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| 54 | |
| 55 | <H1><A NAME="SECTION007600000000000000000"> |
| 56 | 5.6 <tt class="module">decimal</tt> -- |
| 57 | Decimal floating point arithmetic</A> |
| 58 | </H1> |
| 59 | |
| 60 | <P> |
| 61 | <A NAME="module-decimal"></A> |
| 62 | |
| 63 | <P> |
| 64 | |
| 65 | <P> |
| 66 | |
| 67 | <P> |
| 68 | |
| 69 | <span class="versionnote">New in version 2.4.</span> |
| 70 | |
| 71 | <P> |
| 72 | The <tt class="module">decimal</tt> module provides support for decimal floating point |
| 73 | arithmetic. It offers several advantages over the <tt class="class">float()</tt> datatype: |
| 74 | |
| 75 | <P> |
| 76 | |
| 77 | <UL> |
| 78 | <LI>Decimal numbers can be represented exactly. In contrast, numbers like |
| 79 | <tt class="constant">1.1</tt> do not have an exact representation in binary floating point. |
| 80 | End users typically would not expect <tt class="constant">1.1</tt> to display as |
| 81 | <tt class="constant">1.1000000000000001</tt> as it does with binary floating point. |
| 82 | |
| 83 | <P> |
| 84 | </LI> |
| 85 | <LI>The exactness carries over into arithmetic. In decimal floating point, |
| 86 | "<tt class="samp">0.1 + 0.1 + 0.1 - 0.3</tt>" is exactly equal to zero. In binary floating |
| 87 | point, result is <tt class="constant">5.5511151231257827e-017</tt>. While near to zero, the |
| 88 | differences prevent reliable equality testing and differences can accumulate. |
| 89 | For this reason, decimal would be preferred in accounting applications which |
| 90 | have strict equality invariants. |
| 91 | |
| 92 | <P> |
| 93 | </LI> |
| 94 | <LI>The decimal module incorporates a notion of significant places so that |
| 95 | "<tt class="samp">1.30 + 1.20</tt>" is <tt class="constant">2.50</tt>. The trailing zero is kept to indicate |
| 96 | significance. This is the customary presentation for monetary applications. For |
| 97 | multiplication, the ``schoolbook'' approach uses all the figures in the |
| 98 | multiplicands. For instance, "<tt class="samp">1.3 * 1.2</tt>" gives <tt class="constant">1.56</tt> while |
| 99 | "<tt class="samp">1.30 * 1.20</tt>" gives <tt class="constant">1.5600</tt>. |
| 100 | |
| 101 | <P> |
| 102 | </LI> |
| 103 | <LI>Unlike hardware based binary floating point, the decimal module has a user |
| 104 | settable precision (defaulting to 28 places) which can be as large as needed for |
| 105 | a given problem: |
| 106 | |
| 107 | <P> |
| 108 | <div class="verbatim"><pre> |
| 109 | >>> getcontext().prec = 6 |
| 110 | >>> Decimal(1) / Decimal(7) |
| 111 | Decimal("0.142857") |
| 112 | >>> getcontext().prec = 28 |
| 113 | >>> Decimal(1) / Decimal(7) |
| 114 | Decimal("0.1428571428571428571428571429") |
| 115 | </pre></div> |
| 116 | |
| 117 | <P> |
| 118 | </LI> |
| 119 | <LI>Both binary and decimal floating point are implemented in terms of published |
| 120 | standards. While the built-in float type exposes only a modest portion of its |
| 121 | capabilities, the decimal module exposes all required parts of the standard. |
| 122 | When needed, the programmer has full control over rounding and signal handling. |
| 123 | |
| 124 | <P> |
| 125 | </LI> |
| 126 | </UL> |
| 127 | |
| 128 | <P> |
| 129 | The module design is centered around three concepts: the decimal number, the |
| 130 | context for arithmetic, and signals. |
| 131 | |
| 132 | <P> |
| 133 | A decimal number is immutable. It has a sign, coefficient digits, and an |
| 134 | exponent. To preserve significance, the coefficient digits do not truncate |
| 135 | trailing zeroes. Decimals also include special values such as |
| 136 | <tt class="constant">Infinity</tt>, <tt class="constant">-Infinity</tt>, and <tt class="constant">NaN</tt>. The standard |
| 137 | also differentiates <tt class="constant">-0</tt> from <tt class="constant">+0</tt>. |
| 138 | |
| 139 | <P> |
| 140 | The context for arithmetic is an environment specifying precision, rounding |
| 141 | rules, limits on exponents, flags indicating the results of operations, |
| 142 | and trap enablers which determine whether signals are treated as |
| 143 | exceptions. Rounding options include <tt class="constant">ROUND_CEILING</tt>, |
| 144 | <tt class="constant">ROUND_DOWN</tt>, <tt class="constant">ROUND_FLOOR</tt>, <tt class="constant">ROUND_HALF_DOWN</tt>, |
| 145 | <tt class="constant">ROUND_HALF_EVEN</tt>, <tt class="constant">ROUND_HALF_UP</tt>, and <tt class="constant">ROUND_UP</tt>. |
| 146 | |
| 147 | <P> |
| 148 | Signals are groups of exceptional conditions arising during the course of |
| 149 | computation. Depending on the needs of the application, signals may be |
| 150 | ignored, considered as informational, or treated as exceptions. The signals in |
| 151 | the decimal module are: <tt class="constant">Clamped</tt>, <tt class="constant">InvalidOperation</tt>, |
| 152 | <tt class="constant">DivisionByZero</tt>, <tt class="constant">Inexact</tt>, <tt class="constant">Rounded</tt>, |
| 153 | <tt class="constant">Subnormal</tt>, <tt class="constant">Overflow</tt>, and <tt class="constant">Underflow</tt>. |
| 154 | |
| 155 | <P> |
| 156 | For each signal there is a flag and a trap enabler. When a signal is |
| 157 | encountered, its flag incremented from zero and, then, if the trap enabler |
| 158 | is set to one, an exception is raised. Flags are sticky, so the user |
| 159 | needs to reset them before monitoring a calculation. |
| 160 | |
| 161 | <P> |
| 162 | <div class="seealso"> |
| 163 | <p class="heading">See Also:</p> |
| 164 | |
| 165 | <div class="seetext"><p>IBM's General Decimal Arithmetic Specification, |
| 166 | <em class="citetitle"><a |
| 167 | href="http://www2.hursley.ibm.com/decimal/decarith.html" |
| 168 | title="The General Decimal Arithmetic Specification" |
| 169 | >The General Decimal Arithmetic Specification</a></em>.</p></div> |
| 170 | |
| 171 | <P> |
| 172 | <div class="seetext"><p>IEEE standard 854-1987, |
| 173 | <em class="citetitle"><a |
| 174 | href="http://www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html" |
| 175 | title="Unofficial IEEE 854 Text" |
| 176 | >Unofficial IEEE 854 Text</a></em>.</p></div> |
| 177 | </div> |
| 178 | |
| 179 | <P> |
| 180 | |
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| 182 | <div class='online-navigation'> |
| 183 | <!--Table of Child-Links--> |
| 184 | <A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></a> |
| 185 | |
| 186 | <UL CLASS="ChildLinks"> |
| 187 | <LI><A href="decimal-tutorial.html">5.6.1 Quick-start Tutorial</a> |
| 188 | <LI><A href="node178.html">5.6.2 Decimal objects</a> |
| 189 | <LI><A href="decimal-decimal.html">5.6.3 Context objects</a> |
| 190 | <LI><A href="decimal-signals.html">5.6.4 Signals</a> |
| 191 | <LI><A href="decimal-notes.html">5.6.5 Floating Point Notes</a> |
| 192 | <UL> |
| 193 | <LI><A href="node182.html">5.6.5.1 Mitigating round-off error with increased precision</a> |
| 194 | <LI><A href="node183.html">5.6.5.2 Special values</a> |
| 195 | </ul> |
| 196 | <LI><A href="decimal-threads.html">5.6.6 Working with threads</a> |
| 197 | <LI><A href="decimal-recipes.html">5.6.7 Recipes</a> |
| 198 | <LI><A href="decimal-faq.html">5.6.8 Decimal FAQ</a> |
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