Class: BigDecimal

Inherits:
Numeric
  • Object
show all
Defined in:
ext/bigdecimal/bigdecimal.c,
lib/bigdecimal.rb,
lib/bigdecimal.rb,
lib/bigdecimal/util.rb,
sig/big_decimal.rbs,
sig/big_decimal_util.rbs,
ext/bigdecimal/bigdecimal.c

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("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

A Note About Precision

For a calculation using a BigDecimal and another value, the precision of the result depends on the type of value:

  • If value is a Float, the precision is Float::DIG + 1.
  • If value is a Rational, the precision is larger than Float::DIG + 1.
  • If value is a BigDecimal, the precision is +value+'s precision in the internal representation, which is platform-dependent.
  • If value is other object, the precision is determined by the result of BigDecimal(value).

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, String, Complex, and NilClass 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
 Complex(0.1234567, 0).to_d(4)   # => 0.1235e0
 nil.to_d                        # => 0.0

Methods for Working with JSON

  • ::json_create: Returns a new BigDecimal object constructed from the given object.
  • #as_json: Returns a 2-element hash representing self.
  • #to_json: Returns a JSON string representing self.

These methods are provided by the JSON gem. To make these methods available:

require 'json/add/bigdecimal'

  • License

Copyright (C) 2002 by Shigeo Kobayashi [email protected].

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

Maintained by mrkn [email protected] and ruby-core members.

Documented by zzak [email protected], mathew [email protected], and many other contributors.

Defined Under Namespace

Modules: Internal

Constant Summary collapse

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)BASE)
EXCEPTION_ALL =

Determines whether overflow, underflow or zero divide result in an exception being thrown. See BigDecimal.mode.

0xff
EXCEPTION_INFINITY =

Determines what happens when the result of a computation is infinity. See BigDecimal.mode.

0x01
EXCEPTION_NaN =

Determines what happens when the result of a computation is not a number (NaN). See BigDecimal.mode.

0x02
EXCEPTION_OVERFLOW =

Determines what happens when the result of a computation is an overflow (a result too large to be represented). See BigDecimal.mode.

0x01
EXCEPTION_UNDERFLOW =

Determines what happens when the result of a computation is an underflow (a result too small to be represented). See BigDecimal.mode.

0x04
EXCEPTION_ZERODIVIDE =

Determines what happens when a division by zero is performed. See BigDecimal.mode.

0x10
INFINITY =

BigDecimal@Infinity] value.

Positive infinity[rdoc-ref
NAN =

BigDecimal@Not+a+Number]' value.

'{Not a Number}[rdoc-ref
ROUND_CEILING =

Round towards +Infinity. See BigDecimal.mode.

5
ROUND_DOWN =

Indicates that values should be rounded towards zero. See BigDecimal.mode.

2
ROUND_FLOOR =

Round towards -Infinity. See BigDecimal.mode.

6
ROUND_HALF_DOWN =

Indicates that digits >= 6 should be rounded up, others rounded down. See BigDecimal.mode.

4
ROUND_HALF_EVEN =

Round towards the even neighbor. See BigDecimal.mode.

7
ROUND_HALF_UP =

Indicates that digits >= 5 should be rounded up, others rounded down. See BigDecimal.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 BigDecimal.mode.

0x100
ROUND_UP =

Indicates that values should be rounded away from zero. See BigDecimal.mode.

1
SIGN_NEGATIVE_FINITE =

Indicates that a value is negative and finite. See BigDecimal.sign.

-2
SIGN_NEGATIVE_INFINITE =

Indicates that a value is negative and infinite. See BigDecimal.sign.

-3
SIGN_NEGATIVE_ZERO =

Indicates that a value is -0. See BigDecimal.sign.

-1
SIGN_NaN =

Indicates that a value is not a number. See BigDecimal.sign.

0
SIGN_POSITIVE_FINITE =

Indicates that a value is positive and finite. See BigDecimal.sign.

2
SIGN_POSITIVE_INFINITE =

Indicates that a value is positive and infinite. See BigDecimal.sign.

3
SIGN_POSITIVE_ZERO =

Indicates that a value is +0. See BigDecimal.sign.

1
VERSION =

The version of bigdecimal library

rb_str_new2(BIGDECIMAL_VERSION)

Class Method Summary collapse

Instance Method Summary collapse

Class Method Details

._load(str) ⇒ Object

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



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# File 'sig/big_decimal.rbs', line 13

def self._load: (String) -> BigDecimal

.double_fig ⇒ Integer

Returns the number of digits a Float object is allowed to have; the result is system-dependent:

BigDecimal.double_fig # => 16

Returns:



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# File 'sig/big_decimal.rbs', line 24

def self.double_fig: () -> Integer

.interpret_loosely(string) ⇒ Object

Returns the BigDecimal converted loosely from string.



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# File 'sig/big_decimal.rbs', line 31

def self.interpret_loosely: (string) -> BigDecimal

.limit(digits) ⇒ Object

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.



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# File 'sig/big_decimal.rbs', line 46

def self.limit: (?Integer? digits) -> Integer

.mode(mode, setting = nil) ⇒ Integer

Returns an integer representing the mode settings for exception handling and rounding.

These modes control exception handling:

  • BigDecimal::EXCEPTION_NaN.
  • BigDecimal::EXCEPTION_INFINITY.
  • BigDecimal::EXCEPTION_UNDERFLOW.
  • BigDecimal::EXCEPTION_OVERFLOW.
  • BigDecimal::EXCEPTION_ZERODIVIDE.
  • BigDecimal::EXCEPTION_ALL.

Values for setting for exception handling:

  • true: sets the given mode to true.
  • false: sets the given mode to false.
  • nil: does not modify the mode settings.

You can use method BigDecimal.save_exception_mode to temporarily change, and then automatically restore, exception modes.

For clarity, some examples below begin by setting all exception modes to false.

This mode controls the way rounding is to be performed:

  • BigDecimal::ROUND_MODE

You can use method BigDecimal.save_rounding_mode to temporarily change, and then automatically restore, the rounding mode.

NaNs

Mode BigDecimal::EXCEPTION_NaN controls behavior when a BigDecimal NaN is created.

Settings:

  • false (default): Returns BigDecimal('NaN').
  • true: Raises FloatDomainError.

Examples:

BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false) # => 0
BigDecimal('NaN')                                 # => NaN
BigDecimal.mode(BigDecimal::EXCEPTION_NaN, true)  # => 2
BigDecimal('NaN') # Raises FloatDomainError

Infinities

Mode BigDecimal::EXCEPTION_INFINITY controls behavior when a BigDecimal Infinity or -Infinity is created. Settings:

  • false (default): Returns BigDecimal('Infinity') or BigDecimal('-Infinity').
  • true: Raises FloatDomainError.

Examples:

BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)     # => 0
BigDecimal('Infinity')                                # => Infinity
BigDecimal('-Infinity')                               # => -Infinity
BigDecimal.mode(BigDecimal::EXCEPTION_INFINITY, true) # => 1
BigDecimal('Infinity')  # Raises FloatDomainError
BigDecimal('-Infinity') # Raises FloatDomainError

Underflow

Mode BigDecimal::EXCEPTION_UNDERFLOW controls behavior when a BigDecimal underflow occurs. Settings:

  • false (default): Returns BigDecimal('0') or BigDecimal('-Infinity').
  • true: Raises FloatDomainError.

Examples:

BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)      # => 0
def flow_under
x = BigDecimal('0.1')
100.times { x *= x }
end
flow_under                                             # => 100
BigDecimal.mode(BigDecimal::EXCEPTION_UNDERFLOW, true) # => 4
flow_under # Raises FloatDomainError

Overflow

Mode BigDecimal::EXCEPTION_OVERFLOW controls behavior when a BigDecimal overflow occurs. Settings:

  • false (default): Returns BigDecimal('Infinity') or BigDecimal('-Infinity').
  • true: Raises FloatDomainError.

Examples:

BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)     # => 0
def flow_over
x = BigDecimal('10')
100.times { x *= x }
end
flow_over                                             # => 100
BigDecimal.mode(BigDecimal::EXCEPTION_OVERFLOW, true) # => 1
flow_over # Raises FloatDomainError

Zero Division

Mode BigDecimal::EXCEPTION_ZERODIVIDE controls behavior when a zero-division occurs. Settings:

  • false (default): Returns BigDecimal('Infinity') or BigDecimal('-Infinity').
  • true: Raises FloatDomainError.

Examples:

BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)       # => 0
one = BigDecimal('1')
zero = BigDecimal('0')
one / zero                                              # => Infinity
BigDecimal.mode(BigDecimal::EXCEPTION_ZERODIVIDE, true) # => 16
one / zero # Raises FloatDomainError

All Exceptions

Mode BigDecimal::EXCEPTION_ALL controls all of the above:

BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false) # => 0
BigDecimal.mode(BigDecimal::EXCEPTION_ALL, true)  # => 23

Rounding

Mode BigDecimal::ROUND_MODE controls the way rounding is to be performed; its setting values are:

  • ROUND_UP: Round away from zero. Aliased as :up.
  • ROUND_DOWN: Round toward zero. Aliased as :down and :truncate.
  • ROUND_HALF_UP: Round toward the nearest neighbor; if the neighbors are equidistant, round away from zero. Aliased as :half_up and :default.
  • ROUND_HALF_DOWN: Round toward the nearest neighbor; if the neighbors are equidistant, round toward zero. Aliased as :half_down.
  • ROUND_HALF_EVEN (Banker's rounding): Round toward the nearest neighbor; if the neighbors are equidistant, round toward the even neighbor. Aliased as :half_even and :banker.
  • ROUND_CEILING: Round toward positive infinity. Aliased as :ceiling and :ceil.
  • ROUND_FLOOR: Round toward negative infinity. Aliased as :floor:.

Returns:



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# File 'sig/big_decimal.rbs', line 200

def self.mode: (round_mode, ?(round_mode_integer | round_mode_symbol)) -> Integer
| (Integer exception_mode, ?bool? setting) -> Integer

.save_exception_mode { ... } ⇒ Object

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

Yields:

  • []



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# File 'sig/big_decimal.rbs', line 222

def self.save_exception_mode: () { (?nil) -> void } -> void

.save_limit { ... } ⇒ Object

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

Yields:

  • []



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# File 'sig/big_decimal.rbs', line 238

def self.save_limit: () { (?nil) -> void } -> void

.save_rounding_mode { ... } ⇒ Object

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

Yields:

  • []



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# File 'sig/big_decimal.rbs', line 255

def self.save_rounding_mode: () { (?nil) -> void } -> void

Instance Method Details

#% ⇒ Object

%: a%b = a - (a.to_f/b).floor * b



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# File 'sig/big_decimal.rbs', line 266

def %: (real | BigDecimal) -> BigDecimal

#*(b) ⇒ Object

Multiply by the specified value.

The result precision will be the precision of the sum of each precision.

See BigDecimal#mult.



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# File 'sig/big_decimal.rbs', line 273

def *: (real | BigDecimal) -> BigDecimal
| (Complex) -> Complex

#**(arg0) ⇒ BigDecimal #**(arg0) ⇒ Complex

Returns the BigDecimal value of self raised to power other:

b = BigDecimal('3.14')
b ** 2              # => 0.98596e1
b ** 2.0            # => 0.98596e1
b ** Rational(2, 1) # => 0.98596e1

Related: BigDecimal#power.

Overloads:

  • #**(arg0) ⇒ BigDecimal

    Parameters:

    Returns:

  • #**(arg0) ⇒ Complex

    Parameters:

    Returns:



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# File 'lib/bigdecimal.rb', line 127

def **(y)
  case y
  when BigDecimal, Integer, Float, Rational
    power(y)
  when nil
    raise TypeError, 'wrong argument type NilClass'
  else
    x, y = y.coerce(self)
    x**y
  end
end

#+(value) ⇒ Object

Returns the BigDecimal sum of self and value:

b = BigDecimal('111111.111') # => 0.111111111e6
b + 2                        # => 0.111113111e6
b + 2.0                      # => 0.111113111e6
b + Rational(2, 1)           # => 0.111113111e6
b + Complex(2, 0)            # => (0.111113111e6+0i)

See the Note About Precision.



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# File 'sig/big_decimal.rbs', line 307

def +: (real | BigDecimal) -> BigDecimal
| (Complex) -> Complex

#+ ⇒ self

Returns self:

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

Returns:



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# File 'sig/big_decimal.rbs', line 319

def +@: () -> BigDecimal

#-(value) ⇒ Object

Returns the BigDecimal difference of self and value:

b = BigDecimal('333333.333') # => 0.333333333e6
b - 2                        # => 0.333331333e6
b - 2.0                      # => 0.333331333e6
b - Rational(2, 1)           # => 0.333331333e6
b - Complex(2, 0)            # => (0.333331333e6+0i)

See the Note About Precision.



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# File 'sig/big_decimal.rbs', line 336

def -: (real | BigDecimal) -> BigDecimal
| (Complex) -> Complex

#- ⇒ Object

Returns the BigDecimal negation of self:

b0 = BigDecimal('1.5')
b1 = -b0 # => -0.15e1
b2 = -b1 # => 0.15e1



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# File 'sig/big_decimal.rbs', line 349

def -@: () -> BigDecimal

#/ ⇒ Object

For c = self/r: with round operation



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# File 'sig/big_decimal.rbs', line 362

def /: (real | BigDecimal) -> BigDecimal
| (Complex) -> Complex

#<(other) ⇒ Boolean

Returns true if self is less than other, false otherwise:

b = BigDecimal('1.5') # => 0.15e1
b < 2                 # => true
b < 2.0               # => true
b < Rational(2, 1)    # => true
b < 1.5               # => false

Raises an exception if the comparison cannot be made.

Returns:



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# File 'sig/big_decimal.rbs', line 379

def <: (real | BigDecimal) -> bool

#<=(other) ⇒ Boolean

Returns true if self is less or equal to than other, false otherwise:

b = BigDecimal('1.5') # => 0.15e1
b <= 2                # => true
b <= 2.0              # => true
b <= Rational(2, 1)   # => true
b <= 1.5              # => true
b < 1                 # => false

Raises an exception if the comparison cannot be made.

Returns:



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# File 'sig/big_decimal.rbs', line 396

def <=: (real | BigDecimal) -> bool

#<=>(r) ⇒ Object

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



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# File 'sig/big_decimal.rbs', line 404

def <=>: (untyped) -> Integer?

#==(r) ⇒ Object

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



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# File 'sig/big_decimal.rbs', line 419

def ==: (untyped) -> bool

#===(r) ⇒ Object

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



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# File 'sig/big_decimal.rbs', line 431

def ===: (untyped) -> bool

#>(other) ⇒ Boolean

Returns true if self is greater than other, false otherwise:

b = BigDecimal('1.5')
b > 1              # => true
b > 1.0            # => true
b > Rational(1, 1) # => true
b > 2              # => false

Raises an exception if the comparison cannot be made.

Returns:



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# File 'sig/big_decimal.rbs', line 447

def >: (real | BigDecimal) -> bool

#>=(other) ⇒ Boolean

Returns true if self is greater than or equal to other, false otherwise:

b = BigDecimal('1.5')
b >= 1              # => true
b >= 1.0            # => true
b >= Rational(1, 1) # => true
b >= 1.5            # => true
b > 2               # => false

Raises an exception if the comparison cannot be made.

Returns:



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# File 'sig/big_decimal.rbs', line 465

def >=: (real | BigDecimal) -> bool

#_decimal_shift(v) ⇒ Object

Returns self * 10**v without changing the precision. This method is currently for internal use.

BigDecimal("0.123e10")._decimal_shift(20) #=> "0.123e30"
BigDecimal("0.123e10")._decimal_shift(-20) #=> "0.123e-10"



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# File 'lib/bigdecimal.rb', line 5

def _decimal_shift(i) # :nodoc:
  to_java.move_point_right(i).to_d
end

#_dump ⇒ String

Returns a string representing the marshalling of self. See module Marshal.

inf = BigDecimal('Infinity') # => Infinity
dumped = inf._dump           # => "9:Infinity"
BigDecimal._load(dumped)     # => Infinity

Returns:



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# File 'sig/big_decimal.rbs', line 477

def _dump: (?untyped) -> String

#abs ⇒ Object

Returns the BigDecimal absolute value of self:

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



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# File 'sig/big_decimal.rbs', line 488

def abs: () -> BigDecimal

#add(value, ndigits) ⇒ Object

Returns the BigDecimal sum of self and value with a precision of ndigits decimal digits.

When ndigits is less than the number of significant digits in the sum, the sum is rounded to that number of digits, according to the current rounding mode; see BigDecimal.mode.

Examples:

# Set the rounding mode.
BigDecimal.mode(BigDecimal::ROUND_MODE, :half_up)
b = BigDecimal('111111.111')
b.add(1, 0)               # => 0.111112111e6
b.add(1, 3)               # => 0.111e6
b.add(1, 6)               # => 0.111112e6
b.add(1, 15)              # => 0.111112111e6
b.add(1.0, 15)            # => 0.111112111e6
b.add(Rational(1, 1), 15) # => 0.111112111e6



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# File 'sig/big_decimal.rbs', line 513

def add: (real | BigDecimal value, Integer digits) -> BigDecimal

#ceil(n) ⇒ Object

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



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# File 'sig/big_decimal.rbs', line 534

def ceil: () -> Integer
| (int n) -> BigDecimal

#clone ⇒ Object

:nodoc:



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# File 'sig/big_decimal.rbs', line 542

def clone: () -> self

#coerce(other) ⇒ Object

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.



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# File 'sig/big_decimal.rbs', line 562

def coerce: (Numeric) -> [ BigDecimal, BigDecimal ]

#div(*args) ⇒ Object

call-seq:

div(value)  -> integer
div(value, digits)  -> bigdecimal or integer

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.

See BigDecimal#/. See BigDecimal#quo.

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



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# File 'sig/big_decimal.rbs', line 597

def div: (real | BigDecimal value) -> Integer
| (real | BigDecimal value, int digits) -> BigDecimal

#divmod(value) ⇒ Object

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.



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# File 'sig/big_decimal.rbs', line 623

def divmod: (real | BigDecimal) -> [ Integer, BigDecimal ]

#dup ⇒ Object

:nodoc:



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# File 'sig/big_decimal.rbs', line 630

def dup: () -> self

#eql?(r) ⇒ Boolean

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:



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# File 'sig/big_decimal.rbs', line 642

def eql?: (untyped) -> bool

#exponent ⇒ Object

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.



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# File 'sig/big_decimal.rbs', line 653

def exponent: () -> Integer

#finite? ⇒ Boolean

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

Returns:



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# File 'sig/big_decimal.rbs', line 661

def finite?: () -> bool

#fix ⇒ Object

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



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# File 'sig/big_decimal.rbs', line 669

def fix: () -> BigDecimal

#floor(n) ⇒ Object

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



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# File 'sig/big_decimal.rbs', line 689

def floor: () -> Integer
| (int n) -> BigDecimal

#frac ⇒ Object

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



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# File 'sig/big_decimal.rbs', line 698

def frac: () -> BigDecimal

#hash ⇒ Integer

Returns the integer hash value for self.

Two instances of BigDecimal have the same hash value if and only if they have equal:

  • Sign.
  • Fractional part.
  • Exponent.

Returns:



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# File 'sig/big_decimal.rbs', line 713

def hash: () -> Integer

#infinite? ⇒ Boolean

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

Returns:



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# File 'sig/big_decimal.rbs', line 722

def infinite?: () -> Integer?

#initialize_copy ⇒ self

Parameters:

Returns:



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# File 'sig/big_decimal.rbs', line 1052

def initialize_copy: (self) -> self

#inspect ⇒ Object

Returns a string representation of self.

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



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# File 'sig/big_decimal.rbs', line 733

def inspect: () -> String

#modulo ⇒ Object

%: a%b = a - (a.to_f/b).floor * b



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# File 'sig/big_decimal.rbs', line 740

def modulo: (real | BigDecimal b) -> BigDecimal

#mult(other, ndigits) ⇒ Object

Returns the BigDecimal product of self and value with a precision of ndigits decimal digits.

When ndigits is less than the number of significant digits in the sum, the sum is rounded to that number of digits, according to the current rounding mode; see BigDecimal.mode.

Examples:

# Set the rounding mode.
BigDecimal.mode(BigDecimal::ROUND_MODE, :half_up)
b = BigDecimal('555555.555')
b.mult(3, 0)              # => 0.1666666665e7
b.mult(3, 3)              # => 0.167e7
b.mult(3, 6)              # => 0.166667e7
b.mult(3, 15)             # => 0.1666666665e7
b.mult(3.0, 0)            # => 0.1666666665e7
b.mult(Rational(3, 1), 0) # => 0.1666666665e7
b.mult(Complex(3, 0), 0)  # => (0.1666666665e7+0.0i)



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# File 'sig/big_decimal.rbs', line 766

def mult: (real | BigDecimal value, int digits) -> BigDecimal

#n_significant_digits ⇒ Integer

Returns the number of decimal significant digits in self.

BigDecimal("0").n_significant_digits         # => 0
BigDecimal("1").n_significant_digits         # => 1
BigDecimal("1.1").n_significant_digits       # => 2
BigDecimal("3.1415").n_significant_digits    # => 5
BigDecimal("-1e20").n_significant_digits     # => 1
BigDecimal("1e-20").n_significant_digits     # => 1
BigDecimal("Infinity").n_significant_digits  # => 0
BigDecimal("-Infinity").n_significant_digits # => 0
BigDecimal("NaN").n_significant_digits       # => 0

Returns:



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# File 'ext/bigdecimal/bigdecimal.c', line 571

static VALUE
BigDecimal_n_significant_digits(VALUE self)
{
    BDVALUE v = GetBDValueMust(self);
    if (VpIsZero(v.real) || !VpIsDef(v.real)) {
        return INT2FIX(0);
    }

    ssize_t n = v.real->Prec;  /* The length of frac without trailing zeros. */
    for (n = v.real->Prec; n > 0 && v.real->frac[n-1] == 0; --n);
    if (n == 0) return INT2FIX(0);

    DECDIG x;
    int nlz = BASE_FIG;
    for (x = v.real->frac[0]; x > 0; x /= 10) --nlz;

    int ntz = 0;
    for (x = v.real->frac[n-1]; x > 0 && x % 10 == 0; x /= 10) ++ntz;

    RB_GC_GUARD(v.bigdecimal);
    ssize_t n_significant_digits = BASE_FIG*n - nlz - ntz;
    return SSIZET2NUM(n_significant_digits);
}

#nan? ⇒ Boolean

Returns True if the value is Not a Number.

Returns:



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# File 'sig/big_decimal.rbs', line 774

def nan?: () -> bool

#newton_raphson_inverse(prec) ⇒ Object 



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# File 'ext/bigdecimal/bigdecimal.c', line 3248

VALUE
BigDecimal_newton_raphson_inverse(VALUE self, VALUE prec) {
    return newton_raphson_inverse(self, NUM2SIZET(prec));
}

#nonzero? ⇒ Boolean

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

Returns:



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# File 'sig/big_decimal.rbs', line 782

def nonzero?: () -> self?

#nttmult(v) ⇒ Object 



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# File 'ext/bigdecimal/bigdecimal.c', line 3265

VALUE
BigDecimal_nttmult(VALUE self, VALUE v) {
    BDVALUE a,b,c;
    a = GetBDValueMust(self);
    b = GetBDValueMust(v);
    c = NewZeroWrap(1, VPMULT_RESULT_PREC(a.real, b.real) * BASE_FIG);
    ntt_multiply(a.real->Prec, b.real->Prec, a.real->frac, b.real->frac, c.real->frac);
    VpSetSign(c.real, a.real->sign * b.real->sign);
    c.real->exponent = a.real->exponent + b.real->exponent;
    c.real->Prec = a.real->Prec + b.real->Prec;
    VpNmlz(c.real);
    RB_GC_GUARD(a.bigdecimal);
    RB_GC_GUARD(b.bigdecimal);
    return c.bigdecimal;
}

#power(y, prec = 0) ⇒ BigDecimal

Returns the value raised to the power of n.

Also available as the operator **.

Parameters:

  • (defaults to: 0)

Returns:



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# File 'lib/bigdecimal.rb', line 147

def power(y, prec = 0)
  prec = Internal.coerce_validate_prec(prec, :power, accept_zero: true)
  x = self
  y = Internal.coerce_to_bigdecimal(y, prec.nonzero? || n_significant_digits, :power)

  return Internal.nan_computation_result if x.nan? || y.nan?
  return BigDecimal(1) if y.zero?

  if y.infinite?
    if x < 0
      return BigDecimal(0) if x < -1 && y.negative?
      return BigDecimal(0) if x > -1 && y.positive?
      raise Math::DomainError, 'Result undefined for negative base raised to infinite power'
    elsif x < 1
      return y.positive? ? BigDecimal(0) : BigDecimal::Internal.infinity_computation_result
    elsif x == 1
      return BigDecimal(1)
    else
      return y.positive? ? BigDecimal::Internal.infinity_computation_result : BigDecimal(0)
    end
  end

  if x.infinite? && y < 0
    # Computation result will be +0 or -0. Avoid overflow.
    neg = x < 0 && y.frac.zero? && y % 2 == 1
    return neg ? -BigDecimal(0) : BigDecimal(0)
  end

  if x.zero?
    return BigDecimal(1) if y.zero?
    return BigDecimal(0) if y > 0
    if y.frac.zero? && y % 2 == 1 && x.sign == -1
      return -BigDecimal::Internal.infinity_computation_result
    else
      return BigDecimal::Internal.infinity_computation_result
    end
  elsif x < 0
    if y.frac.zero?
      if y % 2 == 0
        return (-x).power(y, prec)
      else
        return -(-x).power(y, prec)
      end
    else
      raise Math::DomainError, 'Computation results in complex number'
    end
  elsif x == 1
    return BigDecimal(1)
  end

  limit = BigDecimal.limit
  frac_part = y.frac

  if frac_part.zero? && prec.zero? && limit.zero?
    # Infinite precision calculation for `x ** int` and `x.power(int)`
    int_part = y.fix.to_i
    int_part = -int_part if (neg = int_part < 0)
    ans = BigDecimal(1)
    n = 1
    xn = x
    while true
      ans *= xn if int_part.allbits?(n)
      n <<= 1
      break if n > int_part
      xn *= xn
      # Detect overflow/underflow before consuming infinite memory
      if (xn.exponent.abs - 1) * int_part / n >= 0x7FFFFFFFFFFFFFFF
        return ((xn.exponent > 0) ^ neg ? BigDecimal::Internal.infinity_computation_result : BigDecimal(0)) * (int_part.even? || x > 0 ? 1 : -1)
      end
    end
    return neg ? BigDecimal(1) / ans : ans
  end

  result_prec = prec.nonzero? || [x.n_significant_digits, y.n_significant_digits, BigDecimal.double_fig].max + BigDecimal.double_fig
  result_prec = [result_prec, limit].min if prec.zero? && limit.nonzero?

  prec2 = result_prec + BigDecimal::Internal::EXTRA_PREC

  if y < 0
    inv = x.power(-y, prec2)
    return BigDecimal(0) if inv.infinite?
    return BigDecimal::Internal.infinity_computation_result if inv.zero?
    return BigDecimal(1).div(inv, result_prec)
  end

  if frac_part.zero? && y.exponent < Math.log(result_prec) * 5 + 20
    # Use exponentiation by squaring if y is an integer and not too large
    pow_prec = prec2 + y.exponent
    n = 1
    xn = x
    ans = BigDecimal(1)
    int_part = y.fix.to_i
    while true
      ans = ans.mult(xn, pow_prec) if int_part.allbits?(n)
      n <<= 1
      break if n > int_part
      xn = xn.mult(xn, pow_prec)
    end
    ans.mult(1, result_prec)
  else
    if x > 1 && x.finite?
      # To calculate exp(z, prec), z needs prec+max(z.exponent, 0) precision if z > 0.
      # Estimate (y*log(x)).exponent
      logx_exponent = x < 2 ? (x - 1).exponent : Math.log10(x.exponent).round
      ylogx_exponent = y.exponent + logx_exponent
      prec2 += [ylogx_exponent, 0].max
    end
    BigMath.exp(BigMath.log(x, prec2).mult(y, prec2), result_prec)
  end
end

#precision ⇒ Integer

Returns the number of decimal digits in self:

BigDecimal("0").precision         # => 0
BigDecimal("1").precision         # => 1
BigDecimal("1.1").precision       # => 2
BigDecimal("3.1415").precision    # => 5
BigDecimal("-1e20").precision     # => 21
BigDecimal("1e-20").precision     # => 20
BigDecimal("Infinity").precision  # => 0
BigDecimal("-Infinity").precision # => 0
BigDecimal("NaN").precision       # => 0

Returns:



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# File 'ext/bigdecimal/bigdecimal.c', line 505

static VALUE
BigDecimal_precision(VALUE self)
{
    ssize_t precision;
    BigDecimal_count_precision_and_scale(self, &precision, NULL);
    return SSIZET2NUM(precision);
}

#precision_scale ⇒ Array

Returns a 2-length array; the first item is the result of BigDecimal#precision and the second one is of BigDecimal#scale.

See BigDecimal#precision. See BigDecimal#scale.

Returns:



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# File 'ext/bigdecimal/bigdecimal.c', line 547

static VALUE
BigDecimal_precision_scale(VALUE self)
{
    ssize_t precision, scale;
    BigDecimal_count_precision_and_scale(self, &precision, &scale);
    return rb_assoc_new(SSIZET2NUM(precision), SSIZET2NUM(scale));
}

#quo(value) ⇒ Object #quo(value, digits) ⇒ Object

Divide by the specified value.

digits

If specified and less than the number of significant digits of the result, the result is rounded to the given number of digits, according to the rounding mode indicated by BigDecimal.mode.

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

See BigDecimal#/. See BigDecimal#div.



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# File 'sig/big_decimal.rbs', line 812

def quo: (real | BigDecimal) -> BigDecimal
| (Complex) -> Complex

#remainder ⇒ Object

remainder



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# File 'sig/big_decimal.rbs', line 823

def remainder: (real | BigDecimal) -> BigDecimal

#round(n, mode) ⇒ Object

Round to the nearest integer (by default), returning the result as a BigDecimal if n is specified and positive, or as an Integer if it isn't.

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

BigDecimal('3.14159').round(2).class.name #=> "BigDecimal" BigDecimal('3.14159').round.class.name #=> "Integer" BigDecimal('3.14159').round(0).class.name #=> "Integer"

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, and return value will be an Integer.

BigDecimal('3.14159').round(3) #=> 3.142 BigDecimal('13345.234').round(-2) #=> 13300

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



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# File 'sig/big_decimal.rbs', line 851

def round: () -> Integer
| (int n) -> (Integer | BigDecimal)
| (int n, round_mode_integer | round_mode_symbol) -> BigDecimal
| (?int n, half: :up | :down | :even) -> BigDecimal

#scale ⇒ Integer

Returns the number of decimal digits following the decimal digits in self.

BigDecimal("0").scale         # => 0
BigDecimal("1").scale         # => 0
BigDecimal("1.1").scale       # => 1
BigDecimal("3.1415").scale    # => 4
BigDecimal("-1e20").scale     # => 0
BigDecimal("1e-20").scale     # => 20
BigDecimal("Infinity").scale  # => 0
BigDecimal("-Infinity").scale # => 0
BigDecimal("NaN").scale       # => 0

Returns:



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# File 'ext/bigdecimal/bigdecimal.c', line 529

static VALUE
BigDecimal_scale(VALUE self)
{
    ssize_t scale;
    BigDecimal_count_precision_and_scale(self, NULL, &scale);
    return SSIZET2NUM(scale);
}

#sign ⇒ Object

Returns the sign of the value.

Returns a positive value if > 0, a negative value if < 0. It behaves the same with zeros - it returns a positive value for a positive zero (BigDecimal('0')) and a negative value for a negative zero (BigDecimal('-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



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# File 'sig/big_decimal.rbs', line 890

def sign: () -> Integer

#split ⇒ Object

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.)



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# File 'sig/big_decimal.rbs', line 920

def split: () -> [ Integer, String, Integer, Integer ]

#sqrt(prec) ⇒ BigDecimal

Returns the square root of the value.

Result has at least prec significant digits.

Parameters:

Returns:



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# File 'lib/bigdecimal.rb', line 262

def sqrt(prec)
  prec = Internal.coerce_validate_prec(prec, :sqrt, accept_zero: true)
  return Internal.infinity_computation_result if infinite? == 1

  raise FloatDomainError, 'sqrt of negative value' if self < 0
  raise FloatDomainError, "sqrt of 'NaN'(Not a Number)" if nan?
  return self if zero?

  if prec == 0
    limit = BigDecimal.limit
    prec = n_significant_digits + BigDecimal.double_fig
    prec = [limit, prec].min if limit.nonzero?
  end

  ex = exponent / 2
  x = _decimal_shift(-2 * ex)
  y = BigDecimal(Math.sqrt(x.to_f), 0)
  Internal.newton_loop(prec + BigDecimal::Internal::EXTRA_PREC) do |p|
    y = y.add(x.div(y, p), p).div(2, p)
  end
  y._decimal_shift(ex).mult(1, prec)
end

#sub(value, digits) ⇒ Object

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.



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# File 'sig/big_decimal.rbs', line 946

def sub: (real | BigDecimal value, int digits) -> BigDecimal

#to_d ⇒ BigDecimal

Returns self.

require 'bigdecimal/util'

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

Returns:



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# File 'lib/bigdecimal/util.rb', line 110

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/util'

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

Returns:



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# File 'lib/bigdecimal/util.rb', line 90

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 ⇒ Object

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.



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# File 'sig/big_decimal.rbs', line 956

def to_f: () -> Float

#to_i ⇒ Object

Returns the value as an Integer.

If the BigDecimal is infinity or NaN, raises FloatDomainError.



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# File 'sig/big_decimal.rbs', line 966

def to_i: () -> Integer

#to_int ⇒ Object

Returns the value as an Integer.

If the BigDecimal is infinity or NaN, raises FloatDomainError.



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# File 'sig/big_decimal.rbs', line 973

def to_int: () -> Integer

#to_r ⇒ Object

Converts a BigDecimal to a Rational.



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# File 'sig/big_decimal.rbs', line 981

def to_r: () -> Rational

#to_s(s) ⇒ Object

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 digits, starting from '.' and counting outwards.

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

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

Examples:

BigDecimal('-1234567890123.45678901234567890').to_s('5F')
#=> '-123 45678 90123.45678 90123 45678 9'

BigDecimal('1234567890123.45678901234567890').to_s('+8F')
#=> '+12345 67890123.45678901 23456789'

BigDecimal('1234567890123.45678901234567890').to_s(' F')
#=> ' 1234567890123.4567890123456789'



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# File 'sig/big_decimal.rbs', line 1017

def to_s: (?String | int s) -> String

#truncate(n) ⇒ Object

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



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# File 'sig/big_decimal.rbs', line 1039

def truncate: () -> Integer
| (int n) -> BigDecimal

#vpdivd(r, cprec) ⇒ Object 



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# File 'ext/bigdecimal/bigdecimal.c', line 3238

VALUE
BigDecimal_vpdivd(VALUE self, VALUE r, VALUE cprec) {
  return BigDecimal_vpdivd_generic(self, r, cprec, VpDivdNormal);
}

#vpdivd_newton(r, cprec) ⇒ Object 



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# File 'ext/bigdecimal/bigdecimal.c', line 3243

VALUE
BigDecimal_vpdivd_newton(VALUE self, VALUE r, VALUE cprec) {
    return BigDecimal_vpdivd_generic(self, r, cprec, VpDivdNewton);
}

#vpmult(v) ⇒ Object 



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# File 'ext/bigdecimal/bigdecimal.c', line 3253

VALUE
BigDecimal_vpmult(VALUE self, VALUE v) {
    BDVALUE a,b,c;
    a = GetBDValueMust(self);
    b = GetBDValueMust(v);
    c = NewZeroWrap(1, VPMULT_RESULT_PREC(a.real, b.real) * BASE_FIG);
    VpMult(c.real, a.real, b.real);
    RB_GC_GUARD(a.bigdecimal);
    RB_GC_GUARD(b.bigdecimal);
    return c.bigdecimal;
}

#zero? ⇒ Boolean

Returns True if the value is zero.

Returns:



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# File 'sig/big_decimal.rbs', line 1048

def zero?: () -> bool