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| <h4 class="subsection">20.8.5 Setting and modifying single bits of FP values</h4> |
| |
| <p><a name="index-FP-arithmetic-2481"></a> |
| There are some operations that are too complicated or expensive to |
| perform by hand on floating-point numbers. ISO C99<!-- /@w --> defines |
| functions to do these operations, which mostly involve changing single |
| bits. |
| |
| <!-- math.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Function: double <b>copysign</b> (<var>double x, double y</var>)<var><a name="index-copysign-2482"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: float <b>copysignf</b> (<var>float x, float y</var>)<var><a name="index-copysignf-2483"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: long double <b>copysignl</b> (<var>long double x, long double y</var>)<var><a name="index-copysignl-2484"></a></var><br> |
| <blockquote><p>These functions return <var>x</var> but with the sign of <var>y</var>. They work |
| even if <var>x</var> or <var>y</var> are NaN or zero. Both of these can carry a |
| sign (although not all implementations support it) and this is one of |
| the few operations that can tell the difference. |
| |
| <p><code>copysign</code> never raises an exception. |
| <!-- except signalling NaNs --> |
| |
| <p>This function is defined in IEC 559<!-- /@w --> (and the appendix with |
| recommended functions in IEEE 754<!-- /@w -->/IEEE 854<!-- /@w -->). |
| </p></blockquote></div> |
| |
| <!-- math.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Function: int <b>signbit</b> (<em>float-type</em><var> x</var>)<var><a name="index-signbit-2485"></a></var><br> |
| <blockquote><p><code>signbit</code> is a generic macro which can work on all floating-point |
| types. It returns a nonzero value if the value of <var>x</var> has its sign |
| bit set. |
| |
| <p>This is not the same as <code>x < 0.0</code>, because IEEE 754<!-- /@w --> floating |
| point allows zero to be signed. The comparison <code>-0.0 < 0.0</code> is |
| false, but <code>signbit (-0.0)</code> will return a nonzero value. |
| </p></blockquote></div> |
| |
| <!-- math.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Function: double <b>nextafter</b> (<var>double x, double y</var>)<var><a name="index-nextafter-2486"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: float <b>nextafterf</b> (<var>float x, float y</var>)<var><a name="index-nextafterf-2487"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: long double <b>nextafterl</b> (<var>long double x, long double y</var>)<var><a name="index-nextafterl-2488"></a></var><br> |
| <blockquote><p>The <code>nextafter</code> function returns the next representable neighbor of |
| <var>x</var> in the direction towards <var>y</var>. The size of the step between |
| <var>x</var> and the result depends on the type of the result. If |
| <var>x</var> = <var>y</var> the function simply returns <var>y</var>. If either |
| value is <code>NaN</code>, <code>NaN</code> is returned. Otherwise |
| a value corresponding to the value of the least significant bit in the |
| mantissa is added or subtracted, depending on the direction. |
| <code>nextafter</code> will signal overflow or underflow if the result goes |
| outside of the range of normalized numbers. |
| |
| <p>This function is defined in IEC 559<!-- /@w --> (and the appendix with |
| recommended functions in IEEE 754<!-- /@w -->/IEEE 854<!-- /@w -->). |
| </p></blockquote></div> |
| |
| <!-- math.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Function: double <b>nexttoward</b> (<var>double x, long double y</var>)<var><a name="index-nexttoward-2489"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: float <b>nexttowardf</b> (<var>float x, long double y</var>)<var><a name="index-nexttowardf-2490"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: long double <b>nexttowardl</b> (<var>long double x, long double y</var>)<var><a name="index-nexttowardl-2491"></a></var><br> |
| <blockquote><p>These functions are identical to the corresponding versions of |
| <code>nextafter</code> except that their second argument is a <code>long |
| double</code>. |
| </p></blockquote></div> |
| |
| <p><a name="index-NaN-2492"></a><!-- math.h --> |
| <!-- ISO --> |
| |
| <div class="defun"> |
| — Function: double <b>nan</b> (<var>const char *tagp</var>)<var><a name="index-nan-2493"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: float <b>nanf</b> (<var>const char *tagp</var>)<var><a name="index-nanf-2494"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: long double <b>nanl</b> (<var>const char *tagp</var>)<var><a name="index-nanl-2495"></a></var><br> |
| <blockquote><p>The <code>nan</code> function returns a representation of NaN, provided that |
| NaN is supported by the target platform. |
| <code>nan ("</code><var>n-char-sequence</var><code>")</code> is equivalent to |
| <code>strtod ("NAN(</code><var>n-char-sequence</var><code>)")</code>. |
| |
| <p>The argument <var>tagp</var> is used in an unspecified manner. On IEEE 754<!-- /@w --> systems, there are many representations of NaN, and <var>tagp</var> |
| selects one. On other systems it may do nothing. |
| </p></blockquote></div> |
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