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| 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 | |
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