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<title>Num</title>
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<center><h1>Module <a href="type_Num.html">Num</a></h1></center>
<br>
<pre><span class="keyword">module</span> Num: <code class="code"><span class="keyword">sig</span></code> <a href="Num.html">..</a> <code class="code"><span class="keyword">end</span></code></pre>Operation on arbitrary-precision numbers.
<p>
Numbers (type <code class="code">num</code>) are arbitrary-precision rational numbers,
plus the special elements <code class="code">1/0</code> (infinity) and <code class="code">0/0</code> (undefined).<br>
<hr width="100%">
<br><code><span class="keyword">type</span> <a name="TYPEnum"></a><code class="type"></code>num = </code><table class="typetable">
<tr>
<td align="left" valign="top" >
<code><span class="keyword">|</span></code></td>
<td align="left" valign="top" >
<code><span class="constructor">Int</span> <span class="keyword">of</span> <code class="type">int</code></code></td>
</tr>
<tr>
<td align="left" valign="top" >
<code><span class="keyword">|</span></code></td>
<td align="left" valign="top" >
<code><span class="constructor">Big_int</span> <span class="keyword">of</span> <code class="type"><a href="Big_int.html#TYPEbig_int">Big_int.big_int</a></code></code></td>
</tr>
<tr>
<td align="left" valign="top" >
<code><span class="keyword">|</span></code></td>
<td align="left" valign="top" >
<code><span class="constructor">Ratio</span> <span class="keyword">of</span> <code class="type">Ratio.ratio</code></code></td>
</tr></table>
<div class="info">
The type of numbers.<br>
</div>
<br>
<a name="6_Arithmeticoperations"></a>
<h6>Arithmetic operations</h6><br>
<pre><span class="keyword">val</span> <a name="VAL(+/)"></a>(+/) : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Same as <a href="Num.html#VALadd_num"><code class="code"><span class="constructor">Num</span>.add_num</code></a>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALadd_num"></a>add_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Addition<br>
</div>
<pre><span class="keyword">val</span> <a name="VALminus_num"></a>minus_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Unary negation.<br>
</div>
<pre><span class="keyword">val</span> <a name="VAL(-/)"></a>(-/) : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Same as <a href="Num.html#VALsub_num"><code class="code"><span class="constructor">Num</span>.sub_num</code></a>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALsub_num"></a>sub_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Subtraction<br>
</div>
<pre><span class="keyword">val</span> <a name="VAL(*/)"></a>(*/) : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Same as <a href="Num.html#VALmult_num"><code class="code"><span class="constructor">Num</span>.mult_num</code></a>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALmult_num"></a>mult_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Multiplication<br>
</div>
<pre><span class="keyword">val</span> <a name="VALsquare_num"></a>square_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Squaring<br>
</div>
<pre><span class="keyword">val</span> <a name="VAL(//)"></a>(//) : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Same as <a href="Num.html#VALdiv_num"><code class="code"><span class="constructor">Num</span>.div_num</code></a>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALdiv_num"></a>div_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Division<br>
</div>
<pre><span class="keyword">val</span> <a name="VALquo_num"></a>quo_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Euclidean division: quotient.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALmod_num"></a>mod_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Euclidean division: remainder.<br>
</div>
<pre><span class="keyword">val</span> <a name="VAL(**/)"></a>(**/) : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Same as <a href="Num.html#VALpower_num"><code class="code"><span class="constructor">Num</span>.power_num</code></a>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALpower_num"></a>power_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Exponentiation<br>
</div>
<pre><span class="keyword">val</span> <a name="VALabs_num"></a>abs_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Absolute value.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALsucc_num"></a>succ_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
<code class="code">succ n</code> is <code class="code">n+1</code><br>
</div>
<pre><span class="keyword">val</span> <a name="VALpred_num"></a>pred_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
<code class="code">pred n</code> is <code class="code">n-1</code><br>
</div>
<pre><span class="keyword">val</span> <a name="VALincr_num"></a>incr_num : <code class="type"><a href="Num.html#TYPEnum">num</a> <a href="Pervasives.html#TYPEref">ref</a> -> unit</code></pre><div class="info">
<code class="code">incr r</code> is <code class="code">r:=!r+1</code>, where <code class="code">r</code> is a reference to a number.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALdecr_num"></a>decr_num : <code class="type"><a href="Num.html#TYPEnum">num</a> <a href="Pervasives.html#TYPEref">ref</a> -> unit</code></pre><div class="info">
<code class="code">decr r</code> is <code class="code">r:=!r-1</code>, where <code class="code">r</code> is a reference to a number.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALis_integer_num"></a>is_integer_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> bool</code></pre><div class="info">
Test if a number is an integer<br>
</div>
<br>
The four following functions approximate a number by an integer :<br>
<pre><span class="keyword">val</span> <a name="VALinteger_num"></a>integer_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
<code class="code">integer_num n</code> returns the integer closest to <code class="code">n</code>. In case of ties,
rounds towards zero.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALfloor_num"></a>floor_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
<code class="code">floor_num n</code> returns the largest integer smaller or equal to <code class="code">n</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALround_num"></a>round_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
<code class="code">round_num n</code> returns the integer closest to <code class="code">n</code>. In case of ties,
rounds off zero.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALceiling_num"></a>ceiling_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
<code class="code">ceiling_num n</code> returns the smallest integer bigger or equal to <code class="code">n</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALsign_num"></a>sign_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> int</code></pre><div class="info">
Return <code class="code">-1</code>, <code class="code">0</code> or <code class="code">1</code> according to the sign of the argument.<br>
</div>
<br>
<a name="7_Comparisonsbetweennumbers"></a>
<div class="h7">Comparisons between numbers</div><br>
<pre><span class="keyword">val</span> <a name="VAL(=/)"></a>(=/) : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre><pre><span class="keyword">val</span> <a name="VAL(</)"></a>(</) : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre><pre><span class="keyword">val</span> <a name="VAL(>/)"></a>(>/) : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre><pre><span class="keyword">val</span> <a name="VAL(<=/)"></a>(<=/) : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre><pre><span class="keyword">val</span> <a name="VAL(>=/)"></a>(>=/) : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre><pre><span class="keyword">val</span> <a name="VAL(<>/)"></a>(<>/) : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre><pre><span class="keyword">val</span> <a name="VALeq_num"></a>eq_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre><pre><span class="keyword">val</span> <a name="VALlt_num"></a>lt_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre><pre><span class="keyword">val</span> <a name="VALle_num"></a>le_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre><pre><span class="keyword">val</span> <a name="VALgt_num"></a>gt_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre><pre><span class="keyword">val</span> <a name="VALge_num"></a>ge_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre><pre><span class="keyword">val</span> <a name="VALcompare_num"></a>compare_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> int</code></pre><div class="info">
Return <code class="code">-1</code>, <code class="code">0</code> or <code class="code">1</code> if the first argument is less than,
equal to, or greater than the second argument.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALmax_num"></a>max_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Return the greater of the two arguments.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALmin_num"></a>min_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Return the smaller of the two arguments.<br>
</div>
<br>
<a name="6_Coercionswithstrings"></a>
<h6>Coercions with strings</h6><br>
<pre><span class="keyword">val</span> <a name="VALstring_of_num"></a>string_of_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> string</code></pre><div class="info">
Convert a number to a string, using fractional notation.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALapprox_num_fix"></a>approx_num_fix : <code class="type">int -> <a href="Num.html#TYPEnum">num</a> -> string</code></pre><div class="info">
See <a href="Num.html#VALapprox_num_exp"><code class="code"><span class="constructor">Num</span>.approx_num_exp</code></a>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALapprox_num_exp"></a>approx_num_exp : <code class="type">int -> <a href="Num.html#TYPEnum">num</a> -> string</code></pre><div class="info">
Approximate a number by a decimal. The first argument is the
required precision. The second argument is the number to
approximate. <a href="Num.html#VALapprox_num_fix"><code class="code"><span class="constructor">Num</span>.approx_num_fix</code></a> uses decimal notation; the first
argument is the number of digits after the decimal point.
<code class="code">approx_num_exp</code> uses scientific (exponential) notation; the
first argument is the number of digits in the mantissa.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALnum_of_string"></a>num_of_string : <code class="type">string -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info">
Convert a string to a number.<br>
</div>
<br>
<a name="6_Coercionsbetweennumericaltypes"></a>
<h6>Coercions between numerical types</h6><br>
<pre><span class="keyword">val</span> <a name="VALint_of_num"></a>int_of_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> int</code></pre><pre><span class="keyword">val</span> <a name="VALnum_of_int"></a>num_of_int : <code class="type">int -> <a href="Num.html#TYPEnum">num</a></code></pre><pre><span class="keyword">val</span> <a name="VALnat_of_num"></a>nat_of_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> Nat.nat</code></pre><pre><span class="keyword">val</span> <a name="VALnum_of_nat"></a>num_of_nat : <code class="type">Nat.nat -> <a href="Num.html#TYPEnum">num</a></code></pre><pre><span class="keyword">val</span> <a name="VALnum_of_big_int"></a>num_of_big_int : <code class="type"><a href="Big_int.html#TYPEbig_int">Big_int.big_int</a> -> <a href="Num.html#TYPEnum">num</a></code></pre><pre><span class="keyword">val</span> <a name="VALbig_int_of_num"></a>big_int_of_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Big_int.html#TYPEbig_int">Big_int.big_int</a></code></pre><pre><span class="keyword">val</span> <a name="VALratio_of_num"></a>ratio_of_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> Ratio.ratio</code></pre><pre><span class="keyword">val</span> <a name="VALnum_of_ratio"></a>num_of_ratio : <code class="type">Ratio.ratio -> <a href="Num.html#TYPEnum">num</a></code></pre><pre><span class="keyword">val</span> <a name="VALfloat_of_num"></a>float_of_num : <code class="type"><a href="Num.html#TYPEnum">num</a> -> float</code></pre></body></html>
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