class Integer

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.

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.

Returns self modulo other as a real numeric (Integer, Float, or Rational).

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)

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).

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)

Returns the numeric product of self and other:

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)

Returns the numeric product of self and other:

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)

Returns self raised to the power exponent:

# Result for non-negative Integer exponent is Integer.
2 ** 0   # => 1
2 ** 1   # => 2
2 ** 2   # => 4
2 ** 3   # => 8
-2 ** 3  # => -8
# Result for negative Integer exponent is Rational, not Float.
2 ** -3  # => (1/8)
-2 ** -3 # => (-1/8)

# Result for Float exponent is Float.
2 ** 0.0   # => 1.0
2 ** 1.0   # => 2.0
2 ** 2.0   # => 4.0
2 ** 3.0   # => 8.0
-2 ** 3.0  # => -8.0
2 ** -3.0  # => 0.125
-2 ** -3.0 # => -0.125

# Result for non-negative Complex exponent is Complex with Integer parts.
2 ** Complex(0, 0)   # => (1+0i)
2 ** Complex(1, 0)   # => (2+0i)
2 ** Complex(2, 0)   # => (4+0i)
2 ** Complex(3, 0)   # => (8+0i)
-2 ** Complex(3, 0) # => (-8+0i)
# Result for negative Complex exponent is Complex with Rational parts.
2 ** Complex(-3, 0)  # => ((1/8)+(0/1)*i)
-2 ** Complex(-3, 0) # => ((-1/8)+(0/1)*i)

# Result for Rational exponent is Rational.
2 ** Rational(0, 1)   # => (1/1)
2 ** Rational(1, 1)   # => (2/1)
2 ** Rational(2, 1)   # => (4/1)
2 ** Rational(3, 1)   # => (8/1)
-2 ** Rational(3, 1)  # => (-8/1)
2 ** Rational(-3, 1)  # => (1/8)
-2 ** Rational(-3, 1) # => (-1/8)

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)

Returns the sum of self and other:

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

For a computation involving Floats, the result may be inexact (see Float#+):

1 + 3.14           # => 4.140000000000001

Returns the sum of self and other:

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

For a computation involving Floats, the result may be inexact (see Float#+):

1 + 3.14           # => 4.140000000000001

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)

Returns the difference of self and other:

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)

Returns the difference of self and other:

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)

Returns self, negated:

-1    # => -1
-(-1) # => 1
-0    # => 0

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)

Returns the quotient of self and other.

For integer other, truncates the result to an integer:

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

For non-integer other, returns a non-integer result:

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

Returns the quotient of self and other.

For integer other, truncates the result to an integer:

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

For non-integer other, returns a non-integer result:

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

Returns whether the value of self is less than the value of other; other must be numeric, but may not be Complex:

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

Returns self with bits shifted count positions to the left, or to the right if count is negative:

n = 0b11110000
"%08b" % (n << 1)  # => "111100000"
"%08b" % (n << 3)  # => "11110000000"
"%08b" % (n << -1) # => "01111000"
"%08b" % (n << -3) # => "00011110"

Related: Integer#>>.

Returns whether the value of self is less than or equal to the value of other; other must be numeric, but may not be Complex:

  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.

Compares self and other.

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

Class Integer includes module Comparable, each of whose methods uses Integer#<=> for comparison.

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).

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.

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.

Returns self with bits shifted count positions to the right, or to the left if count is negative:

n = 0b11110000
"%08b" % (n >> 1)  # => "01111000"
"%08b" % (n >> 3)  # => "00011110"
"%08b" % (n >> -1) # => "111100000"
"%08b" % (n >> -3) # => "11110000000"

Related: Integer#<<.

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.

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).

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).

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"

Returns the absolute value of self.

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

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)

Related: Integer#anybits?, Integer#nobits?.

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)

Related: Integer#allbits?, Integer#nobits?.

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

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 Related: Integer#floor.

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

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.

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]

Returns 1.

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.

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.

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)]

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.

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

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.

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 Related: Integer#ceil.

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

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]

Since self is already an Integer, always returns true.

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

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)

Related: Integer#allbits?, Integer#anybits?.

Returns self.

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

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

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

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

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

Related: Integer#succ (successor value).

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

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)

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.

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

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

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

Related: Integer#pred (predecessor value).

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.

Returns the value of int as a BigDecimal.

require 'bigdecimal'
require 'bigdecimal/util'

42.to_d   # => 0.42e2

See also Kernel.BigDecimal.

Returns the value of int as a BigDecimal.

require 'bigdecimal'
require 'bigdecimal/util'

42.to_d   # => 0.42e2

See also Kernel.BigDecimal.

Returns the value of int as a BigDecimal.

require 'bigdecimal'
require 'bigdecimal/util'

42.to_d   # => 0.42e2

See also Kernel.BigDecimal.

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

Returns self (which is already an Integer).

Returns a JSON string representation for this Integer number.

Returns the value as a rational.

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

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.

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.

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.

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