gmp_init

Here's a way to parse a decimal (eg 3.25) into an integer and exponent:
<?
if (preg_match("/^[0-9]+\.[0-9]+$/",$input)){ 
 //Input is a base-10 decimal. Multiply as necessary to remove the decimal
 //point. Convert that to a gmp_resource, then decrement the exponent 
 //to compensate.
 $pieces=explode(".", $input); //Split at the d.p.
 $input="$pieces[0]$pieces[1]"; //Remove the decimal point.
 $input=ltrim($input,'0'); 
 //Remove any leading zeros, or gmp_init will parse the number as octal.
 if ($input==''){ //Deal with "0.0" which would otherwise be ''.
 $input=0;
 }
 $integer=gmp_init($input); 
 $ns_exponent=-strlen($pieces[1]); 
 //exponent = (-) the number of characters after the decimal point.
}
?>

Unless the base is 16, gpm_init will fail if the string begins with "0b". 
> php -r '$v = gmp_init("b83", 17); print("$v\n");'
Resource id #4
> php -r '$v = gmp_init("0b83", 17); print("$v\n");'
[nothing prints]
In may case, where I am explicitly specifying the base, the solution is to apply ltrim first:
> php -r '$v = gmp_init(ltrim("0b83", "0"), 17); print("$v\n");'
Resource id #4

I discovered that the gmp functions use [0-9a-f] up to base 16, but [0-9A-Za-z] (i.e. upper case first) from bases 17 to 62. This differs from most of the base-62 implementations I've found that tend to use lower case first.

Missing from the documentation: gmp_init() return false in case it failed to parse $num
<?php
var_dump(gmp_init(""));
// returns "bool(false)" and not a GMP object as hinted by the documentation, it also triggers a Warning "PHP Warning: gmp_init(): Unable to convert variable to GMP - string is not an integer in php shell code on line 1"
?>

gmp_* functions don't accept strings with a leading '+':
<?php
echo gmp_strval(gmp_init('+42')); #0
echo gmp_strval(gmp_add('42', '+42')); #42
echo bcadd('+42', '+42'); #84
?>

Note: Leading zeros will make gmp_init parse this as octal.
Thus gmp_init(010) becomes 8. 
$a=010; //8
$b="010" + 0; //10
$c=gmp_strval(gmp_init(010)); //8
$d=gmp_strval(gmp_init("010")); //8
This behaviour is inconsistent: either $d should equal $b, or
$b should equal $a.

If you call a gmp_* function directly with an interger as parameter, this integer MUST NOT be 0:
for($i=-1;$i<=1;$i++) { echo gmp_strval(gmp_add(2,gmp_mul(1,$i))) . ' '; }
The result is 1 0 3 (wrong)
In this case you have to use gmp_init():
for($i=-1;$i<=1;$i++) { echo gmp_strval(gmp_add(2,gmp_mul(1,gmp_init($i)))) . ' '; }
The result is 1 2 3 (right)
Happy number crunching! :-)