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<H2><A NAME="SECTION007630000000000000000"></A><A NAME="decimal-decimal"></A>
<BR>
5.6.3 Context objects
</H2>

<P>
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.

<P>
Each thread has its own current context which is accessed or changed using
the <tt class="function">getcontext()</tt> and <tt class="function">setcontext()</tt> functions:

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1208' xml:id='l2h-1208' class="function">getcontext</tt></b>(</nobr></td>
  <td><var></var>)</td></tr></table></dt>
<dd>
  Return the current context for the active thread.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1209' xml:id='l2h-1209' class="function">setcontext</tt></b>(</nobr></td>
  <td><var>c</var>)</td></tr></table></dt>
<dd>
  Set the current context for the active thread to <var>c</var>.
</dl>

<P>
New contexts can formed using the <tt class="class">Context</tt> constructor described below.
In addition, the module provides three pre-made contexts:

<P>
<dl><dt><b><span class="typelabel">class</span>&nbsp;<tt id='l2h-1210' xml:id='l2h-1210' class="class">BasicContext</tt></b>
<dd>
  This is a standard context defined by the General Decimal Arithmetic
  Specification.  Precision is set to nine.  Rounding is set to
  <tt class="constant">ROUND_HALF_UP</tt>.  All flags are cleared.  All traps are enabled
  (treated as exceptions) except <tt class="constant">Inexact</tt>, <tt class="constant">Rounded</tt>, and
  <tt class="constant">Subnormal</tt>.

<P>
Because many of the traps are enabled, this context is useful for debugging.
</dl>

<P>
<dl><dt><b><span class="typelabel">class</span>&nbsp;<tt id='l2h-1211' xml:id='l2h-1211' class="class">ExtendedContext</tt></b>
<dd>
  This is a standard context defined by the General Decimal Arithmetic
  Specification.  Precision is set to nine.  Rounding is set to
  <tt class="constant">ROUND_HALF_EVEN</tt>.  All flags are cleared.  No traps are enabled
  (so that exceptions are not raised during computations).

<P>
Because the trapped are disabled, this context is useful for applications
  that prefer to have result value of <tt class="constant">NaN</tt> or <tt class="constant">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.
</dl>

<P>
<dl><dt><b><span class="typelabel">class</span>&nbsp;<tt id='l2h-1212' xml:id='l2h-1212' class="class">DefaultContext</tt></b>
<dd>
  This context is used by the <tt class="class">Context</tt> constructor as a prototype for
  new contexts.  Changing a field (such a precision) has the effect of
  changing the default for new contexts creating by the <tt class="class">Context</tt>
  constructor.

<P>
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.

<P>
In single threaded environments, it is preferable to not use this context
  at all.  Instead, simply create contexts explicitly as described below.

<P>
The default values are precision=28, rounding=ROUND_HALF_EVEN, and enabled
  traps for Overflow, InvalidOperation, and DivisionByZero.
</dl>

<P>
In addition to the three supplied contexts, new contexts can be created
with the <tt class="class">Context</tt> constructor.

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><span class="typelabel">class</span>&nbsp;<tt id='l2h-1213' xml:id='l2h-1213' class="class">Context</tt></b>(</nobr></td>
  <td><var>prec=None, rounding=None, traps=None,
        flags=None, Emin=None, Emax=None, capitals=1</var>)</td></tr></table></dt>
<dd>
  Creates a new context.  If a field is not specified or is <tt class="constant">None</tt>,
  the default values are copied from the <tt class="constant">DefaultContext</tt>.  If the
  <var>flags</var> field is not specified or is <tt class="constant">None</tt>, all flags are
  cleared.

<P>
The <var>prec</var> field is a positive integer that sets the precision for
  arithmetic operations in the context.

<P>
The <var>rounding</var> option is one of:

<UL>
<LI><tt class="constant">ROUND_CEILING</tt> (towards <tt class="constant">Infinity</tt>),
</LI>
<LI><tt class="constant">ROUND_DOWN</tt> (towards zero),
</LI>
<LI><tt class="constant">ROUND_FLOOR</tt> (towards <tt class="constant">-Infinity</tt>),
</LI>
<LI><tt class="constant">ROUND_HALF_DOWN</tt> (to nearest with ties going towards zero),
</LI>
<LI><tt class="constant">ROUND_HALF_EVEN</tt> (to nearest with ties going to nearest even integer),
</LI>
<LI><tt class="constant">ROUND_HALF_UP</tt> (to nearest with ties going away from zero), or
</LI>
<LI><tt class="constant">ROUND_UP</tt> (away from zero).

</LI>
</UL>

<P>
The <var>traps</var> and <var>flags</var> fields list any signals to be set.
  Generally, new contexts should only set traps and leave the flags clear.

<P>
The <var>Emin</var> and <var>Emax</var> fields are integers specifying the outer
  limits allowable for exponents.

<P>
The <var>capitals</var> field is either <tt class="constant">0</tt> or <tt class="constant">1</tt> (the
  default). If set to <tt class="constant">1</tt>, exponents are printed with a capital
  <tt class="constant">E</tt>; otherwise, a lowercase <tt class="constant">e</tt> is used:
  <tt class="constant">Decimal('6.02e+23')</tt>.
</dl>

<P>
The <tt class="class">Context</tt> class defines several general purpose methods as well as a
large number of methods for doing arithmetic directly in a given context.

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1214' xml:id='l2h-1214' class="method">clear_flags</tt></b>(</nobr></td>
  <td><var></var>)</td></tr></table></dt>
<dd>
  Resets all of the flags to <tt class="constant">0</tt>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1215' xml:id='l2h-1215' class="method">copy</tt></b>(</nobr></td>
  <td><var></var>)</td></tr></table></dt>
<dd>
  Return a duplicate of the context.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1216' xml:id='l2h-1216' class="method">create_decimal</tt></b>(</nobr></td>
  <td><var>num</var>)</td></tr></table></dt>
<dd>
  Creates a new Decimal instance from <var>num</var> but using <var>self</var> as
  context. Unlike the <tt class="class">Decimal</tt> constructor, the context precision,
  rounding method, flags, and traps are applied to the conversion.

<P>
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:

<P>
<div class="verbatim"><pre>
    &gt;&gt;&gt; getcontext().prec = 3
    &gt;&gt;&gt; Decimal("3.4445") + Decimal("1.0023")
    Decimal("4.45")
    &gt;&gt;&gt; Decimal("3.4445") + Decimal(0) + Decimal("1.0023")
    Decimal("4.44")
</pre></div>

<P>
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1217' xml:id='l2h-1217' class="method">Etiny</tt></b>(</nobr></td>
  <td><var></var>)</td></tr></table></dt>
<dd>
  Returns a value equal to "<tt class="samp">Emin - prec + 1</tt>" which is the minimum
  exponent value for subnormal results.  When underflow occurs, the
  exponent is set to <tt class="constant">Etiny</tt>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1218' xml:id='l2h-1218' class="method">Etop</tt></b>(</nobr></td>
  <td><var></var>)</td></tr></table></dt>
<dd>
  Returns a value equal to "<tt class="samp">Emax - prec + 1</tt>".
</dl>

<P>
The usual approach to working with decimals is to create <tt class="class">Decimal</tt>
instances and then apply arithmetic operations which take place within the
current context for the active thread.  An alternate approach is to use
context methods for calculating within a specific context.  The methods are
similar to those for the <tt class="class">Decimal</tt> class and are only briefly recounted
here.

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1219' xml:id='l2h-1219' class="method">abs</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
  Returns the absolute value of <var>x</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1220' xml:id='l2h-1220' class="method">add</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Return the sum of <var>x</var> and <var>y</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1221' xml:id='l2h-1221' class="method">compare</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Compares values numerically.

<P>
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-1222' xml:id='l2h-1222' class="method">divide</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Return <var>x</var> divided by <var>y</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1223' xml:id='l2h-1223' class="method">divmod</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Divides two numbers and returns the integer part of the result.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1224' xml:id='l2h-1224' class="method">max</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Compare two values numerically and return the maximum.

<P>
If they are numerically equal then the left-hand operand is chosen as the
  result.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1225' xml:id='l2h-1225' class="method">min</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Compare two values numerically and return the minimum.

<P>
If they are numerically equal then the left-hand operand is chosen as the
  result.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1226' xml:id='l2h-1226' class="method">minus</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
  Minus corresponds to the unary prefix minus operator in Python.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1227' xml:id='l2h-1227' class="method">multiply</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Return the product of <var>x</var> and <var>y</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1228' xml:id='l2h-1228' class="method">normalize</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
  Normalize reduces an operand to its simplest form.

<P>
Essentially a <tt class="method">plus</tt> operation with all trailing zeros removed from
  the result.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1229' xml:id='l2h-1229' class="method">plus</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
  Plus corresponds to the unary prefix plus operator in Python.  This
  operation applies the context precision and rounding, so it is
  <em>not</em> an identity operation.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1230' xml:id='l2h-1230' class="method">power</tt></b>(</nobr></td>
  <td><var>x, y</var><big>[</big><var>, modulo</var><big>]</big><var></var>)</td></tr></table></dt>
<dd>
  Return "<tt class="samp">x ** y</tt>" to the <var>modulo</var> if given.

<P>
The right-hand operand must be a whole number whose integer part (after any
  exponent has been applied) has no more than 9 digits and whose fractional
  part (if any) is all zeros before any rounding. The operand may be positive,
  negative, or zero; if negative, the absolute value of the power is used, and
  the left-hand operand is inverted (divided into 1) before use.

<P>
If the increased precision needed for the intermediate calculations exceeds
  the capabilities of the implementation then an <tt class="constant">InvalidOperation</tt>
  condition is signaled.

<P>
If, when raising to a negative power, an underflow occurs during the
  division into 1, the operation is not halted at that point but continues.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1231' xml:id='l2h-1231' class="method">quantize</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Returns a value equal to <var>x</var> after rounding and having the exponent of
  <var>y</var>.

<P>
Unlike other operations, if the length of the coefficient after the quantize
  operation would be greater than precision, then an
  <tt class="constant">InvalidOperation</tt> is signaled. This guarantees that, unless there
  is an error condition, the quantized exponent is always equal to that of the
  right-hand operand.

<P>
Also unlike other operations, quantize never signals Underflow, even
  if the result is subnormal and inexact.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1232' xml:id='l2h-1232' class="method">remainder</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Returns the remainder from integer division.

<P>
The sign of the result, if non-zero, is the same as that of the original
  dividend.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1233' xml:id='l2h-1233' class="method">remainder_near</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Computed 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-1234' xml:id='l2h-1234' class="method">same_quantum</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Test whether <var>x</var> and <var>y</var> 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-1235' xml:id='l2h-1235' class="method">sqrt</tt></b>(</nobr></td>
  <td><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-1236' xml:id='l2h-1236' class="method">subtract</tt></b>(</nobr></td>
  <td><var>x, y</var>)</td></tr></table></dt>
<dd>
  Return the difference between <var>x</var> and <var>y</var>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1237' xml:id='l2h-1237' class="method">to_eng_string</tt></b>(</nobr></td>
  <td><var></var>)</td></tr></table></dt>
<dd>
  Convert to 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-1238' xml:id='l2h-1238' class="method">to_integral</tt></b>(</nobr></td>
  <td><var>x</var>)</td></tr></table></dt>
<dd>
  Rounds to the nearest integer without signaling <tt class="constant">Inexact</tt>
  or <tt class="constant">Rounded</tt>.
</dl>

<P>
<dl><dt><table cellpadding="0" cellspacing="0"><tr valign="baseline">
  <td><nobr><b><tt id='l2h-1239' xml:id='l2h-1239' class="method">to_sci_string</tt></b>(</nobr></td>
  <td><var></var>)</td></tr></table></dt>
<dd>
  Converts a number to a string using scientific notation.
</dl>

<P>

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