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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <title>9.4. decimal — Decimal fixed point and floating point arithmetic — Python 2.7.5 documentation</title> <link rel="stylesheet" href="../_static/default.css" type="text/css" /> <link rel="stylesheet" href="../_static/pygments.css" type="text/css" /> <script type="text/javascript"> var DOCUMENTATION_OPTIONS = { URL_ROOT: '../', VERSION: '2.7.5', COLLAPSE_INDEX: false, FILE_SUFFIX: '.html', HAS_SOURCE: true }; </script> <script type="text/javascript" src="../_static/jquery.js"></script> <script type="text/javascript" src="../_static/underscore.js"></script> <script type="text/javascript" src="../_static/doctools.js"></script> <script type="text/javascript" src="../_static/sidebar.js"></script> <link rel="search" type="application/opensearchdescription+xml" title="Search within Python 2.7.5 documentation" href="../_static/opensearch.xml"/> <link rel="author" title="About these documents" href="../about.html" /> <link rel="copyright" title="Copyright" href="../copyright.html" /> <link rel="top" title="Python 2.7.5 documentation" href="../index.html" /> <link rel="up" title="9. 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Numeric and Mathematical Modules</a> »</li> </ul> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body"> <div class="section" id="module-decimal"> <h1>9.4. <a class="reference internal" href="#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic Specification."><tt class="xref py py-mod docutils literal">decimal</tt></a> — Decimal fixed point and floating point arithmetic<a class="headerlink" href="#module-decimal" title="Permalink to this headline">¶</a></h1> New in version 2.4. The <a class="reference internal" href="#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic Specification."><tt class="xref py py-mod docutils literal">decimal</tt></a> module provides support for decimal floating point arithmetic. It offers several advantages over the <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal">float</tt></a> datatype: <ul> <li>Decimal “is based on a floating-point model 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 <tt class="xref py py-const docutils literal">1.1</tt> and <tt class="xref py py-const docutils literal">2.2</tt> do not have exact representations in binary floating point. End users typically would not expect <tt class="docutils literal">1.1 + 2.2</tt> to display as <tt class="xref py py-const docutils literal">3.3000000000000003</tt> as it does with binary floating point. </li> <li>The exactness carries over into arithmetic. In decimal floating point, <tt class="docutils literal">0.1 + 0.1 + 0.1 - 0.3</tt> is exactly equal to zero. In binary floating point, the result is <tt class="xref py py-const docutils literal">5.5511151231257827e-017</tt>. 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 <tt class="docutils literal">1.30 + 1.20</tt> is <tt class="xref py py-const docutils literal">2.50</tt>. 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, <tt class="docutils literal">1.3 * 1.2</tt> gives <tt class="xref py py-const docutils literal">1.56</tt> while <tt class="docutils literal">1.30 * 1.20</tt> gives <tt class="xref py py-const docutils literal">1.5600</tt>. </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="highlight-python"><div class="highlight"><pre>>>> from decimal import * >>> getcontext().prec = 6 >>> Decimal(1) / Decimal(7) Decimal('0.142857') >>> getcontext().prec = 28 >>> Decimal(1) / Decimal(7) 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 <tt class="xref py py-const docutils literal">Infinity</tt>, <tt class="xref py py-const docutils literal">-Infinity</tt>, and <tt class="xref py py-const docutils literal">NaN</tt>. The standard also differentiates <tt class="xref py py-const docutils literal">-0</tt> from <tt class="xref py py-const docutils literal">+0</tt>. 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 <tt class="xref py py-const docutils literal">ROUND_CEILING</tt>, <tt class="xref py py-const docutils literal">ROUND_DOWN</tt>, <tt class="xref py py-const docutils literal">ROUND_FLOOR</tt>, <tt class="xref py py-const docutils literal">ROUND_HALF_DOWN</tt>, <tt class="xref py py-const docutils literal">ROUND_HALF_EVEN</tt>, <tt class="xref py py-const docutils literal">ROUND_HALF_UP</tt>, <tt class="xref py py-const docutils literal">ROUND_UP</tt>, and <tt class="xref py py-const docutils literal">ROUND_05UP</tt>. 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"><tt class="xref py py-const docutils literal">Clamped</tt></a>, <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><tt class="xref py py-const docutils literal">InvalidOperation</tt></a>, <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><tt class="xref py py-const docutils literal">DivisionByZero</tt></a>, <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><tt class="xref py py-const docutils literal">Inexact</tt></a>, <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><tt class="xref py py-const docutils literal">Rounded</tt></a>, <a class="reference internal" href="#decimal.Subnormal" title="decimal.Subnormal"><tt class="xref py py-const docutils literal">Subnormal</tt></a>, <a class="reference internal" href="#decimal.Overflow" title="decimal.Overflow"><tt class="xref py py-const docutils literal">Overflow</tt></a>, and <a class="reference internal" href="#decimal.Underflow" title="decimal.Underflow"><tt class="xref py py-const docutils literal">Underflow</tt></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. <div class="admonition-see-also admonition seealso"> See also <ul class="last simple"> <li>IBM’s General Decimal Arithmetic Specification, <a class="reference external" href="http://speleotrove.com/decimal/">The General Decimal Arithmetic Specification</a>.</li> <li>IEEE standard 854-1987, <a class="reference external" href="http://754r.ucbtest.org/standards/854.pdf">Unofficial IEEE 854 Text</a>.</li> </ul> </div> <div class="section" id="quick-start-tutorial"> <h2>9.4.1. Quick-start Tutorial<a class="headerlink" href="#quick-start-tutorial" title="Permalink to this headline">¶</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"><tt class="xref py py-func docutils literal">getcontext()</tt></a> and, if necessary, setting new values for precision, rounding, or enabled traps: <div class="highlight-python"><div class="highlight"><pre>>>> from decimal import * >>> getcontext() Context(prec=28, rounding=ROUND_HALF_EVEN, Emin=-999999999, Emax=999999999, capitals=1, 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 <tt class="xref py py-const docutils literal">NaN</tt> which stands for “Not a number”, positive and negative <tt class="xref py py-const docutils literal">Infinity</tt>, and <tt class="xref py py-const docutils literal">-0</tt>. <div class="highlight-python"><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('1.41421356237') >>> Decimal(2) ** Decimal('0.5') Decimal('1.414213562373095048801688724') >>> Decimal('NaN') Decimal('NaN') >>> Decimal('-Infinity') Decimal('-Infinity') </pre></div> </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-python"><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('3.1415926535') + Decimal('2.7182818285') Decimal('5.85988') </pre></div> </div> Decimals interact well with much of the rest of Python. Here is a small decimal floating point flying circus: <div class="highlight-python"><div class="highlight"><pre>>>> data = 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) # round() first converts to binary floating point 1.3 >>> int(a) 1 >>> a * 5 Decimal('6.70') >>> a * b Decimal('2.5058') >>> c % a Decimal('0.77') </pre></div> </div> And some mathematical functions are also available to Decimal: <div class="highlight-python"><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('10').log10() Decimal('1') </pre></div> </div> The <tt class="xref py py-meth docutils literal">quantize()</tt> 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="highlight-python"><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"><tt class="xref py py-func docutils literal">getcontext()</tt></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 Context() constructor. To make an alternate active, use the <a class="reference internal" href="#decimal.setcontext" title="decimal.setcontext"><tt class="xref py py-func docutils literal">setcontext()</tt></a> function. In accordance with the standard, the <tt class="xref py py-mod docutils literal">Decimal</tt> module provides two ready to use standard contexts, <a class="reference internal" href="#decimal.BasicContext" title="decimal.BasicContext"><tt class="xref py py-const docutils literal">BasicContext</tt></a> and <a class="reference internal" href="#decimal.ExtendedContext" title="decimal.ExtendedContext"><tt class="xref py py-const docutils literal">ExtendedContext</tt></a>. The former is especially useful for debugging because many of the traps are enabled: <div class="highlight-python"><div class="highlight"><pre>>>> 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=-999999999, Emax=999999999, capitals=1, 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 </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 <tt class="xref py py-meth docutils literal">clear_flags()</tt> method. <div class="highlight-python"><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=-999999999, Emax=999999999, capitals=1, flags=[Rounded, Inexact], traps=[]) </pre></div> </div> The flags entry shows that the rational approximation to <tt class="xref py py-const docutils literal">Pi</tt> 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 <tt class="xref py py-attr docutils literal">traps</tt> field of a context: <div class="highlight-python"><div class="highlight"><pre>>>> 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 </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"><tt class="xref py py-class docutils literal">Decimal</tt></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. </div> <div class="section" id="decimal-objects"> <h2>9.4.2. Decimal objects<a class="headerlink" href="#decimal-objects" title="Permalink to this headline">¶</a></h2> <dl class="class"> <dt id="decimal.Decimal"> class <tt class="descclassname">decimal.</tt><tt class="descname">Decimal</tt><big>(</big>[value[, context]]<big>)</big><a class="headerlink" href="#decimal.Decimal" title="Permalink to this definition">¶</a></dt> <dd>Construct a new <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> object based from value. value can be an integer, string, tuple, <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal">float</tt></a>, or another <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> object. If no value is given, returns <tt class="docutils literal">Decimal('0')</tt>. If value is a string, it should conform to the decimal numeric string syntax after leading and trailing whitespace characters are removed: <div class="highlight-python"><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> If value is a unicode string then other Unicode decimal digits are also permitted where <tt class="docutils literal">digit</tt> appears above. These include decimal digits from various other alphabets (for example, Arabic-Indic and Devanāgarī digits) along with the fullwidth digits <tt class="docutils literal">u'\uff10'</tt> through <tt class="docutils literal">u'\uff19'</tt>. If value is a <a class="reference internal" href="functions.html#tuple" title="tuple"><tt class="xref py py-class docutils literal">tuple</tt></a>, it should have three components, a sign (<tt class="xref py py-const docutils literal">0</tt> for positive or <tt class="xref py py-const docutils literal">1</tt> for negative), a <a class="reference internal" href="functions.html#tuple" title="tuple"><tt class="xref py py-class docutils literal">tuple</tt></a> of digits, and an integer exponent. For example, <tt class="docutils literal">Decimal((0, (1, 4, 1, 4), -3))</tt> returns <tt class="docutils literal">Decimal('1.414')</tt>. If value is a <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal">float</tt></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, <tt class="docutils literal">Decimal(float('1.1'))</tt> converts to <tt class="docutils literal">Decimal('1.100000000000000088817841970012523233890533447265625')</tt>. The context precision does not affect how many digits are stored. That is determined exclusively by the number of digits in value. For example, <tt class="docutils literal">Decimal('3.00000')</tt> 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"><tt class="xref py py-const docutils literal">InvalidOperation</tt></a>, an exception is raised; otherwise, the constructor returns a new Decimal with the value of <tt class="xref py py-const docutils literal">NaN</tt>. Once constructed, <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> objects are immutable. Changed in version 2.6: leading and trailing whitespace characters are permitted when creating a Decimal instance from a string. Changed in version 2.7: The argument to the constructor is now permitted to be a <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal">float</tt></a> instance. 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"><tt class="xref py py-class docutils literal">float</tt></a> and <a class="reference internal" href="functions.html#int" title="int"><tt class="xref py py-class docutils literal">int</tt></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 <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal">float</tt></a> or <a class="reference internal" href="functions.html#long" title="long"><tt class="xref py py-class docutils literal">long</tt></a>). There are some small differences between arithmetic on Decimal objects and arithmetic on integers and floats. When the remainder operator <tt class="docutils literal">%</tt> 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-python"><div class="highlight"><pre>>>> (-7) % 4 1 >>> Decimal(-7) % Decimal(4) Decimal('-3') </pre></div> </div> The integer division operator <tt class="docutils literal">//</tt> behaves analogously, returning the integer part of the true quotient (truncating towards zero) rather than its floor, so as to preserve the usual identity <tt class="docutils literal">x == (x // y) * y + x % y</tt>: <div class="highlight-python"><div class="highlight"><pre>>>> -7 // 4 -2 >>> Decimal(-7) // Decimal(4) Decimal('-1') </pre></div> </div> The <tt class="docutils literal">%</tt> and <tt class="docutils literal">//</tt> operators implement the <tt class="docutils literal">remainder</tt> and <tt class="docutils literal">divide-integer</tt> operations (respectively) as described in the specification. Decimal objects cannot generally be combined with floats in arithmetic operations: an attempt to add a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> to a <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal">float</tt></a>, for example, will raise a <a class="reference internal" href="exceptions.html#exceptions.TypeError" title="exceptions.TypeError"><tt class="xref py py-exc docutils literal">TypeError</tt></a>. There’s one exception to this rule: it’s possible to use Python’s comparison operators to compare a <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal">float</tt></a> instance <tt class="docutils literal">x</tt> with a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instance <tt class="docutils literal">y</tt>. Without this exception, comparisons between <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> and <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal">float</tt></a> instances would follow the general rules for comparing objects of different types described in the <a class="reference internal" href="../reference/expressions.html#expressions">Expressions</a> section of the reference manual, leading to confusing results. Changed in version 2.7: A comparison between a <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal">float</tt></a> instance <tt class="docutils literal">x</tt> and a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instance <tt class="docutils literal">y</tt> now returns a result based on the values of <tt class="docutils literal">x</tt> and <tt class="docutils literal">y</tt>. In earlier versions <tt class="docutils literal">x < y</tt> returned the same (arbitrary) result for any <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instance <tt class="docutils literal">x</tt> and any <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal">float</tt></a> instance <tt class="docutils literal">y</tt>. In addition to the standard numeric properties, decimal floating point objects also have a number of specialized methods: <dl class="method"> <dt id="decimal.Decimal.adjusted"> <tt class="descname">adjusted</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.adjusted" title="Permalink to this definition">¶</a></dt> <dd>Return the adjusted exponent after shifting out the coefficient’s rightmost digits until only the lead digit remains: <tt class="docutils literal">Decimal('321e+5').adjusted()</tt> returns seven. Used for determining the position of the most significant digit with respect to the decimal point. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.as_tuple"> <tt class="descname">as_tuple</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.as_tuple" title="Permalink 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: <tt class="docutils literal">DecimalTuple(sign, digits, exponent)</tt>. Changed in version 2.6: Use a named tuple. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.canonical"> <tt class="descname">canonical</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.canonical" title="Permalink to this definition">¶</a></dt> <dd>Return the canonical encoding of the argument. Currently, the encoding of a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instance is always canonical, so this operation returns its argument unchanged. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.compare"> <tt class="descname">compare</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.compare" title="Permalink to this definition">¶</a></dt> <dd>Compare the values of two Decimal instances. This operation behaves in the same way as the usual comparison method <a class="reference internal" href="../reference/datamodel.html#object.__cmp__" title="object.__cmp__"><tt class="xref py py-meth docutils literal">__cmp__()</tt></a>, except that <a class="reference internal" href="#decimal.Decimal.compare" title="decimal.Decimal.compare"><tt class="xref py py-meth docutils literal">compare()</tt></a> returns a Decimal instance rather than an integer, and if either operand is a NaN then the result is a NaN: <div class="highlight-python"><pre>a or b is a NaN ==> Decimal('NaN') a Decimal('-1') a == b ==> Decimal('0') a > b ==> Decimal('1')</pre> </div> </dd></dl> <dl class="method"> <dt id="decimal.Decimal.compare_signal"> <tt class="descname">compare_signal</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.compare_signal" title="Permalink to this definition">¶</a></dt> <dd>This operation is identical to the <a class="reference internal" href="#decimal.Decimal.compare" title="decimal.Decimal.compare"><tt class="xref py py-meth docutils literal">compare()</tt></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. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.compare_total"> <tt class="descname">compare_total</tt><big>(</big>other<big>)</big><a class="headerlink" href="#decimal.Decimal.compare_total" title="Permalink 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"><tt class="xref py py-meth docutils literal">compare()</tt></a> method, but the result gives a total ordering on <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instances. Two <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instances with the same numeric value but different representations compare unequal in this ordering: <div class="highlight-python"><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 <tt class="docutils literal">Decimal('0')</tt> if both operands have the same representation, <tt class="docutils literal">Decimal('-1')</tt> if the first operand is lower in the total order than the second, and <tt class="docutils literal">Decimal('1')</tt> if the first operand is higher in the total order than the second operand. See the specification for details of the total order. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.compare_total_mag"> <tt class="descname">compare_total_mag</tt><big>(</big>other<big>)</big><a class="headerlink" href="#decimal.Decimal.compare_total_mag" title="Permalink 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"><tt class="xref py py-meth docutils literal">compare_total()</tt></a>, but ignoring the sign of each operand. <tt class="docutils literal">x.compare_total_mag(y)</tt> is equivalent to <tt class="docutils literal">x.copy_abs().compare_total(y.copy_abs())</tt>. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.conjugate"> <tt class="descname">conjugate</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.conjugate" title="Permalink to this definition">¶</a></dt> <dd>Just returns self, this method is only to comply with the Decimal Specification. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.copy_abs"> <tt class="descname">copy_abs</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.copy_abs" title="Permalink 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. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.copy_negate"> <tt class="descname">copy_negate</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.copy_negate" title="Permalink 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. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.copy_sign"> <tt class="descname">copy_sign</tt><big>(</big>other<big>)</big><a class="headerlink" href="#decimal.Decimal.copy_sign" title="Permalink 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="highlight-python"><div class="highlight"><pre>>>> Decimal('2.3').copy_sign(Decimal('-1.5')) Decimal('-2.3') </pre></div> </div> This operation is unaffected by the context and is quiet: no flags are changed and no rounding is performed. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.exp"> <tt class="descname">exp</tt><big>(</big>[context]<big>)</big><a class="headerlink" href="#decimal.Decimal.exp" title="Permalink to this definition">¶</a></dt> <dd>Return the value of the (natural) exponential function <tt class="docutils literal">e**x</tt> at the given number. The result is correctly rounded using the <tt class="xref py py-const docutils literal">ROUND_HALF_EVEN</tt> rounding mode. <div class="highlight-python"><div class="highlight"><pre>>>> Decimal(1).exp() Decimal('2.718281828459045235360287471') >>> Decimal(321).exp() Decimal('2.561702493119680037517373933E+139') </pre></div> </div> New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.from_float"> <tt class="descname">from_float</tt><big>(</big>f<big>)</big><a class="headerlink" href="#decimal.Decimal.from_float" title="Permalink to this definition">¶</a></dt> <dd>Classmethod that converts a float to a decimal number, exactly. Note <cite>Decimal.from_float(0.1)</cite> is not the same as <cite>Decimal(‘0.1’)</cite>. Since 0.1 is not exactly representable in binary floating point, the value is stored as the nearest representable value which is <cite>0x1.999999999999ap-4</cite>. That equivalent value in decimal is <cite>0.1000000000000000055511151231257827021181583404541015625</cite>. <div class="admonition note"> Note From Python 2.7 onwards, a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instance can also be constructed directly from a <a class="reference internal" href="functions.html#float" title="float"><tt class="xref py py-class docutils literal">float</tt></a>. </div> <div class="highlight-python"><div class="highlight"><pre>>>> 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') </pre></div> </div> New in version 2.7. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.fma"> <tt class="descname">fma</tt><big>(</big>other, third[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.fma" title="Permalink to this definition">¶</a></dt> <dd>Fused multiply-add. Return self*other+third with no rounding of the intermediate product self*other. <div class="highlight-python"><div class="highlight"><pre>>>> Decimal(2).fma(3, 5) Decimal('11') </pre></div> </div> New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.is_canonical"> <tt class="descname">is_canonical</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.is_canonical" title="Permalink to this definition">¶</a></dt> <dd>Return <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a> if the argument is canonical and <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> otherwise. Currently, a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instance is always canonical, so this operation always returns <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a>. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.is_finite"> <tt class="descname">is_finite</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.is_finite" title="Permalink to this definition">¶</a></dt> <dd>Return <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a> if the argument is a finite number, and <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> if the argument is an infinity or a NaN. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.is_infinite"> <tt class="descname">is_infinite</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.is_infinite" title="Permalink to this definition">¶</a></dt> <dd>Return <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a> if the argument is either positive or negative infinity and <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> otherwise. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.is_nan"> <tt class="descname">is_nan</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.is_nan" title="Permalink to this definition">¶</a></dt> <dd>Return <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a> if the argument is a (quiet or signaling) NaN and <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> otherwise. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.is_normal"> <tt class="descname">is_normal</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.is_normal" title="Permalink to this definition">¶</a></dt> <dd>Return <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a> if the argument is a normal finite non-zero number with an adjusted exponent greater than or equal to Emin. Return <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> if the argument is zero, subnormal, infinite or a NaN. Note, the term normal is used here in a different sense with the <a class="reference internal" href="#decimal.Decimal.normalize" title="decimal.Decimal.normalize"><tt class="xref py py-meth docutils literal">normalize()</tt></a> method which is used to create canonical values. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.is_qnan"> <tt class="descname">is_qnan</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.is_qnan" title="Permalink to this definition">¶</a></dt> <dd>Return <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a> if the argument is a quiet NaN, and <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> otherwise. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.is_signed"> <tt class="descname">is_signed</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.is_signed" title="Permalink to this definition">¶</a></dt> <dd>Return <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a> if the argument has a negative sign and <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> otherwise. Note that zeros and NaNs can both carry signs. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.is_snan"> <tt class="descname">is_snan</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.is_snan" title="Permalink to this definition">¶</a></dt> <dd>Return <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a> if the argument is a signaling NaN and <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> otherwise. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.is_subnormal"> <tt class="descname">is_subnormal</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.is_subnormal" title="Permalink to this definition">¶</a></dt> <dd>Return <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a> if the argument is subnormal, and <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> otherwise. A number is subnormal is if it is nonzero, finite, and has an adjusted exponent less than Emin. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.is_zero"> <tt class="descname">is_zero</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.is_zero" title="Permalink to this definition">¶</a></dt> <dd>Return <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a> if the argument is a (positive or negative) zero and <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> otherwise. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.ln"> <tt class="descname">ln</tt><big>(</big>[context]<big>)</big><a class="headerlink" href="#decimal.Decimal.ln" title="Permalink to this definition">¶</a></dt> <dd>Return the natural (base e) logarithm of the operand. The result is correctly rounded using the <tt class="xref py py-const docutils literal">ROUND_HALF_EVEN</tt> rounding mode. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.log10"> <tt class="descname">log10</tt><big>(</big>[context]<big>)</big><a class="headerlink" href="#decimal.Decimal.log10" title="Permalink to this definition">¶</a></dt> <dd>Return the base ten logarithm of the operand. The result is correctly rounded using the <tt class="xref py py-const docutils literal">ROUND_HALF_EVEN</tt> rounding mode. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.logb"> <tt class="descname">logb</tt><big>(</big>[context]<big>)</big><a class="headerlink" href="#decimal.Decimal.logb" title="Permalink to this definition">¶</a></dt> <dd>For a nonzero number, return the adjusted exponent of its operand as a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instance. If the operand is a zero then <tt class="docutils literal">Decimal('-Infinity')</tt> is returned and the <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><tt class="xref py py-const docutils literal">DivisionByZero</tt></a> flag is raised. If the operand is an infinity then <tt class="docutils literal">Decimal('Infinity')</tt> is returned. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.logical_and"> <tt class="descname">logical_and</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.logical_and" title="Permalink to this definition">¶</a></dt> <dd><a class="reference internal" href="#decimal.Decimal.logical_and" title="decimal.Decimal.logical_and"><tt class="xref py py-meth docutils literal">logical_and()</tt></a> 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 <tt class="docutils literal">and</tt> of the two operands. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.logical_invert"> <tt class="descname">logical_invert</tt><big>(</big>[context]<big>)</big><a class="headerlink" href="#decimal.Decimal.logical_invert" title="Permalink to this definition">¶</a></dt> <dd><a class="reference internal" href="#decimal.Decimal.logical_invert" title="decimal.Decimal.logical_invert"><tt class="xref py py-meth docutils literal">logical_invert()</tt></a> is a logical operation. The result is the digit-wise inversion of the operand. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.logical_or"> <tt class="descname">logical_or</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.logical_or" title="Permalink to this definition">¶</a></dt> <dd><a class="reference internal" href="#decimal.Decimal.logical_or" title="decimal.Decimal.logical_or"><tt class="xref py py-meth docutils literal">logical_or()</tt></a> 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 <tt class="docutils literal">or</tt> of the two operands. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.logical_xor"> <tt class="descname">logical_xor</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.logical_xor" title="Permalink to this definition">¶</a></dt> <dd><a class="reference internal" href="#decimal.Decimal.logical_xor" title="decimal.Decimal.logical_xor"><tt class="xref py py-meth docutils literal">logical_xor()</tt></a> 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. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.max"> <tt class="descname">max</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.max" title="Permalink to this definition">¶</a></dt> <dd>Like <tt class="docutils literal">max(self, other)</tt> except that the context rounding rule is applied before returning and that <tt class="xref py py-const docutils literal">NaN</tt> values are either signaled or ignored (depending on the context and whether they are signaling or quiet). </dd></dl> <dl class="method"> <dt id="decimal.Decimal.max_mag"> <tt class="descname">max_mag</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.max_mag" title="Permalink to this definition">¶</a></dt> <dd>Similar to the <a class="reference internal" href="#decimal.Decimal.max" title="decimal.Decimal.max"><tt class="xref py py-meth docutils literal">max()</tt></a> method, but the comparison is done using the absolute values of the operands. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.min"> <tt class="descname">min</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.min" title="Permalink to this definition">¶</a></dt> <dd>Like <tt class="docutils literal">min(self, other)</tt> except that the context rounding rule is applied before returning and that <tt class="xref py py-const docutils literal">NaN</tt> values are either signaled or ignored (depending on the context and whether they are signaling or quiet). </dd></dl> <dl class="method"> <dt id="decimal.Decimal.min_mag"> <tt class="descname">min_mag</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.min_mag" title="Permalink to this definition">¶</a></dt> <dd>Similar to the <a class="reference internal" href="#decimal.Decimal.min" title="decimal.Decimal.min"><tt class="xref py py-meth docutils literal">min()</tt></a> method, but the comparison is done using the absolute values of the operands. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.next_minus"> <tt class="descname">next_minus</tt><big>(</big>[context]<big>)</big><a class="headerlink" href="#decimal.Decimal.next_minus" title="Permalink to this definition">¶</a></dt> <dd>Return the largest number representable in the given context (or in the current thread’s context if no context is given) that is smaller than the given operand. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.next_plus"> <tt class="descname">next_plus</tt><big>(</big>[context]<big>)</big><a class="headerlink" href="#decimal.Decimal.next_plus" title="Permalink to this definition">¶</a></dt> <dd>Return the smallest number representable in the given context (or in the current thread’s context if no context is given) that is larger than the given operand. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.next_toward"> <tt class="descname">next_toward</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.next_toward" title="Permalink to this definition">¶</a></dt> <dd>If the two operands are unequal, return the number closest to the first operand in the direction of the second operand. If both operands are numerically equal, return a copy of the first operand with the sign set to be the same as the sign of the second operand. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.normalize"> <tt class="descname">normalize</tt><big>(</big>[context]<big>)</big><a class="headerlink" href="#decimal.Decimal.normalize" title="Permalink to this definition">¶</a></dt> <dd>Normalize the number by stripping the rightmost trailing zeros and converting any result equal to <tt class="xref py py-const docutils literal">Decimal('0')</tt> to <tt class="xref py py-const docutils literal">Decimal('0e0')</tt>. Used for producing canonical values for attributes of an equivalence class. For example, <tt class="docutils literal">Decimal('32.100')</tt> and <tt class="docutils literal">Decimal('0.321000e+2')</tt> both normalize to the equivalent value <tt class="docutils literal">Decimal('32.1')</tt>. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.number_class"> <tt class="descname">number_class</tt><big>(</big>[context]<big>)</big><a class="headerlink" href="#decimal.Decimal.number_class" title="Permalink to this definition">¶</a></dt> <dd>Return a string describing the class of the operand. The returned value is one of the following ten strings. <ul class="simple"> <li><tt class="docutils literal">"-Infinity"</tt>, indicating that the operand is negative infinity.</li> <li><tt class="docutils literal">"-Normal"</tt>, indicating that the operand is a negative normal number.</li> <li><tt class="docutils literal">"-Subnormal"</tt>, indicating that the operand is negative and subnormal.</li> <li><tt class="docutils literal">"-Zero"</tt>, indicating that the operand is a negative zero.</li> <li><tt class="docutils literal">"+Zero"</tt>, indicating that the operand is a positive zero.</li> <li><tt class="docutils literal">"+Subnormal"</tt>, indicating that the operand is positive and subnormal.</li> <li><tt class="docutils literal">"+Normal"</tt>, indicating that the operand is a positive normal number.</li> <li><tt class="docutils literal">"+Infinity"</tt>, indicating that the operand is positive infinity.</li> <li><tt class="docutils literal">"NaN"</tt>, indicating that the operand is a quiet NaN (Not a Number).</li> <li><tt class="docutils literal">"sNaN"</tt>, indicating that the operand is a signaling NaN.</li> </ul> New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.quantize"> <tt class="descname">quantize</tt><big>(</big>exp[, rounding[, context[, watchexp]]]<big>)</big><a class="headerlink" href="#decimal.Decimal.quantize" title="Permalink to this definition">¶</a></dt> <dd>Return a value equal to the first operand after rounding and having the exponent of the second operand. <div class="highlight-python"><div class="highlight"><pre>>>> Decimal('1.41421356').quantize(Decimal('1.000')) Decimal('1.414') </pre></div> </div> Unlike other operations, if the length of the coefficient after the quantize operation would be greater than precision, then an <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><tt class="xref py py-const docutils literal">InvalidOperation</tt></a> is signaled. This guarantees that, unless there is an error condition, the quantized exponent is always equal to that of the right-hand operand. Also unlike other operations, quantize never signals Underflow, even if the result is subnormal and inexact. If the exponent of the second operand is larger than that of the first then rounding may be necessary. In this case, the rounding mode is determined by the <tt class="docutils literal">rounding</tt> argument if given, else by the given <tt class="docutils literal">context</tt> argument; if neither argument is given the rounding mode of the current thread’s context is used. If watchexp is set (default), then an error is returned whenever the resulting exponent is greater than <tt class="xref py py-attr docutils literal">Emax</tt> or less than <tt class="xref py py-attr docutils literal">Etiny</tt>. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.radix"> <tt class="descname">radix</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Decimal.radix" title="Permalink to this definition">¶</a></dt> <dd>Return <tt class="docutils literal">Decimal(10)</tt>, the radix (base) in which the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> class does all its arithmetic. Included for compatibility with the specification. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.remainder_near"> <tt class="descname">remainder_near</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.remainder_near" title="Permalink to this definition">¶</a></dt> <dd>Return the remainder from dividing self by other. This differs from <tt class="docutils literal">self % other</tt> in that the sign of the remainder is chosen so as to minimize its absolute value. More precisely, the return value is <tt class="docutils literal">self - n * other</tt> where <tt class="docutils literal">n</tt> is the integer nearest to the exact value of <tt class="docutils literal">self / other</tt>, and if two integers are equally near then the even one is chosen. If the result is zero then its sign will be the sign of self. <div class="highlight-python"><div class="highlight"><pre>>>> Decimal(18).remainder_near(Decimal(10)) Decimal('-2') >>> Decimal(25).remainder_near(Decimal(10)) Decimal('5') >>> Decimal(35).remainder_near(Decimal(10)) Decimal('-5') </pre></div> </div> </dd></dl> <dl class="method"> <dt id="decimal.Decimal.rotate"> <tt class="descname">rotate</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.rotate" title="Permalink to this definition">¶</a></dt> <dd>Return the result of rotating the digits of the first operand by an amount specified by the second operand. The second operand must be an integer in the range -precision through precision. The absolute value of the second operand gives the number of places to rotate. If the second operand is positive then rotation is to the left; otherwise rotation is to the right. The coefficient of the first operand is padded on the left with zeros to length precision if necessary. The sign and exponent of the first operand are unchanged. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.same_quantum"> <tt class="descname">same_quantum</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.same_quantum" title="Permalink to this definition">¶</a></dt> <dd>Test whether self and other have the same exponent or whether both are <tt class="xref py py-const docutils literal">NaN</tt>. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.scaleb"> <tt class="descname">scaleb</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.scaleb" title="Permalink to this definition">¶</a></dt> <dd>Return the first operand with exponent adjusted by the second. Equivalently, return the first operand multiplied by <tt class="docutils literal">10**other</tt>. The second operand must be an integer. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.shift"> <tt class="descname">shift</tt><big>(</big>other[, context]<big>)</big><a class="headerlink" href="#decimal.Decimal.shift" title="Permalink to this definition">¶</a></dt> <dd>Return the result of shifting the digits of the first operand by an amount specified by the second operand. The second operand must be an integer in the range -precision through precision. The absolute value of the second operand gives the number of places to shift. If the second operand is positive then the shift is to the left; otherwise the shift is to the right. Digits shifted into the coefficient are zeros. The sign and exponent of the first operand are unchanged. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.sqrt"> <tt class="descname">sqrt</tt><big>(</big>[context]<big>)</big><a class="headerlink" href="#decimal.Decimal.sqrt" title="Permalink to this definition">¶</a></dt> <dd>Return the square root of the argument to full precision. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.to_eng_string"> <tt class="descname">to_eng_string</tt><big>(</big>[context]<big>)</big><a class="headerlink" href="#decimal.Decimal.to_eng_string" title="Permalink to this definition">¶</a></dt> <dd>Convert to an engineering-type string. Engineering notation has an exponent which is a multiple of 3, so there are up to 3 digits left of the decimal place. For example, converts <tt class="docutils literal">Decimal('123E+1')</tt> to <tt class="docutils literal">Decimal('1.23E+3')</tt> </dd></dl> <dl class="method"> <dt id="decimal.Decimal.to_integral"> <tt class="descname">to_integral</tt><big>(</big>[rounding[, context]]<big>)</big><a class="headerlink" href="#decimal.Decimal.to_integral" title="Permalink to this definition">¶</a></dt> <dd>Identical to the <a class="reference internal" href="#decimal.Decimal.to_integral_value" title="decimal.Decimal.to_integral_value"><tt class="xref py py-meth docutils literal">to_integral_value()</tt></a> method. The <tt class="docutils literal">to_integral</tt> name has been kept for compatibility with older versions. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.to_integral_exact"> <tt class="descname">to_integral_exact</tt><big>(</big>[rounding[, context]]<big>)</big><a class="headerlink" href="#decimal.Decimal.to_integral_exact" title="Permalink to this definition">¶</a></dt> <dd>Round to the nearest integer, signaling <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><tt class="xref py py-const docutils literal">Inexact</tt></a> or <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><tt class="xref py py-const docutils literal">Rounded</tt></a> as appropriate if rounding occurs. The rounding mode is determined by the <tt class="docutils literal">rounding</tt> parameter if given, else by the given <tt class="docutils literal">context</tt>. If neither parameter is given then the rounding mode of the current context is used. New in version 2.6. </dd></dl> <dl class="method"> <dt id="decimal.Decimal.to_integral_value"> <tt class="descname">to_integral_value</tt><big>(</big>[rounding[, context]]<big>)</big><a class="headerlink" href="#decimal.Decimal.to_integral_value" title="Permalink to this definition">¶</a></dt> <dd>Round to the nearest integer without signaling <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><tt class="xref py py-const docutils literal">Inexact</tt></a> or <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><tt class="xref py py-const docutils literal">Rounded</tt></a>. If given, applies rounding; otherwise, uses the rounding method in either the supplied context or the current context. Changed in version 2.6: renamed from <tt class="docutils literal">to_integral</tt> to <tt class="docutils literal">to_integral_value</tt>. The old name remains valid for compatibility. </dd></dl> </dd></dl> <div class="section" id="logical-operands"> <h3>9.4.2.1. Logical operands<a class="headerlink" href="#logical-operands" title="Permalink to this headline">¶</a></h3> The <tt class="xref py py-meth docutils literal">logical_and()</tt>, <tt class="xref py py-meth docutils literal">logical_invert()</tt>, <tt class="xref py py-meth docutils literal">logical_or()</tt>, and <tt class="xref py py-meth docutils literal">logical_xor()</tt> methods expect their arguments to be logical operands. A logical operand is a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instance whose exponent and sign are both zero, and whose digits are all either <tt class="xref py py-const docutils literal">0</tt> or <tt class="xref py py-const docutils literal">1</tt>. </div> </div> <div class="section" id="context-objects"> <h2>9.4.3. Context objects<a class="headerlink" href="#context-objects" title="Permalink to this headline">¶</a></h2> Contexts are environments for arithmetic operations. They govern precision, set rules for rounding, determine which signals are treated as exceptions, and limit the range for exponents. Each thread has its own current context which is accessed or changed using the <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><tt class="xref py py-func docutils literal">getcontext()</tt></a> and <a class="reference internal" href="#decimal.setcontext" title="decimal.setcontext"><tt class="xref py py-func docutils literal">setcontext()</tt></a> functions: <dl class="function"> <dt id="decimal.getcontext"> <tt class="descclassname">decimal.</tt><tt class="descname">getcontext</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.getcontext" title="Permalink to this definition">¶</a></dt> <dd>Return the current context for the active thread. </dd></dl> <dl class="function"> <dt id="decimal.setcontext"> <tt class="descclassname">decimal.</tt><tt class="descname">setcontext</tt><big>(</big>c<big>)</big><a class="headerlink" href="#decimal.setcontext" title="Permalink to this definition">¶</a></dt> <dd>Set the current context for the active thread to c. </dd></dl> Beginning with Python 2.5, you can also use the <a class="reference internal" href="../reference/compound_stmts.html#with"><tt class="xref std std-keyword docutils literal">with</tt></a> statement and the <a class="reference internal" href="#decimal.localcontext" title="decimal.localcontext"><tt class="xref py py-func docutils literal">localcontext()</tt></a> function to temporarily change the active context. <dl class="function"> <dt id="decimal.localcontext"> <tt class="descclassname">decimal.</tt><tt class="descname">localcontext</tt><big>(</big>[c]<big>)</big><a class="headerlink" href="#decimal.localcontext" title="Permalink to this definition">¶</a></dt> <dd>Return a context manager that will set the current context for the active thread to a copy of c on entry to the with-statement and restore the previous context when exiting the with-statement. If no context is specified, a copy of the current context is used. New in version 2.5. For example, the following code sets the current decimal precision to 42 places, performs a calculation, and then automatically restores the previous context: <div class="highlight-python"><div class="highlight"><pre>from decimal import localcontext with localcontext() as ctx: ctx.prec = 42 # Perform a high precision calculation s = calculate_something() s = +s # Round the final result back to the default precision with localcontext(BasicContext): # temporarily use the BasicContext print Decimal(1) / Decimal(7) print Decimal(355) / Decimal(113) </pre></div> </div> </dd></dl> New contexts can also be created using the <a class="reference internal" href="#decimal.Context" title="decimal.Context"><tt class="xref py py-class docutils literal">Context</tt></a> constructor described below. In addition, the module provides three pre-made contexts: <dl class="class"> <dt id="decimal.BasicContext"> class <tt class="descclassname">decimal.</tt><tt class="descname">BasicContext</tt><a class="headerlink" href="#decimal.BasicContext" title="Permalink to this definition">¶</a></dt> <dd>This is a standard context defined by the General Decimal Arithmetic Specification. Precision is set to nine. Rounding is set to <tt class="xref py py-const docutils literal">ROUND_HALF_UP</tt>. All flags are cleared. All traps are enabled (treated as exceptions) except <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><tt class="xref py py-const docutils literal">Inexact</tt></a>, <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><tt class="xref py py-const docutils literal">Rounded</tt></a>, and <a class="reference internal" href="#decimal.Subnormal" title="decimal.Subnormal"><tt class="xref py py-const docutils literal">Subnormal</tt></a>. Because many of the traps are enabled, this context is useful for debugging. </dd></dl> <dl class="class"> <dt id="decimal.ExtendedContext"> class <tt class="descclassname">decimal.</tt><tt class="descname">ExtendedContext</tt><a class="headerlink" href="#decimal.ExtendedContext" title="Permalink to this definition">¶</a></dt> <dd>This is a standard context defined by the General Decimal Arithmetic Specification. Precision is set to nine. Rounding is set to <tt class="xref py py-const docutils literal">ROUND_HALF_EVEN</tt>. All flags are cleared. No traps are enabled (so that exceptions are not raised during computations). Because the traps are disabled, this context is useful for applications that prefer to have result value of <tt class="xref py py-const docutils literal">NaN</tt> or <tt class="xref py py-const docutils literal">Infinity</tt> instead of raising exceptions. This allows an application to complete a run in the presence of conditions that would otherwise halt the program. </dd></dl> <dl class="class"> <dt id="decimal.DefaultContext"> class <tt class="descclassname">decimal.</tt><tt class="descname">DefaultContext</tt><a class="headerlink" href="#decimal.DefaultContext" title="Permalink to this definition">¶</a></dt> <dd>This context is used by the <a class="reference internal" href="#decimal.Context" title="decimal.Context"><tt class="xref py py-class docutils literal">Context</tt></a> constructor as a prototype for new contexts. Changing a field (such a precision) has the effect of changing the default for new contexts created by the <a class="reference internal" href="#decimal.Context" title="decimal.Context"><tt class="xref py py-class docutils literal">Context</tt></a> constructor. This context is most useful in multi-threaded environments. Changing one of the fields before threads are started has the effect of setting system-wide defaults. Changing the fields after threads have started is not recommended as it would require thread synchronization to prevent race conditions. In single threaded environments, it is preferable to not use this context at all. Instead, simply create contexts explicitly as described below. The default values are precision=28, rounding=ROUND_HALF_EVEN, and enabled traps for Overflow, InvalidOperation, and DivisionByZero. </dd></dl> In addition to the three supplied contexts, new contexts can be created with the <a class="reference internal" href="#decimal.Context" title="decimal.Context"><tt class="xref py py-class docutils literal">Context</tt></a> constructor. <dl class="class"> <dt id="decimal.Context"> class <tt class="descclassname">decimal.</tt><tt class="descname">Context</tt><big>(</big>prec=None, rounding=None, traps=None, flags=None, Emin=None, Emax=None, capitals=1<big>)</big><a class="headerlink" href="#decimal.Context" title="Permalink to this definition">¶</a></dt> <dd>Creates a new context. If a field is not specified or is <a class="reference internal" href="constants.html#None" title="None"><tt class="xref py py-const docutils literal">None</tt></a>, the default values are copied from the <a class="reference internal" href="#decimal.DefaultContext" title="decimal.DefaultContext"><tt class="xref py py-const docutils literal">DefaultContext</tt></a>. If the flags field is not specified or is <a class="reference internal" href="constants.html#None" title="None"><tt class="xref py py-const docutils literal">None</tt></a>, all flags are cleared. The prec field is a positive integer that sets the precision for arithmetic operations in the context. The rounding option is one of: <ul class="simple"> <li><tt class="xref py py-const docutils literal">ROUND_CEILING</tt> (towards <tt class="xref py py-const docutils literal">Infinity</tt>),</li> <li><tt class="xref py py-const docutils literal">ROUND_DOWN</tt> (towards zero),</li> <li><tt class="xref py py-const docutils literal">ROUND_FLOOR</tt> (towards <tt class="xref py py-const docutils literal">-Infinity</tt>),</li> <li><tt class="xref py py-const docutils literal">ROUND_HALF_DOWN</tt> (to nearest with ties going towards zero),</li> <li><tt class="xref py py-const docutils literal">ROUND_HALF_EVEN</tt> (to nearest with ties going to nearest even integer),</li> <li><tt class="xref py py-const docutils literal">ROUND_HALF_UP</tt> (to nearest with ties going away from zero), or</li> <li><tt class="xref py py-const docutils literal">ROUND_UP</tt> (away from zero).</li> <li><tt class="xref py py-const docutils literal">ROUND_05UP</tt> (away from zero if last digit after rounding towards zero would have been 0 or 5; otherwise towards zero)</li> </ul> The traps and flags fields list any signals to be set. Generally, new contexts should only set traps and leave the flags clear. The Emin and Emax fields are integers specifying the outer limits allowable for exponents. The capitals field is either <tt class="xref py py-const docutils literal">0</tt> or <tt class="xref py py-const docutils literal">1</tt> (the default). If set to <tt class="xref py py-const docutils literal">1</tt>, exponents are printed with a capital <tt class="xref py py-const docutils literal">E</tt>; otherwise, a lowercase <tt class="xref py py-const docutils literal">e</tt> is used: <tt class="xref py py-const docutils literal">Decimal('6.02e+23')</tt>. Changed in version 2.6: The <tt class="xref py py-const docutils literal">ROUND_05UP</tt> rounding mode was added. The <a class="reference internal" href="#decimal.Context" title="decimal.Context"><tt class="xref py py-class docutils literal">Context</tt></a> class defines several general purpose methods as well as a large number of methods for doing arithmetic directly in a given context. In addition, for each of the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> methods described above (with the exception of the <tt class="xref py py-meth docutils literal">adjusted()</tt> and <tt class="xref py py-meth docutils literal">as_tuple()</tt> methods) there is a corresponding <a class="reference internal" href="#decimal.Context" title="decimal.Context"><tt class="xref py py-class docutils literal">Context</tt></a> method. For example, for a <a class="reference internal" href="#decimal.Context" title="decimal.Context"><tt class="xref py py-class docutils literal">Context</tt></a> instance <tt class="docutils literal">C</tt> and <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instance <tt class="docutils literal">x</tt>, <tt class="docutils literal">C.exp(x)</tt> is equivalent to <tt class="docutils literal">x.exp(context=C)</tt>. Each <a class="reference internal" href="#decimal.Context" title="decimal.Context"><tt class="xref py py-class docutils literal">Context</tt></a> method accepts a Python integer (an instance of <a class="reference internal" href="functions.html#int" title="int"><tt class="xref py py-class docutils literal">int</tt></a> or <a class="reference internal" href="functions.html#long" title="long"><tt class="xref py py-class docutils literal">long</tt></a>) anywhere that a Decimal instance is accepted. <dl class="method"> <dt id="decimal.Context.clear_flags"> <tt class="descname">clear_flags</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Context.clear_flags" title="Permalink to this definition">¶</a></dt> <dd>Resets all of the flags to <tt class="xref py py-const docutils literal">0</tt>. </dd></dl> <dl class="method"> <dt id="decimal.Context.copy"> <tt class="descname">copy</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Context.copy" title="Permalink to this definition">¶</a></dt> <dd>Return a duplicate of the context. </dd></dl> <dl class="method"> <dt id="decimal.Context.copy_decimal"> <tt class="descname">copy_decimal</tt><big>(</big>num<big>)</big><a class="headerlink" href="#decimal.Context.copy_decimal" title="Permalink to this definition">¶</a></dt> <dd>Return a copy of the Decimal instance num. </dd></dl> <dl class="method"> <dt id="decimal.Context.create_decimal"> <tt class="descname">create_decimal</tt><big>(</big>num<big>)</big><a class="headerlink" href="#decimal.Context.create_decimal" title="Permalink to this definition">¶</a></dt> <dd>Creates a new Decimal instance from num but using self as context. Unlike the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> constructor, the context precision, rounding method, flags, and traps are applied to the conversion. This is useful because constants are often given to a greater precision than is needed by the application. Another benefit is that rounding immediately eliminates unintended effects from digits beyond the current precision. In the following example, using unrounded inputs means that adding zero to a sum can change the result: <div class="highlight-python"><div class="highlight"><pre>>>> getcontext().prec = 3 >>> Decimal('3.4445') + Decimal('1.0023') Decimal('4.45') >>> Decimal('3.4445') + Decimal(0) + Decimal('1.0023') Decimal('4.44') </pre></div> </div> This method implements the to-number operation of the IBM specification. If the argument is a string, no leading or trailing whitespace is permitted. </dd></dl> <dl class="method"> <dt id="decimal.Context.create_decimal_from_float"> <tt class="descname">create_decimal_from_float</tt><big>(</big>f<big>)</big><a class="headerlink" href="#decimal.Context.create_decimal_from_float" title="Permalink to this definition">¶</a></dt> <dd>Creates a new Decimal instance from a float f but rounding using self as the context. Unlike the <a class="reference internal" href="#decimal.Decimal.from_float" title="decimal.Decimal.from_float"><tt class="xref py py-meth docutils literal">Decimal.from_float()</tt></a> class method, the context precision, rounding method, flags, and traps are applied to the conversion. <div class="highlight-python"><div class="highlight"><pre>>>> context = Context(prec=5, rounding=ROUND_DOWN) >>> context.create_decimal_from_float(math.pi) Decimal('3.1415') >>> context = Context(prec=5, traps=[Inexact]) >>> context.create_decimal_from_float(math.pi) Traceback (most recent call last): ... Inexact: None </pre></div> </div> New in version 2.7. </dd></dl> <dl class="method"> <dt id="decimal.Context.Etiny"> <tt class="descname">Etiny</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Context.Etiny" title="Permalink to this definition">¶</a></dt> <dd>Returns a value equal to <tt class="docutils literal">Emin - prec + 1</tt> which is the minimum exponent value for subnormal results. When underflow occurs, the exponent is set to <a class="reference internal" href="#decimal.Context.Etiny" title="decimal.Context.Etiny"><tt class="xref py py-const docutils literal">Etiny</tt></a>. </dd></dl> <dl class="method"> <dt id="decimal.Context.Etop"> <tt class="descname">Etop</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Context.Etop" title="Permalink to this definition">¶</a></dt> <dd>Returns a value equal to <tt class="docutils literal">Emax - prec + 1</tt>. </dd></dl> The usual approach to working with decimals is to create <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> instances and then apply arithmetic operations which take place within the current context for the active thread. An alternative approach is to use context methods for calculating within a specific context. The methods are similar to those for the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> class and are only briefly recounted here. <dl class="method"> <dt id="decimal.Context.abs"> <tt class="descname">abs</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.abs" title="Permalink to this definition">¶</a></dt> <dd>Returns the absolute value of x. </dd></dl> <dl class="method"> <dt id="decimal.Context.add"> <tt class="descname">add</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.add" title="Permalink to this definition">¶</a></dt> <dd>Return the sum of x and y. </dd></dl> <dl class="method"> <dt id="decimal.Context.canonical"> <tt class="descname">canonical</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.canonical" title="Permalink to this definition">¶</a></dt> <dd>Returns the same Decimal object x. </dd></dl> <dl class="method"> <dt id="decimal.Context.compare"> <tt class="descname">compare</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.compare" title="Permalink to this definition">¶</a></dt> <dd>Compares x and y numerically. </dd></dl> <dl class="method"> <dt id="decimal.Context.compare_signal"> <tt class="descname">compare_signal</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.compare_signal" title="Permalink to this definition">¶</a></dt> <dd>Compares the values of the two operands numerically. </dd></dl> <dl class="method"> <dt id="decimal.Context.compare_total"> <tt class="descname">compare_total</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.compare_total" title="Permalink to this definition">¶</a></dt> <dd>Compares two operands using their abstract representation. </dd></dl> <dl class="method"> <dt id="decimal.Context.compare_total_mag"> <tt class="descname">compare_total_mag</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.compare_total_mag" title="Permalink to this definition">¶</a></dt> <dd>Compares two operands using their abstract representation, ignoring sign. </dd></dl> <dl class="method"> <dt id="decimal.Context.copy_abs"> <tt class="descname">copy_abs</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.copy_abs" title="Permalink to this definition">¶</a></dt> <dd>Returns a copy of x with the sign set to 0. </dd></dl> <dl class="method"> <dt id="decimal.Context.copy_negate"> <tt class="descname">copy_negate</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.copy_negate" title="Permalink to this definition">¶</a></dt> <dd>Returns a copy of x with the sign inverted. </dd></dl> <dl class="method"> <dt id="decimal.Context.copy_sign"> <tt class="descname">copy_sign</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.copy_sign" title="Permalink to this definition">¶</a></dt> <dd>Copies the sign from y to x. </dd></dl> <dl class="method"> <dt id="decimal.Context.divide"> <tt class="descname">divide</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.divide" title="Permalink to this definition">¶</a></dt> <dd>Return x divided by y. </dd></dl> <dl class="method"> <dt id="decimal.Context.divide_int"> <tt class="descname">divide_int</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.divide_int" title="Permalink to this definition">¶</a></dt> <dd>Return x divided by y, truncated to an integer. </dd></dl> <dl class="method"> <dt id="decimal.Context.divmod"> <tt class="descname">divmod</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.divmod" title="Permalink to this definition">¶</a></dt> <dd>Divides two numbers and returns the integer part of the result. </dd></dl> <dl class="method"> <dt id="decimal.Context.exp"> <tt class="descname">exp</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.exp" title="Permalink to this definition">¶</a></dt> <dd>Returns <cite>e ** x</cite>. </dd></dl> <dl class="method"> <dt id="decimal.Context.fma"> <tt class="descname">fma</tt><big>(</big>x, y, z<big>)</big><a class="headerlink" href="#decimal.Context.fma" title="Permalink to this definition">¶</a></dt> <dd>Returns x multiplied by y, plus z. </dd></dl> <dl class="method"> <dt id="decimal.Context.is_canonical"> <tt class="descname">is_canonical</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.is_canonical" title="Permalink to this definition">¶</a></dt> <dd>Returns True if x is canonical; otherwise returns False. </dd></dl> <dl class="method"> <dt id="decimal.Context.is_finite"> <tt class="descname">is_finite</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.is_finite" title="Permalink to this definition">¶</a></dt> <dd>Returns True if x is finite; otherwise returns False. </dd></dl> <dl class="method"> <dt id="decimal.Context.is_infinite"> <tt class="descname">is_infinite</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.is_infinite" title="Permalink to this definition">¶</a></dt> <dd>Returns True if x is infinite; otherwise returns False. </dd></dl> <dl class="method"> <dt id="decimal.Context.is_nan"> <tt class="descname">is_nan</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.is_nan" title="Permalink to this definition">¶</a></dt> <dd>Returns True if x is a qNaN or sNaN; otherwise returns False. </dd></dl> <dl class="method"> <dt id="decimal.Context.is_normal"> <tt class="descname">is_normal</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.is_normal" title="Permalink to this definition">¶</a></dt> <dd>Returns True if x is a normal number; otherwise returns False. </dd></dl> <dl class="method"> <dt id="decimal.Context.is_qnan"> <tt class="descname">is_qnan</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.is_qnan" title="Permalink to this definition">¶</a></dt> <dd>Returns True if x is a quiet NaN; otherwise returns False. </dd></dl> <dl class="method"> <dt id="decimal.Context.is_signed"> <tt class="descname">is_signed</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.is_signed" title="Permalink to this definition">¶</a></dt> <dd>Returns True if x is negative; otherwise returns False. </dd></dl> <dl class="method"> <dt id="decimal.Context.is_snan"> <tt class="descname">is_snan</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.is_snan" title="Permalink to this definition">¶</a></dt> <dd>Returns True if x is a signaling NaN; otherwise returns False. </dd></dl> <dl class="method"> <dt id="decimal.Context.is_subnormal"> <tt class="descname">is_subnormal</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.is_subnormal" title="Permalink to this definition">¶</a></dt> <dd>Returns True if x is subnormal; otherwise returns False. </dd></dl> <dl class="method"> <dt id="decimal.Context.is_zero"> <tt class="descname">is_zero</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.is_zero" title="Permalink to this definition">¶</a></dt> <dd>Returns True if x is a zero; otherwise returns False. </dd></dl> <dl class="method"> <dt id="decimal.Context.ln"> <tt class="descname">ln</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.ln" title="Permalink to this definition">¶</a></dt> <dd>Returns the natural (base e) logarithm of x. </dd></dl> <dl class="method"> <dt id="decimal.Context.log10"> <tt class="descname">log10</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.log10" title="Permalink to this definition">¶</a></dt> <dd>Returns the base 10 logarithm of x. </dd></dl> <dl class="method"> <dt id="decimal.Context.logb"> <tt class="descname">logb</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.logb" title="Permalink to this definition">¶</a></dt> <dd>Returns the exponent of the magnitude of the operand’s MSD. </dd></dl> <dl class="method"> <dt id="decimal.Context.logical_and"> <tt class="descname">logical_and</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.logical_and" title="Permalink to this definition">¶</a></dt> <dd>Applies the logical operation and between each operand’s digits. </dd></dl> <dl class="method"> <dt id="decimal.Context.logical_invert"> <tt class="descname">logical_invert</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.logical_invert" title="Permalink to this definition">¶</a></dt> <dd>Invert all the digits in x. </dd></dl> <dl class="method"> <dt id="decimal.Context.logical_or"> <tt class="descname">logical_or</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.logical_or" title="Permalink to this definition">¶</a></dt> <dd>Applies the logical operation or between each operand’s digits. </dd></dl> <dl class="method"> <dt id="decimal.Context.logical_xor"> <tt class="descname">logical_xor</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.logical_xor" title="Permalink to this definition">¶</a></dt> <dd>Applies the logical operation xor between each operand’s digits. </dd></dl> <dl class="method"> <dt id="decimal.Context.max"> <tt class="descname">max</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.max" title="Permalink to this definition">¶</a></dt> <dd>Compares two values numerically and returns the maximum. </dd></dl> <dl class="method"> <dt id="decimal.Context.max_mag"> <tt class="descname">max_mag</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.max_mag" title="Permalink to this definition">¶</a></dt> <dd>Compares the values numerically with their sign ignored. </dd></dl> <dl class="method"> <dt id="decimal.Context.min"> <tt class="descname">min</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.min" title="Permalink to this definition">¶</a></dt> <dd>Compares two values numerically and returns the minimum. </dd></dl> <dl class="method"> <dt id="decimal.Context.min_mag"> <tt class="descname">min_mag</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.min_mag" title="Permalink to this definition">¶</a></dt> <dd>Compares the values numerically with their sign ignored. </dd></dl> <dl class="method"> <dt id="decimal.Context.minus"> <tt class="descname">minus</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.minus" title="Permalink to this definition">¶</a></dt> <dd>Minus corresponds to the unary prefix minus operator in Python. </dd></dl> <dl class="method"> <dt id="decimal.Context.multiply"> <tt class="descname">multiply</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.multiply" title="Permalink to this definition">¶</a></dt> <dd>Return the product of x and y. </dd></dl> <dl class="method"> <dt id="decimal.Context.next_minus"> <tt class="descname">next_minus</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.next_minus" title="Permalink to this definition">¶</a></dt> <dd>Returns the largest representable number smaller than x. </dd></dl> <dl class="method"> <dt id="decimal.Context.next_plus"> <tt class="descname">next_plus</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.next_plus" title="Permalink to this definition">¶</a></dt> <dd>Returns the smallest representable number larger than x. </dd></dl> <dl class="method"> <dt id="decimal.Context.next_toward"> <tt class="descname">next_toward</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.next_toward" title="Permalink to this definition">¶</a></dt> <dd>Returns the number closest to x, in direction towards y. </dd></dl> <dl class="method"> <dt id="decimal.Context.normalize"> <tt class="descname">normalize</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.normalize" title="Permalink to this definition">¶</a></dt> <dd>Reduces x to its simplest form. </dd></dl> <dl class="method"> <dt id="decimal.Context.number_class"> <tt class="descname">number_class</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.number_class" title="Permalink to this definition">¶</a></dt> <dd>Returns an indication of the class of x. </dd></dl> <dl class="method"> <dt id="decimal.Context.plus"> <tt class="descname">plus</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.plus" title="Permalink to this definition">¶</a></dt> <dd>Plus corresponds to the unary prefix plus operator in Python. This operation applies the context precision and rounding, so it is not an identity operation. </dd></dl> <dl class="method"> <dt id="decimal.Context.power"> <tt class="descname">power</tt><big>(</big>x, y[, modulo]<big>)</big><a class="headerlink" href="#decimal.Context.power" title="Permalink to this definition">¶</a></dt> <dd>Return <tt class="docutils literal">x</tt> to the power of <tt class="docutils literal">y</tt>, reduced modulo <tt class="docutils literal">modulo</tt> if given. With two arguments, compute <tt class="docutils literal">x**y</tt>. If <tt class="docutils literal">x</tt> is negative then <tt class="docutils literal">y</tt> must be integral. The result will be inexact unless <tt class="docutils literal">y</tt> is integral and the result is finite and can be expressed exactly in ‘precision’ digits. The result should always be correctly rounded, using the rounding mode of the current thread’s context. With three arguments, compute <tt class="docutils literal">(x**y) % modulo</tt>. For the three argument form, the following restrictions on the arguments hold: <blockquote> <div><ul class="simple"> <li>all three arguments must be integral</li> <li><tt class="docutils literal">y</tt> must be nonnegative</li> <li>at least one of <tt class="docutils literal">x</tt> or <tt class="docutils literal">y</tt> must be nonzero</li> <li><tt class="docutils literal">modulo</tt> must be nonzero and have at most ‘precision’ digits</li> </ul> </div></blockquote> The value resulting from <tt class="docutils literal">Context.power(x, y, modulo)</tt> is equal to the value that would be obtained by computing <tt class="docutils literal">(x**y) % modulo</tt> with unbounded precision, but is computed more efficiently. The exponent of the result is zero, regardless of the exponents of <tt class="docutils literal">x</tt>, <tt class="docutils literal">y</tt> and <tt class="docutils literal">modulo</tt>. The result is always exact. Changed in version 2.6: <tt class="docutils literal">y</tt> may now be nonintegral in <tt class="docutils literal">x**y</tt>. Stricter requirements for the three-argument version. </dd></dl> <dl class="method"> <dt id="decimal.Context.quantize"> <tt class="descname">quantize</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.quantize" title="Permalink to this definition">¶</a></dt> <dd>Returns a value equal to x (rounded), having the exponent of y. </dd></dl> <dl class="method"> <dt id="decimal.Context.radix"> <tt class="descname">radix</tt><big>(</big><big>)</big><a class="headerlink" href="#decimal.Context.radix" title="Permalink to this definition">¶</a></dt> <dd>Just returns 10, as this is Decimal, :) </dd></dl> <dl class="method"> <dt id="decimal.Context.remainder"> <tt class="descname">remainder</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.remainder" title="Permalink to this definition">¶</a></dt> <dd>Returns the remainder from integer division. The sign of the result, if non-zero, is the same as that of the original dividend. </dd></dl> <dl class="method"> <dt id="decimal.Context.remainder_near"> <tt class="descname">remainder_near</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.remainder_near" title="Permalink to this definition">¶</a></dt> <dd>Returns <tt class="docutils literal">x - y * n</tt>, where n is the integer nearest the exact value of <tt class="docutils literal">x / y</tt> (if the result is 0 then its sign will be the sign of x). </dd></dl> <dl class="method"> <dt id="decimal.Context.rotate"> <tt class="descname">rotate</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.rotate" title="Permalink to this definition">¶</a></dt> <dd>Returns a rotated copy of x, y times. </dd></dl> <dl class="method"> <dt id="decimal.Context.same_quantum"> <tt class="descname">same_quantum</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.same_quantum" title="Permalink to this definition">¶</a></dt> <dd>Returns True if the two operands have the same exponent. </dd></dl> <dl class="method"> <dt id="decimal.Context.scaleb"> <tt class="descname">scaleb</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.scaleb" title="Permalink to this definition">¶</a></dt> <dd>Returns the first operand after adding the second value its exp. </dd></dl> <dl class="method"> <dt id="decimal.Context.shift"> <tt class="descname">shift</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.shift" title="Permalink to this definition">¶</a></dt> <dd>Returns a shifted copy of x, y times. </dd></dl> <dl class="method"> <dt id="decimal.Context.sqrt"> <tt class="descname">sqrt</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.sqrt" title="Permalink to this definition">¶</a></dt> <dd>Square root of a non-negative number to context precision. </dd></dl> <dl class="method"> <dt id="decimal.Context.subtract"> <tt class="descname">subtract</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#decimal.Context.subtract" title="Permalink to this definition">¶</a></dt> <dd>Return the difference between x and y. </dd></dl> <dl class="method"> <dt id="decimal.Context.to_eng_string"> <tt class="descname">to_eng_string</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.to_eng_string" title="Permalink to this definition">¶</a></dt> <dd>Converts a number to a string, using scientific notation. </dd></dl> <dl class="method"> <dt id="decimal.Context.to_integral_exact"> <tt class="descname">to_integral_exact</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.to_integral_exact" title="Permalink to this definition">¶</a></dt> <dd>Rounds to an integer. </dd></dl> <dl class="method"> <dt id="decimal.Context.to_sci_string"> <tt class="descname">to_sci_string</tt><big>(</big>x<big>)</big><a class="headerlink" href="#decimal.Context.to_sci_string" title="Permalink to this definition">¶</a></dt> <dd>Converts a number to a string using scientific notation. </dd></dl> </dd></dl> </div> <div class="section" id="signals"> <h2>9.4.4. Signals<a class="headerlink" href="#signals" title="Permalink to this headline">¶</a></h2> Signals represent conditions that arise during computation. Each corresponds to one context flag and one context trap enabler. The context flag is set whenever the condition is encountered. After the computation, flags may be checked for informational purposes (for instance, to determine whether a computation was exact). After checking the flags, be sure to clear all flags before starting the next computation. If the context’s trap enabler is set for the signal, then the condition causes a Python exception to be raised. For example, if the <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><tt class="xref py py-class docutils literal">DivisionByZero</tt></a> trap is set, then a <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><tt class="xref py py-exc docutils literal">DivisionByZero</tt></a> exception is raised upon encountering the condition. <dl class="class"> <dt id="decimal.Clamped"> class <tt class="descclassname">decimal.</tt><tt class="descname">Clamped</tt><a class="headerlink" href="#decimal.Clamped" title="Permalink to this definition">¶</a></dt> <dd>Altered an exponent to fit representation constraints. Typically, clamping occurs when an exponent falls outside the context’s <tt class="xref py py-attr docutils literal">Emin</tt> and <tt class="xref py py-attr docutils literal">Emax</tt> limits. If possible, the exponent is reduced to fit by adding zeros to the coefficient. </dd></dl> <dl class="class"> <dt id="decimal.DecimalException"> class <tt class="descclassname">decimal.</tt><tt class="descname">DecimalException</tt><a class="headerlink" href="#decimal.DecimalException" title="Permalink to this definition">¶</a></dt> <dd>Base class for other signals and a subclass of <a class="reference internal" href="exceptions.html#exceptions.ArithmeticError" title="exceptions.ArithmeticError"><tt class="xref py py-exc docutils literal">ArithmeticError</tt></a>. </dd></dl> <dl class="class"> <dt id="decimal.DivisionByZero"> class <tt class="descclassname">decimal.</tt><tt class="descname">DivisionByZero</tt><a class="headerlink" href="#decimal.DivisionByZero" title="Permalink to this definition">¶</a></dt> <dd>Signals the division of a non-infinite number by zero. Can occur with division, modulo division, or when raising a number to a negative power. If this signal is not trapped, returns <tt class="xref py py-const docutils literal">Infinity</tt> or <tt class="xref py py-const docutils literal">-Infinity</tt> with the sign determined by the inputs to the calculation. </dd></dl> <dl class="class"> <dt id="decimal.Inexact"> class <tt class="descclassname">decimal.</tt><tt class="descname">Inexact</tt><a class="headerlink" href="#decimal.Inexact" title="Permalink to this definition">¶</a></dt> <dd>Indicates that rounding occurred and the result is not exact. Signals when non-zero digits were discarded during rounding. The rounded result is returned. The signal flag or trap is used to detect when results are inexact. </dd></dl> <dl class="class"> <dt id="decimal.InvalidOperation"> class <tt class="descclassname">decimal.</tt><tt class="descname">InvalidOperation</tt><a class="headerlink" href="#decimal.InvalidOperation" title="Permalink to this definition">¶</a></dt> <dd>An invalid operation was performed. Indicates that an operation was requested that does not make sense. If not trapped, returns <tt class="xref py py-const docutils literal">NaN</tt>. Possible causes include: <div class="highlight-python"><div class="highlight"><pre>Infinity - Infinity 0 * Infinity Infinity / Infinity x % 0 Infinity % x x._rescale( non-integer ) sqrt(-x) and x > 0 0 ** 0 x ** (non-integer) x ** Infinity </pre></div> </div> </dd></dl> <dl class="class"> <dt id="decimal.Overflow"> class <tt class="descclassname">decimal.</tt><tt class="descname">Overflow</tt><a class="headerlink" href="#decimal.Overflow" title="Permalink to this definition">¶</a></dt> <dd>Numerical overflow. Indicates the exponent is larger than <tt class="xref py py-attr docutils literal">Emax</tt> after rounding has occurred. If not trapped, the result depends on the rounding mode, either pulling inward to the largest representable finite number or rounding outward to <tt class="xref py py-const docutils literal">Infinity</tt>. In either case, <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><tt class="xref py py-class docutils literal">Inexact</tt></a> and <a class="reference internal" href="#decimal.Rounded" title="decimal.Rounded"><tt class="xref py py-class docutils literal">Rounded</tt></a> are also signaled. </dd></dl> <dl class="class"> <dt id="decimal.Rounded"> class <tt class="descclassname">decimal.</tt><tt class="descname">Rounded</tt><a class="headerlink" href="#decimal.Rounded" title="Permalink to this definition">¶</a></dt> <dd>Rounding occurred though possibly no information was lost. Signaled whenever rounding discards digits; even if those digits are zero (such as rounding <tt class="xref py py-const docutils literal">5.00</tt> to <tt class="xref py py-const docutils literal">5.0</tt>). If not trapped, returns the result unchanged. This signal is used to detect loss of significant digits. </dd></dl> <dl class="class"> <dt id="decimal.Subnormal"> class <tt class="descclassname">decimal.</tt><tt class="descname">Subnormal</tt><a class="headerlink" href="#decimal.Subnormal" title="Permalink to this definition">¶</a></dt> <dd>Exponent was lower than <tt class="xref py py-attr docutils literal">Emin</tt> prior to rounding. Occurs when an operation result is subnormal (the exponent is too small). If not trapped, returns the result unchanged. </dd></dl> <dl class="class"> <dt id="decimal.Underflow"> class <tt class="descclassname">decimal.</tt><tt class="descname">Underflow</tt><a class="headerlink" href="#decimal.Underflow" title="Permalink to this definition">¶</a></dt> <dd>Numerical underflow with result rounded to zero. Occurs when a subnormal result is pushed to zero by rounding. <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><tt class="xref py py-class docutils literal">Inexact</tt></a> and <a class="reference internal" href="#decimal.Subnormal" title="decimal.Subnormal"><tt class="xref py py-class docutils literal">Subnormal</tt></a> are also signaled. </dd></dl> The following table summarizes the hierarchy of signals: <div class="highlight-python"><pre>exceptions.ArithmeticError(exceptions.StandardError) DecimalException Clamped DivisionByZero(DecimalException, exceptions.ZeroDivisionError) Inexact Overflow(Inexact, Rounded) Underflow(Inexact, Rounded, Subnormal) InvalidOperation Rounded Subnormal</pre> </div> </div> <div class="section" id="floating-point-notes"> <h2>9.4.5. Floating Point Notes<a class="headerlink" href="#floating-point-notes" title="Permalink to this headline">¶</a></h2> <div class="section" id="mitigating-round-off-error-with-increased-precision"> <h3>9.4.5.1. Mitigating round-off error with increased precision<a class="headerlink" href="#mitigating-round-off-error-with-increased-precision" title="Permalink to this headline">¶</a></h3> The use of decimal floating point eliminates decimal representation error (making it possible to represent <tt class="xref py py-const docutils literal">0.1</tt> exactly); however, some operations can still incur round-off error when non-zero digits exceed the fixed precision. The effects of round-off error can be amplified by the addition or subtraction of nearly offsetting quantities resulting in loss of significance. Knuth provides two instructive examples where rounded floating point arithmetic with insufficient precision causes the breakdown of the associative and distributive properties of addition: <div class="highlight-python"><pre># Examples from Seminumerical Algorithms, Section 4.2.2. >>> from decimal import Decimal, getcontext >>> getcontext().prec = 8 >>> u, v, w = Decimal(11111113), Decimal(-11111111), Decimal('7.51111111') >>> (u + v) + w Decimal('9.5111111') >>> u + (v + w) Decimal('10') >>> u, v, w = Decimal(20000), Decimal(-6), Decimal('6.0000003') >>> (u*v) + (u*w) Decimal('0.01') >>> u * (v+w) Decimal('0.0060000')</pre> </div> The <a class="reference internal" href="#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic Specification."><tt class="xref py py-mod docutils literal">decimal</tt></a> module makes it possible to restore the identities by expanding the precision sufficiently to avoid loss of significance: <div class="highlight-python"><div class="highlight"><pre>>>> getcontext().prec = 20 >>> u, v, w = Decimal(11111113), Decimal(-11111111), Decimal('7.51111111') >>> (u + v) + w Decimal('9.51111111') >>> u + (v + w) Decimal('9.51111111') >>> >>> u, v, w = Decimal(20000), Decimal(-6), Decimal('6.0000003') >>> (u*v) + (u*w) Decimal('0.0060000') >>> u * (v+w) Decimal('0.0060000') </pre></div> </div> </div> <div class="section" id="special-values"> <h3>9.4.5.2. Special values<a class="headerlink" href="#special-values" title="Permalink to this headline">¶</a></h3> The number system for the <a class="reference internal" href="#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic Specification."><tt class="xref py py-mod docutils literal">decimal</tt></a> module provides special values including <tt class="xref py py-const docutils literal">NaN</tt>, <tt class="xref py py-const docutils literal">sNaN</tt>, <tt class="xref py py-const docutils literal">-Infinity</tt>, <tt class="xref py py-const docutils literal">Infinity</tt>, and two zeros, <tt class="xref py py-const docutils literal">+0</tt> and <tt class="xref py py-const docutils literal">-0</tt>. Infinities can be constructed directly with: <tt class="docutils literal">Decimal('Infinity')</tt>. Also, they can arise from dividing by zero when the <a class="reference internal" href="#decimal.DivisionByZero" title="decimal.DivisionByZero"><tt class="xref py py-exc docutils literal">DivisionByZero</tt></a> signal is not trapped. Likewise, when the <a class="reference internal" href="#decimal.Overflow" title="decimal.Overflow"><tt class="xref py py-exc docutils literal">Overflow</tt></a> signal is not trapped, infinity can result from rounding beyond the limits of the largest representable number. The infinities are signed (affine) and can be used in arithmetic operations where they get treated as very large, indeterminate numbers. For instance, adding a constant to infinity gives another infinite result. Some operations are indeterminate and return <tt class="xref py py-const docutils literal">NaN</tt>, or if the <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><tt class="xref py py-exc docutils literal">InvalidOperation</tt></a> signal is trapped, raise an exception. For example, <tt class="docutils literal">0/0</tt> returns <tt class="xref py py-const docutils literal">NaN</tt> which means “not a number”. This variety of <tt class="xref py py-const docutils literal">NaN</tt> is quiet and, once created, will flow through other computations always resulting in another <tt class="xref py py-const docutils literal">NaN</tt>. This behavior can be useful for a series of computations that occasionally have missing inputs — it allows the calculation to proceed while flagging specific results as invalid. A variant is <tt class="xref py py-const docutils literal">sNaN</tt> which signals rather than remaining quiet after every operation. This is a useful return value when an invalid result needs to interrupt a calculation for special handling. The behavior of Python’s comparison operators can be a little surprising where a <tt class="xref py py-const docutils literal">NaN</tt> is involved. A test for equality where one of the operands is a quiet or signaling <tt class="xref py py-const docutils literal">NaN</tt> always returns <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> (even when doing <tt class="docutils literal">Decimal('NaN')==Decimal('NaN')</tt>), while a test for inequality always returns <a class="reference internal" href="constants.html#True" title="True"><tt class="xref py py-const docutils literal">True</tt></a>. An attempt to compare two Decimals using any of the <tt class="docutils literal"><</tt>, <tt class="docutils literal"><=</tt>, <tt class="docutils literal">></tt> or <tt class="docutils literal">>=</tt> operators will raise the <a class="reference internal" href="#decimal.InvalidOperation" title="decimal.InvalidOperation"><tt class="xref py py-exc docutils literal">InvalidOperation</tt></a> signal if either operand is a <tt class="xref py py-const docutils literal">NaN</tt>, and return <a class="reference internal" href="constants.html#False" title="False"><tt class="xref py py-const docutils literal">False</tt></a> if this signal is not trapped. Note that the General Decimal Arithmetic specification does not specify the behavior of direct comparisons; these rules for comparisons involving a <tt class="xref py py-const docutils literal">NaN</tt> were taken from the IEEE 854 standard (see Table 3 in section 5.7). To ensure strict standards-compliance, use the <tt class="xref py py-meth docutils literal">compare()</tt> and <tt class="xref py py-meth docutils literal">compare-signal()</tt> methods instead. The signed zeros can result from calculations that underflow. They keep the sign that would have resulted if the calculation had been carried out to greater precision. Since their magnitude is zero, both positive and negative zeros are treated as equal and their sign is informational. In addition to the two signed zeros which are distinct yet equal, there are various representations of zero with differing precisions yet equivalent in value. This takes a bit of getting used to. For an eye accustomed to normalized floating point representations, it is not immediately obvious that the following calculation returns a value equal to zero: <div class="highlight-python"><div class="highlight"><pre>>>> 1 / Decimal('Infinity') Decimal('0E-1000000026') </pre></div> </div> </div> </div> <div class="section" id="working-with-threads"> <h2>9.4.6. Working with threads<a class="headerlink" href="#working-with-threads" title="Permalink to this headline">¶</a></h2> The <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><tt class="xref py py-func docutils literal">getcontext()</tt></a> function accesses a different <a class="reference internal" href="#decimal.Context" title="decimal.Context"><tt class="xref py py-class docutils literal">Context</tt></a> object for each thread. Having separate thread contexts means that threads may make changes (such as <tt class="docutils literal">getcontext.prec=10</tt>) without interfering with other threads. Likewise, the <a class="reference internal" href="#decimal.setcontext" title="decimal.setcontext"><tt class="xref py py-func docutils literal">setcontext()</tt></a> function automatically assigns its target to the current thread. If <a class="reference internal" href="#decimal.setcontext" title="decimal.setcontext"><tt class="xref py py-func docutils literal">setcontext()</tt></a> has not been called before <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><tt class="xref py py-func docutils literal">getcontext()</tt></a>, then <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><tt class="xref py py-func docutils literal">getcontext()</tt></a> will automatically create a new context for use in the current thread. The new context is copied from a prototype context called DefaultContext. To control the defaults so that each thread will use the same values throughout the application, directly modify the DefaultContext object. This should be done before any threads are started so that there won’t be a race condition between threads calling <a class="reference internal" href="#decimal.getcontext" title="decimal.getcontext"><tt class="xref py py-func docutils literal">getcontext()</tt></a>. For example: <div class="highlight-python"><pre># Set applicationwide defaults for all threads about to be launched DefaultContext.prec = 12 DefaultContext.rounding = ROUND_DOWN DefaultContext.traps = ExtendedContext.traps.copy() DefaultContext.traps[InvalidOperation] = 1 setcontext(DefaultContext) # Afterwards, the threads can be started t1.start() t2.start() t3.start() . . .</pre> </div> </div> <div class="section" id="recipes"> <h2>9.4.7. Recipes<a class="headerlink" href="#recipes" title="Permalink to this headline">¶</a></h2> Here are a few recipes that serve as utility functions and that demonstrate ways to work with the <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a> class: <div class="highlight-python"><div class="highlight"><pre>def moneyfmt(value, places=2, curr='', sep=',', dp='.', pos='', neg='-', trailneg=''): """Convert Decimal to a money formatted string. places: required number of places after the decimal point curr: optional currency symbol before the sign (may be blank) sep: optional grouping separator (comma, period, space, or blank) dp: decimal point indicator (comma or period) only specify as blank when places is zero pos: optional sign for positive numbers: '+', space or blank neg: optional sign for negative numbers: '-', '(', space or blank trailneg:optional trailing minus indicator: '-', ')', space or blank >>> d = Decimal('-1234567.8901') >>> moneyfmt(d, curr='$') '-$1,234,567.89' >>> moneyfmt(d, places=0, sep='.', dp='', neg='', trailneg='-') '1.234.568-' >>> moneyfmt(d, curr='$', neg='(', trailneg=')') '($1,234,567.89)' >>> moneyfmt(Decimal(123456789), sep=' ') '123 456 789.00' >>> moneyfmt(Decimal('-0.02'), neg='<', trailneg='>') '<0.02>' """ q = Decimal(10) ** -places # 2 places --> '0.01' sign, digits, exp = value.quantize(q).as_tuple() result = [] digits = map(str, digits) build, next = result.append, digits.pop if sign: build(trailneg) for i in range(places): build(next() if digits else '0') build(dp) if not digits: build('0') i = 0 while digits: build(next()) i += 1 if i == 3 and digits: i = 0 build(sep) build(curr) build(neg if sign else pos) return ''.join(reversed(result)) def pi(): """Compute Pi to the current precision. >>> print pi() 3.141592653589793238462643383 """ getcontext().prec += 2 # extra digits for intermediate steps three = Decimal(3) # substitute "three=3.0" for regular floats lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24 while s != lasts: lasts = s n, na = n+na, na+8 d, da = d+da, da+32 t = (t * n) / d s += t getcontext().prec -= 2 return +s # unary plus applies the new precision def exp(x): """Return e raised to the power of x. Result type matches input type. >>> print exp(Decimal(1)) 2.718281828459045235360287471 >>> print exp(Decimal(2)) 7.389056098930650227230427461 >>> print exp(2.0) 7.38905609893 >>> print exp(2+0j) (7.38905609893+0j) """ getcontext().prec += 2 i, lasts, s, fact, num = 0, 0, 1, 1, 1 while s != lasts: lasts = s i += 1 fact *= i num *= x s += num / fact getcontext().prec -= 2 return +s def cos(x): """Return the cosine of x as measured in radians. >>> print cos(Decimal('0.5')) 0.8775825618903727161162815826 >>> print cos(0.5) 0.87758256189 >>> print cos(0.5+0j) (0.87758256189+0j) """ getcontext().prec += 2 i, lasts, s, fact, num, sign = 0, 0, 1, 1, 1, 1 while s != lasts: lasts = s i += 2 fact *= i * (i-1) num *= x * x sign *= -1 s += num / fact * sign getcontext().prec -= 2 return +s def sin(x): """Return the sine of x as measured in radians. >>> print sin(Decimal('0.5')) 0.4794255386042030002732879352 >>> print sin(0.5) 0.479425538604 >>> print sin(0.5+0j) (0.479425538604+0j) """ getcontext().prec += 2 i, lasts, s, fact, num, sign = 1, 0, x, 1, x, 1 while s != lasts: lasts = s i += 2 fact *= i * (i-1) num *= x * x sign *= -1 s += num / fact * sign getcontext().prec -= 2 return +s </pre></div> </div> </div> <div class="section" id="decimal-faq"> <h2>9.4.8. Decimal FAQ<a class="headerlink" href="#decimal-faq" title="Permalink to this headline">¶</a></h2> Q. It is cumbersome to type <tt class="docutils literal">decimal.Decimal('1234.5')</tt>. Is there a way to minimize typing when using the interactive interpreter? A. Some users abbreviate the constructor to just a single letter: <div class="highlight-python"><div class="highlight"><pre>>>> D = decimal.Decimal >>> D('1.23') + D('3.45') Decimal('4.68') </pre></div> </div> Q. In a fixed-point application with two decimal places, some inputs have many places and need to be rounded. Others are not supposed to have excess digits and need to be validated. What methods should be used? A. The <tt class="xref py py-meth docutils literal">quantize()</tt> method rounds to a fixed number of decimal places. If the <a class="reference internal" href="#decimal.Inexact" title="decimal.Inexact"><tt class="xref py py-const docutils literal">Inexact</tt></a> trap is set, it is also useful for validation: <div class="highlight-python"><div class="highlight"><pre>>>> TWOPLACES = Decimal(10) ** -2 # same as Decimal('0.01') </pre></div> </div> <div class="highlight-python"><div class="highlight"><pre>>>> # Round to two places >>> Decimal('3.214').quantize(TWOPLACES) Decimal('3.21') </pre></div> </div> <div class="highlight-python"><div class="highlight"><pre>>>> # Validate that a number does not exceed two places >>> Decimal('3.21').quantize(TWOPLACES, context=Context(traps=[Inexact])) Decimal('3.21') </pre></div> </div> <div class="highlight-python"><div class="highlight"><pre>>>> Decimal('3.214').quantize(TWOPLACES, context=Context(traps=[Inexact])) Traceback (most recent call last): ... Inexact: None </pre></div> </div> Q. Once I have valid two place inputs, how do I maintain that invariant throughout an application? A. Some operations like addition, subtraction, and multiplication by an integer will automatically preserve fixed point. Others operations, like division and non-integer multiplication, will change the number of decimal places and need to be followed-up with a <tt class="xref py py-meth docutils literal">quantize()</tt> step: <div class="highlight-python"><div class="highlight"><pre>>>> a = Decimal('102.72') # Initial fixed-point values >>> b = Decimal('3.17') >>> a + b # Addition preserves fixed-point Decimal('105.89') >>> a - b Decimal('99.55') >>> a * 42 # So does integer multiplication Decimal('4314.24') >>> (a * b).quantize(TWOPLACES) # Must quantize non-integer multiplication Decimal('325.62') >>> (b / a).quantize(TWOPLACES) # And quantize division Decimal('0.03') </pre></div> </div> In developing fixed-point applications, it is convenient to define functions to handle the <tt class="xref py py-meth docutils literal">quantize()</tt> step: <div class="highlight-python"><div class="highlight"><pre>>>> def mul(x, y, fp=TWOPLACES): ... return (x * y).quantize(fp) >>> def div(x, y, fp=TWOPLACES): ... return (x / y).quantize(fp) </pre></div> </div> <div class="highlight-python"><div class="highlight"><pre>>>> mul(a, b) # Automatically preserve fixed-point Decimal('325.62') >>> div(b, a) Decimal('0.03') </pre></div> </div> Q. There are many ways to express the same value. The numbers <tt class="xref py py-const docutils literal">200</tt>, <tt class="xref py py-const docutils literal">200.000</tt>, <tt class="xref py py-const docutils literal">2E2</tt>, and <tt class="xref py py-const docutils literal">02E+4</tt> all have the same value at various precisions. Is there a way to transform them to a single recognizable canonical value? A. The <tt class="xref py py-meth docutils literal">normalize()</tt> method maps all equivalent values to a single representative: <div class="highlight-python"><div class="highlight"><pre>>>> values = map(Decimal, '200 200.000 2E2 .02E+4'.split()) >>> [v.normalize() for v in values] [Decimal('2E+2'), Decimal('2E+2'), Decimal('2E+2'), Decimal('2E+2')] </pre></div> </div> Q. Some decimal values always print with exponential notation. Is there a way to get a non-exponential representation? A. For some values, exponential notation is the only way to express the number of significant places in the coefficient. For example, expressing <tt class="xref py py-const docutils literal">5.0E+3</tt> as <tt class="xref py py-const docutils literal">5000</tt> keeps the value constant but cannot show the original’s two-place significance. If an application does not care about tracking significance, it is easy to remove the exponent and trailing zeros, losing significance, but keeping the value unchanged: <div class="highlight-python"><div class="highlight"><pre>def remove_exponent(d): '''Remove exponent and trailing zeros. >>> remove_exponent(Decimal('5E+3')) Decimal('5000') ''' return d.quantize(Decimal(1)) if d == d.to_integral() else d.normalize() </pre></div> </div> Q. Is there a way to convert a regular float to a <a class="reference internal" href="#decimal.Decimal" title="decimal.Decimal"><tt class="xref py py-class docutils literal">Decimal</tt></a>? A. Yes, any binary floating point number can be exactly expressed as a Decimal though an exact conversion may take more precision than intuition would suggest: <div class="highlight-python"><div class="highlight"><pre>>>> Decimal(math.pi) Decimal('3.141592653589793115997963468544185161590576171875') </pre></div> </div> Q. Within a complex calculation, how can I make sure that I haven’t gotten a spurious result because of insufficient precision or rounding anomalies. A. The decimal module makes it easy to test results. A best practice is to re-run calculations using greater precision and with various rounding modes. Widely differing results indicate insufficient precision, rounding mode issues, ill-conditioned inputs, or a numerically unstable algorithm. Q. I noticed that context precision is applied to the results of operations but not to the inputs. Is there anything to watch out for when mixing values of different precisions? A. Yes. The principle is that all values are considered to be exact and so is the arithmetic on those values. Only the results are rounded. The advantage for inputs is that “what you type is what you get”. A disadvantage is that the results can look odd if you forget that the inputs haven’t been rounded: <div class="highlight-python"><div class="highlight"><pre>>>> getcontext().prec = 3 >>> Decimal('3.104') + Decimal('2.104') Decimal('5.21') >>> Decimal('3.104') + Decimal('0.000') + Decimal('2.104') Decimal('5.20') </pre></div> </div> The solution is either to increase precision or to force rounding of inputs using the unary plus operation: <div class="highlight-python"><div class="highlight"><pre>>>> getcontext().prec = 3 >>> +Decimal('1.23456789') # unary plus triggers rounding Decimal('1.23') </pre></div> </div> Alternatively, inputs can be rounded upon creation using the <a class="reference internal" href="#decimal.Context.create_decimal" title="decimal.Context.create_decimal"><tt class="xref py py-meth docutils literal">Context.create_decimal()</tt></a> method: <div class="highlight-python"><div class="highlight"><pre>>>> Context(prec=5, rounding=ROUND_DOWN).create_decimal('1.2345678') Decimal('1.2345') </pre></div> </div> </div> </div> </div> </div> </div> <div class="sphinxsidebar"> <div class="sphinxsidebarwrapper"> <h3><a href="../contents.html">Table Of Contents</a></h3> <ul> <li><a class="reference internal" href="#">9.4. <tt class="docutils literal">decimal</tt> — Decimal fixed point and floating point arithmetic</a><ul> <li><a class="reference internal" href="#quick-start-tutorial">9.4.1. Quick-start Tutorial</a></li> <li><a class="reference internal" href="#decimal-objects">9.4.2. Decimal objects</a><ul> <li><a class="reference internal" href="#logical-operands">9.4.2.1. Logical operands</a></li> </ul> </li> <li><a class="reference internal" href="#context-objects">9.4.3. Context objects</a></li> <li><a class="reference internal" href="#signals">9.4.4. Signals</a></li> <li><a class="reference internal" href="#floating-point-notes">9.4.5. Floating Point Notes</a><ul> <li><a class="reference internal" href="#mitigating-round-off-error-with-increased-precision">9.4.5.1. Mitigating round-off error with increased precision</a></li> <li><a class="reference internal" href="#special-values">9.4.5.2. Special values</a></li> </ul> </li> <li><a class="reference internal" href="#working-with-threads">9.4.6. Working with threads</a></li> <li><a class="reference internal" href="#recipes">9.4.7. Recipes</a></li> <li><a class="reference internal" href="#decimal-faq">9.4.8. Decimal FAQ</a></li> </ul> </li> </ul> <h4>Previous topic</h4> <a href="cmath.html" title="previous chapter">9.3. <tt class="docutils literal">cmath</tt> — Mathematical functions for complex numbers</a> <h4>Next topic</h4> <a href="fractions.html" title="next chapter">9.5. <tt class="docutils literal">fractions</tt> — Rational numbers</a> <h3>This Page</h3> <ul class="this-page-menu"> <li><a href="../bugs.html">Report a Bug</a></li> <li><a href="../_sources/library/decimal.txt" rel="nofollow">Show Source</a></li> </ul> <div id="searchbox" style="display: none"> <h3>Quick search</h3> <form class="search" action="../search.html" method="get"> <input type="text" name="q" /> <input type="submit" value="Go" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form> Enter search terms or a module, class or function name. </div> <script type="text/javascript">$('#searchbox').show(0);</script> </div> </div> <div class="clearer"></div> </div> <div class="related"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" >index</a></li> <li class="right" > <a href="../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="fractions.html" title="9.5. fractions — Rational numbers" >next</a> |</li> <li class="right" > <a href="cmath.html" title="9.3. cmath — Mathematical functions for complex numbers" >previous</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="http://www.python.org/">Python</a> »</li> <li> <a href="../index.html">Python 2.7.5 documentation</a> » </li> <li><a href="index.html" >The Python Standard Library</a> »</li> <li><a href="numeric.html" >9. Numeric and Mathematical Modules</a> »</li> </ul> </div> <div class="footer"> © <a href="../copyright.html">Copyright</a> 1990-2019, Python Software Foundation. The Python Software Foundation is a non-profit corporation. <a href="http://www.python.org/psf/donations/">Please donate.</a> Last updated on Jul 03, 2019. <a href="../bugs.html">Found a bug</a>? Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.1.3. </div> </body> </html>

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bastion.html	11.04 KB	July 03 2019 16:47:51	root / root	0644
bdb.html	36.682 KB	July 03 2019 16:47:51	root / root	0644
binascii.html	20.665 KB	July 03 2019 16:47:51	root / root	0644
binhex.html	10.577 KB	July 03 2019 16:47:51	root / root	0644
bisect.html	23.236 KB	July 03 2019 16:47:51	root / root	0644
bsddb.html	26.433 KB	July 03 2019 16:47:51	root / root	0644
bz2.html	26.082 KB	July 03 2019 16:47:51	root / root	0644
calendar.html	37.788 KB	July 03 2019 16:47:51	root / root	0644
carbon.html	48.944 KB	July 03 2019 16:47:51	root / root	0644
cd.html	27.96 KB	July 03 2019 16:47:52	root / root	0644
cgi.html	49.924 KB	July 03 2019 16:47:52	root / root	0644
cgihttpserver.html	13.099 KB	July 03 2019 16:47:52	root / root	0644
cgitb.html	11.411 KB	July 03 2019 16:47:52	root / root	0644
chunk.html	14.664 KB	July 03 2019 16:47:52	root / root	0644
cmath.html	25.632 KB	July 03 2019 16:47:52	root / root	0644
cmd.html	26.095 KB	July 03 2019 16:47:52	root / root	0644
code.html	24.577 KB	July 03 2019 16:47:52	root / root	0644
codecs.html	100.638 KB	July 03 2019 16:47:52	root / root	0644
codeop.html	14.841 KB	July 03 2019 16:47:52	root / root	0644
collections.html	133.964 KB	July 03 2019 16:47:53	root / root	0644
colorpicker.html	7.523 KB	July 03 2019 16:47:53	root / root	0644
colorsys.html	11.037 KB	July 03 2019 16:47:53	root / root	0644
commands.html	14.361 KB	July 03 2019 16:47:53	root / root	0644
compileall.html	16.827 KB	July 03 2019 16:47:53	root / root	0644
compiler.html	67.75 KB	July 03 2019 16:47:53	root / root	0644
configparser.html	62.131 KB	July 03 2019 16:47:53	root / root	0644
constants.html	12.834 KB	July 03 2019 16:47:53	root / root	0644
contextlib.html	19.388 KB	July 03 2019 16:47:53	root / root	0644
cookie.html	39.068 KB	July 03 2019 16:47:53	root / root	0644
cookielib.html	83.822 KB	July 03 2019 16:47:53	root / root	0644
copy.html	12.189 KB	July 03 2019 16:47:53	root / root	0644
copy_reg.html	13.765 KB	July 03 2019 16:47:53	root / root	0644
crypt.html	10.041 KB	July 03 2019 16:47:53	root / root	0644
crypto.html	7.591 KB	July 03 2019 16:47:53	root / root	0644
csv.html	67.371 KB	July 03 2019 16:47:54	root / root	0644
ctypes.html	238.781 KB	July 03 2019 16:47:54	root / root	0644
curses.ascii.html	22.288 KB	July 03 2019 16:47:55	root / root	0644
curses.html	146.633 KB	July 03 2019 16:47:55	root / root	0644
curses.panel.html	14.388 KB	July 03 2019 16:47:55	root / root	0644
custominterp.html	7.624 KB	July 03 2019 16:47:55	root / root	0644
datatypes.html	16.845 KB	July 03 2019 16:47:55	root / root	0644
datetime.html	226.595 KB	July 03 2019 16:47:55	root / root	0644
dbhash.html	15.482 KB	July 03 2019 16:47:55	root / root	0644
dbm.html	12.068 KB	July 03 2019 16:47:55	root / root	0644
debug.html	10.151 KB	July 03 2019 16:47:55	root / root	0644
decimal.html	194.439 KB	July 03 2019 16:47:56	root / root	0644
development.html	14.168 KB	July 03 2019 16:47:56	root / root	0644
difflib.html	84.829 KB	July 03 2019 16:47:56	root / root	0644
dircache.html	11.407 KB	July 03 2019 16:47:56	root / root	0644
dis.html	69.951 KB	July 03 2019 16:47:56	root / root	0644
distutils.html	8.055 KB	July 03 2019 16:47:56	root / root	0644
dl.html	16.327 KB	July 03 2019 16:47:56	root / root	0644
doctest.html	165.542 KB	July 03 2019 16:47:57	root / root	0644
docxmlrpcserver.html	16.432 KB	July 03 2019 16:47:57	root / root	0644
dumbdbm.html	14.021 KB	July 03 2019 16:47:57	root / root	0644
dummy_thread.html	9.432 KB	July 03 2019 16:47:57	root / root	0644
dummy_threading.html	8.368 KB	July 03 2019 16:47:57	root / root	0644
easydialogs.html	30.546 KB	July 03 2019 16:47:57	root / root	0644
email-examples.html	45.654 KB	July 03 2019 16:47:57	root / root	0644
email.charset.html	26.804 KB	July 03 2019 16:47:57	root / root	0644
email.encoders.html	11.856 KB	July 03 2019 16:47:57	root / root	0644
email.errors.html	15.767 KB	July 03 2019 16:47:57	root / root	0644
email.generator.html	20.771 KB	July 03 2019 16:47:57	root / root	0644
email.header.html	26.922 KB	July 03 2019 16:47:57	root / root	0644
email.html	44.235 KB	July 03 2019 16:47:57	root / root	0644
email.iterators.html	11.521 KB	July 03 2019 16:47:57	root / root	0644
email.message.html	63.156 KB	July 03 2019 16:47:57	root / root	0644
email.mime.html	27.928 KB	July 03 2019 16:47:57	root / root	0644
email.parser.html	30.452 KB	July 03 2019 16:47:58	root / root	0644
email.util.html	24.461 KB	July 03 2019 16:47:58	root / root	0644
errno.html	37.994 KB	July 03 2019 16:47:58	root / root	0644
exceptions.html	56.126 KB	July 03 2019 16:47:58	root / root	0644
fcntl.html	22.673 KB	July 03 2019 16:47:58	root / root	0644
filecmp.html	22.299 KB	July 03 2019 16:47:58	root / root	0644
fileformats.html	9.136 KB	July 03 2019 16:47:58	root / root	0644
fileinput.html	24.278 KB	July 03 2019 16:47:58	root / root	0644
filesys.html	10.203 KB	July 03 2019 16:47:58	root / root	0644
fl.html	49.923 KB	July 03 2019 16:47:58	root / root	0644
fm.html	11.905 KB	July 03 2019 16:47:58	root / root	0644
fnmatch.html	14.577 KB	July 03 2019 16:47:58	root / root	0644
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fpectl.html	16.008 KB	July 03 2019 16:47:58	root / root	0644
fpformat.html	10.587 KB	July 03 2019 16:47:58	root / root	0644
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frameworks.html	7.143 KB	July 03 2019 16:47:59	root / root	0644
ftplib.html	43.989 KB	July 03 2019 16:47:59	root / root	0644
functions.html	183.145 KB	July 03 2019 16:47:59	root / root	0644
functools.html	27.169 KB	July 03 2019 16:47:59	root / root	0644
future_builtins.html	13.04 KB	July 03 2019 16:47:59	root / root	0644
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gdbm.html	15.965 KB	July 03 2019 16:47:59	root / root	0644
gensuitemodule.html	11.513 KB	July 03 2019 16:47:59	root / root	0644
getopt.html	23.662 KB	July 03 2019 16:47:59	root / root	0644
getpass.html	10.652 KB	July 03 2019 16:47:59	root / root	0644
gettext.html	78.757 KB	July 03 2019 16:48:00	root / root	0644
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htmllib.html	25.315 KB	July 03 2019 16:48:00	root / root	0644
htmlparser.html	39.114 KB	July 03 2019 16:48:00	root / root	0644
httplib.html	62.95 KB	July 03 2019 16:48:00	root / root	0644
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idle.html	20.896 KB	July 03 2019 16:48:00	root / root	0644
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imputil.html	31.808 KB	July 03 2019 16:48:01	root / root	0644
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internet.html	24.872 KB	July 03 2019 16:48:01	root / root	0644
intro.html	8.935 KB	July 03 2019 16:48:01	root / root	0644
io.html	98.13 KB	July 03 2019 16:48:02	root / root	0644
ipc.html	13.405 KB	July 03 2019 16:48:02	root / root	0644
itertools.html	115.905 KB	July 03 2019 16:48:02	root / root	0644
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keyword.html	7.677 KB	July 03 2019 16:48:02	root / root	0644
language.html	11.027 KB	July 03 2019 16:48:02	root / root	0644
linecache.html	10.591 KB	July 03 2019 16:48:02	root / root	0644
locale.html	55.137 KB	July 03 2019 16:48:02	root / root	0644
logging.config.html	63.355 KB	July 03 2019 16:48:03	root / root	0644
logging.handlers.html	69.645 KB	July 03 2019 16:48:03	root / root	0644
logging.html	95.645 KB	July 03 2019 16:48:03	root / root	0644
mac.html	21.787 KB	July 03 2019 16:48:03	root / root	0644
macos.html	14.758 KB	July 03 2019 16:48:03	root / root	0644
macosa.html	12.959 KB	July 03 2019 16:48:03	root / root	0644
macostools.html	15.516 KB	July 03 2019 16:48:03	root / root	0644
macpath.html	7.764 KB	July 03 2019 16:48:03	root / root	0644
mailbox.html	156.753 KB	July 03 2019 16:48:03	root / root	0644
mailcap.html	13.215 KB	July 03 2019 16:48:03	root / root	0644
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marshal.html	17.977 KB	July 03 2019 16:48:04	root / root	0644
math.html	39.242 KB	July 03 2019 16:48:04	root / root	0644
md5.html	13.968 KB	July 03 2019 16:48:04	root / root	0644
mhlib.html	21.537 KB	July 03 2019 16:48:04	root / root	0644
mimetools.html	19.251 KB	July 03 2019 16:48:04	root / root	0644
mimetypes.html	28.39 KB	July 03 2019 16:48:04	root / root	0644
mimewriter.html	15.016 KB	July 03 2019 16:48:04	root / root	0644
mimify.html	13.361 KB	July 03 2019 16:48:04	root / root	0644
miniaeframe.html	12.199 KB	July 03 2019 16:48:04	root / root	0644
misc.html	6.868 KB	July 03 2019 16:48:04	root / root	0644
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mmap.html	28.364 KB	July 03 2019 16:48:04	root / root	0644
modulefinder.html	15.313 KB	July 03 2019 16:48:04	root / root	0644
modules.html	8.456 KB	July 03 2019 16:48:04	root / root	0644
msilib.html	52.431 KB	July 03 2019 16:48:04	root / root	0644
msvcrt.html	19.372 KB	July 03 2019 16:48:04	root / root	0644
multifile.html	24.297 KB	July 03 2019 16:48:04	root / root	0644
multiprocessing.html	365.706 KB	July 03 2019 16:48:05	root / root	0644
mutex.html	11.231 KB	July 03 2019 16:48:05	root / root	0644
netdata.html	16.983 KB	July 03 2019 16:48:05	root / root	0644
netrc.html	12.305 KB	July 03 2019 16:48:05	root / root	0644
new.html	12.122 KB	July 03 2019 16:48:05	root / root	0644
nis.html	10.636 KB	July 03 2019 16:48:05	root / root	0644
nntplib.html	41.919 KB	July 03 2019 16:48:05	root / root	0644
numbers.html	37.748 KB	July 03 2019 16:48:05	root / root	0644
numeric.html	13.553 KB	July 03 2019 16:48:05	root / root	0644
operator.html	82 KB	July 03 2019 16:48:06	root / root	0644
optparse.html	222.556 KB	July 03 2019 16:48:06	root / root	0644
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os.path.html	38.341 KB	July 03 2019 16:48:07	root / root	0644
ossaudiodev.html	41.503 KB	July 03 2019 16:48:07	root / root	0644
othergui.html	9.084 KB	July 03 2019 16:48:07	root / root	0644
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pdb.html	33.961 KB	July 03 2019 16:48:07	root / root	0644
persistence.html	14.865 KB	July 03 2019 16:48:07	root / root	0644
pickle.html	102.271 KB	July 03 2019 16:48:07	root / root	0644
pickletools.html	10.631 KB	July 03 2019 16:48:07	root / root	0644
pipes.html	18.01 KB	July 03 2019 16:48:08	root / root	0644
pkgutil.html	25.107 KB	July 03 2019 16:48:08	root / root	0644
platform.html	28.367 KB	July 03 2019 16:48:08	root / root	0644
plistlib.html	17.028 KB	July 03 2019 16:48:08	root / root	0644
popen2.html	25.431 KB	July 03 2019 16:48:08	root / root	0644
poplib.html	22.321 KB	July 03 2019 16:48:08	root / root	0644
posix.html	14.413 KB	July 03 2019 16:48:08	root / root	0644
posixfile.html	19.763 KB	July 03 2019 16:48:08	root / root	0644
pprint.html	29.922 KB	July 03 2019 16:48:08	root / root	0644
profile.html	63.556 KB	July 03 2019 16:48:08	root / root	0644
pty.html	9.478 KB	July 03 2019 16:48:08	root / root	0644
pwd.html	11.428 KB	July 03 2019 16:48:08	root / root	0644
py_compile.html	11.116 KB	July 03 2019 16:48:08	root / root	0644
pyclbr.html	14.707 KB	July 03 2019 16:48:08	root / root	0644
pydoc.html	11.484 KB	July 03 2019 16:48:08	root / root	0644
pyexpat.html	71.528 KB	July 03 2019 16:48:08	root / root	0644
python.html	12.274 KB	July 03 2019 16:48:09	root / root	0644
queue.html	24.22 KB	July 03 2019 16:48:09	root / root	0644
quopri.html	11.896 KB	July 03 2019 16:48:09	root / root	0644
random.html	37.835 KB	July 03 2019 16:48:09	root / root	0644
re.html	134.742 KB	July 03 2019 16:48:09	root / root	0644
readline.html	28.24 KB	July 03 2019 16:48:09	root / root	0644
repr.html	20.427 KB	July 03 2019 16:48:09	root / root	0644
resource.html	26.483 KB	July 03 2019 16:48:09	root / root	0644
restricted.html	11.647 KB	July 03 2019 16:48:09	root / root	0644
rexec.html	37.41 KB	July 03 2019 16:48:09	root / root	0644
rfc822.html	42.22 KB	July 03 2019 16:48:09	root / root	0644
rlcompleter.html	13.506 KB	July 03 2019 16:48:09	root / root	0644
robotparser.html	12.268 KB	July 03 2019 16:48:10	root / root	0644
runpy.html	19.339 KB	July 03 2019 16:48:10	root / root	0644
sched.html	18.543 KB	July 03 2019 16:48:10	root / root	0644
scrolledtext.html	9.315 KB	July 03 2019 16:48:10	root / root	0644
select.html	39.672 KB	July 03 2019 16:48:10	root / root	0644
sets.html	36.918 KB	July 03 2019 16:48:10	root / root	0644
sgi.html	9.712 KB	July 03 2019 16:48:10	root / root	0644
sgmllib.html	30.771 KB	July 03 2019 16:48:10	root / root	0644
sha.html	12.088 KB	July 03 2019 16:48:10	root / root	0644
shelve.html	27.021 KB	July 03 2019 16:48:10	root / root	0644
shlex.html	32.102 KB	July 03 2019 16:48:10	root / root	0644
shutil.html	40.218 KB	July 03 2019 16:48:10	root / root	0644
signal.html	31.136 KB	July 03 2019 16:48:10	root / root	0644
simplehttpserver.html	18.41 KB	July 03 2019 16:48:10	root / root	0644
simplexmlrpcserver.html	31.388 KB	July 03 2019 16:48:10	root / root	0644
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smtpd.html	12.465 KB	July 03 2019 16:48:10	root / root	0644
smtplib.html	42.127 KB	July 03 2019 16:48:11	root / root	0644
sndhdr.html	10.018 KB	July 03 2019 16:48:11	root / root	0644
socket.html	106.338 KB	July 03 2019 16:48:11	root / root	0644
socketserver.html	59.829 KB	July 03 2019 16:48:11	root / root	0644
someos.html	15.106 KB	July 03 2019 16:48:11	root / root	0644
spwd.html	10.328 KB	July 03 2019 16:48:11	root / root	0644
sqlite3.html	139.502 KB	July 03 2019 16:48:11	root / root	0644
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stat.html	32.31 KB	July 03 2019 16:48:12	root / root	0644
statvfs.html	10.604 KB	July 03 2019 16:48:12	root / root	0644
stdtypes.html	260.401 KB	July 03 2019 16:48:12	root / root	0644
string.html	106.649 KB	July 03 2019 16:48:13	root / root	0644
stringio.html	18.813 KB	July 03 2019 16:48:13	root / root	0644
stringprep.html	16.13 KB	July 03 2019 16:48:13	root / root	0644
strings.html	14.927 KB	July 03 2019 16:48:13	root / root	0644
struct.html	40.878 KB	July 03 2019 16:48:13	root / root	0644
subprocess.html	84.912 KB	July 03 2019 16:48:13	root / root	0644
sun.html	6.843 KB	July 03 2019 16:48:13	root / root	0644
sunau.html	27.104 KB	July 03 2019 16:48:13	root / root	0644
sunaudio.html	17.795 KB	July 03 2019 16:48:13	root / root	0644
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symtable.html	22.937 KB	July 03 2019 16:48:13	root / root	0644
sys.html	98.698 KB	July 03 2019 16:48:13	root / root	0644
sysconfig.html	23.844 KB	July 03 2019 16:48:14	root / root	0644
syslog.html	17.919 KB	July 03 2019 16:48:14	root / root	0644
tabnanny.html	10.631 KB	July 03 2019 16:48:14	root / root	0644
tarfile.html	78.683 KB	July 03 2019 16:48:14	root / root	0644
telnetlib.html	25.479 KB	July 03 2019 16:48:14	root / root	0644
tempfile.html	29.416 KB	July 03 2019 16:48:14	root / root	0644
termios.html	16.011 KB	July 03 2019 16:48:14	root / root	0644
test.html	52.621 KB	July 03 2019 16:48:14	root / root	0644
textwrap.html	27.253 KB	July 03 2019 16:48:14	root / root	0644
thread.html	20.468 KB	July 03 2019 16:48:14	root / root	0644
threading.html	76.69 KB	July 03 2019 16:48:14	root / root	0644
time.html	56.927 KB	July 03 2019 16:48:15	root / root	0644
timeit.html	36.267 KB	July 03 2019 16:48:15	root / root	0644
tix.html	46.959 KB	July 03 2019 16:48:15	root / root	0644
tk.html	23.644 KB	July 03 2019 16:48:15	root / root	0644
tkinter.html	67.666 KB	July 03 2019 16:48:15	root / root	0644
token.html	19.617 KB	July 03 2019 16:48:15	root / root	0644
tokenize.html	18.445 KB	July 03 2019 16:48:15	root / root	0644
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traceback.html	33.438 KB	July 03 2019 16:48:15	root / root	0644
ttk.html	101.749 KB	July 03 2019 16:48:16	root / root	0644
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turtle.html	211.742 KB	July 03 2019 16:48:16	root / root	0644
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undoc.html	23.156 KB	July 03 2019 16:48:16	root / root	0644
unicodedata.html	18.546 KB	July 03 2019 16:48:16	root / root	0644
unittest.html	202.848 KB	July 03 2019 16:48:17	root / root	0644
unix.html	10.551 KB	July 03 2019 16:48:17	root / root	0644
urllib.html	58.682 KB	July 03 2019 16:48:17	root / root	0644
urllib2.html	100.578 KB	July 03 2019 16:48:17	root / root	0644
urlparse.html	40.414 KB	July 03 2019 16:48:17	root / root	0644
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userdict.html	29.729 KB	July 03 2019 16:48:17	root / root	0644
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uuid.html	28.191 KB	July 03 2019 16:48:18	root / root	0644
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