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

Similarly:

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

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

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

(See BigDecimal.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.

bigdecimal/util

When you require bigdecimal/util, the to_d method will be available on BigDecimal and the native Integer, Float, Rational, and String classes:

require 'bigdecimal/util'

42.to_d         # => 0.42e2
0.5.to_d        # => 0.5e0
(2/3r).to_d(3)  # => 0.667e0
"0.5".to_d      # => 0.5e0

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.


Returns the modulus from dividing by b.

See BigDecimal#divmod.

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.

Returns the value raised to the power of n.

See BigDecimal#power.

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.

+BigDecimal('5')  #=> 0.5e1

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.

-BigDecimal('5')  #=> -0.5e1

Divide by the specified value.

See BigDecimal#div.

Returns true if a is less than b.

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

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

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

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

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('1.0') == 1.0  #=> true

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('1.0') == 1.0  #=> true

Returns true if a is greater than b.

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

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

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

Method used to provide marshalling support.

inf = BigDecimal('Infinity')
  #=> Infinity
BigDecimal._load(inf._dump)
  #=> Infinity

See the Marshal module.

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

Returns the absolute value, as a BigDecimal.

BigDecimal('5').abs  #=> 0.5e1
BigDecimal('-3').abs #=> 0.3e1

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.

Marshal the object to JSON.

method used for JSON marshalling support.

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
No documentation available

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("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.

Divide by the specified value.

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.

If digits is 0, the result is the same as for the / operator or quo.

If digits is not specified, the result is an integer, by analogy with Float#div; see also BigDecimal#divmod.

Examples:

a = BigDecimal("4")
b = BigDecimal("3")

a.div(b, 3)  # => 0.133e1

a.div(b, 0)  # => 0.1333333333333333333e1
a / b        # => 0.1333333333333333333e1
a.quo(b)     # => 0.1333333333333333333e1

a.div(b)     # => 1

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("42")
b = BigDecimal("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.

The BigDecimal.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.

No documentation available

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('1.0') == 1.0  #=> true

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.

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

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

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

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

Creates a hash for this BigDecimal.

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

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

Returns a string representation of self.

BigDecimal("1234.5678").inspect
  #=> "0.12345678e4"

Import a JSON Marshalled object.

method used for JSON marshalling support.

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

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:

BigDecimal::EXCEPTION_NaN BigDecimal::EXCEPTION_INFINITY BigDecimal::EXCEPTION_UNDERFLOW BigDecimal::EXCEPTION_OVERFLOW BigDecimal::EXCEPTION_ZERODIVIDE BigDecimal::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: BigDecimal::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)

Returns the modulus from dividing by b.

See BigDecimal#divmod.

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.

Returns True if the value is Not a Number.

No documentation available

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

Returns the value raised to the power of n.

Note that n must be an Integer.

Also available as the operator **.

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.

BigDecimal('5').precs #=> [9, 18]

Divide by the specified value.

See BigDecimal#div.

Returns the remainder from dividing by the value.

x.remainder(y) means x-y*(x/y).truncate

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

For use with the BigDecimal::EXCEPTION_*

See BigDecimal.mode

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

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 BigDecimal.mode

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

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.)

Returns the square root of the value.

Result has at least n significant digits.

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.

Returns self.

require 'bigdecimal/util'

d = BigDecimal("3.14")
d.to_d                       # => 0.314e1

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

require 'bigdecimal/util'

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

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.

Returns the value as an Integer.

If the BigDecimal is infinity or NaN, raises FloatDomainError.

Returns the value as an Integer.

If the BigDecimal is infinity or NaN, raises FloatDomainError.

return the JSON value

Converts a BigDecimal to a Rational.

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

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

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

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

Returns True if the value is zero.