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
-
BASE =
Base value used in internal calculations. On a 32 bit system,
BASE
is 10000, indicating that calculation is done in groups of 4 digits. (If it were larger, BASE**2 wouldn't fit in 32 bits, so you couldn't guarantee that two groups could always be multiplied together without overflow.)INT2FIX((SIGNED_VALUE)VpBaseVal())
-
EXCEPTION_ALL =
Determines whether overflow, underflow or zero divide result in an exception being thrown. See .mode.
0xff
-
EXCEPTION_INFINITY =
Determines what happens when the result of a computation is infinity. See .mode.
0x01
-
EXCEPTION_NaN =
Determines what happens when the result of a computation is not a number (NaN). See .mode.
0x02
-
EXCEPTION_OVERFLOW =
Determines what happens when the result of a computation is an overflow (a result too large to be represented). See .mode.
0x01
-
EXCEPTION_UNDERFLOW =
Determines what happens when the result of a computation is an underflow (a result too small to be represented). See .mode.
0x04
-
EXCEPTION_ZERODIVIDE =
Determines what happens when a division by zero is performed. See .mode.
0x01
-
INFINITY =
Positive infinity value.
BigDecimal_global_new(1, &arg, rb_cBigDecimal)
-
NAN =
'Not a Number' value.
BigDecimal_global_new(1, &arg, rb_cBigDecimal)
-
ROUND_CEILING =
Round towards +Infinity. See .mode.
5
-
ROUND_DOWN =
Indicates that values should be rounded towards zero. See .mode.
2
-
ROUND_FLOOR =
Round towards -Infinity. See .mode.
6
-
ROUND_HALF_DOWN =
Indicates that digits >= 6 should be rounded up, others rounded down. See .mode.
4
-
ROUND_HALF_EVEN =
Round towards the even neighbor. See .mode.
7
-
ROUND_HALF_UP =
Indicates that digits >= 5 should be rounded up, others rounded down. See .mode.
3
-
ROUND_MODE =
Determines what happens when a result must be rounded in order to fit in the appropriate number of significant digits. See .mode.
0x100
-
ROUND_UP =
Indicates that values should be rounded away from zero. See .mode.
1
-
SIGN_NEGATIVE_FINITE =
Indicates that a value is negative and finite. See #sign.
-2
-
SIGN_NEGATIVE_INFINITE =
Indicates that a value is negative and infinite. See #sign.
-3
-
SIGN_NEGATIVE_ZERO =
Indicates that a value is -0. See #sign.
-1
-
SIGN_NaN =
Indicates that a value is not a number. See #sign.
0
-
SIGN_POSITIVE_FINITE =
Indicates that a value is positive and finite. See #sign.
2
-
SIGN_POSITIVE_INFINITE =
Indicates that a value is positive and infinite. See #sign.
3
-
SIGN_POSITIVE_ZERO =
Indicates that a value is +0. See #sign.
1
Class Method Summary
-
._load(str)
Internal method used to provide marshalling support.
-
.double_fig
The
double_fig
class method returns the number of digits a ::Float number is allowed to have. -
.limit(digits)
Limit the number of significant digits in newly created
BigDecimal
numbers to the specified value. -
.mode(mode, value)
Controls handling of arithmetic exceptions and rounding.
-
.new(initial, digits)
constructor
Create a new
BigDecimal
object. -
.save_exception_mode
Execute the provided block, but preserve the exception mode.
-
.save_limit
Execute the provided block, but preserve the precision limit.
-
.save_rounding_mode
Execute the provided block, but preserve the rounding mode.
-
.ver
Returns the
BigDecimal
version number.
Instance Attribute Summary
-
#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 Summary
- #%
-
#mult(value, digits)
Multiply by the specified value.
-
#**(n) ⇒ BigDecimal
Returns the value raised to the power of n.
-
#add(value, digits)
Add the specified value.
-
#+@
Return self.
-
#-(b) ⇒ BigDecimal
Subtract the specified value.
-
#-@
Return the negation of self.
- #/
-
#<(b)
Returns true if a is less than b.
-
#<=(b)
Returns true if a is less than or equal to b.
-
#<=>(r)
The comparison operator.
-
#==(r)
(also: #===, #eql?)
Tests for value equality; returns true if the values are equal.
-
#===(r)
Alias for #==.
-
#>(b)
Returns true if a is greater than b.
-
#>=(b)
Returns true if a is greater than or equal to b.
-
#_dump
Method used to provide marshalling support.
-
#abs
Returns the absolute value, as a
BigDecimal
. -
#add(value, digits)
Add the specified value.
-
#ceil(n)
Return the smallest integer greater than or equal to the value, as a
BigDecimal
. -
#coerce(other)
The coerce method provides support for Ruby type coercion.
- #div(*args)
-
#divmod(value)
Divides by the specified value, and returns the quotient and modulus as
BigDecimal
numbers. -
#eql?(r)
Alias for #==.
-
#exponent
Returns the exponent of the
BigDecimal
number, as an ::Integer. -
#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
. -
#frac
Return the fractional part of the number, as a
BigDecimal
. -
#hash
Creates a hash for this
BigDecimal
. -
#inspect
Returns debugging information about the value as a string of comma-separated values in angle brackets with a leading #:
- #modulo
-
#mult(value, digits)
Multiply by the specified value.
-
#power(n)
Returns the value raised to the power of n.
-
#precs
Returns an Array of two ::Integer values.
- #quo
- #remainder
-
#round(n, mode)
Round to the nearest integer (by default), returning the result as a
BigDecimal
. -
#sign
Returns the sign of the value.
-
#split
Splits a
BigDecimal
number into four parts, returned as an array of values. -
#sqrt(n)
Returns the square root of the value.
-
#sub(value, digits) ⇒ BigDecimal
Subtract the specified value.
-
#to_d ⇒ BigDecimal
Returns self.
-
#to_digits ⇒ String
Converts a
BigDecimal
to a ::String of the form “nnnnnn.mmm”. -
#to_f
Returns a new ::Float object having approximately the same value as the
BigDecimal
number. -
#to_i
(also: #to_int)
Returns the value as an integer (Fixnum or Bignum).
-
#to_int
Alias for #to_i.
-
#to_r
Converts a
BigDecimal
to a ::Rational. -
#to_s(s) ⇒ ?
Converts the value to a string.
-
#truncate(n)
Truncate to the nearest integer (by default), returning the result as a
BigDecimal
.
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 thedigits
is larger than Float::DIG + 1, this exception is raised. - ArgumentError
-
If the
initial
is a ::Float or ::Rational, and thedigits
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
.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
#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.
# File 'ext/bigdecimal/lib/bigdecimal/util.rb', line 97
def to_d self end
#to_digits ⇒ String
#to_f
#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