Raising to Power in PHP

Raising to power in PHP

The caret is the bit-wise XOR operator in PHP. You need to use pow() for integers.

What is ** Exponentiation operator in php?

It is exponentiation operator.

Functionality :

It gives Result of raising one variable to the other varibale's power
So if we want nth power of any number for that this operator is used

Example :

$x = 5;
$y = 3;
$z = $x ** $y; //<----- raising 3 power of 5 i.e we can say 5 raise to 3 in simple language . $x = base and $y= It is `exponentiation` operator.
echo $z; //results 125

How I can create my own pow function using PHP?

Oopsika, couldn't have asked a more obvious question. Use the built-in function named pow (as in a lot of languages)

echo pow(3, 3);

Edit

Let's create our own function.

function raiseToPower($base,$exponent)
{
    // multiply the base to itself exponent number of times
    $result=1;
    for($i=1;$i<=$exponent;$i++)
    {
      $result = $result * $base;  
    }
    return $result;
}

Exponents without using the pow() function

I don’t really know how to describe what’s wrong, here – your code doesn’t make sense for calculating an exponent. Start with 1, multiply by the base $exponent times.

$result = 1;

for ($i = 0; $i < $exponent; $i++) {
    $result *= $base;
}

echo $result;

PHP: How to raise number to (tiny) fractional exponent?

Your best bet is probably to use the Taylor series expansion. As you noted, PHP's bcpow is limited to raising to integer exponentiation.

So what you can do is roll your own bc factorial function and use the wiki page to implement a Taylor series expansion of the exponential function.

function bcfac($num) { 
    if ($num==0) return 1;
    $result = '1';
    for ( ; $num > 0; $num--)
        $result = bcmul($result,$num);
    return $result;
}
$mysum = '0';
for ($i=0; $i<300; $i++) {
    $mysum = bcadd($mysum, bcdiv(bcpow($pow,$i), bcfac($i)) );
}
print $mysum;

Obviously, the $i<300 is an approximation for infinity... You can change it to suit your performance needs.

With $i=20, I got

1.00000000000000000010842021724855044340662275184110560868263421994092888869270293594926619547803962155136242752708629105688492780863293090291376157887898519458498571566021915144483905034693109606778068801680332504212458366799913406541920812216634834265692913062346724688397654924947370526356787052264726969653983148004800229537555582281617497990286595977830803702329470381960270717424849203303593850108090101578510305396615293917807977774686848422213799049363135722460179809890014584148659937665374616

This is comforting since that small of an exponent should yield something really close to 1.0.

Returning the next nearest power of 2 for the given integer number

Try this :

pow(2,ceil(log($number,2)))

A more effective one :

function next_pow($number)
{
    if($number < 2) return 1;
    for($i = 0 ; $number > 1 ; $i++)
    {
        $number = $number >> 1;
    }
    return 1<<($i+1);
}

php pow function returns NAN

After some consultation with the experts in Room #11, pow() won't work with the root of a negative number.
Should the answer be 0.8215 or -0.8215?

Quirkily, using the ** (power) operator will work with the root of a negative number

echo -0.3741569180353 ** 0.2 ;

because ** has higher precedence than -, so effectively what you're doing is

echo -(0.3741569180353 ** 0.2) ;

PHP Power of a number

I think I have an approach. It hinges on three simple observations:

1. BCMath library contains a sqrt function
2. You can break pow(x, a) into pow(x, int(a)) * fracpow(x, frac(a)) where pow exists in the BCMath library, and fracpow is a function we need to create (for an exponent a between 0 and 1)

3. A factional power can be expressed as the product of a number of square roots:

   x^(0.22) = x^(1/8 + 1/16 + 1/32 + ...) = sqrt(sqrt(sqrt(x)))) * sqrt(sqrt(sqrt(sqrt(x)))) * ...

In other words - the approach to take is the following:

1. Find the fractional part of the exponent
2. Express that in powers of 2 (binary representation, basically)
3. Keep taking the square root of your number
4. Multiply your result by the new square root every time your factor should be included

This is not a fast method, and I suspect you need quite a few more digits of precision in the intermediate stages in order to ensure sufficient accuracy in the final result. But it will work...

If you need help implementing this let me know - I may have time later (or one of the other people looking at this answer may be inspired to write the code).

How to print power series in php

You can do this:

function exponentArr($num){
    $arr = array();
    for($i=0;$i <= $num;$i++){
        $arr[$i] = pow(2, $i);
    }
    return $arr;
}

This will give you an array $arr with the required output.

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