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| 55 | <H2><A NAME="SECTION007640000000000000000"></A><A NAME="decimal-signals"></A> |
| 56 | <BR> |
| 57 | 5.6.4 Signals |
| 58 | </H2> |
| 59 | |
| 60 | <P> |
| 61 | Signals represent conditions that arise during computation. |
| 62 | Each corresponds to one context flag and one context trap enabler. |
| 63 | |
| 64 | <P> |
| 65 | The context flag is incremented whenever the condition is encountered. |
| 66 | After the computation, flags may be checked for informational |
| 67 | purposes (for instance, to determine whether a computation was exact). |
| 68 | After checking the flags, be sure to clear all flags before starting |
| 69 | the next computation. |
| 70 | |
| 71 | <P> |
| 72 | If the context's trap enabler is set for the signal, then the condition |
| 73 | causes a Python exception to be raised. For example, if the |
| 74 | <tt class="class">DivisionByZero</tt> trap is set, then a <tt class="exception">DivisionByZero</tt> |
| 75 | exception is raised upon encountering the condition. |
| 76 | |
| 77 | <P> |
| 78 | <dl><dt><b><span class="typelabel">class</span> <tt id='l2h-1240' xml:id='l2h-1240' class="class">Clamped</tt></b> |
| 79 | <dd> |
| 80 | Altered an exponent to fit representation constraints. |
| 81 | |
| 82 | <P> |
| 83 | Typically, clamping occurs when an exponent falls outside the context's |
| 84 | <tt class="member">Emin</tt> and <tt class="member">Emax</tt> limits. If possible, the exponent is |
| 85 | reduced to fit by adding zeroes to the coefficient. |
| 86 | </dl> |
| 87 | |
| 88 | <P> |
| 89 | <dl><dt><b><span class="typelabel">class</span> <tt id='l2h-1241' xml:id='l2h-1241' class="class">DecimalException</tt></b> |
| 90 | <dd> |
| 91 | Base class for other signals and is a subclass of |
| 92 | <tt class="exception">ArithmeticError</tt>. |
| 93 | </dl> |
| 94 | |
| 95 | <P> |
| 96 | <dl><dt><b><span class="typelabel">class</span> <tt id='l2h-1242' xml:id='l2h-1242' class="class">DivisionByZero</tt></b> |
| 97 | <dd> |
| 98 | Signals the division of a non-infinite number by zero. |
| 99 | |
| 100 | <P> |
| 101 | Can occur with division, modulo division, or when raising a number to a |
| 102 | negative power. If this signal is not trapped, returns |
| 103 | <tt class="constant">Infinity</tt> or <tt class="constant">-Infinity</tt> with the sign determined by |
| 104 | the inputs to the calculation. |
| 105 | </dl> |
| 106 | |
| 107 | <P> |
| 108 | <dl><dt><b><span class="typelabel">class</span> <tt id='l2h-1243' xml:id='l2h-1243' class="class">Inexact</tt></b> |
| 109 | <dd> |
| 110 | Indicates that rounding occurred and the result is not exact. |
| 111 | |
| 112 | <P> |
| 113 | Signals when non-zero digits were discarded during rounding. The rounded |
| 114 | result is returned. The signal flag or trap is used to detect when |
| 115 | results are inexact. |
| 116 | </dl> |
| 117 | |
| 118 | <P> |
| 119 | <dl><dt><b><span class="typelabel">class</span> <tt id='l2h-1244' xml:id='l2h-1244' class="class">InvalidOperation</tt></b> |
| 120 | <dd> |
| 121 | An invalid operation was performed. |
| 122 | |
| 123 | <P> |
| 124 | Indicates that an operation was requested that does not make sense. |
| 125 | If not trapped, returns <tt class="constant">NaN</tt>. Possible causes include: |
| 126 | |
| 127 | <P> |
| 128 | <div class="verbatim"><pre> |
| 129 | Infinity - Infinity |
| 130 | 0 * Infinity |
| 131 | Infinity / Infinity |
| 132 | x % 0 |
| 133 | Infinity % x |
| 134 | x._rescale( non-integer ) |
| 135 | sqrt(-x) and x > 0 |
| 136 | 0 ** 0 |
| 137 | x ** (non-integer) |
| 138 | x ** Infinity |
| 139 | </pre></div> |
| 140 | </dl> |
| 141 | |
| 142 | <P> |
| 143 | <dl><dt><b><span class="typelabel">class</span> <tt id='l2h-1245' xml:id='l2h-1245' class="class">Overflow</tt></b> |
| 144 | <dd> |
| 145 | Numerical overflow. |
| 146 | |
| 147 | <P> |
| 148 | Indicates the exponent is larger than <tt class="member">Emax</tt> after rounding has |
| 149 | occurred. If not trapped, the result depends on the rounding mode, either |
| 150 | pulling inward to the largest representable finite number or rounding |
| 151 | outward to <tt class="constant">Infinity</tt>. In either case, <tt class="class">Inexact</tt> and |
| 152 | <tt class="class">Rounded</tt> are also signaled. |
| 153 | </dl> |
| 154 | |
| 155 | <P> |
| 156 | <dl><dt><b><span class="typelabel">class</span> <tt id='l2h-1246' xml:id='l2h-1246' class="class">Rounded</tt></b> |
| 157 | <dd> |
| 158 | Rounding occurred though possibly no information was lost. |
| 159 | |
| 160 | <P> |
| 161 | Signaled whenever rounding discards digits; even if those digits are |
| 162 | zero (such as rounding <tt class="constant">5.00</tt> to <tt class="constant">5.0</tt>). If not |
| 163 | trapped, returns the result unchanged. This signal is used to detect |
| 164 | loss of significant digits. |
| 165 | </dl> |
| 166 | |
| 167 | <P> |
| 168 | <dl><dt><b><span class="typelabel">class</span> <tt id='l2h-1247' xml:id='l2h-1247' class="class">Subnormal</tt></b> |
| 169 | <dd> |
| 170 | Exponent was lower than <tt class="member">Emin</tt> prior to rounding. |
| 171 | |
| 172 | <P> |
| 173 | Occurs when an operation result is subnormal (the exponent is too small). |
| 174 | If not trapped, returns the result unchanged. |
| 175 | </dl> |
| 176 | |
| 177 | <P> |
| 178 | <dl><dt><b><span class="typelabel">class</span> <tt id='l2h-1248' xml:id='l2h-1248' class="class">Underflow</tt></b> |
| 179 | <dd> |
| 180 | Numerical underflow with result rounded to zero. |
| 181 | |
| 182 | <P> |
| 183 | Occurs when a subnormal result is pushed to zero by rounding. |
| 184 | <tt class="class">Inexact</tt> and <tt class="class">Subnormal</tt> are also signaled. |
| 185 | </dl> |
| 186 | |
| 187 | <P> |
| 188 | The following table summarizes the hierarchy of signals: |
| 189 | |
| 190 | <P> |
| 191 | <div class="verbatim"><pre> |
| 192 | exceptions.ArithmeticError(exceptions.StandardError) |
| 193 | DecimalException |
| 194 | Clamped |
| 195 | DivisionByZero(DecimalException, exceptions.ZeroDivisionError) |
| 196 | Inexact |
| 197 | Overflow(Inexact, Rounded) |
| 198 | Underflow(Inexact, Rounded, Subnormal) |
| 199 | InvalidOperation |
| 200 | Rounded |
| 201 | Subnormal |
| 202 | </pre></div> |
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