PHP, Mathematical Functions

This function returns the result as STRING.

If numbers are not positive integers may give unexpected results.

If $modulus = 0 or $exponent < 0,
this function returns:
Warning in PHP 7.4.XX or
Fatal error in PHP 8.0.XX.

This function is used in encryption and decryption algoritims.

If $scale is omited, this function will default to the scale set globally with the bcscale function, or fallback to 0 if this has not been set.


<?php



string bcpowmod ( string $num, 

                              string $exponent, 

                              string $modulus, 

                                 ?int $scale = null )





where,



$num = The base as STRING



$exponent = The exponent as STRING



$modulus = The modulus, as an integral STRING



$scale = The number of decimal places 

                                     considered by this operation



?>

$base

The base treated as STRING.

$exponent

The exponent treated as STRING.

$modulus

The modulus as an integral treated as STRING.

$scale

The number of decimal places to be considered.

This is nullable as of PHP 8.0.XX.

EXERCISE


<?php



$a = '3';



$mod01 = 17;



for ($b = 0; $b <=9; $b++)

{

$xbcpwmd = bcpowmod($a, $b, $mod01);

$xbcpw = bcpow($a,$b);

$xbcmd = bcmod($xbcpw, $mod01);



echo '<br>bcpow(' . $a . ', ' . $b . ') = ' . $xbcpw . '&nbsp;=>&nbsp;';



echo 'bcmod(' . $xbcpw . ', ' . $mod01 . ') = ' . $xbcmd . '<br>';



echo 'bcpowmod(' . $a . ', ' . $b . ', ' . $mod01 . ') = ' . 

                                                             $xbcpwmd . '<br>';

}



?>

RESULT

modulus = 17

A

bcpow(3, 0) = 1 => bcmod(1, 17) = 1
bcpowmod(3, 0, 17) = 1

where:

3 ** 0 = 1
and
3 * 0 ≡ 1

B

bcpow(3, 1) = 3 => bcmod(3, 17) = 3
bcpowmod(3, 1, 17) = 3

where:

3 ** 1 = 3
and
3 * 1 = 3

C

bcpow(3, 2) = 9 => bcmod(9, 17) = 9
bcpowmod(3, 2, 17) = 9

where:

3 ** 2 = 9
and
3 * 3 = 9

D

bcpow(3, 3) = 27 => bcmod(27, 17) = 10
bcpowmod(3, 3, 17) = 10

where:

( 3 ** 3 ) = 27
and
( 3 * 9 ) = 27 = ( 17 * 1 + 10 ) ⇒ 27 ≡ 10

E

bcpow(3, 4) = 81 => bcmod(81, 17) = 13
bcpowmod(3, 4, 17) = 13

where:

( 3 ** 4 ) = 81
and
( 3 * 27 ) = 81 = ( 17 * 4 + 13 ) ⇒ 81 ≡ 13
or
3 * 10 ) = 30 = ( 17 * 1 ) + 13 ⇒ 30 ≡ 13

F

bcpow(3, 5) = 243 => bcmod(243, 17) = 5
bcpowmod(3, 5, 17) = 5

where:

( 3 ** 13 ) = 39 = ( 17 * 2 ) + 5 ⇒ 39 ≡ 5

G

bcpow(3, 6) = 729 => bcmod(729, 17) = 15
bcpowmod(3, 6, 17) = 15

H

bcpow(3, 7) = 2187 => bcmod(2187, 17) = 11
bcpowmod(3, 7, 17) = 11

I

bcpow(3, 8) = 6561 => bcmod(6561, 17) = 16
bcpowmod(3, 8, 17) = 16

J

bcpow(3, 9) = 19683 => bcmod(19683, 17) = 14
bcpowmod(3, 9, 17) = 14

Try to solve as the proposed on A, B, C, D, E and F...
... the same conditions imposed on G, H, I and J.

EXERCISE


<?php



$base= 3;



$exp = -3;



$mod = 0;



$xbcpwmd = bcpowmod($base, $exp, $mod);

$xbcpw = bcpow($base,$exp);

$xbcmd = bcmod($xbcpw, $mod);



echo '<br>bcpow(' . $base. ', ' . $exp . ') = ' . $xbcpw . 

                                                    '&nbsp;=>&nbsp;';



echo 'bcmod(' . $xbcpw . ', ' . $mod . ') = ' . $xbcmd . '<br>';



echo 'bcpowmod(' . $base. ', ' . $exp . ', ' . $mod . ') = ' . 

                                                 $xbcpwmd . '<br>';



?>