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