|  | @@ -0,0 +1,520 @@
 | 
	
		
			
				|  |  | +#pragma once
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +#include <cinttypes>
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +struct Fixed128
 | 
	
		
			
				|  |  | +{
 | 
	
		
			
				|  |  | +    uint64_t upper;
 | 
	
		
			
				|  |  | +    uint64_t lower;
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    Fixed128(const Fixed128&) = default;
 | 
	
		
			
				|  |  | +    ~Fixed128() = default;
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed128(uint64_t upper, uint64_t lower) :
 | 
	
		
			
				|  |  | +        upper{ upper }, lower{ lower }
 | 
	
		
			
				|  |  | +    {
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed128(uint32_t a, uint32_t b, uint32_t c, uint32_t d) :
 | 
	
		
			
				|  |  | +        upper{ (uint64_t(a) << 32) | b }, lower{ (uint64_t(c) << 32) | d }
 | 
	
		
			
				|  |  | +    {
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed128(double x)
 | 
	
		
			
				|  |  | +    {
 | 
	
		
			
				|  |  | +        const double twoToThe32 = double(0x100000000ULL);
 | 
	
		
			
				|  |  | +        upper = uint64_t(int64_t(x * twoToThe32));
 | 
	
		
			
				|  |  | +        double remainder = x - double(upper) / twoToThe32;
 | 
	
		
			
				|  |  | +        lower = uint64_t(int64_t(x * twoToThe32 * twoToThe32 * twoToThe32));
 | 
	
		
			
				|  |  | +        /*int integerPart = ::floor(x);
 | 
	
		
			
				|  |  | +        double fractionalPart = x - integerPart;
 | 
	
		
			
				|  |  | +        upper = int64_t(integerPart) << 32;
 | 
	
		
			
				|  |  | +        upper |= uint64_t(fractionalPart * (1ULL << 32)) & 0xFFFFFFFFULL;
 | 
	
		
			
				|  |  | +        lower = 0;// uint64_t(fractionalPart * (1ULL << 32) * (1ULL << 63) * 2);*/
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed128 operator + (const Fixed128& other) const {
 | 
	
		
			
				|  |  | +        uint64_t lowerAdded = lower + other.lower;
 | 
	
		
			
				|  |  | +        uint64_t upperAdded = upper + other.upper + (lowerAdded < lower);
 | 
	
		
			
				|  |  | +        return Fixed128{ upperAdded, lowerAdded };
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +    
 | 
	
		
			
				|  |  | +    inline Fixed128& operator +=(const Fixed128& other) {
 | 
	
		
			
				|  |  | +        uint64_t lowerAdded = lower + other.lower;
 | 
	
		
			
				|  |  | +        upper += other.upper + (lowerAdded < lower);
 | 
	
		
			
				|  |  | +        lower = lowerAdded;
 | 
	
		
			
				|  |  | +        return *this;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed128 operator - (const Fixed128& other) const {
 | 
	
		
			
				|  |  | +        uint64_t lowerSubbed = lower - other.lower;
 | 
	
		
			
				|  |  | +        uint64_t upperSubbed = upper - other.upper - (lowerSubbed > lower);
 | 
	
		
			
				|  |  | +        return Fixed128{ upperSubbed, lowerSubbed };
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed128 operator - (void) const {
 | 
	
		
			
				|  |  | +        return this->operator~() + Fixed128{ 0, 0, 0, 1 };
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +//private:
 | 
	
		
			
				|  |  | +    static inline std::pair<uint64_t, uint64_t> mul64(int64_t a, int64_t b) {
 | 
	
		
			
				|  |  | +        int32_t aa[2] = { a >> 32, a & 0xFFFFFFFF };
 | 
	
		
			
				|  |  | +        int32_t bb[2] = { b >> 32, b & 0xFFFFFFFF };
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        int32_t res[4];
 | 
	
		
			
				|  |  | +        int64_t temp = int64_t(aa[1]) * bb[1];
 | 
	
		
			
				|  |  | +        res[3] = temp & 0xFFFFFFFF;
 | 
	
		
			
				|  |  | +        int32_t carry = temp >> 32;
 | 
	
		
			
				|  |  | +        temp = int64_t(aa[0]) * bb[1] + int64_t(aa[1]) * bb[0] + carry;
 | 
	
		
			
				|  |  | +        res[2] = temp & 0xFFFFFFFF;
 | 
	
		
			
				|  |  | +        carry = temp >> 32;
 | 
	
		
			
				|  |  | +        temp = int64_t(aa[0]) * bb[0] + carry;
 | 
	
		
			
				|  |  | +        res[1] = temp & 0xFFFFFFFF;
 | 
	
		
			
				|  |  | +        res[0] = temp >> 32;
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        return std::make_pair(uint64_t((int64_t(res[0]) << 32) | res[1]), uint64_t((int64_t(res[2]) << 32) | res[3]));
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    static inline std::pair<uint64_t, uint64_t> mulu64(uint64_t a, uint64_t b) {
 | 
	
		
			
				|  |  | +        uint32_t aa[2] = { a >> 32, a & 0xFFFFFFFF };
 | 
	
		
			
				|  |  | +        uint32_t bb[2] = { b >> 32, b & 0xFFFFFFFF };
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        uint32_t res[4];
 | 
	
		
			
				|  |  | +        uint64_t temp = uint64_t(aa[1]) * bb[1];
 | 
	
		
			
				|  |  | +        res[3] = temp & 0xFFFFFFFF;
 | 
	
		
			
				|  |  | +        uint32_t carry = temp >> 32;
 | 
	
		
			
				|  |  | +        temp = uint64_t(aa[0]) * bb[1] + uint64_t(aa[1]) * bb[0] + carry;
 | 
	
		
			
				|  |  | +        res[2] = temp & 0xFFFFFFFF;
 | 
	
		
			
				|  |  | +        carry = temp >> 32;
 | 
	
		
			
				|  |  | +        temp = uint64_t(aa[0]) * bb[0] + carry;
 | 
	
		
			
				|  |  | +        res[1] = temp & 0xFFFFFFFF;
 | 
	
		
			
				|  |  | +        res[0] = temp >> 32;
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        return std::make_pair((uint64_t(res[0]) << 32) | res[1], (uint64_t(res[2]) << 32) | res[3] );
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +public:
 | 
	
		
			
				|  |  | +    inline Fixed128 operator * (const Fixed128& other) const {
 | 
	
		
			
				|  |  | +        if (isNegative()) {
 | 
	
		
			
				|  |  | +            return -(other * this->operator-());
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +        if (other.isNegative()) {
 | 
	
		
			
				|  |  | +            return -(*this * (-other));
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +        auto [uuc, uu] = mulu64(upper, other.upper);
 | 
	
		
			
				|  |  | +        auto [ulc, ul] = mulu64(upper, other.lower);
 | 
	
		
			
				|  |  | +        auto [luc, lu] = mulu64(lower, other.upper);
 | 
	
		
			
				|  |  | +        auto [llc, ll] = mulu64(lower, other.lower);
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        uint64_t res[4] = { 0, 0, 0, 0 };
 | 
	
		
			
				|  |  | +        res[3] = ll;
 | 
	
		
			
				|  |  | +        res[2] += lu;
 | 
	
		
			
				|  |  | +        res[2] += ul;
 | 
	
		
			
				|  |  | +        if (res[2] < ul)
 | 
	
		
			
				|  |  | +            res[1]++;
 | 
	
		
			
				|  |  | +        res[2] += llc;
 | 
	
		
			
				|  |  | +        if (res[2] < llc)
 | 
	
		
			
				|  |  | +            res[1]++;
 | 
	
		
			
				|  |  | +        res[1] += uu;
 | 
	
		
			
				|  |  | +        if (res[1] < uu)
 | 
	
		
			
				|  |  | +            res[0]++;
 | 
	
		
			
				|  |  | +        res[1] += ulc;
 | 
	
		
			
				|  |  | +        if (res[1] < ulc)
 | 
	
		
			
				|  |  | +            res[0]++;
 | 
	
		
			
				|  |  | +        res[1] += luc;
 | 
	
		
			
				|  |  | +        if (res[1] < luc)
 | 
	
		
			
				|  |  | +            res[0]++;
 | 
	
		
			
				|  |  | +        res[0] += uuc;
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        return Fixed128{ uint32_t(res[0] & 0xFFFFFFFF), uint32_t(int64_t(res[1]) >> 32), uint32_t(res[1] & 0xFFFFFFFF), uint32_t(int64_t(res[2]) >> 32) };
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        /*if (isNegative()) {
 | 
	
		
			
				|  |  | +            return -(this->operator-() * other);
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +        if (other.isNegative()) {
 | 
	
		
			
				|  |  | +            return -(*this * (-other));
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        bool otherNegative = other.isNegative();
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        uint32_t quarters[4] = {
 | 
	
		
			
				|  |  | +            (upper >> 32) & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            upper & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            (lower >> 32) & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            lower & 0xFFFFFFFF
 | 
	
		
			
				|  |  | +        };
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        auto [a, ra] = other.mul(quarters[0]);
 | 
	
		
			
				|  |  | +        auto [b, rb] = other.mul(quarters[1]);
 | 
	
		
			
				|  |  | +        auto [c, rc] = other.mul(quarters[2]);
 | 
	
		
			
				|  |  | +        auto [d, rd] = other.mul(quarters[3]);
 | 
	
		
			
				|  |  | +        b.arshift(1);
 | 
	
		
			
				|  |  | +        c.arshift(2);
 | 
	
		
			
				|  |  | +        d.arshift(3);
 | 
	
		
			
				|  |  | +        Fixed128 carries = { uint32_t(rb), uint32_t(rc), uint32_t(rd), 0 };
 | 
	
		
			
				|  |  | +        Fixed128 result = a + b + c + d + carries;
 | 
	
		
			
				|  |  | +        return result;*/
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline std::pair<Fixed128, uint32_t> mul(uint32_t factor) const {
 | 
	
		
			
				|  |  | +        uint32_t quarters[4] = {
 | 
	
		
			
				|  |  | +            (upper >> 32) & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            upper & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            (lower >> 32) & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            lower & 0xFFFFFFFF
 | 
	
		
			
				|  |  | +        };
 | 
	
		
			
				|  |  | +        uint32_t newQ[4];
 | 
	
		
			
				|  |  | +        uint32_t carry = 0;
 | 
	
		
			
				|  |  | +        for (int i = 3; i >= 0; i--) {
 | 
	
		
			
				|  |  | +            int64_t prod = int64_t(quarters[i]) * factor + carry;
 | 
	
		
			
				|  |  | +            newQ[i] = prod & 0xFFFFFFFF;
 | 
	
		
			
				|  |  | +            carry = prod >> 32;
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +        /*    newQ[i] = quarters[i] * factor;
 | 
	
		
			
				|  |  | +        uint64_t tempLower = newQ[3];
 | 
	
		
			
				|  |  | +        uint64_t newLower = tempLower + (newQ[2] << 32);
 | 
	
		
			
				|  |  | +        uint64_t newUpper = (newQ[2] >> 32) + newQ[1] + (newQ[0] << 32) + (newLower < tempLower ? 1 : 0);*/
 | 
	
		
			
				|  |  | +        return std::make_pair(Fixed128{ newQ[0], newQ[1], newQ[2], newQ[3] }, carry);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    /*
 | 
	
		
			
				|  |  | +    inline void arshift(int fac32) {
 | 
	
		
			
				|  |  | +        uint32_t temp = 0;
 | 
	
		
			
				|  |  | +        switch (fac32) {
 | 
	
		
			
				|  |  | +        case 0:
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        case 1:
 | 
	
		
			
				|  |  | +            temp = upper & 0xFFFFFFFF;
 | 
	
		
			
				|  |  | +            upper = uint64_t(int64_t(upper) >> 32);
 | 
	
		
			
				|  |  | +            lower >>= 32;
 | 
	
		
			
				|  |  | +            lower |= uint64_t(temp) << 32;
 | 
	
		
			
				|  |  | +        case 2:
 | 
	
		
			
				|  |  | +            lower = upper;
 | 
	
		
			
				|  |  | +            upper = uint64_t(int64_t(upper) >> 63);
 | 
	
		
			
				|  |  | +        case 3:
 | 
	
		
			
				|  |  | +            lower = uint64_t(int64_t(upper) >> 32);
 | 
	
		
			
				|  |  | +            upper = uint64_t(int64_t(upper) >> 63);
 | 
	
		
			
				|  |  | +        default:
 | 
	
		
			
				|  |  | +            lower = uint64_t(int64_t(upper) >> 63);
 | 
	
		
			
				|  |  | +            upper = uint64_t(int64_t(upper) >> 63);
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +    }*/
 | 
	
		
			
				|  |  | +    /*
 | 
	
		
			
				|  |  | +    inline Fixed128 operator * (const Fixed128& other) const {
 | 
	
		
			
				|  |  | +        int32_t quarters[4] = {
 | 
	
		
			
				|  |  | +            (upper >> 32) & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            upper & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            (lower >> 32) & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            lower & 0xFFFFFFFF
 | 
	
		
			
				|  |  | +        };
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        int32_t otherQuarters[4] = {
 | 
	
		
			
				|  |  | +            (other.upper >> 32) & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            other.upper & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            (other.lower >> 32) & 0xFFFFFFFF,
 | 
	
		
			
				|  |  | +            other.lower & 0xFFFFFFFF
 | 
	
		
			
				|  |  | +        };
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        int64_t prods[4][4];
 | 
	
		
			
				|  |  | +        for (int i = 0; i < 4; i++) {
 | 
	
		
			
				|  |  | +            for (int j = 0; j < 4 && j + i < 5; j++) {
 | 
	
		
			
				|  |  | +                if (i == 0 || j == 0)
 | 
	
		
			
				|  |  | +                    prods[i][j] = int64_t(quarters[i]) * int64_t(otherQuarters[j]);
 | 
	
		
			
				|  |  | +                else
 | 
	
		
			
				|  |  | +                    prods[i][j] = uint64_t(uint32_t(quarters[i])) * uint64_t(uint32_t(otherQuarters[j]));
 | 
	
		
			
				|  |  | +            }
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        Fixed128 ret = { 0, 0 };
 | 
	
		
			
				|  |  | +        for (int i = 0; i < 4; i++) {
 | 
	
		
			
				|  |  | +            for (int j = 0; j < 4 && j + i < 5; j++) {
 | 
	
		
			
				|  |  | +                if (i == 0 || j == 0)
 | 
	
		
			
				|  |  | +                    ret.addSigned(prods[i][j], i + j);
 | 
	
		
			
				|  |  | +                else
 | 
	
		
			
				|  |  | +                    ret.add(prods[i][j], i + j);
 | 
	
		
			
				|  |  | +            }
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +        return ret;
 | 
	
		
			
				|  |  | +        
 | 
	
		
			
				|  |  | +        /*
 | 
	
		
			
				|  |  | +        int64_t x00 = int64_t(quarters[0]) * int64_t(otherQuarters[0]);
 | 
	
		
			
				|  |  | +        int64_t x01 = int64_t(quarters[0]) * int64_t(otherQuarters[1]);
 | 
	
		
			
				|  |  | +        int64_t x02 = int64_t(quarters[0]) * int64_t(otherQuarters[2]);
 | 
	
		
			
				|  |  | +        int64_t x03 = int64_t(quarters[0]) * int64_t(otherQuarters[3]);
 | 
	
		
			
				|  |  | +        int64_t x10 = int64_t(quarters[1]) * int64_t(otherQuarters[0]);
 | 
	
		
			
				|  |  | +        int64_t x11 = int64_t(quarters[1]) * int64_t(otherQuarters[1]);
 | 
	
		
			
				|  |  | +        int64_t x12 = int64_t(quarters[1]) * int64_t(otherQuarters[2]);
 | 
	
		
			
				|  |  | +        int64_t x13 = int64_t(quarters[1]) * int64_t(otherQuarters[3]);
 | 
	
		
			
				|  |  | +        int64_t x20 = int64_t(quarters[2]) * int64_t(otherQuarters[0]);
 | 
	
		
			
				|  |  | +        int64_t x21 = int64_t(quarters[2]) * int64_t(otherQuarters[1]);
 | 
	
		
			
				|  |  | +        int64_t x22 = int64_t(quarters[2]) * int64_t(otherQuarters[2]);
 | 
	
		
			
				|  |  | +        int64_t x30 = int64_t(quarters[3]) * int64_t(otherQuarters[0]);
 | 
	
		
			
				|  |  | +        int64_t x31 = int64_t(quarters[3]) * int64_t(otherQuarters[1]);
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        Fixed128 ret = { 0, 0 };
 | 
	
		
			
				|  |  | +        /*uint32_t newQuarters[4] = {
 | 
	
		
			
				|  |  | +            x00,
 | 
	
		
			
				|  |  | +            x01 + x10,
 | 
	
		
			
				|  |  | +            x02 + x11 + x20,
 | 
	
		
			
				|  |  | +            x03 + x12 + x21 + x30,
 | 
	
		
			
				|  |  | +        };*//*
 | 
	
		
			
				|  |  | +        ret.add(x00, 0);
 | 
	
		
			
				|  |  | +        ret.add(x01 + x10, 1);
 | 
	
		
			
				|  |  | +        ret.add(x02 + x11 + x20, 2);
 | 
	
		
			
				|  |  | +        ret.add(x03 + x12 + x21 + x30, 3);
 | 
	
		
			
				|  |  | +        ret.add(x13 + x22 + x31, 4);
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        return ret;*/
 | 
	
		
			
				|  |  | +    /*}*/
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +private:
 | 
	
		
			
				|  |  | +    inline void add(uint64_t val, int b32offset) {
 | 
	
		
			
				|  |  | +        switch (b32offset) {
 | 
	
		
			
				|  |  | +        case 0:
 | 
	
		
			
				|  |  | +            upper += val << 32;
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        case 1:
 | 
	
		
			
				|  |  | +            upper += val;
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        case 2:
 | 
	
		
			
				|  |  | +            upper += val >> 32;
 | 
	
		
			
				|  |  | +            lower += val << 32;
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        case 3: {
 | 
	
		
			
				|  |  | +            uint64_t newLower = lower + val;
 | 
	
		
			
				|  |  | +            if (newLower < lower) upper++;
 | 
	
		
			
				|  |  | +            lower = newLower;
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +        case 4:
 | 
	
		
			
				|  |  | +            uint64_t newLower = lower + (val >> 32);
 | 
	
		
			
				|  |  | +            if (lower > newLower) upper++;
 | 
	
		
			
				|  |  | +            lower += newLower;
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +    inline void addSigned(int64_t val, int b32offset) {
 | 
	
		
			
				|  |  | +        switch (b32offset) {
 | 
	
		
			
				|  |  | +        case 0:
 | 
	
		
			
				|  |  | +            upper += val << 32;
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        case 1:
 | 
	
		
			
				|  |  | +            upper += val;
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        case 2:
 | 
	
		
			
				|  |  | +            upper += val >> 32;
 | 
	
		
			
				|  |  | +            lower += val << 32;
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        case 3:
 | 
	
		
			
				|  |  | +            lower += val;
 | 
	
		
			
				|  |  | +            if (val < 0) upper--;
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        
 | 
	
		
			
				|  |  | +        case 4: {
 | 
	
		
			
				|  |  | +            uint64_t newLower = lower + (val >> 32);
 | 
	
		
			
				|  |  | +            if (lower > newLower) upper++;
 | 
	
		
			
				|  |  | +            lower = newLower;
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +        default:
 | 
	
		
			
				|  |  | +            if (val < 0) {
 | 
	
		
			
				|  |  | +                if (lower == 0) upper--;
 | 
	
		
			
				|  |  | +                lower--;
 | 
	
		
			
				|  |  | +            }
 | 
	
		
			
				|  |  | +            return;
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +public:
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    bool isNegative(void) const {
 | 
	
		
			
				|  |  | +        return (upper & (uint64_t(1) << 63)) != 0;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    operator double(void) const {
 | 
	
		
			
				|  |  | +        const int64_t twoToThe32 = 0x100000000ULL;
 | 
	
		
			
				|  |  | +        return double(int64_t(upper)) / twoToThe32 + int64_t(lower) / twoToThe32 / twoToThe32 / twoToThe32;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed128 operator ~ (void) const {
 | 
	
		
			
				|  |  | +        return Fixed128{ ~upper, ~lower };
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator == (const Fixed128& other) const {
 | 
	
		
			
				|  |  | +        return upper == other.upper && lower == other.lower;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator != (const Fixed128& other) const {
 | 
	
		
			
				|  |  | +        return !operator==(other);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator < (const Fixed128& other) const {
 | 
	
		
			
				|  |  | +        return upper < other.upper || (upper == other.upper && lower < other.lower);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator <= (const Fixed128& other) const {
 | 
	
		
			
				|  |  | +        return operator<(other) || operator==(other);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator > (const Fixed128& other) const {
 | 
	
		
			
				|  |  | +        return upper > other.upper || (upper == other.upper && lower > other.lower);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator >= (const Fixed128& other) const {
 | 
	
		
			
				|  |  | +        return operator>(other) || operator==(other);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +};
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +struct Fixed64
 | 
	
		
			
				|  |  | +{
 | 
	
		
			
				|  |  | +    bool sign;
 | 
	
		
			
				|  |  | +    uint64_t bits;
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    Fixed64(const Fixed64&) = default;
 | 
	
		
			
				|  |  | +    ~Fixed64() = default;
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed64(uint64_t bits, bool dummy) :
 | 
	
		
			
				|  |  | +        bits{ bits }
 | 
	
		
			
				|  |  | +    {
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed64(double x)
 | 
	
		
			
				|  |  | +    {
 | 
	
		
			
				|  |  | +        if (x < 0) {
 | 
	
		
			
				|  |  | +            sign = true;
 | 
	
		
			
				|  |  | +            x *= -1;
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +        else {
 | 
	
		
			
				|  |  | +            sign = false;
 | 
	
		
			
				|  |  | +        }
 | 
	
		
			
				|  |  | +        int integerPart = int(x);
 | 
	
		
			
				|  |  | +        double fractionalPart = x - integerPart;
 | 
	
		
			
				|  |  | +        bits = uint64_t(integerPart) << 32;
 | 
	
		
			
				|  |  | +        bits |= uint64_t(fractionalPart * (1ULL << 32)) & 0xFFFFFFFF;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed64 operator + (const Fixed64& other) {
 | 
	
		
			
				|  |  | +        return Fixed64{ bits + other.bits, true };
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +    
 | 
	
		
			
				|  |  | +    inline Fixed64& operator +=(const Fixed64& other) {
 | 
	
		
			
				|  |  | +        bits += other.bits;
 | 
	
		
			
				|  |  | +        return *this;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed64 operator - (const Fixed64& other) {
 | 
	
		
			
				|  |  | +        return Fixed64{ bits - other.bits, true };
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed64 operator * (const Fixed64& other) {
 | 
	
		
			
				|  |  | +        /*int32_t upper = bits >> 32;
 | 
	
		
			
				|  |  | +        uint32_t lower = uint32_t(bits & 0xFFFFFFFF);
 | 
	
		
			
				|  |  | +        int64_t upup = int64_t(upper) * int64_t(upper);
 | 
	
		
			
				|  |  | +        int64_t loup = int64_t(upper) * int64_t(lower);
 | 
	
		
			
				|  |  | +        int64_t lolo = int64_t(lower) * int64_t(lower);
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        int32_t newUp = upup & 0xFFFFFFFF + (loup >> 32);
 | 
	
		
			
				|  |  | +        int32_t newLo = loup & 0xFFFFFFFF + (lolo >> 32);*/
 | 
	
		
			
				|  |  | +        double d = int32_t(bits >> 32) + double(uint32_t(bits)) / (1ULL << 32);
 | 
	
		
			
				|  |  | +        double od = int32_t(other.bits >> 32) + double(uint32_t(other.bits)) / (1ULL << 32);
 | 
	
		
			
				|  |  | +        return d * od * (other.sign != sign) ? -1 : 1;
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +        //return Fixed64{ (uint64_t(newUp) << 32) | newLo, true };
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator == (const Fixed64& other) {
 | 
	
		
			
				|  |  | +        return bits == other.bits;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator != (const Fixed64& other) {
 | 
	
		
			
				|  |  | +        return !operator==(other);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator < (const Fixed64& other) {
 | 
	
		
			
				|  |  | +        return bits < other.bits;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator <= (const Fixed64& other) {
 | 
	
		
			
				|  |  | +        return operator<(other) || operator==(other);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator > (const Fixed64& other) {
 | 
	
		
			
				|  |  | +        return bits > other.bits;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator >= (const Fixed64& other) {
 | 
	
		
			
				|  |  | +        return operator>(other) || operator==(other);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +};
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +struct Fixed32
 | 
	
		
			
				|  |  | +{
 | 
	
		
			
				|  |  | +    int32_t bits;
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    Fixed32(const Fixed32&) = default;
 | 
	
		
			
				|  |  | +    ~Fixed32() = default;
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed32(int32_t bits, bool dummy) :
 | 
	
		
			
				|  |  | +        bits{ bits }
 | 
	
		
			
				|  |  | +    {
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed32(double x)
 | 
	
		
			
				|  |  | +    {
 | 
	
		
			
				|  |  | +        int integerPart = ::floor(x);
 | 
	
		
			
				|  |  | +        double fractionalPart = x - integerPart;
 | 
	
		
			
				|  |  | +        /*if (x < 0) {
 | 
	
		
			
				|  |  | +            integerPart--;
 | 
	
		
			
				|  |  | +            fractionalPart = 1.0 - fractionalPart;
 | 
	
		
			
				|  |  | +        }*/
 | 
	
		
			
				|  |  | +        bits = int32_t(integerPart) << 16;
 | 
	
		
			
				|  |  | +        bits |= uint32_t(fractionalPart * (1ULL << 16)) & 0xFFFF;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed32 operator + (const Fixed32& other) {
 | 
	
		
			
				|  |  | +        return Fixed32{ bits + other.bits, true };
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +    
 | 
	
		
			
				|  |  | +    inline Fixed32& operator +=(const Fixed32& other) {
 | 
	
		
			
				|  |  | +        bits += other.bits;
 | 
	
		
			
				|  |  | +        return *this;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed32 operator - (const Fixed32& other) {
 | 
	
		
			
				|  |  | +        return Fixed32{ bits - other.bits, true };
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline Fixed32 operator * (const Fixed32& other) {
 | 
	
		
			
				|  |  | +        int64_t prod = int64_t(bits) * int64_t(other.bits);
 | 
	
		
			
				|  |  | +        return Fixed32{ int32_t(prod >> 16), true };
 | 
	
		
			
				|  |  | +        //return Fixed32{ (uint64_t(newUp) << 32) | newLo, true };
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator == (const Fixed32& other) {
 | 
	
		
			
				|  |  | +        return bits == other.bits;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator != (const Fixed32& other) {
 | 
	
		
			
				|  |  | +        return !operator==(other);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator < (const Fixed32& other) {
 | 
	
		
			
				|  |  | +        return bits < other.bits;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator <= (const Fixed32& other) {
 | 
	
		
			
				|  |  | +        return operator<(other) || operator==(other);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator > (const Fixed32& other) {
 | 
	
		
			
				|  |  | +        return bits > other.bits;
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +
 | 
	
		
			
				|  |  | +    inline bool operator >= (const Fixed32& other) {
 | 
	
		
			
				|  |  | +        return operator>(other) || operator==(other);
 | 
	
		
			
				|  |  | +    }
 | 
	
		
			
				|  |  | +};
 | 
	
		
			
				|  |  | +
 |