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<H2><A NAME="SECTION007620000000000000000"></A><A NAME="decimal-decimal"></A>
<BR>
5.6.2 Decimal objects 
</H2>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><span class="typelabel">class</span>&nbsp;<tt id='l2h-1195' xml:id='l2h-1195' class="class">Decimal</tt></b>(</nobr></td>
  <td><var></var><big>[</big><var>value </var><big>[</big><var>, context</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
  Constructs a new <tt class="class">Decimal</tt> object based from <var>value</var>.

<P>
<var>value</var> can be an integer, string, tuple, or another <tt class="class">Decimal</tt>
  object. If no <var>value</var> is given, returns <code>Decimal("0")</code>.  If
  <var>value</var> is a string, it should conform to the decimal numeric string
  syntax:

<P>
<div class="verbatim"><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>

<P>
If <var>value</var> is a <tt class="class">tuple</tt>, it should have three components,
  a sign (<tt class="constant">0</tt> for positive or <tt class="constant">1</tt> for negative),
  a <tt class="class">tuple</tt> of digits, and an integer exponent. For example,
  "<tt class="samp">Decimal((0, (1, 4, 1, 4), -3))</tt>" returns <code>Decimal("1.414")</code>.

<P>
The <var>context</var> precision does not affect how many digits are stored.
  That is determined exclusively by the number of digits in <var>value</var>. For
  example, "<tt class="samp">Decimal("3.00000")</tt>" records all five zeroes even if the
  context precision is only three.

<P>
The purpose of the <var>context</var> argument is determining what to do if
  <var>value</var> is a malformed string.  If the context traps
  <tt class="constant">InvalidOperation</tt>, an exception is raised; otherwise, the
  constructor returns a new Decimal with the value of <tt class="constant">NaN</tt>.

<P>
Once constructed, <tt class="class">Decimal</tt> objects are immutable.
</dl>

<P>
Decimal floating point objects share many properties with the other builtin
numeric types such as <tt class="class">float</tt> and <tt class="class">int</tt>.  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 <tt class="class">float</tt>
or <tt class="class">long</tt>).

<P>
In addition to the standard numeric properties, decimal floating point objects
also have a number of specialized methods:

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1196' xml:id='l2h-1196' class="method">adjusted</tt></b>(</nobr></td>
  <td><var></var>)</td></tr></table></dt>
<dd>
  Return the adjusted exponent after shifting out the coefficient's rightmost
  digits until only the lead digit remains: <code>Decimal("321e+5").adjusted()</code>
  returns seven.  Used for determining the position of the most significant
  digit with respect to the decimal point.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1197' xml:id='l2h-1197' class="method">as_tuple</tt></b>(</nobr></td>
  <td><var></var>)</td></tr></table></dt>
<dd>
  Returns a tuple representation of the number:
  "<tt class="samp">(sign, digittuple, exponent)</tt>".
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1198' xml:id='l2h-1198' class="method">compare</tt></b>(</nobr></td>
  <td><var>other</var><big>[</big><var>, context</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
  Compares like <tt class="method">__cmp__()</tt> but returns a decimal instance:
  <div class="verbatim"><pre>
        a or b is a NaN ==&gt; Decimal("NaN")
        a &lt; b           ==&gt; Decimal("-1")
        a == b          ==&gt; Decimal("0")
        a &gt; b           ==&gt; Decimal("1")
</pre></div>
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1199' xml:id='l2h-1199' class="method">max</tt></b>(</nobr></td>
  <td><var>other</var><big>[</big><var>, context</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
  Like "<tt class="samp">max(self, other)</tt>" except that the context rounding rule
  is applied before returning and that <tt class="constant">NaN</tt> values are
  either signalled or ignored (depending on the context and whether
  they are signaling or quiet).
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1200' xml:id='l2h-1200' class="method">min</tt></b>(</nobr></td>
  <td><var>other</var><big>[</big><var>, context</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
  Like "<tt class="samp">min(self, other)</tt>" except that the context rounding rule
  is applied before returning and that <tt class="constant">NaN</tt> values are
  either signalled or ignored (depending on the context and whether
  they are signaling or quiet).
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1201' xml:id='l2h-1201' class="method">normalize</tt></b>(</nobr></td>
  <td><var></var><big>[</big><var>context</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
  Normalize the number by stripping the rightmost trailing zeroes and
  converting any result equal to <tt class="constant">Decimal("0")</tt> to
  <tt class="constant">Decimal("0e0")</tt>. Used for producing canonical values for members
  of an equivalence class. For example, <code>Decimal("32.100")</code> and
  <code>Decimal("0.321000e+2")</code> both normalize to the equivalent value
  <code>Decimal("32.1")</code>.
</dl>                                              

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1202' xml:id='l2h-1202' class="method">quantize</tt></b>(</nobr></td>
  <td><var>exp </var><big>[</big><var>, rounding</var><big>[</big><var>, context</var><big>[</big><var>, watchexp</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
  Quantize makes the exponent the same as <var>exp</var>.  Searches for a
  rounding method in <var>rounding</var>, then in <var>context</var>, and then
  in the current context.

<P>
If <var>watchexp</var> is set (default), then an error is returned whenever
  the resulting exponent is greater than <tt class="member">Emax</tt> or less than
  <tt class="member">Etiny</tt>.
</dl> 

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1203' xml:id='l2h-1203' class="method">remainder_near</tt></b>(</nobr></td>
  <td><var>other</var><big>[</big><var>, context</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
  Computes the modulo as either a positive or negative value depending
  on which is closest to zero.  For instance,
  "<tt class="samp">Decimal(10).remainder_near(6)</tt>" returns <code>Decimal("-2")</code>
  which is closer to zero than <code>Decimal("4")</code>.

<P>
If both are equally close, the one chosen will have the same sign
  as <var>self</var>.
</dl>  

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1204' xml:id='l2h-1204' class="method">same_quantum</tt></b>(</nobr></td>
  <td><var>other</var><big>[</big><var>, context</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
  Test whether self and other have the same exponent or whether both
  are <tt class="constant">NaN</tt>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1205' xml:id='l2h-1205' class="method">sqrt</tt></b>(</nobr></td>
  <td><var></var><big>[</big><var>context</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
  Return the square root to full precision.
</dl>                    

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1206' xml:id='l2h-1206' class="method">to_eng_string</tt></b>(</nobr></td>
  <td><var></var><big>[</big><var>context</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
  Convert to an engineering-type string.

<P>
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
  <code>Decimal('123E+1')</code> to <code>Decimal("1.23E+3")</code>
</dl>  

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1207' xml:id='l2h-1207' class="method">to_integral</tt></b>(</nobr></td>
  <td><var></var><big>[</big><var>rounding</var><big>[</big><var>, context</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
<dd>                   
  Rounds to the nearest integer without signaling <tt class="constant">Inexact</tt>
  or <tt class="constant">Rounded</tt>.  If given, applies <var>rounding</var>; otherwise,
  uses the rounding method in either the supplied <var>context</var> or the
  current context.
</dl> 

<P>

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	54
	55	<H2><A NAME="SECTION007620000000000000000"></A><A NAME="decimal-decimal"></A>
	56	<BR>
	57	5.6.2 Decimal objects
	58	</H2>
	59
	60	<P>
	61	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
	62	<td><nobr><b><span class="typelabel">class</span> <tt id='l2h-1195' xml:id='l2h-1195' class="class">Decimal</tt></b>(</nobr></td>
	63	<td><var></var><big>[</big><var>value </var><big>[</big><var>, context</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
	64	<dd>
65	Constructs a new <tt class="class">Decimal</tt> object based from <var>value</var>.
66
67	<P>
68	<var>value</var> can be an integer, string, tuple, or another <tt class="class">Decimal</tt>
69	object. If no <var>value</var> is given, returns <code>Decimal("0")</code>. If
70	<var>value</var> is a string, it should conform to the decimal numeric string
71	syntax:
72
73	<P>
74	<div class="verbatim"><pre>
75	sign ::= '+' \| '-'
76	digit ::= '0' \| '1' \| '2' \| '3' \| '4' \| '5' \| '6' \| '7' \| '8' \| '9'
77	indicator ::= 'e' \| 'E'
78	digits ::= digit [digit]...
79	decimal-part ::= digits '.' [digits] \| ['.'] digits
80	exponent-part ::= indicator [sign] digits
81	infinity ::= 'Infinity' \| 'Inf'
82	nan ::= 'NaN' [digits] \| 'sNaN' [digits]
83	numeric-value ::= decimal-part [exponent-part] \| infinity
84	numeric-string ::= [sign] numeric-value \| [sign] nan
85	</pre></div>
86
87	<P>
88	If <var>value</var> is a <tt class="class">tuple</tt>, it should have three components,
89	a sign (<tt class="constant">0</tt> for positive or <tt class="constant">1</tt> for negative),
90	a <tt class="class">tuple</tt> of digits, and an integer exponent. For example,
91	"<tt class="samp">Decimal((0, (1, 4, 1, 4), -3))</tt>" returns <code>Decimal("1.414")</code>.
92
93	<P>
94	The <var>context</var> precision does not affect how many digits are stored.
95	That is determined exclusively by the number of digits in <var>value</var>. For
96	example, "<tt class="samp">Decimal("3.00000")</tt>" records all five zeroes even if the
97	context precision is only three.
98
99	<P>
100	The purpose of the <var>context</var> argument is determining what to do if
101	<var>value</var> is a malformed string. If the context traps
102	<tt class="constant">InvalidOperation</tt>, an exception is raised; otherwise, the
103	constructor returns a new Decimal with the value of <tt class="constant">NaN</tt>.
104
105	<P>
106	Once constructed, <tt class="class">Decimal</tt> objects are immutable.
107	</dl>
108
109	<P>
110	Decimal floating point objects share many properties with the other builtin
111	numeric types such as <tt class="class">float</tt> and <tt class="class">int</tt>. All of the usual
112	math operations and special methods apply. Likewise, decimal objects can
113	be copied, pickled, printed, used as dictionary keys, used as set elements,
114	compared, sorted, and coerced to another type (such as <tt class="class">float</tt>
115	or <tt class="class">long</tt>).
116
117	<P>
118	In addition to the standard numeric properties, decimal floating point objects
119	also have a number of specialized methods:
120
121	<P>
122	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
123	<td><nobr><b><tt id='l2h-1196' xml:id='l2h-1196' class="method">adjusted</tt></b>(</nobr></td>
124	<td><var></var>)</td></tr></table></dt>
125	<dd>
126	Return the adjusted exponent after shifting out the coefficient's rightmost
127	digits until only the lead digit remains: <code>Decimal("321e+5").adjusted()</code>
128	returns seven. Used for determining the position of the most significant
129	digit with respect to the decimal point.
130	</dl>
131
132	<P>
133	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
134	<td><nobr><b><tt id='l2h-1197' xml:id='l2h-1197' class="method">as_tuple</tt></b>(</nobr></td>
135	<td><var></var>)</td></tr></table></dt>
136	<dd>
137	Returns a tuple representation of the number:
138	"<tt class="samp">(sign, digittuple, exponent)</tt>".
139	</dl>
140
141	<P>
142	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
143	<td><nobr><b><tt id='l2h-1198' xml:id='l2h-1198' class="method">compare</tt></b>(</nobr></td>
144	<td><var>other</var><big>[</big><var>, context</var><big>]</big><var></var>)</td></tr></table></dt>
145	<dd>
146	Compares like <tt class="method">__cmp__()</tt> but returns a decimal instance:
147	<div class="verbatim"><pre>
148	a or b is a NaN ==> Decimal("NaN")
149	a < b ==> Decimal("-1")
150	a == b ==> Decimal("0")
151	a > b ==> Decimal("1")
152	</pre></div>
153	</dl>
154
155	<P>
156	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
157	<td><nobr><b><tt id='l2h-1199' xml:id='l2h-1199' class="method">max</tt></b>(</nobr></td>
158	<td><var>other</var><big>[</big><var>, context</var><big>]</big><var></var>)</td></tr></table></dt>
159	<dd>
160	Like "<tt class="samp">max(self, other)</tt>" except that the context rounding rule
161	is applied before returning and that <tt class="constant">NaN</tt> values are
162	either signalled or ignored (depending on the context and whether
163	they are signaling or quiet).
164	</dl>
165
166	<P>
167	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
168	<td><nobr><b><tt id='l2h-1200' xml:id='l2h-1200' class="method">min</tt></b>(</nobr></td>
169	<td><var>other</var><big>[</big><var>, context</var><big>]</big><var></var>)</td></tr></table></dt>
170	<dd>
171	Like "<tt class="samp">min(self, other)</tt>" except that the context rounding rule
172	is applied before returning and that <tt class="constant">NaN</tt> values are
173	either signalled or ignored (depending on the context and whether
174	they are signaling or quiet).
175	</dl>
176
177	<P>
178	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
179	<td><nobr><b><tt id='l2h-1201' xml:id='l2h-1201' class="method">normalize</tt></b>(</nobr></td>
180	<td><var></var><big>[</big><var>context</var><big>]</big><var></var>)</td></tr></table></dt>
181	<dd>
182	Normalize the number by stripping the rightmost trailing zeroes and
183	converting any result equal to <tt class="constant">Decimal("0")</tt> to
184	<tt class="constant">Decimal("0e0")</tt>. Used for producing canonical values for members
185	of an equivalence class. For example, <code>Decimal("32.100")</code> and
186	<code>Decimal("0.321000e+2")</code> both normalize to the equivalent value
187	<code>Decimal("32.1")</code>.
188	</dl>
189
190	<P>
191	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
192	<td><nobr><b><tt id='l2h-1202' xml:id='l2h-1202' class="method">quantize</tt></b>(</nobr></td>
193	<td><var>exp </var><big>[</big><var>, rounding</var><big>[</big><var>, context</var><big>[</big><var>, watchexp</var><big>]</big><var></var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
194	<dd>
195	Quantize makes the exponent the same as <var>exp</var>. Searches for a
196	rounding method in <var>rounding</var>, then in <var>context</var>, and then
197	in the current context.
198
199	<P>
200	If <var>watchexp</var> is set (default), then an error is returned whenever
201	the resulting exponent is greater than <tt class="member">Emax</tt> or less than
202	<tt class="member">Etiny</tt>.
203	</dl>
204
205	<P>
206	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
207	<td><nobr><b><tt id='l2h-1203' xml:id='l2h-1203' class="method">remainder_near</tt></b>(</nobr></td>
208	<td><var>other</var><big>[</big><var>, context</var><big>]</big><var></var>)</td></tr></table></dt>
209	<dd>
210	Computes the modulo as either a positive or negative value depending
211	on which is closest to zero. For instance,
212	"<tt class="samp">Decimal(10).remainder_near(6)</tt>" returns <code>Decimal("-2")</code>
213	which is closer to zero than <code>Decimal("4")</code>.
214
215	<P>
216	If both are equally close, the one chosen will have the same sign
217	as <var>self</var>.
218	</dl>
219
220	<P>
221	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
222	<td><nobr><b><tt id='l2h-1204' xml:id='l2h-1204' class="method">same_quantum</tt></b>(</nobr></td>
223	<td><var>other</var><big>[</big><var>, context</var><big>]</big><var></var>)</td></tr></table></dt>
224	<dd>
225	Test whether self and other have the same exponent or whether both
226	are <tt class="constant">NaN</tt>.
227	</dl>
228
229	<P>
230	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
231	<td><nobr><b><tt id='l2h-1205' xml:id='l2h-1205' class="method">sqrt</tt></b>(</nobr></td>
232	<td><var></var><big>[</big><var>context</var><big>]</big><var></var>)</td></tr></table></dt>
233	<dd>
234	Return the square root to full precision.
235	</dl>
236
237	<P>
238	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
239	<td><nobr><b><tt id='l2h-1206' xml:id='l2h-1206' class="method">to_eng_string</tt></b>(</nobr></td>
240	<td><var></var><big>[</big><var>context</var><big>]</big><var></var>)</td></tr></table></dt>
241	<dd>
242	Convert to an engineering-type string.
243
244	<P>
245	Engineering notation has an exponent which is a multiple of 3, so there
246	are up to 3 digits left of the decimal place. For example, converts
247	<code>Decimal('123E+1')</code> to <code>Decimal("1.23E+3")</code>
248	</dl>
249
250	<P>
251	<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
252	<td><nobr><b><tt id='l2h-1207' xml:id='l2h-1207' class="method">to_integral</tt></b>(</nobr></td>
253	<td><var></var><big>[</big><var>rounding</var><big>[</big><var>, context</var><big>]</big><var></var><big>]</big><var></var>)</td></tr></table></dt>
254	<dd>
255	Rounds to the nearest integer without signaling <tt class="constant">Inexact</tt>
256	or <tt class="constant">Rounded</tt>. If given, applies <var>rounding</var>; otherwise,
257	uses the rounding method in either the supplied <var>context</var> or the
258	current context.
259	</dl>
260
261	<P>
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