SoftwareRenderer/fastmath.hpp

#ifndef FASTMATH_H
#define FASTMATH_H

#include <cmath>
#include <iostream>
#include <sstream>
#include <stdint.h>
#include <stdlib.h>
#include <vector>
#define SHIFT_AMOUNT 16
#define HALF_SHIFT (SHIFT_AMOUNT / 2)

#define SHIFT_MASK ((1 << SHIFT_AMOUNT) - 1)
#define TO_FLOAT(x)                                                            \
    (((float)(x >> SHIFT_AMOUNT)) +                                            \
     ((double)(x & SHIFT_MASK) / (1 << SHIFT_AMOUNT)))
#define TO_INT(x) ((int32_t)(x * (1 << SHIFT_AMOUNT)))
#define MUL_F(a, b) (((a) >> HALF_SHIFT) * ((b) >> HALF_SHIFT))
#define DIV_F(a, b) ((((a) << HALF_SHIFT) / (b)) << HALF_SHIFT)

struct decimal {

    const int32_t i;

    decimal() : i(0) {}
    decimal(float i) : i(TO_INT(i)) {}
    decimal(double i) : i(TO_INT(i)) {}
    decimal(int32_t i) : i(i) {}

    friend std::ostream &operator<<(std::ostream &os, const decimal &d) {
        return (os << TO_FLOAT(d.i));
    }

    friend decimal operator+(const decimal &d1, const decimal &d2) {
        return {d1.i + d2.i};
    }
    decimal &operator+=(const decimal &d) { return (*this) = {i + d.i}; }

    friend decimal operator-(const decimal &d1, const decimal &d2) {
        return {d1.i - d2.i};
    }
    friend decimal operator-(const decimal &d) { return {-d.i}; }

    friend decimal operator*(const decimal &d1, const decimal &d2) {
        return {MUL_F(d1.i, d2.i)};
    }

    friend decimal operator/(const decimal &d1, const decimal &d2) {
        return {DIV_F(d1.i, d2.i)};
    }

    friend bool operator<(const decimal &d1, const decimal &d2) {
        return d1.i < d2.i;
    }

    friend bool operator>(const decimal &d1, const decimal &d2) {
        return d1.i > d2.i;
    }

    friend bool operator==(const decimal &d1, const decimal &d2) {
        return d1.i == d2.i;
    }

    decimal &operator=(decimal const &in) {
        if (this != &in) {
            std::destroy_at(this);
            std::construct_at(this, in);
        }
        return *this;
    }

    decimal sqrt() { return {((int32_t)sqrtf(i)) << HALF_SHIFT}; }

    float to_float() { return TO_FLOAT(i); }
};

template <int n, class Dev> struct vec {

    vec(decimal newV[n]) {
        for (int i = 0; i < n; i++) {
            v[i] = newV[i];
        }
    }

    vec(std::vector<decimal> newV) {
        for (int i = 0; i < n; i++) {
            v[i] = newV[i];
        }
    }

    vec() : v{} {}

    friend Dev operator+(const vec<n, Dev> &v1, const vec<n, Dev> &v2) {
        Dev newV = {};

        for (int i = 0; i < n; i++) {
            newV.v[i] = v1.v[i] + v2.v[i];
        }
        return newV;
    }

    friend Dev operator-(const vec<n, Dev> &v1, const vec<n, Dev> &v2) {
        Dev newV = {};

        for (int i = 0; i < n; i++) {
            newV.v[i] = v1.v[i] - v2.v[i];
        }
        return static_cast<Dev>(newV);
    }

    friend std::ostream &operator<<(std::ostream &os, const vec<n, Dev> &v) {
        os << "(" << v.v[0];
        for (int i = 1; i < n; i++) {
            os << ", " << v.v[i];
        }
        return (os << ")" << std::endl);
    }

    Dev operator-() {
        Dev newV = {};
        for (int i = 0; i < n; i++) {
            newV.v[i] = -v[i];
        }
        return newV;
    }

    friend Dev operator*(const vec<n, Dev> &v, const decimal &d) {
        int32_t f = d.i >> HALF_SHIFT;

        Dev newV = {};
        for (int i = 0; i < n; i++) {
            newV.v[i] = (v.v[i].i >> HALF_SHIFT) * f;
        }
        return newV;
    }

    friend Dev operator*(const decimal &d, const vec<n, Dev> &v) {
        return v * d;
    }

    decimal operator*(const vec<n, Dev> &vec) {
        decimal res;
        for (int i = 0; i < n; i++) {
            res += vec.v[i] * v[i];
        }
        return res;
    }

    friend bool operator==(const vec<n, Dev> &v1, const vec<n, Dev> &v2) {
        bool res = true;
        for (int i = 0; i < n; i++) {
            res &= v1.v[i] == v2.v[i];
        }
        return res;
    }

    decimal len_sq() { return *this * *this; }

    decimal len() { return this->len_sq().sqrt(); }

    Dev normalize() {
        decimal f = decimal(1.0) / this->len();
        return (*this * f);
    }

  protected:
    decimal v[n];
};

struct vec3 : public vec<3, vec3> {

    vec3() : vec<3, vec3>() {}

    vec3(float x, float y, float z)
        : vec<3, vec3>({decimal(x), decimal(y), decimal(z)}) {}

    vec3(double x, double y, double z)
        : vec<3, vec3>({decimal(x), decimal(y), decimal(z)}) {}

    vec3(int32_t x, int32_t y, int32_t z)
        : vec<3, vec3>({decimal(x), decimal(y), decimal(z)}) {}

    vec3(decimal x, decimal y, decimal z) : vec<3, vec3>({x, y, z}) {}

    decimal x() const { return v[0]; }
    decimal y() const { return v[1]; }
    decimal z() const { return v[2]; }

    vec3 cross(const vec3 &v) {
        return vec3((y() * v.z()) - (z() * v.y()),
                    (z() * v.x()) - (x() * v.z()),
                    (x() * v.y()) - (y() * v.x()));
    }
};
#endif