struct BigInt

Overview

A BigInt can represent arbitrarily large integers.

It is implemented under the hood with GMP.

NOTE To use BigInt, you must explicitly import it with require "big"

big.cr
big/big_int.cr
big/number.cr

Constructors

• .new(str : String, base = 10)

Creates a BigInt with the value denoted by str in the given base.

• .new(num : Int::Primitive)

Creates a BigInt from the given num.

• .new(num : Float::Primitive)

Returns a read-only Slice of the limbs that make up this integer, which is effectively abs.digits(2 ** N) where N is the number of bits in LibGMP::MpLimb, except that an empty Slice is returned for zero.

• .new(num : BigFloat)

Returns a read-only Slice of the limbs that make up this integer, which is effectively abs.digits(2 ** N) where N is the number of bits in LibGMP::MpLimb, except that an empty Slice is returned for zero.

• .new(num : BigDecimal)

Returns a read-only Slice of the limbs that make up this integer, which is effectively abs.digits(2 ** N) where N is the number of bits in LibGMP::MpLimb, except that an empty Slice is returned for zero.

• .new(num : BigRational)

Returns a read-only Slice of the limbs that make up this integer, which is effectively abs.digits(2 ** N) where N is the number of bits in LibGMP::MpLimb, except that an empty Slice is returned for zero.

• .new(num : BigInt)

Returns num.

• .new

Creates a BigInt with the value zero.

Constructor Detail

def self.new(str : String, base = 10) #

Creates a BigInt with the value denoted by str in the given base.

Raises ArgumentError if the string doesn't denote a valid integer.

require "big"

BigInt.new("123456789123456789123456789123456789") # => 123456789123456789123456789123456789
BigInt.new("123_456_789_123_456_789_123_456_789")  # => 123456789123456789123456789
BigInt.new("1234567890ABCDEF", base: 16)           # => 1311768467294899695

def self.new(num : Int::Primitive) #

Creates a BigInt from the given num.

def self.new(num : Float::Primitive) #

Returns a read-only Slice of the limbs that make up this integer, which is effectively abs.digits(2 ** N) where N is the number of bits in LibGMP::MpLimb, except that an empty Slice is returned for zero.

This assumes GMP wasn't built with its experimental nails support: https://gmplib.org/manual/Low_002dlevel-Functions

num must be finite.

def self.new(num : BigFloat) #

Returns a read-only Slice of the limbs that make up this integer, which is effectively abs.digits(2 ** N) where N is the number of bits in LibGMP::MpLimb, except that an empty Slice is returned for zero.

This assumes GMP wasn't built with its experimental nails support: https://gmplib.org/manual/Low_002dlevel-Functions

def self.new(num : BigDecimal) #

Returns a read-only Slice of the limbs that make up this integer, which is effectively abs.digits(2 ** N) where N is the number of bits in LibGMP::MpLimb, except that an empty Slice is returned for zero.

This assumes GMP wasn't built with its experimental nails support: https://gmplib.org/manual/Low_002dlevel-Functions

def self.new(num : BigRational) #

Returns a read-only Slice of the limbs that make up this integer, which is effectively abs.digits(2 ** N) where N is the number of bits in LibGMP::MpLimb, except that an empty Slice is returned for zero.

This assumes GMP wasn't built with its experimental nails support: https://gmplib.org/manual/Low_002dlevel-Functions

def self.new(num : BigInt) #

Returns num. Useful for generic code that does T.new(...) with T being a Number.

def self.new #

Creates a BigInt with the value zero.

require "big"

BigInt.new # => 0

Instance Method Detail

def %(other : Int) : BigInt #
Description copied from struct Int

Returns self modulo other.

This uses floored division.

See Int#/ for more details.

def &(other : BigInt) : BigInt #

def &(other : Int) : BigInt #

def &*(other) : BigInt #

def &+(other) : BigInt #

def &-(other) : BigInt #

def *(other : BigInt) : BigInt #

def *(other : Int) : BigInt #

def **(other : Int) : BigInt #
Description copied from struct Int

Returns the value of raising self to the power of exponent.

Raises ArgumentError if exponent is negative: if this is needed, either use a float base or a float exponent.

Raises OverflowError in case of overflow.

2 ** 3  # => 8
2 ** 0  # => 1
2 ** -1 # ArgumentError

def +(other : BigInt) : BigInt #

def +(other : Int) : BigInt #

def -(other : BigInt) : BigInt #

def -(other : Int) : BigInt #

def - : BigInt #

def /(other : BigInt) : BigFloat #

def /(other : BigDecimal) : BigDecimal #

def /(other : BigRational) : BigRational #

def /(other : Int8) : BigFloat #

def /(other : UInt8) : BigFloat #

def /(other : Int16) : BigFloat #

def /(other : UInt16) : BigFloat #

def /(other : Int32) : BigFloat #

def /(other : UInt32) : BigFloat #

def /(other : Int64) : BigFloat #

def /(other : UInt64) : BigFloat #

def /(other : Int128) : BigFloat #

def /(other : UInt128) : BigFloat #

def /(other : Float32) : BigFloat #

def /(other : Float64) : BigFloat #

def //(other : Int) : BigInt #

def <<(other : Int) : BigInt #
Description copied from struct Int

Returns the result of shifting this number's bits count positions to the left.

• If count is greater than the number of bits of this integer, returns 0
• If count is negative, a right shift is performed
8000 << 1  # => 16000
8000 << 2  # => 32000
8000 << 32 # => 0
8000 << -1 # => 4000

def <=>(other : BigInt) #

def <=>(other : Int) #

def <=>(other : Float::Primitive) #

def >>(other : Int) : BigInt #
Description copied from struct Int

Returns the result of shifting this number's bits count positions to the right. Also known as arithmetic right shift.

• If count is greater than the number of bits of this integer, returns 0
• If count is negative, a left shift is performed
8000 >> 1  # => 4000
8000 >> 2  # => 2000
8000 >> 32 # => 0
8000 >> -1 # => 16000

-8000 >> 1 # => -4000

def ^(other : BigInt) : BigInt #

def ^(other : Int) : BigInt #

def |(other : BigInt) : BigInt #

def |(other : Int) : BigInt #

def ~ : BigInt #

def abs : BigInt #
Description copied from struct Number

Returns the absolute value of this number.

123.abs  # => 123
-123.abs # => 123

def bit(bit : Int) #

def bit_length : Int32 #
Description copied from struct Int

Returns the number of bits of this int value.

“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(self < 0 ? -self : self + 1)).

0.bit_length # => 0
1.bit_length # => 1
2.bit_length # => 2
3.bit_length # => 2
4.bit_length # => 3
5.bit_length # => 3

# The above is the same as
0b0.bit_length   # => 0
0b1.bit_length   # => 1
0b10.bit_length  # => 2
0b11.bit_length  # => 2
0b100.bit_length # => 3
0b101.bit_length # => 3

def clone #

def digits(base = 10) : Array(Int32) #
Description copied from struct Int

Returns the digits of a number in a given base. The digits are returned as an array with the least significant digit as the first array element.

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

-12345.digits(7) # => ArgumentError

def divisible_by?(number : BigInt) : Bool #

def divisible_by?(number : Int) : Bool #

def divmod(number : Int) : Tuple(BigInt, BigInt) #

def factorial : BigInt #

def gcd(other : BigInt) : BigInt #

Returns the greatest common divisor of self and other.

def gcd(other : Int) : Int #

Returns the greatest common divisor of self and other.

def hash(hasher) #

TODO check hash equality for numbers >= 2**63

def lcm(other : BigInt) : BigInt #

Returns the least common multiple of self and other.

def lcm(other : Int) : BigInt #

Returns the least common multiple of self and other.

def popcount : Int #
Description copied from struct Int

Counts 1-bits in the binary representation of this integer.

5.popcount   # => 2
-15.popcount # => 29

def remainder(other : Int) : BigInt #
Description copied from struct Int

Returns self remainder other.

This uses truncated division.

See Int#tdiv for more details.

def tdiv(other : Int) : BigInt #
Description copied from struct Int

Divides self by other using truncated division.

In truncated division, given two integers x and y:

• q = x.tdiv(y) is rounded toward zero
• r = x.remainder(y) has the sign of the first argument
• x == q*y + r

For example:

x     y     x / y     x % y
5     3       1         2
-5     3      -1        -2
5    -3      -1         2
-5    -3       1        -2

Raises if other is 0, or if other is -1 and self is signed and is the minimum value for that integer type.

def to_big_d : BigDecimal #
Description copied from struct Int

Converts self to BigDecimal.

require "big"
123456789012345678.to_big_d

def to_big_f : BigFloat #

def to_big_i : BigInt #
Description copied from struct Int

Returns a BigInt representing this integer.

require "big"

123.to_big_i

def to_big_r : BigRational #
Description copied from struct Int

Returns a BigRational representing this integer.

require "big"

123.to_big_r

def to_f : Float64 #

def to_f! #

def to_f32 : Float32 #

def to_f32! #

def to_f64 : Float64 #

def to_f64! #

def to_i : Int32 #

def to_i! : Int32 #

def to_i128 : Int128 #

def to_i128! : Int128 #

def to_i16 : Int16 #

def to_i16! : Int16 #

def to_i32 : Int32 #

def to_i32! : Int32 #

def to_i64 : Int64 #

def to_i64! : Int64 #

def to_i8 : Int8 #

def to_i8! : Int8 #

def to_s(io : IO, base : Int = 10, *, precision : Int = 1, upcase : Bool = false) : Nil #
Description copied from struct Int

Appends a string representation of this integer to the given io.

base specifies the radix of the written string, and must be either 62 or a number between 2 and 36. By default, digits above 9 are represented by ASCII lowercase letters (a for 10, b for 11, etc.), but uppercase letters may be used if upcase is true, unless base 62 is used. In that case, lowercase letters are used for 10 to 35, and uppercase ones for 36 to 61, and upcase must be false.

precision specifies the minimum number of digits in the written string. If there are fewer digits than this number, the string is left-padded by zeros. If self and precision are both zero, returns an empty string.

def to_s(base : Int = 10, *, precision : Int = 1, upcase : Bool = false) : String #
Description copied from struct Int

Returns a string representation of this integer.

base specifies the radix of the returned string, and must be either 62 or a number between 2 and 36. By default, digits above 9 are represented by ASCII lowercase letters (a for 10, b for 11, etc.), but uppercase letters may be used if upcase is true, unless base 62 is used. In that case, lowercase letters are used for 10 to 35, and uppercase ones for 36 to 61, and upcase must be false.

precision specifies the minimum number of digits in the returned string. If there are fewer digits than this number, the string is left-padded by zeros. If self and precision are both zero, returns an empty string.

1234.to_s                   # => "1234"
1234.to_s(2)                # => "10011010010"
1234.to_s(16)               # => "4d2"
1234.to_s(16, upcase: true) # => "4D2"
1234.to_s(36)               # => "ya"
1234.to_s(62)               # => "jU"
1234.to_s(precision: 2)     # => "1234"
1234.to_s(precision: 6)     # => "001234"

def to_u : UInt32 #

def to_u! : UInt32 #

def to_u128 : UInt128 #

def to_u128! : UInt128 #

def to_u16 : UInt16 #

def to_u16! : UInt16 #

def to_u32 : UInt32 #

def to_u32! : UInt32 #

def to_u64 : UInt64 #

def to_u64! : UInt64 #

def to_u8 : UInt8 #

def to_u8! : UInt8 #

def to_unsafe #

def trailing_zeros_count : Int #
Description copied from struct Int

Returns the number of trailing 0-bits.

def unsafe_floored_div(other : BigInt) : BigInt #

def unsafe_floored_div(other : Int) : BigInt #

def unsafe_floored_divmod(number : BigInt) : Tuple(BigInt, BigInt) #

def unsafe_floored_divmod(number : Int) : Tuple(BigInt, BigInt) #

def unsafe_floored_mod(other : BigInt) : BigInt #

def unsafe_floored_mod(other : Int) : BigInt #

def unsafe_truncated_div(other : BigInt) : BigInt #

def unsafe_truncated_div(other : Int) : BigInt #

def unsafe_truncated_divmod(number : BigInt) #

def unsafe_truncated_divmod(number : Int) #

def unsafe_truncated_mod(other : BigInt) : BigInt #

def unsafe_truncated_mod(other : Int) : BigInt #