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mth(3) AFNIX Module mth(3)NAMEmth - standard math moduleSTANDARD MATH MODULEThe Standard Mathematicalmodule is an original implementation of vari- ous mathematical facilities. The module can be divided into several catgeories which include convenient functions, linear algebra and real analysis.RandomnumberservicesThe mathmodule provides various functions that generate random numbers in different formats. Function Description get-random-integer return a random integer number get-random-real return a random real number between 0.0 and 1.0 get-random-relatif return a random relatif number get-random-prime return a random probable prime relatif number The numbers are generated with the help of the system random generator. Such generator is machine dependant and results can vary from one ma- chine to another.PrimalitytestingservicesThe mathmodule provides various predicates that test a number for a primality condition. Most of these predicates are intricate and are normally not used except the prime-probable-ppredicate. Predicate Description fermat-p Fermat test predicate miller-rabin-p Miller-Rabin test predicate prime-probable-p general purpose prime probable test get-random-prime return a random probable prime relatif number The fermat-pand miller-rabin-ppredicates return true if the primality condition is verified. These predicate operate with a base number. The prime number to test is the second argument.FermatprimalitytestingThe fermat-ppredicate is a simple primality test based on the "little Fermat theorem". A base number greater than 1 and less than the number to test must be given to run the test. afnix:mth:fermat-p 2 7 In the preceeding example, the number 7 is tested, and the fermat- ppredicate returns true. If a number is prime, it is guaranted to pass the test. The oppositte is not true. For example, 561 is a composite number, but the Fermat test will succeed with the base 2. Numbers that successfully pass the Fermat test but which are composite are called Carmichael numbers. For those numbers, a better test needs to be em- ployed, such like the Miller-Rabin test.Miller-RabinprimalitytestingThe miller-rabin-ppredicate is a complex primality test that is more efficient in detecting prime number at the cost of a longer computa- tion. A base number greater than 1 and less than the number to test must be given to run the test. afnix:mth:miller-rabin-p 2 561 In the preceeding example, the number 561, which is a Carmichael num- ber, is tested, and the miller-rabin-ppredicate returns false. The probability that a number is prime depends on the number of times the test is ran. Numerous studies have been made to determine the optimal number of passes that are needed to declare that a number is prime with a good probability. The prime-probable-ppredicate takes care to run the optimal number of passes.GeneralprimalitytestingThe prime-probable-ppredicate is a complex primality test that incorpo- rates various primality tests. To make the story short, the prime can- didate is first tested with a series of small prime numbers. Then a fast Fermat test is executed. Finally, a series of Miller-Rabin tests are executed. Unlike the other primality tests, this predicate operates with a number only and optionally, the number of test passes. This predicate is the recommended test for the folks who want to test their numbers. afnix:mth:prime-probable-p 17863STANDARD MATH REFERENCEFunctionsget-random-integer->Integer(none|Integer)The get-random-integerfunction returns a random integer number. Without argument, the integer range is machine dependent. With one integer argument, the resulting integer number is less than the specified maximum bound.get-random-real->Real(none|Boolean)The get-random-realfunction returns a random real number between 0.0 and 1.0. In the first form, without argument, the random number is between 0.0 and 1.0 with 1.0 included. In the second form, the boolean flag controls whether or not the 1.0 is in- cluded in the result. If the argument is false, the 1.0 value is guaranted to be excluded from the result. If the argument is true, the 1.0 is a possible random real value. Calling this function with the argument set to true is equivalent to the first form without argument.get-random-relatif->Relatif(Integer|IntegerBoolean)The get-random-relatiffunction returns a n bits random positive relatif number. In the first form, the argument is the number of bits. In the second form, the first argument is the number of bits and the second argument, when true produce an odd number, or an even number when false.get-random-prime->Relatif(Integer)The get-random-primefunction returns a n bits random positive relatif probable prime number. The argument is the number of bits. The prime number is generated by using the Miller-Rabin primality test. As such, the returned number is declared proba- ble prime. The more bits needed, the longer it takes to generate such number.get-random-bitset->Bitset(Integer)The get-random-bitsetfunction returns a n bits random bitset. The argument is the number of bits.fermat-p->Boolean(Integer|RelatifInteger|Relatif)The fermat-ppredicate returns true if the little fermat theorem is validated. The first argument is the base number and the sec- ond argument is the prime number to validate.miller-rabin-p->Boolean(Integer|RelatifInteger|Relatif)The miller-rabin-ppredicate returns true if the Miller-Rabin test is validated. The first argument is the base number and the second argument is the prime number to validate.prime-probable-p->Boolean(Integer|Relatif[Integer])The prime-probable-ppredicate returns true if the argument is a probable prime. In the first form, only an integer or relatif number is required. In the second form, the number of iterations is specified as the second argument. By default, the number of iterations is specified to 56. AFNIX 2017-04-29 mth(3)

NAME | STANDARD MATH MODULE | STANDARD MATH REFERENCE

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