GMP These functions allow you to work with arbitrary-length integers using the GNU MP library. In order to have these functions available, you must compile PHP with GMP support by using the --with-gmp option. You can download the GMP library from &url.gmp;. This site also has the GMP manual available. You will need GMP version 2 or better to use these functions. Some functions may require more recent version of the GMP library. These functions have been added in PHP 4.0.4. Most GMP functions accept GMP number arguments, defined as resource below. However, most of these functions will also accept numeric and string arguments, given that it is possible to convert the latter to a number. Also, if there is a faster function that can operate on integer arguments, it would be used instead of the slower function when the supplied arguments are integers. This is done transparently, so the bottom line is that you can use integers in every function that expects GMP number. See also the gmp_init function. If you want to explicitely specify a large integer, specify it as a string. If you don't do that, PHP will interpret the integer-literal first, possibly resulting in loss of precision, even before GMP comes into play. ]]> This will calculate factiorial of 1000 (pretty big number) very fast. gmp_init Create GMP number resource gmp_init mixed number Creates a GMP number from an integer or string. String representation can be decimal or hexadecimal. In the latter case, the string should start with 0x. ]]> It is not necessary to call this function if you want to use integer or string in place of GMP number in GMP functions, like gmp_add. Function arguments are automatically converted to GMP numbers, if such conversion is possible and needed, using the same rules as gmp_init. gmp_intval Convert GMP number to integer int gmp_intval resource gmpnumber This function allows to convert GMP number to integer. This function returns a useful result only if the number actually fits the PHP integer (i.e., signed long type). If you want just to print the GMP number, use gmp_strval. gmp_strval Convert GMP number to string string gmp_strval resource gmpnumber int base Convert GMP number to string representation in base base. The default base is 10. Allowed values for the base are from 2 to 36. ]]> gmp_add Add numbers resource gmp_add resource a resource b Add two GMP numbers. The result will be a GMP number representing the sum of the arguments. gmp_sub Subtract numbers resource gmp_sub resource a resource b Subtracts b from a and returns the result. gmp_mul Multiply numbers resource gmp_mul resource a resource b Multiplies a by b and returns the result. gmp_div_q Divide numbers resource gmp_div_q resource a resource b int round Divides a by b and returns the integer result. The result rounding is defined by the round, which can have the following values: GMP_ROUND_ZERO: The result is truncated towards 0. GMP_ROUND_PLUSINF: The result is rounded towards +infinity. GMP_ROUND_MINUSINF: The result is rounded towards -infinity. This function can also be called as gmp_div. See also gmp_div_r, gmp_div_qr gmp_div_r Remainder of the division of numbers resource gmp_div_r resource n resource d int round Calculates remainder of the integer division of n by d. The remainder has the sign of the n argument, if not zero. See the gmp_div_q function for description of the round argument. See also gmp_div_q, gmp_div_qr gmp_div_qr Divide numbers and get quotient and remainder array gmp_div_qr resource n resource d int round The function divides n by d and returns array, with the first element being [n/d] (the integer result of the division) and the second being (n - [n/d] * d) (the remainder of the division). See the gmp_div_q function for description of the round argument. ]]> See also gmp_div_q, gmp_div_r. gmp_div Divide numbers resource gmp_div resource a resource b This function is an alias to gmp_div_q. gmp_mod Modulo operation resource gmp_mod resource n resource d Calculates n modulo d. The result is always non-negative, the sign of d is ignored. gmp_divexact Exact division of numbers resource gmp_divexact resource n resource d Divides n by d, using fast "exact division" algorithm. This function produces correct results only when it is known in advance that d divides n. gmp_cmp Compare numbers int gmp_cmp resource a resource b Returns a positive value if a > b, zero if a = b and negative value if a < b. gmp_neg Negate number resource gmp_neg resource a Returns -a. gmp_com Calculates one's complement of a resource gmp_com resource a &warn.undocumented.func; gmp_abs Absolute value resource gmp_abs resource a Returns absolute value of a. gmp_sign Sign of number int gmp_sign resource a Return sign of a - 1 if a is positive and -1 if it's negative. gmp_fact Factorial resource gmp_fact int a Calculates factorial (a!) of a. gmp_sqrt Square root resource gmp_sqrt resource a Calculates square root of a. gmp_sqrtrm Square root with remainder array gmp_sqrtrm resource a Returns array where first element is the integer square root of a (see also gmp_sqrt), and the second is the remainder (i.e., the difference between a and the first element squared). gmp_perfect_square Perfect square check bool gmp_perfect_square resource a Returns &true; if a is a perfect square, &false; otherwise. See also: gmp_sqrt, gmp_sqrtrm. gmp_pow Raise number into power resource gmp_pow resource base int exp Raise base into power exp. The case of 0^0 yields 1. exp cannot be negative. gmp_powm Raise number into power with modulo resource gmp_powm resource base resource exp resource mod Calculate (base raised into power exp) modulo mod. If exp is negative, result is undefined. gmp_prob_prime Check if number is "probably prime" int gmp_prob_prime resource a int reps If this function returns 0, a is definitely not prime. If it returns 1, then a is "probably" prime. If it returns 2, then a is surely prime. Reasonable values of reps vary from 5 to 10 (default being 10); a higher value lowers the probability for a non-prime to pass as a "probable" prime. The function uses Miller-Rabin's probabilistic test. gmp_gcd Calculate GCD resource gmp_gcd resource a resource b Calculate greatest common divisor of a and b. The result is always positive even if either of, or both, input operands are negative. gmp_gcdext Calculate GCD and multipliers array gmp_gcdext resource a resource b Calculates g, s, and t, such that a*s + b*t = g = gcd(a,b), where gcd is the greatest common divisor. Returns an array with respective elements g, s and t. gmp_invert Inverse by modulo resource gmp_invert resource a resource b Computes the inverse of a modulo b. Returns &false; if an inverse does not exist. gmp_legendre Legendre symbol int gmp_legendre resource a resource p Compute the Legendre symbol of a and p. p should be odd and must be positive. gmp_jacobi Jacobi symbol int gmp_jacobi resource a resource p Computes Jacobi symbol of a and p. p should be odd and must be positive. gmp_random Random number resource gmp_random int limiter Generate a random number. The number will be up to limiter words long. If limiter is negative, negative numbers are generated. gmp_and Logical AND resource gmp_and resource a resource b Calculates logical AND of two GMP numbers. gmp_or Logical OR resource gmp_or resource a resource b Calculates logical inclusive OR of two GMP numbers. gmp_xor Logical XOR resource gmp_xor resource a resource b Calculates logical exclusive OR (XOR) of two GMP numbers. gmp_setbit Set bit resource gmp_setbit resource &a int index bool set_clear Sets bit index in a. set_clear defines if the bit is set to 0 or 1. By default the bit is set to 1. gmp_clrbit Clear bit resource gmp_clrbit resource &a int index Clears (sets to 0) bit index in a. gmp_scan0 Scan for 0 int gmp_scan0 resource a int start Scans a, starting with bit start, towards more significant bits, until the first clear bit is found. Returns the index of the found bit. gmp_scan1 Scan for 1 int gmp_scan1 resource a int start Scans a, starting with bit start, towards more significant bits, until the first set bit is found. Returns the index of the found bit. gmp_popcount Population count int gmp_popcount resource a Return the population count of a. gmp_hamdist Hamming distance int gmp_hamdist resource a resource b Returns the hamming distance between a and b. Both operands should be non-negative.