struct BigInt

Overview

A BigInt can represent arbitrarily large integers.

It is implemented under the hood with GMP.

Included Modules

Defined in:

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

Constructors

Instance Method Summary

Instance methods inherited from module Comparable(Float)

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

Instance methods inherited from module Comparable(BigInt)

<, <=(other : T) <=, <=>(other : T) <=>, ==(other : T) ==, >(other : T) : Bool >, >=(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) : Bool >, >=(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) : Bool >, >=(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 : BigInt) : BigInt
*(other : BigRational) : BigRational
*(other : BigDecimal) : BigDecimal *
, **(exponent : Int) : self
**(exponent : Float) : Float64 **
, +(other : BigInt) : BigInt
+(other : BigRational) : BigRational
+(other : BigDecimal) : BigDecimal +
, -(other : BigInt) : BigInt
-(other : BigRational) : BigRational
-(other : BigDecimal) : BigDecimal -
, /(other : BigRational) /, //(other : Int::Primitive) //, < <<, <=>(other : BigInt)
<=>(other : Int) : Int32
<=>(other : BigRational)
<=>(other : BigDecimal) <=>
, ===(char : Char) ===, >>(count : Int) >>, abs : self abs, bit(bit) bit, bit_length : Int32 bit_length, bits(range : Range) bits, bits_set?(mask) : Bool bits_set?, ceil : self ceil, chr : Char chr, day : Time::Span day, days : Time::Span days, digits(base = 10) : Array(Int32) digits, divisible_by?(num) : Bool divisible_by?, downto(to, &block : self -> ) : Nil
downto(to) downto
, even? : Bool even?, fdiv(other) : Float64 fdiv, floor : self floor, gcd(other : self) : self
gcd(other : BigInt) : Int gcd
, 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 : BigInt) : BigInt
lcm(other : Int) 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? : Bool odd?, popcount popcount, pred : self pred, remainder(other : Int) remainder, round(mode : RoundingMode) : self round, round_away round_away, round_even : self round_even, second : Time::Span second, seconds : Time::Span seconds, succ : self succ, tdiv(other : Int) tdiv, times(&block : self -> ) : Nil
times times
, to(to, &block : self -> ) : Nil
to(to) to
, to_big_d : BigDecimal to_big_d, to_big_i : BigInt to_big_i, to_big_r : BigRational to_big_r, to_io(io : IO, format : IO::ByteFormat) : Nil to_io, to_json(json : JSON::Builder) : Nil to_json, to_json_object_key : String to_json_object_key, to_s(io : IO, base : Int = 10, *, precision : Int = 1, upcase : Bool = false) : Nil
to_s(base : Int = 10, *, precision : Int = 1, upcase : Bool = false) : String to_s
, trailing_zeros_count trailing_zeros_count, trunc : self trunc, upto(to, &block : self -> ) : Nil
upto(to) 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) : Bool >, >=(other : T) >=, clamp(min, max)
clamp(range : Range) clamp

Instance methods inherited from module Comparable(BigRational)

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

Instance methods inherited from module Comparable(BigInt)

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

Instance methods inherited from struct Number

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

Constructor methods inherited from struct Number

additive_identity : self additive_identity, multiplicative_identity : self multiplicative_identity, 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) : Bool >, >=(other : T) >=, clamp(min, max)
clamp(range : Range) clamp

Instance methods inherited from module Steppable

step(*, to limit = nil, by step, exclusive : Bool = false, &) : Nil
step(*, to limit = nil, by step, exclusive : Bool = false) step

Instance methods inherited from module Comparable(Number)

<, <=(other : T) <=, <=>(other : T) <=>, ==(other : T) ==, >(other : T) : Bool >, >=(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

! : Bool !, !=(other) !=, !~(other) !~, ==(other) ==, ===(other : JSON::Any)
===(other : YAML::Any)
===(other) ===
, =~(other) =~, as(type : Class) as, as?(type : Class) as?, class class, dup dup, hash(hasher)
hash hash
, in?(collection : Object) : Bool
in?(*values : Object) : Bool in?
, inspect(io : IO) : Nil
inspect : String inspect
, is_a?(type : Class) : Bool is_a?, itself itself, nil? : Bool nil?, not_nil! not_nil!, pretty_inspect(width = 79, newline = "\n", indent = 0) : String pretty_inspect, pretty_print(pp : PrettyPrint) : Nil pretty_print, responds_to?(name : Symbol) : Bool responds_to?, tap(&) tap, to_json(io : IO) : Nil
to_json : String to_json
, to_pretty_json(indent : String = " ") : String
to_pretty_json(io : IO, indent : String = " ") : Nil to_pretty_json
, to_s(io : IO) : Nil
to_s : String to_s
, to_yaml(io : IO) : Nil
to_yaml : String 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)Source

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)Source

Creates a BigInt from the given num.

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

Creates a BigInt from the given num.

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

Creates a BigInt from the given num.

def self.new(num : BigFloat)Source

Creates a BigInt from the given num.

def self.new(num : BigDecimal)Source

Creates a BigInt from the given num.

def self.new(num : BigRational)Source

Creates a BigInt from the given num.

def self.new(num : BigInt)Source

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

def self.newSource

Creates a BigInt with the value zero.

require "big"

BigInt.new # => 0

Instance Method Detail

def %(other : Int) : BigIntSource

Description copied from struct Int

Returns self modulo other.

This uses floored division.

See Int#/ for more details.

def &(other : Int) : BigIntSource

def &*(other) : BigIntSource

def &+(other) : BigIntSource

def &-(other) : BigIntSource

def *(other : BigInt) : BigIntSource

def *(other : LibGMP::IntPrimitiveSigned) : BigIntSource

def *(other : LibGMP::IntPrimitiveUnsigned) : BigIntSource

def *(other : Int) : BigIntSource

def **(other : Int) : BigIntSource

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) : BigIntSource

def +(other : Int) : BigIntSource

def -(other : BigInt) : BigIntSource

def -(other : Int) : BigIntSource

def - : BigIntSource

def /(other : BigInt) : BigFloatSource

def /(other : BigDecimal) : BigDecimalSource

def /(other : BigRational) : BigRationalSource

def /(other : Int8) : BigFloatSource

def /(other : UInt8) : BigFloatSource

def /(other : Int16) : BigFloatSource

def /(other : UInt16) : BigFloatSource

def /(other : Int32) : BigFloatSource

def /(other : UInt32) : BigFloatSource

def /(other : Int64) : BigFloatSource

def /(other : UInt64) : BigFloatSource

def /(other : Int128) : BigFloatSource

def /(other : UInt128) : BigFloatSource

def /(other : Float32) : BigFloatSource

def /(other : Float64) : BigFloatSource

def //(other : Int::Unsigned) : BigIntSource

def //(other : Int) : BigIntSource

def <<(other : Int) : BigIntSource

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)Source

def <=>(other : Int::Signed)Source

def <=>(other : Int::Unsigned)Source

def <=>(other : Float)Source

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 greater 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) : BigIntSource

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) : BigIntSource

def abs : BigIntSource

Description copied from struct Number

Returns the absolute value of this number.

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

def bit_length : Int32Source

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 cloneSource

def digits(base = 10) : Array(Int32)Source

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 divmod(number : BigInt) : Tuple(BigInt, BigInt)Source

def divmod(number : LibGMP::ULong)Source

def divmod(number : Int::Signed) : Tuple(BigInt, BigInt)Source

def divmod(number : Int::Unsigned)Source

def factorial : BigIntSource

def gcd(other : BigInt) : BigIntSource

Returns the greatest common divisor of self and other.

def gcd(other : Int) : IntSource

Returns the greatest common divisor of self and other.

def hash(hasher)Source

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

def lcm(other : BigInt) : BigIntSource

Returns the least common multiple of self and other.

def lcm(other : Int) : BigIntSource

Returns the least common multiple of self and other.

def popcount : IntSource

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) : BigIntSource

Description copied from struct Int

Returns self remainder other.

This uses truncated division.

See Int#tdiv for more details.

def tdiv(other : Int) : BigIntSource

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 : BigDecimalSource

Description copied from struct Int

Converts self to BigDecimal.

require "big"
12123415151254124124.to_big_d

def to_big_f : BigFloatSource

def to_big_i : BigIntSource

Description copied from struct Int

Returns a BigInt representing this integer.

require "big"

123.to_big_i

def to_big_r : BigRationalSource

Description copied from struct Int

Returns a BigRational representing this integer.

require "big"

123.to_big_r

def to_f : Float64Source

def to_f!Source

def to_f32 : Float32Source

def to_f32!Source

def to_f64 : Float64Source

def to_f64!Source

def to_i : Int32Source

def to_i!Source

def to_i16 : Int16Source

def to_i16! : Int16Source

def to_i32 : Int32Source

def to_i32! : Int32Source

def to_i64 : Int64Source

def to_i64! : Int64Source

def to_i8 : Int8Source

def to_i8! : Int8Source

def to_s(io : IO, base : Int = 10, *, precision : Int = 1, upcase : Bool = false) : NilSource

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) : StringSource

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 : UInt32Source

def to_u!Source

def to_u16 : UInt16Source

def to_u16! : UInt16Source

def to_u32 : UInt32Source

def to_u32! : UInt32Source

def to_u64 : UInt64Source

def to_u64! : UInt64Source

def to_u8 : UInt8Source

def to_u8! : UInt8Source

def to_unsafeSource

def trailing_zeros_count : IntSource

Description copied from struct Int

Returns the number of trailing 0-bits.

def unsafe_floored_div(other : BigInt) : BigIntSource

def unsafe_floored_div(other : Int) : BigIntSource

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

def unsafe_floored_divmod(number : LibGMP::ULong) : Tuple(BigInt, BigInt)Source

def unsafe_floored_mod(other : BigInt) : BigIntSource

def unsafe_floored_mod(other : Int) : BigIntSource

def unsafe_truncated_div(other : BigInt) : BigIntSource

def unsafe_truncated_div(other : Int) : BigIntSource

def unsafe_truncated_divmod(number : BigInt)Source

def unsafe_truncated_divmod(number : LibGMP::ULong)Source

def unsafe_truncated_mod(other : BigInt) : BigIntSource

def unsafe_truncated_mod(other : LibGMP::IntPrimitive) : BigIntSource

def unsafe_truncated_mod(other : Int) : BigIntSource

def |(other : Int) : BigIntSource

def ~ : BigIntSource

© 2012–2021 Manas Technology Solutions.
Licensed under the Apache License, Version 2.0.
https://crystal-lang.org/api/1.2.1/BigInt.html