<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <link rel="stylesheet" href="style.css" type="text/css"> <meta content="text/html; charset=iso-8859-1" http-equiv="Content-Type"> <link rel="Start" href="index.html"> <link rel="previous" href="Nativeint.html"> <link rel="next" href="Obj.html"> <link rel="Up" href="index.html"> <link title="Index of types" rel=Appendix href="index_types.html"> <link title="Index of exceptions" rel=Appendix href="index_exceptions.html"> <link title="Index of values" rel=Appendix href="index_values.html"> <link title="Index of modules" rel=Appendix href="index_modules.html"> <link title="Index of module types" rel=Appendix href="index_module_types.html"> <link title="Arg" rel="Chapter" href="Arg.html"> <link title="Arith_status" rel="Chapter" href="Arith_status.html"> <link title="Array" rel="Chapter" href="Array.html"> <link title="ArrayLabels" rel="Chapter" href="ArrayLabels.html"> <link title="Big_int" rel="Chapter" 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href="Tk.html"> <link title="Unix" rel="Chapter" href="Unix.html"> <link title="UnixLabels" rel="Chapter" href="UnixLabels.html"> <link title="Weak" rel="Chapter" href="Weak.html"><link title="Arithmetic operations" rel="Section" href="#6_Arithmeticoperations"> <link title="Coercions with strings" rel="Section" href="#6_Coercionswithstrings"> <link title="Coercions between numerical types" rel="Section" href="#6_Coercionsbetweennumericaltypes"> <link title="Comparisons between numbers" rel="Subsection" href="#7_Comparisonsbetweennumbers"> <title>Num</title> </head> <body> <div class="navbar"><a class="pre" href="Nativeint.html" title="Nativeint">Previous</a> <a class="up" href="index.html" title="Index">Up</a> <a class="post" href="Obj.html" title="Obj">Next</a> </div> <h1>Module <a href="type_Num.html">Num</a></h1> <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><div class="info module top"> 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> </div> <hr width="100%"> <pre><code><span id="TYPEnum"><span class="keyword">type</span> <code class="type"></code>num</span> = </code></pre><table class="typetable"> <tr> <td align="left" valign="top" > <code><span class="keyword">|</span></code></td> <td align="left" valign="top" > <code><span id="TYPEELTnum.Int"><span class="constructor">Int</span></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 id="TYPEELTnum.Big_int"><span class="constructor">Big_int</span></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 id="TYPEELTnum.Ratio"><span class="constructor">Ratio</span></span> <span class="keyword">of</span> <code class="type"><a href="Ratio.html#TYPEratio">Ratio.ratio</a></code></code></td> </tr></table> <div class="info "> The type of numbers.<br> </div> <br> <h6 id="6_Arithmeticoperations">Arithmetic operations</h6><br> <pre><span id="VAL(+/)"><span class="keyword">val</span> (+/)</span> : <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 id="VALadd_num"><span class="keyword">val</span> add_num</span> : <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 id="VALminus_num"><span class="keyword">val</span> minus_num</span> : <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 id="VAL(-/)"><span class="keyword">val</span> (-/)</span> : <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 id="VALsub_num"><span class="keyword">val</span> sub_num</span> : <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 id="VAL( */ )"><span class="keyword">val</span> ( */ )</span> : <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 id="VALmult_num"><span class="keyword">val</span> mult_num</span> : <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 id="VALsquare_num"><span class="keyword">val</span> square_num</span> : <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 id="VAL(//)"><span class="keyword">val</span> (//)</span> : <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 id="VALdiv_num"><span class="keyword">val</span> div_num</span> : <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 id="VALquo_num"><span class="keyword">val</span> quo_num</span> : <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 id="VALmod_num"><span class="keyword">val</span> mod_num</span> : <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 id="VAL( **/ )"><span class="keyword">val</span> ( **/ )</span> : <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 id="VALpower_num"><span class="keyword">val</span> power_num</span> : <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 id="VALabs_num"><span class="keyword">val</span> abs_num</span> : <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 id="VALsucc_num"><span class="keyword">val</span> succ_num</span> : <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 id="VALpred_num"><span class="keyword">val</span> pred_num</span> : <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 id="VALincr_num"><span class="keyword">val</span> incr_num</span> : <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 id="VALdecr_num"><span class="keyword">val</span> decr_num</span> : <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 id="VALis_integer_num"><span class="keyword">val</span> is_integer_num</span> : <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 id="VALinteger_num"><span class="keyword">val</span> integer_num</span> : <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 id="VALfloor_num"><span class="keyword">val</span> floor_num</span> : <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 id="VALround_num"><span class="keyword">val</span> round_num</span> : <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 id="VALceiling_num"><span class="keyword">val</span> ceiling_num</span> : <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 id="VALsign_num"><span class="keyword">val</span> sign_num</span> : <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> <div class="h7" id="7_Comparisonsbetweennumbers">Comparisons between numbers</div><br> <pre><span id="VAL(=/)"><span class="keyword">val</span> (=/)</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre> <pre><span id="VAL(</)"><span class="keyword">val</span> (</)</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre> <pre><span id="VAL(>/)"><span class="keyword">val</span> (>/)</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre> <pre><span id="VAL(<=/)"><span class="keyword">val</span> (<=/)</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre> <pre><span id="VAL(>=/)"><span class="keyword">val</span> (>=/)</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre> <pre><span id="VAL(<>/)"><span class="keyword">val</span> (<>/)</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre> <pre><span id="VALeq_num"><span class="keyword">val</span> eq_num</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre> <pre><span id="VALlt_num"><span class="keyword">val</span> lt_num</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre> <pre><span id="VALle_num"><span class="keyword">val</span> le_num</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre> <pre><span id="VALgt_num"><span class="keyword">val</span> gt_num</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre> <pre><span id="VALge_num"><span class="keyword">val</span> ge_num</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Num.html#TYPEnum">num</a> -> bool</code></pre> <pre><span id="VALcompare_num"><span class="keyword">val</span> compare_num</span> : <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 id="VALmax_num"><span class="keyword">val</span> max_num</span> : <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 id="VALmin_num"><span class="keyword">val</span> min_num</span> : <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> <h6 id="6_Coercionswithstrings">Coercions with strings</h6><br> <pre><span id="VALstring_of_num"><span class="keyword">val</span> string_of_num</span> : <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 id="VALapprox_num_fix"><span class="keyword">val</span> approx_num_fix</span> : <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 id="VALapprox_num_exp"><span class="keyword">val</span> approx_num_exp</span> : <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 id="VALnum_of_string"><span class="keyword">val</span> num_of_string</span> : <code class="type">string -> <a href="Num.html#TYPEnum">num</a></code></pre><div class="info "> Convert a string to a number. Raise <code class="code"><span class="constructor">Failure</span> <span class="string">"num_of_string"</span></code> if the given string is not a valid representation of an integer<br> </div> <br> <h6 id="6_Coercionsbetweennumericaltypes">Coercions between numerical types</h6><br> <pre><span id="VALint_of_num"><span class="keyword">val</span> int_of_num</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> int</code></pre> <pre><span id="VALnum_of_int"><span class="keyword">val</span> num_of_int</span> : <code class="type">int -> <a href="Num.html#TYPEnum">num</a></code></pre> <pre><span id="VALnat_of_num"><span class="keyword">val</span> nat_of_num</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> Nat.nat</code></pre> <pre><span id="VALnum_of_nat"><span class="keyword">val</span> num_of_nat</span> : <code class="type">Nat.nat -> <a href="Num.html#TYPEnum">num</a></code></pre> <pre><span id="VALnum_of_big_int"><span class="keyword">val</span> num_of_big_int</span> : <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 id="VALbig_int_of_num"><span class="keyword">val</span> big_int_of_num</span> : <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 id="VALratio_of_num"><span class="keyword">val</span> ratio_of_num</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> <a href="Ratio.html#TYPEratio">Ratio.ratio</a></code></pre> <pre><span id="VALnum_of_ratio"><span class="keyword">val</span> num_of_ratio</span> : <code class="type"><a href="Ratio.html#TYPEratio">Ratio.ratio</a> -> <a href="Num.html#TYPEnum">num</a></code></pre> <pre><span id="VALfloat_of_num"><span class="keyword">val</span> float_of_num</span> : <code class="type"><a href="Num.html#TYPEnum">num</a> -> float</code></pre></body></html>
