# struct BigFloat

- BigFloat
- Float
- Number
- Value
- Object

##
Overview

A `BigFloat` can represent arbitrarily large floats.

It is implemented under the hood with GMP.

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

##
Included Modules

- Comparable(Float)
- Comparable(BigFloat)
- Comparable(Int)

##
Defined in:

big.cr
big/big_decimal.cr
big/big_float.cr
big/big_rational.cr
big/number.cr

##
Constructors

- .new(num : Float, precision : Int)
- .new(str : String)
- .new(num : BigInt)
- .new(num : BigRational)
- .new(num : BigFloat)
- .new(num : Int)
- .new(num : Float::Primitive)
- .new(num : Number)
- .new(mpf : LibGMP::MPF)
- .new
- .new(&)

##
Class Method Summary

- .default_precision
- .default_precision=(prec : Int)

##
Instance Method Summary

- #*(other : Number) : BigFloat
- #**(other : BigInt) : BigFloat
- #**(other : Int) : BigFloat
- #+(other : Number) : BigFloat
- #-(other : Number) : BigFloat
- #- : BigFloat
- #/(other : BigFloat) : BigFloat
- #/(other : BigInt) : BigFloat
- #/(other : BigDecimal) : BigDecimal
- #/(other : BigRational) : BigRational
- #/(other : Int::Primitive) : BigFloat
- #/(other : Float32) : BigFloat
- #/(other : Float64) : BigFloat
- #<=>(other : BigFloat)

  The comparison operator.

- #<=>(other : BigInt)
- #<=>(other : Float::Primitive)
- #<=>(other : Int)
- #<=>(other : BigRational)
- #<=>(other : BigDecimal)
- #<=>(other : Number)
- #abs : BigFloat

  Returns the absolute value of this number.

- #ceil : BigFloat

  Rounds towards positive infinity.

- #clone
- #fdiv(other : Number::Primitive) : self
- #floor : BigFloat

  Rounds towards negative infinity.

- #hash(hasher)

  TODO improve this

- #integer? : Bool

  Returns `true` if `self` is an integer.

- #round_away : self

  Rounds towards the nearest integer.

- #round_even : self

  Rounds towards the nearest integer.

- #to_big_f : BigFloat
- #to_big_i : BigInt

  Returns a `BigInt` representing this float (rounded using `#floor`).

- #to_f : Float64
- #to_f! : Float64
- #to_f32 : Float32
- #to_f32! : Float32
- #to_f64 : Float64
- #to_f64! : Float64
- #to_i : Int32
- #to_i! : Int32
- #to_i16 : Int16
- #to_i16! : Int16
- #to_i32 : Int32
- #to_i32! : Int32
- #to_i64 : Int64
- #to_i64! : Int64
- #to_i8 : Int8
- #to_i8! : Int8
- #to_s(io : IO) : Nil

  Prints a nicely readable and concise string representation of this object, typically intended for users, to io.

- #to_u : UInt32
- #to_u! : UInt32
- #to_u16 : UInt16
- #to_u16! : UInt16
- #to_u32 : UInt32
- #to_u32! : UInt32
- #to_u64 : UInt64
- #to_u64! : UInt64
- #to_u8 : UInt8
- #to_u8! : UInt8
- #to_unsafe
- #trunc : BigFloat

  Rounds towards zero.

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

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

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

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

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

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

### Instance methods inherited from struct `Float`

%(other) %, - -, //(other) //, <=>(other : BigInt)
<=>(other : BigFloat)
<=>(other : BigRational)
<=>(other : BigDecimal) <=>, days : Time::Span days, fdiv(other : BigInt | BigFloat | BigDecimal | BigRational) : self fdiv, finite? : Bool finite?, hash(hasher) hash, hours : Time::Span hours, infinite? : Int32 | Nil infinite?, microseconds : Time::Span microseconds, milliseconds : Time::Span milliseconds, minutes : Time::Span minutes, modulo(other) modulo, nan? : Bool nan?, nanoseconds : Time::Span nanoseconds, remainder(other) remainder, seconds : Time::Span seconds, 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_yaml(yaml : YAML::Nodes::Builder) : Nil to_yaml, weeks : Time::Span weeks

### Constructor methods inherited from struct `Float`

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

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

<(other : T) : Bool <, <=(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) : Bool <, <=(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) : Bool <, <=(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) : Int32 | Nil <=>, ==(other : Complex) ==, abs : self abs, abs2 abs2, cis : Complex cis, divmod(number) divmod, format(io : IO, separator = '.', delimiter = ',', decimal_places : Int | Nil = nil, *, group : Int = 3, only_significant : Bool = false) : Nil
format(separator = '.', delimiter = ',', decimal_places : Int | Nil = 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, integer? : Bool integer?, 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 | Nil si_prefix

### Macros inherited from struct `Number`

[](*nums) [], slice(*nums, read_only = false) slice, static_array(*nums) static_array

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

<(other : T) : Bool <, <=(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) : Bool <, <=(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!(message)
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

### Macros inherited from class `Object`

class_getter(*names, &block) class_getter, class_getter!(*names) class_getter!, class_getter?(*names, &block) class_getter?, class_property(*names, &block) class_property, class_property!(*names) class_property!, class_property?(*names, &block) class_property?, class_setter(*names) class_setter, def_clone def_clone, def_equals(*fields) def_equals, def_equals_and_hash(*fields) def_equals_and_hash, def_hash(*fields) def_hash, delegate(*methods, to object) delegate, forward_missing_to(delegate) forward_missing_to, getter(*names, &block) getter, getter!(*names) getter!, getter?(*names, &block) getter?, property(*names, &block) property, property!(*names) property!, property?(*names, &block) property?, setter(*names) setter

##
Constructor Detail

def self.new(num : Float, precision : Int) #
def self.new(str : String) #
def self.new(num : BigInt) #
def self.new(num : BigRational) #
def self.new(num : BigFloat) #
def self.new(num : Int) #
def self.new(num : Float::Primitive) #
def self.new(num : Number) #
def self.new(mpf : LibGMP::MPF) #
def self.new #
def self.new(&) #

##
Class Method Detail

def self.default_precision #
def self.default_precision=(prec : Int) #

##
Instance Method Detail

def *(other : Number) : BigFloat #
def **(other : BigInt) : BigFloat #
def **(other : Int) : BigFloat #
def +(other : Number) : BigFloat #
def -(other : Number) : BigFloat #
def - : BigFloat #
def /(other : BigFloat) : BigFloat #
def /(other : BigInt) : BigFloat #
def /(other : BigDecimal) : BigDecimal #
def /(other : BigRational) : BigRational #
def /(other : Int::Primitive) : BigFloat #
def /(other : Float32) : BigFloat #
def /(other : Float64) : BigFloat #
def <=>(other : BigFloat) #
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 : BigInt) #
def <=>(other : Float::Primitive) #
def <=>(other : Int) #
def <=>(other : BigRational) #
def <=>(other : BigDecimal) #
def <=>(other : Number) #
def abs : BigFloat #
Description copied from struct Number

Returns the absolute value of this number.

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

def ceil : BigFloat #

Rounds towards positive infinity.

def clone #
def fdiv(other : Number::Primitive) : self #
def floor : BigFloat #

Rounds towards negative infinity.

def hash(hasher) #

TODO improve this

def integer? : Bool #

Returns `true` if `self` is an integer.

Non-integer types may return `true` as long as `self` denotes a finite value without any fractional parts.

    1.integer?       # => true
    1.0.integer?     # => true
    1.2.integer?     # => false
    (1 / 0).integer? # => false
    (0 / 0).integer? # => false

def round_away : self #

Rounds towards the nearest integer. If both neighboring integers are equidistant, rounds away from zero.

def round_even : self #

Rounds towards the nearest integer. If both neighboring integers are equidistant, rounds towards the even neighbor (Banker's rounding).

def to_big_f : BigFloat #
def to_big_i : BigInt #
Description copied from struct Float

Returns a `BigInt` representing this float (rounded using `#floor`).

    require "big"

    1212341515125412412412421.0.to_big_i

def to_f : Float64 #
def to_f! : Float64 #
def to_f32 : Float32 #
def to_f32! : Float32 #
def to_f64 : Float64 #
def to_f64! : Float64 #
def to_i : Int32 #
def to_i! : Int32 #
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) : Nil #
Description copied from class Object

Prints a nicely readable and concise string representation of this object, typically intended for users, to io.

This method is called when an object is interpolated in a string literal:

    "foo #{bar} baz" # calls bar.to_io with the builder for this string

`IO#<<` calls this method to append an object to itself:

    io << bar # calls bar.to_s(io)

Thus implementations must not interpolate `self` in a string literal or call `io << self` which both would lead to an endless loop.

Also see `#inspect(IO)`.

def to_u : UInt32 #
def to_u! : UInt32 #
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 trunc : BigFloat #

Rounds towards zero.