Simplify the Miller-Rabin witness

We can just let it do the full `modpow` in REDC.

Author: cuviper

examples/primes.rs

@@ -86,9 +86,17 @@ fn is_prime(n: &BigUint) -> bool {
         }
     }
 
+    // Test a possible Miller-Rabin witness to the compositeness of n.
+    //
+    // Computes a**(n-1) (mod n), and checks if the result gives evidence that
+    // n is composite.  Returning false means that n is likely prime, but not
+    // necessarily.
+    let n_m1 = n - 1u32;
+    let witness = move |a: &BigUint| !a.modpow(&n_m1, n).is_one();
+
     // try series of primes as witnesses
     for &(p, u) in &A014233 {
-        if witness(&BigUint::from(p), n) {
+        if witness(&BigUint::from(p)) {
             return false;
         }
         if let Some(n) = n64 {
@@ -104,46 +112,9 @@ fn is_prime(n: &BigUint) -> bool {
     let max = n - 3u32;
     for _ in 0..10 {
         let w = rng.gen_biguint_below(&max) + 2u32;
-        if witness(&w, n) {
-            return false;
-        }
-    }
-    true
-}
-
-/// Test a possible witness to the compositeness of n.
-///
-/// Computes a**(n-1) (mod n), and checks if the result gives evidence that
-/// n is composite.  Returning false means that n is likely prime, but not
-/// necessarily.
-#[cfg(feature = "rand")]
-fn witness(a: &BigUint, n: &BigUint) -> bool {
-    // let n-1 = (2**t)*u, where t ≥ 1 and u is odd
-    // TODO `trailing_zeros` would make this trivial
-    let n_m1 = n - 1u32;
-    let (t, u) = if n_m1.is_even() {
-        let mut t = 1usize;
-        let mut u = n_m1.clone() >> 1;
-        while u.is_even() {
-            t += 1;
-            u >>= 1;
-        }
-        (t, u)
-    } else {
-        (0, n_m1.clone())
-    };
-
-    let mut x = a.modpow(&u, n);
-    if x.is_one() || x == n_m1 {
-        return false;
-    }
-
-    for _ in 1..t {
-        x = &x * &x % n;
-        if x == n_m1 {
+        if witness(&w) {
             return false;
         }
     }
-
     true
 }