Just signed up, because my mind is blowing up on this stupid error.
I was calculating elliptic curves in a quick and dirty way with everything in 1 source-file. Then I thought about cleaning up my code and start to separate the functions and classes in different files. It's been a long time for me programming in C++ so I guess it is a really stupid beginner mistake.
So I am getting LNK1169-Error and LNK2005-Error and the solutions I found are about including .cpp which I am not doing. I although found out about the extern-keyword, but that seems to be kind of the solution for global variables.
Maybe someone can help me.
EDIT: Sorry for putting that much code. I just don't know what is relevant for the error and what's not.
The error I am getting are like this:
fatal error LNK1169: one or more multiply defined symbols found. Elliptic 1 C:\Users\Björn\documents\visual studio 2015\Projects\Elliptic 1\Debug\Elliptic 1.exe
error LNK2005 "public: int __thiscall Value::operator==(class Value const &)" (??8Value@@QAEHABV0@@Z) already defined in Tests.obj
error LNK2005 "public: int __thiscall Value::operator==(int)" (??8Value@@QAEHH@Z) already defined in Tests.obj
Here is my code:
Value.hpp
#pragma once
extern int PRIME;
// An own Int-Class to overload operators with modulo
class Value
{
public:
int v;
static friend std::ostream& operator<<(std::ostream& os, const Value& a);
Value()
{
this->v = 0;
}
Value(int a)
{
this->v = a;
}
Value operator+(const Value& other)
{
return Value((this->v + other.v) % PRIME);
}
Value operator+(int a)
{
return Value((this->v + a) % PRIME);
}
Value operator-(const Value& other)
{
Value t = Value((v - other.v) % PRIME);
if (t.v < 0)
{
t = t + PRIME;
return t;
}
return t;
}
Value operator-(int a)
{
Value t = Value((v - a) % PRIME);
if (t.v < 0)
{
t = t + PRIME;
return t;
}
return t;
}
void operator=(const Value other)
{
this->v = other.v;
}
Value operator*(const Value& a);
Value operator*(int a);
Value operator^(int a);
Value operator/(const Value& a);
int operator!=(int b);
int operator!=(const Value& b);
int operator==(int b);
int operator==(const Value& b);
Value operator~();
};
Value Value::operator*(const Value& a)
{
return Value((this->v*a.v) % PRIME);
}
Value Value::operator*(int a)
{
return Value((this->v*a) % PRIME);
}
Value Value::operator^(int b)
{
Value ret(1);
Value mul(this->v);
while (b)
{
if (b & 1)
ret = (ret * mul);
b = (b >> 1);
mul = mul * mul;
}
return ret;
}
Value Value::operator/(const Value& a)
{
if (a.v == 0)
return Value(0);
Value f = (Value)a ^ (PRIME - 2);
return *this * f;
}
int Value::operator!=(int b)
{
if (this->v != b)
return 1;
return 0;
}
int Value::operator!=(const Value& b)
{
if (this->v != b.v)
return 1;
return 0;
}
int Value::operator==(int b)
{
if (this->v == b)
return 1;
return 0;
}
int Value::operator==(const Value& b)
{
if (this->v == b.v)
return 1;
return 0;
}
Value Value::operator~()
{
return *this ^ ((PRIME - 1 + 2) / 4);
}
std::ostream& operator<<(std::ostream& os, const Value& a)
{
return os << a.v;
}
Point.hpp
#pragma once
#include "Value.hpp"
#include <iostream>
class Point
{
public:
Value x;
Value y;
Value z = 0;
static friend std::ostream& operator<<(std::ostream& os, const Point& p);
Point(int a, int b)
{
x.v = a;
y.v = b;
}
Point(int a, int b, int c)
{
x.v = a;
y.v = b;
z.v = c;
}
Point(Value a, Value b)
{
x.v = a.v;
y.v = b.v;
}
Point(Value a, Value b, Value c)
{
x.v = a.v;
y.v = b.v;
z.v = c.v;
}
Point& operator=(const Point& other)
{
x.v = other.x.v;
y.v = other.y.v;
z.v = other.z.v;
return *this;
}
int operator==(Point& other)
{
if (this->x == other.x && this->y == other.y && this->z == other.z)
return 1;
return 0;
}
int operator!=(Point& other)
{
if (this->x != other.x || this->y != other.y || this->z != other.z)
return 1;
return 0;
}
};
std::ostream& operator<<(std::ostream& os, const Point& p)
{
if ((Value)p.z == 0)
return os << "(" << p.x.v << "," << p.y.v << ")";
else
return os << "(" << p.x.v << "," << p.y.v << "," << p.z.v << ")";
}
Helper.hpp
#pragma once
#include "Point.hpp"
#include <vector>
// Forward declaration
int isEC(Value a, Value b);
Value calcEC(int x, Value a, Value b);
int testSqr(Value ySqr);
// Point Addition
Point add(Point p1, Point p2, Value a)
{
// 2D Addition
if (p1.z == 0 && p2.z == 0)
{
// 2 different points
if (p1.x.v != p2.x.v || p1.y.v != p2.y.v)
{
// m = (y2-y1)/(x2-x1)
Value h = p2.y - p1.y;
Value j = p2.x - p1.x;
Value m = h / j;
// x3 = m^2-x1-x2
Value f = m*m;
Value g = f - p1.x;
Value x3 = g - p2.x;
// y3 = m(x1-x3)-y1
Value t = p1.x - x3;
Value l = m * t;
Value y3 = l - p1.y;
if (x3.v < 0)
x3 = x3 + PRIME;
if (y3.v < 0)
y3 = y3 + PRIME;
return Point(x3, y3);
}
// Same points
else
{
// m = (3*x1^2+a)/(2*y1)
Value f = p1.x ^ 2;
Value g = f * 3;
Value h = g + a;
Value j = p1.y * 2;
Value m = h / j;
// x3 = m^2-2*x1
Value t = m*m;
Value x = p1.x * 2;
Value x3 = t - x;
// y3 = m(x1-x3)-y1
Value z = p1.x - x3;
Value i = m * z;
Value y3 = i - p1.y;
if (x3.v < 0)
x3 = x3 + PRIME;
if (y3.v < 0)
y3 = y3 + PRIME;
return Point(x3, y3);
}
}
// 3D Addition - Same points
else if (p1 == p2 && p1.z == 1 && p2.z == 1)
{
Value A = p1.y ^ 2;
Value B = p1.x * A * 4;
Value C = (A ^ 2) * 8;
Value D = (p1.x ^ 2)* 3 + a*(p1.z ^ 4);
//Value x3 = (((3 * (p1.x ^ 2) + a*(p1.z ^ 4)) ^ 2) - 8 * p1.x*(p1.y ^ 2));
Value x3 = (D ^ 2) - B * 2;
//Value y3 = (3 * (p1.x ^ 2) + a*(p1.z ^ 4)*(4 * p1.x*(p1.y ^ 2) - x3) - 8 * (p1.y ^ 4));
Value y3 = D*(B - x3) - C;
Value z3 = p1.y*p1.z * 2;
return Point(x3, y3, z3);
}
// 3D Addition - 2 different points
else if (p1 != p2)
{
Value A = p1.z ^ 2;
Value B = p1.z * A;
Value C = p2.x * A;
Value D = p2.y * B;
Value E = C - p1.x;
Value F = D - p1.y;
Value G = E ^ 2;
Value H = G * E;
Value I = p1.x * G;
Value x3 = (F ^ 2) - (H + (I * 2));
Value y3 = F*(I - x3) - p1.y*H;
Value z3 = p1.z * E;
return Point(x3, y3, z3);
}
return Point(0, 0, 0);
}
// Find all points and print them
std::vector<Point> findAllPoints(Value a, Value b)
{
Value ySqr;
std::vector<Point> vec;
std::cout << "Alle Punkte fuer a = " << a << ", b = " << b << " und Prime = " << PRIME << std::endl;
// Is it an elliptic curve?
if (isEC(a, b))
{
// Test all x-Values
for (int x = 0; x <= PRIME - 1;x++)
{
// y^2
ySqr = calcEC(x, a, b);
// Test ySqr for square by root
if (testSqr(ySqr))
{
//sqrt operator ~
Value yPos = ~ySqr;
std::cout << "(" << x << "," << yPos << ")\t";
Value yNeg = yPos - (yPos * 2);
// Save found points into vector
vec.push_back(Point(x, yPos));
vec.push_back(Point(x, yNeg));
if (yNeg != 0)
std::cout << "(" << x << "," << yNeg << ")\t";
}
}
//vec.insert(vec.begin(), Point(INFINITY, INFINITY));
std::cout << std::endl;
}
else
// Not an ellpitic curve
std::cout << "\na and b are not leading to an ellptic curve.";
return vec;
}
// Test if a and b lead to an EC
int isEC(Value a, Value b)
{
if ((a ^ 3) * 4 + (b ^ 2) * 27 != 0)
return 1;
return 0;
}
// Calculate y^2
Value calcEC(int x, Value a, Value b)
{
return Value(a*x + (x ^ 3) + b);
}
// Test ySqr for square by root
int testSqr(Value ySqr)
{
if ((ySqr ^ ((PRIME - 1) / 2)) == 1 || ySqr == 0)
return 1;
return 0;
}
Tests.hpp
#pragma once
#include "Helper.hpp"
class Tests
{
public:
void twoDAdd(Value a, Value b);
void twoDDoubling(Value a, Value b);
void threeDAdd(Value a, Value b);
void threeDDoubling(Value a, Value b);
};
Tests.cpp
#pragma once
#include <stdlib.h>
#include <vector>
#include <iostream>
#include <math.h>
#include <time.h>
#include "Tests.hpp"
// 2D - Addition
void Tests::twoDAdd(Value a, Value b)
{
std::cout << "\n========== 2D Addition ==========\n";
Point p2D1 = Point(5, 22);
Point p2D2 = Point(16, 27);
std::cout << p2D1 << " + " << p2D2 << " = " << add(p2D1, p2D2, a);
std::cout << std::endl;
}
// 2D - Doubling
void Tests::twoDDoubling(Value a, Value b)
{
std::cout << "\n========== 2D Doubling ==========\n";
Point p2D1 = Point(5, 22);
std::cout << "2 * " << p2D1 << " = " << add(p2D1, p2D1, a);
std::cout << std::endl << std::endl;
}
// 3D - Addition
void Tests::threeDAdd(Value a, Value b)
{
std::cout << "\n========== 3D Addition ==========\n";
std::cout << "All points for a = " << a << ", b = " << b << " and prime = " << PRIME << std::endl;
std::vector<Point> allPoints = findAllPoints(a, b);
std::srand(time(NULL));
int random = std::rand() % (allPoints.capacity() - 1);
Point tmp = allPoints.at(random);
std::cout << std::endl << "Random Point 1: " << tmp << std::endl << std::endl;
tmp.z = 1;
Point p1 = add(tmp, tmp, a);
std::cout << p1 << std::endl;
random = std::rand() % (allPoints.capacity() - 1);
tmp = allPoints.at(random);
std::cout << std::endl << "Random Point 2: " << tmp << std::endl << std::endl;
tmp.z = 1;
Point p2 = add(tmp, tmp, a);
std::cout << p2 << std::endl;
Point p3 = add(p1, p2, a);
std::cout << p3 << std::endl;
}
// 3D - Doubling
void Tests::threeDDoubling(Value a, Value b)
{
std::cout << "\n========== 3D Doubling ==========\n";
std::cout << "All points for a = " << a << ", b = " << b << " and prime = " << PRIME << std::endl;
std::vector<Point> allPoints = findAllPoints(a, b);
int random = std::rand() % (allPoints.capacity() - 1);
Point tmp = allPoints[random];
std::cout << std::endl << "Random Point: " << tmp << std::endl << std::endl;
Point p1 = add(tmp, tmp, a);
std::cout << p1 << std::endl;
tmp.z = 1;
Point p2 = add(tmp, tmp, a);
std::cout << p2 << std::endl;
Point p3 = Point(p2.x / (p2.z ^ 2), p2.y / (p2.z ^ 3));
std::cout << p3 << std::endl;
if (p1 == p3)
std::cout << "Point p1 == Point p3" << std::endl;
else
std::cout << "Point p1 != Point p3" << std::endl;
}
Main.cpp
#pragma once
#include <stdlib.h>
#include <vector>
#include <iostream>
#include <math.h>
#include <time.h>
#include "Tests.hpp"
int PRIME = 29;
void main()
{/*
Value a = 4;
Value b = 20;
std::vector<Point> allPoints = findAllPoints(a, b);
/*
// Tests ausfuehren
twoDAdd(a, b);
twoDDoubling(a, b);
threeDAdd(a, b);
threeDDoubling(a, b);
*/
std::cout << std::endl;
system("pause");
}
Thanks in advance and please excuse my "inperfect" way of coding.
This is happening because you have function definition in header files. Every file that we'll import your header files will have a body function - this is the reason why you have this error. If you want to have the definitions inside header files, you must use inline keyword. Otherwise you need to implement them in .cpp files (the "correct" way of solving this issue).
e.g
// Test if a and b lead to an EC
inline int isEC(Value a, Value b)
{
if ((a ^ 3) * 4 + (b ^ 2) * 27 != 0)
return 1;
return 0;
}
// Calculate y^2
inline Value calcEC(int x, Value a, Value b)
{
return Value(a*x + (x ^ 3) + b);
}
// Test ySqr for square by root
inline int testSqr(Value ySqr)
{
if ((ySqr ^ ((PRIME - 1) / 2)) == 1 || ySqr == 0)
return 1;
return 0;
}