abacus: bignum: add sqrt

src/bignum/bignum.cc

@@ -179,6 +179,23 @@ digits_type do_pow(digits_type lhs, digits_type rhs) {
     return lhs;
 }
 
+digits_type do_sqrt(digits_type const& num) {
+    digits_type one;
+    one.push_back(1);
+    digits_type max = num;
+    digits_type min = do_addition(max, one);
+    min = do_halve(min);
+
+    while (do_less_than(min, max)) {
+        max = min;
+        std::tie(min, std::ignore) = do_div_mod(num, max);
+        min = do_addition(min, max);
+        min = do_halve(min);
+    }
+
+    return max;
+}
+
 } // namespace
 
 BigNum::BigNum(std::int64_t number) {
@@ -431,4 +448,24 @@ BigNum pow(BigNum const& lhs, BigNum const& rhs) {
     return res;
 }
 
+BigNum sqrt(BigNum const& num) {
+    assert(num.is_canonicalized());
+
+    if (num.is_zero()) {
+        return BigNum();
+    } else if (num.is_negative()) {
+        throw std::invalid_argument(
+            "attempt to take the square root of a negative number");
+    }
+
+    BigNum res;
+
+    res.digits_ = do_sqrt(num.digits_);
+    res.sign_ = 1;
+
+    assert(res.is_canonicalized());
+
+    return res;
+}
+
 } // namespace abacus::bignum

src/bignum/bignum.hh

@@ -89,6 +89,8 @@ public:
 
     friend BigNum pow(BigNum const& lhs, BigNum const& rhs);
 
+    friend BigNum sqrt(BigNum const& num);
+
     friend bool operator==(BigNum const& lhs, BigNum const& rhs) {
         return lhs.equal(rhs);
     }

tests/unit/bignum.cc

@@ -338,3 +338,41 @@ TEST(BigNum, pow_negative) {
     EXPECT_EQ(pow(minus_three, three), minus_twenty_seven);
     EXPECT_EQ(pow(three, four), eighty_one);
 }
+
+TEST(BigNum, sqrt_zero) {
+    auto const zero = BigNum(0);
+
+    EXPECT_EQ(sqrt(zero), zero);
+}
+
+TEST(BigNum, sqrt_one) {
+    auto const one = BigNum(1);
+
+    EXPECT_EQ(sqrt(one), one);
+}
+
+TEST(BigNum, sqrt_truncation) {
+    auto const one = BigNum(1);
+    auto const two = BigNum(2);
+    auto const three = BigNum(3);
+
+    EXPECT_EQ(sqrt(two), one);
+    EXPECT_EQ(sqrt(three), one);
+}
+
+TEST(BigNum, sqrt) {
+    auto const two = BigNum(2);
+    auto const three = BigNum(3);
+    auto const four = BigNum(4);
+    auto const nine = BigNum(9);
+    auto const ten = BigNum(10);
+    auto const eighty_one = BigNum(81);
+    auto const ninety_nine = BigNum(99);
+    auto const hundred = BigNum(100);
+
+    EXPECT_EQ(sqrt(four), two);
+    EXPECT_EQ(sqrt(nine), three);
+    EXPECT_EQ(sqrt(eighty_one), nine);
+    EXPECT_EQ(sqrt(ninety_nine), nine);
+    EXPECT_EQ(sqrt(hundred), ten);
+}