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Class: BigDecimal

Relationships & Source Files
Super Chains via Extension / Inclusion / Inheritance
Class Chain:
self, ::Numeric
Instance Chain:
self, ::Numeric
Inherits: Numeric
Defined in: ext/bigdecimal/bigdecimal.c,
ext/bigdecimal/bigdecimal.c,
ext/bigdecimal/lib/bigdecimal/util.rb

Overview

BigDecimal provides arbitrary-precision floating point decimal arithmetic.

Introduction

Ruby provides built-in support for arbitrary precision integer arithmetic.

For example:

42**13  #=>   1265437718438866624512

BigDecimal provides similar support for very large or very accurate floating point numbers.

Decimal arithmetic is also useful for general calculation, because it provides the correct answers people expect–whereas normal binary floating point arithmetic often introduces subtle errors because of the conversion between base 10 and base 2.

For example, try:

sum = 0
10_000.times do
  sum = sum + 0.0001
end
print sum #=> 0.9999999999999062

and contrast with the output from:

require 'bigdecimal'

sum = BigDecimal.new("0")
10_000.times do
  sum = sum + BigDecimal.new("0.0001")
end
print sum #=> 0.1E1

Similarly:

(BigDecimal.new("1.2") - BigDecimal("1.0")) == BigDecimal("0.2") #=> true

(1.2 - 1.0) == 0.2 #=> false

Special features of accurate decimal arithmetic

Because BigDecimal is more accurate than normal binary floating point arithmetic, it requires some special values.

Infinity

BigDecimal sometimes needs to return infinity, for example if you divide a value by zero.

BigDecimal.new("1.0") / BigDecimal.new("0.0")  #=> Infinity
BigDecimal.new("-1.0") / BigDecimal.new("0.0")  #=> -Infinity

You can represent infinite numbers to BigDecimal using the strings 'Infinity', '+Infinity' and '-Infinity' (case-sensitive)

Not a Number

When a computation results in an undefined value, the special value NaN (for 'not a number') is returned.

Example:

BigDecimal.new("0.0") / BigDecimal.new("0.0") #=> NaN

You can also create undefined values.

NaN is never considered to be the same as any other value, even NaN itself:

n = BigDecimal.new('NaN')
n == 0.0 #=> false
n == n #=> false

Positive and negative zero

If a computation results in a value which is too small to be represented as a BigDecimal within the currently specified limits of precision, zero must be returned.

If the value which is too small to be represented is negative, a BigDecimal value of negative zero is returned.

BigDecimal.new("1.0") / BigDecimal.new("-Infinity") #=> -0.0

If the value is positive, a value of positive zero is returned.

BigDecimal.new("1.0") / BigDecimal.new("Infinity") #=> 0.0

(See .mode for how to specify limits of precision.)

Note that -0.0 and 0.0 are considered to be the same for the purposes of comparison.

Note also that in mathematics, there is no particular concept of negative or positive zero; true mathematical zero has no sign.

License

Copyright (C) 2002 by Shigeo Kobayashi <shigeo@tinyforest.gr.jp>.

BigDecimal is released under the Ruby and 2-clause BSD licenses. See LICENSE.txt for details.

Maintained by mrkn <mrkn@mrkn.jp> and ruby-core members.

Documented by zzak <zachary@zacharyscott.net>, mathew <meta@pobox.com>, and many other contributors.

Constant Summary

Class Method Summary

Instance Attribute Summary

Instance Method Summary

Constructor Details

.new(initial, digits)

Create a new BigDecimal object.

initial

The initial value, as an ::Integer, a ::Float, a ::Rational, a BigDecimal, or a String.

If it is a String, spaces are ignored and unrecognized characters terminate the value.

digits

The number of significant digits, as a Fixnum. If omitted or 0, the number of significant digits is determined from the initial value.

The actual number of significant digits used in computation is usually larger than the specified number.

Exceptions

TypeError

If the initial type is neither Fixnum, Bignum, ::Float, Rational, nor BigDecimal, this exception is raised.

TypeError

If the digits is not a Fixnum, this exception is raised.

ArgumentError

If initial is a ::Float, and the digits is larger than Float::DIG + 1, this exception is raised.

ArgumentError

If the initial is a ::Float or ::Rational, and the digits value is omitted, this exception is raised.

Class Method Details

._load(str)

Internal method used to provide marshalling support. See the Marshal module.

.double_fig

The double_fig class method returns the number of digits a ::Float number is allowed to have. The result depends upon the CPU and OS in use.

.limit(digits)

Limit the number of significant digits in newly created BigDecimal numbers to the specified value. Rounding is performed as necessary, as specified by .mode.

A limit of 0, the default, means no upper limit.

The limit specified by this method takes less priority over any limit specified to instance methods such as ceil, floor, truncate, or round.

.mode(mode, value)

Controls handling of arithmetic exceptions and rounding. If no value is supplied, the current value is returned.

Six values of the mode parameter control the handling of arithmetic exceptions:

EXCEPTION_NaN EXCEPTION_INFINITY EXCEPTION_UNDERFLOW EXCEPTION_OVERFLOW EXCEPTION_ZERODIVIDE EXCEPTION_ALL

For each mode parameter above, if the value set is false, computation continues after an arithmetic exception of the appropriate type. When computation continues, results are as follows:

EXCEPTION_NaN

NaN

EXCEPTION_INFINITY

+Infinity or -Infinity

EXCEPTION_UNDERFLOW

0

EXCEPTION_OVERFLOW

+Infinity or -Infinity

EXCEPTION_ZERODIVIDE

+Infinity or -Infinity

One value of the mode parameter controls the rounding of numeric values: ROUND_MODE. The values it can take are:

ROUND_UP, :up

round away from zero

ROUND_DOWN, :down, :truncate

round towards zero (truncate)

ROUND_HALF_UP, :half_up, :default

round towards the nearest neighbor, unless both neighbors are equidistant, in which case round away from zero. (default)

ROUND_HALF_DOWN, :half_down

round towards the nearest neighbor, unless both neighbors are equidistant, in which case round towards zero.

ROUND_HALF_EVEN, :half_even, :banker

round towards the nearest neighbor, unless both neighbors are equidistant, in which case round towards the even neighbor (Banker's rounding)

ROUND_CEILING, :ceiling, :ceil

round towards positive infinity (ceil)

ROUND_FLOOR, :floor

round towards negative infinity (floor)

.save_exception_mode

Execute the provided block, but preserve the exception mode

BigDecimal.save_exception_mode do
  BigDecimal.mode(BigDecimal::EXCEPTION_OVERFLOW, false)
  BigDecimal.mode(BigDecimal::EXCEPTION_NaN, false)

  BigDecimal.new(BigDecimal('Infinity'))
  BigDecimal.new(BigDecimal('-Infinity'))
  BigDecimal(BigDecimal.new('NaN'))
end

For use with the BigDecimal::EXCEPTION_*

See .mode

.save_limit

Execute the provided block, but preserve the precision limit

BigDecimal.limit(100)
puts BigDecimal.limit
BigDecimal.save_limit do
    BigDecimal.limit(200)
    puts BigDecimal.limit
end
puts BigDecimal.limit

.save_rounding_mode

Execute the provided block, but preserve the rounding mode

BigDecimal.save_rounding_mode do
  BigDecimal.mode(BigDecimal::ROUND_MODE, :up)
  puts BigDecimal.mode(BigDecimal::ROUND_MODE)
end

For use with the BigDecimal::ROUND_*

See .mode

.ver

Returns the BigDecimal version number.

Instance Attribute Details

#finite? ⇒ Boolean (readonly)

Returns True if the value is finite (not NaN or infinite).

#infinite? ⇒ Boolean (readonly)

Returns nil, -1, or 1 depending on whether the value is finite, -Infinity, or Infinity.

#nan? ⇒ Boolean (readonly)

Returns True if the value is Not a Number.

#nonzero? ⇒ Boolean (readonly)

Returns self if the value is non-zero, nil otherwise.

#zero? ⇒ Boolean (readonly)

Returns True if the value is zero.

Instance Method Details

#%

#mult(value, digits)

Multiply by the specified value.

e.g.

c = a.mult(b,n)
c = a * b
digits

If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.

#**(n) ⇒ BigDecimal

Returns the value raised to the power of n.

See #power.

#add(value, digits)

Add the specified value.

e.g.

c = a.add(b,n)
c = a + b
digits

If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.

#+@

Return self.

e.g.

b = +a  # b == a

#-(b) ⇒ BigDecimal

Subtract the specified value.

e.g.

c = a - b

The precision of the result value depends on the type of b.

If b is a ::Float, the precision of the result is Float::DIG+1.

If b is a BigDecimal, the precision of the result is b's precision of internal representation from platform. So, it's return value is platform dependent.

#-@

Return the negation of self.

e.g.

b = -a
b == a * -1

#/

#<(b)

Returns true if a is less than b.

Values may be coerced to perform the comparison (see ==, #coerce).

#<=(b)

Returns true if a is less than or equal to b.

Values may be coerced to perform the comparison (see ==, #coerce).

#<=>(r)

The comparison operator. a <=> b is 0 if a == b, 1 if a > b, -1 if a < b.

#==(r) Also known as: #===, #eql?

Tests for value equality; returns true if the values are equal.

The == and === operators and the eql? method have the same implementation for BigDecimal.

Values may be coerced to perform the comparison:

BigDecimal.new('1.0') == 1.0  #=> true

#===(r)

Alias for #==.

#>(b)

Returns true if a is greater than b.

Values may be coerced to perform the comparison (see ==, #coerce).

#>=(b)

Returns true if a is greater than or equal to b.

Values may be coerced to perform the comparison (see ==, #coerce)

#_dump

Method used to provide marshalling support.

inf = BigDecimal.new('Infinity')
  #=> #<BigDecimal:1e16fa8,'Infinity',9(9)>
BigDecimal._load(inf._dump)
  #=> #<BigDecimal:1df8dc8,'Infinity',9(9)>

See the Marshal module.

#abs

Returns the absolute value, as a BigDecimal.

BigDecimal('5').abs #=> 5
BigDecimal('-3').abs #=> 3

#add(value, digits)

Add the specified value.

e.g.

c = a.add(b,n)
c = a + b
digits

If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.

#ceil(n)

Return the smallest integer greater than or equal to the value, as a BigDecimal.

BigDecimal('3.14159').ceil #=> 4
BigDecimal('-9.1').ceil #=> -9

If n is specified and positive, the fractional part of the result has no more than that many digits.

If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.

BigDecimal('3.14159').ceil(3) #=> 3.142
BigDecimal('13345.234').ceil(-2) #=> 13400.0

#coerce(other)

The coerce method provides support for Ruby type coercion. It is not enabled by default.

This means that binary operations like + * / or - can often be performed on a BigDecimal and an object of another type, if the other object can be coerced into a BigDecimal value.

e.g.

a = BigDecimal.new("1.0")
b = a / 2.0 #=> 0.5

Note that coercing a ::String to a BigDecimal is not supported by default; it requires a special compile-time option when building Ruby.

#div(*args)

#divmod(value)

Divides by the specified value, and returns the quotient and modulus as BigDecimal numbers. The quotient is rounded towards negative infinity.

For example:

require 'bigdecimal'

a = BigDecimal.new("42")
b = BigDecimal.new("9")

q, m = a.divmod(b)

c = q * b + m

a == c  #=> true

The quotient q is (a/b).floor, and the modulus is the amount that must be added to q * b to get a.

#eql?(r)

Alias for #==.

#exponent

Returns the exponent of the BigDecimal number, as an ::Integer.

If the number can be represented as 0.xxxxxx*10**n where xxxxxx is a string of digits with no leading zeros, then n is the exponent.

#fix

Return the integer part of the number, as a BigDecimal.

#floor(n)

Return the largest integer less than or equal to the value, as a BigDecimal.

BigDecimal('3.14159').floor #=> 3
BigDecimal('-9.1').floor #=> -10

If n is specified and positive, the fractional part of the result has no more than that many digits.

If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.

BigDecimal('3.14159').floor(3) #=> 3.141
BigDecimal('13345.234').floor(-2) #=> 13300.0

#frac

Return the fractional part of the number, as a BigDecimal.

#hash

Creates a hash for this BigDecimal.

Two BigDecimals with equal sign, fractional part and exponent have the same hash.

#inspect

Returns debugging information about the value as a string of comma-separated values in angle brackets with a leading #:

BigDecimal.new("1234.5678").inspect
  #=> "#<BigDecimal:b7ea1130,'0.12345678E4',8(12)>"

The first part is the address, the second is the value as a string, and the final part ss(mm) is the current number of significant digits and the maximum number of significant digits, respectively.

#modulo

#mult(value, digits)

Multiply by the specified value.

e.g.

c = a.mult(b,n)
c = a * b
digits

If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.

#power(n) #power(n, prec)

Returns the value raised to the power of n.

Note that n must be an ::Integer.

Also available as the operator **.

#precs

Returns an Array of two ::Integer values.

The first value is the current number of significant digits in the BigDecimal. The second value is the maximum number of significant digits for the BigDecimal.

#quo

#remainder

#round(n, mode)

Round to the nearest integer (by default), returning the result as a BigDecimal.

BigDecimal('3.14159').round #=> 3
BigDecimal('8.7').round #=> 9
BigDecimal('-9.9').round #=> -10

If n is specified and positive, the fractional part of the result has no more than that many digits.

If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.

BigDecimal('3.14159').round(3) #=> 3.142
BigDecimal('13345.234').round(-2) #=> 13300.0

The value of the optional mode argument can be used to determine how rounding is performed; see .mode.

#sign

Returns the sign of the value.

Returns a positive value if > 0, a negative value if < 0, and a zero if == 0.

The specific value returned indicates the type and sign of the BigDecimal, as follows:

BigDecimal::SIGN_NaN

value is Not a Number

BigDecimal::SIGN_POSITIVE_ZERO

value is +0

BigDecimal::SIGN_NEGATIVE_ZERO

value is -0

BigDecimal::SIGN_POSITIVE_INFINITE

value is +Infinity

BigDecimal::SIGN_NEGATIVE_INFINITE

value is -Infinity

BigDecimal::SIGN_POSITIVE_FINITE

value is positive

BigDecimal::SIGN_NEGATIVE_FINITE

value is negative

#split

Splits a BigDecimal number into four parts, returned as an array of values.

The first value represents the sign of the BigDecimal, and is -1 or 1, or 0 if the BigDecimal is Not a Number.

The second value is a string representing the significant digits of the BigDecimal, with no leading zeros.

The third value is the base used for arithmetic (currently always 10) as an ::Integer.

The fourth value is an ::Integer exponent.

If the BigDecimal can be represented as 0.xxxxxx*10**n, then xxxxxx is the string of significant digits with no leading zeros, and n is the exponent.

From these values, you can translate a BigDecimal to a float as follows:

sign, significant_digits, base, exponent = a.split
f = sign * "0.#{significant_digits}".to_f * (base ** exponent)

(Note that the to_f method is provided as a more convenient way to translate a BigDecimal to a ::Float.)

#sqrt(n)

Returns the square root of the value.

Result has at least n significant digits.

#sub(value, digits) ⇒ BigDecimal

Subtract the specified value.

e.g.

c = a.sub(b,n)
digits

If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.

#to_d ⇒ BigDecimal

Returns self.

[ GitHub ] 

  


# File 'ext/bigdecimal/lib/bigdecimal/util.rb', line 97



def to_d
  self
end


  








  

    #to_digits  ⇒ String   



  

    

Converts a BigDecimal to a ::String of the form “nnnnnn.mmm”. This method is deprecated; use BigDecimal#to_s(“F”) instead.



require 'bigdecimal'
require 'bigdecimal/util'

d = BigDecimal.new("3.14")
d.to_digits
# => "3.14"


  



  [ GitHub ]


  

  


# File 'ext/bigdecimal/lib/bigdecimal/util.rb', line 83



def to_digits
  if self.nan? || self.infinite? || self.zero?
    self.to_s
  else
    i       = self.to_i.to_s
    _,f,_,z = self.frac.split
    i + "." + ("0"*(-z)) + f
  end
end


  








  

    #to_f  
  



  

    

Returns a new ::Float object having approximately the same value as the BigDecimal number. Normal accuracy limits and built-in errors of binary ::Float arithmetic apply.


  









  

    #to_i  
    Also known as: #to_int
  



  

    

Returns the value as an integer (Fixnum or Bignum).



If the BigNumber is infinity or NaN, raises FloatDomainError.


  









  

    #to_int  
  



  

    

Alias for #to_i.


  









  

    #to_r  
  



  

    

Converts a BigDecimal to a ::Rational.


  









  

    #to_s(s)  ⇒ ?   



  

    

Converts the value to a string.



The default format looks like  0.xxxxEnn.



The optional parameter s consists of either an integer; or an optional '+' or ' ', followed by an optional number, followed by an optional 'E' or 'F'.



If there is a '+' at the start of s, positive values are returned with a leading '+'.



A space at the start of s returns positive values with a leading space.



If s contains a number, a space is inserted after each group of that many fractional digits.



If s ends with an 'E', engineering notation (0.xxxxEnn) is used.



If s ends with an 'F', conventional floating point notation is used.



Examples:



BigDecimal.new('-123.45678901234567890').to_s('5F')
  #=> '-123.45678 90123 45678 9'

BigDecimal.new('123.45678901234567890').to_s('+8F')
  #=> '+123.45678901 23456789'

BigDecimal.new('123.45678901234567890').to_s(' F')
  #=> ' 123.4567890123456789'


  









  

    #truncate(n)    



  

    

Truncate to the nearest integer (by default), returning the result as a BigDecimal.



BigDecimal('3.14159').truncate #=> 3
BigDecimal('8.7').truncate #=> 8
BigDecimal('-9.9').truncate #=> -9



If n is specified and positive, the fractional part of the result has no more than that many digits.



If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.



BigDecimal('3.14159').truncate(3) #=> 3.141
BigDecimal('13345.234').truncate(-2) #=> 13300.0