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<h1>Module <a href="type_Float.html">Float</a></h1>
<pre><span id="MODULEFloat"><span class="keyword">module</span> Float</span>: <code class="code"><span class="keyword">sig</span></code> <a href="Float.html">..</a> <code class="code"><span class="keyword">end</span></code></pre><div class="info module top">
<div class="info-desc">
<h2 id="1_Floatingpointarithmetic">Floating-point arithmetic</h2>
<p>OCaml's floating-point numbers follow the
IEEE 754 standard, using double precision (64 bits) numbers.
Floating-point operations never raise an exception on overflow,
underflow, division by zero, etc. Instead, special IEEE numbers
are returned as appropriate, such as <code class="code">infinity</code> for <code class="code">1.0 /. 0.0</code>,
<code class="code">neg_infinity</code> for <code class="code">-1.0 /. 0.0</code>, and <code class="code">nan</code> ('not a number')
for <code class="code">0.0 /. 0.0</code>. These special numbers then propagate through
floating-point computations as expected: for instance,
<code class="code">1.0 /. infinity</code> is <code class="code">0.0</code>, and any arithmetic operation with <code class="code">nan</code>
as argument returns <code class="code">nan</code> as result.</p>
</div>
<ul class="info-attributes">
<li><b>Since</b> 4.07.0</li>
</ul>
</div>
<hr width="100%">
<pre><span id="VALneg"><span class="keyword">val</span> neg</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Unary negation.</p>
</div>
</div>
<pre><span id="VALadd"><span class="keyword">val</span> add</span> : <code class="type">float -> float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Floating-point addition.</p>
</div>
</div>
<pre><span id="VALsub"><span class="keyword">val</span> sub</span> : <code class="type">float -> float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Floating-point subtraction.</p>
</div>
</div>
<pre><span id="VALmul"><span class="keyword">val</span> mul</span> : <code class="type">float -> float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Floating-point multiplication.</p>
</div>
</div>
<pre><span id="VALdiv"><span class="keyword">val</span> div</span> : <code class="type">float -> float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Floating-point division.</p>
</div>
</div>
<pre><span id="VALrem"><span class="keyword">val</span> rem</span> : <code class="type">float -> float -> float</code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">rem a b</code> returns the remainder of <code class="code">a</code> with respect to <code class="code">b</code>. The returned
value is <code class="code">a -. n *. b</code>, where <code class="code">n</code> is the quotient <code class="code">a /. b</code> rounded towards
zero to an integer.</p>
</div>
</div>
<pre><span id="VALabs"><span class="keyword">val</span> abs</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">abs f</code> returns the absolute value of <code class="code">f</code>.</p>
</div>
</div>
<pre><span id="VALinfinity"><span class="keyword">val</span> infinity</span> : <code class="type">float</code></pre><div class="info ">
<div class="info-desc">
<p>Positive infinity.</p>
</div>
</div>
<pre><span id="VALneg_infinity"><span class="keyword">val</span> neg_infinity</span> : <code class="type">float</code></pre><div class="info ">
<div class="info-desc">
<p>Negative infinity.</p>
</div>
</div>
<pre><span id="VALnan"><span class="keyword">val</span> nan</span> : <code class="type">float</code></pre><div class="info ">
<div class="info-desc">
<p>A special floating-point value denoting the result of an
undefined operation such as <code class="code">0.0 /. 0.0</code>. Stands for
'not a number'. Any floating-point operation with <code class="code">nan</code> as
argument returns <code class="code">nan</code> as result. As for floating-point comparisons,
<code class="code">=</code>, <code class="code"><</code>, <code class="code"><=</code>, <code class="code">></code> and <code class="code">>=</code> return <code class="code"><span class="keyword">false</span></code> and <code class="code"><></code> returns <code class="code"><span class="keyword">true</span></code>
if one or both of their arguments is <code class="code">nan</code>.</p>
</div>
</div>
<pre><span id="VALpi"><span class="keyword">val</span> pi</span> : <code class="type">float</code></pre><div class="info ">
<div class="info-desc">
<p>The constant pi.</p>
</div>
</div>
<pre><span id="VALmax_float"><span class="keyword">val</span> max_float</span> : <code class="type">float</code></pre><div class="info ">
<div class="info-desc">
<p>The largest positive finite value of type <code class="code">float</code>.</p>
</div>
</div>
<pre><span id="VALmin_float"><span class="keyword">val</span> min_float</span> : <code class="type">float</code></pre><div class="info ">
<div class="info-desc">
<p>The smallest positive, non-zero, non-denormalized value of type <code class="code">float</code>.</p>
</div>
</div>
<pre><span id="VALepsilon"><span class="keyword">val</span> epsilon</span> : <code class="type">float</code></pre><div class="info ">
<div class="info-desc">
<p>The difference between <code class="code">1.0</code> and the smallest exactly representable
floating-point number greater than <code class="code">1.0</code>.</p>
</div>
</div>
<pre><span id="VALof_int"><span class="keyword">val</span> of_int</span> : <code class="type">int -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Convert an integer to floating-point.</p>
</div>
</div>
<pre><span id="VALto_int"><span class="keyword">val</span> to_int</span> : <code class="type">float -> int</code></pre><div class="info ">
<div class="info-desc">
<p>Truncate the given floating-point number to an integer.
The result is unspecified if the argument is <code class="code">nan</code> or falls outside the
range of representable integers.</p>
</div>
</div>
<pre><span id="VALof_string"><span class="keyword">val</span> of_string</span> : <code class="type">string -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Convert the given string to a float. The string is read in decimal
(by default) or in hexadecimal (marked by <code class="code">0x</code> or <code class="code">0<span class="constructor">X</span></code>).
The format of decimal floating-point numbers is
<code class="code"> [-] dd.ddd (e<span class="keywordsign">|</span><span class="constructor">E</span>) [+|-] dd </code>, where <code class="code">d</code> stands for a decimal digit.
The format of hexadecimal floating-point numbers is
<code class="code"> [-] 0(x<span class="keywordsign">|</span><span class="constructor">X</span>) hh.hhh (p<span class="keywordsign">|</span><span class="constructor">P</span>) [+|-] dd </code>, where <code class="code">h</code> stands for an
hexadecimal digit and <code class="code">d</code> for a decimal digit.
In both cases, at least one of the integer and fractional parts must be
given; the exponent part is optional.
The <code class="code">_</code> (underscore) character can appear anywhere in the string
and is ignored.
Depending on the execution platforms, other representations of
floating-point numbers can be accepted, but should not be relied upon.
Raise <code class="code"><span class="constructor">Failure</span> <span class="string">"float_of_string"</span></code> if the given string is not a valid
representation of a float.</p>
</div>
</div>
<pre><span id="VALof_string_opt"><span class="keyword">val</span> of_string_opt</span> : <code class="type">string -> float option</code></pre><div class="info ">
<div class="info-desc">
<p>Same as <code class="code">of_string</code>, but returns <code class="code"><span class="constructor">None</span></code> instead of raising.</p>
</div>
</div>
<pre><span id="VALto_string"><span class="keyword">val</span> to_string</span> : <code class="type">float -> string</code></pre><div class="info ">
<div class="info-desc">
<p>Return the string representation of a floating-point number.</p>
</div>
</div>
<pre><span id="TYPEfpclass"><span class="keyword">type</span> <code class="type"></code>fpclass</span> = <code class="type"><a href="Pervasives.html#TYPEfpclass">fpclass</a></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="TYPEELTfpclass.FP_normal"><span class="constructor">FP_normal</span></span></code></td>
<td class="typefieldcomment" align="left" valign="top" ><code>(*</code></td><td class="typefieldcomment" align="left" valign="top" ><div class="info ">
<div class="info-desc">
<p>Normal number, none of the below</p>
</div>
</div>
</td><td class="typefieldcomment" align="left" valign="bottom" ><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="TYPEELTfpclass.FP_subnormal"><span class="constructor">FP_subnormal</span></span></code></td>
<td class="typefieldcomment" align="left" valign="top" ><code>(*</code></td><td class="typefieldcomment" align="left" valign="top" ><div class="info ">
<div class="info-desc">
<p>Number very close to 0.0, has reduced precision</p>
</div>
</div>
</td><td class="typefieldcomment" align="left" valign="bottom" ><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="TYPEELTfpclass.FP_zero"><span class="constructor">FP_zero</span></span></code></td>
<td class="typefieldcomment" align="left" valign="top" ><code>(*</code></td><td class="typefieldcomment" align="left" valign="top" ><div class="info ">
<div class="info-desc">
<p>Number is 0.0 or -0.0</p>
</div>
</div>
</td><td class="typefieldcomment" align="left" valign="bottom" ><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="TYPEELTfpclass.FP_infinite"><span class="constructor">FP_infinite</span></span></code></td>
<td class="typefieldcomment" align="left" valign="top" ><code>(*</code></td><td class="typefieldcomment" align="left" valign="top" ><div class="info ">
<div class="info-desc">
<p>Number is positive or negative infinity</p>
</div>
</div>
</td><td class="typefieldcomment" align="left" valign="bottom" ><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="TYPEELTfpclass.FP_nan"><span class="constructor">FP_nan</span></span></code></td>
<td class="typefieldcomment" align="left" valign="top" ><code>(*</code></td><td class="typefieldcomment" align="left" valign="top" ><div class="info ">
<div class="info-desc">
<p>Not a number: result of an undefined operation</p>
</div>
</div>
</td><td class="typefieldcomment" align="left" valign="bottom" ><code>*)</code></td>
</tr></table>
<div class="info ">
<div class="info-desc">
<p>The five classes of floating-point numbers, as determined by
the <a href="Float.html#VALclassify_float"><code class="code"><span class="constructor">Float</span>.classify_float</code></a> function.</p>
</div>
</div>
<pre><span id="VALclassify_float"><span class="keyword">val</span> classify_float</span> : <code class="type">float -> <a href="Float.html#TYPEfpclass">fpclass</a></code></pre><div class="info ">
<div class="info-desc">
<p>Return the class of the given floating-point number:
normal, subnormal, zero, infinite, or not a number.</p>
</div>
</div>
<pre><span id="VALpow"><span class="keyword">val</span> pow</span> : <code class="type">float -> float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Exponentiation.</p>
</div>
</div>
<pre><span id="VALsqrt"><span class="keyword">val</span> sqrt</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Square root.</p>
</div>
</div>
<pre><span id="VALexp"><span class="keyword">val</span> exp</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Exponential.</p>
</div>
</div>
<pre><span id="VALlog"><span class="keyword">val</span> log</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Natural logarithm.</p>
</div>
</div>
<pre><span id="VALlog10"><span class="keyword">val</span> log10</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Base 10 logarithm.</p>
</div>
</div>
<pre><span id="VALexpm1"><span class="keyword">val</span> expm1</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">expm1 x</code> computes <code class="code">exp x -. 1.0</code>, giving numerically-accurate results
even if <code class="code">x</code> is close to <code class="code">0.0</code>.</p>
</div>
</div>
<pre><span id="VALlog1p"><span class="keyword">val</span> log1p</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">log1p x</code> computes <code class="code">log(1.0 +. x)</code> (natural logarithm),
giving numerically-accurate results even if <code class="code">x</code> is close to <code class="code">0.0</code>.</p>
</div>
</div>
<pre><span id="VALcos"><span class="keyword">val</span> cos</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Cosine. Argument is in radians.</p>
</div>
</div>
<pre><span id="VALsin"><span class="keyword">val</span> sin</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Sine. Argument is in radians.</p>
</div>
</div>
<pre><span id="VALtan"><span class="keyword">val</span> tan</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Tangent. Argument is in radians.</p>
</div>
</div>
<pre><span id="VALacos"><span class="keyword">val</span> acos</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Arc cosine. The argument must fall within the range <code class="code">[-1.0, 1.0]</code>.
Result is in radians and is between <code class="code">0.0</code> and <code class="code">pi</code>.</p>
</div>
</div>
<pre><span id="VALasin"><span class="keyword">val</span> asin</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Arc sine. The argument must fall within the range <code class="code">[-1.0, 1.0]</code>.
Result is in radians and is between <code class="code">-pi/2</code> and <code class="code">pi/2</code>.</p>
</div>
</div>
<pre><span id="VALatan"><span class="keyword">val</span> atan</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Arc tangent.
Result is in radians and is between <code class="code">-pi/2</code> and <code class="code">pi/2</code>.</p>
</div>
</div>
<pre><span id="VALatan2"><span class="keyword">val</span> atan2</span> : <code class="type">float -> float -> float</code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">atan2 y x</code> returns the arc tangent of <code class="code">y /. x</code>. The signs of <code class="code">x</code>
and <code class="code">y</code> are used to determine the quadrant of the result.
Result is in radians and is between <code class="code">-pi</code> and <code class="code">pi</code>.</p>
</div>
</div>
<pre><span id="VALhypot"><span class="keyword">val</span> hypot</span> : <code class="type">float -> float -> float</code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">hypot x y</code> returns <code class="code">sqrt(x *. x + y *. y)</code>, that is, the length
of the hypotenuse of a right-angled triangle with sides of length
<code class="code">x</code> and <code class="code">y</code>, or, equivalently, the distance of the point <code class="code">(x,y)</code>
to origin. If one of <code class="code">x</code> or <code class="code">y</code> is infinite, returns <code class="code">infinity</code>
even if the other is <code class="code">nan</code>.</p>
</div>
</div>
<pre><span id="VALcosh"><span class="keyword">val</span> cosh</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Hyperbolic cosine. Argument is in radians.</p>
</div>
</div>
<pre><span id="VALsinh"><span class="keyword">val</span> sinh</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Hyperbolic sine. Argument is in radians.</p>
</div>
</div>
<pre><span id="VALtanh"><span class="keyword">val</span> tanh</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Hyperbolic tangent. Argument is in radians.</p>
</div>
</div>
<pre><span id="VALceil"><span class="keyword">val</span> ceil</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Round above to an integer value.
<code class="code">ceil f</code> returns the least integer value greater than or equal to <code class="code">f</code>.
The result is returned as a float.</p>
</div>
</div>
<pre><span id="VALfloor"><span class="keyword">val</span> floor</span> : <code class="type">float -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Round below to an integer value.
<code class="code">floor f</code> returns the greatest integer value less than or
equal to <code class="code">f</code>.
The result is returned as a float.</p>
</div>
</div>
<pre><span id="VALcopysign"><span class="keyword">val</span> copysign</span> : <code class="type">float -> float -> float</code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">copysign x y</code> returns a float whose absolute value is that of <code class="code">x</code>
and whose sign is that of <code class="code">y</code>. If <code class="code">x</code> is <code class="code">nan</code>, returns <code class="code">nan</code>.
If <code class="code">y</code> is <code class="code">nan</code>, returns either <code class="code">x</code> or <code class="code">-. x</code>, but it is not
specified which.</p>
</div>
</div>
<pre><span id="VALfrexp"><span class="keyword">val</span> frexp</span> : <code class="type">float -> float * int</code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">frexp f</code> returns the pair of the significant
and the exponent of <code class="code">f</code>. When <code class="code">f</code> is zero, the
significant <code class="code">x</code> and the exponent <code class="code">n</code> of <code class="code">f</code> are equal to
zero. When <code class="code">f</code> is non-zero, they are defined by
<code class="code">f = x *. 2 ** n</code> and <code class="code">0.5 <= x < 1.0</code>.</p>
</div>
</div>
<pre><span id="VALldexp"><span class="keyword">val</span> ldexp</span> : <code class="type">float -> int -> float</code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">ldexp x n</code> returns <code class="code">x *. 2 ** n</code>.</p>
</div>
</div>
<pre><span id="VALmodf"><span class="keyword">val</span> modf</span> : <code class="type">float -> float * float</code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">modf f</code> returns the pair of the fractional and integral
part of <code class="code">f</code>.</p>
</div>
</div>
<pre><span id="TYPEt"><span class="keyword">type</span> <code class="type"></code>t</span> = <code class="type">float</code> </pre>
<div class="info ">
<div class="info-desc">
<p>An alias for the type of floating-point numbers.</p>
</div>
</div>
<pre><span id="VALcompare"><span class="keyword">val</span> compare</span> : <code class="type"><a href="Float.html#TYPEt">t</a> -> <a href="Float.html#TYPEt">t</a> -> int</code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">compare x y</code> returns <code class="code">0</code> if <code class="code">x</code> is equal to <code class="code">y</code>, a negative integer if <code class="code">x</code>
is less than <code class="code">y</code>, and a positive integer if <code class="code">x</code> is greater than
<code class="code">y</code>. <code class="code">compare</code> treats <code class="code">nan</code> as equal to itself and less than any other float
value. This treatment of <code class="code">nan</code> ensures that <code class="code">compare</code> defines a total
ordering relation.</p>
</div>
</div>
<pre><span id="VALequal"><span class="keyword">val</span> equal</span> : <code class="type"><a href="Float.html#TYPEt">t</a> -> <a href="Float.html#TYPEt">t</a> -> bool</code></pre><div class="info ">
<div class="info-desc">
<p>The equal function for floating-point numbers, compared using <a href="Float.html#VALcompare"><code class="code"><span class="constructor">Float</span>.compare</code></a>.</p>
</div>
</div>
<pre><span id="VALhash"><span class="keyword">val</span> hash</span> : <code class="type"><a href="Float.html#TYPEt">t</a> -> int</code></pre><div class="info ">
<div class="info-desc">
<p>The hash function for floating-point numbers.</p>
</div>
</div>
<pre><span id="MODULEArray"><span class="keyword">module</span> <a href="Float.Array.html">Array</a></span>: <code class="code"><span class="keyword">sig</span></code> <a href="Float.Array.html">..</a> <code class="code"><span class="keyword">end</span></code></pre></body></html>
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