jchamberlain - 1 year ago 89

PHP Question

I'm doing a calculation in PHP using

`bcmath`

`e`

`bcpow()`

For example:

`$e = exp(1);`

$pow = "0.000000000000000000108420217248550443400745280086994171142578125";

$result = bcpow($e, $pow);

Result is

`"1"`

Is there another function I can use instead of

`bcpow()`

Answer Source

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.