# struct BigFloat

- BigFloat
- Float
- Number
- Value
- Object

##
Overview

A `BigFloat` can represent arbitrarily large floats.

It is implemented under the hood with GMP.

##
Included Modules

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

##
Defined in:

##
Constructors

- .new(num : Float, precision : Int)
- .new(str : String)
- .new(num : BigInt)
- .new(num : BigRational)
- .new(num : BigFloat)
- .new(num : Int8 | Int16 | Int32)
- .new(num : UInt8 | UInt16 | UInt32)
- .new(num : Int64)
- .new(num : UInt64)
- .new(num : Number)
- .new(mpf : LibGMP::MPF)
- .new
- .new(&)

##
Class Method Summary

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

##
Instance Method Summary

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

  The comparison operator.

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

  The comparison operator.

- #abs

  Returns the absolute value of this number.

- #ceil
- #clone
- #floor
- #hash(hasher)

  TODO improve this

- #to_big_f
- #to_big_i

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

- #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(io : IO) : Nil

  Appends a `String` representation of this object to the given `IO` object.

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

### 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(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(Int)`

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

### Instance methods inherited from struct `Float`

%(other) %, - -, //(other) //, <=>(other : BigDecimal)
<=>(other : BigRational)
<=>(other : BigInt) <=>, days : Time::Span days, fdiv(other) : self fdiv, finite? finite?, hash(hasher) hash, hours : Time::Span hours, infinite? infinite?, microseconds : Time::Span microseconds, milliseconds : Time::Span milliseconds, minutes : Time::Span minutes, modulo(other) modulo, nan? nan?, nanoseconds : Time::Span nanoseconds, remainder(other) remainder, seconds : Time::Span seconds, 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, 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) <, <=(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(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 : Int8 | Int16 | Int32) #
def self.new(num : UInt8 | UInt16 | UInt32) #
def self.new(num : Int64) #
def self.new(num : UInt64) #
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) #
def **(other : Int) #
def +(other : Number) #
def -(other : Number) #
def - #
def /(other : UInt8 | UInt16 | UInt32 | UInt64) #
def /(other : Float64) : BigFloat #
def /(other : Float32) : BigFloat #
def /(other : UInt128) : BigFloat #
def /(other : Int128) : BigFloat #
def /(other : Int64) : BigFloat #
def /(other : Int32) : BigFloat #
def /(other : Int16) : BigFloat #
def /(other : Int8) : BigFloat #
def /(other : BigRational) : BigRational #
def /(other : BigDecimal) : BigDecimal #
def /(other : BigInt) : BigFloat #
def /(other : BigFloat) #
def <=>(other : Number) #
def <=>(other : Float32 | Float64) #
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 : BigInt) #
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 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 abs #
Description copied from struct Number

Returns the absolute value of this number.

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

def ceil #
def clone #
def floor #
def hash(hasher) #

TODO improve this

def to_big_f #
def to_big_i #
Description copied from struct Float

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

    require "big"

    1212341515125412412412421.0.to_big_i

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(io : IO) : Nil #
Description copied from class Object

Appends a `String` representation of this object to the given `IO` object.

An object must never append itself to the io argument, as this will in turn call `#to_s(io)` on it.

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 trunc #