As per the answer on stackoverflow, a numeric string that starts with a 0 will be interpreted as an octal number.

var_dump(gmp_add('010', '010')); // 16

https://3v4l.org/seoQt

Just as binary numbers do not have the character "2", octal numbers do not have the characters "8" and "9".

Therefore, if a numeric string that is to be interpreted as octal contains an "8" or a "9", it is an invalid string.

Making this a doc bug: the parameters say "numeric string" and then link to the strings page, which should have been a link to the numeric strings page except that "numeric string" isn't actually meant as PHP defines it but as GMP::__construct and gmp_init describe it:

The base may vary from 2 to 62. If base is 0 (default value), the actual base is determined from the leading characters: if the first two characters are 0x or 0X, hexadecimal is assumed, if the first two characters are 0b or 0B, binary is assumed, otherwise if the first character is 0, octal is assumed, otherwise decimal is assumed. For bases up to 36, case is ignored; upper-case and lower-case letters have the same value. For bases 37 to 62, upper-case letter represent the usual 10 to 35 while lower-case letter represent 36 to 61.

Applies to all the GMP functions, or at least presumably to all usages of &gmp.parameter;.