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ruby/numeric.c

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/**********************************************************************
numeric.c -
$Author$
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;
}
#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);
return rb_assoc_new(rb_Float(y), rb_Float(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)
{
do_coerce(&x, &y, Qtrue);
return rb_funcall(x, rb_frame_this_func(), 1, y);
}
VALUE
rb_num_coerce_cmp(VALUE x, VALUE y)
{
if (do_coerce(&x, &y, Qfalse))
return rb_funcall(x, rb_frame_this_func(), 1, y);
return Qnil;
}
VALUE
rb_num_coerce_relop(VALUE x, VALUE y)
{
VALUE c, x0 = x, y0 = y;
if (!do_coerce(&x, &y, Qfalse) ||
NIL_P(c = rb_funcall(x, rb_frame_this_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)
{
/* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */
/* Numerics should be values; singleton_methods should not be added to them */
rb_raise(rb_eTypeError,
"can't define singleton method \"%s\" for %s",
rb_id2name(rb_to_id(name)),
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
* num.fdiv(numeric) => result
*
* Equivalent to <code>Numeric#/</code>, but overridden in subclasses.
*/
static VALUE
num_quo(VALUE x, VALUE y)
{
return rb_funcall(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)
{
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.scalar? -> true or false
*
* Returns <code>true</code> if <i>num</i> is an <code>Scalar</code>
* (i.e. non <code>Complex</code>).
*/
static VALUE
num_scalar_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");
sprintf(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.) */
sprintf(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 DOUBLE2NUM(-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 DOUBLE2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
case T_BIGNUM:
return DOUBLE2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
case T_FLOAT:
return DOUBLE2NUM(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 DOUBLE2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
case T_BIGNUM:
return DOUBLE2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
case T_FLOAT:
return DOUBLE2NUM(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 DOUBLE2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
case T_BIGNUM:
return DOUBLE2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
case T_FLOAT:
return DOUBLE2NUM(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 DOUBLE2NUM(RFLOAT_VALUE(x) / (double)f_y);
case T_BIGNUM:
d = rb_big2dbl(y);
return DOUBLE2NUM(RFLOAT_VALUE(x) / d);
case T_FLOAT:
return DOUBLE2NUM(RFLOAT_VALUE(x) / RFLOAT_VALUE(y));
default:
return rb_num_coerce_bin(x, 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 DOUBLE2NUM(mod);
}
/*
* call-seq:
* flt.divmod(numeric) => array
*
* See <code>Numeric#divmod</code>.
*/
static VALUE
flo_divmod(VALUE x, VALUE y)
{
double fy, div, mod, val;
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);
}
flodivmod(RFLOAT_VALUE(x), fy, &div, &mod);
if (FIXABLE(div)) {
val = round(div);
a = LONG2FIX(val);
}
else if (isnan(div) || isinf(div)) {
a = rb_float_new(div);
}
else {
a = rb_dbl2big(div);
}
b = DOUBLE2NUM(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 DOUBLE2NUM(pow(RFLOAT_VALUE(x), (double)FIX2LONG(y)));
case T_BIGNUM:
return DOUBLE2NUM(pow(RFLOAT_VALUE(x), rb_big2dbl(y)));
case T_FLOAT:
return DOUBLE2NUM(pow(RFLOAT_VALUE(x), RFLOAT_VALUE(y)));
default:
return rb_num_coerce_bin(x, y);
}
}
/*
* 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);
}
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);
}
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);
}
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 DOUBLE2NUM(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 (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 (ndigits < 0) number /= f;
else number *= f;
number = round(number);
if (ndigits < 0) number *= f;
else number /= f;
if (ndigits > 0) return DOUBLE2NUM(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 (err>0.5) err=0.5;
n = floor(n + err) + 1;
for (i=0; i<n; i++) {
rb_yield(DOUBLE2NUM(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)
{
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;
sprintf(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);
return NUM2LONG(val);
}
}
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;
}
#ifdef LONG_LONG_VALUE
rb_raise(rb_eRangeError, "integer %lld too %s to convert to `int'", num, s);
#else
rb_raise(rb_eRangeError, "integer %ld too %s to convert to `int'", num, s);
#endif
}
static void
check_uint(VALUE num)
{
if (num > UINT_MAX) {
#ifdef LONG_LONG_VALUE
rb_raise(rb_eRangeError, "integer %llu too big to convert to `unsigned int'", num);
#else
rb_raise(rb_eRangeError, "integer %lu too big to convert to `unsigned int'", num);
#endif
}
}
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);
if (RTEST(rb_funcall(INT2FIX(0), '<', 1, val))) {
check_uint(num);
}
return num;
}
unsigned long
rb_fix2uint(VALUE val)
{
unsigned long num;
if (!FIXNUM_P(val)) {
return rb_num2uint(val);
}
num = FIX2ULONG(val);
if (FIX2LONG(val) > 0) {
check_uint(num);
}
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 %ld 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;
sprintf(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 */
/*
* 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, "%ld 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;
}
/********************************************************************
*
* 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:
* Fixnum.induced_from(obj) => fixnum
*
* Convert <code>obj</code> to a Fixnum. Works with numeric parameters.
* Also works with Symbols, but this is deprecated.
*/
static VALUE
rb_fix_induced_from(VALUE klass, VALUE x)
{
return rb_num2fix(x);
}
/*
* call-seq:
* Integer.induced_from(obj) => fixnum, bignum
*
* Convert <code>obj</code> to an Integer.
*/
static VALUE
rb_int_induced_from(VALUE klass, VALUE x)
{
switch (TYPE(x)) {
case T_FIXNUM:
case T_BIGNUM:
return x;
case T_FLOAT:
return rb_funcall(x, id_to_i, 0);
default:
rb_raise(rb_eTypeError, "failed to convert %s into Integer",
rb_obj_classname(x));
}
}
/*
* call-seq:
* Float.induced_from(obj) => float
*
* Convert <code>obj</code> to a float.
*/
static VALUE
rb_flo_induced_from(VALUE klass, VALUE x)
{
switch (TYPE(x)) {
case T_FIXNUM:
case T_BIGNUM:
return rb_funcall(x, rb_intern("to_f"), 0);
case T_FLOAT:
return x;
default:
rb_raise(rb_eTypeError, "failed to convert %s into Float",
rb_obj_classname(x));
}
}
/*
* 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)
{
VALUE b;
int base;
rb_scan_args(argc, argv, "01", &b);
if (argc == 0) base = 10;
else 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 DOUBLE2NUM((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 DOUBLE2NUM((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 DOUBLE2NUM((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.quo(numeric) => float
* fix.fdiv(numeric) => float
*
* Returns the floating point result of dividing <i>fix</i> by
* <i>numeric</i>.
*
* 654321.quo(13731) #=> 47.6528293642124
* 654321.quo(13731.24) #=> 47.6519964693647
*
*/
static VALUE
fix_quo(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
return DOUBLE2NUM((double)FIX2LONG(x) / (double)FIX2LONG(y));
}
switch (TYPE(y)) {
case T_BIGNUM:
return DOUBLE2NUM((double)FIX2LONG(x) / rb_big2dbl(y));
case T_FLOAT:
return DOUBLE2NUM((double)FIX2LONG(x) / RFLOAT_VALUE(y));
default:
return rb_num_coerce_bin(x, y);
}
}
static VALUE
fix_divide(VALUE x, VALUE y, int flo)
{
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:
if (flo) {
return DOUBLE2NUM((double)FIX2LONG(x) / RFLOAT_VALUE(y));
}
else {
long div = (double)FIX2LONG(x) / RFLOAT_VALUE(y);
return LONG2NUM(div);
}
default:
return rb_num_coerce_bin(x, y);
}
}
/*
* 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, Qtrue);
}
/*
* 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, Qfalse);
}
/*
* 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 DOUBLE2NUM(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 = DOUBLE2NUM(div);
b = DOUBLE2NUM(mod);
return rb_assoc_new(a, b);
}
default:
return rb_num_coerce_bin(x, y);
}
}
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 INT2FIX(1);
if (b == 1) return x;
if (a == 0) {
if (b > 0) return INT2FIX(0);
return DOUBLE2NUM(1.0 / zero);
}
if (a == 1) return INT2FIX(1);
if (a == -1) {
if (b % 2 == 0)
return INT2FIX(1);
else
return INT2FIX(-1);
}
if (b > 0) {
return int_pow(a, b);
}
return DOUBLE2NUM(pow((double)a, (double)b));
}
switch (TYPE(y)) {
case T_BIGNUM:
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 DOUBLE2NUM(1.0);
if (a == 0) {
return DOUBLE2NUM(RFLOAT_VALUE(y) < 0 ? (1.0 / zero) : 0.0);
}
if (a == 1) return DOUBLE2NUM(1.0);
return DOUBLE2NUM(pow((double)a, RFLOAT_VALUE(y)));
default:
return rb_num_coerce_bin(x, y);
}
}
/*
* 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);
}
}
/*
* 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);
}
}
/*
* 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);
}
}
/*
* 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);
}
/*
* call-seq:
* fix & other => integer
*
* Bitwise AND.
*/
static VALUE
fix_and(VALUE x, VALUE y)
{
long val;
if (TYPE(y) == T_BIGNUM) {
return rb_big_and(y, x);
}
val = FIX2LONG(x) & NUM2LONG(y);
return LONG2NUM(val);
}
/*
* call-seq:
* fix | other => integer
*
* Bitwise OR.
*/
static VALUE
fix_or(VALUE x, VALUE y)
{
long val;
if (TYPE(y) == T_BIGNUM) {
return rb_big_or(y, x);
}
val = FIX2LONG(x) | NUM2LONG(y);
return LONG2NUM(val);
}
/*
* call-seq:
* fix ^ other => integer
*
* Bitwise EXCLUSIVE OR.
*/
static VALUE
fix_xor(VALUE x, VALUE y)
{
long val;
if (TYPE(y) == T_BIGNUM) {
return rb_big_xor(y, x);
}
val = FIX2LONG(x) ^ NUM2LONG(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;
if (TYPE(idx) == T_BIGNUM) {
idx = rb_big_norm(idx);
if (!FIXNUM_P(idx)) {
if (!RBIGNUM_SIGN(idx) || val >= 0)
return INT2FIX(0);
return INT2FIX(1);
}
}
i = NUM2LONG(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 DOUBLE2NUM(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.id2name -> string or nil
*
* Returns the name of the object whose symbol id is <i>fix</i>. If
* there is no symbol in the symbol table with this value, returns
* <code>nil</code>. <code>id2name</code> has nothing to do with the
* <code>Object.id</code> method. See also <code>Fixnum#to_sym</code>,
* <code>String#intern</code>, and class <code>Symbol</code>.
*
* symbol = :@inst_var #=> :@inst_var
* id = symbol.to_i #=> 9818
* id.id2name #=> "@inst_var"
*/
static VALUE
fix_id2name(VALUE fix)
{
VALUE name = rb_id2str(FIX2UINT(fix));
if (name) return rb_str_dup(name);
return Qnil;
}
/*
* call-seq:
* fix.to_sym -> aSymbol
*
* Returns the symbol whose integer value is <i>fix</i>. See also
* <code>Fixnum#id2name</code>.
*
* fred = :fred.to_i
* fred.id2name #=> "fred"
* fred.to_sym #=> :fred
*/
static VALUE
fix_to_sym(VALUE fix)
{
ID id = FIX2UINT(fix);
if (rb_id2name(id)) {
return ID2SYM(id);
}
return Qnil;
}
/*
* 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)
{
#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_quo, 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, "to_int", num_to_int, 0);
rb_define_method(rb_cNumeric, "scalar?", num_scalar_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_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_include_module(rb_cInteger, rb_mPrecision);
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, "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_cFixnum = rb_define_class("Fixnum", rb_cInteger);
rb_include_module(rb_cFixnum, rb_mPrecision);
rb_define_singleton_method(rb_cFixnum, "induced_from", rb_fix_induced_from, 1);
rb_define_singleton_method(rb_cInteger, "induced_from", rb_int_induced_from, 1);
rb_define_method(rb_cFixnum, "to_s", fix_to_s, -1);
rb_define_method(rb_cFixnum, "id2name", fix_id2name, 0);
rb_define_method(rb_cFixnum, "to_sym", fix_to_sym, 0);
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, "quo", fix_quo, 1);
rb_define_method(rb_cFixnum, "fdiv", fix_quo, 1);
rb_define_method(rb_cFixnum, "**", fix_pow, 1);
rb_define_method(rb_cFixnum, "abs", 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_singleton_method(rb_cFloat, "induced_from", rb_flo_induced_from, 1);
rb_include_module(rb_cFloat, rb_mPrecision);
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", DOUBLE2NUM(DBL_MIN));
rb_define_const(rb_cFloat, "MAX", DOUBLE2NUM(DBL_MAX));
rb_define_const(rb_cFloat, "EPSILON", DOUBLE2NUM(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, "%", 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, "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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