Basic 3d vector operations. Testing with GoogleTest.

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+//
+// Created by Keuin on 2022/4/11.
+//
+
+#include <cmath>
+
+static inline bool eq(int a, int b) {
+    return a == b;
+}
+
+static inline bool eq(double a, double b) {
+    // FIXME broken on large values
+    // https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
+    // https://stackoverflow.com/a/253874/14332799
+    const double c = a - b;
+    return c <= 1e-14 && c >= -1e-14;
+}
+
+// 3-dim vector
+template<typename T>
+struct vec3 {
+    T x;
+    T y;
+    T z;
+
+    vec3 operator+(vec3 &b) const {
+        return vec3{.x=x + b.x, .y=y + b.y, .z=z + b.z};
+    }
+
+    vec3 operator-() const {
+        return vec3{.x = -x, .y = -y, .z = -z};
+    }
+
+    vec3 operator-(vec3 &b) const {
+        return vec3{.x=x - b.x, .y=y - b.y, .z=z - b.z};
+    }
+
+    // cross product
+    vec3 operator*(vec3 &b) const {
+        return vec3{.x=y * b.z - z * b.y, .y=x * b.z - z * b.x, .z=x * b.y - y * b.x};
+    }
+
+    bool operator==(vec3 b) const {
+        return eq(x, b.x) && eq(y, b.y) && eq(z, b.z);
+    }
+
+    // dot product
+    int dot(vec3 &b) const {
+        return x * b.x + y * b.y + z * b.z;
+    }
+
+    // norm value
+    int norm(int level = 2) const {
+        if (level == 2) {
+            return std::abs(x * x + y * y + z * z);
+        } else if (level == 1) {
+            return std::abs(x + y + z);
+        } else {
+            return (int) std::abs(powl(x, level) + powl(y, level) + powl(z, level));
+        }
+    }
+};
+
+// 3-dim vector (int)
+using vec3i = vec3<int>;
+
+// 3-dim vector (long long)
+using vec3l = vec3<long long>;
+
+// 3-dim vector (float)
+using vec3f = vec3<float>;
+
+// 3-dim vector (double)
+using vec3d = vec3<double>;