Python Decimal

Summary: in this tutorial, you’ll learn about the Python decimal module that supports fast correctly-rounded decimal floating-point arithmetic.

Introduction to the Python decimal module

Many decimal numbers don’t have exact representations in binary floating-point such as 0.1. When using these numbers in arithmetic operations, you’ll get a result that you would not expect. For example:

x = 0.1 y = 0.1 z = 0.1 s = x + y + z print(s)
Code language: PHP (php)

Output:

0.30000000000000004
Code language: CSS (css)

The result is 0.30000000000000004, not 0.3.

To solve this problem, you use the Decimal class from the decimal module as follows:

import decimal from decimal import Decimal x = Decimal('0.1') y = Decimal('0.1') z = Decimal('0.1') s = x + y + z print(s)
Code language: JavaScript (javascript)

Output:

0.3
Code language: CSS (css)

The output is as expected.

The Python decimal module supports arithmetic that works the same as the arithmetic you learn at school.

Unlike floats, Python represents decimal numbers exactly. And the exactness carries over into arithmetic. For example, the following expression returns exactly 0.0:

Decimal('0.1') + Decimal('0.1') + Decimal('0.1') - Decimal('0.3')
Code language: JavaScript (javascript)

Decimal context

Decimal always associates with a context that controls the following aspects:

  • Precision during an arithmetic operation
  • Rounding algorithm

By default, the context is global. The global context is the default context. Also, you can set a temporary context that will take effect locally without affecting the global context.

To get the default context, you call the getcontext() function from the decimal module:

decimal.getcontext()
Code language: CSS (css)

The getcontext() function returns the default context, which can be global or local.

To create a new context copied from another context, you use the localcontext() function:

decimal.localcontext(ctx=None)

The localcontext() returns a new context copied from the context ctx if specified.

Once getting the context object, you can access the precision and rouding via the prec and rounding property respectively:

  • ctx.pre: get or set the precision. The ctx.pre is an integer which defaults to 28
  • ctx.rounding: get or set the rounding mechanism. The rounding is a string. It defaults to 'ROUND_HALF_EVEN'. Note floats also use this rounding mechanism.

Python provides the following rounding mechanisms:

RoundingDescription
ROUND_UPround away from zero
ROUND_DOWNround towards zero
ROUND_CEILINGround to ceiling (towards positive infinity)
ROUND_FLOORround to floor (towards negative infinity)
ROUND_HALF_UPround to nearest, ties away from zero
ROUND_HALF_DOWNround to nearest, ties towards zero
ROUND_HALF_EVENround to nearest, ties to even (least significant digit)

This example illustrates how to get the default precision and rounding of the default context:

import decimal ctx = decimal.getcontext() print(ctx.prec) print(ctx.rounding)
Code language: PHP (php)

Output:

28 ROUND_HALF_EVEN

The following example shows how the 'ROUND_HALF_EVEN' rounding mechanism takes effect:

import decimal from decimal import Decimal x = Decimal('2.25') y = Decimal('3.35') print(round(x, 1)) print(round(y, 1))
Code language: JavaScript (javascript)

Output:

2.2 3.4
Code language: CSS (css)

If you change the rounding to 'ROUND_HALF_UP', you’ll get a different result:

import decimal from decimal import Decimal ctx = decimal.getcontext() ctx.rounding = decimal.ROUND_HALF_UP x = Decimal('2.25') y = Decimal('3.35') print(round(x, 1)) print(round(y, 1))
Code language: JavaScript (javascript)

Output:

2.3 3.4
Code language: CSS (css)

The following example shows you how to copy the default context and change the rounding to 'ROUND_HALF_UP':

import decimal from decimal import Decimal x = Decimal('2.25') y = Decimal('3.35') with decimal.localcontext() as ctx: print('Local context:') ctx.rounding = decimal.ROUND_HALF_UP print(round(x, 1)) print(round(y, 1)) print('Global context:') print(round(x, 1)) print(round(y, 1))
Code language: PHP (php)

Output:

Local context: 2.3 3.4 Global context: 2.2 3.4
Code language: CSS (css)

Notice that the local context doesn’t affect the global context. After the with block, Python uses the default rounding mechanism.

Decimal constructor

The Decimal constructor allows you to create a new Decimal object based on a value:

Decimal(value='0', context=None)
Code language: JavaScript (javascript)

The value argument can be an integer, string, tuple, float, or another Decimal object. If you don’t provide the value argument, it defaults to '0'.

If the 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:

(sign, (digit1,digit2, digit3,...), exponent)

For example:

3.14 = 314 x 10^-2

The tuple has three elements as follows:

  • sign is 0
  • digits is (3,1,4)
  • exponent is -2

Therefore, you’ll need to pass the following tuple to the Decimal constructor:

import decimal from decimal import Decimal x = Decimal((0, (3, 1, 4), -2)) print(x)
Code language: JavaScript (javascript)

Output:

3.14
Code language: CSS (css)

Notice that the decimal context precision only affects the arithmetic operation, not the Decimal constructor. For example:

import decimal from decimal import Decimal decimal.getcontext().prec = 2 pi = Decimal('3.14159') radius = 1 print(pi) area = pi * radius * radius print(area)
Code language: JavaScript (javascript)

When you use a float that doesn’t have an exact binary float representation, the Decimal constructor cannot create an accurate decimal representation. For example:

import decimal from decimal import Decimal x = Decimal(0.1) print(x)
Code language: JavaScript (javascript)

Output:

0.1000000000000000055511151231257827021181583404541015625
Code language: CSS (css)

In practice, you’ll use a string or a tuple to construct a Decimal.

Decimal arithmetic operations

Some arithmetic operators don’t work the same as floats or integers, such as div (//) and mod (%).

For decimal numbers, the // operator performs a truncated division:

x // y = trunc( x / y)
Code language: JavaScript (javascript)

The Decimal class provides some mathematical operations such as sqrt and log. However, it doesn’t have all the functions defined in the math module.

When you use functions from the math module for decimal numbers, Python will cast the Decimal objects to floats before carrying arithmetic operations. This results in losing the precision built in the decimal objects.

Summary

  • Use the Python decimal module when you want to support fast correctly-rounded decimal floating-point arithmetic.
  • Use the Decimal class from the decimal module to create Decimal object from strings, integers, and tuples.
  • The Decimal numbers have a context that controls the precision and rounding mechanism.
  • The Decimal class doesn’t have all methods defined in the math module. However, you should use the Decimal’s arithmetic methods if they’re available.
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