svn: /phpdoc/en/trunk/language/types/ float.xml

cataphract Sat, 20 Nov 2010 16:10:04 +0000 Revision: http://svn.php.net/viewvc?view=revision&revision=305581 Log: - Fixed inaccurate information on floats. Closes bug #53365. Bug: http://bugs.php.net/53365 (Open) Inaccurate information on floats. Changed paths: U phpdoc/en/trunk/language/types/float.xml Modified: phpdoc/en/trunk/language/types/float.xml =================================================================== --- phpdoc/en/trunk/language/types/float.xml 2010-11-20 02:09:04 UTC (rev 305580) +++ phpdoc/en/trunk/language/types/float.xml 2010-11-20 16:10:04 UTC (rev 305581) @@ -44,23 +44,28 @@ <title>Floating point precision</title> <para> - It is typical that simple decimal fractions like <literal>0.1</literal> or - <literal>0.7</literal> cannot be converted into their internal binary + 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 progragation 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 role="infdec">7.9</literal>. + <literal>7.9999999999999991118...</literal>. </para> <para> - This is due to the fact that it is impossible to express some - fractions in decimal notation with a finite number of digits. For instance, - <literal>1/3</literal> in decimal form becomes - <literal role="infdec">0.3</literal>. - </para> - - <para> So never trust floating number results to the last digit, and never compare floating point numbers for equality. If higher precision is necessary, the <link linkend="ref.bc">arbitrary precision math functions</link> and