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<!DOCTYPE html>

<head>

<title>decimal --- Decimal fixed-point and floating-point arithmetic — مستندات Python3.14.6</title><meta name="viewport" content="width=device-width, initial-scale=1.0">

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<h3><a href="../contents.html">فهرست عناوین</a></h3>

<ul>

<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate">decimal</code> --- Decimal fixed-point and floating-point arithmetic</a><ul>

<li><a class="reference internal" href="#quick-start-tutorial">Quick-start tutorial</a></li>

<li><a class="reference internal" href="#decimal-objects">Decimal objects</a><ul>

<li><a class="reference internal" href="#logical-operands">Logical operands</a></li>

</ul>

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<li><a class="reference internal" href="#context-objects">Context objects</a></li>

<li><a class="reference internal" href="#constants">Constants</a></li>

<li><a class="reference internal" href="#rounding-modes">Rounding modes</a></li>

<li><a class="reference internal" href="#signals">Signals</a></li>

<li><a class="reference internal" href="#floating-point-notes">Floating-point notes</a><ul>

<li><a class="reference internal" href="#mitigating-round-off-error-with-increased-precision">Mitigating round-off error with increased precision</a></li>

<li><a class="reference internal" href="#special-values">Special values</a></li>

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<li><a class="reference internal" href="#working-with-threads">Working with threads</a></li>

<li><a class="reference internal" href="#recipes">Recipes</a></li>

<li><a class="reference internal" href="#decimal-faq">Decimal FAQ</a></li>

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<h1><code class="xref py py-mod docutils literal notranslate">decimal</code> --- Decimal fixed-point and floating-point arithmetic<a class="headerlink" href="#module-decimal" title="Link to this heading">¶</a></h1>

Source code: <a class="extlink-source reference external" href="https://github.com/python/cpython/tree/3.14/Lib/decimal.py">Lib/decimal.py</a>

The <code class="xref py py-mod docutils literal notranslate">decimal</code> module provides support for fast correctly rounded

decimal floating-point arithmetic. It offers several advantages over the

<a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a> datatype:

<ul>

<li>Decimal "is based on a <a class="reference external" href="https://speleotrove.com/decimal/damodel.html#refnumber">floating-point model</a> which was designed

with people in mind, and necessarily has a paramount guiding principle --

computers must provide an arithmetic that works in the same way as the

arithmetic that people learn at school." -- excerpt from the decimal

arithmetic specification.</li>

<li>Decimal numbers can be represented exactly. In contrast, numbers like

<code class="docutils literal notranslate">1.1</code> and <code class="docutils literal notranslate">2.2</code> do not have exact representations in binary

floating point. End users typically would not expect <code class="docutils literal notranslate">1.1 + 2.2</code> to display

as <code class="docutils literal notranslate">3.3000000000000003</code> as it does with binary floating point.</li>

<li>The exactness carries over into arithmetic. In decimal floating point, <code class="docutils literal notranslate">0.1

+ 0.1 + 0.1 - 0.3</code> is exactly equal to zero. In binary floating point, the result

is <code class="docutils literal notranslate">5.5511151231257827e-017</code>. While near to zero, the differences

prevent reliable equality testing and differences can accumulate. For this

reason, decimal is preferred in accounting applications which have strict

equality invariants.</li>

<li>The decimal module incorporates a notion of significant places so that <code class="docutils literal notranslate">1.30

+ 1.20</code> is <code class="docutils literal notranslate">2.50</code>. The trailing zero is kept to indicate significance.

This is the customary presentation for monetary applications. For

multiplication, the "schoolbook" approach uses all the figures in the

multiplicands. For instance, <code class="docutils literal notranslate">1.3 * 1.2</code> gives <code class="docutils literal notranslate">1.56</code> while <code class="docutils literal notranslate">1.30 *

1.20</code> gives <code class="docutils literal notranslate">1.5600</code>.</li>

<li>Unlike hardware based binary floating point, the decimal module has a user

alterable precision (defaulting to 28 places) which can be as large as needed for

a given problem:

<div class="doctest highlight-default notranslate"><div class="highlight"><pre>>>> from decimal import *

>>> getcontext().prec = 6

>>> Decimal(1) / Decimal(7)

Decimal('0.142857')

>>> getcontext().prec = 28

Decimal('0.1428571428571428571428571429')

</pre></div>

</div>

</li>

<li>Both binary and decimal floating point are implemented in terms of published

standards. While the built-in float type exposes only a modest portion of its

capabilities, the decimal module exposes all required parts of the standard.

When needed, the programmer has full control over rounding and signal handling.

This includes an option to enforce exact arithmetic by using exceptions

to block any inexact operations.</li>

<li>The decimal module was designed to support "without prejudice, both exact

unrounded decimal arithmetic (sometimes called fixed-point arithmetic)

and rounded floating-point arithmetic." -- excerpt from the decimal

arithmetic specification.</li>

</ul>

The module design is centered around three concepts: the decimal number, the

context for arithmetic, and signals.

A decimal number is immutable. It has a sign, coefficient digits, and an

exponent. To preserve significance, the coefficient digits do not truncate

trailing zeros. Decimals also include special values such as

<code class="docutils literal notranslate">Infinity</code>, <code class="docutils literal notranslate">-Infinity</code>, and <code class="docutils literal notranslate">NaN</code>. The standard also

differentiates <code class="docutils literal notranslate">-0</code> from <code class="docutils literal notranslate">+0</code>.

The context for arithmetic is an environment specifying precision, rounding

rules, limits on exponents, flags indicating the results of operations, and trap

enablers which determine whether signals are treated as exceptions. Rounding

options include <a class="reference internal" href="#decimal.ROUND_CEILING" title="decimal.ROUND_CEILING"><code class="xref py py-const docutils literal notranslate">ROUND_CEILING</code></a>, <a class="reference internal" href="#decimal.ROUND_DOWN" title="decimal.ROUND_DOWN"><code class="xref py py-const docutils literal notranslate">ROUND_DOWN</code></a>,

<a class="reference internal" href="#decimal.ROUND_FLOOR" title="decimal.ROUND_FLOOR"><code class="xref py py-const docutils literal notranslate">ROUND_FLOOR</code></a>, <a class="reference internal" href="#decimal.ROUND_HALF_DOWN" title="decimal.ROUND_HALF_DOWN"><code class="xref py py-const docutils literal notranslate">ROUND_HALF_DOWN</code></a>, <a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal notranslate">ROUND_HALF_EVEN</code></a>,

<a class="reference internal" href="#decimal.ROUND_HALF_UP" title="decimal.ROUND_HALF_UP"><code class="xref py py-const docutils literal notranslate">ROUND_HALF_UP</code></a>, <a class="reference internal" href="#decimal.ROUND_UP" title="decimal.ROUND_UP"><code class="xref py py-const docutils literal notranslate">ROUND_UP</code></a>, and <a class="reference internal" href="#decimal.ROUND_05UP" title="decimal.ROUND_05UP"><code class="xref py py-const docutils literal notranslate">ROUND_05UP</code></a>.

Signals are groups of exceptional conditions arising during the course of

computation. Depending on the needs of the application, signals may be ignored,

considered as informational, or treated as exceptions. The signals in the

decimal module are: <a class="reference internal" href="#decimal.Clamped" title="decimal.Clamped"><code class="xref py py-const docutils literal notranslate">Clamped</code></a>, <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-const docutils literal notranslate">InvalidOperation</code></a>,

<a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-const docutils literal notranslate">DivisionByZero</code></a>, <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><code class="xref py py-const docutils literal notranslate">Inexact</code></a>, <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><code class="xref py py-const docutils literal notranslate">Rounded</code></a>, <a class="reference internal" href="#decimal.Subnormal" title="decimal.Subnormal"><code class="xref py py-const docutils literal notranslate">Subnormal</code></a>,

<a class="reference internal" href="#decimal.Overflow" title="decimal.Overflow"><code class="xref py py-const docutils literal notranslate">Overflow</code></a>, <a class="reference internal" href="#decimal.Underflow" title="decimal.Underflow"><code class="xref py py-const docutils literal notranslate">Underflow</code></a> and <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-const docutils literal notranslate">FloatOperation</code></a>.

For each signal there is a flag and a trap enabler. When a signal is

encountered, its flag is set to one, then, if the trap enabler is

set to one, an exception is raised. Flags are sticky, so the user needs to

reset them before monitoring a calculation.

همچنین ملاحظه نمائید

<li>IBM's General Decimal Arithmetic Specification, <a class="reference external" href="https://speleotrove.com/decimal/decarith.html">The General Decimal Arithmetic

Specification</a>.</li>

</ul>

</div>

<h2>Quick-start tutorial<a class="headerlink" href="#quick-start-tutorial" title="Link to this heading">¶</a></h2>

The usual start to using decimals is importing the module, viewing the current

context with <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal notranslate">getcontext()</code></a> and, if necessary, setting new values for

precision, rounding, or enabled traps:

<div class="highlight-python3 notranslate"><div class="highlight"><pre>>>> 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

</pre></div>

</div>

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

<code class="docutils literal notranslate">NaN</code> which stands for "Not a number", positive and negative

<code class="docutils literal notranslate">Infinity</code>, and <code class="docutils literal notranslate">-0</code>:

<div class="highlight-python3 notranslate"><div class="highlight"><pre>>>> 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')

</pre></div>

</div>

If the <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-exc docutils literal notranslate">FloatOperation</code></a> signal is trapped, accidental mixing of

decimals and floats in constructors or ordering comparisons raises

an exception:

<div class="highlight-python3 notranslate"><div class="highlight"><pre>>>> 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

</pre></div>

</div>

Added in version 3.3.

</div>

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.

<div class="highlight-pycon notranslate"><div class="highlight"><pre>>>> 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('5.85988')

</pre></div>

</div>

If the internal limits of the C version are exceeded, constructing

a decimal raises <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-class docutils literal notranslate">InvalidOperation</code></a>:

<div class="highlight-python3 notranslate"><div class="highlight"><pre>>>> Decimal("1e9999999999999999999")

Traceback (most recent call last):

File "<stdin>", line 1, in <module>

decimal.InvalidOperation: [<class 'decimal.InvalidOperation'>]

</pre></div>

</div>

تغییر داده شده در نسخه 3.3.

</div>

Decimals interact well with much of the rest of Python. Here is a small decimal

floating-point flying circus:

<div class="highlight-pycon notranslate"><div class="highlight"><pre>>>> 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')

</pre></div>

</div>

Decimals can be formatted (with <a class="reference internal" href="functions.html#format" title="format"><code class="xref py py-func docutils literal notranslate">format()</code></a> built-in or <a class="reference internal" href="../reference/lexical_analysis.html#f-strings">f-strings</a>) in

fixed-point or scientific notation, using the same formatting syntax (see

<a class="reference internal" href="string.html#formatspec">Format specification mini-language</a>) as builtin <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a> type:

<div class="highlight-pycon notranslate"><div class="highlight"><pre>>>> format(Decimal('2.675'), "f")

'2.675'

>>> format(Decimal('2.675'), ".2f")

'2.68'

>>> f"{Decimal('2.675'):.2f}"

'2.68'

'2.68e+0'

>>> with localcontext() as ctx:

... ctx.rounding = ROUND_DOWN

... print(format(Decimal('2.675'), ".2f"))

...

2.67

</pre></div>

</div>

And some mathematical functions are also available to Decimal:

<div class="doctest highlight-default notranslate"><div class="highlight"><pre>>>> getcontext().prec = 28

>>> Decimal(2).sqrt()

Decimal('1.414213562373095048801688724')

>>> Decimal(1).exp()

Decimal('2.718281828459045235360287471')

>>> Decimal('10').ln()

Decimal('2.302585092994045684017991455')

Decimal('1')

</pre></div>

</div>

The <a class="reference internal" href="#decimal.Decimal.quantize" title="decimal.Decimal.quantize"><code class="xref py py-meth docutils literal notranslate">quantize()</code></a> 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:

<div class="doctest highlight-default notranslate"><div class="highlight"><pre>>>> Decimal('7.325').quantize(Decimal('.01'), rounding=ROUND_DOWN)

Decimal('7.32')

>>> Decimal('7.325').quantize(Decimal('1.'), rounding=ROUND_UP)

Decimal('8')

</pre></div>

</div>

As shown above, the <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><code class="xref py py-func docutils literal notranslate">getcontext()</code></a> 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

<a class="reference internal" href="#decimal.Context" title="decimal.Context"><code class="xref py py-meth docutils literal notranslate">Context()</code></a> constructor. To make an alternate active, use the <a class="reference internal" href="#decimal.setcontext" title="decimal.setcontext"><code class="xref py py-func docutils literal notranslate">setcontext()</code></a>

function.

In accordance with the standard, the <code class="xref py py-mod docutils literal notranslate">decimal</code> module provides two ready to

use standard contexts, <a class="reference internal" href="#decimal.BasicContext" title="decimal.BasicContext"><code class="xref py py-const docutils literal notranslate">BasicContext</code></a> and <a class="reference internal" href="#decimal.ExtendedContext" title="decimal.ExtendedContext"><code class="xref py py-const docutils literal notranslate">ExtendedContext</code></a>. The

former is especially useful for debugging because many of the traps are

enabled:

<div class="highlight-pycon notranslate"><div class="highlight"><pre>>>> myothercontext = Context(prec=60, rounding=ROUND_HALF_DOWN)

>>> setcontext(myothercontext)

Decimal('0.142857142857142857142857142857142857142857142857142857142857')

>>> ExtendedContext

Context(prec=9, rounding=ROUND_HALF_EVEN, Emin=-999999, Emax=999999,

capitals=1, clamp=0, flags=[], traps=[])

>>> setcontext(ExtendedContext)

Decimal('0.142857143')

>>> Decimal(42) / Decimal(0)

Decimal('Infinity')

>>> setcontext(BasicContext)

Traceback (most recent call last):

File "<pyshell#143>", line 1, in -toplevel-

Decimal(42) / Decimal(0)

DivisionByZero: x / 0

</pre></div>

</div>

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 <a class="reference internal" href="#decimal.Context.clear_flags" title="decimal.Context.clear_flags"><code class="xref py py-meth docutils literal notranslate">clear_flags()</code></a> method.

<div class="highlight-python3 notranslate"><div class="highlight"><pre>>>> 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=[])

</pre></div>

</div>

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 <a class="reference internal" href="#decimal.Context.traps" title="decimal.Context.traps"><code class="xref py py-attr docutils literal notranslate">traps</code></a>

attribute of a context:

<div class="highlight-pycon notranslate"><div class="highlight"><pre>>>> setcontext(ExtendedContext)

Decimal('Infinity')

>>> getcontext().traps[DivisionByZero] = 1

Traceback (most recent call last):

File "<pyshell#112>", line 1, in -toplevel-

Decimal(1) / Decimal(0)

DivisionByZero: x / 0

</pre></div>

</div>

Most programs adjust the current context only once, at the beginning of the

program. And, in many applications, data is converted to <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate">Decimal</code></a> 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.

</section>

<h2>Decimal objects<a class="headerlink" href="#decimal-objects" title="Link to this heading">¶</a></h2>

class decimal.Decimal(value='0', context=None)<a class="headerlink" href="#decimal.Decimal" title="Link to this definition">¶</a></dt>

<dd>Construct a new <code class="xref py py-class docutils literal notranslate">Decimal</code> object based from value.

value can be an integer, string, tuple, <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a>, or another <code class="xref py py-class docutils literal notranslate">Decimal</code>

object. If no value is given, returns <code class="docutils literal notranslate">Decimal('0')</code>. 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:

<div class="highlight-python3 notranslate"><div class="highlight"><pre>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

</pre></div>

</div>

Other Unicode decimal digits are also permitted where <code class="docutils literal notranslate">digit</code>

appears above. These include decimal digits from various other

alphabets (for example, Arabic-Indic and Devanāgarī digits) along

with the fullwidth digits <code class="docutils literal notranslate">'\uff10'</code> through <code class="docutils literal notranslate">'\uff19'</code>.

Case is not significant, so, for example, <code class="docutils literal notranslate">inf</code>, <code class="docutils literal notranslate">Inf</code>, <code class="docutils literal notranslate">INFINITY</code>,

and <code class="docutils literal notranslate">iNfINity</code> are all acceptable spellings for positive infinity.

If value is a <a class="reference internal" href="stdtypes.html#tuple" title="tuple"><code class="xref py py-class docutils literal notranslate">tuple</code></a>, it should have three components, a sign

(<code class="docutils literal notranslate">0</code> for positive or <code class="docutils literal notranslate">1</code> for negative), a <code class="xref py py-class docutils literal notranslate">tuple</code> of

digits, and an integer exponent. For example, <code class="docutils literal notranslate">Decimal((0, (1, 4, 1, 4), -3))</code>

returns <code class="docutils literal notranslate">Decimal('1.414')</code>.

If value is a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a>, 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, <code class="docutils literal notranslate">Decimal(float('1.1'))</code>

converts to

<code class="docutils literal notranslate">Decimal('1.100000000000000088817841970012523233890533447265625')</code>.

The context precision does not affect how many digits are stored. That is

determined exclusively by the number of digits in value. For example,

<code class="docutils literal notranslate">Decimal('3.00000')</code> 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 <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><code class="xref py py-const docutils literal notranslate">InvalidOperation</code></a>, an exception

is raised; otherwise, the constructor returns a new Decimal with the value of

<code class="docutils literal notranslate">NaN</code>.

Once constructed, <code class="xref py py-class docutils literal notranslate">Decimal</code> objects are immutable.

تغییر داده شده در نسخه 3.2: The argument to the constructor is now permitted to be a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a>

instance.

</div>

تغییر داده شده در نسخه 3.3: <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a> arguments raise an exception if the <a class="reference internal" href="#decimal.FloatOperation" title="decimal.FloatOperation"><code class="xref py py-exc docutils literal notranslate">FloatOperation</code></a>

trap is set. By default the trap is off.

</div>

تغییر داده شده در نسخه 3.6: Underscores are allowed for grouping, as with integral and floating-point

literals in code.

</div>

Decimal floating-point objects share many properties with the other built-in

numeric types such as <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a> and <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate">int</code></a>. 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 <code class="xref py py-class docutils literal notranslate">float</code> or

<code class="xref py py-class docutils literal notranslate">int</code>).

There are some small differences between arithmetic on Decimal objects and

arithmetic on integers and floats. When the remainder operator <code class="docutils literal notranslate">%</code> is

applied to Decimal objects, the sign of the result is the sign of the

dividend rather than the sign of the divisor:

<div class="highlight-python3 notranslate"><div class="highlight"><pre>>>> (-7) % 4

1

>>> Decimal(-7) % Decimal(4)

Decimal('-3')

</pre></div>

</div>

The integer division operator <code class="docutils literal notranslate">//</code> behaves analogously, returning the

integer part of the true quotient (truncating towards zero) rather than its

floor, so as to preserve the usual identity <code class="docutils literal notranslate">x == (x // y) * y + x % y</code>:

<div class="highlight-python3 notranslate"><div class="highlight"><pre>>>> -7 // 4

-2

>>> Decimal(-7) // Decimal(4)

Decimal('-1')

</pre></div>

</div>

The <code class="docutils literal notranslate">%</code> and <code class="docutils literal notranslate">//</code> operators implement the <code class="docutils literal notranslate">remainder</code> and

<code class="docutils literal notranslate">divide-integer</code> operations (respectively) as described in the

specification.

Decimal objects cannot generally be combined with floats or

instances of <a class="reference internal" href="fractions.html#fractions.Fraction" title="fractions.Fraction"><code class="xref py py-class docutils literal notranslate">fractions.Fraction</code></a> in arithmetic operations:

an attempt to add a <code class="xref py py-class docutils literal notranslate">Decimal</code> to a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a>, for

example, will raise a <a class="reference internal" href="exceptions.html#TypeError" title="TypeError"><code class="xref py py-exc docutils literal notranslate">TypeError</code></a>. However, it is possible to

use Python's comparison operators to compare a <code class="xref py py-class docutils literal notranslate">Decimal</code>

instance <code class="docutils literal notranslate">x</code> with another number <code class="docutils literal notranslate">y</code>. This avoids confusing results

when doing equality comparisons between numbers of different types.

تغییر داده شده در نسخه 3.2: Mixed-type comparisons between <code class="xref py py-class docutils literal notranslate">Decimal</code> instances and other

numeric types are now fully supported.

</div>

In addition to the standard numeric properties, decimal floating-point

objects also have a number of specialized methods:

adjusted()<a class="headerlink" href="#decimal.Decimal.adjusted" title="Link to this definition">¶</a></dt>

<dd>Return the adjusted exponent after shifting out the coefficient's

rightmost digits until only the lead digit remains:

<code class="docutils literal notranslate">Decimal('321e+5').adjusted()</code> returns seven. Used for determining the

position of the most significant digit with respect to the decimal point.

</dd></dl>

as_integer_ratio()<a class="headerlink" href="#decimal.Decimal.as_integer_ratio" title="Link to this definition">¶</a></dt>

<dd>Return a pair <code class="docutils literal notranslate">(n, d)</code> of integers that represent the given

<code class="xref py py-class docutils literal notranslate">Decimal</code> instance as a fraction, in lowest terms and

with a positive denominator:

<div class="highlight-python3 notranslate"><div class="highlight"><pre>>>> Decimal('-3.14').as_integer_ratio()

(-157, 50)

</pre></div>

</div>

The conversion is exact. Raise OverflowError on infinities and ValueError

on NaNs.

</dd></dl>

Added in version 3.6.

</div>

as_tuple()<a class="headerlink" href="#decimal.Decimal.as_tuple" title="Link to this definition">¶</a></dt>

<dd>Return a <a class="reference internal" href="../glossary.html#term-named-tuple">named tuple</a> representation of the number:

<code class="docutils literal notranslate">DecimalTuple(sign, digits, exponent)</code>.

</dd></dl>

canonical()<a class="headerlink" href="#decimal.Decimal.canonical" title="Link to this definition">¶</a></dt>

<dd>Return the canonical encoding of the argument. Currently, the encoding of

a <code class="xref py py-class docutils literal notranslate">Decimal</code> instance is always canonical, so this operation returns

its argument unchanged.

</dd></dl>

compare(other, context=None)<a class="headerlink" href="#decimal.Decimal.compare" title="Link to this definition">¶</a></dt>

<dd>Compare the values of two Decimal instances. <code class="xref py py-meth docutils literal notranslate">compare()</code> returns a

Decimal instance, and if either operand is a NaN then the result is a

NaN:

<div class="highlight-python3 notranslate"><div class="highlight"><pre>a or b is a NaN ==> Decimal('NaN')

a < b ==> Decimal('-1')

a == b ==> Decimal('0')

a > b ==> Decimal('1')

</pre></div>

</div>

</dd></dl>

compare_signal(other, context=None)<a class="headerlink" href="#decimal.Decimal.compare_signal" title="Link to this definition">¶</a></dt>

<dd>This operation is identical to the <a class="reference internal" href="#decimal.Decimal.compare" title="decimal.Decimal.compare"><code class="xref py py-meth docutils literal notranslate">compare()</code></a> 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.

</dd></dl>

compare_total(other, context=None)<a class="headerlink" href="#decimal.Decimal.compare_total" title="Link to this definition">¶</a></dt>

<dd>Compare two operands using their abstract representation rather than their

numerical value. Similar to the <a class="reference internal" href="#decimal.Decimal.compare" title="decimal.Decimal.compare"><code class="xref py py-meth docutils literal notranslate">compare()</code></a> method, but the result

gives a total ordering on <code class="xref py py-class docutils literal notranslate">Decimal</code> instances. Two

<code class="xref py py-class docutils literal notranslate">Decimal</code> instances with the same numeric value but different

representations compare unequal in this ordering:

<div class="doctest highlight-default notranslate"><div class="highlight"><pre>>>> Decimal('12.0').compare_total(Decimal('12'))

Decimal('-1')

</pre></div>

</div>

Quiet and signaling NaNs are also included in the total ordering. The

result of this function is <code class="docutils literal notranslate">Decimal('0')</code> if both operands have the same

representation, <code class="docutils literal notranslate">Decimal('-1')</code> if the first operand is lower in the

total order than the second, and <code class="docutils literal notranslate">Decimal('1')</code> 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.

</dd></dl>

compare_total_mag(other, context=None)<a class="headerlink" href="#decimal.Decimal.compare_total_mag" title="Link to this definition">¶</a></dt>

<dd>Compare two operands using their abstract representation rather than their

value as in <a class="reference internal" href="#decimal.Decimal.compare_total" title="decimal.Decimal.compare_total"><code class="xref py py-meth docutils literal notranslate">compare_total()</code></a>, but ignoring the sign of each operand.

<code class="docutils literal notranslate">x.compare_total_mag(y)</code> is equivalent to

<code class="docutils literal notranslate">x.copy_abs().compare_total(y.copy_abs())</code>.

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.

</dd></dl>

conjugate()<a class="headerlink" href="#decimal.Decimal.conjugate" title="Link to this definition">¶</a></dt>

<dd>Just returns self, this method is only to comply with the Decimal

Specification.

</dd></dl>

copy_abs()<a class="headerlink" href="#decimal.Decimal.copy_abs" title="Link to this definition">¶</a></dt>

<dd>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.

</dd></dl>

copy_negate()<a class="headerlink" href="#decimal.Decimal.copy_negate" title="Link to this definition">¶</a></dt>

<dd>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.

</dd></dl>

copy_sign(other, context=None)<a class="headerlink" href="#decimal.Decimal.copy_sign" title="Link to this definition">¶</a></dt>

<dd>Return a copy of the first operand with the sign set to be the same as the

sign of the second operand. For example:

<div class="doctest highlight-default notranslate"><div class="highlight"><pre>>>> Decimal('2.3').copy_sign(Decimal('-1.5'))

Decimal('-2.3')

</pre></div>

</div>

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.

</dd></dl>

exp(context=None)<a class="headerlink" href="#decimal.Decimal.exp" title="Link to this definition">¶</a></dt>

<dd>Return the value of the (natural) exponential function <code class="docutils literal notranslate">e**x</code> at the

given number. The result is correctly rounded using the

<a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal notranslate">ROUND_HALF_EVEN</code></a> rounding mode.

Decimal('2.718281828459045235360287471')

>>> Decimal(321).exp()

Decimal('2.561702493119680037517373933E+139')

</pre></div>

</div>

</dd></dl>

classmethod from_float(f, <abbr title="Positional-only parameter separator (PEP 570)">/</abbr>)<a class="headerlink" href="#decimal.Decimal.from_float" title="Link to this definition">¶</a></dt>

<dd>Alternative constructor that only accepts instances of <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a> or

<a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate">int</code></a>.

Note <code class="docutils literal notranslate">Decimal.from_float(0.1)</code> is not the same as <code class="docutils literal notranslate">Decimal('0.1')</code>.

Since 0.1 is not exactly representable in binary floating point, the

value is stored as the nearest representable value which is

<code class="docutils literal notranslate">0x1.999999999999ap-4</code>. That equivalent value in decimal is

<code class="docutils literal notranslate">0.1000000000000000055511151231257827021181583404541015625</code>.

توجه

From Python 3.2 onwards, a <code class="xref py py-class docutils literal notranslate">Decimal</code> instance

can also be constructed directly from a <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a>.

</div>

<div class="highlight-pycon notranslate"><div class="highlight"><pre>>>> Decimal.from_float(0.1)

Decimal('0.1000000000000000055511151231257827021181583404541015625')

>>> Decimal.from_float(float('nan'))

Decimal('NaN')

Decimal('Infinity')

Decimal('-Infinity')

</pre></div>

</div>

Added in version 3.1.

</div>

</dd></dl>

classmethod from_number(number, <abbr title="Positional-only parameter separator (PEP 570)">/</abbr>)<a class="headerlink" href="#decimal.Decimal.from_number" title="Link to this definition">¶</a></dt>

<dd>Alternative constructor that only accepts instances of

<a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a>, <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate">int</code></a> or <code class="xref py py-class docutils literal notranslate">Decimal</code>, but not strings

or tuples.

<div class="highlight-pycon notranslate"><div class="highlight"><pre>>>> Decimal.from_number(314)

Decimal('314')

>>> Decimal.from_number(0.1)

Decimal('0.1000000000000000055511151231257827021181583404541015625')

>>> Decimal.from_number(Decimal('3.14'))

Decimal('3.14')

</pre></div>

</div>

Added in version 3.14.

</div>

</dd></dl>

fma(other, third, context=None)<a class="headerlink" href="#decimal.Decimal.fma" title="Link to this definition">¶</a></dt>

<dd>Fused multiply-add. Return self*other+third with no rounding of the

intermediate product self*other.

<div class="doctest highlight-default notranslate"><div class="highlight"><pre>>>> Decimal(2).fma(3, 5)

Decimal('11')

</pre></div>

</div>

</dd></dl>

is_canonical()<a class="headerlink" href="#decimal.Decimal.is_canonical" title="Link to this definition">¶</a></dt>

<dd>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate">True</code></a> if the argument is canonical and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate">False</code></a>

otherwise. Currently, a <code class="xref py py-class docutils literal notranslate">Decimal</code> instance is always canonical, so

this operation always returns <code class="xref py py-const docutils literal notranslate">True</code>.

</dd></dl>

is_finite()<a class="headerlink" href="#decimal.Decimal.is_finite" title="Link to this definition">¶</a></dt>

<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate">False</code></a> if the argument is an infinity or a NaN.

</dd></dl>

is_infinite()<a class="headerlink" href="#decimal.Decimal.is_infinite" title="Link to this definition">¶</a></dt>

infinity and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate">False</code></a> otherwise.

</dd></dl>

is_nan()<a class="headerlink" href="#decimal.Decimal.is_nan" title="Link to this definition">¶</a></dt>

<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate">False</code></a> otherwise.

</dd></dl>

is_normal(context=None)<a class="headerlink" href="#decimal.Decimal.is_normal" title="Link to this definition">¶</a></dt>

</dd></dl>

is_qnan()<a class="headerlink" href="#decimal.Decimal.is_qnan" title="Link to this definition">¶</a></dt>

<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate">False</code></a> otherwise.

</dd></dl>

is_signed()<a class="headerlink" href="#decimal.Decimal.is_signed" title="Link to this definition">¶</a></dt>

</dd></dl>

is_snan()<a class="headerlink" href="#decimal.Decimal.is_snan" title="Link to this definition">¶</a></dt>

<dd>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate">True</code></a> if the argument is a signaling NaN and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate">False</code></a>

otherwise.

</dd></dl>

is_subnormal(context=None)<a class="headerlink" href="#decimal.Decimal.is_subnormal" title="Link to this definition">¶</a></dt>

<dd>Return <a class="reference internal" href="constants.html#True" title="True"><code class="xref py py-const docutils literal notranslate">True</code></a> if the argument is subnormal, and <a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate">False</code></a>

otherwise.

</dd></dl>

is_zero()<a class="headerlink" href="#decimal.Decimal.is_zero" title="Link to this definition">¶</a></dt>

<a class="reference internal" href="constants.html#False" title="False"><code class="xref py py-const docutils literal notranslate">False</code></a> otherwise.

</dd></dl>

ln(context=None)<a class="headerlink" href="#decimal.Decimal.ln" title="Link to this definition">¶</a></dt>

<dd>Return the natural (base e) logarithm of the operand. The result is

correctly rounded using the <a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal notranslate">ROUND_HALF_EVEN</code></a> rounding mode.

</dd></dl>

log10(context=None)<a class="headerlink" href="#decimal.Decimal.log10" title="Link to this definition">¶</a></dt>

<dd>Return the base ten logarithm of the operand. The result is correctly

rounded using the <a class="reference internal" href="#decimal.ROUND_HALF_EVEN" title="decimal.ROUND_HALF_EVEN"><code class="xref py py-const docutils literal notranslate">ROUND_HALF_EVEN</code></a> rounding mode.

</dd></dl>

logb(context=None)<a class="headerlink" href="#decimal.Decimal.logb" title="Link to this definition">¶</a></dt>

<dd>For a nonzero number, return the adjusted exponent of its operand as a

<code class="xref py py-class docutils literal notranslate">Decimal</code> instance. If the operand is a zero then

<code class="docutils literal notranslate">Decimal('-Infinity')</code> is returned and the <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><code class="xref py py-const docutils literal notranslate">DivisionByZero</code></a> flag

is raised. If the operand is an infinity then <code class="docutils literal notranslate">Decimal('Infinity')</code> is

returned.

</dd></dl>

logical_and(other, context=None)<a class="headerlink" href="#decimal.Decimal.logical_and" title="Link to this definition">¶</a></dt>

<dd><code class="xref py py-meth docutils literal notranslate">logical_and()</code> is a logical operation which takes two logical

operands (see <a class="reference internal" href="#logical-operands-label">Logical operands</a>). The result is the

digit-wise <code class="docutils literal notranslate">and</code> of the two operands.

</dd></dl>

logical_invert(context=None)<a class="headerlink" href="#decimal.Decimal.logical_invert" title="Link to this definition">¶</a></dt>

<dd><code class="xref py py-meth docutils literal notranslate">logical_invert()</code> is a logical operation. The

result is the digit-wise inversion of the operand.

</dd></dl>

logical_or(other, context=None)<a class="headerlink" href="#decimal.Decimal.logical_or" title="Link to this definition">¶</a></dt>

<dd><code class="xref py py-meth docutils literal notranslate">logical_or()</code> is a logical operation which takes two logical

operands (see <a class="reference internal" href="#logical-operands-label">Logical operands</a>). The result is the

digit-wise <code class="docutils literal notranslate">or</code> of the two operands.

</dd></dl>

logical_xor(other, context=None)<a class="headerlink" href="#decimal.Decimal.logical_xor" title="Link to this definition">¶</a></dt>

<dd><code class="xref py py-meth docutils literal notranslate">logical_xor()</code> is a logical operation which takes two logical

operands (see <a class="reference internal" href="#logical-operands-label">Logical operands</a>). The result is the

digit-wise exclusive or of the two operands.

</dd></dl>

max(other, context=None)<a class="headerlink" href="#decimal.Decimal.max" title="Link to this definition">¶</a></dt>

<dd>Like <code class="docutils literal notranslate">max(self, other)</code> except that the context rounding rule is applied

before returning and that <code class="docutils literal notranslate">NaN</code> values are either signaled or

ignored (depending on the context and whether they are signaling or

quiet).

</dd></dl>

max_mag(other, context=None)<a class="headerlink" href="#decimal.Decimal.max_mag" title="Link to this definition">¶</a></dt>

<dd>Similar to the <a class="reference internal" href="#decimal.Decimal.max" title="decimal.Decimal.max"><code class="xref py py-meth docutils literal notranslate">max()</code></a> method, but the comparison is done using the

absolute values of the operands.

</dd></dl>

min(other, context=None)<a class="headerlink" href="#decimal.Decimal.min" title="Link to this definition">¶</a></dt>

<dd>Like <code class="docutils literal notranslate">min(self, other)</code> except that the context rounding rule is applied

before returning and that <code class="docutils literal notranslate">NaN</code> values are either signaled or

ignored (depending on the context and whether they are signaling or

quiet).

</dd></dl>

min_mag(other, context=None)<a class="headerlink" href="#decimal.Decimal.min_mag" title="Link to this definition">¶</a></dt>

<dd>Similar to the <a class="reference internal" href="#decimal.Decimal.min" title="decimal.Decimal.min"><code class="xref py py-meth docutils literal notranslate">min()</code></a> method, but the comparison is done using the

absolute values of the operands.

</dd></dl>

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