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# Numeric

Document-class: FloatDomainError

Raised when attempting to convert special float values (in particular infinite or NaN) to numerical classes which don't support them.

```Float::INFINITY.to_r
```

raises the exception:

`FloatDomainError: Infinity`

### Public Instance Methods

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

Equivalent to num.divmod(aNumeric).

See `Numeric#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);
}
```
num <=> other → 0 or nil click to toggle source

Returns zero if num equals other, `nil` otherwise.

```
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
```
```
static VALUE
num_abs(VALUE num)
{
if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) {
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 `Integer` greater than or equal to num. Class `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 aNumeric is the same type as num, returns an array containing aNumeric and num. Otherwise, returns an array with both aNumeric 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(aNumeric).

See `Numeric#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 anInteger 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);
}
```
integer? → true or false click to toggle source

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

```
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
```
```
static VALUE
num_abs(VALUE num)
{
if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) {
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(aNumeric).

See `Numeric#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(numeric) → real click to toggle source

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);
}
```
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` (i.e. non `Complex`).

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

Returns an array; [num, 0].

```
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
```
rect → 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 `Numeric#divmod`.

```
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;
}
```
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`

```
static VALUE
{
ID mid = 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_id(rb_singleton_class(x), mid);
rb_raise(rb_eTypeError,
"can't define singleton method \"%s\" for %s",
rb_id2name(mid),
rb_obj_classname(x));
return Qnil;                /* not reached */
}
```
step(limit[, step]) {|i| block } → self click to toggle source
step(limit[, step]) → an_enumerator

Invokes block with the sequence of numbers starting at num, incremented by step (default 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). 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 floor(n + n*epsilon)+ 1 times, where n = (limit - num)/step. Otherwise, the loop starts at num, uses either the `<` or `>` operator to compare the counter against limit, and increments itself using the `+` operator.

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

```1.step(10, 2) { |i| print i, " " }
Math::E.step(Math::PI, 0.2) { |f| print f, " " }
```

produces:

```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 (%d for 1..2)", argc);
}
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 (!ruby_float_step(from, to, step, FALSE)) {
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;
}
```
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.

```
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;
}
```