Final examples for templates

5 files changed, 383 insertions, 2 deletions

diff --git a/templates/bigint.h b/templates/bigint.h
new file mode 100644
index 0000000..8380211
--- /dev/null
+++ b/templates/bigint.h
@@ -0,0 +1,255 @@
+// Taken from https://git.tronto.net/zmodn
+
+#ifndef BIGUNSIGNED_H
+#define BIGUNSIGNED_H
+
+#include <cstdint>
+#include <iostream>
+#include <string_view>
+
+constexpr uint64_t abs64(int64_t);
+constexpr uint64_t pow10(uint64_t);
+
+// Big integer class for numbers of at most N decimal digits.
+// The number E is used to tune the size of each digit, mostly for
+// testing purposes.
+
+template<uint64_t N = 50, uint64_t E = 9>
+requires (E < 10)
+class BigInt {
+public:
+        // The member variables sign and digits are declared public so that
+        // BigInt becomes a structural type and can be used in templates.
+
+        static constexpr uint64_t M = pow10(E);
+        static constexpr uint64_t D = (N / E) + 1;
+
+        bool sign;
+        uint64_t digits[D];
+
+        constexpr BigInt() : sign{true} {
+                std::fill(digits, digits+D, 0);
+        }
+
+        constexpr BigInt(int64_t n) : sign{n >= 0} {
+                std::fill(digits, digits+D, 0);
+                digits[0] = abs64(n);
+                carryover();
+        }
+
+        constexpr BigInt(const std::string_view s) : sign{true} {
+                std::fill(digits, digits+D, 0);
+                if (s.size() == 0)
+                        return;
+                for (int i = s.size()-1, j = 0; i >= 0; i--, j++) {
+                        if (s[i] == '\'')
+                                continue;
+                        if (i == 0 && s[i] == '-') {
+                                sign = false;
+                                break;
+                        }
+                        digits[j/E] += (pow10(j % E))
+                            * static_cast<uint64_t>(s[i] - '0');
+                }
+        }
+
+        constexpr auto operator<=>(const BigInt& other) const {
+                if (sign != other.sign)
+                        return sign <=> other.sign;
+
+                for (int i = D-1; i >= 0; i--)
+                        if (digits[i] != other.digits[i])
+                                return sign ?
+                                    digits[i] <=> other.digits[i] :
+                                    other.digits[i] <=> digits[i];
+
+                return 0 <=> 0;
+        }
+
+        constexpr bool operator==(const BigInt& other) const = default;
+
+        constexpr BigInt abs() const {
+                BigInt ret = *this;
+                ret.sign = true;
+                return ret;
+        }
+
+        constexpr BigInt operator-() const {
+                if (*this == 0)
+                        return 0;
+                BigInt ret = *this;
+                ret.sign = !ret.sign;
+                return ret;
+        }
+
+        constexpr BigInt operator+(const BigInt& z) const {
+                if (sign && z.sign)
+                        return positive_sum(*this, z);
+                else if (sign && !z.sign)
+                        return positive_diff(*this, -z);
+                else if (!sign && z.sign)
+                        return positive_diff(z, -*this);
+                else
+                        return -positive_sum(-*this, -z);
+        }
+
+        constexpr BigInt operator-(const BigInt& z) const {
+                return *this + (-z);
+        }
+
+        constexpr BigInt operator*(const BigInt& z) const {
+                BigInt ret;
+                ret.sign = !(sign ^ z.sign);
+                for (int i = 0; i < D; i++)
+                        for (int j = 0; i+j < D; j++)
+                                ret.digits[i+j] += digits[i] * z.digits[j];
+                ret.carryover();
+                return ret;
+        }
+
+        constexpr BigInt operator/(const BigInt& z) const {
+                auto [q, r] = euclidean_division(*this, z);
+                return q;
+        }
+
+        constexpr BigInt operator%(const BigInt& z) const {
+                auto [q, r] = euclidean_division(*this, z);
+                return r;
+        }
+
+        constexpr BigInt operator+=(const BigInt& z) { return *this = *this + z; }
+        constexpr BigInt operator++() { return *this += 1; }
+        constexpr BigInt operator-=(const BigInt& z) { return *this = *this - z; }
+        constexpr BigInt operator--() { return *this -= 1; }
+        constexpr BigInt operator*=(const BigInt& z) { return *this = *this * z; }
+        constexpr BigInt operator/=(const BigInt& z) { return *this = *this / z; }
+        constexpr BigInt operator%=(const BigInt& z) { return *this = *this % z; }
+
+        friend std::ostream& operator<<(std::ostream& os, const BigInt<N, E>& z) {
+                if (z == 0) {
+                        os << "0";
+                        return os;
+                }
+
+                if (!z.sign)
+                        os << "-";
+
+                int j;
+                for (j = z.D-1; z.digits[j] == 0; j--) ;
+                os << z.digits[j]; // Top digit is not padded
+
+                for (int i = j-1; i >= 0; i--) {
+                        std::string num = std::to_string(z.digits[i]);
+                        os << std::string(E - num.length(), '0') << num;
+                }
+                return os;
+        }
+
+private:
+        constexpr void carryover() {
+                for (int i = 1; i < D; i++) {
+                        auto c = digits[i-1] / M;
+                        digits[i-1] -= c * M;
+                        digits[i] += c;
+                }
+        }
+
+        constexpr BigInt half() const {
+                BigInt ret;
+                uint64_t carry = 0;
+                for (int i = D-1; i >= 0; i--) {
+                        ret.digits[i] += (digits[i] + M * carry) / 2;
+                        carry = digits[i] % 2;
+                }
+                return ret;
+        }
+
+        static constexpr BigInt powM(uint64_t e) {
+                BigInt ret;
+                ret.digits[e] = 1;
+                return ret;
+        }
+
+        // Sum of non-negative integers
+        static constexpr BigInt positive_sum(const BigInt& x, const BigInt& y) {
+                BigInt ret;
+                for (int i = 0; i < D; i++)
+                        ret.digits[i] = x.digits[i] + y.digits[i];
+                ret.carryover();
+                return ret;
+        }
+
+        // Difference of non-negative integers (result may be negative)
+        static constexpr BigInt positive_diff(const BigInt& x, const BigInt& y) {
+                if (y > x)
+                        return -positive_diff(y, x);
+
+                BigInt ret;
+                uint64_t carry = 0;
+                for (int i = 0; i < D; i++) {
+                        uint64_t oldcarry = carry;
+                        if (x.digits[i] < y.digits[i] + oldcarry) {
+                                ret.digits[i] = M;
+                                carry = 1;
+                        } else {
+                                carry = 0;
+                        }
+                        ret.digits[i] += x.digits[i];
+                        ret.digits[i] -= y.digits[i] + oldcarry;
+                }
+                ret.carryover();
+                return ret;
+        }
+
+        // Division with remainder, UB if y == 0
+        static constexpr std::pair<BigInt, BigInt>
+        euclidean_division(const BigInt& x, const BigInt& y) {
+                auto [q, r] = positive_div(x.abs(), y.abs());
+                if (x.sign && y.sign)
+                        return std::pair(q, r);
+                else if (x.sign && !y.sign)
+                        return r == 0 ? std::pair(-q, 0) : std::pair(-q-1, y+r);
+                else if (!x.sign && y.sign)
+                        return r == 0 ? std::pair(-q, r) : std::pair(-q-1, y-r);
+                else
+                        return std::pair(q, -r);
+        }
+
+        // Division with remainder of non-negative integers, UB if y == 0
+        // This method is inefficient (O(log(x/y)) BigInt multiplications)
+        static constexpr std::pair<BigInt, BigInt>
+        positive_div(const BigInt& x, const BigInt& y) {
+                BigInt q = 0;
+                BigInt r = x;
+
+                if (y > x)
+                        return std::pair(q, r);
+
+                BigInt lb = 0;
+                BigInt ub = x;
+                while (true) {
+                        BigInt q = (ub + lb).half();
+                        BigInt r = x - y*q;
+
+                        if (r < 0)
+                                ub = q;
+                        else if (r >= y)
+                                lb = q+1;
+                        else
+                                return std::pair(q, r);
+                }
+        }
+};
+
+constexpr uint64_t abs64(int64_t x) {
+        return static_cast<uint64_t>(x > 0 ? x : -x);
+}
+
+constexpr uint64_t pow10(uint64_t e) {
+        if (e == 0)
+                return 1;
+        else
+                return 10 * pow10(e-1);
+}
+
+#endif
diff --git a/templates/zmodn-1.cpp b/templates/zmodn-1.cpp
index a8e26ca..1c1450b 100644
--- a/templates/zmodn-1.cpp
+++ b/templates/zmodn-1.cpp
@@ -14,7 +14,6 @@ public:
         int value;
 
         Zmod(int z) : value{(z%N + N) % N} {}
-        int toint() const { return value; }
 
         Zmod operator+(const Zmod& z) const { return value + z.value; }
         Zmod operator-(const Zmod& z) const { return value - z.value; }
diff --git a/templates/zmodn-2.cpp b/templates/zmodn-2.cpp
index f96ef8c..d71f2ac 100644
--- a/templates/zmodn-2.cpp
+++ b/templates/zmodn-2.cpp
@@ -15,7 +15,6 @@ public:
         int value;
 
         Zmod(int z) : value{(z%N + N) % N} {}
-        int toint() const { return value; }
 
         Zmod operator+(const Zmod& z) const { return value + z.value; }
         Zmod operator-(const Zmod& z) const { return value - z.value; }
diff --git a/templates/zmodn-3.cpp b/templates/zmodn-3.cpp
new file mode 100644
index 0000000..ca73783
--- /dev/null
+++ b/templates/zmodn-3.cpp
@@ -0,0 +1,57 @@
+#include "bigint.h"
+
+#include <iostream>
+#include <optional>
+#include <tuple>
+#include <type_traits>
+
+template<typename T>
+std::tuple<T, T, T> extended_gcd(T a, T b) {
+        if (b == 0) return {a, 1, 0};
+        auto [g, x, y] = extended_gcd(b, a%b);
+        return {g, y, x - y*(a/b)};
+}
+
+template<auto N>
+requires (N > 1)
+class Zmod {
+public:
+        decltype(N) value;
+
+        Zmod(decltype(N) z) : value{(z%N + N) % N} {}
+
+        Zmod operator+(const Zmod& z) const { return value + z.value; }
+        Zmod operator-(const Zmod& z) const { return value - z.value; }
+        Zmod operator*(const Zmod& z) const { return value * z.value; }
+
+        std::optional<Zmod> inverse() const {
+                auto [g, a, _] = extended_gcd(value, N);
+                return g == 1 ? Zmod(a) : std::optional<Zmod>{};
+        }
+
+        std::optional<Zmod> operator/(const Zmod& d) const {
+                auto i = d.inverse();
+                return i ? (*this) * i.value() : i;
+        }
+
+        std::optional<Zmod> operator/=(const Zmod& d) {
+                auto q = *this / d;
+                return q ? (*this = q.value()) : q;
+        }
+};
+
+int main() {
+        constexpr BigInt N("1000000000000000000000000000000");
+        Zmod<N> x(BigInt("123456781234567812345678"));
+        Zmod<N> y(BigInt("987654321987654321"));
+
+        std::cout << x.value << " * "
+                  << y.value << " (mod " << N << ") = "
+                  << (x * y).value << std::endl;
+
+        // The following gives a compile error on the first % operation
+        // constexpr double M = 3.14;
+        // Zmod<M> z(4);
+
+        return 0;
+}
diff --git a/templates/zmodn-4.cpp b/templates/zmodn-4.cpp
new file mode 100644
index 0000000..d3530c2
--- /dev/null
+++ b/templates/zmodn-4.cpp
@@ -0,0 +1,71 @@
+#include "bigint.h"
+
+#include <iostream>
+#include <optional>
+#include <tuple>
+#include <type_traits>
+
+template<typename T>
+concept Integer = requires(T a, T b, int i) {
+        {T(i)};
+
+        {a + b} -> std::same_as<T>;
+        {a - b} -> std::same_as<T>;
+        {a * b} -> std::same_as<T>;
+        {a / b} -> std::same_as<T>;
+        {a % b} -> std::same_as<T>;
+
+        {a == b} -> std::same_as<bool>;
+        {a != b} -> std::same_as<bool>;
+};
+
+template<Integer T>
+std::tuple<T, T, T> extended_gcd(T a, T b) {
+        if (b == 0) return {a, 1, 0};
+        auto [g, x, y] = extended_gcd(b, a%b);
+        return {g, y, x - y*(a/b)};
+}
+
+template<Integer auto N>
+requires (N > 1)
+class Zmod {
+public:
+        decltype(N) value;
+
+        Zmod(decltype(N) z) : value{(z%N + N) % N} {}
+
+        Zmod operator+(const Zmod& z) const { return value + z.value; }
+        Zmod operator-(const Zmod& z) const { return value - z.value; }
+        Zmod operator*(const Zmod& z) const { return value * z.value; }
+
+        std::optional<Zmod> inverse() const {
+                auto [g, a, _] = extended_gcd(value, N);
+                return g == 1 ? Zmod(a) : std::optional<Zmod>{};
+        }
+
+        std::optional<Zmod> operator/(const Zmod& d) const {
+                auto i = d.inverse();
+                return i ? (*this) * i.value() : i;
+        }
+
+        std::optional<Zmod> operator/=(const Zmod& d) {
+                auto q = *this / d;
+                return q ? (*this = q.value()) : q;
+        }
+};
+
+int main() {
+        constexpr BigInt N("1000000000000000000000000000000");
+        Zmod<N> x(BigInt("123456781234567812345678"));
+        Zmod<N> y(BigInt("987654321987654321"));
+
+        std::cout << x.value << " * "
+                  << y.value << " (mod " << N << ") = "
+                  << (x * y).value << std::endl;
+
+        // The following line gives an error when trying to specialize Zmod<M>
+        // constexpr double M = 3.14;
+        // Zmod<M> z(4);
+
+        return 0;
+}