# struct BigInt

- BigInt
- Int
- Number
- Value
- Object

##
Overview

A `BigInt` can represent arbitrarily large integers.

It is implemented under the hood with GMP.

##
Included Modules

- Comparable(Float)
- Comparable(BigInt)
- Comparable(UInt128 | UInt16 | UInt32 | UInt64 | UInt8)
- Comparable(Int128 | Int16 | Int32 | Int64 | Int8)

##
Defined in:

##
Constructors

- .new(str : String, base = 10)

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

- .new(num : Int::Signed)

  Creates a `BigInt` from the given num.

- .new(num : Int::Unsigned)

  Creates a `BigInt` from the given num.

- .new(num : Float::Primitive)

  Creates a `BigInt` from the given num.

- .new(num : BigFloat)

  Creates a `BigInt` from the given num.

- .new(num : BigDecimal)

  Creates a `BigInt` from the given num.

- .new(num : BigRational)

  Creates a `BigInt` from the given num.

- .new(num : BigInt)

  Returns num.

- .new

  Creates a `BigInt` with the value zero.

##
Instance Method Summary

- #%(other : Int) : BigInt

  Returns `self` modulo other.

- #&(other : Int) : BigInt
- #&*(other) : BigInt
- #&+(other) : BigInt
- #&-(other) : BigInt
- #*(other : Int) : BigInt
- #*(other : LibGMP::IntPrimitiveUnsigned) : BigInt
- #*(other : LibGMP::IntPrimitiveSigned) : BigInt
- #*(other : BigInt) : BigInt
- #**(other : Int) : BigInt

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

- #+(other : Int) : BigInt
- #+(other : BigInt) : BigInt
- #- : BigInt
- #-(other : Int) : BigInt
- #-(other : BigInt) : BigInt
- #/(other : Float64) : BigFloat
- #/(other : Float32) : BigFloat
- #/(other : UInt128) : BigFloat
- #/(other : Int128) : BigFloat
- #/(other : UInt64) : BigFloat
- #/(other : Int64) : BigFloat
- #/(other : UInt32) : BigFloat
- #/(other : Int32) : BigFloat
- #/(other : UInt16) : BigFloat
- #/(other : Int16) : BigFloat
- #/(other : Int8) : BigFloat
- #/(other : BigRational) : BigRational
- #/(other : BigDecimal) : BigDecimal
- #/(other : BigInt) : BigFloat
- #/(other : UInt8) : BigFloat
- #//(other : Int) : BigInt
- #//(other : Int::Unsigned) : BigInt
- #<<(other : Int) : BigInt

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

- #<=>(other : BigInt)
- #<=>(other : Float)

  The comparison operator.

- #<=>(other : Int::Unsigned)
- #<=>(other : Int::Signed)
- #>>(other : Int) : BigInt

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

- #^(other : Int) : BigInt
- #abs : BigInt

  Returns the absolute value of this number.

- #clone
- #digits : Array(Int32)
- #divmod(number : Int::Unsigned)
- #divmod(number : Int::Signed)
- #divmod(number : LibGMP::ULong)
- #divmod(number : BigInt)
- #gcd(other : Int) : Int
- #gcd(other : BigInt) : BigInt
- #hash(hasher)

  TODO improve this

- #lcm(other : Int) : BigInt
- #lcm(other : BigInt) : BigInt
- #popcount

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

- #remainder(other : Int) : BigInt

  Returns `self` remainder other.

- #tdiv(other : Int) : BigInt

  Divides `self` by other using truncated division.

- #to_big_d

  Converts `self` to `BigDecimal`.

- #to_big_f
- #to_big_i

  Returns a `BigInt` representing this integer.

- #to_big_r

  Returns a `BigRational` representing this integer.

- #to_f
- #to_f!
- #to_f32
- #to_f32!
- #to_f64
- #to_f64!
- #to_i
- #to_i!
- #to_i16
- #to_i16!
- #to_i32
- #to_i32!
- #to_i64
- #to_i64!
- #to_i8
- #to_i8!
- #to_s : String

  Returns a string representation of self.

- #to_s(base : Int) : String

  Returns a string containing the representation of big radix base (2 through 36).

- #to_s(io : IO) : Nil

  Returns a string representation of self.

- #to_u
- #to_u!
- #to_u16
- #to_u16!
- #to_u32
- #to_u32!
- #to_u64
- #to_u64!
- #to_u8
- #to_u8!
- #to_unsafe
- #trailing_zeros_count

  Returns the number of trailing `0`-bits.

- #unsafe_floored_div(other : BigInt) : BigInt
- #unsafe_floored_div(other : Int) : BigInt
- #unsafe_floored_divmod(number : LibGMP::ULong)
- #unsafe_floored_divmod(number : BigInt)
- #unsafe_floored_mod(other : BigInt) : BigInt
- #unsafe_floored_mod(other : Int) : BigInt
- #unsafe_truncated_div(other : BigInt) : BigInt
- #unsafe_truncated_div(other : Int) : BigInt
- #unsafe_truncated_divmod(number : BigInt)
- #unsafe_truncated_divmod(number : LibGMP::ULong)
- #unsafe_truncated_mod(other : BigInt) : BigInt
- #unsafe_truncated_mod(other : Int) : BigInt
- #unsafe_truncated_mod(other : LibGMP::IntPrimitive) : BigInt
- #|(other : Int) : BigInt
- #~ : BigInt

### Instance methods inherited from module `Comparable(Float)`

<(other : T) <, <=(other : T) <=, <=>(other : T) <=>, ==(other : T) ==, >(other : T) >, >=(other : T) >=, clamp(min, max)
clamp(range : Range) clamp

### Instance methods inherited from module `Comparable(BigInt)`

<(other : T) <, <=(other : T) <=, <=>(other : T) <=>, ==(other : T) ==, >(other : T) >, >=(other : T) >=, clamp(min, max)
clamp(range : Range) clamp

### Instance methods inherited from module `Comparable(UInt128 | UInt16 | UInt32 | UInt64 | UInt8)`

<(other : T | T | T | T | T) <, <=(other : T | T | T | T | T) <=, <=>(other : T | T | T | T | T) <=>, ==(other : T | T | T | T | T) ==, >(other : T | T | T | T | T) >, >=(other : T | T | T | T | T) >=, clamp(min, max)
clamp(range : Range) clamp

### Instance methods inherited from module `Comparable(Int128 | Int16 | Int32 | Int64 | Int8)`

<(other : T | T | T | T | T) <, <=(other : T | T | T | T | T) <=, <=>(other : T | T | T | T | T) <=>, ==(other : T | T | T | T | T) ==, >(other : T | T | T | T | T) >, >=(other : T | T | T | T | T) >=, clamp(min, max)
clamp(range : Range) clamp

### Instance methods inherited from struct `Int`

%(other : BigInt) : BigInt
%(other : Int) %, &*(other : BigInt) : BigInt &*, &**(exponent : Int) : self &**, &+(other : BigInt) : BigInt &+, &-(other : BigInt) : BigInt &-, *(other : BigDecimal)
*(other : BigRational)
*(other : BigInt) : BigInt *, **(exponent : Float) : Float64
**(exponent : Int) : self **, +(other : BigDecimal)
+(other : BigRational)
+(other : BigInt) : BigInt +, -(other : BigInt) : BigInt
-(other : BigDecimal)
-(other : BigRational) -, /(other : BigRational) /, //(other : Int::Primitive) //, <<(count : Int) <<, <=>(other : BigDecimal)
<=>(other : BigRational)
<=>(other : Int) : Int32
<=>(other : BigInt) <=>, ===(char : Char) ===, >>(count : Int) >>, abs abs, bit(bit) bit, bits(range : Range) bits, bits_set?(mask) bits_set?, ceil ceil, chr chr, day : Time::Span day, days : Time::Span days, divisible_by?(num) divisible_by?, downto(to, &block : self -> ) : Nil
downto(to) downto, even? even?, fdiv(other) fdiv, floor floor, gcd(other : self) : self gcd, gcm(other : BigInt) : Int gcm, hash(hasher) hash, hour : Time::Span hour, hours : Time::Span hours, humanize_bytes(io : IO, precision : Int = 3, separator = '.', *, significant : Bool = true, format : BinaryPrefixFormat = :IEC) : Nil
humanize_bytes(precision : Int = 3, separator = '.', *, significant : Bool = true, format : BinaryPrefixFormat = :IEC) : String humanize_bytes, lcm(other : Int)
lcm(other : BigInt) : BigInt lcm, microsecond : Time::Span microsecond, microseconds : Time::Span microseconds, millisecond : Time::Span millisecond, milliseconds : Time::Span milliseconds, minute : Time::Span minute, minutes : Time::Span minutes, modulo(other) modulo, month : Time::MonthSpan month, months : Time::MonthSpan months, nanosecond : Time::Span nanosecond, nanoseconds : Time::Span nanoseconds, odd? odd?, popcount popcount, pred pred, remainder(other : Int) remainder, round round, second : Time::Span second, seconds : Time::Span seconds, succ succ, tdiv(other : Int) tdiv, times
times(&block : self -> ) : Nil times, to(to, &block : self -> ) : Nil
to(to) to, to_big_d to_big_d, to_big_i : BigInt to_big_i, to_big_r to_big_r, to_io(io : IO, format : IO::ByteFormat) to_io, to_json(json : JSON::Builder) to_json, to_json_object_key to_json_object_key, to_s : String
to_s(io : IO) : Nil
to_s(base : Int, io : IO, upcase : Bool = false) : Nil
to_s(base : Int, upcase : Bool = false) : String to_s, trailing_zeros_count trailing_zeros_count, trunc trunc, upto(to)
upto(to, &block : self -> ) : Nil upto, week : Time::Span week, weeks : Time::Span weeks, year : Time::MonthSpan year, years : Time::MonthSpan years, ~ ~

### Constructor methods inherited from struct `Int`

from_io(io : IO, format : IO::ByteFormat) : self from_io

### Instance methods inherited from module `Comparable(BigDecimal)`

<(other : T) <, <=(other : T) <=, <=>(other : T) <=>, ==(other : T) ==, >(other : T) >, >=(other : T) >=, clamp(min, max)
clamp(range : Range) clamp

### Instance methods inherited from module `Comparable(BigRational)`

<(other : T) <, <=(other : T) <=, <=>(other : T) <=>, ==(other : T) ==, >(other : T) >, >=(other : T) >=, clamp(min, max)
clamp(range : Range) clamp

### Instance methods inherited from module `Comparable(BigInt)`

<(other : T) <, <=(other : T) <=, <=>(other : T) <=>, ==(other : T) ==, >(other : T) >, >=(other : T) >=, clamp(min, max)
clamp(range : Range) clamp

### Instance methods inherited from struct `Number`

*(other : Complex)
*(other : BigFloat) *, +(other : BigFloat)
+(other : Complex)
+ +, -(other : Complex)
-(other : BigFloat) -, /(other : Complex)
/(other : BigFloat) /, //(other) //, <=>(other : BigFloat)
<=>(other) : Int32? <=>, ==(other : Complex) ==, abs abs, abs2 abs2, cis cis, divmod(number) divmod, format(separator = '.', delimiter = ',', decimal_places : Int? = nil, *, group : Int = 3, only_significant : Bool = false) : String
format(io : IO, separator = '.', delimiter = ',', decimal_places : Int? = nil, *, group : Int = 3, only_significant : Bool = false) : Nil format, humanize(io : IO, precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, prefixes : Indexable = SI_PREFIXES) : Nil
humanize(precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, prefixes : Proc) : Nil
humanize(precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, &) : String
humanize(io : IO, precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, &prefixes : Int32, Float64 -> Tuple(Int32, _) | Tuple(Int32, _, Bool)) : Nil
humanize(precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, prefixes = SI_PREFIXES) : String
humanize(io : IO, precision = 3, separator = '.', delimiter = ',', *, base = 10 ** 3, significant = true, prefixes : Proc) : Nil humanize, i i, round(digits = 0, base = 10) round, sign sign, significant(digits, base = 10) significant, step(*, to = nil, by = 1)
step(*, to = nil, by = 1, &) step, to_big_f to_big_f, to_c to_c, to_yaml(yaml : YAML::Nodes::Builder) to_yaml, zero? : Bool zero?

### Constructor methods inherited from struct `Number`

zero : self zero

### Class methods inherited from struct `Number`

si_prefix(magnitude : Int, prefixes = SI_PREFIXES) : Char? si_prefix

### Instance methods inherited from module `Comparable(BigFloat)`

<(other : T) <, <=(other : T) <=, <=>(other : T) <=>, ==(other : T) ==, >(other : T) >, >=(other : T) >=, clamp(min, max)
clamp(range : Range) clamp

### Instance methods inherited from module `Comparable(Number)`

<(other : T) <, <=(other : T) <=, <=>(other : T) <=>, ==(other : T) ==, >(other : T) >, >=(other : T) >=, clamp(min, max)
clamp(range : Range) clamp

### Instance methods inherited from struct `Value`

==(other : JSON::Any)
==(other : YAML::Any)
==(other) ==, dup dup

### Instance methods inherited from class `Object`

!=(other) !=, !~(other) !~, ==(other) ==, ===(other : JSON::Any)
===(other : YAML::Any)
===(other) ===, =~(other) =~, __crystal_pseudo_! : Bool __crystal_pseudo_!, __crystal_pseudo_as(type : Class) __crystal_pseudo_as, __crystal_pseudo_as?(type : Class) __crystal_pseudo_as?, __crystal_pseudo_is_a?(type : Class) : Bool __crystal_pseudo_is_a?, __crystal_pseudo_nil? : Bool __crystal_pseudo_nil?, __crystal_pseudo_responds_to?(name : Symbol) : Bool __crystal_pseudo_responds_to?, class class, dup dup, hash(hasher)
hash hash, inspect : String
inspect(io : IO) : Nil inspect, itself itself, not_nil! not_nil!, pretty_inspect(width = 79, newline = "\n", indent = 0) : String pretty_inspect, pretty_print(pp : PrettyPrint) : Nil pretty_print, tap(&) tap, to_json(io : IO)
to_json to_json, to_pretty_json(indent : String = " ")
to_pretty_json(io : IO, indent : String = " ") to_pretty_json, to_s : String
to_s(io : IO) : Nil to_s, to_yaml(io : IO)
to_yaml to_yaml, try(&) try, unsafe_as(type : T.class) forall T unsafe_as

### Class methods inherited from class `Object`

from_json(string_or_io, root : String)
from_json(string_or_io) from_json, from_yaml(string_or_io : String | IO) from_yaml

##
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::Signed) #

Creates a `BigInt` from the given num.

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

Creates a `BigInt` from the given num.

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

Creates a `BigInt` from the given num.

def self.new(num : BigFloat) #

Creates a `BigInt` from the given num.

def self.new(num : BigDecimal) #

Creates a `BigInt` from the given num.

def self.new(num : BigRational) #

Creates a `BigInt` from the given num.

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 : Int) : BigInt #
def &*(other) : BigInt #
def &+(other) : BigInt #
def &-(other) : BigInt #
def *(other : Int) : BigInt #
def *(other : LibGMP::IntPrimitiveUnsigned) : BigInt #
def *(other : LibGMP::IntPrimitiveSigned) : BigInt #
def *(other : BigInt) : 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 : Int) : BigInt #
def +(other : BigInt) : BigInt #
def - : BigInt #
def -(other : Int) : BigInt #
def -(other : BigInt) : BigInt #
def /(other : Float64) : BigFloat #
def /(other : Float32) : BigFloat #
def /(other : UInt128) : BigFloat #
def /(other : Int128) : BigFloat #
def /(other : UInt64) : BigFloat #
def /(other : Int64) : BigFloat #
def /(other : UInt32) : BigFloat #
def /(other : Int32) : BigFloat #
def /(other : UInt16) : BigFloat #
def /(other : Int16) : BigFloat #
def /(other : Int8) : BigFloat #
def /(other : BigRational) : BigRational #
def /(other : BigDecimal) : BigDecimal #
def /(other : BigInt) : BigFloat #
def /(other : UInt8) : BigFloat #
def //(other : Int) : BigInt #
def //(other : Int::Unsigned) : 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 : Float) #
Description copied from module Comparable(Float)

The comparison operator. Returns `0` if the two objects are equal, a negative number if this object is considered less than other, a positive number if this object is considered greter than other, or `nil` if the two objects are not comparable.

Subclasses define this method to provide class-specific ordering.

The comparison operator is usually used to sort values:

    # Sort in a descending way:
    [3, 1, 2].sort { |x, y| y <=> x } # => [3, 2, 1]

    # Sort in an ascending way:
    [3, 1, 2].sort { |x, y| x <=> y } # => [1, 2, 3]

def <=>(other : Int::Unsigned) #
def <=>(other : Int::Signed) #
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 : Int) : BigInt #
def abs : BigInt #
Description copied from struct Number

Returns the absolute value of this number.

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

def clone #
def digits : Array(Int32) #
def divmod(number : Int::Unsigned) #
def divmod(number : Int::Signed) #
def divmod(number : LibGMP::ULong) #
def divmod(number : BigInt) #
def gcd(other : Int) : Int #
def gcd(other : BigInt) : BigInt #
def hash(hasher) #

TODO improve this

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

Converts `self` to `BigDecimal`.

    require "big"
    12123415151254124124.to_big_d

def to_big_f #
def to_big_i #
Description copied from struct Int

Returns a `BigInt` representing this integer.

    require "big"

    123.to_big_i

def to_big_r #
Description copied from struct Int

Returns a `BigRational` representing this integer.

    require "big"

    123.to_big_r

def to_f #
def to_f! #
def to_f32 #
def to_f32! #
def to_f64 #
def to_f64! #
def to_i #
def to_i! #
def to_i16 #
def to_i16! #
def to_i32 #
def to_i32! #
def to_i64 #
def to_i64! #
def to_i8 #
def to_i8! #
def to_s : String #

Returns a string representation of self.

    require "big"

    BigInt.new("123456789101101987654321").to_s # => 123456789101101987654321

def to_s(base : Int) : String #

Returns a string containing the representation of big radix base (2 through 36).

    require "big"

    BigInt.new("123456789101101987654321").to_s(8)  # => "32111154373025463465765261"
    BigInt.new("123456789101101987654321").to_s(16) # => "1a249b1f61599cd7eab1"
    BigInt.new("123456789101101987654321").to_s(36) # => "k3qmt029k48nmpd"

def to_s(io : IO) : Nil #

Returns a string representation of self.

    require "big"

    BigInt.new("123456789101101987654321").to_s # => 123456789101101987654321

def to_u #
def to_u! #
def to_u16 #
def to_u16! #
def to_u32 #
def to_u32! #
def to_u64 #
def to_u64! #
def to_u8 #
def to_u8! #
def to_unsafe #
def trailing_zeros_count #
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 : LibGMP::ULong) #
def unsafe_floored_divmod(number : 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 : LibGMP::ULong) #
def unsafe_truncated_mod(other : BigInt) : BigInt #
def unsafe_truncated_mod(other : Int) : BigInt #
def unsafe_truncated_mod(other : LibGMP::IntPrimitive) : BigInt #
def |(other : Int) : BigInt #
def ~ : BigInt #