Data commit

Task/Miller-Rabin-primality-test/Maxima/miller-rabin-primality-test.maxima

@@ -0,0 +1,47 @@
+/* Miller-Rabin algorithm is builtin, see function primep. Here is another implementation */
+
+
+/* find highest power of p, p^s, that divide n, and return s and n / p^s */
+
+facpow(n, p) := block(
+   [s: 0],
+   while mod(n, p) = 0 do (s: s + 1, n: quotient(n, p)),
+   [s, n]
+)$
+
+/* check whether n is a strong pseudoprime to base a; s and d are given by facpow(n - 1, 2) */
+
+sppp(n, a, s, d) := block(
+   [x: power_mod(a, d, n), q: false],
+   if x = 1 or x = n - 1 then true else (
+      from 2 thru s do (
+         x: mod(x * x, n),
+         if x = 1 then return(q: false) elseif x = n - 1 then return(q: true)
+      ),
+      q
+   )
+)$
+
+/* Miller-Rabin primality test. For n < 341550071728321, the test is deterministic;
+   for larger n, the number of bases tested is given by the option variable
+   primep_number_of_tests, which is used by Maxima in primep. The bound for deterministic
+   test is also the same as in primep. */
+
+miller_rabin(n) := block(
+   [v: [2, 3, 5, 7, 11, 13, 17], s, d, q: true, a],
+   if n < 19 then member(n, v) else (
+      [s, d]: facpow(n - 1, 2),
+      if n < 341550071728321 then (    /* see http://oeis.org/A014233 */
+         for a in v do (
+            if not sppp(n, a, s, d) then return(q: false)
+         ),
+         q
+      ) else (
+         thru primep_number_of_tests do (
+            a: 2 + random(n - 3),
+            if not sppp(n, a, s, d) then return(q: false)
+         ),
+         q
+      )
+   )
+)$