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| <h4 class="subsection">20.5.4 Error Reporting by Mathematical Functions</h4> |
| |
| <p><a name="index-errors_002c-mathematical-2383"></a><a name="index-domain-error-2384"></a><a name="index-range-error-2385"></a> |
| Many of the math functions are defined only over a subset of the real or |
| complex numbers. Even if they are mathematically defined, their result |
| may be larger or smaller than the range representable by their return |
| type. These are known as <dfn>domain errors</dfn>, <dfn>overflows</dfn>, and |
| <dfn>underflows</dfn>, respectively. Math functions do several things when |
| one of these errors occurs. In this manual we will refer to the |
| complete response as <dfn>signalling</dfn> a domain error, overflow, or |
| underflow. |
| |
| <p>When a math function suffers a domain error, it raises the invalid |
| exception and returns NaN. It also sets <var>errno</var> to <code>EDOM</code>; |
| this is for compatibility with old systems that do not support IEEE 754<!-- /@w --> exception handling. Likewise, when overflow occurs, math |
| functions raise the overflow exception and return &infin; or |
| -&infin; as appropriate. They also set <var>errno</var> to |
| <code>ERANGE</code>. When underflow occurs, the underflow exception is |
| raised, and zero (appropriately signed) is returned. <var>errno</var> may be |
| set to <code>ERANGE</code>, but this is not guaranteed. |
| |
| <p>Some of the math functions are defined mathematically to result in a |
| complex value over parts of their domains. The most familiar example of |
| this is taking the square root of a negative number. The complex math |
| functions, such as <code>csqrt</code>, will return the appropriate complex value |
| in this case. The real-valued functions, such as <code>sqrt</code>, will |
| signal a domain error. |
| |
| <p>Some older hardware does not support infinities. On that hardware, |
| overflows instead return a particular very large number (usually the |
| largest representable number). <samp><span class="file">math.h</span></samp> defines macros you can use |
| to test for overflow on both old and new hardware. |
| |
| <!-- math.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Macro: double <b>HUGE_VAL</b><var><a name="index-HUGE_005fVAL-2386"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Macro: float <b>HUGE_VALF</b><var><a name="index-HUGE_005fVALF-2387"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Macro: long double <b>HUGE_VALL</b><var><a name="index-HUGE_005fVALL-2388"></a></var><br> |
| <blockquote><p>An expression representing a particular very large number. On machines |
| that use IEEE 754<!-- /@w --> floating point format, <code>HUGE_VAL</code> is infinity. |
| On other machines, it's typically the largest positive number that can |
| be represented. |
| |
| <p>Mathematical functions return the appropriately typed version of |
| <code>HUGE_VAL</code> or <code>−HUGE_VAL</code> when the result is too large |
| to be represented. |
| </p></blockquote></div> |
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