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| <h3 class="section">19.1 Predefined Mathematical Constants</h3> |
| |
| <p><a name="index-constants-2068"></a><a name="index-mathematical-constants-2069"></a> |
| The header <samp><span class="file">math.h</span></samp> defines several useful mathematical constants. |
| All values are defined as preprocessor macros starting with <code>M_</code>. |
| The values provided are: |
| |
| <dl> |
| <dt><code>M_E</code><a name="index-M_005fE-2070"></a><dd>The base of natural logarithms. |
| <br><dt><code>M_LOG2E</code><a name="index-M_005fLOG2E-2071"></a><dd>The logarithm to base <code>2</code> of <code>M_E</code>. |
| <br><dt><code>M_LOG10E</code><a name="index-M_005fLOG10E-2072"></a><dd>The logarithm to base <code>10</code> of <code>M_E</code>. |
| <br><dt><code>M_LN2</code><a name="index-M_005fLN2-2073"></a><dd>The natural logarithm of <code>2</code>. |
| <br><dt><code>M_LN10</code><a name="index-M_005fLN10-2074"></a><dd>The natural logarithm of <code>10</code>. |
| <br><dt><code>M_PI</code><a name="index-M_005fPI-2075"></a><dd>Pi, the ratio of a circle's circumference to its diameter. |
| <br><dt><code>M_PI_2</code><a name="index-M_005fPI_005f2-2076"></a><dd>Pi divided by two. |
| <br><dt><code>M_PI_4</code><a name="index-M_005fPI_005f4-2077"></a><dd>Pi divided by four. |
| <br><dt><code>M_1_PI</code><a name="index-M_005f1_005fPI-2078"></a><dd>The reciprocal of pi (1/pi) |
| <br><dt><code>M_2_PI</code><a name="index-M_005f2_005fPI-2079"></a><dd>Two times the reciprocal of pi. |
| <br><dt><code>M_2_SQRTPI</code><a name="index-M_005f2_005fSQRTPI-2080"></a><dd>Two times the reciprocal of the square root of pi. |
| <br><dt><code>M_SQRT2</code><a name="index-M_005fSQRT2-2081"></a><dd>The square root of two. |
| <br><dt><code>M_SQRT1_2</code><a name="index-M_005fSQRT1_005f2-2082"></a><dd>The reciprocal of the square root of two (also the square root of 1/2). |
| </dl> |
| |
| <p>These constants come from the Unix98 standard and were also available in |
| 4.4BSD; therefore they are only defined if <code>_BSD_SOURCE</code> or |
| <code>_XOPEN_SOURCE=500</code>, or a more general feature select macro, is |
| defined. The default set of features includes these constants. |
| See <a href="Feature-Test-Macros.html#Feature-Test-Macros">Feature Test Macros</a>. |
| |
| <p>All values are of type <code>double</code>. As an extension, the GNU C |
| library also defines these constants with type <code>long double</code>. The |
| <code>long double</code> macros have a lowercase ‘<samp><span class="samp">l</span></samp>’ appended to their |
| names: <code>M_El</code>, <code>M_PIl</code>, and so forth. These are only |
| available if <code>_GNU_SOURCE</code> is defined. |
| |
| <p><a name="index-PI-2083"></a><em>Note:</em> Some programs use a constant named <code>PI</code> which has the |
| same value as <code>M_PI</code>. This constant is not standard; it may have |
| appeared in some old AT&T headers, and is mentioned in Stroustrup's book |
| on C++. It infringes on the user's name space, so the GNU C library |
| does not define it. Fixing programs written to expect it is simple: |
| replace <code>PI</code> with <code>M_PI</code> throughout, or put ‘<samp><span class="samp">-DPI=M_PI</span></samp>’ |
| on the compiler command line. |
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