PHP: rfc:raising_zero_to_power_of_negative_number

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====== PHP RFC: Raising zero to the power of negative number ======
  * Version: 1.0
  * Date: 2024-01-11
  * Author: Jorg Sowa <jorg.sowa@gmail.com>
  * Status: Accepted
  * First Published at: http://wiki.php.net/rfc/raising_zero_to_power_of_negative_number

===== Introduction =====

Raising a number to the power of a negative number is equivalent to taking the reciprocal of the number raised to the positive opposite of the power.

If we raise the number zero to the power of a negative number we end up with the one divided by zero, which gives an undefined result. Currently in PHP, such operation results in <php>INF</php>, while explicit division by zero gives a <php>DivisionByZeroError</php>.

<code php>
var_dump(0 ** -1); //float(INF)
var_dump(0 ** -1.1); //float(INF)

var_dump(pow(0, -1)); //float(INF)
var_dump(pow(0, -1.1)); //float(INF)

var_dump(1 / 0); //DivisionByZeroError: Division by zero

</code>

===== Proposal =====
The RFC proposes to change the behavior of this operation to match the division by zero operation. In the next minor version raising a number to the power of a negative number will throw a Deprecation, and in the major version, this operation will throw DivisionByZeroError.

<code php>
//PHP 8.4
var_dump(0 ** -1); //Deprecated: Zero raised to a negative power is deprecated
var_dump(0 ** -1.1); //Deprecated: Zero raised to a negative power is deprecated
 
var_dump(pow(0, -1)); //Deprecated: Zero raised to a negative power is deprecated
var_dump(pow(0, -1.1)); //Deprecated: Zero raised to a negative power is deprecated
 
var_dump(1 / 0); //DivisionByZeroError: Division by zero
</code>


<code php>
//PHP 9.0
var_dump(0 ** -1); //DivisionByZeroError: Zero cannot be raised to a negative power
var_dump(0 ** -1.1); //DivisionByZeroError: Zero cannot be raised to a negative power
 
var_dump(pow(0, -1)); //DivisionByZeroError: Zero cannot be raised to a negative power
var_dump(pow(0, -1.1)); //DivisionByZeroError: Zero cannot be raised to a negative power
 
var_dump(1 / 0); //DivisionByZeroError: Division by zero
</code>

To provide a way to compute the numbers according to the IEEE 754 rules, the RFC proposes adding the function <php>fpow</php> similarly to the function <php>fdiv</php> that exists for the division operation, and <php>fmod</php> for the module operation for floating numbers.

<code php>
//PHP 8.4
var_dump(fpow(0, -1)); //float(INF)
var_dump(fpow(0, -1.1)); //float(INF)
</code>

===== Backward Incompatible Changes =====
This change will break code including raising the zero number to a negative power. Such cases may keep their current behavior by using the new <php>fpow</php> function.

===== Proposed PHP Version(s) =====
Deprecation Notice in the next minor PHP version 8.4.

Function <php>fpow</php> in the next minor PHP version 8.4.

Throwing <php>DivisionByZeroError</php> in the next major PHP version: 9.0.

===== Proposed Voting Choices =====

As per the voting RFC, a yes/no vote with a 2/3 majority is needed for this proposal to be accepted.

Voting started on 2024-04-05 and will end on 2024-04-20 00:00 GMT.

<doodle title="RFC: Raising zero to the power of negative number" auth="jorg_sowa" voteType="single" closed="false" closeon="2024-04-20T00:00:00Z">
   * Yes
   * No
</doodle>

===== Implementation =====
https://github.com/php/php-src/pull/13128 (without fpow yet)

The implementation is based on Ilija Tovilo's PoC:
https://github.com/php/php-src/issues/8015#issuecomment-1193391843

===== References =====
Issue GH-8015: https://github.com/php/php-src/issues/8015
RFC Division by zero: https://wiki.php.net/rfc/engine_warnings
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