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# Numeric

The top-level number class.

### Public Instance Methods

modulo(numeric) → real click to toggle source
`x.modulo(y) means x-y*(x/y).floor`

Equivalent to `num.divmod(numeric)[1]`.

See #divmod.

```
static VALUE
num_modulo(VALUE x, VALUE y)
{
return rb_funcall(x, '-', 1,
rb_funcall(y, '*', 1,
rb_funcall(x, rb_intern("div"), 1, y)));
}
```
+num → num click to toggle source

```
static VALUE
num_uplus(VALUE num)
{
return num;
}
```
-num → numeric click to toggle source

Unary Minusâ€”Returns the receiver's value, negated.

```
static VALUE
num_uminus(VALUE num)
{
VALUE zero;

zero = INT2FIX(0);
do_coerce(&zero, &num, TRUE);

return rb_funcall(zero, '-', 1, num);
}
```
number <=> other → 0 or nil click to toggle source

Returns zero if `number` equals `other`, otherwise `nil` is returned if the two values are incomparable.

```
static VALUE
num_cmp(VALUE x, VALUE y)
{
if (x == y) return INT2FIX(0);
return Qnil;
}
```
abs → numeric click to toggle source

Returns the absolute value of `num`.

```12.abs         #=> 12
(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
```

#magnitude is an alias of #abs.

```
static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return rb_funcall(num, rb_intern("-@"), 0);
}
return num;
}
```
abs2 → real click to toggle source

Returns square of self.

```
static VALUE
numeric_abs2(VALUE self)
{
return f_mul(self, self);
}
```
angle → 0 or float click to toggle source

Returns 0 if the value is positive, pi otherwise.

```
static VALUE
numeric_arg(VALUE self)
{
if (f_positive_p(self))
return INT2FIX(0);
return rb_const_get(rb_mMath, id_PI);
}
```
arg → 0 or float click to toggle source

Returns 0 if the value is positive, pi otherwise.

```
static VALUE
numeric_arg(VALUE self)
{
if (f_positive_p(self))
return INT2FIX(0);
return rb_const_get(rb_mMath, id_PI);
}
```
ceil → integer click to toggle source

Returns the smallest possible Integer that is greater than or equal to `num`.

Numeric achieves this by converting itself to a Float then invoking Float#ceil.

```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));
}
```
coerce(numeric) → array click to toggle source

If a +numeric is the same type as `num`, returns an array containing `numeric` and `num`. Otherwise, returns an array with both a `numeric` and `num` represented as Float 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);
}
```
conj → self click to toggle source
conjugate → self

Returns self.

```
static VALUE
numeric_conj(VALUE self)
{
return self;
}
```
conjugate → self click to toggle source

Returns self.

```
static VALUE
numeric_conj(VALUE self)
{
return self;
}
```
denominator → integer click to toggle source

Returns the denominator (always positive).

```
static VALUE
numeric_denominator(VALUE self)
{
return f_denominator(f_to_r(self));
}
```
div(numeric) → integer click to toggle source

Uses `/` to perform division, then converts the result to an integer. `numeric` does not define the `/` operator; this is left to subclasses.

Equivalent to `num.divmod(numeric)[0]`.

See #divmod.

```
static VALUE
num_div(VALUE x, VALUE y)
{
if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv();
return rb_funcall(rb_funcall(x, '/', 1, y), rb_intern("floor"), 0);
}
```
divmod(numeric) → array click to toggle source

Returns an array containing the quotient and modulus obtained by dividing `num` by `numeric`.

If `q, r = * x.divmod(y)`, then

```q = floor(x/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     |  -4     |   -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), num_modulo(x, y));
}
```
eql?(numeric) → true or false click to toggle source

Returns `true` if `num` and `numeric` 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);
}
```
fdiv(numeric) → float click to toggle source

Returns float division.

```
static VALUE
num_fdiv(VALUE x, VALUE y)
{
return rb_funcall(rb_Float(x), '/', 1, y);
}
```
floor → integer click to toggle source

Returns the largest integer less than or equal to `num`.

Numeric implements this by converting an Integer to a Float and invoking Float#floor.

```1.floor      #=> 1
(-1).floor   #=> -1
```
```
static VALUE
num_floor(VALUE num)
{
return flo_floor(rb_Float(num));
}
```
i → Complex(0,num) click to toggle source

Returns the corresponding imaginary number. Not available for complex numbers.

```
static VALUE
num_imaginary(VALUE num)
{
return rb_complex_new(INT2FIX(0), num);
}
```
imag → 0 click to toggle source
imaginary → 0

Returns zero.

```
static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}
```
imaginary → 0 click to toggle source

Returns zero.

```
static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}
```
initialize_copy(p1) click to toggle source

Numerics are immutable values, which should not be copied.

Any attempt to use this method on a Numeric will raise a TypeError.

```
static VALUE
num_init_copy(VALUE x, VALUE y)
{
rb_raise(rb_eTypeError, "can't copy %"PRIsVALUE, rb_obj_class(x));

UNREACHABLE;
}
```
integer? → true or false click to toggle source

Returns `true` if `num` is an Integer (including Fixnum and Bignum).

```(1.0).integer? #=> false
(1).integer?   #=> true
```
```
static VALUE
num_int_p(VALUE num)
{
return Qfalse;
}
```
magnitude → numeric click to toggle source

Returns the absolute value of `num`.

```12.abs         #=> 12
(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
```

#magnitude is an alias of #abs.

```
static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return rb_funcall(num, rb_intern("-@"), 0);
}
return num;
}
```
modulo(numeric) → real click to toggle source
`x.modulo(y) means x-y*(x/y).floor`

Equivalent to `num.divmod(numeric)[1]`.

See #divmod.

```
static VALUE
num_modulo(VALUE x, VALUE y)
{
return rb_funcall(x, '-', 1,
rb_funcall(y, '*', 1,
rb_funcall(x, rb_intern("div"), 1, y)));
}
```
nonzero? → self or nil click to toggle source

Returns `self` if `num` is not zero, `nil` 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;
}
```
numerator → integer click to toggle source

Returns the numerator.

```
static VALUE
numeric_numerator(VALUE self)
{
return f_numerator(f_to_r(self));
}
```
phase → 0 or float click to toggle source

Returns 0 if the value is positive, pi otherwise.

```
static VALUE
numeric_arg(VALUE self)
{
if (f_positive_p(self))
return INT2FIX(0);
return rb_const_get(rb_mMath, id_PI);
}
```
polar → array click to toggle source

Returns an array; [num.abs, num.arg].

```
static VALUE
numeric_polar(VALUE self)
{
return rb_assoc_new(f_abs(self), f_arg(self));
}
```
quo(int_or_rat) → rat click to toggle source
quo(flo) → flo

Returns most exact division (rational for integers, float for floats).

```
static VALUE
numeric_quo(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FLOAT)) {
return f_fdiv(x, y);
}

#ifdef CANON
if (canonicalization) {
x = rb_rational_raw1(x);
}
else
#endif
{
x = rb_convert_type(x, T_RATIONAL, "Rational", "to_r");
}
return rb_funcall(x, '/', 1, y);
}
```
real → self click to toggle source

Returns self.

```
static VALUE
numeric_real(VALUE self)
{
return self;
}
```
real? → true or false click to toggle source

Returns `true` if `num` is a Real number. (i.e. not Complex).

```
static VALUE
num_real_p(VALUE num)
{
return Qtrue;
}
```
rect → array click to toggle source
rectangular → array

Returns an array; [num, 0].

```
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
```
rectangular → array click to toggle source

Returns an array; [num, 0].

```
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
```
remainder(numeric) → real click to toggle source
`x.remainder(y) means x-y*(x/y).truncate`

See #divmod.

```
static VALUE
num_remainder(VALUE x, VALUE y)
{
VALUE z = rb_funcall(x, '%', 1, y);

if ((!rb_equal(z, INT2FIX(0))) &&
((negative_int_p(x) &&
positive_int_p(y)) ||
(positive_int_p(x) &&
negative_int_p(y)))) {
return rb_funcall(z, '-', 1, y);
}
return z;
}
```
round([ndigits]) → integer or float click to toggle source

Rounds `num` to a given precision in decimal digits (default 0 digits).

Precision may be negative. Returns a floating point number when `ndigits` is more than zero.

Numeric implements this by converting itself to a Float and invoking Float#round.

```
static VALUE
num_round(int argc, VALUE* argv, VALUE num)
{
return flo_round(argc, argv, rb_Float(num));
}
```

Trap attempts to add methods to Numeric objects. Always raises a TypeError.

Numerics should be values; singleton_methods should not be added to them.

```
static VALUE
{
ID mid = rb_to_id(name);
/* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */
rb_remove_method_id(rb_singleton_class(x), mid);
rb_raise(rb_eTypeError,
"can't define singleton method \"%"PRIsVALUE"\" for %"PRIsVALUE,
rb_id2str(mid),
rb_obj_class(x));

UNREACHABLE;
}
```
step(by: step, to: limit) {|i| block } → self click to toggle source
step(by: step, to: limit) → an_enumerator
step(limit=nil, step=1) {|i| block } → self
step(limit=nil, step=1) → an_enumerator

Invokes the given block with the sequence of numbers starting at `num`, incremented by `step` (defaulted to `1`) on each call.

The loop finishes when the value to be passed to the block is greater than `limit` (if `step` is positive) or less than `limit` (if `step` is negative), where limit is defaulted to infinity.

In the recommended keyword argument style, either or both of `step` and `limit` (default infinity) can be omitted. In the fixed position argument style, zero as a step (i.e. num.step(limit, 0)) is not allowed for historical compatibility reasons.

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 the following expression:

```floor(n + n*epsilon)+ 1
```

Where the `n` is the following:

```n = (limit - num)/step
```

Otherwise, the loop starts at `num`, uses either the less-than (<) or greater-than (>) operator to compare the counter against `limit`, and increments itself using the `+` operator.

If no block is given, an Enumerator is returned instead.

For example:

```p 1.step.take(4)
p 10.step(by: -1).take(4)
3.step(to: 5) { |i| print i, " " }
1.step(10, 2) { |i| print i, " " }
Math::E.step(to: Math::PI, by: 0.2) { |f| print f, " " }
```

Will produce:

```[1, 2, 3, 4]
[10, 9, 8, 7]
3 4 5
1 3 5 7 9
2.71828182845905 2.91828182845905 3.11828182845905```
```
static VALUE
num_step(int argc, VALUE *argv, VALUE from)
{
VALUE to, step;
int desc, inf;

RETURN_SIZED_ENUMERATOR(from, argc, argv, num_step_size);

desc = num_step_scan_args(argc, argv, &to, &step);
if (RTEST(rb_num_coerce_cmp(step, INT2FIX(0), id_eq))) {
inf = 1;
}
else if (RB_TYPE_P(to, T_FLOAT)) {
double f = RFLOAT_VALUE(to);
inf = isinf(f) && (signbit(f) ? desc : !desc);
}
else inf = 0;

if (FIXNUM_P(from) && (inf || FIXNUM_P(to)) && FIXNUM_P(step)) {
long i = FIX2LONG(from);
long diff = FIX2LONG(step);

if (inf) {
for (;; i += diff)
rb_yield(LONG2FIX(i));
}
else {
long end = FIX2LONG(to);

if (desc) {
for (; i >= end; i += diff)
rb_yield(LONG2FIX(i));
}
else {
for (; i <= end; i += diff)
rb_yield(LONG2FIX(i));
}
}
}
else if (!ruby_float_step(from, to, step, FALSE)) {
VALUE i = from;

if (inf) {
for (;; i = rb_funcall(i, '+', 1, step))
rb_yield(i);
}
else {
ID cmp = desc ? '<' : '>';

for (; !RTEST(rb_funcall(i, cmp, 1, to)); i = rb_funcall(i, '+', 1, step))
rb_yield(i);
}
}
return from;
}
```
to_c → complex click to toggle source

Returns the value as a complex.

```
static VALUE
numeric_to_c(VALUE self)
{
return rb_complex_new1(self);
}
```
to_int → integer click to toggle source

Invokes the child class's `to_i` method to convert `num` to an integer.

```1.0.class => Float
1.0.to_int.class => Fixnum
1.0.to_i.class => Fixnum```
```
static VALUE
num_to_int(VALUE num)
{
return rb_funcall(num, id_to_i, 0, 0);
}
```
truncate → integer click to toggle source

Returns `num` truncated to an Integer.

Numeric implements this by converting its value to a Float and invoking Float#truncate.

```
static VALUE
num_truncate(VALUE num)
{
return flo_truncate(rb_Float(num));
}
```
zero? → true or false click to toggle source

Returns `true` if `num` has a zero value.

```
static VALUE
num_zero_p(VALUE num)
{
if (rb_equal(num, INT2FIX(0))) {
return Qtrue;
}
return Qfalse;
}
```