decimal — Decimal fixed-point and floating-point arithmetic¶

Quick-start tutorial¶

The usual start to using decimals is importing the module, viewing the current context with getcontext() and, if necessary, setting new values for precision, rounding, or enabled traps:

>>> from decimal import *
>>> getcontext()
Context(prec=28, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,
        capitals=1, clamp=0, flags=[], traps=[Overflow, DivisionByZero,
        InvalidOperation])

>>> getcontext().prec = 7       # Set a new precision

Decimal instances can be constructed from integers, strings, floats, or tuples. Construction from an integer or a float performs an exact conversion of the value of that integer or float. Decimal numbers include special values such as NaN which stands for “Not a number”, positive and negative Infinity, and -0:

>>> getcontext().prec = 28
>>> Decimal(10)
Decimal('10')
>>> Decimal('3.14')
Decimal('3.14')
>>> Decimal(3.14)
Decimal('3.140000000000000124344978758017532527446746826171875')
>>> Decimal((0, (3, 1, 4), -2))
Decimal('3.14')
>>> Decimal(str(2.0 ** 0.5))
Decimal('1.4142135623730951')
>>> Decimal(2) ** Decimal('0.5')
Decimal('1.414213562373095048801688724')
>>> Decimal('NaN')
Decimal('NaN')
>>> Decimal('-Infinity')
Decimal('-Infinity')

If the FloatOperation signal is trapped, accidental mixing of decimals and floats in constructors or ordering comparisons raises an exception:

>>> c = getcontext()
>>> c.traps[FloatOperation] = True
>>> Decimal(3.14)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
decimal.FloatOperation: [<class 'decimal.FloatOperation'>]
>>> Decimal('3.5') < 3.7
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
decimal.FloatOperation: [<class 'decimal.FloatOperation'>]
>>> Decimal('3.5') == 3.5
True

The significance of a new Decimal is determined solely by the number of digits input. Context precision and rounding only come into play during arithmetic operations.

>>> getcontext().prec = 6
>>> Decimal('3.0')
Decimal('3.0')
>>> Decimal('3.1415926535')
Decimal('3.1415926535')
>>> Decimal('3.1415926535') + Decimal('2.7182818285')
Decimal('5.85987')
>>> getcontext().rounding = ROUND_UP
>>> Decimal('3.1415926535') + Decimal('2.7182818285')
Decimal('5.85988')

If the internal limits of the C version are exceeded, constructing a decimal raises InvalidOperation:

>>> Decimal("1e9999999999999999999")
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
decimal.InvalidOperation: [<class 'decimal.InvalidOperation'>]

Decimals interact well with much of the rest of Python. Here is a small decimal floating-point flying circus:

>>> data = list(map(Decimal, '1.34 1.87 3.45 2.35 1.00 0.03 9.25'.split()))
>>> max(data)
Decimal('9.25')
>>> min(data)
Decimal('0.03')
>>> sorted(data)
[Decimal('0.03'), Decimal('1.00'), Decimal('1.34'), Decimal('1.87'),
 Decimal('2.35'), Decimal('3.45'), Decimal('9.25')]
>>> sum(data)
Decimal('19.29')
>>> a,b,c = data[:3]
>>> str(a)
'1.34'
>>> float(a)
1.34
>>> round(a, 1)
Decimal('1.3')
>>> int(a)
1
>>> a * 5
Decimal('6.70')
>>> a * b
Decimal('2.5058')
>>> c % a
Decimal('0.77')

And some mathematical functions are also available to Decimal:

>>> getcontext().prec = 28
>>> Decimal(2).sqrt()
Decimal('1.414213562373095048801688724')
>>> Decimal(1).exp()
Decimal('2.718281828459045235360287471')
>>> Decimal('10').ln()
Decimal('2.302585092994045684017991455')
>>> Decimal('10').log10()
Decimal('1')

The quantize() method rounds a number to a fixed exponent. This method is useful for monetary applications that often round results to a fixed number of places:

>>> Decimal('7.325').quantize(Decimal('.01'), rounding=ROUND_DOWN)
Decimal('7.32')
>>> Decimal('7.325').quantize(Decimal('1.'), rounding=ROUND_UP)
Decimal('8')

As shown above, the getcontext() function accesses the current context and allows the settings to be changed. This approach meets the needs of most applications.

For more advanced work, it may be useful to create alternate contexts using the Context() constructor. To make an alternate active, use the setcontext() function.

In accordance with the standard, the decimal module provides two ready to use standard contexts, BasicContext and ExtendedContext. The former is especially useful for debugging because many of the traps are enabled:

>>> myothercontext = Context(prec=60, rounding=ROUND_HALF_DOWN)
>>> setcontext(myothercontext)
>>> Decimal(1) / Decimal(7)
Decimal('0.142857142857142857142857142857142857142857142857142857142857')

>>> ExtendedContext
Context(prec=9, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,
        capitals=1, clamp=0, flags=[], traps=[])
>>> setcontext(ExtendedContext)
>>> Decimal(1) / Decimal(7)
Decimal('0.142857143')
>>> Decimal(42) / Decimal(0)
Decimal('Infinity')

>>> setcontext(BasicContext)
>>> Decimal(42) / Decimal(0)
Traceback (most recent call last):
  File "<pyshell#143>", line 1, in -toplevel-
    Decimal(42) / Decimal(0)
DivisionByZero: x / 0

Contexts also have signal flags for monitoring exceptional conditions encountered during computations. The flags remain set until explicitly cleared, so it is best to clear the flags before each set of monitored computations by using the clear_flags() method.

>>> setcontext(ExtendedContext)
>>> getcontext().clear_flags()
>>> Decimal(355) / Decimal(113)
Decimal('3.14159292')
>>> getcontext()
Context(prec=9, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,
        capitals=1, clamp=0, flags=[Inexact, Rounded], traps=[])

The flags entry shows that the rational approximation to pi was rounded (digits beyond the context precision were thrown away) and that the result is inexact (some of the discarded digits were non-zero).

Individual traps are set using the dictionary in the traps attribute of a context:

>>> setcontext(ExtendedContext)
>>> Decimal(1) / Decimal(0)
Decimal('Infinity')
>>> getcontext().traps[DivisionByZero] = 1
>>> Decimal(1) / Decimal(0)
Traceback (most recent call last):
  File "<pyshell#112>", line 1, in -toplevel-
    Decimal(1) / Decimal(0)
DivisionByZero: x / 0

Most programs adjust the current context only once, at the beginning of the program. And, in many applications, data is converted to Decimal with a single cast inside a loop. With context set and decimals created, the bulk of the program manipulates the data no differently than with other Python numeric types.

Decimal objects¶

class decimal.Decimal(value='0', context=None)¶

Construct a new Decimal object based from value.

value can be an integer, string, tuple, float, or another Decimal object. If no value is given, returns Decimal('0'). If value is a string, it should conform to the decimal numeric string syntax after leading and trailing whitespace characters, as well as underscores throughout, are removed:

sign           ::=  '+' | '-'
digit          ::=  '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'
indicator      ::=  'e' | 'E'
digits         ::=  digit [digit]...
decimal-part   ::=  digits '.' [digits] | ['.'] digits
exponent-part  ::=  indicator [sign] digits
infinity       ::=  'Infinity' | 'Inf'
nan            ::=  'NaN' [digits] | 'sNaN' [digits]
numeric-value  ::=  decimal-part [exponent-part] | infinity
numeric-string ::=  [sign] numeric-value | [sign] nan

Other Unicode decimal digits are also permitted where digit appears above. These include decimal digits from various other alphabets (for example, Arabic-Indic and Devanāgarī digits) along with the fullwidth digits '\uff10' through '\uff19'. Case is not significant, so, for example, inf, Inf, INFINITY, and iNfINity are all acceptable spellings for positive infinity.

If value is a tuple, it should have three components, a sign (0 for positive or 1 for negative), a tuple of digits, and an integer exponent. For example, Decimal((0, (1, 4, 1, 4), -3)) returns Decimal('1.414').

If value is a float, the binary floating-point value is losslessly converted to its exact decimal equivalent. This conversion can often require 53 or more digits of precision. For example, Decimal(float('1.1')) converts to Decimal('1.100000000000000088817841970012523233890533447265625').

The context precision does not affect how many digits are stored. That is determined exclusively by the number of digits in value. For example, Decimal('3.00000') records all five zeros even if the context precision is only three.

The purpose of the context argument is determining what to do if value is a malformed string. If the context traps InvalidOperation, an exception is raised; otherwise, the constructor returns a new Decimal with the value of NaN.

Once constructed, Decimal objects are immutable.

Changed in version 3.2: The argument to the constructor is now permitted to be a float instance.

Changed in version 3.3: float arguments raise an exception if the FloatOperation trap is set. By default the trap is off.

Changed in version 3.6: Underscores are allowed for grouping, as with integral and floating-point literals in code.

Decimal floating-point objects share many properties with the other built-in numeric types such as float and int. All of the usual math operations and special methods apply. Likewise, decimal objects can be copied, pickled, printed, used as dictionary keys, used as set elements, compared, sorted, and coerced to another type (such as float or int).

There are some small differences between arithmetic on Decimal objects and arithmetic on integers and floats. When the remainder operator % is applied to Decimal objects, the sign of the result is the sign of the dividend rather than the sign of the divisor:

>>> (-7) % 4
1
>>> Decimal(-7) % Decimal(4)
Decimal('-3')

The integer division operator // behaves analogously, returning the integer part of the true quotient (truncating towards zero) rather than its floor, so as to preserve the usual identity x == (x // y) * y + x % y:

>>> -7 // 4
-2
>>> Decimal(-7) // Decimal(4)
Decimal('-1')

The % and // operators implement the remainder and divide-integer operations (respectively) as described in the specification.

Decimal objects cannot generally be combined with floats or instances of fractions.Fraction in arithmetic operations: an attempt to add a Decimal to a float, for example, will raise a TypeError. However, it is possible to use Python’s comparison operators to compare a Decimal instance x with another number y. This avoids confusing results when doing equality comparisons between numbers of different types.

Changed in version 3.2: Mixed-type comparisons between Decimal instances and other numeric types are now fully supported.

In addition to the standard numeric properties, decimal floating-point objects also have a number of specialized methods:

adjusted()¶

Return the adjusted exponent after shifting out the coefficient’s rightmost digits until only the lead digit remains: Decimal('321e+5').adjusted() returns seven. Used for determining the position of the most significant digit with respect to the decimal point.

as_integer_ratio()¶

Return a pair (n, d) of integers that represent the given Decimal instance as a fraction, in lowest terms and with a positive denominator:

>>> Decimal('-3.14').as_integer_ratio()
(-157, 50)

The conversion is exact. Raise OverflowError on infinities and ValueError on NaNs.

Added in version 3.6.

as_tuple()¶

Return a named tuple representation of the number: DecimalTuple(sign, digits, exponent).

canonical()¶

Return the canonical encoding of the argument. Currently, the encoding of a Decimal instance is always canonical, so this operation returns its argument unchanged.

compare(other, context=None)¶

Compare the values of two Decimal instances. compare() returns a Decimal instance, and if either operand is a NaN then the result is a NaN:

a or b is a NaN  ==> Decimal('NaN')
a < b            ==> Decimal('-1')
a == b           ==> Decimal('0')
a > b            ==> Decimal('1')

compare_signal(other, context=None)¶

This operation is identical to the compare() method, except that all NaNs signal. That is, if neither operand is a signaling NaN then any quiet NaN operand is treated as though it were a signaling NaN.

compare_total(other, context=None)¶

Compare two operands using their abstract representation rather than their numerical value. Similar to the compare() method, but the result gives a total ordering on Decimal instances. Two Decimal instances with the same numeric value but different representations compare unequal in this ordering:

>>> Decimal('12.0').compare_total(Decimal('12'))
Decimal('-1')

Quiet and signaling NaNs are also included in the total ordering. The result of this function is Decimal('0') if both operands have the same representation, Decimal('-1') if the first operand is lower in the total order than the second, and Decimal('1') if the first operand is higher in the total order than the second operand. See the specification for details of the total order.

This operation is unaffected by context and is quiet: no flags are changed and no rounding is performed. As an exception, the C version may raise InvalidOperation if the second operand cannot be converted exactly.

compare_total_mag(other, context=None)¶

Compare two operands using their abstract representation rather than their value as in compare_total(), but ignoring the sign of each operand. x.compare_total_mag(y) is equivalent to x.copy_abs().compare_total(y.copy_abs()).

This operation is unaffected by context and is quiet: no flags are changed and no rounding is performed. As an exception, the C version may raise InvalidOperation if the second operand cannot be converted exactly.

conjugate()¶

Just returns self, this method is only to comply with the Decimal Specification.

copy_abs()¶

Return the absolute value of the argument. This operation is unaffected by the context and is quiet: no flags are changed and no rounding is performed.

copy_negate()¶

Return the negation of the argument. This operation is unaffected by the context and is quiet: no flags are changed and no rounding is performed.

copy_sign(other, context=None)¶

Return a copy of the first operand with the sign set to be the same as the sign of the second operand. For example:

>>> Decimal('2.3').copy_sign(Decimal('-1.5'))
Decimal('-2.3')

This operation is unaffected by context and is quiet: no flags are changed and no rounding is performed. As an exception, the C version may raise InvalidOperation if the second operand cannot be converted exactly.

exp(context=None)¶

Return the value of the (natural) exponential function e**x at the given number. The result is correctly rounded using the ROUND_HALF_EVEN rounding mode.

>>> Decimal(1).exp()
Decimal('2.718281828459045235360287471')
>>> Decimal(321).exp()
Decimal('2.561702493119680037517373933E+139')

classmethod from_float(f, /)¶

Alternative constructor that only accepts instances of float or int.

Note Decimal.from_float(0.1) is not the same as Decimal('0.1'). Since 0.1 is not exactly representable in binary floating point, the value is stored as the nearest representable value which is 0x1.999999999999ap-4. That equivalent value in decimal is 0.1000000000000000055511151231257827021181583404541015625.

Note

From Python 3.2 onwards, a Decimal instance can also be constructed directly from a float.

>>> Decimal.from_float(0.1)
Decimal('0.1000000000000000055511151231257827021181583404541015625')
>>> Decimal.from_float(float('nan'))
Decimal('NaN')
>>> Decimal.from_float(float('inf'))
Decimal('Infinity')
>>> Decimal.from_float(float('-inf'))
Decimal('-Infinity')

Added in version 3.1.

classmethod from_number(number, /)¶

Alternative constructor that only accepts instances of float, int or Decimal, but not strings or tuples.

>>> Decimal.from_number(314)
Decimal('314')
>>> Decimal.from_number(0.1)
Decimal('0.1000000000000000055511151231257827021181583404541015625')
>>> Decimal.from_number(Decimal('3.14'))
Decimal('3.14')

Added in version 3.14.

fma(other, third, context=None)¶

Fused multiply-add. Return self*other+third with no rounding of the intermediate product self*other.

>>> Decimal(2).fma(3, 5)
Decimal('11')

is_canonical()¶

Return True if the argument is canonical and False otherwise. Currently, a Decimal instance is always canonical, so this operation always returns True.

is_finite()¶

Return True if the argument is a finite number, and False if the argument is an infinity or a NaN.

is_infinite()¶

Return True if the argument is either positive or negative infinity and False otherwise.

is_nan()¶

Return True if the argument is a (quiet or signaling) NaN and False otherwise.

is_normal(context=None)¶

Return True if the argument is a normal finite number. Return False if the argument is zero, subnormal, infinite or a NaN.

is_qnan()¶

Return