php-doc-en/language/types/float.xml

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<sect1 xml:id="language.types.float" xmlns:xlink="http://www.w3.org/1999/xlink">
 <title>Floating point numbers</title>

 <para>
  Floating point numbers (also known as "floats", "doubles", or "real numbers")
  can be specified using any of the following syntaxes:
 </para>

 <informalexample>
  <programlisting role="php">
<![CDATA[
<?php
$a = 1.234; 
$b = 1.2e3; 
$c = 7E-10;
$d = 1_234.567; // as of PHP 7.4.0
?>
]]>
  </programlisting>
 </informalexample>

 <para>
  Formally as of PHP 7.4.0 (previously, underscores have not been allowed):
 </para>

 <informalexample>
  <programlisting>
<![CDATA[
LNUM          [0-9]+(_[0-9]+)*
DNUM          ([0-9]*(_[0-9]+)*[\.]{LNUM}) | ({LNUM}[\.][0-9]*(_[0-9]+)*)
EXPONENT_DNUM (({LNUM} | {DNUM}) [eE][+-]? {LNUM})
]]>
  </programlisting>
 </informalexample>

 <para>
  The size of a float is platform-dependent, although a maximum of approximately 1.8e308 
  with a precision of roughly 14 decimal digits is a common value (the 64 bit IEEE
  format).
 </para>

 <warning xml:id="warn.float-precision">
  <title>Floating point precision</title>

  <para>
   Floating point numbers have limited precision. Although it depends on the
   system, PHP typically uses the IEEE 754 double precision format, which will
   give a maximum relative error due to rounding in the order of 1.11e-16.
   Non elementary arithmetic operations may give larger errors, and, of course,
   error propagation must be considered when several operations are
   compounded.
  </para>
  
  <para>
   Additionally, rational numbers that are exactly representable as floating
   point numbers in base 10, like <literal>0.1</literal> or
   <literal>0.7</literal>, do not have an exact representation as floating
   point numbers in base 2, which is used internally, no matter the size of
   the mantissa. Hence, they cannot be converted into their internal binary
   counterparts without a small loss of precision. This can lead to confusing
   results: for example, <literal>floor((0.1+0.7)*10)</literal> will usually
   return <literal>7</literal> instead of the expected <literal>8</literal>,
   since the internal representation will be something like
   <literal>7.9999999999999991118...</literal>.
  </para>

  <para>
   So never trust floating number results to the last digit, and do not compare 
   floating point numbers directly for equality. If higher precision is
   necessary, the <link linkend="ref.bc">arbitrary precision math functions</link>
   and <link linkend="ref.gmp">gmp</link> functions are available.
  </para>
  
  <para>
   For a "simple" explanation, see the <link xlink:href="&url.floating.point.guide;">floating point guide</link>
   that's also titled "Why don’t my numbers add up?"
  </para>
 </warning>

 <sect2 xml:id="language.types.float.casting">
  <title>Converting to float</title>

  <sect3 xml:id="language.types.float.casting.from-string">
   <title>From strings</title>

   <simpara>
    If the string is
    <link linkend="language.types.numeric-strings">numeric</link>
    or leading numeric then it will resolve to the
    corresponding float value, otherwise it is converted to zero
    (<literal>0</literal>).
   </simpara>
  </sect3>

  <sect3 xml:id="language.types.float.casting.from-other">
   <title>From other types</title>

   <para>
    For values of other types, the conversion is performed by converting the
    value to <type>int</type> first and then to <type>float</type>. See
    <link linkend="language.types.integer.casting">Converting to integer</link>
    for more information.
   </para>

   <note>
    <para>
     As certain types have undefined behavior when converting to
     <type>int</type>, this is also the case when converting to
     <type>float</type>.
    </para>
   </note>
  </sect3>
 </sect2>

 <sect2 xml:id="language.types.float.comparison">
  <title>Comparing floats</title>

  <para>
   As noted in the warning above, testing floating point values for equality is
   problematic, due to the way that they are represented internally. However,
   there are ways to make comparisons of floating point values that work around
   these limitations.
  </para>

  <para>
   To test floating point values for equality, an upper bound on the relative
   error due to rounding is used. This value is known as the machine epsilon,
   or unit roundoff, and is the smallest acceptable difference in calculations.
  </para>
  
  <informalexample>
   <simpara>
    <varname>$a</varname> and <varname>$b</varname> are equal to 5 digits of
    precision.
   </simpara>
   <programlisting role="php">
<![CDATA[
<?php
$a = 1.23456789;
$b = 1.23456780;
$epsilon = 0.00001;

if(abs($a-$b) < $epsilon) {
    echo "true";
}
?>
]]>
   </programlisting>
  </informalexample>
 </sect2>
 
 <sect2 xml:id="language.types.float.nan">
  <title>NaN</title>
  <para>
   Some numeric operations can result in a value represented by the constant
   <constant>NAN</constant>. This result represents an undefined or
   unrepresentable value in floating-point calculations. Any loose or strict
   comparisons of this value against any other value, including itself, but except &true;, will
   have a result of &false;.
  </para>
  <para>
   Because <constant>NAN</constant> represents any number of different values,
   <constant>NAN</constant> should not be compared to other values, including
   itself, and instead should be checked for using <function>is_nan</function>.
  </para>
 </sect2>
</sect1>

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