obj => true or false
+ *
+ * Returns <code>true</code> only if <i>obj</i> has the same value
+ * as <i>flt</i>. Contrast this with <code>Float#eql?</code>, which
+ * requires <i>obj</i> to be a <code>Float</code>.
+ *
+ * 1.0 == 1 #=> true
+ *
+ */
+
+static VALUE
+flo_eq(VALUE x, VALUE y)
+{
+ volatile double a, b;
+
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ b = FIX2LONG(y);
+ break;
+ case T_BIGNUM:
+ b = rb_big2dbl(y);
+ break;
+ case T_FLOAT:
+ b = RFLOAT_VALUE(y);
+ if (isnan(b)) return Qfalse;
+ break;
+ default:
+ return num_equal(x, y);
+ }
+ a = RFLOAT_VALUE(x);
+ if (isnan(a)) return Qfalse;
+ return (a == b)?Qtrue:Qfalse;
+}
+
+/*
+ * call-seq:
+ * flt.hash => integer
+ *
+ * Returns a hash code for this float.
+ */
+
+static VALUE
+flo_hash(VALUE num)
+{
+ double d;
+ int hash;
+
+ d = RFLOAT_VALUE(num);
+ hash = rb_memhash(&d, sizeof(d));
+ return INT2FIX(hash);
+}
+
+VALUE
+rb_dbl_cmp(double a, double b)
+{
+ if (isnan(a) || isnan(b)) return Qnil;
+ if (a == b) return INT2FIX(0);
+ if (a > b) return INT2FIX(1);
+ if (a < b) return INT2FIX(-1);
+ return Qnil;
+}
+
+/*
+ * call-seq:
+ * flt <=> numeric => -1, 0, +1
+ *
+ * Returns -1, 0, or +1 depending on whether <i>flt</i> is less than,
+ * equal to, or greater than <i>numeric</i>. This is the basis for the
+ * tests in <code>Comparable</code>.
+ */
+
+static VALUE
+flo_cmp(VALUE x, VALUE y)
+{
+ double a, b;
+
+ a = RFLOAT_VALUE(x);
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ b = (double)FIX2LONG(y);
+ break;
+
+ case T_BIGNUM:
+ b = rb_big2dbl(y);
+ break;
+
+ case T_FLOAT:
+ b = RFLOAT_VALUE(y);
+ break;
+
+ default:
+ return rb_num_coerce_cmp(x, y, rb_intern("<=>"));
+ }
+ return rb_dbl_cmp(a, b);
+}
+
+/*
+ * call-seq:
+ * flt > other => true or false
+ *
+ * <code>true</code> if <code>flt</code> is greater than <code>other</code>.
+ */
+
+static VALUE
+flo_gt(VALUE x, VALUE y)
+{
+ double a, b;
+
+ a = RFLOAT_VALUE(x);
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ b = (double)FIX2LONG(y);
+ break;
+
+ case T_BIGNUM:
+ b = rb_big2dbl(y);
+ break;
+
+ case T_FLOAT:
+ b = RFLOAT_VALUE(y);
+ if (isnan(b)) return Qfalse;
+ break;
+
+ default:
+ return rb_num_coerce_relop(x, y, '>');
+ }
+ if (isnan(a)) return Qfalse;
+ return (a > b)?Qtrue:Qfalse;
+}
+
+/*
+ * call-seq:
+ * flt >= other => true or false
+ *
+ * <code>true</code> if <code>flt</code> is greater than
+ * or equal to <code>other</code>.
+ */
+
+static VALUE
+flo_ge(VALUE x, VALUE y)
+{
+ double a, b;
+
+ a = RFLOAT_VALUE(x);
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ b = (double)FIX2LONG(y);
+ break;
+
+ case T_BIGNUM:
+ b = rb_big2dbl(y);
+ break;
+
+ case T_FLOAT:
+ b = RFLOAT_VALUE(y);
+ if (isnan(b)) return Qfalse;
+ break;
+
+ default:
+ return rb_num_coerce_relop(x, y, rb_intern(">="));
+ }
+ if (isnan(a)) return Qfalse;
+ return (a >= b)?Qtrue:Qfalse;
+}
+
+/*
+ * call-seq:
+ * flt < other => true or false
+ *
+ * <code>true</code> if <code>flt</code> is less than <code>other</code>.
+ */
+
+static VALUE
+flo_lt(VALUE x, VALUE y)
+{
+ double a, b;
+
+ a = RFLOAT_VALUE(x);
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ b = (double)FIX2LONG(y);
+ break;
+
+ case T_BIGNUM:
+ b = rb_big2dbl(y);
+ break;
+
+ case T_FLOAT:
+ b = RFLOAT_VALUE(y);
+ if (isnan(b)) return Qfalse;
+ break;
+
+ default:
+ return rb_num_coerce_relop(x, y, '<');
+ }
+ if (isnan(a)) return Qfalse;
+ return (a < b)?Qtrue:Qfalse;
+}
+
+/*
+ * call-seq:
+ * flt <= other => true or false
+ *
+ * <code>true</code> if <code>flt</code> is less than
+ * or equal to <code>other</code>.
+ */
+
+static VALUE
+flo_le(VALUE x, VALUE y)
+{
+ double a, b;
+
+ a = RFLOAT_VALUE(x);
+ switch (TYPE(y)) {
+ case T_FIXNUM:
+ b = (double)FIX2LONG(y);
+ break;
+
+ case T_BIGNUM:
+ b = rb_big2dbl(y);
+ break;
+
+ case T_FLOAT:
+ b = RFLOAT_VALUE(y);
+ if (isnan(b)) return Qfalse;
+ break;
+
+ default:
+ return rb_num_coerce_relop(x, y, rb_intern("<="));
+ }
+ if (isnan(a)) return Qfalse;
+ return (a <= b)?Qtrue:Qfalse;
+}
+
+/*
+ * call-seq:
+ * flt.eql?(obj) => true or false
+ *
+ * Returns <code>true</code> only if <i>obj</i> is a
+ * <code>Float</code> with the same value as <i>flt</i>. Contrast this
+ * with <code>Float#==</code>, which performs type conversions.
+ *
+ * 1.0.eql?(1) #=> false
+ */
+
+static VALUE
+flo_eql(VALUE x, VALUE y)
+{
+ if (TYPE(y) == T_FLOAT) {
+ double a = RFLOAT_VALUE(x);
+ double b = RFLOAT_VALUE(y);
+
+ if (isnan(a) || isnan(b)) return Qfalse;
+ if (a == b) return Qtrue;
+ }
+ return Qfalse;
+}
+
+/*
+ * call-seq:
+ * flt.to_f => flt
+ *
+ * As <code>flt</code> is already a float, returns <i>self</i>.
+ */
+
+static VALUE
+flo_to_f(VALUE num)
+{
+ return num;
+}
+
+/*
+ * call-seq:
+ * flt.abs => float
+ *
+ * Returns the absolute value of <i>flt</i>.
+ *
+ * (-34.56).abs #=> 34.56
+ * -34.56.abs #=> 34.56
+ *
+ */
+
+static VALUE
+flo_abs(VALUE flt)
+{
+ double val = fabs(RFLOAT_VALUE(flt));
+ return DBL2NUM(val);
+}
+
+/*
+ * call-seq:
+ * flt.zero? -> true or false
+ *
+ * Returns <code>true</code> if <i>flt</i> is 0.0.
+ *
+ */
+
+static VALUE
+flo_zero_p(VALUE num)
+{
+ if (RFLOAT_VALUE(num) == 0.0) {
+ return Qtrue;
+ }
+ return Qfalse;
+}
+
+/*
+ * call-seq:
+ * flt.nan? -> true or false
+ *
+ * Returns <code>true</code> if <i>flt</i> is an invalid IEEE floating
+ * point number.
+ *
+ * a = -1.0 #=> -1.0
+ * a.nan? #=> false
+ * a = 0.0/0.0 #=> NaN
+ * a.nan? #=> true
+ */
+
+static VALUE
+flo_is_nan_p(VALUE num)
+{
+ double value = RFLOAT_VALUE(num);
+
+ return isnan(value) ? Qtrue : Qfalse;
+}
+
+/*
+ * call-seq:
+ * flt.infinite? -> nil, -1, +1
+ *
+ * Returns <code>nil</code>, -1, or +1 depending on whether <i>flt</i>
+ * is finite, -infinity, or +infinity.
+ *
+ * (0.0).infinite? #=> nil
+ * (-1.0/0.0).infinite? #=> -1
+ * (+1.0/0.0).infinite? #=> 1
+ */
+
+static VALUE
+flo_is_infinite_p(VALUE num)
+{
+ double value = RFLOAT_VALUE(num);
+
+ if (isinf(value)) {
+ return INT2FIX( value < 0 ? -1 : 1 );
+ }
+
+ return Qnil;
+}
+
+/*
+ * call-seq:
+ * flt.finite? -> true or false
+ *
+ * Returns <code>true</code> if <i>flt</i> is a valid IEEE floating
+ * point number (it is not infinite, and <code>nan?</code> is
+ * <code>false</code>).
+ *
+ */
+
+static VALUE
+flo_is_finite_p(VALUE num)
+{
+ double value = RFLOAT_VALUE(num);
+
+#if HAVE_FINITE
+ if (!finite(value))
+ return Qfalse;
+#else
+ if (isinf(value) || isnan(value))
+ return Qfalse;
+#endif
+
+ return Qtrue;
+}
+
+/*
+ * call-seq:
+ * flt.floor => integer
+ *
+ * Returns the largest integer less than or equal to <i>flt</i>.
+ *
+ * 1.2.floor #=> 1
+ * 2.0.floor #=> 2
+ * (-1.2).floor #=> -2
+ * (-2.0).floor #=> -2
+ */
+
+static VALUE
+flo_floor(VALUE num)
+{
+ double f = floor(RFLOAT_VALUE(num));
+ long val;
+
+ if (!FIXABLE(f)) {
+ return rb_dbl2big(f);
+ }
+ val = f;
+ return LONG2FIX(val);
+}
+
+/*
+ * call-seq:
+ * flt.ceil => integer
+ *
+ * Returns the smallest <code>Integer</code> greater than or equal to
+ * <i>flt</i>.
+ *
+ * 1.2.ceil #=> 2
+ * 2.0.ceil #=> 2
+ * (-1.2).ceil #=> -1
+ * (-2.0).ceil #=> -2
+ */
+
+static VALUE
+flo_ceil(VALUE num)
+{
+ double f = ceil(RFLOAT_VALUE(num));
+ long val;
+
+ if (!FIXABLE(f)) {
+ return rb_dbl2big(f);
+ }
+ val = f;
+ return LONG2FIX(val);
+}
+
+/*
+ * call-seq:
+ * flt.round([ndigits]) => integer or float
+ *
+ * Rounds <i>flt</i> to a given precision in decimal digits (default 0 digits).
+ * Precision may be negative. Returns a a floating point number when ndigits
+ * is more than one.
+ *
+ * 1.5.round #=> 2
+ * (-1.5).round #=> -2
+ */
+
+static VALUE
+flo_round(int argc, VALUE *argv, VALUE num)
+{
+ VALUE nd;
+ double number, f;
+ int ndigits = 0, i;
+ long val;
+
+ if (argc > 0 && rb_scan_args(argc, argv, "01", &nd) == 1) {
+ ndigits = NUM2INT(nd);
+ }
+ number = RFLOAT_VALUE(num);
+ f = 1.0;
+ i = abs(ndigits);
+ while (--i >= 0)
+ f = f*10.0;
+
+ if (isinf(f)) {
+ if (ndigits < 0) number = 0;
+ }
+ else {
+ if (ndigits < 0) number /= f;
+ else number *= f;
+ number = round(number);
+ if (ndigits < 0) number *= f;
+ else number /= f;
+ }
+
+ if (ndigits > 0) return DBL2NUM(number);
+
+ if (!FIXABLE(number)) {
+ return rb_dbl2big(number);
+ }
+ val = number;
+ return LONG2FIX(val);
+}
+
+/*
+ * call-seq:
+ * flt.to_i => integer
+ * flt.to_int => integer
+ * flt.truncate => integer
+ *
+ * Returns <i>flt</i> truncated to an <code>Integer</code>.
+ */
+
+static VALUE
+flo_truncate(VALUE num)
+{
+ double f = RFLOAT_VALUE(num);
+ long val;
+
+ if (f > 0.0) f = floor(f);
+ if (f < 0.0) f = ceil(f);
+
+ if (!FIXABLE(f)) {
+ return rb_dbl2big(f);
+ }
+ val = f;
+ return LONG2FIX(val);
+}
+
+
+/*
+ * call-seq:
+ * num.floor => integer
+ *
+ * Returns the largest integer less than or equal to <i>num</i>.
+ * <code>Numeric</code> implements this by converting <i>anInteger</i>
+ * to a <code>Float</code> and invoking <code>Float#floor</code>.
+ *
+ * 1.floor #=> 1
+ * (-1).floor #=> -1
+ */
+
+static VALUE
+num_floor(VALUE num)
+{
+ return flo_floor(rb_Float(num));
+}
+
+
+/*
+ * call-seq:
+ * num.ceil => integer
+ *
+ * Returns the smallest <code>Integer</code> greater than or equal to
+ * <i>num</i>. Class <code>Numeric</code> achieves this by converting
+ * itself to a <code>Float</code> then invoking
+ * <code>Float#ceil</code>.
+ *
+ * 1.ceil #=> 1
+ * 1.2.ceil #=> 2
+ * (-1.2).ceil #=> -1
+ * (-1.0).ceil #=> -1
+ */
+
+static VALUE
+num_ceil(VALUE num)
+{
+ return flo_ceil(rb_Float(num));
+}
+
+/*
+ * call-seq:
+ * num.round([ndigits]) => integer or float
+ *
+ * Rounds <i>num</i> to a given precision in decimal digits (default 0 digits).
+ * Precision may be negative. Returns a a floating point number when ndigits
+ * is more than one. <code>Numeric</code> implements this by converting itself
+ * to a <code>Float</code> and invoking <code>Float#round</code>.
+ */
+
+static VALUE
+num_round(int argc, VALUE* argv, VALUE num)
+{
+ return flo_round(argc, argv, rb_Float(num));
+}
+
+/*
+ * call-seq:
+ * num.truncate => integer
+ *
+ * Returns <i>num</i> truncated to an integer. <code>Numeric</code>
+ * implements this by converting its value to a float and invoking
+ * <code>Float#truncate</code>.
+ */
+
+static VALUE
+num_truncate(VALUE num)
+{
+ return flo_truncate(rb_Float(num));
+}
+
+
+/*
+ * call-seq:
+ * num.step(limit, step ) {|i| block } => num
+ *
+ * Invokes <em>block</em> with the sequence of numbers starting at
+ * <i>num</i>, incremented by <i>step</i> on each call. The loop
+ * finishes when the value to be passed to the block is greater than
+ * <i>limit</i> (if <i>step</i> is positive) or less than
+ * <i>limit</i> (if <i>step</i> is negative). If all the arguments are
+ * integers, the loop operates using an integer counter. If any of the
+ * arguments are floating point numbers, all are converted to floats,
+ * and the loop is executed <i>floor(n + n*epsilon)+ 1</i> times,
+ * where <i>n = (limit - num)/step</i>. Otherwise, the loop
+ * starts at <i>num</i>, uses either the <code><</code> or
+ * <code>></code> operator to compare the counter against
+ * <i>limit</i>, and increments itself using the <code>+</code>
+ * operator.
+ *
+ * 1.step(10, 2) { |i| print i, " " }
+ * Math::E.step(Math::PI, 0.2) { |f| print f, " " }
+ *
+ * <em>produces:</em>
+ *
+ * 1 3 5 7 9
+ * 2.71828182845905 2.91828182845905 3.11828182845905
+ */
+
+static VALUE
+num_step(int argc, VALUE *argv, VALUE from)
+{
+ VALUE to, step;
+
+ RETURN_ENUMERATOR(from, argc, argv);
+ if (argc == 1) {
+ to = argv[0];
+ step = INT2FIX(1);
+ }
+ else {
+ if (argc == 2) {
+ to = argv[0];
+ step = argv[1];
+ }
+ else {
+ rb_raise(rb_eArgError, "wrong number of arguments");
+ }
+ if (rb_equal(step, INT2FIX(0))) {
+ rb_raise(rb_eArgError, "step can't be 0");
+ }
+ }
+
+ if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) {
+ long i, end, diff;
+
+ i = FIX2LONG(from);
+ end = FIX2LONG(to);
+ diff = FIX2LONG(step);
+
+ if (diff > 0) {
+ while (i <= end) {
+ rb_yield(LONG2FIX(i));
+ i += diff;
+ }
+ }
+ else {
+ while (i >= end) {
+ rb_yield(LONG2FIX(i));
+ i += diff;
+ }
+ }
+ }
+ else if (TYPE(from) == T_FLOAT || TYPE(to) == T_FLOAT || TYPE(step) == T_FLOAT) {
+ const double epsilon = DBL_EPSILON;
+ double beg = NUM2DBL(from);
+ double end = NUM2DBL(to);
+ double unit = NUM2DBL(step);
+ double n = (end - beg)/unit;
+ double err = (fabs(beg) + fabs(end) + fabs(end-beg)) / fabs(unit) * epsilon;
+ long i;
+
+ if (isinf(unit)) {
+ if (unit > 0) rb_yield(DBL2NUM(beg));
+ }
+ else {
+ if (err>0.5) err=0.5;
+ n = floor(n + err) + 1;
+ for (i=0; i<n; i++) {
+ rb_yield(DBL2NUM(i*unit+beg));
+ }
+ }
+ }
+ else {
+ VALUE i = from;
+ ID cmp;
+
+ 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;
+}
+
+SIGNED_VALUE
+rb_num2long(VALUE val)
+{
+ again:
+ if (NIL_P(val)) {
+ rb_raise(rb_eTypeError, "no implicit conversion from nil to integer");
+ }
+
+ if (FIXNUM_P(val)) return FIX2LONG(val);
+
+ switch (TYPE(val)) {
+ case T_FLOAT:
+ if (RFLOAT_VALUE(val) <= (double)LONG_MAX
+ && RFLOAT_VALUE(val) >= (double)LONG_MIN) {
+ return (SIGNED_VALUE)(RFLOAT_VALUE(val));
+ }
+ else {
+ char buf[24];
+ char *s;
+
+ snprintf(buf, sizeof(buf), "%-.10g", RFLOAT_VALUE(val));
+ if ((s = strchr(buf, ' ')) != 0) *s = '\0';
+ rb_raise(rb_eRangeError, "float %s out of range of integer", buf);
+ }
+
+ case T_BIGNUM:
+ return rb_big2long(val);
+
+ default:
+ val = rb_to_int(val);
+ goto again;
+ }
+}
+
+VALUE
+rb_num2ulong(VALUE val)
+{
+ if (TYPE(val) == T_BIGNUM) {
+ return rb_big2ulong(val);
+ }
+ return (VALUE)rb_num2long(val);
+}
+
+#if SIZEOF_INT < SIZEOF_VALUE
+static void
+check_int(SIGNED_VALUE num)
+{
+ const char *s;
+
+ if (num < INT_MIN) {
+ s = "small";
+ }
+ else if (num > INT_MAX) {
+ s = "big";
+ }
+ else {
+ return;
+ }
+ rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too %s to convert to `int'", num, s);
+}
+
+static void
+check_uint(VALUE num, VALUE sign)
+{
+ static const VALUE mask = ~(VALUE)UINT_MAX;
+
+ if (RTEST(sign)) {
+ /* minus */
+ if ((num & mask) != mask || (num & ~mask) <= INT_MAX + 1UL)
+ rb_raise(rb_eRangeError, "integer %"PRIdVALUE " too small to convert to `unsigned int'", num);
+ }
+ else {
+ /* plus */
+ if ((num & mask) != 0)
+ rb_raise(rb_eRangeError, "integer %"PRIuVALUE " too big to convert to `unsigned int'", num);
+ }
+}
+
+long
+rb_num2int(VALUE val)
+{
+ long num = rb_num2long(val);
+
+ check_int(num);
+ return num;
+}
+
+long
+rb_fix2int(VALUE val)
+{
+ long num = FIXNUM_P(val)?FIX2LONG(val):rb_num2long(val);
+
+ check_int(num);
+ return num;
+}
+
+unsigned long
+rb_num2uint(VALUE val)
+{
+ unsigned long num = rb_num2ulong(val);
+
+ check_uint(num, rb_funcall(val, '<', 1, INT2FIX(0)));
+ return num;
+}
+
+unsigned long
+rb_fix2uint(VALUE val)
+{
+ unsigned long num;
+
+ if (!FIXNUM_P(val)) {
+ return rb_num2uint(val);
+ }
+ num = FIX2ULONG(val);
+
+ check_uint(num, rb_funcall(val, '<', 1, INT2FIX(0)));
+ return num;
+}
+#else
+long
+rb_num2int(VALUE val)
+{
+ return rb_num2long(val);
+}
+
+long
+rb_fix2int(VALUE val)
+{
+ return FIX2INT(val);
+}
+#endif
+
+VALUE
+rb_num2fix(VALUE val)
+{
+ long v;
+
+ if (FIXNUM_P(val)) return val;
+
+ v = rb_num2long(val);
+ if (!FIXABLE(v))
+ rb_raise(rb_eRangeError, "integer %"PRIdVALUE " out of range of fixnum", v);
+ return LONG2FIX(v);
+}
+
+#if HAVE_LONG_LONG
+
+LONG_LONG
+rb_num2ll(VALUE val)
+{
+ if (NIL_P(val)) {
+ rb_raise(rb_eTypeError, "no implicit conversion from nil");
+ }
+
+ if (FIXNUM_P(val)) return (LONG_LONG)FIX2LONG(val);
+
+ switch (TYPE(val)) {
+ case T_FLOAT:
+ if (RFLOAT_VALUE(val) <= (double)LLONG_MAX
+ && RFLOAT_VALUE(val) >= (double)LLONG_MIN) {
+ return (LONG_LONG)(RFLOAT_VALUE(val));
+ }
+ else {
+ char buf[24];
+ char *s;
+
+ snprintf(buf, sizeof(buf), "%-.10g", RFLOAT_VALUE(val));
+ if ((s = strchr(buf, ' ')) != 0) *s = '\0';
+ rb_raise(rb_eRangeError, "float %s out of range of long long", buf);
+ }
+
+ case T_BIGNUM:
+ return rb_big2ll(val);
+
+ case T_STRING:
+ rb_raise(rb_eTypeError, "no implicit conversion from string");
+ return Qnil; /* not reached */
+
+ case T_TRUE:
+ case T_FALSE:
+ rb_raise(rb_eTypeError, "no implicit conversion from boolean");
+ return Qnil; /* not reached */
+
+ default:
+ val = rb_to_int(val);
+ return NUM2LL(val);
+ }
+}
+
+unsigned LONG_LONG
+rb_num2ull(VALUE val)
+{
+ if (TYPE(val) == T_BIGNUM) {
+ return rb_big2ull(val);
+ }
+ return (unsigned LONG_LONG)rb_num2ll(val);
+}
+
+#endif /* HAVE_LONG_LONG */
+
+static VALUE
+num_numerator(VALUE num)
+{
+ return rb_funcall(rb_Rational1(num), rb_intern("numerator"), 0);
+}
+
+static VALUE
+num_denominator(VALUE num)
+{
+ return rb_funcall(rb_Rational1(num), rb_intern("denominator"), 0);
+}
+
+/*
+ * Document-class: Integer
+ *
+ * <code>Integer</code> is the basis for the two concrete classes that
+ * hold whole numbers, <code>Bignum</code> and <code>Fixnum</code>.
+ *
+ */
+
+
+/*
+ * call-seq:
+ * int.to_i => int
+ * int.to_int => int
+ * int.floor => int
+ * int.ceil => int
+ * int.round => int
+ * int.truncate => int
+ *
+ * As <i>int</i> is already an <code>Integer</code>, all these
+ * methods simply return the receiver.
+ */
+
+static VALUE
+int_to_i(VALUE num)
+{
+ return num;
+}
+
+/*
+ * call-seq:
+ * int.integer? -> true
+ *
+ * Always returns <code>true</code>.
+ */
+
+static VALUE
+int_int_p(VALUE num)
+{
+ return Qtrue;
+}
+
+/*
+ * call-seq:
+ * int.odd? -> true or false
+ *
+ * Returns <code>true</code> if <i>int</i> is an odd number.
+ */
+
+static VALUE
+int_odd_p(VALUE num)
+{
+ if (rb_funcall(num, '%', 1, INT2FIX(2)) != INT2FIX(0)) {
+ return Qtrue;
+ }
+ return Qfalse;
+}
+
+/*
+ * call-seq:
+ * int.even? -> true or false
+ *
+ * Returns <code>true</code> if <i>int</i> is an even number.
+ */
+
+static VALUE
+int_even_p(VALUE num)
+{
+ if (rb_funcall(num, '%', 1, INT2FIX(2)) == INT2FIX(0)) {
+ return Qtrue;
+ }
+ return Qfalse;
+}
+
+/*
+ * call-seq:
+ * fixnum.next => integer
+ * fixnum.succ => integer
+ *
+ * Returns the <code>Integer</code> equal to <i>int</i> + 1.
+ *
+ * 1.next #=> 2
+ * (-1).next #=> 0
+ */
+
+static VALUE
+fix_succ(VALUE num)
+{
+ long i = FIX2LONG(num) + 1;
+ return LONG2NUM(i);
+}
+
+/*
+ * call-seq:
+ * int.next => integer
+ * int.succ => integer
+ *
+ * Returns the <code>Integer</code> equal to <i>int</i> + 1.
+ *
+ * 1.next #=> 2
+ * (-1).next #=> 0
+ */
+
+static VALUE
+int_succ(VALUE num)
+{
+ if (FIXNUM_P(num)) {
+ long i = FIX2LONG(num) + 1;
+ return LONG2NUM(i);
+ }
+ return rb_funcall(num, '+', 1, INT2FIX(1));
+}
+
+/*
+ * call-seq:
+ * int.pred => integer
+ *
+ * Returns the <code>Integer</code> equal to <i>int</i> - 1.
+ *
+ * 1.pred #=> 0
+ * (-1).pred #=> -2
+ */
+
+static VALUE
+int_pred(VALUE num)
+{
+ if (FIXNUM_P(num)) {
+ long i = FIX2LONG(num) - 1;
+ return LONG2NUM(i);
+ }
+ return rb_funcall(num, '-', 1, INT2FIX(1));
+}
+
+/*
+ * call-seq:
+ * int.chr([encoding]) => string
+ *
+ * Returns a string containing the character represented by the
+ * receiver's value according to +encoding+.
+ *
+ * 65.chr #=> "A"
+ * 230.chr #=> "\346"
+ * 255.chr(Encoding::UTF_8) #=> "\303\277"
+ */
+
+static VALUE
+int_chr(int argc, VALUE *argv, VALUE num)
+{
+ char c;
+ int n;
+ long i = NUM2LONG(num);
+ rb_encoding *enc;
+ VALUE str;
+
+ switch (argc) {
+ case 0:
+ if (i < 0 || 0xff < i) {
+ out_of_range:
+ rb_raise(rb_eRangeError, "%"PRIdVALUE " out of char range", i);
+ }
+ c = i;
+ if (i < 0x80) {
+ return rb_usascii_str_new(&c, 1);
+ }
+ else {
+ return rb_str_new(&c, 1);
+ }
+ case 1:
+ break;
+ default:
+ rb_raise(rb_eArgError, "wrong number of arguments (%d for 0 or 1)", argc);
+ break;
+ }
+ enc = rb_to_encoding(argv[0]);
+ if (!enc) enc = rb_ascii8bit_encoding();
+ if (i < 0 || (n = rb_enc_codelen(i, enc)) <= 0) goto out_of_range;
+ str = rb_enc_str_new(0, n, enc);
+ rb_enc_mbcput(i, RSTRING_PTR(str), enc);
+ return str;
+}
+
+/*
+ * call-seq:
+ * int.ord => int
+ *
+ * Returns the int itself.
+ *
+ * ?a.ord #=> 97
+ *
+ * This method is intended for compatibility to
+ * character constant in Ruby 1.9.
+ * For example, ?a.ord returns 97 both in 1.8 and 1.9.
+ */
+
+static VALUE
+int_ord(num)
+ VALUE num;
+{
+ return num;
+}
+
+static VALUE
+int_numerator(VALUE num)
+{
+ return num;
+}
+
+static VALUE
+int_denominator(VALUE num)
+{
+ return INT2FIX(1);
+}
+
+/********************************************************************
+ *
+ * Document-class: Fixnum
+ *
+ * A <code>Fixnum</code> holds <code>Integer</code> values that can be
+ * represented in a native machine word (minus 1 bit). If any operation
+ * on a <code>Fixnum</code> exceeds this range, the value is
+ * automatically converted to a <code>Bignum</code>.
+ *
+ * <code>Fixnum</code> objects have immediate value. This means that
+ * when they are assigned or passed as parameters, the actual object is
+ * passed, rather than a reference to that object. Assignment does not
+ * alias <code>Fixnum</code> objects. There is effectively only one
+ * <code>Fixnum</code> object instance for any given integer value, so,
+ * for example, you cannot add a singleton method to a
+ * <code>Fixnum</code>.
+ */
+
+
+/*
+ * call-seq:
+ * -fix => integer
+ *
+ * Negates <code>fix</code> (which might return a Bignum).
+ */
+
+static VALUE
+fix_uminus(VALUE num)
+{
+ return LONG2NUM(-FIX2LONG(num));
+}
+
+VALUE
+rb_fix2str(VALUE x, int base)
+{
+ extern const char ruby_digitmap[];
+ char buf[SIZEOF_VALUE*CHAR_BIT + 2], *b = buf + sizeof buf;
+ long val = FIX2LONG(x);
+ int neg = 0;
+
+ if (base < 2 || 36 < base) {
+ rb_raise(rb_eArgError, "invalid radix %d", base);
+ }
+ if (val == 0) {
+ return rb_usascii_str_new2("0");
+ }
+ if (val < 0) {
+ val = -val;
+ neg = 1;
+ }
+ *--b = '\0';
+ do {
+ *--b = ruby_digitmap[(int)(val % base)];
+ } while (val /= base);
+ if (neg) {
+ *--b = '-';
+ }
+
+ return rb_usascii_str_new2(b);
+}
+
+/*
+ * call-seq:
+ * fix.to_s( base=10 ) -> aString
+ *
+ * Returns a string containing the representation of <i>fix</i> radix
+ * <i>base</i> (between 2 and 36).
+ *
+ * 12345.to_s #=> "12345"
+ * 12345.to_s(2) #=> "11000000111001"
+ * 12345.to_s(8) #=> "30071"
+ * 12345.to_s(10) #=> "12345"
+ * 12345.to_s(16) #=> "3039"
+ * 12345.to_s(36) #=> "9ix"
+ *
+ */
+static VALUE
+fix_to_s(int argc, VALUE *argv, VALUE x)
+{
+ int base;
+
+ if (argc == 0) base = 10;
+ else {
+ VALUE b;
+
+ rb_scan_args(argc, argv, "01", &b);
+ base = NUM2INT(b);
+ }
+
+ return rb_fix2str(x, base);
+}
+
+/*
+ * call-seq:
+ * fix + numeric => numeric_result
+ *
+ * Performs addition: the class of the resulting object depends on
+ * the class of <code>numeric</code> and on the magnitude of the
+ * result.
+ */
+
+static VALUE
+fix_plus(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(y)) {
+ long a, b, c;
+ VALUE r;
+
+ a = FIX2LONG(x);
+ b = FIX2LONG(y);
+ c = a + b;
+ r = LONG2NUM(c);
+
+ return r;
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ return rb_big_plus(y, x);
+ case T_FLOAT:
+ return DBL2NUM((double)FIX2LONG(x) + RFLOAT_VALUE(y));
+ default:
+ return rb_num_coerce_bin(x, y, '+');
+ }
+}
+
+/*
+ * call-seq:
+ * fix - numeric => numeric_result
+ *
+ * Performs subtraction: the class of the resulting object depends on
+ * the class of <code>numeric</code> and on the magnitude of the
+ * result.
+ */
+
+static VALUE
+fix_minus(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(y)) {
+ long a, b, c;
+ VALUE r;
+
+ a = FIX2LONG(x);
+ b = FIX2LONG(y);
+ c = a - b;
+ r = LONG2NUM(c);
+
+ return r;
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ x = rb_int2big(FIX2LONG(x));
+ return rb_big_minus(x, y);
+ case T_FLOAT:
+ return DBL2NUM((double)FIX2LONG(x) - RFLOAT_VALUE(y));
+ default:
+ return rb_num_coerce_bin(x, y, '-');
+ }
+}
+
+#define SQRT_LONG_MAX ((SIGNED_VALUE)1<<((SIZEOF_LONG*CHAR_BIT-1)/2))
+/*tests if N*N would overflow*/
+#define FIT_SQRT_LONG(n) (((n)<SQRT_LONG_MAX)&&((n)>=-SQRT_LONG_MAX))
+
+/*
+ * call-seq:
+ * fix * numeric => numeric_result
+ *
+ * Performs multiplication: the class of the resulting object depends on
+ * the class of <code>numeric</code> and on the magnitude of the
+ * result.
+ */
+
+static VALUE
+fix_mul(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(y)) {
+#ifdef __HP_cc
+/* avoids an optimization bug of HP aC++/ANSI C B3910B A.06.05 [Jul 25 2005] */
+ volatile
+#endif
+ SIGNED_VALUE a, b;
+#if SIZEOF_VALUE * 2 <= SIZEOF_LONG_LONG
+ LONG_LONG d;
+#else
+ SIGNED_VALUE c;
+ VALUE r;
+#endif
+
+ a = FIX2LONG(x);
+ b = FIX2LONG(y);
+
+#if SIZEOF_VALUE * 2 <= SIZEOF_LONG_LONG
+ d = (LONG_LONG)a * b;
+ if (FIXABLE(d)) return LONG2FIX(d);
+ return rb_ll2inum(d);
+#else
+ if (FIT_SQRT_LONG(a) && FIT_SQRT_LONG(b))
+ return LONG2FIX(a*b);
+ c = a * b;
+ r = LONG2FIX(c);
+
+ if (a == 0) return x;
+ if (FIX2LONG(r) != c || c/a != b) {
+ r = rb_big_mul(rb_int2big(a), rb_int2big(b));
+ }
+ return r;
+#endif
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ return rb_big_mul(y, x);
+ case T_FLOAT:
+ return DBL2NUM((double)FIX2LONG(x) * RFLOAT_VALUE(y));
+ default:
+ return rb_num_coerce_bin(x, y, '*');
+ }
+}
+
+static void
+fixdivmod(long x, long y, long *divp, long *modp)
+{
+ long div, mod;
+
+ if (y == 0) rb_num_zerodiv();
+ if (y < 0) {
+ if (x < 0)
+ div = -x / -y;
+ else
+ div = - (x / -y);
+ }
+ else {
+ if (x < 0)
+ div = - (-x / y);
+ else
+ div = x / y;
+ }
+ mod = x - div*y;
+ if ((mod < 0 && y > 0) || (mod > 0 && y < 0)) {
+ mod += y;
+ div -= 1;
+ }
+ if (divp) *divp = div;
+ if (modp) *modp = mod;
+}
+
+/*
+ * call-seq:
+ * fix.fdiv(numeric) => float
+ *
+ * Returns the floating point result of dividing <i>fix</i> by
+ * <i>numeric</i>.
+ *
+ * 654321.fdiv(13731) #=> 47.6528293642124
+ * 654321.fdiv(13731.24) #=> 47.6519964693647
+ *
+ */
+
+static VALUE
+fix_fdiv(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(y)) {
+ return DBL2NUM((double)FIX2LONG(x) / (double)FIX2LONG(y));
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ return DBL2NUM((double)FIX2LONG(x) / rb_big2dbl(y));
+ case T_FLOAT:
+ return DBL2NUM((double)FIX2LONG(x) / RFLOAT_VALUE(y));
+ default:
+ return rb_num_coerce_bin(x, y, rb_intern("fdiv"));
+ }
+}
+
+static VALUE
+fix_divide(VALUE x, VALUE y, ID op)
+{
+ if (FIXNUM_P(y)) {
+ long div;
+
+ fixdivmod(FIX2LONG(x), FIX2LONG(y), &div, 0);
+ return LONG2NUM(div);
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ x = rb_int2big(FIX2LONG(x));
+ return rb_big_div(x, y);
+ case T_FLOAT:
+ {
+ double div;
+
+ if (op == '/') {
+ div = (double)FIX2LONG(x) / RFLOAT_VALUE(y);
+ return DBL2NUM(div);
+ }
+ else {
+ if (RFLOAT_VALUE(y) == 0) rb_num_zerodiv();
+ div = (double)FIX2LONG(x) / RFLOAT_VALUE(y);
+ return rb_dbl2big(floor(div));
+ }
+ }
+ default:
+ return rb_num_coerce_bin(x, y, op);
+ }
+}
+
+/*
+ * call-seq:
+ * fix / numeric => numeric_result
+ *
+ * Performs division: the class of the resulting object depends on
+ * the class of <code>numeric</code> and on the magnitude of the
+ * result.
+ */
+
+static VALUE
+fix_div(VALUE x, VALUE y)
+{
+ return fix_divide(x, y, '/');
+}
+
+/*
+ * call-seq:
+ * fix.div(numeric) => numeric_result
+ *
+ * Performs integer division: returns integer value.
+ */
+
+static VALUE
+fix_idiv(VALUE x, VALUE y)
+{
+ return fix_divide(x, y, rb_intern("div"));
+}
+
+/*
+ * call-seq:
+ * fix % other => Numeric
+ * fix.modulo(other) => Numeric
+ *
+ * Returns <code>fix</code> modulo <code>other</code>.
+ * See <code>Numeric.divmod</code> for more information.
+ */
+
+static VALUE
+fix_mod(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(y)) {
+ long mod;
+
+ fixdivmod(FIX2LONG(x), FIX2LONG(y), 0, &mod);
+ return LONG2NUM(mod);
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ x = rb_int2big(FIX2LONG(x));
+ return rb_big_modulo(x, y);
+ case T_FLOAT:
+ {
+ double mod;
+
+ flodivmod((double)FIX2LONG(x), RFLOAT_VALUE(y), 0, &mod);
+ return DBL2NUM(mod);
+ }
+ default:
+ return rb_num_coerce_bin(x, y, '%');
+ }
+}
+
+/*
+ * call-seq:
+ * fix.divmod(numeric) => array
+ *
+ * See <code>Numeric#divmod</code>.
+ */
+static VALUE
+fix_divmod(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(y)) {
+ long div, mod;
+
+ fixdivmod(FIX2LONG(x), FIX2LONG(y), &div, &mod);
+
+ return rb_assoc_new(LONG2NUM(div), LONG2NUM(mod));
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ x = rb_int2big(FIX2LONG(x));
+ return rb_big_divmod(x, y);
+ case T_FLOAT:
+ {
+ double div, mod;
+ volatile VALUE a, b;
+
+ flodivmod((double)FIX2LONG(x), RFLOAT_VALUE(y), &div, &mod);
+ a = dbl2ival(div);
+ b = DBL2NUM(mod);
+ return rb_assoc_new(a, b);
+ }
+ default:
+ return rb_num_coerce_bin(x, y, rb_intern("divmod"));
+ }
+}
+
+static VALUE
+int_pow(long x, unsigned long y)
+{
+ int neg = x < 0;
+ long z = 1;
+
+ if (neg) x = -x;
+ if (y & 1)
+ z = x;
+ else
+ neg = 0;
+ y &= ~1;
+ do {
+ while (y % 2 == 0) {
+ if (!FIT_SQRT_LONG(x)) {
+ VALUE v;
+ bignum:
+ v = rb_big_pow(rb_int2big(x), LONG2NUM(y));
+ if (z != 1) v = rb_big_mul(rb_int2big(neg ? -z : z), v);
+ return v;
+ }
+ x = x * x;
+ y >>= 1;
+ }
+ {
+ long xz = x * z;
+ if (!POSFIXABLE(xz) || xz / x != z) {
+ goto bignum;
+ }
+ z = xz;
+ }
+ } while (--y);
+ if (neg) z = -z;
+ return LONG2NUM(z);
+}
+
+/*
+ * call-seq:
+ * fix ** other => Numeric
+ *
+ * Raises <code>fix</code> to the <code>other</code> power, which may
+ * be negative or fractional.
+ *
+ * 2 ** 3 #=> 8
+ * 2 ** -1 #=> 0.5
+ * 2 ** 0.5 #=> 1.4142135623731
+ */
+
+static VALUE
+fix_pow(VALUE x, VALUE y)
+{
+ static const double zero = 0.0;
+ long a = FIX2LONG(x);
+
+ if (FIXNUM_P(y)) {
+ long b = FIX2LONG(y);
+
+ if (b < 0)
+ return rb_funcall(rb_rational_raw1(x), rb_intern("**"), 1, y);
+
+ if (b == 0) return INT2FIX(1);
+ if (b == 1) return x;
+ if (a == 0) {
+ if (b > 0) return INT2FIX(0);
+ return DBL2NUM(1.0 / zero);
+ }
+ if (a == 1) return INT2FIX(1);
+ if (a == -1) {
+ if (b % 2 == 0)
+ return INT2FIX(1);
+ else
+ return INT2FIX(-1);
+ }
+ return int_pow(a, b);
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+
+ if (rb_funcall(y, '<', 1, INT2FIX(0)))
+ return rb_funcall(rb_rational_raw1(x), rb_intern("**"), 1, y);
+
+ if (a == 0) return INT2FIX(0);
+ if (a == 1) return INT2FIX(1);
+ if (a == -1) {
+ if (int_even_p(y)) return INT2FIX(1);
+ else return INT2FIX(-1);
+ }
+ x = rb_int2big(FIX2LONG(x));
+ return rb_big_pow(x, y);
+ case T_FLOAT:
+ if (RFLOAT_VALUE(y) == 0.0) return DBL2NUM(1.0);
+ if (a == 0) {
+ return DBL2NUM(RFLOAT_VALUE(y) < 0 ? (1.0 / zero) : 0.0);
+ }
+ if (a == 1) return DBL2NUM(1.0);
+ return DBL2NUM(pow((double)a, RFLOAT_VALUE(y)));
+ default:
+ return rb_num_coerce_bin(x, y, rb_intern("**"));
+ }
+}
+
+/*
+ * call-seq:
+ * fix == other
+ *
+ * Return <code>true</code> if <code>fix</code> equals <code>other</code>
+ * numerically.
+ *
+ * 1 == 2 #=> false
+ * 1 == 1.0 #=> true
+ */
+
+static VALUE
+fix_equal(VALUE x, VALUE y)
+{
+ if (x == y) return Qtrue;
+ if (FIXNUM_P(y)) return Qfalse;
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ return rb_big_eq(y, x);
+ case T_FLOAT:
+ return (double)FIX2LONG(x) == RFLOAT_VALUE(y) ? Qtrue : Qfalse;
+ default:
+ return num_equal(x, y);
+ }
+}
+
+/*
+ * call-seq:
+ * fix <=> numeric => -1, 0, +1
+ *
+ * Comparison---Returns -1, 0, or +1 depending on whether <i>fix</i> is
+ * less than, equal to, or greater than <i>numeric</i>. This is the
+ * basis for the tests in <code>Comparable</code>.
+ */
+
+static VALUE
+fix_cmp(VALUE x, VALUE y)
+{
+ if (x == y) return INT2FIX(0);
+ if (FIXNUM_P(y)) {
+ if (FIX2LONG(x) > FIX2LONG(y)) return INT2FIX(1);
+ return INT2FIX(-1);
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ return rb_big_cmp(rb_int2big(FIX2LONG(x)), y);
+ case T_FLOAT:
+ return rb_dbl_cmp((double)FIX2LONG(x), RFLOAT_VALUE(y));
+ default:
+ return rb_num_coerce_cmp(x, y, rb_intern("<=>"));
+ }
+}
+
+/*
+ * call-seq:
+ * fix > other => true or false
+ *
+ * Returns <code>true</code> if the value of <code>fix</code> is
+ * greater than that of <code>other</code>.
+ */
+
+static VALUE
+fix_gt(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(y)) {
+ if (FIX2LONG(x) > FIX2LONG(y)) return Qtrue;
+ return Qfalse;
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) > 0 ? Qtrue : Qfalse;
+ case T_FLOAT:
+ return (double)FIX2LONG(x) > RFLOAT_VALUE(y) ? Qtrue : Qfalse;
+ default:
+ return rb_num_coerce_relop(x, y, '>');
+ }
+}
+
+/*
+ * call-seq:
+ * fix >= other => true or false
+ *
+ * Returns <code>true</code> if the value of <code>fix</code> is
+ * greater than or equal to that of <code>other</code>.
+ */
+
+static VALUE
+fix_ge(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(y)) {
+ if (FIX2LONG(x) >= FIX2LONG(y)) return Qtrue;
+ return Qfalse;
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) >= 0 ? Qtrue : Qfalse;
+ case T_FLOAT:
+ return (double)FIX2LONG(x) >= RFLOAT_VALUE(y) ? Qtrue : Qfalse;
+ default:
+ return rb_num_coerce_relop(x, y, rb_intern(">="));
+ }
+}
+
+/*
+ * call-seq:
+ * fix < other => true or false
+ *
+ * Returns <code>true</code> if the value of <code>fix</code> is
+ * less than that of <code>other</code>.
+ */
+
+static VALUE
+fix_lt(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(y)) {
+ if (FIX2LONG(x) < FIX2LONG(y)) return Qtrue;
+ return Qfalse;
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) < 0 ? Qtrue : Qfalse;
+ case T_FLOAT:
+ return (double)FIX2LONG(x) < RFLOAT_VALUE(y) ? Qtrue : Qfalse;
+ default:
+ return rb_num_coerce_relop(x, y, '<');
+ }
+}
+
+/*
+ * call-seq:
+ * fix <= other => true or false
+ *
+ * Returns <code>true</code> if the value of <code>fix</code> is
+ * less than or equal to that of <code>other</code>.
+ */
+
+static VALUE
+fix_le(VALUE x, VALUE y)
+{
+ if (FIXNUM_P(y)) {
+ if (FIX2LONG(x) <= FIX2LONG(y)) return Qtrue;
+ return Qfalse;
+ }
+ switch (TYPE(y)) {
+ case T_BIGNUM:
+ return FIX2INT(rb_big_cmp(rb_int2big(FIX2LONG(x)), y)) <= 0 ? Qtrue : Qfalse;
+ case T_FLOAT:
+ return (double)FIX2LONG(x) <= RFLOAT_VALUE(y) ? Qtrue : Qfalse;
+ default:
+ return rb_num_coerce_relop(x, y, rb_intern("<="));
+ }
+}
+
+/*
+ * call-seq:
+ * ~fix => integer
+ *
+ * One's complement: returns a number where each bit is flipped.
+ */
+
+static VALUE
+fix_rev(VALUE num)
+{
+ long val = FIX2LONG(num);
+
+ val = ~val;
+ return LONG2NUM(val);
+}
+
+static VALUE
+bit_coerce(VALUE x)
+{
+ while (!FIXNUM_P(x) && TYPE(x) != T_BIGNUM) {
+ if (TYPE(x) == T_FLOAT) {
+ rb_raise(rb_eTypeError, "can't convert Float into Integer");
+ }
+ x = rb_to_int(x);
+ }
+ return x;
+}
+
+/*
+ * call-seq:
+ * fix & other => integer
+ *
+ * Bitwise AND.
+ */
+
+static VALUE
+fix_and(VALUE x, VALUE y)
+{
+ long val;
+
+ if (!FIXNUM_P(y = bit_coerce(y))) {
+ return rb_big_and(y, x);
+ }
+ val = FIX2LONG(x) & FIX2LONG(y);
+ return LONG2NUM(val);
+}
+
+/*
+ * call-seq:
+ * fix | other => integer
+ *
+ * Bitwise OR.
+ */
+
+static VALUE
+fix_or(VALUE x, VALUE y)
+{
+ long val;
+
+ if (!FIXNUM_P(y = bit_coerce(y))) {
+ return rb_big_or(y, x);
+ }
+ val = FIX2LONG(x) | FIX2LONG(y);
+ return LONG2NUM(val);
+}
+
+/*
+ * call-seq:
+ * fix ^ other => integer
+ *
+ * Bitwise EXCLUSIVE OR.
+ */
+
+static VALUE
+fix_xor(VALUE x, VALUE y)
+{
+ long val;
+
+ if (!FIXNUM_P(y = bit_coerce(y))) {
+ return rb_big_xor(y, x);
+ }
+ val = FIX2LONG(x) ^ FIX2LONG(y);
+ return LONG2NUM(val);
+}
+
+static VALUE fix_lshift(long, unsigned long);
+static VALUE fix_rshift(long, unsigned long);
+
+/*
+ * call-seq:
+ * fix << count => integer
+ *
+ * Shifts _fix_ left _count_ positions (right if _count_ is negative).
+ */
+
+static VALUE
+rb_fix_lshift(VALUE x, VALUE y)
+{
+ long val, width;
+
+ val = NUM2LONG(x);
+ if (!FIXNUM_P(y))
+ return rb_big_lshift(rb_int2big(val), y);
+ width = FIX2LONG(y);
+ if (width < 0)
+ return fix_rshift(val, (unsigned long)-width);
+ return fix_lshift(val, width);
+}
+
+static VALUE
+fix_lshift(long val, unsigned long width)
+{
+ if (width > (SIZEOF_LONG*CHAR_BIT-1)
+ || ((unsigned long)val)>>(SIZEOF_LONG*CHAR_BIT-1-width) > 0) {
+ return rb_big_lshift(rb_int2big(val), ULONG2NUM(width));
+ }
+ val = val << width;
+ return LONG2NUM(val);
+}
+
+/*
+ * call-seq:
+ * fix >> count => integer
+ *
+ * Shifts _fix_ right _count_ positions (left if _count_ is negative).
+ */
+
+static VALUE
+rb_fix_rshift(VALUE x, VALUE y)
+{
+ long i, val;
+
+ val = FIX2LONG(x);
+ if (!FIXNUM_P(y))
+ return rb_big_rshift(rb_int2big(val), y);
+ i = FIX2LONG(y);
+ if (i == 0) return x;
+ if (i < 0)
+ return fix_lshift(val, (unsigned long)-i);
+ return fix_rshift(val, i);
+}
+
+static VALUE
+fix_rshift(long val, unsigned long i)
+{
+ if (i >= sizeof(long)*CHAR_BIT-1) {
+ if (val < 0) return INT2FIX(-1);
+ return INT2FIX(0);
+ }
+ val = RSHIFT(val, i);
+ return LONG2FIX(val);
+}
+
+/*
+ * call-seq:
+ * fix[n] => 0, 1
+ *
+ * Bit Reference---Returns the <em>n</em>th bit in the binary
+ * representation of <i>fix</i>, where <i>fix</i>[0] is the least
+ * significant bit.
+ *
+ * a = 0b11001100101010
+ * 30.downto(0) do |n| print a[n] end
+ *
+ * <em>produces:</em>
+ *
+ * 0000000000000000011001100101010
+ */
+
+static VALUE
+fix_aref(VALUE fix, VALUE idx)
+{
+ long val = FIX2LONG(fix);
+ long i;
+
+ idx = rb_to_int(idx);
+ if (!FIXNUM_P(idx)) {
+ idx = rb_big_norm(idx);
+ if (!FIXNUM_P(idx)) {
+ if (!RBIGNUM_SIGN(idx) || val >= 0)
+ return INT2FIX(0);
+ return INT2FIX(1);
+ }
+ }
+ i = FIX2LONG(idx);
+
+ if (i < 0) return INT2FIX(0);
+ if (SIZEOF_LONG*CHAR_BIT-1 < i) {
+ if (val < 0) return INT2FIX(1);
+ return INT2FIX(0);
+ }
+ if (val & (1L<<i))
+ return INT2FIX(1);
+ return INT2FIX(0);
+}
+
+/*
+ * call-seq:
+ * fix.to_f -> float
+ *
+ * Converts <i>fix</i> to a <code>Float</code>.
+ *
+ */
+
+static VALUE
+fix_to_f(VALUE num)
+{
+ double val;
+
+ val = (double)FIX2LONG(num);
+
+ return DBL2NUM(val);
+}
+
+/*
+ * call-seq:
+ * fix.abs -> aFixnum
+ *
+ * Returns the absolute value of <i>fix</i>.
+ *
+ * -12345.abs #=> 12345
+ * 12345.abs #=> 12345
+ *
+ */
+
+static VALUE
+fix_abs(VALUE fix)
+{
+ long i = FIX2LONG(fix);
+
+ if (i < 0) i = -i;
+
+ return LONG2NUM(i);
+}
+
+
+
+/*
+ * call-seq:
+ * fix.size -> fixnum
+ *
+ * Returns the number of <em>bytes</em> in the machine representation
+ * of a <code>Fixnum</code>.
+ *
+ * 1.size #=> 4
+ * -1.size #=> 4
+ * 2147483647.size #=> 4
+ */
+
+static VALUE
+fix_size(VALUE fix)
+{
+ return INT2FIX(sizeof(long));
+}
+
+/*
+ * call-seq:
+ * int.upto(limit) {|i| block } => int
+ *
+ * Iterates <em>block</em>, passing in integer values from <i>int</i>
+ * up to and including <i>limit</i>.
+ *
+ * 5.upto(10) { |i| print i, " " }
+ *
+ * <em>produces:</em>
+ *
+ * 5 6 7 8 9 10
+ */
+
+static VALUE
+int_upto(VALUE from, VALUE to)
+{
+ RETURN_ENUMERATOR(from, 1, &to);
+ if (FIXNUM_P(from) && FIXNUM_P(to)) {
+ long i, end;
+
+ end = FIX2LONG(to);
+ for (i = FIX2LONG(from); i <= end; i++) {
+ rb_yield(LONG2FIX(i));
+ }
+ }
+ else {
+ VALUE i = from, c;
+
+ while (!(c = rb_funcall(i, '>', 1, to))) {
+ rb_yield(i);
+ i = rb_funcall(i, '+', 1, INT2FIX(1));
+ }
+ if (NIL_P(c)) rb_cmperr(i, to);
+ }
+ return from;
+}
+
+/*
+ * call-seq:
+ * int.downto(limit) {|i| block } => int
+ *
+ * Iterates <em>block</em>, passing decreasing values from <i>int</i>
+ * down to and including <i>limit</i>.
+ *
+ * 5.downto(1) { |n| print n, ".. " }
+ * print " Liftoff!\n"
+ *
+ * <em>produces:</em>
+ *
+ * 5.. 4.. 3.. 2.. 1.. Liftoff!
+ */
+
+static VALUE
+int_downto(VALUE from, VALUE to)
+{
+ RETURN_ENUMERATOR(from, 1, &to);
+ if (FIXNUM_P(from) && FIXNUM_P(to)) {
+ long i, end;
+
+ end = FIX2LONG(to);
+ for (i=FIX2LONG(from); i >= end; i--) {
+ rb_yield(LONG2FIX(i));
+ }
+ }
+ else {
+ VALUE i = from, c;
+
+ while (!(c = rb_funcall(i, '<', 1, to))) {
+ rb_yield(i);
+ i = rb_funcall(i, '-', 1, INT2FIX(1));
+ }
+ if (NIL_P(c)) rb_cmperr(i, to);
+ }
+ return from;
+}
+
+/*
+ * call-seq:
+ * int.times {|i| block } => int
+ *
+ * Iterates block <i>int</i> times, passing in values from zero to
+ * <i>int</i> - 1.
+ *
+ * 5.times do |i|
+ * print i, " "
+ * end
+ *
+ * <em>produces:</em>
+ *
+ * 0 1 2 3 4
+ */
+
+static VALUE
+int_dotimes(VALUE num)
+{
+ RETURN_ENUMERATOR(num, 0, 0);
+
+ if (FIXNUM_P(num)) {
+ long i, end;
+
+ end = FIX2LONG(num);
+ for (i=0; i<end; i++) {
+ rb_yield(LONG2FIX(i));
+ }
+ }
+ else {
+ 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;
+}
+
+static VALUE
+int_round(int argc, VALUE* argv, VALUE num)
+{
+ VALUE n, f, h, r;
+ int ndigits;
+
+ if (argc == 0) return num;
+ rb_scan_args(argc, argv, "1", &n);
+ ndigits = NUM2INT(n);
+ if (ndigits > 0) {
+ return rb_Float(num);
+ }
+ if (ndigits == 0) {
+ return num;
+ }
+ ndigits = -ndigits;
+ if (ndigits < 0) {
+ rb_raise(rb_eArgError, "ndigits out of range");
+ }
+ f = int_pow(10, ndigits);
+ if (FIXNUM_P(num) && FIXNUM_P(f)) {
+ SIGNED_VALUE x = FIX2LONG(num), y = FIX2LONG(f);
+ int neg = x < 0;
+ if (neg) x = -x;
+ x = (x + y / 2) / y * y;
+ if (neg) x = -x;
+ return LONG2NUM(x);
+ }
+ h = rb_funcall(f, '/', 1, INT2FIX(2));
+ r = rb_funcall(num, '%', 1, f);
+ n = rb_funcall(num, '-', 1, r);
+ if (!RTEST(rb_funcall(r, '<', 1, h))) {
+ n = rb_funcall(n, '+', 1, f);
+ }
+ return n;
+}
+
+/*
+ * call-seq:
+ * fix.zero? => true or false
+ *
+ * Returns <code>true</code> if <i>fix</i> is zero.
+ *
+ */
+
+static VALUE
+fix_zero_p(VALUE num)
+{
+ if (FIX2LONG(num) == 0) {
+ return Qtrue;
+ }
+ return Qfalse;
+}
+
+/*
+ * call-seq:
+ * fix.odd? -> true or false
+ *
+ * Returns <code>true</code> if <i>fix</i> is an odd number.
+ */
+
+static VALUE
+fix_odd_p(VALUE num)
+{
+ if (num & 2) {
+ return Qtrue;
+ }
+ return Qfalse;
+}
+
+/*
+ * call-seq:
+ * fix.even? -> true or false
+ *
+ * Returns <code>true</code> if <i>fix</i> is an even number.
+ */
+
+static VALUE
+fix_even_p(VALUE num)
+{
+ if (num & 2) {
+ return Qfalse;
+ }
+ return Qtrue;
+}
+
+void
+Init_Numeric(void)
+{
+#undef rb_intern
+#define rb_intern(str) rb_intern_const(str)
+
+#if defined(__FreeBSD__) && __FreeBSD__ < 4
+ /* allow divide by zero -- Inf */
+ fpsetmask(fpgetmask() & ~(FP_X_DZ|FP_X_INV|FP_X_OFL));
+#elif defined(_UNICOSMP)
+ /* Turn off floating point exceptions for divide by zero, etc. */
+ _set_Creg(0, 0);
+#elif defined(__BORLANDC__)
+ /* Turn off floating point exceptions for overflow, etc. */
+ _control87(MCW_EM, MCW_EM);
+#endif
+ id_coerce = rb_intern("coerce");
+ id_to_i = rb_intern("to_i");
+ id_eq = rb_intern("==");
+
+ rb_eZeroDivError = rb_define_class("ZeroDivisionError", rb_eStandardError);
+ rb_eFloatDomainError = rb_define_class("FloatDomainError", rb_eRangeError);
+ rb_cNumeric = rb_define_class("Numeric", rb_cObject);
+
+ rb_define_method(rb_cNumeric, "singleton_method_added", num_sadded, 1);
+ rb_include_module(rb_cNumeric, rb_mComparable);
+ rb_define_method(rb_cNumeric, "initialize_copy", num_init_copy, 1);
+ rb_define_method(rb_cNumeric, "coerce", num_coerce, 1);
+
+ rb_define_method(rb_cNumeric, "+@", num_uplus, 0);
+ rb_define_method(rb_cNumeric, "-@", num_uminus, 0);
+ rb_define_method(rb_cNumeric, "<=>", num_cmp, 1);
+ rb_define_method(rb_cNumeric, "eql?", num_eql, 1);
+ rb_define_method(rb_cNumeric, "quo", num_quo, 1);
+ rb_define_method(rb_cNumeric, "fdiv", num_fdiv, 1);
+ rb_define_method(rb_cNumeric, "div", num_div, 1);
+ rb_define_method(rb_cNumeric, "divmod", num_divmod, 1);
+ rb_define_method(rb_cNumeric, "modulo", num_modulo, 1);
+ rb_define_method(rb_cNumeric, "remainder", num_remainder, 1);
+ rb_define_method(rb_cNumeric, "abs", num_abs, 0);
+ rb_define_method(rb_cNumeric, "magnitude", num_abs, 0);
+ rb_define_method(rb_cNumeric, "to_int", num_to_int, 0);
+
+ rb_define_method(rb_cNumeric, "real?", num_real_p, 0);
+ rb_define_method(rb_cNumeric, "integer?", num_int_p, 0);
+ rb_define_method(rb_cNumeric, "zero?", num_zero_p, 0);
+ rb_define_method(rb_cNumeric, "nonzero?", num_nonzero_p, 0);
+
+ rb_define_method(rb_cNumeric, "floor", num_floor, 0);
+ rb_define_method(rb_cNumeric, "ceil", num_ceil, 0);
+ rb_define_method(rb_cNumeric, "round", num_round, -1);
+ rb_define_method(rb_cNumeric, "truncate", num_truncate, 0);
+ rb_define_method(rb_cNumeric, "step", num_step, -1);
+
+ rb_define_method(rb_cNumeric, "numerator", num_numerator, 0);
+ rb_define_method(rb_cNumeric, "denominator", num_denominator, 0);
+
+ rb_cInteger = rb_define_class("Integer", rb_cNumeric);
+ rb_undef_alloc_func(rb_cInteger);
+ rb_undef_method(CLASS_OF(rb_cInteger), "new");
+
+ rb_define_method(rb_cInteger, "integer?", int_int_p, 0);
+ rb_define_method(rb_cInteger, "odd?", int_odd_p, 0);
+ rb_define_method(rb_cInteger, "even?", int_even_p, 0);
+ rb_define_method(rb_cInteger, "upto", int_upto, 1);
+ rb_define_method(rb_cInteger, "downto", int_downto, 1);
+ rb_define_method(rb_cInteger, "times", int_dotimes, 0);
+ rb_define_method(rb_cInteger, "succ", int_succ, 0);
+ rb_define_method(rb_cInteger, "next", int_succ, 0);
+ rb_define_method(rb_cInteger, "pred", int_pred, 0);
+ rb_define_method(rb_cInteger, "chr", int_chr, -1);
+ rb_define_method(rb_cInteger, "ord", int_ord, 0);
+ rb_define_method(rb_cInteger, "to_i", int_to_i, 0);
+ rb_define_method(rb_cInteger, "to_int", int_to_i, 0);
+ rb_define_method(rb_cInteger, "floor", int_to_i, 0);
+ rb_define_method(rb_cInteger, "ceil", int_to_i, 0);
+ rb_define_method(rb_cInteger, "truncate", int_to_i, 0);
+ rb_define_method(rb_cInteger, "round", int_round, -1);
+
+ rb_define_method(rb_cInteger, "numerator", int_numerator, 0);
+ rb_define_method(rb_cInteger, "denominator", int_denominator, 0);
+
+ rb_cFixnum = rb_define_class("Fixnum", rb_cInteger);
+
+ rb_define_method(rb_cFixnum, "to_s", fix_to_s, -1);
+
+ rb_define_method(rb_cFixnum, "-@", fix_uminus, 0);
+ rb_define_method(rb_cFixnum, "+", fix_plus, 1);
+ rb_define_method(rb_cFixnum, "-", fix_minus, 1);
+ rb_define_method(rb_cFixnum, "*", fix_mul, 1);
+ rb_define_method(rb_cFixnum, "/", fix_div, 1);
+ rb_define_method(rb_cFixnum, "div", fix_idiv, 1);
+ rb_define_method(rb_cFixnum, "%", fix_mod, 1);
+ rb_define_method(rb_cFixnum, "modulo", fix_mod, 1);
+ rb_define_method(rb_cFixnum, "divmod", fix_divmod, 1);
+ rb_define_method(rb_cFixnum, "fdiv", fix_fdiv, 1);
+ rb_define_method(rb_cFixnum, "**", fix_pow, 1);
+
+ rb_define_method(rb_cFixnum, "abs", fix_abs, 0);
+ rb_define_method(rb_cFixnum, "magnitude", fix_abs, 0);
+
+ rb_define_method(rb_cFixnum, "==", fix_equal, 1);
+ rb_define_method(rb_cFixnum, "<=>", fix_cmp, 1);
+ rb_define_method(rb_cFixnum, ">", fix_gt, 1);
+ rb_define_method(rb_cFixnum, ">=", fix_ge, 1);
+ rb_define_method(rb_cFixnum, "<", fix_lt, 1);
+ rb_define_method(rb_cFixnum, "<=", fix_le, 1);
+
+ rb_define_method(rb_cFixnum, "~", fix_rev, 0);
+ rb_define_method(rb_cFixnum, "&", fix_and, 1);
+ rb_define_method(rb_cFixnum, "|", fix_or, 1);
+ rb_define_method(rb_cFixnum, "^", fix_xor, 1);
+ rb_define_method(rb_cFixnum, "[]", fix_aref, 1);
+
+ rb_define_method(rb_cFixnum, "<<", rb_fix_lshift, 1);
+ rb_define_method(rb_cFixnum, ">>", rb_fix_rshift, 1);
+
+ rb_define_method(rb_cFixnum, "to_f", fix_to_f, 0);
+ rb_define_method(rb_cFixnum, "size", fix_size, 0);
+ rb_define_method(rb_cFixnum, "zero?", fix_zero_p, 0);
+ rb_define_method(rb_cFixnum, "odd?", fix_odd_p, 0);
+ rb_define_method(rb_cFixnum, "even?", fix_even_p, 0);
+ rb_define_method(rb_cFixnum, "succ", fix_succ, 0);
+
+ rb_cFloat = rb_define_class("Float", rb_cNumeric);
+
+ rb_undef_alloc_func(rb_cFloat);
+ rb_undef_method(CLASS_OF(rb_cFloat), "new");
+
+ rb_define_const(rb_cFloat, "ROUNDS", INT2FIX(FLT_ROUNDS));
+ rb_define_const(rb_cFloat, "RADIX", INT2FIX(FLT_RADIX));
+ rb_define_const(rb_cFloat, "MANT_DIG", INT2FIX(DBL_MANT_DIG));
+ rb_define_const(rb_cFloat, "DIG", INT2FIX(DBL_DIG));
+ rb_define_const(rb_cFloat, "MIN_EXP", INT2FIX(DBL_MIN_EXP));
+ rb_define_const(rb_cFloat, "MAX_EXP", INT2FIX(DBL_MAX_EXP));
+ rb_define_const(rb_cFloat, "MIN_10_EXP", INT2FIX(DBL_MIN_10_EXP));
+ rb_define_const(rb_cFloat, "MAX_10_EXP", INT2FIX(DBL_MAX_10_EXP));
+ rb_define_const(rb_cFloat, "MIN", DBL2NUM(DBL_MIN));
+ rb_define_const(rb_cFloat, "MAX", DBL2NUM(DBL_MAX));
+ rb_define_const(rb_cFloat, "EPSILON", DBL2NUM(DBL_EPSILON));
+
+ rb_define_method(rb_cFloat, "to_s", flo_to_s, 0);
+ rb_define_method(rb_cFloat, "coerce", flo_coerce, 1);
+ rb_define_method(rb_cFloat, "-@", flo_uminus, 0);
+ rb_define_method(rb_cFloat, "+", flo_plus, 1);
+ rb_define_method(rb_cFloat, "-", flo_minus, 1);
+ rb_define_method(rb_cFloat, "*", flo_mul, 1);
+ rb_define_method(rb_cFloat, "/", flo_div, 1);
+ rb_define_method(rb_cFloat, "quo", flo_quo, 1);
+ rb_define_method(rb_cFloat, "fdiv", flo_quo, 1);
+ rb_define_method(rb_cFloat, "%", flo_mod, 1);
+ rb_define_method(rb_cFloat, "modulo", flo_mod, 1);
+ rb_define_method(rb_cFloat, "divmod", flo_divmod, 1);
+ rb_define_method(rb_cFloat, "**", flo_pow, 1);
+ rb_define_method(rb_cFloat, "==", flo_eq, 1);
+ rb_define_method(rb_cFloat, "<=>", flo_cmp, 1);
+ rb_define_method(rb_cFloat, ">", flo_gt, 1);
+ rb_define_method(rb_cFloat, ">=", flo_ge, 1);
+ rb_define_method(rb_cFloat, "<", flo_lt, 1);
+ rb_define_method(rb_cFloat, "<=", flo_le, 1);
+ 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, "zero?", flo_zero_p, 0);
+
+ rb_define_method(rb_cFloat, "to_i", flo_truncate, 0);
+ rb_define_method(rb_cFloat, "to_int", flo_truncate, 0);
+ rb_define_method(rb_cFloat, "floor", flo_floor, 0);
+ rb_define_method(rb_cFloat, "ceil", flo_ceil, 0);
+ rb_define_method(rb_cFloat, "round", flo_round, -1);
+ rb_define_method(rb_cFloat, "truncate", flo_truncate, 0);
+
+ rb_define_method(rb_cFloat, "nan?", flo_is_nan_p, 0);
+ rb_define_method(rb_cFloat, "infinite?", flo_is_infinite_p, 0);
+ rb_define_method(rb_cFloat, "finite?", flo_is_finite_p, 0);
+}
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