Integer

Class

An Integer object represents an integer value.

You can create an Integer object explicitly with:

An integer literal.

You can convert certain objects to Integers with:

Method Integer.

An attempt to add a singleton method to an instance of this class causes an exception to be raised.

What’s Here

First, what’s elsewhere. Class Integer:

Inherits from class Numeric and class Object.
Includes module Comparable.

Here, class Integer provides methods for:

Querying

allbits?: Returns whether all bits in self are set.
anybits?: Returns whether any bits in self are set.
nobits?: Returns whether no bits in self are set.

Comparing

<: Returns whether self is less than the given value.
<=: Returns whether self is less than or equal to the given value.
<=>: Returns a number indicating whether self is less than, equal to, or greater than the given value.
== (aliased as ===): Returns whether self is equal to the given
```
value.
```
>: Returns whether self is greater than the given value.
>=: Returns whether self is greater than or equal to the given value.

Converting

::sqrt: Returns the integer square root of the given value.
::try_convert: Returns the given value converted to an Integer.
% (aliased as modulo): Returns self modulo the given value.
&: Returns the bitwise AND of self and the given value.
*: Returns the product of self and the given value.
**: Returns the value of self raised to the power of the given value.
+: Returns the sum of self and the given value.
-: Returns the difference of self and the given value.
/: Returns the quotient of self and the given value.
<<: Returns the value of self after a leftward bit-shift.
>>: Returns the value of self after a rightward bit-shift.
[]: Returns a slice of bits from self.
^: Returns the bitwise EXCLUSIVE OR of self and the given value.
ceil: Returns the smallest number greater than or equal to self.
chr: Returns a 1-character string containing the character represented by the value of self.
digits: Returns an array of integers representing the base-radix digits of self.
div: Returns the integer result of dividing self by the given value.
divmod: Returns a 2-element array containing the quotient and remainder results of dividing self by the given value.
fdiv: Returns the Float result of dividing self by the given value.
floor: Returns the greatest number smaller than or equal to self.
pow: Returns the modular exponentiation of self.
pred: Returns the integer predecessor of self.
remainder: Returns the remainder after dividing self by the given value.
round: Returns self rounded to the nearest value with the given precision.
succ (aliased as next): Returns the integer successor of self.
to_f: Returns self converted to a Float.
to_s (aliased as inspect): Returns a string containing the place-value representation of self in the given radix.
truncate: Returns self truncated to the given precision.
|: Returns the bitwise OR of self and the given value.

Other

downto: Calls the given block with each integer value from self down to the given value.
times: Calls the given block self times with each integer in (0..self-1).
upto: Calls the given block with each integer value from self up to the given value.

Constants

Integer.sqrt(numeric) → integer

numeric.c View on GitHub

          
            static VALUE
rb_int_s_isqrt(VALUE self, VALUE num)
{
    unsigned long n, sq;
    num = rb_to_int(num);
    if (FIXNUM_P(num)) {
        if (FIXNUM_NEGATIVE_P(num)) {
            domain_error("isqrt");
        }
        n = FIX2ULONG(num);
        sq = rb_ulong_isqrt(n);
        return LONG2FIX(sq);
    }
    else {
        size_t biglen;
        if (RBIGNUM_NEGATIVE_P(num)) {
            domain_error("isqrt");
        }
        biglen = BIGNUM_LEN(num);
        if (biglen == 0) return INT2FIX(0);
#if SIZEOF_BDIGIT <= SIZEOF_LONG
        /* short-circuit */
        if (biglen == 1) {
            n = BIGNUM_DIGITS(num)[0];
            sq = rb_ulong_isqrt(n);
            return ULONG2NUM(sq);
        }
#endif
        return rb_big_isqrt(num);
    }
}

Returns the integer square root of the non-negative integer n, which is the largest non-negative integer less than or equal to the square root of numeric.

Integer.sqrt(0)       # => 0
Integer.sqrt(1)       # => 1
Integer.sqrt(24)      # => 4
Integer.sqrt(25)      # => 5
Integer.sqrt(10**400) # => 10**200

If numeric is not an Integer, it is converted to an Integer:

Integer.sqrt(Complex(4, 0))  # => 2
Integer.sqrt(Rational(4, 1)) # => 2
Integer.sqrt(4.0)            # => 2
Integer.sqrt(3.14159)        # => 1

This method is equivalent to Math.sqrt(numeric).floor, except that the result of the latter code may differ from the true value due to the limited precision of floating point arithmetic.

Integer.sqrt(10**46)    # => 100000000000000000000000
Math.sqrt(10**46).floor # => 99999999999999991611392

Raises an exception if numeric is negative.

Integer.try_convert(object) → object, integer, or nil

numeric.c View on GitHub

          
            static VALUE
int_s_try_convert(VALUE self, VALUE num)
{
    return rb_check_integer_type(num);
}

If object is an Integer object, returns object.

Integer.try_convert(1) # => 1

Otherwise if object responds to :to_int, calls object.to_int and returns the result.

Integer.try_convert(1.25) # => 1

Returns nil if object does not respond to :to_int

Integer.try_convert([]) # => nil

Raises an exception unless object.to_int returns an Integer object.

Instance Methods

self % other → real_number

numeric.c View on GitHub

          
            VALUE
rb_int_modulo(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_mod(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_modulo(x, y);
    }
    return num_modulo(x, y);
}

Returns self modulo other as a real number.

For integer n and real number r, these expressions are equivalent:

n % r
n-r*(n/r).floor
n.divmod(r)[1]

See Numeric#divmod.

Examples:

10 % 2              # => 0
10 % 3              # => 1
10 % 4              # => 2

10 % -2             # => 0
10 % -3             # => -2
10 % -4             # => -2

10 % 3.0            # => 1.0
10 % Rational(3, 1) # => (1/1)

self & other → integer

numeric.c View on GitHub

          
            VALUE
rb_int_and(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_and(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_and(x, y);
    }
    return Qnil;
}

Bitwise AND; each bit in the result is 1 if both corresponding bits in self and other are 1, 0 otherwise:

"%04b" % (0b0101 & 0b0110) # => "0100"

Raises an exception if other is not an Integer.

Related: Integer#| (bitwise OR), Integer#^ (bitwise EXCLUSIVE OR).

self * numeric → numeric_result

numeric.c View on GitHub

          
            VALUE
rb_int_mul(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_mul(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_mul(x, y);
    }
    return rb_num_coerce_bin(x, y, '*');
}

Performs multiplication:

4 * 2              # => 8
4 * -2             # => -8
-4 * 2             # => -8
4 * 2.0            # => 8.0
4 * Rational(1, 3) # => (4/3)
4 * Complex(2, 0)  # => (8+0i)

self ** numeric → numeric_result

numeric.c View on GitHub

          
            VALUE
rb_int_pow(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_pow(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_pow(x, y);
    }
    return Qnil;
}

Raises self to the power of numeric:

2 ** 3              # => 8
2 ** -3             # => (1/8)
-2 ** 3             # => -8
-2 ** -3            # => (-1/8)
2 ** 3.3            # => 9.849155306759329
2 ** Rational(3, 1) # => (8/1)
2 ** Complex(3, 0)  # => (8+0i)

self + numeric → numeric_result

numeric.c View on GitHub

          
            VALUE
rb_int_plus(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_plus(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_plus(x, y);
    }
    return rb_num_coerce_bin(x, y, '+');
}

Performs addition:

2 + 2              # => 4
-2 + 2             # => 0
-2 + -2            # => -4
2 + 2.0            # => 4.0
2 + Rational(2, 1) # => (4/1)
2 + Complex(2, 0)  # => (4+0i)

self - numeric → numeric_result

numeric.c View on GitHub

          
            VALUE
rb_int_minus(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_minus(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_minus(x, y);
    }
    return rb_num_coerce_bin(x, y, '-');
}

Performs subtraction:

4 - 2              # => 2
-4 - 2             # => -6
-4 - -2            # => -2
4 - 2.0            # => 2.0
4 - Rational(2, 1) # => (2/1)
4 - Complex(2, 0)  # => (2+0i)

self / numeric → numeric_result

numeric.c View on GitHub

          
            VALUE
rb_int_div(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_div(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_div(x, y);
    }
    return Qnil;
}

Performs division; for integer numeric, truncates the result to an integer:

 4 / 3              # => 1
 4 / -3             # => -2
 -4 / 3             # => -2
 -4 / -3            # => 1

For other +numeric+, returns non-integer result:

 4 / 3.0            # => 1.3333333333333333
 4 / Rational(3, 1) # => (4/3)
 4 / Complex(3, 0)  # => ((4/3)+0i)

self < other → true or false

numeric.c View on GitHub

          
            static VALUE
int_lt(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_lt(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_lt(x, y);
    }
    return Qnil;
}

Returns true if the value of self is less than that of other:

  1 < 0              # => false
  1 < 1              # => false
  1 < 2              # => true
  1 < 0.5            # => false
  1 < Rational(1, 2) # => false

Raises an exception if the comparison cannot be made.

self <= real → true or false

numeric.c View on GitHub

          
            static VALUE
int_le(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_le(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_le(x, y);
    }
    return Qnil;
}

Returns true if the value of self is less than or equal to that of other:

1 <= 0              # => false
1 <= 1              # => true
1 <= 2              # => true
1 <= 0.5            # => false
1 <= Rational(1, 2) # => false

Raises an exception if the comparison cannot be made.

self <=> other → -1, 0, +1, or nil

numeric.c View on GitHub

          
            VALUE
rb_int_cmp(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_cmp(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_cmp(x, y);
    }
    else {
        rb_raise(rb_eNotImpError, "need to define '<=>' in %s", rb_obj_classname(x));
    }
}

Returns:

-1, if self is less than other.
0, if self is equal to other.
1, if self is greater then other.
nil, if self and other are incomparable.

Examples:

1 <=> 2              # => -1
1 <=> 1              # => 0
1 <=> 0              # => 1
1 <=> 'foo'          # => nil

1 <=> 1.0            # => 0
1 <=> Rational(1, 1) # => 0
1 <=> Complex(1, 0)  # => 0

This method is the basis for comparisons in module Comparable.

self == other → true or false

numeric.c View on GitHub

An alias for ===

self == other -> true or false

numeric.c View on GitHub

          
            VALUE
rb_int_equal(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_equal(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_eq(x, y);
    }
    return Qnil;
}

Returns true if self is numerically equal to other; false otherwise.

1 == 2     #=> false
1 == 1.0   #=> true

Related: Integer#eql? (requires other to be an Integer).

self > other → true or false

numeric.c View on GitHub

          
            VALUE
rb_int_gt(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_gt(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_gt(x, y);
    }
    return Qnil;
}

Returns true if the value of self is greater than that of other:

  1 > 0              # => true
  1 > 1              # => false
  1 > 2              # => false
  1 > 0.5            # => true
  1 > Rational(1, 2) # => true

Raises an exception if the comparison cannot be made.

self >= real → true or false

numeric.c View on GitHub

          
            VALUE
rb_int_ge(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_ge(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_ge(x, y);
    }
    return Qnil;
}

Returns true if the value of self is greater than or equal to that of other:

1 >= 0              # => true
1 >= 1              # => true
1 >= 2              # => false
1 >= 0.5            # => true
1 >= Rational(1, 2) # => true

Raises an exception if the comparison cannot be made.

self[range] → integer

numeric.c View on GitHub

          
            static VALUE
int_aref(int const argc, VALUE * const argv, VALUE const num)
{
    rb_check_arity(argc, 1, 2);
    if (argc == 2) {
        return int_aref2(num, argv[0], argv[1]);
    }
    return int_aref1(num, argv[0]);

    return Qnil;
}

Returns a slice of bits from self.

With argument offset, returns the bit at the given offset, where offset 0 refers to the least significant bit:

n = 0b10 # => 2
n[0]     # => 0
n[1]     # => 1
n[2]     # => 0
n[3]     # => 0

In principle, n[i] is equivalent to (n >> i) & 1. Thus, negative index always returns zero:

255[-1] # => 0

With arguments offset and size, returns size bits from self, beginning at offset and including bits of greater significance:

n = 0b111000       # => 56
"%010b" % n[0, 10] # => "0000111000"
"%010b" % n[4, 10] # => "0000000011"

With argument range, returns range.size bits from self, beginning at range.begin and including bits of greater significance:

n = 0b111000      # => 56
"%010b" % n[0..9] # => "0000111000"
"%010b" % n[4..9] # => "0000000011"

Raises an exception if the slice cannot be constructed.

self ^ other → integer

numeric.c View on GitHub

          
            static VALUE
int_xor(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_xor(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_xor(x, y);
    }
    return Qnil;
}

Bitwise EXCLUSIVE OR; each bit in the result is 1 if the corresponding bits in self and other are different, 0 otherwise:

"%04b" % (0b0101 ^ 0b0110) # => "0011"

Raises an exception if other is not an Integer.

Related: Integer#& (bitwise AND), Integer#| (bitwise OR).

abs → integer

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 113
def abs
  Primitive.attr! :leaf
  Primitive.cexpr! 'rb_int_abs(self)'
end

Returns the absolute value of self.

(-12345).abs # => 12345
-12345.abs   # => 12345
12345.abs    # => 12345

allbits?(mask) → true or false

numeric.c View on GitHub

          
            static VALUE
int_allbits_p(VALUE num, VALUE mask)
{
    mask = rb_to_int(mask);
    return rb_int_equal(rb_int_and(num, mask), mask);
}

Returns true if all bits that are set (=1) in mask are also set in self; returns false otherwise.

Example values:

0b1010101  self
0b1010100  mask
0b1010100  self & mask
     true  self.allbits?(mask)

0b1010100  self
0b1010101  mask
0b1010100  self & mask
    false  self.allbits?(mask)

anybits?(mask) → true or false

numeric.c View on GitHub

          
            static VALUE
int_anybits_p(VALUE num, VALUE mask)
{
    mask = rb_to_int(mask);
    return RBOOL(!int_zero_p(rb_int_and(num, mask)));
}

Returns true if any bit that is set (=1) in mask is also set in self; returns false otherwise.

Example values:

0b10000010  self
0b11111111  mask
0b10000010  self & mask
      true  self.anybits?(mask)

0b00000000  self
0b11111111  mask
0b00000000  self & mask
     false  self.anybits?(mask)

bit_length → integer

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 160
def bit_length
  Primitive.attr! :leaf
  Primitive.cexpr! 'rb_int_bit_length(self)'
end

Returns the number of bits of the value of self, which is the bit position of the highest-order bit that is different from the sign bit (where the least significant bit has bit position 1). If there is no such bit (zero or minus one), returns zero.

This method returns ceil(log2(self < 0 ? -self : self + 1))>.

(-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

For Integer n, this method can be used to detect overflow in Array#pack:

if n.bit_length < 32
  [n].pack('l') # No overflow.
else
  raise 'Overflow'
end

ceil(ndigits = 0) → integer

numeric.c View on GitHub

          
            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 num;
    }
    return rb_int_ceil(num, ndigits);
}

Returns an integer that is a “ceiling” value for self, as specified by the given ndigits, which must be an integer-convertible object.

When self is zero, returns zero (regardless of the value of ndigits):
```
0.ceil(2)  # => 0
0.ceil(-2) # => 0
```
When self is non-zero and ndigits is non-negative, returns self:
```
555.ceil     # => 555
555.ceil(50) # => 555
```
When self is non-zero and ndigits is negative, returns a value based on a computed granularity:
- The granularity is 10 ** ndigits.abs.
- The returned value is the smallest multiple of the granularity that is greater than or equal to self.
Examples with positive self:

ndigits Granularity 1234.ceil(ndigits)

-1 10 1240

-2 100 1300

-3 1000 2000

-4 10000 10000

-5 100000 100000

Examples with negative self:

ndigits Granularity -1234.ceil(ndigits)

-1 10 -1230

-2 100 -1200

-3 1000 -1000

-4 10000 0

-5 100000 0

ndigits	Granularity	1234.ceil(ndigits)
-1	10	1240
-2	100	1300
-3	1000	2000
-4	10000	10000
-5	100000	100000

ndigits	Granularity	-1234.ceil(ndigits)
-1	10	-1230
-2	100	-1200
-3	1000	-1000
-4	10000	0
-5	100000	0

Related: Integer#floor.

ceildiv(numeric) → integer

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 284
def ceildiv(other)
  -div(0 - other)
end

Returns the result of division self by numeric. rounded up to the nearest integer.

3.ceildiv(3)   # => 1
4.ceildiv(3)   # => 2

4.ceildiv(-3)  # => -1
-4.ceildiv(3)  # => -1
-4.ceildiv(-3) # => 2

3.ceildiv(1.2) # => 3

chr → string

chr(encoding) → string

numeric.c View on GitHub

          
            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, "%u 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_error_arity(argc, 0, 1);
    }
    enc = rb_to_encoding(argv[0]);
    if (!enc) enc = rb_ascii8bit_encoding();
  decode:
    return rb_enc_uint_chr(i, enc);
}

Returns a 1-character string containing the character represented by the value of self, according to the given encoding.

65.chr                   # => "A"
0.chr                    # => "\x00"
255.chr                  # => "\xFF"
string = 255.chr(Encoding::UTF_8)
string.encoding          # => Encoding::UTF_8

Raises an exception if self is negative.

Related: Integer#ord.

int.coerce(numeric) → array

bignum.c View on GitHub

          
            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);
    }
}

Returns an array with both a numeric and a int represented as Integer objects or Float objects.

This is achieved by converting numeric to an Integer or a Float.

A TypeError is raised if the numeric is not an Integer or a Float type.

(0x3FFFFFFFFFFFFFFF+1).coerce(42)   #=> [42, 4611686018427387904]

denominator → 1

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 302
def denominator
  1
end

Returns 1.

digits(base = 10) → array_of_integers

numeric.c View on GitHub

          
            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_BIGNUM_TYPE_P(base_value))
            return rb_int_digits_bigbase(num, base_value);

        base = FIX2LONG(base_value);
        if (base < 0)
            rb_raise(rb_eArgError, "negative radix");
        else if (base < 2)
            rb_raise(rb_eArgError, "invalid radix %ld", base);
    }
    else
        base = 10;

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

    return Qnil;
}

Returns an array of integers representing the base-radix digits of self; the first element of the array represents the least significant digit:

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

Raises an exception if self is negative or base is less than 2.

div(numeric) → integer

numeric.c View on GitHub

          
            VALUE
rb_int_idiv(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_idiv(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_idiv(x, y);
    }
    return num_div(x, y);
}

Performs integer division; returns the integer result of dividing self by numeric:

4.div(3)              # => 1
4.div(-3)             # => -2
-4.div(3)             # => -2
-4.div(-3)            # => 1
4.div(3.0)            # => 1
4.div(Rational(3, 1)) # => 1

Raises an exception if numeric does not have method div.

divmod(other) → array

numeric.c View on GitHub

          
            VALUE
rb_int_divmod(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_divmod(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_divmod(x, y);
    }
    return Qnil;
}

Returns a 2-element array [q, r], where

q = (self/other).floor    # Quotient
r = self % other          # Remainder

Examples:

11.divmod(4)              # => [2, 3]
11.divmod(-4)             # => [-3, -1]
-11.divmod(4)             # => [-3, 1]
-11.divmod(-4)            # => [2, -3]

12.divmod(4)              # => [3, 0]
12.divmod(-4)             # => [-3, 0]
-12.divmod(4)             # => [-3, 0]
-12.divmod(-4)            # => [3, 0]

13.divmod(4.0)            # => [3, 1.0]
13.divmod(Rational(4, 1)) # => [3, (1/1)]

downto(limit) {|i| ... } → self

downto(limit) → enumerator

numeric.c View on GitHub

          
            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;
}

Calls the given block with each integer value from self down to limit; returns self:

a = []
10.downto(5) {|i| a << i }              # => 10
a                                       # => [10, 9, 8, 7, 6, 5]
a = []
0.downto(-5) {|i| a << i }              # => 0
a                                       # => [0, -1, -2, -3, -4, -5]
4.downto(5) {|i| fail 'Cannot happen' } # => 4

With no block given, returns an Enumerator.

even? → true or false

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 169
def even?
  Primitive.attr! :leaf
  Primitive.cexpr! 'rb_int_even_p(self)'
end

Returns true if self is an even number, false otherwise.

fdiv(numeric) → float

numeric.c View on GitHub

          
            VALUE
rb_int_fdiv(VALUE x, VALUE y)
{
    if (RB_INTEGER_TYPE_P(x)) {
        return DBL2NUM(rb_int_fdiv_double(x, y));
    }
    return Qnil;
}

Returns the Float result of dividing self by numeric:

4.fdiv(2)      # => 2.0
4.fdiv(-2)      # => -2.0
-4.fdiv(2)      # => -2.0
4.fdiv(2.0)      # => 2.0
4.fdiv(Rational(3, 4))      # => 5.333333333333333

Raises an exception if numeric cannot be converted to a Float.

floor(ndigits = 0) → integer

numeric.c View on GitHub

          
            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 num;
    }
    return rb_int_floor(num, ndigits);
}

Returns an integer that is a “floor” value for self, as specified by the given ndigits, which must be an integer-convertible object.

When self is zero, returns zero (regardless of the value of ndigits):
```
0.floor(2)  # => 0
0.floor(-2) # => 0
```
When self is non-zero and ndigits is non-negative, returns self:
```
555.floor     # => 555
555.floor(50) # => 555
```
When self is non-zero and ndigits is negative, returns a value based on a computed granularity:
- The granularity is 10 ** ndigits.abs.
- The returned value is the largest multiple of the granularity that is less than or equal to self.
Examples with positive self:

ndigits Granularity 1234.floor(ndigits)

-1 10 1230

-2 100 1200

-3 1000 1000

-4 10000 0

-5 100000 0

Examples with negative self:

ndigits Granularity -1234.floor(ndigits)

-1 10 -1240

-2 100 -1300

-3 1000 -2000

-4 10000 -10000

-5 100000 -100000

ndigits	Granularity	1234.floor(ndigits)
-1	10	1230
-2	100	1200
-3	1000	1000
-4	10000	0
-5	100000	0

ndigits	Granularity	-1234.floor(ndigits)
-1	10	-1240
-2	100	-1300
-3	1000	-2000
-4	10000	-10000
-5	100000	-100000

Related: Integer#ceil.

int.gcd(other_int) → integer

rational.c View on GitHub

          
            VALUE
rb_gcd(VALUE self, VALUE other)
{
    other = nurat_int_value(other);
    return f_gcd(self, other);
}

Returns the greatest common divisor of the two integers. The result is always positive. 0.gcd(x) and x.gcd(0) return x.abs.

36.gcd(60)                  #=> 12
2.gcd(2)                    #=> 2
3.gcd(-7)                   #=> 1
((1<<31)-1).gcd((1<<61)-1)  #=> 1

int.gcdlcm(other_int) → array

rational.c View on GitHub

          
            VALUE
rb_gcdlcm(VALUE self, VALUE other)
{
    other = nurat_int_value(other);
    return rb_assoc_new(f_gcd(self, other), f_lcm(self, other));
}

Returns an array with the greatest common divisor and the least common multiple of the two integers, [gcd, lcm].

36.gcdlcm(60)                  #=> [12, 180]
2.gcdlcm(2)                    #=> [2, 2]
3.gcdlcm(-7)                   #=> [1, 21]
((1<<31)-1).gcdlcm((1<<61)-1)  #=> [1, 4951760154835678088235319297]

inspect(*args)

numeric.c View on GitHub

An alias for to_s

integer? → true

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 178
def integer?
  true
end

Since self is already an Integer, always returns true.

int.lcm(other_int) → integer

rational.c View on GitHub

          
            VALUE
rb_lcm(VALUE self, VALUE other)
{
    other = nurat_int_value(other);
    return f_lcm(self, other);
}

Returns the least common multiple of the two integers. The result is always positive. 0.lcm(x) and x.lcm(0) return zero.

36.lcm(60)                  #=> 180
2.lcm(2)                    #=> 2
3.lcm(-7)                   #=> 21
((1<<31)-1).lcm((1<<61)-1)  #=> 4951760154835678088235319297

magnitude

numeric.rb View on GitHub

An alias for abs

modulo(p1)

numeric.c View on GitHub

An alias for %

numeric.c View on GitHub

An alias for succ

nobits?(mask) → true or false

numeric.c View on GitHub

          
            static VALUE
int_nobits_p(VALUE num, VALUE mask)
{
    mask = rb_to_int(mask);
    return RBOOL(int_zero_p(rb_int_and(num, mask)));
}

Returns true if no bit that is set (=1) in mask is also set in self; returns false otherwise.

Example values:

0b11110000  self
0b00001111  mask
0b00000000  self & mask
      true  self.nobits?(mask)

0b00000001  self
0b11111111  mask
0b00000001  self & mask
     false  self.nobits?(mask)

numerator → self

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 294
def numerator
  self
end

Returns self.

odd? → true or false

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 188
def odd?
  Primitive.attr! :leaf
  Primitive.cexpr! 'rb_int_odd_p(self)'
end

Returns true if self is an odd number, false otherwise.

ord → self

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 198
def ord
  self
end

Returns self; intended for compatibility to character literals in Ruby 1.9.

integer.pow(numeric) → numeric

integer.pow(integer, integer) → integer

numeric.c View on GitHub

          
            VALUE
rb_int_powm(int const argc, VALUE * const argv, VALUE const num)
{
    rb_check_arity(argc, 1, 2);

    if (argc == 1) {
        return rb_int_pow(num, argv[0]);
    }
    else {
        VALUE const a = num;
        VALUE const b = argv[0];
        VALUE m = argv[1];
        int nega_flg = 0;
        if ( ! RB_INTEGER_TYPE_P(b)) {
            rb_raise(rb_eTypeError, "Integer#pow() 2nd argument not allowed unless a 1st argument is integer");
        }
        if (rb_int_negative_p(b)) {
            rb_raise(rb_eRangeError, "Integer#pow() 1st argument cannot be negative when 2nd argument specified");
        }
        if (!RB_INTEGER_TYPE_P(m)) {
            rb_raise(rb_eTypeError, "Integer#pow() 2nd argument not allowed unless all arguments are integers");
        }

        if (rb_int_negative_p(m)) {
            m = rb_int_uminus(m);
            nega_flg = 1;
        }

        if (FIXNUM_P(m)) {
            long const half_val = (long)HALF_LONG_MSB;
            long const mm = FIX2LONG(m);
            if (!mm) rb_num_zerodiv();
            if (mm == 1) return INT2FIX(0);
            if (mm <= half_val) {
                return int_pow_tmp1(rb_int_modulo(a, m), b, mm, nega_flg);
            }
            else {
                return int_pow_tmp2(rb_int_modulo(a, m), b, mm, nega_flg);
            }
        }
        else {
            if (rb_bigzero_p(m)) rb_num_zerodiv();
            if (bignorm(m) == INT2FIX(1)) return INT2FIX(0);
            return int_pow_tmp3(rb_int_modulo(a, m), b, m, nega_flg);
        }
    }
    UNREACHABLE_RETURN(Qnil);
}

Returns (modular) exponentiation as:

a.pow(b)     #=> same as a**b
a.pow(b, m)  #=> same as (a**b) % m, but avoids huge temporary values

pred → next_integer

numeric.c View on GitHub

          
            static VALUE
rb_int_pred(VALUE num)
{
    if (FIXNUM_P(num)) {
        long i = FIX2LONG(num) - 1;
        return LONG2NUM(i);
    }
    if (RB_BIGNUM_TYPE_P(num)) {
        return rb_big_minus(num, INT2FIX(1));
    }
    return num_funcall1(num, '-', INT2FIX(1));
}

Returns the predecessor of self (equivalent to self - 1):

1.pred  #=> 0
-1.pred #=> -2

Related: Integer#succ (successor value).

int.rationalize([eps]) → rational

rational.c View on GitHub

          
            static VALUE
integer_rationalize(int argc, VALUE *argv, VALUE self)
{
    rb_check_arity(argc, 0, 1);
    return integer_to_r(self);
}

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

remainder(other) → real_number

numeric.c View on GitHub

          
            static VALUE
int_remainder(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        if (FIXNUM_P(y)) {
            VALUE z = fix_mod(x, y);
            RUBY_ASSERT(FIXNUM_P(z));
            if (z != INT2FIX(0) && (SIGNED_VALUE)(x ^ y) < 0)
                z = fix_minus(z, y);
            return z;
        }
        else if (!RB_BIGNUM_TYPE_P(y)) {
            return num_remainder(x, y);
        }
        x = rb_int2big(FIX2LONG(x));
    }
    else if (!RB_BIGNUM_TYPE_P(x)) {
        return Qnil;
    }
    return rb_big_remainder(x, y);
}

Returns the remainder after dividing self by other.

Examples:

11.remainder(4)              # => 3
11.remainder(-4)             # => 3
-11.remainder(4)             # => -3
-11.remainder(-4)            # => -3

12.remainder(4)              # => 0
12.remainder(-4)             # => 0
-12.remainder(4)             # => 0
-12.remainder(-4)            # => 0

13.remainder(4.0)            # => 1.0
13.remainder(Rational(4, 1)) # => (1/1)

round(ndigits= 0, half: :up) → integer

numeric.c View on GitHub

          
            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 num;
    }
    return rb_int_round(num, ndigits, mode);
}

Returns self rounded to the nearest value with a precision of ndigits decimal digits.

When ndigits is negative, the returned value has at least ndigits.abs trailing zeros:

555.round(-1)      # => 560
555.round(-2)      # => 600
555.round(-3)      # => 1000
-555.round(-2)     # => -600
555.round(-4)      # => 0

Returns self when ndigits is zero or positive.

555.round     # => 555
555.round(1)  # => 555
555.round(50) # => 555

If keyword argument half is given, and self is equidistant from the two candidate values, the rounding is according to the given half value:

:up or nil: round away from zero:

25.round(-1, half: :up)      # => 30
(-25).round(-1, half: :up)   # => -30

:down: round toward zero:

25.round(-1, half: :down)    # => 20
(-25).round(-1, half: :down) # => -20

:even: round toward the candidate whose last nonzero digit is even:

25.round(-1, half: :even)    # => 20
15.round(-1, half: :even)    # => 20
(-25).round(-1, half: :even) # => -20

Raises and exception if the value for half is invalid.

Related: Integer#truncate.

size → integer

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 215
def size
  Primitive.attr! :leaf
  Primitive.cexpr! 'rb_int_size(self)'
end

Returns the number of bytes in the machine representation of self; the value is system-dependent:

1.size             # => 8
-1.size            # => 8
2147483647.size    # => 8
(256**10 - 1).size # => 10
(256**20 - 1).size # => 20
(256**40 - 1).size # => 40

succ → next_integer

numeric.c View on GitHub

          
            VALUE
rb_int_succ(VALUE num)
{
    if (FIXNUM_P(num)) {
        long i = FIX2LONG(num) + 1;
        return LONG2NUM(i);
    }
    if (RB_BIGNUM_TYPE_P(num)) {
        return rb_big_plus(num, INT2FIX(1));
    }
    return num_funcall1(num, '+', INT2FIX(1));
}

Returns the successor integer of self (equivalent to self + 1):

1.succ  #=> 2
-1.succ #=> 0

Related: Integer#pred (predecessor value).

times {|i| ... } → self

times → enumerator

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 231
def times
  Primitive.attr! :inline_block
  unless defined?(yield)
    return Primitive.cexpr! 'SIZED_ENUMERATOR(self, 0, 0, int_dotimes_size)'
  end
  i = 0
  while i < self
    yield i
    i = i.succ
  end
  self
end

Calls the given block self times with each integer in (0..self-1):

a = []
5.times {|i| a.push(i) } # => 5
a                        # => [0, 1, 2, 3, 4]

With no block given, returns an Enumerator.

to_bn

ext/openssl/lib/openssl/bn.rb View on GitHub

          
            # File tmp/rubies/ruby-master/ext/openssl/lib/openssl/bn.rb, line 37
def to_bn
  OpenSSL::BN::new(self)
end

Casts an Integer as an OpenSSL::BN

See ‘man bn` for more info.

to_f → float

numeric.c View on GitHub

          
            static VALUE
int_to_f(VALUE num)
{
    double val;

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

    return DBL2NUM(val);
}

Converts self to a Float:

1.to_f  # => 1.0
-1.to_f # => -1.0

If the value of self does not fit in a Float, the result is infinity:

(10**400).to_f  # => Infinity
(-10**400).to_f # => -Infinity

to_i → self

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 248
def to_i
  self
end

Returns self (which is already an Integer).

to_int → self

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 256
def to_int
  self
end

Returns self (which is already an Integer).

int.to_r → rational

rational.c View on GitHub

          
            static VALUE
integer_to_r(VALUE self)
{
    return rb_rational_new1(self);
}

Returns the value as a rational.

1.to_r        #=> (1/1)
(1<<64).to_r  #=> (18446744073709551616/1)

to_s(base = 10) → string

numeric.c View on GitHub

          
            VALUE
rb_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);
}

Returns a string containing the place-value representation of self in radix base (in 2..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"

Raises an exception if base is out of range.

truncate(ndigits = 0) → integer

numeric.c View on GitHub

          
            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 num;
    }
    return rb_int_truncate(num, ndigits);
}

Returns self truncated (toward zero) to a precision of ndigits decimal digits.

When ndigits is negative, the returned value has at least ndigits.abs trailing zeros:

555.truncate(-1)  # => 550
555.truncate(-2)  # => 500
-555.truncate(-2) # => -500

Returns self when ndigits is zero or positive.

555.truncate     # => 555
555.truncate(50) # => 555

Related: Integer#round.

upto(limit) {|i| ... } → self

upto(limit) → enumerator

numeric.c View on GitHub

          
            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));
        }
        ensure_cmp(c, i, to);
    }
    return from;
}

Calls the given block with each integer value from self up to limit; returns self:

a = []
5.upto(10) {|i| a << i }              # => 5
a                                     # => [5, 6, 7, 8, 9, 10]
a = []
-5.upto(0) {|i| a << i }              # => -5
a                                     # => [-5, -4, -3, -2, -1, 0]
5.upto(4) {|i| fail 'Cannot happen' } # => 5

With no block given, returns an Enumerator.

zero? → true or false

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 264
def zero?
  Primitive.attr! :leaf
  Primitive.cexpr! 'rb_int_zero_p(self)'
end

Returns true if self has a zero value, false otherwise.

self | other → integer

numeric.c View on GitHub

          
            static VALUE
int_or(VALUE x, VALUE y)
{
    if (FIXNUM_P(x)) {
        return fix_or(x, y);
    }
    else if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_or(x, y);
    }
    return Qnil;
}

Bitwise OR; each bit in the result is 1 if either corresponding bit in self or other is 1, 0 otherwise:

"%04b" % (0b0101 | 0b0110) # => "0111"

Raises an exception if other is not an Integer.

Related: Integer#& (bitwise AND), Integer#^ (bitwise EXCLUSIVE OR).

~int → integer

numeric.rb View on GitHub

          
            # File tmp/rubies/ruby-master/numeric.rb, line 99
def ~
  Primitive.attr! :leaf
  Primitive.cexpr! 'rb_int_comp(self)'
end

One’s complement: returns the value of self with each bit inverted.

Because an integer value is conceptually of 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"

Integer

What’s Here

Querying

Comparing

Converting

Other

GMP_VERSION

Integer.sqrt(numeric) → integer

Integer.try_convert(object) → object, integer, or nil

self % other → real_number

self & other → integer

self * numeric → numeric_result

self ** numeric → numeric_result

self + numeric → numeric_result

self - numeric → numeric_result

-int → integer

self / numeric → numeric_result

self < other → true or false

self << count → integer

self <= real → true or false

self <=> other → -1, 0, +1, or nil

self == other → true or false

self == other -> true or false

self > other → true or false

self >= real → true or false

self >> count → integer

self[offset] → 0 or 1

self[offset, size] → integer

self[range] → integer

self ^ other → integer

abs → integer

allbits?(mask) → true or false

anybits?(mask) → true or false

bit_length → integer

ceil(ndigits = 0) → integer

ceildiv(numeric) → integer

chr → string

chr(encoding) → string

int.coerce(numeric) → array

denominator → 1

digits(base = 10) → array_of_integers

div(numeric) → integer

divmod(other) → array

downto(limit) {|i| ... } → self

downto(limit) → enumerator

even? → true or false

fdiv(numeric) → float

floor(ndigits = 0) → integer

int.gcd(other_int) → integer

int.gcdlcm(other_int) → array

inspect(*args)

integer? → true

int.lcm(other_int) → integer

magnitude

modulo(p1)

next

nobits?(mask) → true or false

numerator → self

odd? → true or false

ord → self

integer.pow(numeric) → numeric

integer.pow(integer, integer) → integer

pred → next_integer

int.rationalize([eps]) → rational

remainder(other) → real_number

round(ndigits= 0, half: :up) → integer

size → integer

succ → next_integer

times {|i| ... } → self

times → enumerator

to_bn

to_f → float

to_i → self

to_int → self

int.to_r → rational

to_s(base = 10) → string

truncate(ndigits = 0) → integer

upto(limit) {|i| ... } → self

upto(limit) → enumerator

zero? → true or false