PHP RFC: Internal operator overloading and GMP improvements

• Version: 0.1
• Date: 2013-05-12
• Author: Nikita Popov nikic@php.net
• Status: Draft
• Patch: https://github.com/php/php-src/pull/342
• Target version: PHP 5.6 (or whatever the next one is)

PHP offers facilities for large number and decimal arithmetic (GMP and BCMath), but currently using those is a PITA. This RFC proposes to improve the situation by adding support for operator overloading in internal classes. The operator overloading is exemplarily implemented for the GMP extension, while also improving GMP in various other ways along the way.

There are several reasons why overloaded operators are preferable over gmp_add($a, $b) style functions.

The first is that code using overloaded operators is simply more readable. As an example, consider the following two code snippets, one using gmp_* functions, the other using overloading:

$result = gmp_mod(
    gmp_add(
        gmp_mul($c0, gmp_mul($ms0, gmp_invert($ms0, $n0))),
        gmp_add(
            gmp_mul($c1, gmp_mul($ms1, gmp_invert($ms1, $n1))),
            gmp_mul($c2, gmp_mul($ms2, gmp_invert($ms2, $n2)))
        )
    ),
    gmp_mul($n0, gmp_mul($n1, $n2))
);
 
$result = (
    $c0 * $ms0 * gmp_invert($ms0, $n0)
  + $c1 * $ms1 * gmp_invert($ms1, $n1)
  + $c2 * $ms2 * gmp_invert($ms2, $n2)
) % ($n0 * $n1 * $n2);

Even without understanding what the above code does (it's an excerpt from a Coppersmith attack on RSA), it should be obvious that the second code is a lot clearer. It makes the structure of the code immediately clear (three multiplications are summed up and the modulus is taken), whereas the function-based code actively hides any structure in the code. For mathematical operations infix notation just comes a lot more naturally.

Another advantage of overloaded operators is that it allows polymorphism for functions doing arithmetic operations. As an example, consider manually implementing a function like gmp_powm, which calculates a power of a number modulus some other number. Here is a sample implementation (direct translation of pseudo-code on Wikipedia):

function powm($base, $exponent, $modulus) {
    $result = 1;
    while ($exponent > 0) {
        if ($exponent % 2 == 1) {
            $result = $result * $base % $modulus;
            $exponent--;
        }
        $exponent /= 2;
        $base = ($base * $base) % $modulus;
    }
    return $result;
}

With operator overloading this function will work with any type of “number” that implements the basic arithmetic operators. It can work with normal PHP integers, it can work with GMP numbers, it can work with BCMath instances (assuming the overloading API is implemented for them of course):

var_dump(powm(123, 456, 789)); // int(699)
var_dump(powm(gmp_init(123), gmp_init(456), gmp_init(789))); // GMP(699)
var_dump(powm(
    gmp_init("123456789123456789"),
    gmp_init("987654321987654321"),
    gmp_init("56789567895678956789")
)); // GMP(36912902142130032810)

Without operator overloading this would not be possible. Instead one would have to implement the same function once using the normal + style operators and once using gmp_* functions (and any other set of functions you want to support). Operator overloading brings the advantages of polymorphism (a main reason we use object oriented programming) to the basic operations of the language.

Some examples what the operator overloading capability can be used for, apart from the bignum arithmetic outlined in this RFC:

• Decimal arithmetic. This is particularly important in PHP as PHP commonly deals with monetary values which can not be represented as floating point numbers.
• Date calculations. Also very common in PHP (DateTime::add etc)
• Ratio and complex arithmetic
• Unsigned arithmetic and arithmetic on other integral types PHP does not support (e.g. cross platform 64bit integers)
• Vector and matrix calculations
• (Misuse for DSLs)

The operator overloading is implemented by adding a new object handler do_operation with the following signature:

typedef int (*zend_object_do_operation_t)(zend_uchar opcode, zval *result, zval *op1, zval *op2 TSRMLS_DC);

Here opcode is the opcode of the operation (e.g. ZEND_ADD), result is the target zval, op1 the first operand and op2 the second operand. For binary operations both operands are used, for unary operations the second operand is NULL. The return value can be either SUCCESS or FAILURE. If FAILURE is returned then the code falls back to the default behavior for the respective operator.

The following opcode values are supported:

+   ZEND_ADD
-   ZEND_SUB
*   ZEND_MUL
/   ZEND_DIV
%   ZEND_MOD
<<  ZEND_SL
>>  ZEND_SR
.   ZEND_CONCAT
|   ZEND_BW_OR
&   ZEND_BW_AND
^   ZEND_BW_XOR
xor ZEND_BOOL_XOR
~   ZEND_BW_NOT   (unary)
!   ZEND_BOOL_NOT (unary)
==  ZEND_IS_EQUAL
!=  ZEND_IS_NOT_EQUAL
<   ZEND_IS_SMALLER
<=  ZEND_IS_SMALLER_OR_EQUAL

The operators >, >=, unary + and unary - are indirectly supported by the following compiler transformations:

$a > $b   ==>  $b < $a
$a >= $b  ==>  $b <= $a
+$a       ==>  0 + $a
-$a       ==>  0 - $a

The compound assignment operators +=, -=, *=, /=, %=, <<=, >>=, .=, |=, &= and ^= are supported by the runtime transformation $a op= $b => $a = $a op $b.

The prefix operators ++ and -- are supported by the runtime transformations ++$a => $a = $a + 1 and --$b => $b = $b - 1. The same applies for the corresponding postfix operators, with the difference that a copy of the old value is returned (rather than the newly computed value).

The operators === and !== are explicitly not supported. For objects they have clearly defined semantics (the same object handle) and I see no reason why one should be allowed to break this behavior.

The ability to overload operators is not exposed to userland classes.

Currently GMP is based on resources. This has several disadvantages:

• Cannot be serialized
• Cannot be directly cast to int/float/string
• Cannot be (meaningfully) dumped using var_dump
• Coerces to an integer by returning the resource ID. This can easily lead to bugs if you accidentally use the resource with an arithmetic operation. For example a GMP factorial test from out testsuite has been computing the factorial of the resource ID, rather than the factorial of the number.
• Cannot make use of the new operator overloading APIs
• Bad reporting on leaks. During the port I found that many functions leak resources, especially in error conditions.

This RFC proposes to make GMP use objects (of type GMP) as the underlying structure. Using this new structure, the RFC implements support for serialization, casting, dumping and overloaded operators.

In the following there are examples for some of the new behaviors:

$n = gmp_init(42);
echo $n, "\n";         // 42
var_dump((string) $n); // string(2) "42"
var_dump((int) $n);    // int(42)
var_dump((float) $n);  // float(42)

var_dump($n = gmp_init(42));
var_dump($s = serialize($n));
var_dump(unserialize($s));
// outputs
object(GMP)#%d (1) {
  ["num"]=>
  string(2) "42"
}
string(33) "O:3:"GMP":1:{s:3:"num";s:2:"42";}"
object(GMP)#%d (1) {
  ["num"]=>
  string(2) "42"
}

$a = gmp_init(42);
$b = gmp_init(17);
 
var_dump($a + $b);
var_dump($a + 17);
var_dump(42 + $b);
// Outputs the following 3 times:
object(GMP)#%d (1) {
  ["num"]=>
  string(2) "59"
}

The following operators are supported: +, -, *, /, %, |, &, ^, ~, ==, !=, <, <=, >, >=. The operators <<, >> are not yet supported, but support is planned. All operators work with two GMP values or one GMP value and one GMP-coercible value (e.g. strings and integers).

The addition of operator overloading does not break backwards compatibility.

The switch from GMP resources to objects can break scripts that checked whether something is a GMP integer using code like is_resource($a) && get_resource_type($a) == 'GMP integer'.

The addition of operator overloading does not affect performance (or at least I couldn't find a measurable difference). This is not surprising as the overloading code is usually placed in a rarely reached error/catch-all case.

The changes to GMP improve performance in all scenarios I measured (4M runs each):

                     NEW    OLD
a) gmp_add($a, $b)   1.16   1.25
b) gmp_add($a, 17)   1.08   1.21
c) gmp_add(42, $b)   1.29   1.84
d) $a + $b           0.83   ---

The difference between tests b) and c) is that the former makes use of an operator specialized on integers rather than creating a temporary GMP instance.

The pull request for this RFC can be found here: https://github.com/php/php-src/pull/342

http://markmail.org/message/y7rq5vcd5ucsbcyb (Note: The patch that is being discussed there is not accessible anymore.)