So how big can a $variable in PHP get? I've tried to test this, but I'm not sure that I have enough system memory (~2gb). I figure there has to be some kind of limit. What happens when a string gets too large? Is it concatenated, or does PHP throw an exception?
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PHP's string length is limited by the way strings are represented in PHP; memory does not have anything to do with it.
According to phpinternalsbook.com, strings are stored in struct { char *val; int len; } and since the maximum size of an int in C is 4 bytes, this effectively limits the maximum string size to 2GB.
String can be as large as 2GB.
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To properly answer this qustion you need to consider PHP internals or the target that PHP is built for.
To answer this from a typical Linux perspective on x86...
Sizes of types in C: https://usrmisc.wordpress.com/2012/12/27/integer-sizes-in-c-on-32-bit-and-64-bit-linux/
Types used in PHP for variables: http://php.net/manual/en/internals2.variables.intro.php
Strings are always 2GB as the length is always 32bits and a bit is wasted because it uses int rather than uint. int is impractical for lengths over 2GB as it requires a cast to avoid breaking arithmetic or "than" comparisons. The extra bit is likely being used for overflow checks.
Strangely, hash keys might internally support 4GB as uint is used although I have never put this to the test. PHP hash keys have a +1 to the length for a trailing null byte which to my knowledge gets ignored so it may need to be unsigned for that edge case rather than to allow longer keys.
A 32bit system may impose more external limits.
In a new upcoming php7 among many other features, they added a support for strings bigger than 2^31 bytes:
Support for strings with length >= 2^31 bytes in 64 bit builds.
Sadly they did not specify how much bigger can it be.
The maximum length of a string variable is only 2GiB - (2^(32-1) bits). Variables can be addressed on a character (8 bits/1 byte) basis and the addressing is done by signed integers which is why the limit is what it is. Arrays can contain multiple variables that each follow the previous restriction but can have a total cumulative size up to memory_limit of which a string variable is also subject to.
Source: Stackoverflow.com