Class BigDecimal
In: ext/bigdecimal/bigdecimal.c
Parent: Numeric

BigDecimal provides arbitrary-precision floating point decimal arithmetic.

Copyright (C) 2002 by Shigeo Kobayashi <shigeo@tinyforest.gr.jp>. You may distribute under the terms of either the GNU General Public License or the Artistic License, as specified in the README file of the BigDecimal distribution.

Documented by mathew <meta@pobox.com>.

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
  for i in (1..10000)
    sum = sum + 0.0001
  end
  print sum

and contrast with the output from: 

  require 'bigdecimal'

  sum = BigDecimal.new("0")
  for i in (1..10000)
    sum = sum + BigDecimal.new("0.0001")
  end
  print sum

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 -> nil

n == n -> nil

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

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

BigDecimal.new("1.0") / BigDecimal.new("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.

Methods

%   *   **   +   -   /   <   <=   <=>   ==   ===   >   >=   _load   abs   ceil   coerce   divmod   double_fig   eql?   exponent   finite?   fix   floor   frac   infinite?   inspect   limit   mode   modulo   nan?   new   nonzero?   power   precs   quo   remainder   round   sign   split   sqrt   to_f   to_i   to_int   to_s   truncate   ver   zero?  

Constants

BASE = INT2FIX((S_INT)VpBaseVal())   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.)
EXCEPTION_ALL = INT2FIX(VP_EXCEPTION_ALL)   0xff: Determines whether overflow, underflow or zero divide result in an exception being thrown. See BigDecimal.mode.
EXCEPTION_NaN = INT2FIX(VP_EXCEPTION_NaN)   0x02: Determines what happens when the result of a computation is not a number (NaN). See BigDecimal.mode.
EXCEPTION_INFINITY = INT2FIX(VP_EXCEPTION_INFINITY)   0x01: Determines what happens when the result of a computation is infinity. See BigDecimal.mode.
EXCEPTION_UNDERFLOW = INT2FIX(VP_EXCEPTION_UNDERFLOW)   0x04: Determines what happens when the result of a computation is an underflow (a result too small to be represented). See BigDecimal.mode.
EXCEPTION_OVERFLOW = INT2FIX(VP_EXCEPTION_OVERFLOW)   0x01: Determines what happens when the result of a computation is an underflow (a result too large to be represented). See BigDecimal.mode.
EXCEPTION_ZERODIVIDE = INT2FIX(VP_EXCEPTION_ZERODIVIDE)   0x01: Determines what happens when a division by zero is performed. See BigDecimal.mode.
ROUND_MODE = INT2FIX(VP_ROUND_MODE)   0x100: Determines what happens when a result must be rounded in order to fit in the appropriate number of significant digits. See BigDecimal.mode.
ROUND_UP = INT2FIX(VP_ROUND_UP)   1: Indicates that values should be rounded away from zero. See 
    BigDecimal.mode.
ROUND_DOWN = INT2FIX(VP_ROUND_DOWN)   2: Indicates that values should be rounded towards zero. See 
    BigDecimal.mode.
ROUND_HALF_UP = INT2FIX(VP_ROUND_HALF_UP)   3: Indicates that digits >= 5 should be rounded up, others rounded down. 
    See BigDecimal.mode.
ROUND_HALF_DOWN = INT2FIX(VP_ROUND_HALF_DOWN)   4: Indicates that digits >= 6 should be rounded up, others rounded down. 
    See BigDecimal.mode.
ROUND_CEILING = INT2FIX(VP_ROUND_CEIL)   5: Round towards +infinity. See BigDecimal.mode.
ROUND_FLOOR = INT2FIX(VP_ROUND_FLOOR)   6: Round towards -infinity. See BigDecimal.mode.
ROUND_HALF_EVEN = INT2FIX(VP_ROUND_HALF_EVEN)   7: Round towards the even neighbor. See BigDecimal.mode.
SIGN_NaN = INT2FIX(VP_SIGN_NaN)   0: Indicates that a value is not a number. See BigDecimal.sign.
SIGN_POSITIVE_ZERO = INT2FIX(VP_SIGN_POSITIVE_ZERO)   1: Indicates that a value is +0. See BigDecimal.sign.
SIGN_NEGATIVE_ZERO = INT2FIX(VP_SIGN_NEGATIVE_ZERO)   -1: Indicates that a value is -0. See BigDecimal.sign.
SIGN_POSITIVE_FINITE = INT2FIX(VP_SIGN_POSITIVE_FINITE)   2: Indicates that a value is positive and finite. See BigDecimal.sign.
SIGN_NEGATIVE_FINITE = INT2FIX(VP_SIGN_NEGATIVE_FINITE)   -2: Indicates that a value is negative and finite. See BigDecimal.sign.
SIGN_POSITIVE_INFINITE = INT2FIX(VP_SIGN_POSITIVE_INFINITE)   3: Indicates that a value is positive and infinite. See BigDecimal.sign.
SIGN_NEGATIVE_INFINITE = INT2FIX(VP_SIGN_NEGATIVE_INFINITE)   -3: Indicates that a value is negative and infinite. See BigDecimal.sign.

Public Class methods

_load(p1)

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

BigDecimal.double_fig

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.

BigDecimal.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 BigDecimal.mode.

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

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

BigDecimal.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:

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:round away from zero
ROUND_DOWN:round towards zero (truncate)
ROUND_HALF_UP:round up if the appropriate digit >= 5, otherwise truncate (default)
ROUND_HALF_DOWN:round up if the appropriate digit >= 6, otherwise truncate
ROUND_HALF_EVEN:round towards the even neighbor (Banker‘s rounding)
ROUND_CEILING:round towards positive infinity (ceil)
ROUND_FLOOR:round towards negative infinity (floor)
new(initial, digits)

Create a new BigDecimal object.

initial:The initial value, as a String. Spaces are ignored, 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.

ver()

Returns the BigDecimal version number.

Ruby 1.8.0 returns 1.0.0. Ruby 1.8.1 thru 1.8.3 return 1.0.1.

Public Instance methods

a % b
a.modulo(b)

Returns the modulus from dividing by b. See divmod.

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)

Returns the value raised to the power of n. Note that n must be an Integer.

Also available as the operator **

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.
sub(value, digits)

Subtract the specified value.

e.g. 

  c = a.sub(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.
div(value, digits)
quo(value)

Divide by the specified value.

e.g. 

  c = a.div(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.

If digits is 0, the result is the same as the / operator. If not, the result is an integer BigDecimal, by analogy with Float#div.

The alias quo is provided since div(value, 0) is the same as computing the quotient; see divmod.

a < b

Returns true if a is less than b. Values may be coerced to perform the comparison (see ==, coerce).

a <= b

Returns true if a is less than or equal to b. Values may be coerced to perform the comparison (see ==, coerce).

<=>(p1)

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

==(p1)

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

===(p1)

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

a > b

Returns true if a is greater than b. Values may be coerced to perform the comparison (see ==, coerce).

a >= b

Returns true if a is greater than or equal to b. Values may be coerced to perform the comparison (see ==, coerce)

abs()

Returns the absolute value.

BigDecimal(‘5’).abs -> 5

BigDecimal(’-3’).abs -> 3

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(p1)

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.

divmod(p1)

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?(p1)

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

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.

finite?()

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

fix()

Return the integer part of the number.

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.

infinite?()

Returns True if the value is infinite

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.

a % b
a.modulo(b)

Returns the modulus from dividing by b. See divmod.

nan?()

Returns True if the value is Not a Number

nonzero?()

Returns True if the value is non-zero.

power(n)

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.

div(value, digits)
quo(value)

Divide by the specified value.

e.g. 

  c = a.div(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.

If digits is 0, the result is the same as the / operator. If not, the result is an integer BigDecimal, by analogy with Float#div.

The alias quo is provided since div(value, 0) is the same as computing the quotient; see divmod.

remainder(p1)

Returns the remainder from dividing by the value.

If the values divided are of the same sign, the remainder is the same as the modulus (see divmod).

Otherwise, the remainder is the modulus minus the value divided by.

round(n,mode)

Round to the nearest 1 (by default), returning the result as a BigDecimal.

BigDecimal(‘3.14159’).round -> 3

BigDecimal(‘8.7’).round -> 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’).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.

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.

If n is specified, returns at least that many significant digits.

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()

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

If the BigNumber is infinity or NaN, returns nil.

to_int()

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

If the BigNumber is infinity or NaN, returns nil.

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 1, returning the result as a BigDecimal.

BigDecimal(‘3.14159’).truncate -> 3

BigDecimal(‘8.7’).truncate -> 8

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

zero?()

Returns True if the value is zero.

[Validate]

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