diff --git a/src/lol/math/bigint.h b/src/lol/math/bigint.h
index 135f1937..02116666 100644
--- a/src/lol/math/bigint.h
+++ b/src/lol/math/bigint.h
@@ -94,30 +94,106 @@ public:
     template<int M>
     explicit bigint(bigint<M,T> const &x)
     {
-        for (int i = 0; i < (N < M) ? N : M; ++i)
+        for (unsigned int i = 0; i < (N < M) ? N : M; ++i)
             m_digits[i] = x.m_digits[i];
 
         if (N > M)
         {
             T padding = x.is_negative() ? digit_mask : (T)0;
-            for (int i = M; i < N; ++i)
+            for (unsigned int i = M; i < N; ++i)
                 m_digits[i] = padding;
         }
     }
 
+    /*
+     * bigint bitwise not: we just flip all bits except the unused one.
+     */
+    bigint<N,T> operator ~() const
+    {
+        bigint<N,T> ret;
+        for (unsigned int i = 0; i < N; ++i)
+            ret.m_digits[i] = m_digits[i] ^ digit_mask;
+        return ret;
+    }
+
+    /*
+     * bigint bitwise AND: just perform a bitwise AND on all digits.
+     */
+    bigint<N,T> & operator &=(bigint<N,T> const &x)
+    {
+        for (unsigned int i = 0; i < N; ++i)
+            m_digits[i] &= x.m_digits[i];
+    }
+
+    inline bigint<N,T> operator &(bigint<N,T> const &x) const
+    {
+        return bigint<N,T>(*this) &= x;
+    }
+
+    /*
+     * bigint bitwise OR: just perform a bitwise OR on all digits.
+     */
+    bigint<N,T> & operator |=(bigint<N,T> const &x)
+    {
+        for (unsigned int i = 0; i < N; ++i)
+            m_digits[i] |= x.m_digits[i];
+    }
+
+    inline bigint<N,T> operator |(bigint<N,T> const &x) const
+    {
+        return bigint<N,T>(*this) |= x;
+    }
+
+    /*
+     * bigint bitwise XOR: just perform a bitwise XOR on all digits.
+     */
+    bigint<N,T> & operator ^=(bigint<N,T> const &x)
+    {
+        for (unsigned int i = 0; i < N; ++i)
+            m_digits[i] ^= x.m_digits[i];
+    }
+
+    inline bigint<N,T> operator ^(bigint<N,T> const &x) const
+    {
+        return bigint<N,T>(*this) ^= x;
+    }
+
+    /*
+     * bigint unary plus: a no-op
+     */
+    inline bigint<N,T> operator +() const
+    {
+        return *this;
+    }
+
+    /*
+     * bigint unary minus: flip bits and add one
+     */
+    bigint<N,T> operator -() const
+    {
+        bigint<N,T> ret;
+        T carry(1);
+        for (unsigned int i = 0; i < N; ++i)
+        {
+            T digit = (m_digits[i] ^ digit_mask) + carry;
+            ret.m_digits[i] = digit & digit_mask;
+            carry = (digit & ~digit_mask) ? T(1) : T(0);
+        }
+        return ret;
+    }
+
     /*
      * bigint addition: we add the digits one-to-one, carrying overflows,
-     * and replace digits with padding if one of the two operands is
-     * shorter.
+     * and pad missing digits if one of the two operands is shorter.
      */
-    template<int M>
+    template<unsigned int M>
     bigint<(N > M) ? N : M, T> operator +(bigint<M,T> const &x) const
     {
         bigint<(N > M) ? N : M, T> ret;
         T padding = is_negative() ? digit_mask : (T)0;
         T x_padding = x.is_negative() ? digit_mask : (T)0;
         T carry(0);
-        for (int i = 0; i < (N > M) ? N : M; ++i)
+        for (unsigned int i = 0; i < ((N > M) ? N : M); ++i)
         {
             T digit = (i < N ? m_digits[i] : padding)
                     + (i < M ? x.m_digits[i] : x_padding)
@@ -128,7 +204,80 @@ public:
         return ret;
     }
 
+    /*
+     * bigint subtraction: a combination of addition and unary minus;
+     * we add the result of flipping digits and adding one.
+     */
+    template<unsigned int M>
+    bigint<(N > M) ? N : M, T> operator -(bigint<M,T> const &x) const
+    {
+        bigint<(N > M) ? N : M, T> ret;
+        T padding = is_negative() ? digit_mask : (T)0;
+        T x_padding = x.is_negative() ? digit_mask : (T)0;
+        T carry(1);
+        for (unsigned int i = 0; i < ((N > M) ? N : M); ++i)
+        {
+            T digit = (i < N ? m_digits[i] : padding)
+                    + ((i < M ? x.m_digits[i] : x_padding) ^ digit_mask)
+                    + carry;
+            ret.m_digits[i] = digit & digit_mask;
+            carry = (digit & ~digit_mask) ? T(1) : T(0);
+        }
+        return ret;
+    }
+
+    /*
+     * bigint equality operator: just use memcmp.
+     * FIXME: we could easily support operands of different sizes.
+     */
+    inline bool operator ==(bigint<N,T> const &x) const
+    {
+        return memcmp(m_digits, x.m_digits, sizeof(m_digits)) == 0;
+    }
+
+    inline bool operator !=(bigint<N,T> const &x) const
+    {
+        return !(*this == x);
+    }
+
+    /*
+     * bigint comparison operators: take a quick decision if signs
+     * differ. Otherwise, compare all digits.
+     */
+    bool operator >(bigint<N,T> const &x) const
+    {
+        if (is_negative() ^ x.is_negative())
+            return x.is_negative();
+        for (unsigned int i = 0; i < N; ++i)
+            if (m_digits[i] != x.m_digits[i])
+                return m_digits[i] > x.m_digits[i];
+        return false;
+    }
+
+    bool operator <(bigint<N,T> const &x) const
+    {
+        if (is_negative() ^ x.is_negative())
+            return is_negative();
+        for (unsigned int i = 0; i < N; ++i)
+            if (m_digits[i] != x.m_digits[i])
+                return m_digits[i] < x.m_digits[i];
+        return false;
+    }
+
+    inline bool operator >=(bigint<N,T> const &x) const
+    {
+        return !(*this < x);
+    }
+
+    inline bool operator <=(bigint<N,T> const &x) const
+    {
+        return !(*this > x);
+    }
+
 private:
+    /* Allow other types of bigints to access our private members */
+    template<unsigned int, typename> friend class bigint;
+
     inline bool is_negative() const
     {
         if (N < 1)
@@ -139,5 +288,9 @@ private:
     T m_digits[N];
 };
 
+typedef bigint<8, uint32_t> int248_t;
+typedef bigint<16, uint32_t> int496_t;
+typedef bigint<32, uint32_t> int992_t;
+
 } /* namespace lol */
 
diff --git a/src/t/math/bigint.cpp b/src/t/math/bigint.cpp
index 4e8d00dd..94651b92 100644
--- a/src/t/math/bigint.cpp
+++ b/src/t/math/bigint.cpp
@@ -46,13 +46,178 @@ lolunit_declare_fixture(bigint_test)
         lolunit_assert_equal((uint32_t)c, ~(uint32_t)0);
     }
 
-    lolunit_declare_test(empty_bigint_is_zero)
+    lolunit_declare_test(operator_equal)
     {
-        bigint<0> a, b(1), c(-1);
+        bigint<> a(-1), b(0), c(1);
 
-        lolunit_assert_equal((int)a, 0);
-        lolunit_assert_equal((int)b, 0);
-        lolunit_assert_equal((int)c, 0);
+        lolunit_assert(a == a);
+        lolunit_assert(!(a == b));
+        lolunit_assert(!(a == c));
+
+        lolunit_assert(!(b == a));
+        lolunit_assert(b == b);
+        lolunit_assert(!(b == c));
+
+        lolunit_assert(!(c == a));
+        lolunit_assert(!(c == b));
+        lolunit_assert(c == c);
+    }
+
+    lolunit_declare_test(operator_notequal)
+    {
+        bigint<> a(-1), b(0), c(1);
+
+        lolunit_assert(!(a != a));
+        lolunit_assert(a != b);
+        lolunit_assert(a != c);
+
+        lolunit_assert(b != a);
+        lolunit_assert(!(b != b));
+        lolunit_assert(b != c);
+
+        lolunit_assert(c != a);
+        lolunit_assert(c != b);
+        lolunit_assert(!(c != c));
+    }
+
+    lolunit_declare_test(operator_smaller)
+    {
+        bigint<> a(-10), b(-1), c(0), d(1), e(10);
+
+        lolunit_assert(!(a < a));
+        lolunit_assert(a < b);
+        lolunit_assert(a < c);
+        lolunit_assert(a < d);
+        lolunit_assert(a < e);
+
+        lolunit_assert(!(b < a));
+        lolunit_assert(!(b < b));
+        lolunit_assert(b < c);
+        lolunit_assert(b < d);
+        lolunit_assert(b < e);
+
+        lolunit_assert(!(c < a));
+        lolunit_assert(!(c < b));
+        lolunit_assert(!(c < c));
+        lolunit_assert(c < d);
+        lolunit_assert(c < e);
+
+        lolunit_assert(!(d < a));
+        lolunit_assert(!(d < b));
+        lolunit_assert(!(d < c));
+        lolunit_assert(!(d < d));
+        lolunit_assert(d < e);
+
+        lolunit_assert(!(e < a));
+        lolunit_assert(!(e < b));
+        lolunit_assert(!(e < c));
+        lolunit_assert(!(e < d));
+        lolunit_assert(!(e < e));
+    }
+
+    lolunit_declare_test(operator_smaller_or_equal)
+    {
+        bigint<> a(-10), b(-1), c(0), d(1), e(10);
+
+        lolunit_assert(a <= a);
+        lolunit_assert(a <= b);
+        lolunit_assert(a <= c);
+        lolunit_assert(a <= d);
+        lolunit_assert(a <= e);
+
+        lolunit_assert(!(b <= a));
+        lolunit_assert(b <= b);
+        lolunit_assert(b <= c);
+        lolunit_assert(b <= d);
+        lolunit_assert(b <= e);
+
+        lolunit_assert(!(c <= a));
+        lolunit_assert(!(c <= b));
+        lolunit_assert(c <= c);
+        lolunit_assert(c <= d);
+        lolunit_assert(c <= e);
+
+        lolunit_assert(!(d <= a));
+        lolunit_assert(!(d <= b));
+        lolunit_assert(!(d <= c));
+        lolunit_assert(d <= d);
+        lolunit_assert(d <= e);
+
+        lolunit_assert(!(e <= a));
+        lolunit_assert(!(e <= b));
+        lolunit_assert(!(e <= c));
+        lolunit_assert(!(e <= d));
+        lolunit_assert(e <= e);
+    }
+
+    lolunit_declare_test(operator_greater)
+    {
+        bigint<> a(-10), b(-1), c(0), d(1), e(10);
+
+        lolunit_assert(!(a > a));
+        lolunit_assert(!(a > b));
+        lolunit_assert(!(a > c));
+        lolunit_assert(!(a > d));
+        lolunit_assert(!(a > e));
+
+        lolunit_assert(b > a);
+        lolunit_assert(!(b > b));
+        lolunit_assert(!(b > c));
+        lolunit_assert(!(b > d));
+        lolunit_assert(!(b > e));
+
+        lolunit_assert(c > a);
+        lolunit_assert(c > b);
+        lolunit_assert(!(c > c));
+        lolunit_assert(!(c > d));
+        lolunit_assert(!(c > e));
+
+        lolunit_assert(d > a);
+        lolunit_assert(d > b);
+        lolunit_assert(d > c);
+        lolunit_assert(!(d > d));
+        lolunit_assert(!(d > e));
+
+        lolunit_assert(e > a);
+        lolunit_assert(e > b);
+        lolunit_assert(e > c);
+        lolunit_assert(e > d);
+        lolunit_assert(!(e > e));
+    }
+
+    lolunit_declare_test(operator_greater_or_equal)
+    {
+        bigint<> a(-10), b(-1), c(0), d(1), e(10);
+
+        lolunit_assert(a >= a);
+        lolunit_assert(!(a >= b));
+        lolunit_assert(!(a >= c));
+        lolunit_assert(!(a >= d));
+        lolunit_assert(!(a >= e));
+
+        lolunit_assert(b >= a);
+        lolunit_assert(b >= b);
+        lolunit_assert(!(b >= c));
+        lolunit_assert(!(b >= d));
+        lolunit_assert(!(b >= e));
+
+        lolunit_assert(c >= a);
+        lolunit_assert(c >= b);
+        lolunit_assert(c >= c);
+        lolunit_assert(!(c >= d));
+        lolunit_assert(!(c >= e));
+
+        lolunit_assert(d >= a);
+        lolunit_assert(d >= b);
+        lolunit_assert(d >= c);
+        lolunit_assert(d >= d);
+        lolunit_assert(!(d >= e));
+
+        lolunit_assert(e >= a);
+        lolunit_assert(e >= b);
+        lolunit_assert(e >= c);
+        lolunit_assert(e >= d);
+        lolunit_assert(e >= e);
     }
 };