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| <h4 class="subsection">20.5.2 Infinity and NaN</h4> |
| |
| <p><a name="index-infinity-2368"></a><a name="index-not-a-number-2369"></a><a name="index-NaN-2370"></a> |
| IEEE 754<!-- /@w --> floating point numbers can represent positive or negative |
| infinity, and <dfn>NaN</dfn> (not a number). These three values arise from |
| calculations whose result is undefined or cannot be represented |
| accurately. You can also deliberately set a floating-point variable to |
| any of them, which is sometimes useful. Some examples of calculations |
| that produce infinity or NaN: |
| |
| <pre class="smallexample"> 1/0 = &infin; |
| log (0) = -&infin; |
| sqrt (-1) = NaN |
| </pre> |
| <p>When a calculation produces any of these values, an exception also |
| occurs; see <a href="FP-Exceptions.html#FP-Exceptions">FP Exceptions</a>. |
| |
| <p>The basic operations and math functions all accept infinity and NaN and |
| produce sensible output. Infinities propagate through calculations as |
| one would expect: for example, 2 + &infin; = &infin;, |
| 4/&infin; = 0, atan (&infin;) = &pi;/2. NaN, on |
| the other hand, infects any calculation that involves it. Unless the |
| calculation would produce the same result no matter what real value |
| replaced NaN, the result is NaN. |
| |
| <p>In comparison operations, positive infinity is larger than all values |
| except itself and NaN, and negative infinity is smaller than all values |
| except itself and NaN. NaN is <dfn>unordered</dfn>: it is not equal to, |
| greater than, or less than anything, <em>including itself</em>. <code>x == |
| x</code> is false if the value of <code>x</code> is NaN. You can use this to test |
| whether a value is NaN or not, but the recommended way to test for NaN |
| is with the <code>isnan</code> function (see <a href="Floating-Point-Classes.html#Floating-Point-Classes">Floating Point Classes</a>). In |
| addition, <code><</code>, <code>></code>, <code><=</code>, and <code>>=</code> will raise an |
| exception when applied to NaNs. |
| |
| <p><samp><span class="file">math.h</span></samp> defines macros that allow you to explicitly set a variable |
| to infinity or NaN. |
| |
| <!-- math.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Macro: float <b>INFINITY</b><var><a name="index-INFINITY-2371"></a></var><br> |
| <blockquote><p>An expression representing positive infinity. It is equal to the value |
| produced by mathematical operations like <code>1.0 / 0.0</code>. |
| <code>-INFINITY</code> represents negative infinity. |
| |
| <p>You can test whether a floating-point value is infinite by comparing it |
| to this macro. However, this is not recommended; you should use the |
| <code>isfinite</code> macro instead. See <a href="Floating-Point-Classes.html#Floating-Point-Classes">Floating Point Classes</a>. |
| |
| <p>This macro was introduced in the ISO C99<!-- /@w --> standard. |
| </p></blockquote></div> |
| |
| <!-- math.h --> |
| <!-- GNU --> |
| <div class="defun"> |
| — Macro: float <b>NAN</b><var><a name="index-NAN-2372"></a></var><br> |
| <blockquote><p>An expression representing a value which is “not a number”. This |
| macro is a GNU extension, available only on machines that support the |
| “not a number” value—that is to say, on all machines that support |
| IEEE floating point. |
| |
| <p>You can use ‘<samp><span class="samp">#ifdef NAN</span></samp>’ to test whether the machine supports |
| NaN. (Of course, you must arrange for GNU extensions to be visible, |
| such as by defining <code>_GNU_SOURCE</code>, and then you must include |
| <samp><span class="file">math.h</span></samp>.) |
| </p></blockquote></div> |
| |
| <p>IEEE 754<!-- /@w --> also allows for another unusual value: negative zero. This |
| value is produced when you divide a positive number by negative |
| infinity, or when a negative result is smaller than the limits of |
| representation. Negative zero behaves identically to zero in all |
| calculations, unless you explicitly test the sign bit with |
| <code>signbit</code> or <code>copysign</code>. |
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