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<H3><A NAME="SECTION007652000000000000000">
5.6.5.2 Special values</A>
</H3>

<P>
The number system for the <tt class="module">decimal</tt> module provides special
values including <tt class="constant">NaN</tt>, <tt class="constant">sNaN</tt>, <tt class="constant">-Infinity</tt>,
<tt class="constant">Infinity</tt>, and two zeroes, <tt class="constant">+0</tt> and <tt class="constant">-0</tt>.

<P>
Infinities can be constructed directly with:  <code>Decimal('Infinity')</code>. Also,
they can arise from dividing by zero when the <tt class="exception">DivisionByZero</tt>
signal is not trapped.  Likewise, when the <tt class="exception">Overflow</tt> signal is not
trapped, infinity can result from rounding beyond the limits of the largest
representable number.

<P>
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.

<P>
Some operations are indeterminate and return <tt class="constant">NaN</tt>, or if the
<tt class="exception">InvalidOperation</tt> signal is trapped, raise an exception.  For
example, <code>0/0</code> returns <tt class="constant">NaN</tt> which means ``not a number''.  This
variety of <tt class="constant">NaN</tt> is quiet and, once created, will flow through other
computations always resulting in another <tt class="constant">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.     

<P>
A variant is <tt class="constant">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.

<P>
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.

<P>
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:          

<P>
<div class="verbatim"><pre>
&gt;&gt;&gt; 1 / Decimal('Infinity')
Decimal("0E-1000000026")
</pre></div>

<P>

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920dae64 AT	1	<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
	2	<html>
	3	<head>
	4	<link rel="STYLESHEET" href="lib.css" type='text/css' />
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	10	<link rel='last' href='about.html' title='About this document...' />
	11	<link rel='help' href='about.html' title='About this document...' />
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	16	<title>5.6.5.2 Special values</title>
	17	</head>
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	24	href="node182.html"><img src='../icons/previous.png'
	25	border='0' height='32' alt='Previous Page' width='32' /></A></td>
	26	<td class='online-navigation'><a rel="parent" title="5.6.5 Floating Point Notes"
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	40	border='0' height='32' alt='Index' width='32' /></A></td>
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	44	<a class="sectref" rel="prev" href="node182.html">5.6.5.1 Mitigating round-off error</A>
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	53
	54	<H3><A NAME="SECTION007652000000000000000">
	55	5.6.5.2 Special values</A>
	56	</H3>
	57
	58	<P>
	59	The number system for the <tt class="module">decimal</tt> module provides special
	60	values including <tt class="constant">NaN</tt>, <tt class="constant">sNaN</tt>, <tt class="constant">-Infinity</tt>,
	61	<tt class="constant">Infinity</tt>, and two zeroes, <tt class="constant">+0</tt> and <tt class="constant">-0</tt>.
	62
	63	<P>
	64	Infinities can be constructed directly with: <code>Decimal('Infinity')</code>. Also,
65	they can arise from dividing by zero when the <tt class="exception">DivisionByZero</tt>
66	signal is not trapped. Likewise, when the <tt class="exception">Overflow</tt> signal is not
67	trapped, infinity can result from rounding beyond the limits of the largest
68	representable number.
69
70	<P>
71	The infinities are signed (affine) and can be used in arithmetic operations
72	where they get treated as very large, indeterminate numbers. For instance,
73	adding a constant to infinity gives another infinite result.
74
75	<P>
76	Some operations are indeterminate and return <tt class="constant">NaN</tt>, or if the
77	<tt class="exception">InvalidOperation</tt> signal is trapped, raise an exception. For
78	example, <code>0/0</code> returns <tt class="constant">NaN</tt> which means ``not a number''. This
79	variety of <tt class="constant">NaN</tt> is quiet and, once created, will flow through other
80	computations always resulting in another <tt class="constant">NaN</tt>. This behavior can be
81	useful for a series of computations that occasionally have missing inputs --
82	it allows the calculation to proceed while flagging specific results as
83	invalid.
84
85	<P>
86	A variant is <tt class="constant">sNaN</tt> which signals rather than remaining quiet
87	after every operation. This is a useful return value when an invalid
88	result needs to interrupt a calculation for special handling.
89
90	<P>
91	The signed zeros can result from calculations that underflow.
92	They keep the sign that would have resulted if the calculation had
93	been carried out to greater precision. Since their magnitude is
94	zero, both positive and negative zeros are treated as equal and their
95	sign is informational.
96
97	<P>
98	In addition to the two signed zeros which are distinct yet equal,
99	there are various representations of zero with differing precisions
100	yet equivalent in value. This takes a bit of getting used to. For
101	an eye accustomed to normalized floating point representations, it
102	is not immediately obvious that the following calculation returns
103	a value equal to zero:
104
105	<P>
106	<div class="verbatim"><pre>
107	>>> 1 / Decimal('Infinity')
108	Decimal("0E-1000000026")
109	</pre></div>
110
111	<P>
112
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