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| <h4 class="subsection">20.8.2 Normalization Functions</h4> |
| |
| <p><a name="index-normalization-functions-_0028floating_002dpoint_0029-2417"></a> |
| The functions described in this section are primarily provided as a way |
| to efficiently perform certain low-level manipulations on floating point |
| numbers that are represented internally using a binary radix; |
| see <a href="Floating-Point-Concepts.html#Floating-Point-Concepts">Floating Point Concepts</a>. These functions are required to |
| have equivalent behavior even if the representation does not use a radix |
| of 2, but of course they are unlikely to be particularly efficient in |
| those cases. |
| |
| <p><a name="index-math_002eh-2418"></a>All these functions are declared in <samp><span class="file">math.h</span></samp>. |
| |
| <!-- math.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Function: double <b>frexp</b> (<var>double value, int *exponent</var>)<var><a name="index-frexp-2419"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: float <b>frexpf</b> (<var>float value, int *exponent</var>)<var><a name="index-frexpf-2420"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: long double <b>frexpl</b> (<var>long double value, int *exponent</var>)<var><a name="index-frexpl-2421"></a></var><br> |
| <blockquote><p>These functions are used to split the number <var>value</var> |
| into a normalized fraction and an exponent. |
| |
| <p>If the argument <var>value</var> is not zero, the return value is <var>value</var> |
| times a power of two, and is always in the range 1/2 (inclusive) to 1 |
| (exclusive). The corresponding exponent is stored in |
| <code>*</code><var>exponent</var>; the return value multiplied by 2 raised to this |
| exponent equals the original number <var>value</var>. |
| |
| <p>For example, <code>frexp (12.8, &exponent)</code> returns <code>0.8</code> and |
| stores <code>4</code> in <code>exponent</code>. |
| |
| <p>If <var>value</var> is zero, then the return value is zero and |
| zero is stored in <code>*</code><var>exponent</var>. |
| </p></blockquote></div> |
| |
| <!-- math.h --> |
| <!-- ISO --> |
| <div class="defun"> |
| — Function: double <b>ldexp</b> (<var>double value, int exponent</var>)<var><a name="index-ldexp-2422"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: float <b>ldexpf</b> (<var>float value, int exponent</var>)<var><a name="index-ldexpf-2423"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- ISO --> |
| — Function: long double <b>ldexpl</b> (<var>long double value, int exponent</var>)<var><a name="index-ldexpl-2424"></a></var><br> |
| <blockquote><p>These functions return the result of multiplying the floating-point |
| number <var>value</var> by 2 raised to the power <var>exponent</var>. (It can |
| be used to reassemble floating-point numbers that were taken apart |
| by <code>frexp</code>.) |
| |
| <p>For example, <code>ldexp (0.8, 4)</code> returns <code>12.8</code>. |
| </p></blockquote></div> |
| |
| <p>The following functions, which come from BSD, provide facilities |
| equivalent to those of <code>ldexp</code> and <code>frexp</code>. See also the |
| ISO C<!-- /@w --> function <code>logb</code> which originally also appeared in BSD. |
| |
| <!-- math.h --> |
| <!-- BSD --> |
| <div class="defun"> |
| — Function: double <b>scalb</b> (<var>double value, int exponent</var>)<var><a name="index-scalb-2425"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- BSD --> |
| — Function: float <b>scalbf</b> (<var>float value, int exponent</var>)<var><a name="index-scalbf-2426"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- BSD --> |
| — Function: long double <b>scalbl</b> (<var>long double value, int exponent</var>)<var><a name="index-scalbl-2427"></a></var><br> |
| <blockquote><p>The <code>scalb</code> function is the BSD name for <code>ldexp</code>. |
| </p></blockquote></div> |
| |
| <!-- math.h --> |
| <!-- BSD --> |
| <div class="defun"> |
| — Function: long long int <b>scalbn</b> (<var>double x, int n</var>)<var><a name="index-scalbn-2428"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- BSD --> |
| — Function: long long int <b>scalbnf</b> (<var>float x, int n</var>)<var><a name="index-scalbnf-2429"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- BSD --> |
| — Function: long long int <b>scalbnl</b> (<var>long double x, int n</var>)<var><a name="index-scalbnl-2430"></a></var><br> |
| <blockquote><p><code>scalbn</code> is identical to <code>scalb</code>, except that the exponent |
| <var>n</var> is an <code>int</code> instead of a floating-point number. |
| </p></blockquote></div> |
| |
| <!-- math.h --> |
| <!-- BSD --> |
| <div class="defun"> |
| — Function: long long int <b>scalbln</b> (<var>double x, long int n</var>)<var><a name="index-scalbln-2431"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- BSD --> |
| — Function: long long int <b>scalblnf</b> (<var>float x, long int n</var>)<var><a name="index-scalblnf-2432"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- BSD --> |
| — Function: long long int <b>scalblnl</b> (<var>long double x, long int n</var>)<var><a name="index-scalblnl-2433"></a></var><br> |
| <blockquote><p><code>scalbln</code> is identical to <code>scalb</code>, except that the exponent |
| <var>n</var> is a <code>long int</code> instead of a floating-point number. |
| </p></blockquote></div> |
| |
| <!-- math.h --> |
| <!-- BSD --> |
| <div class="defun"> |
| — Function: long long int <b>significand</b> (<var>double x</var>)<var><a name="index-significand-2434"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- BSD --> |
| — Function: long long int <b>significandf</b> (<var>float x</var>)<var><a name="index-significandf-2435"></a></var><br> |
| <blockquote><!-- math.h --> |
| <!-- BSD --> |
| — Function: long long int <b>significandl</b> (<var>long double x</var>)<var><a name="index-significandl-2436"></a></var><br> |
| <blockquote><p><code>significand</code> returns the mantissa of <var>x</var> scaled to the range |
| [1, 2). |
| It is equivalent to <code>scalb (</code><var>x</var><code>, (double) -ilogb (</code><var>x</var><code>))</code><!-- /@w -->. |
| |
| <p>This function exists mainly for use in certain standardized tests |
| of IEEE 754<!-- /@w --> conformance. |
| </p></blockquote></div> |
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