Implement sqrt for BigInt and BigUint

benches/bigint.rs

@@ -292,3 +292,11 @@ fn modpow_even(b: &mut Bencher) {
 
     b.iter(|| base.modpow(&e, &m));
 }
+
+#[bench]
+fn sqrt(b: &mut Bencher) {
+    let mut rng = get_rng();
+    let n = rng.gen_biguint(2048);
+
+    b.iter(|| n.sqrt());
+}

src/bigint.rs

@@ -2538,6 +2538,18 @@ impl BigInt {
         };
         BigInt::from_biguint(sign, mag)
     }
+
+    /// Finds square root of `self`.
+    ///
+    /// The result is the greatest integer less than or equal to the
+    /// square root of `self`.
+    ///
+    /// Panics if `self` is a negative number.
+    pub fn sqrt(&self) -> Self {
+        assert!(!self.is_negative(), "number is negative");
+
+        BigInt::from_biguint(self.sign, self.data.sqrt())
+    }
 }
 
 impl_sum_iter_type!(BigInt);

src/biguint.rs

@@ -1749,6 +1749,50 @@ impl BigUint {
         }
         acc
     }
+
+    /// Finds square root of `self`.
+    ///
+    /// The result is the greatest integer less than or equal to the
+    /// square root of `self`.
+    pub fn sqrt(&self) -> Self {
+        let one = BigUint::one();
+        let two = BigUint::from(2 as u8);
+
+        // Trivial cases
+        if self.is_zero() {
+            return BigUint::zero();
+        }
+
+        if self.is_one() {
+            return one;
+        }
+
+        // Newton's method to compute the square root of an integer.
+        //
+        // Reference:
+        // Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.13
+        //
+        // Set initial guess to something >= floor(sqrt(self)), but as low
+        // as possible to speed up convergence.
+        let bit_len = self.len() * big_digit::BITS;
+        let guess = one.shl(bit_len/2 + 1);
+
+        let mut u = guess;
+        let mut s: BigUint;
+
+        loop {
+            s = u;
+            let q = self.div_floor(&s);
+            let t: BigUint = &s + &q;
+
+            // Compute the candidate value for next iteration
+            u = t.div_floor(&two);
+
+            if u >= s { break; }
+        }
+
+        s
+    }
 }
 
 /// Returns the number of least-significant bits that are zero,

tests/biguint.rs

@@ -956,6 +956,27 @@ fn test_lcm() {
     check(99, 17, 1683);
 }
 
+#[test]
+fn test_sqrt() {
+    fn check(n: usize, expected: usize) {
+        let big_n: BigUint = FromPrimitive::from_usize(n).unwrap();
+        let big_expected: BigUint = FromPrimitive::from_usize(expected).unwrap();
+
+        assert_eq!(big_n.sqrt(), big_expected);
+    }
+
+    check(0, 0);
+    check(1, 1);
+    check(99, 9);
+    check(100, 10);
+    check(102, 10);
+    check(120, 10);
+
+    let big_n: BigUint = FromStr::from_str("123_456_789").unwrap();
+    let expected : BigUint = FromStr::from_str("11_111").unwrap();
+    assert_eq!(big_n.sqrt(), expected);
+}
+
 #[test]
 fn test_is_even() {
     let one: BigUint = FromStr::from_str("1").unwrap();