# class Integer

BigDecimal extends the native Integer class to provide the to_d method.

When you require the BigDecimal library in your application, this method will be available on Integer objects.

When mathn is required, Integer's division is enhanced to return more precise values from mathematical expressions.

```2/3*3  # => 0
require 'mathn'
2/3*3  # => 2

(2**72) / ((2**70) * 3)  # => 4/3
```

Holds Integer values. You cannot add a singleton method to an Integer. Any attempt to add a singleton method to an Integer object will raise a TypeError.

GMP_VERSION

### Public Class Methods

each_prime(ubound) { |prime| ... } click to toggle source

Iterates the given block over all prime numbers.

See `Prime`#each for more details.

```# File lib/prime.rb, line 48
def Integer.each_prime(ubound, &block) # :yields: prime
Prime.each(ubound, &block)
end```
from_prime_division(pd) click to toggle source

Re-composes a prime factorization and returns the product.

See Prime#int_from_prime_division for more details.

```# File lib/prime.rb, line 21
def Integer.from_prime_division(pd)
Prime.int_from_prime_division(pd)
end```

### Public Instance Methods

int % other → real click to toggle source

Returns `int` modulo `other`.

```VALUE
rb_int_modulo(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_mod(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_modulo(x, y);
}
return num_modulo(x, y);
}```
integer & integer → integer_result click to toggle source

Bitwise AND.

```VALUE
rb_int_and(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_and(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_and(x, y);
}
return Qnil;
}```
int * numeric → numeric_result click to toggle source

Performs multiplication: the class of the resulting object depends on the class of `numeric` and on the magnitude of the result. It may return a Bignum.

```VALUE
rb_int_mul(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_mul(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_mul(x, y);
}
return rb_num_coerce_bin(x, y, '*');
}```
integer ** numeric → numeric_result click to toggle source

Raises `integer` to the power of `numeric`, which may be negative or fractional. The result may be an Integer, or a Float

```2 ** 3      #=> 8
2 ** -1     #=> (1/2)
2 ** 0.5    #=> 1.4142135623731

123456789 ** 2      #=> 15241578750190521
123456789 ** 1.2    #=> 5126464716.09932
123456789 ** -2     #=> (1/15241578750190521)
```
```VALUE
rb_int_pow(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_pow(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_pow(x, y);
}
return Qnil;
}```
int + numeric → numeric_result click to toggle source

Performs addition: the class of the resulting object depends on the class of `numeric` and on the magnitude of the result. It may return a Bignum.

```VALUE
rb_int_plus(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_plus(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_plus(x, y);
}
return rb_num_coerce_bin(x, y, '+');
}```
int - numeric → numeric_result click to toggle source

Performs subtraction: the class of the resulting object depends on the class of `numeric` and on the magnitude of the result. It may return a Bignum.

```VALUE
rb_int_minus(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_minus(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_minus(x, y);
}
return rb_num_coerce_bin(x, y, '-');
}```
-int → integer click to toggle source

Negates `int`. (returns an integer whose value is 0-int)

```VALUE
rb_int_uminus(VALUE num)
{
if (FIXNUM_P(num)) {
return fix_uminus(num);
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_uminus(num);
}
return num_funcall0(num, idUMinus);
}```
int / numeric → numeric_result click to toggle source

Performs division: the class of the resulting object depends on the class of `numeric` and on the magnitude of the result. It may return a Bignum.

```VALUE
rb_int_div(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_div(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_div(x, y);
}
return Qnil;
}```
int < real → true or false click to toggle source

Returns `true` if the value of `int` is less than that of `real`.

```static VALUE
int_lt(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_lt(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_lt(x, y);
}
return Qnil;
}```
int << count → integer click to toggle source

Shifts `int` left `count` positions, or right if `count` is negative.

```VALUE
rb_int_lshift(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return rb_fix_lshift(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_lshift(x, y);
}
return Qnil;
}```
int <= real → true or false click to toggle source

Returns `true` if the value of `int` is less than or equal to that of `real`.

```static VALUE
int_le(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_le(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_le(x, y);
}
return Qnil;
}```
int <=> numeric → -1, 0, +1 or nil click to toggle source

Comparison—Returns `-1`, `0`, +`1` or `nil` depending on whether `int` is less than, equal to, or greater than `numeric`.

This is the basis for the tests in the Comparable module.

`nil` is returned if the two values are incomparable.

```VALUE
rb_int_cmp(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_cmp(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_cmp(x, y);
}
else {
rb_raise(rb_eNotImpError, "need to define `<=>' in %s", rb_obj_classname(x));
}
}```
int == other → true or false click to toggle source

Return `true` if `int` equals `other` numerically. Contrast this with `Integer#eql?`, which requires other to be a `Integer`.

```1 == 2      #=> false
1 == 1.0    #=> true
```
```VALUE
rb_int_equal(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_equal(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_eq(x, y);
}
return Qnil;
}```
===(p1) click to toggle source
```VALUE
rb_int_equal(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_equal(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_eq(x, y);
}
return Qnil;
}```
int > real → true or false click to toggle source

Returns `true` if the value of `int` is greater than that of `real`.

```VALUE
rb_int_gt(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_gt(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_gt(x, y);
}
return Qnil;
}```
int >= real → true or false click to toggle source

Returns `true` if the value of `int` is greater than or equal to that of `real`.

```VALUE
rb_int_ge(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_ge(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_ge(x, y);
}
return Qnil;
}```
int >> count → integer click to toggle source

Shifts `int` right `count` positions, or left if `count` is negative.

```static VALUE
rb_int_rshift(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return rb_fix_rshift(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_rshift(x, y);
}
return Qnil;
}```
int[n] → 0, 1 click to toggle source

Bit Reference—Returns the +n+th bit in the binary representation of `int`, where `int[0]` is the least significant bit.

For example:

```a = 0b11001100101010
30.downto(0) do |n| print a[n] end
#=> 0000000000000000011001100101010

a = 9**15
50.downto(0) do |n|
print a[n]
end
#=> 000101110110100000111000011110010100111100010111001
```
```static VALUE
int_aref(VALUE num, VALUE idx)
{
if (FIXNUM_P(num)) {
return fix_aref(num, idx);
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_aref(num, idx);
}
return Qnil;
}```
integer ^ integer → integer_result click to toggle source

Bitwise EXCLUSIVE OR.

```static VALUE
int_xor(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_xor(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_xor(x, y);
}
return Qnil;
}```
abs → integer click to toggle source

Returns the absolute value of `int`.

```-12345.abs   #=> 12345
12345.abs    #=> 12345
-1234567890987654321.abs   #=> 1234567890987654321
```
```VALUE
rb_int_abs(VALUE num)
{
if (FIXNUM_P(num)) {
return fix_abs(num);
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_abs(num);
}
return Qnil;
}```
bit_length → integer click to toggle source

Returns the number of bits of the value of int.

“the number of bits” means that the bit position of the highest bit which is different to the sign bit. (The bit position of the bit 2**n is n+1.) If there is no such bit (zero or minus one), zero is returned.

I.e. This method returns ceil(log2(int < 0 ? -int : int+1)).

```(-2**10000-1).bit_length  #=> 10001
(-2**10000).bit_length    #=> 10000
(-2**10000+1).bit_length  #=> 10000
(-2**1000-1).bit_length   #=> 1001
(-2**1000).bit_length     #=> 1000
(-2**1000+1).bit_length   #=> 1000
(-2**12-1).bit_length     #=> 13
(-2**12).bit_length       #=> 12
(-2**12+1).bit_length     #=> 12
-0x101.bit_length         #=> 9
-0x100.bit_length         #=> 8
-0xff.bit_length          #=> 8
-2.bit_length             #=> 1
-1.bit_length             #=> 0
0.bit_length              #=> 0
1.bit_length              #=> 1
0xff.bit_length           #=> 8
0x100.bit_length          #=> 9
(2**12-1).bit_length      #=> 12
(2**12).bit_length        #=> 13
(2**12+1).bit_length      #=> 13
(2**1000-1).bit_length    #=> 1000
(2**1000).bit_length      #=> 1001
(2**1000+1).bit_length    #=> 1001
(2**10000-1).bit_length   #=> 10000
(2**10000).bit_length     #=> 10001
(2**10000+1).bit_length   #=> 10001
```

This method can be used to detect overflow in Array#pack as follows.

```if n.bit_length < 32
[n].pack("l") # no overflow
else
raise "overflow"
end
```
```static VALUE
rb_int_bit_length(VALUE num)
{
if (FIXNUM_P(num)) {
return rb_fix_bit_length(num);
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_bit_length(num);
}
return Qnil;
}```
ceil([ndigits]) → integer or float click to toggle source

Returns the smallest number than or equal to `int` in decimal digits (default 0 digits).

Precision may be negative. Returns a floating point number when `ndigits` is positive, `self` for zero, and ceil up for negative.

```1.ceil        #=> 1
1.ceil(2)     #=> 1.0
15.ceil(-1)   #=> 20
```
```static VALUE
int_ceil(int argc, VALUE* argv, VALUE num)
{
int ndigits;

if (!rb_check_arity(argc, 0, 1)) return num;
ndigits = NUM2INT(argv[0]);
if (ndigits > 0) {
return rb_Float(num);
}
if (ndigits == 0) {
return num;
}
return rb_int_ceil(num, ndigits);
}```
chr([encoding]) → string click to toggle source

Returns a string containing the character represented by the `int`'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;
unsigned int i;
rb_encoding *enc;

if (rb_num_to_uint(num, &i) == 0) {
}
else if (FIXNUM_P(num)) {
rb_raise(rb_eRangeError, "%ld out of char range", FIX2LONG(num));
}
else {
rb_raise(rb_eRangeError, "bignum out of char range");
}

switch (argc) {
case 0:
if (0xff < i) {
enc = rb_default_internal_encoding();
if (!enc) {
rb_raise(rb_eRangeError, "%d out of char range", i);
}
goto decode;
}
c = (char)i;
if (i < 0x80) {
return rb_usascii_str_new(&c, 1);
}
else {
return rb_str_new(&c, 1);
}
case 1:
break;
default:
rb_check_arity(argc, 0, 1);
break;
}
enc = rb_to_encoding(argv[0]);
if (!enc) enc = rb_ascii8bit_encoding();
decode:
return rb_enc_uint_chr(i, enc);
}```
coerce(numeric) → array click to toggle source

Returns an array with both a `numeric` and a `big` represented as Bignum objects.

This is achieved by converting `numeric` to a Bignum.

A TypeError is raised if the `numeric` is not a Fixnum or Bignum type.

```(0x3FFFFFFFFFFFFFFF+1).coerce(42)   #=> [42, 4611686018427387904]
```
```static VALUE
rb_int_coerce(VALUE x, VALUE y)
{
if (RB_INTEGER_TYPE_P(y)) {
return rb_assoc_new(y, x);
}
else {
x = rb_Float(x);
y = rb_Float(y);
return rb_assoc_new(y, x);
}
}```
dclone() click to toggle source

provides a unified `clone` operation, for REXML::XPathParser to use across multiple Object types

```# File lib/rexml/xpath_parser.rb, line 22
def dclone ; self ; end```
denominator → 1 click to toggle source

Returns 1.

```static VALUE
integer_denominator(VALUE self)
{
return INT2FIX(1);
}```
digits → [int] click to toggle source
digits(base) → [int]

Returns the array including the digits extracted by place-value notation with radix `base` of `int`.

`base` should be greater than or equal to 2.

```12345.digits      #=> [5, 4, 3, 2, 1]
12345.digits(7)   #=> [4, 6, 6, 0, 5]
12345.digits(100) #=> [45, 23, 1]

-12345.digits(7)  #=> Math::DomainError
```
```static VALUE
rb_int_digits(int argc, VALUE *argv, VALUE num)
{
VALUE base_value;
long base;

if (rb_num_negative_p(num))
rb_raise(rb_eMathDomainError, "out of domain");

if (rb_check_arity(argc, 0, 1)) {
base_value = rb_to_int(argv[0]);
if (!RB_INTEGER_TYPE_P(base_value))
rb_raise(rb_eTypeError, "wrong argument type %s (expected Integer)",
rb_obj_classname(argv[0]));
if (RB_TYPE_P(base_value, T_BIGNUM))
return rb_int_digits_bigbase(num, base_value);

base = FIX2LONG(base_value);
if (base < 0)
else if (base < 2)
}
else
base = 10;

if (FIXNUM_P(num))
return rb_fix_digits(num, base);
else if (RB_TYPE_P(num, T_BIGNUM))
return rb_int_digits_bigbase(num, LONG2FIX(base));

return Qnil;
}```
div(numeric) → integer click to toggle source

Performs integer division: returns integer result of dividing `int` by `numeric`.

```VALUE
rb_int_idiv(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_idiv(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_idiv(x, y);
}
return num_div(x, y);
}```
divmod(numeric) → array click to toggle source

See `Numeric#divmod`.

```VALUE
rb_int_divmod(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_divmod(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_divmod(x, y);
}
return Qnil;
}```
downto(limit) {|i| block } → self click to toggle source
downto(limit) → an_enumerator

Iterates the given block, passing decreasing values from `int` down to and including `limit`.

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

```5.downto(1) { |n| print n, ".. " }
print "  Liftoff!\n"
#=> "5.. 4.. 3.. 2.. 1..   Liftoff!"
```
```static VALUE
int_downto(VALUE from, VALUE to)
{
RETURN_SIZED_ENUMERATOR(from, 1, &to, int_downto_size);
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;
}```
even? → true or false click to toggle source

Returns `true` if `int` is an even number.

```static VALUE
int_even_p(VALUE num)
{
if (FIXNUM_P(num)) {
if ((num & 2) == 0) {
return Qtrue;
}
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_even_p(num);
}
else if (rb_funcall(num, '%', 1, INT2FIX(2)) == INT2FIX(0)) {
return Qtrue;
}
return Qfalse;
}```
fdiv(numeric) → float click to toggle source

Returns the floating point result of dividing `integer` by `numeric`.

```654321.fdiv(13731)      #=> 47.6528293642124
654321.fdiv(13731.24)   #=> 47.6519964693647

-1234567890987654321.fdiv(13731)      #=> -89910996357705.5
-1234567890987654321.fdiv(13731.24)   #=> -89909424858035.7
```
```VALUE
rb_int_fdiv(VALUE x, VALUE y)
{
if (RB_INTEGER_TYPE_P(x)) {
return DBL2NUM(rb_int_fdiv_double(x, y));
}
return Qnil;
}```
floor([ndigits]) → integer or float click to toggle source

Returns the largest number less than or equal to `int` in decimal digits (default 0 digits).

Precision may be negative. Returns a floating point number when `ndigits` is positive, `self` for zero, and floor down for negative.

```1.floor        #=> 1
1.floor(2)     #=> 1.0
15.floor(-1)   #=> 10
```
```static VALUE
int_floor(int argc, VALUE* argv, VALUE num)
{
int ndigits;

if (!rb_check_arity(argc, 0, 1)) return num;
ndigits = NUM2INT(argv[0]);
if (ndigits > 0) {
return rb_Float(num);
}
if (ndigits == 0) {
return num;
}
return rb_int_floor(num, ndigits);
}```
gcd(int2) → integer click to toggle source

Returns the greatest common divisor (always positive). 0.gcd(x) and x.gcd(0) return abs(x).

```2.gcd(2)                    #=> 2
3.gcd(-7)                   #=> 1
((1<<31)-1).gcd((1<<61)-1)  #=> 1
```
```VALUE
rb_gcd(VALUE self, VALUE other)
{
other = nurat_int_value(other);
return f_gcd(self, other);
}```
gcdlcm(int2) → array click to toggle source

Returns an array; [int.gcd(int2), int.lcm(int2)].

```2.gcdlcm(2)                    #=> [2, 2]
3.gcdlcm(-7)                   #=> [1, 21]
((1<<31)-1).gcdlcm((1<<61)-1)  #=> [1, 4951760154835678088235319297]
```
```VALUE
rb_gcdlcm(VALUE self, VALUE other)
{
other = nurat_int_value(other);
return rb_assoc_new(f_gcd(self, other), f_lcm(self, other));
}```
inspect(*args)
Alias for: to_s
integer? → true click to toggle source

Since `int` is already an Integer, this always returns `true`.

```static VALUE
int_int_p(VALUE num)
{
return Qtrue;
}```
lcm(int2) → integer click to toggle source

Returns the least common multiple (always positive). 0.lcm(x) and x.lcm(0) return zero.

```2.lcm(2)                    #=> 2
3.lcm(-7)                   #=> 21
((1<<31)-1).lcm((1<<61)-1)  #=> 4951760154835678088235319297
```
```VALUE
rb_lcm(VALUE self, VALUE other)
{
other = nurat_int_value(other);
return f_lcm(self, other);
}```
magnitude → integer click to toggle source

Returns the absolute value of `int`.

```-12345.abs   #=> 12345
12345.abs    #=> 12345
-1234567890987654321.abs   #=> 1234567890987654321
```
```VALUE
rb_int_abs(VALUE num)
{
if (FIXNUM_P(num)) {
return fix_abs(num);
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_abs(num);
}
return Qnil;
}```
modulo(other) → real click to toggle source

Returns `int` modulo `other`.

```VALUE
rb_int_modulo(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_mod(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_modulo(x, y);
}
return num_modulo(x, y);
}```
next → integer click to toggle source

Returns the Integer equal to `int` + 1.

```1.next      #=> 2
(-1).next   #=> 0
1.succ      #=> 2
(-1).succ   #=> 0
```
```VALUE
rb_int_succ(VALUE num)
{
if (FIXNUM_P(num)) {
long i = FIX2LONG(num) + 1;
return LONG2NUM(i);
}
if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_plus(num, INT2FIX(1));
}
return num_funcall1(num, '+', INT2FIX(1));
}```
numerator → self click to toggle source

Returns self.

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

Returns `true` if `int` is an odd number.

```static VALUE
int_odd_p(VALUE num)
{
if (FIXNUM_P(num)) {
if (num & 2) {
return Qtrue;
}
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_odd_p(num);
}
else if (rb_funcall(num, '%', 1, INT2FIX(2)) != INT2FIX(0)) {
return Qtrue;
}
return Qfalse;
}```
ord → self click to toggle source

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(VALUE num)
{
return num;
}```
pred → integer click to toggle source

Returns the Integer equal to `int` - 1.

```1.pred      #=> 0
(-1).pred   #=> -2
```
```VALUE
rb_int_pred(VALUE num)
{
if (FIXNUM_P(num)) {
long i = FIX2LONG(num) - 1;
return LONG2NUM(i);
}
if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_minus(num, INT2FIX(1));
}
return num_funcall1(num, '-', INT2FIX(1));
}```
prime?() click to toggle source

Returns true if `self` is a prime number, else returns false.

```# File lib/prime.rb, line 33
def prime?
return self >= 2 if self <= 3
return true if self == 5
return false unless 30.gcd(self) == 1
(7..Math.sqrt(self).to_i).step(30) do |p|
return false if
self%(p)    == 0 || self%(p+4)  == 0 || self%(p+6)  == 0 || self%(p+10) == 0 ||
self%(p+12) == 0 || self%(p+16) == 0 || self%(p+22) == 0 || self%(p+24) == 0
end
true
end```
prime_division(generator = Prime::Generator23.new) click to toggle source

Returns the factorization of `self`.

See Prime#prime_division for more details.

```# File lib/prime.rb, line 28
def prime_division(generator = Prime::Generator23.new)
Prime.prime_division(self, generator)
end```
rationalize([eps]) → rational click to toggle source

Returns the value as a rational. The optional argument eps is always ignored.

```static VALUE
integer_rationalize(int argc, VALUE *argv, VALUE self)
{
rb_scan_args(argc, argv, "01", NULL);
return integer_to_r(self);
}```
remainder(numeric) → real click to toggle source

Returns the remainder after dividing big by numeric as:

`x.remainder(y) means x-y*(x/y).truncate`

Examples

```5.remainder(3)    #=> 2
-5.remainder(3)   #=> -2
5.remainder(-3)   #=> 2
-5.remainder(-3)  #=> -2

-1234567890987654321.remainder(13731)      #=> -6966
-1234567890987654321.remainder(13731.24)   #=> -9906.22531493148
```

See Numeric#divmod.

```VALUE
int_remainder(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return num_remainder(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_remainder(x, y);
}
return Qnil;
}```
round([ndigits]) → integer or float click to toggle source

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

Precision may be negative. Returns a floating point number when `ndigits` is positive, `self` for zero, and round down for negative.

```1.round        #=> 1
1.round(2)     #=> 1.0
15.round(-1)   #=> 20
```
```static VALUE
int_round(int argc, VALUE* argv, VALUE num)
{
int ndigits;
int mode;
VALUE nd, opt;

if (!rb_scan_args(argc, argv, "01:", &nd, &opt)) return num;
ndigits = NUM2INT(nd);
mode = rb_num_get_rounding_option(opt);
if (ndigits > 0) {
return rb_Float(num);
}
if (ndigits == 0) {
return num;
}
return rb_int_round(num, ndigits, mode);
}```
size → int click to toggle source

Returns the number of bytes in the machine representation of `int`.

```1.size            #=> 4
-1.size           #=> 4
2147483647.size   #=> 4
(256**10 - 1).size   #=> 12
(256**20 - 1).size   #=> 20
(256**40 - 1).size   #=> 40
```
```static VALUE
int_size(VALUE num)
{
if (FIXNUM_P(num)) {
return fix_size(num);
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_size_m(num);
}
return Qnil;
}```
succ → integer click to toggle source

Returns the Integer equal to `int` + 1.

```1.next      #=> 2
(-1).next   #=> 0
1.succ      #=> 2
(-1).succ   #=> 0
```
```VALUE
rb_int_succ(VALUE num)
{
if (FIXNUM_P(num)) {
long i = FIX2LONG(num) + 1;
return LONG2NUM(i);
}
if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_plus(num, INT2FIX(1));
}
return num_funcall1(num, '+', INT2FIX(1));
}```
times {|i| block } → self click to toggle source
times → an_enumerator

Iterates the given block `int` times, passing in values from zero to `int - 1`.

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

```5.times do |i|
print i, " "
end
#=> 0 1 2 3 4
```
```static VALUE
int_dotimes(VALUE num)
{
RETURN_SIZED_ENUMERATOR(num, 0, 0, int_dotimes_size);

if (FIXNUM_P(num)) {
long i, end;

end = FIX2LONG(num);
for (i=0; i<end; i++) {
rb_yield_1(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;
}```
to_bn() click to toggle source

Casts an Integer as an OpenSSL::BN

```# File ext/openssl/lib/openssl/bn.rb, line 35
def to_bn
OpenSSL::BN::new(self)
end```
to_d → bigdecimal click to toggle source

Convert `int` to a BigDecimal and return it.

```require 'bigdecimal'
require 'bigdecimal/util'

42.to_d
# => 0.42e2
```
```# File ext/bigdecimal/lib/bigdecimal/util.rb, line 17
def to_d
BigDecimal(self)
end```
to_f → float click to toggle source

Converts `int` to a `Float`. If `int` doesn't fit in a `Float`, the result is infinity.

```static VALUE
int_to_f(VALUE num)
{
double val;

if (FIXNUM_P(num)) {
val = (double)FIX2LONG(num);
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
val = rb_big2dbl(num);
}
else {
rb_raise(rb_eNotImpError, "Unknown subclass for to_f: %s", rb_obj_classname(num));
}

return DBL2NUM(val);
}```
to_i → integer click to toggle source

As `int` is already an Integer, all these methods simply return the receiver.

Synonyms is to_int

```static VALUE
int_to_i(VALUE num)
{
return num;
}```
to_i → integer click to toggle source

As `int` is already an Integer, all these methods simply return the receiver.

Synonyms is to_int

```static VALUE
int_to_i(VALUE num)
{
return num;
}```
to_r → rational click to toggle source

Returns the value as a rational.

```1.to_r        #=> (1/1)
(1<<64).to_r  #=> (18446744073709551616/1)
```
```static VALUE
integer_to_r(VALUE self)
{
return rb_rational_new1(self);
}```
to_s(base=10) → string click to toggle source

Returns a string containing the representation of `int` radix `base` (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"
78546939656932.to_s(36)  #=> "rubyrules"
```
```static VALUE
int_to_s(int argc, VALUE *argv, VALUE x)
{
int base;

if (rb_check_arity(argc, 0, 1))
base = NUM2INT(argv[0]);
else
base = 10;
return rb_int2str(x, base);
}```
Also aliased as: inspect
truncate([ndigits]) → integer or float click to toggle source

Returns the smallest number than or equal to `int` in decimal digits (default 0 digits).

Precision may be negative. Returns a floating point number when `ndigits` is positive, `self` for zero, and truncate up for negative.

```1.truncate        #=> 1
1.truncate(2)     #=> 1.0
15.truncate(-1)   #=> 10
```
```static VALUE
int_truncate(int argc, VALUE* argv, VALUE num)
{
int ndigits;

if (!rb_check_arity(argc, 0, 1)) return num;
ndigits = NUM2INT(argv[0]);
if (ndigits > 0) {
return rb_Float(num);
}
if (ndigits == 0) {
return num;
}
return rb_int_truncate(num, ndigits);
}```
upto(limit) {|i| block } → self click to toggle source
upto(limit) → an_enumerator

Iterates the given block, passing in integer values from `int` up to and including `limit`.

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

For example:

```5.upto(10) { |i| print i, " " }
#=> 5 6 7 8 9 10
```
```static VALUE
int_upto(VALUE from, VALUE to)
{
RETURN_SIZED_ENUMERATOR(from, 1, &to, int_upto_size);
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;
}```
integer | integer → integer_result click to toggle source

Bitwise OR.

```static VALUE
int_or(VALUE x, VALUE y)
{
if (FIXNUM_P(x)) {
return fix_or(x, y);
}
else if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_or(x, y);
}
return Qnil;
}```
~integer → integer click to toggle source

One's complement: returns a number where each bit is flipped.

Inverts the bits in an integer. As Integers are conceptually infinite length, the result acts as if it had an infinite number of one bits to the left. In hex representations, this is displayed as two periods to the left of the digits.

```sprintf("%X", ~0x1122334455)    #=> "..FEEDDCCBBAA"
```
```static VALUE
int_comp(VALUE num)
{
if (FIXNUM_P(num)) {
return fix_comp(num);
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
return rb_big_comp(num);
}
return Qnil;
}```