Task: Imaginary base numbers
C: #include <math.h>
#include <stdio.h>
#include <string.h>

int find(char *s, char c) {
    for (char *i = s; *i != 0; i++) {
        if (*i == c) {
            return i - s;
        }
    }
    return -1;
}

void reverse(char *b, char *e) {
    for (e--; b < e; b++, e--) {
        char t = *b;
        *b = *e;
        *e = t;
    }
}



struct Complex {
    double rel, img;
};

void printComplex(struct Complex c) {
    printf("(%3.0f + %3.0fi)", c.rel, c.img);
}

struct Complex makeComplex(double rel, double img) {
    struct Complex c = { rel, img };
    return c;
}

struct Complex addComplex(struct Complex a, struct Complex b) {
    struct Complex c = { a.rel + b.rel, a.img + b.img };
    return c;
}

struct Complex mulComplex(struct Complex a, struct Complex b) {
    struct Complex c = { a.rel * b.rel - a.img * b.img, a.rel * b.img - a.img * b.rel };
    return c;
}

struct Complex mulComplexD(struct Complex a, double b) {
    struct Complex c = { a.rel * b, a.img * b };
    return c;
}

struct Complex negComplex(struct Complex a) {
    return mulComplexD(a, -1.0);
}

struct Complex divComplex(struct Complex a, struct Complex b) {
    double re = a.rel * b.rel + a.img * b.img;
    double im = a.img * b.rel - a.rel * b.img;
    double d = b.rel * b.rel + b.img * b.img;
    struct Complex c = { re / d, im / d };
    return c;
}

struct Complex inv(struct Complex c) {
    double d = c.rel * c.rel + c.img * c.img;
    struct Complex i = { c.rel / d, -c.img / d };
    return i;
}

const struct Complex TWO_I = { 0.0, 2.0 };
const struct Complex INV_TWO_I = { 0.0, -0.5 };



struct QuaterImaginary {
    char *b2i;
    int valid;
};

struct QuaterImaginary makeQuaterImaginary(char *s) {
    struct QuaterImaginary qi = { s, 0 }; 
    size_t i, valid = 1, cnt = 0;

    if (*s != 0) {
        for (i = 0; s[i] != 0; i++) {
            if (s[i] < '0' || '3' < s[i]) {
                if (s[i] == '.') {
                    cnt++;
                } else {
                    valid = 0;
                    break;
                }
            }
        }
        if (valid && cnt > 1) {
            valid = 0;
        }
    }

    qi.valid = valid;
    return qi;
}

void printQuaterImaginary(struct QuaterImaginary qi) {
    if (qi.valid) {
        printf("%8s", qi.b2i);
    } else {
        printf(" ERROR  ");
    }
}



struct Complex qi2c(struct QuaterImaginary qi) {
    size_t len = strlen(qi.b2i);
    int pointPos = find(qi.b2i, '.');
    size_t posLen = (pointPos > 0) ? pointPos : len;
    struct Complex sum = makeComplex(0.0, 0.0);
    struct Complex prod = makeComplex(1.0, 0.0);
    size_t j;

    for (j = 0; j < posLen; j++) {
        double k = qi.b2i[posLen - 1 - j] - '0';
        if (k > 0.0) {
            sum = addComplex(sum, mulComplexD(prod, k));
        }
        prod = mulComplex(prod, TWO_I);
    }
    if (pointPos != -1) {
        prod = INV_TWO_I;
        for (j = posLen + 1; j < len; j++) {
            double k = qi.b2i[j] - '0';
            if (k > 0.0) {
                sum = addComplex(sum, mulComplexD(prod, k));
            }
            prod = mulComplex(prod, INV_TWO_I);
        }
    }
    return sum;
}


struct QuaterImaginary c2qi(struct Complex c, char *out) {
    char *p = out;
    int re, im, fi;

    *p = 0;
    if (c.rel == 0.0 && c.img == 0.0) {
        return makeQuaterImaginary("0");
    }

    re = (int)c.rel;
    im = (int)c.img;
    fi = -1;
    while (re != 0) {
        int rem = re % -4;
        re /= -4;
        if (rem < 0) {
            rem += 4;
            re++;
        }
        *p++ = rem + '0';
        *p++ = '0';
        *p = 0;
    }
    if (im != 0) {
        size_t index = 1;
        struct Complex fc = divComplex((struct Complex) { 0.0, c.img }, (struct Complex) { 0.0, 2.0 });
        double f = fc.rel;
        im = (int)ceil(f);
        f = -4.0 * (f - im);
        while (im != 0) {
            int rem = im % -4;
            im /= -4;
            if (rem < 0) {
                rem += 4;
                im++;
            }
            if (index < (p - out)) {
                out[index] = rem + '0';
            } else {
                *p++ = '0';
                *p++ = rem + '0';
                *p = 0;
            }
            index += 2;
        }
        fi = (int)f;
    }

    reverse(out, p);
    if (fi != -1) {
        *p++ = '.';
        *p++ = fi + '0';
        *p = 0;
    }
    while (out[0] == '0' && out[1] != '.') {
        size_t i;
        for (i = 0; out[i] != 0; i++) {
            out[i] = out[i + 1];
        }
    }
    if (*out == '.') {
        reverse(out, p);
        *p++ = '0';
        *p = 0;
        reverse(out, p);
    }
    return makeQuaterImaginary(out);
}



int main() {
    char buffer[16];
    int i;

    for (i = 1; i <= 16; i++) {
        struct Complex c1 = { i, 0.0 };
        struct QuaterImaginary qi = c2qi(c1, buffer);
        struct Complex c2 = qi2c(qi);
        printComplex(c1);
        printf(" -> ");
        printQuaterImaginary(qi);
        printf(" -> ");
        printComplex(c2);

        printf("     ");

        c1 = negComplex(c1);
        qi = c2qi(c1, buffer);
        c2 = qi2c(qi);
        printComplex(c1);
        printf(" -> ");
        printQuaterImaginary(qi);
        printf(" -> ");
        printComplex(c2);

        printf("\n");
    }

    printf("\n");

    for (i = 1; i <= 16; i++) {
        struct Complex c1 = { 0.0, i };
        struct QuaterImaginary qi = c2qi(c1, buffer);
        struct Complex c2 = qi2c(qi);
        printComplex(c1);
        printf(" -> ");
        printQuaterImaginary(qi);
        printf(" -> ");
        printComplex(c2);

        printf("     ");

        c1 = negComplex(c1);
        qi = c2qi(c1, buffer);
        c2 = qi2c(qi);
        printComplex(c1);
        printf(" -> ");
        printQuaterImaginary(qi);
        printf(" -> ");
        printComplex(c2);

        printf("\n");
    }

    return 0;
}

C++: #include <algorithm>
#include <complex>
#include <iomanip>
#include <iostream>

std::complex<double> inv(const std::complex<double>& c) {
    double denom = c.real() * c.real() + c.imag() * c.imag();
    return std::complex<double>(c.real() / denom, -c.imag() / denom);
}

class QuaterImaginary {
public:
    QuaterImaginary(const std::string& s) : b2i(s) {
        static std::string base("0123.");

        if (b2i.empty()
            || std::any_of(s.cbegin(), s.cend(), [](char c) { return base.find(c) == std::string::npos; })
            || std::count(s.cbegin(), s.cend(), '.') > 1) {
            throw std::runtime_error("Invalid base 2i number");
        }
    }

    QuaterImaginary& operator=(const QuaterImaginary& q) {
        b2i = q.b2i;
        return *this;
    }

    std::complex<double> toComplex() const {
        int pointPos = b2i.find('.');
        int posLen = (pointPos != std::string::npos) ? pointPos : b2i.length();
        std::complex<double> sum(0.0, 0.0);
        std::complex<double> prod(1.0, 0.0);
        for (int j = 0; j < posLen; j++) {
            double k = (b2i[posLen - 1 - j] - '0');
            if (k > 0.0) {
                sum += prod * k;
            }
            prod *= twoI;
        }
        if (pointPos != -1) {
            prod = invTwoI;
            for (size_t j = posLen + 1; j < b2i.length(); j++) {
                double k = (b2i[j] - '0');
                if (k > 0.0) {
                    sum += prod * k;
                }
                prod *= invTwoI;
            }
        }

        return sum;
    }

    friend std::ostream& operator<<(std::ostream&, const QuaterImaginary&);

private:
    const std::complex<double> twoI{ 0.0, 2.0 };
    const std::complex<double> invTwoI = inv(twoI);

    std::string b2i;
};

std::ostream& operator<<(std::ostream& os, const QuaterImaginary& q) {
    return os << q.b2i;
}


QuaterImaginary toQuaterImaginary(const std::complex<double>& c) {
    if (c.real() == 0.0 && c.imag() == 0.0) return QuaterImaginary("0");

    int re = (int)c.real();
    int im = (int)c.imag();
    int fi = -1;
    std::stringstream ss;
    while (re != 0) {
        int rem = re % -4;
        re /= -4;
        if (rem < 0) {
            rem = 4 + rem;
            re++;
        }
        ss << rem << 0;
    }
    if (im != 0) {
        double f = (std::complex<double>(0.0, c.imag()) / std::complex<double>(0.0, 2.0)).real();
        im = (int)ceil(f);
        f = -4.0 * (f - im);
        size_t index = 1;
        while (im != 0) {
            int rem = im % -4;
            im /= -4;
            if (rem < 0) {
                rem = 4 + rem;
                im++;
            }
            if (index < ss.str().length()) {
                ss.str()[index] = (char)(rem + 48);
            } else {
                ss << 0 << rem;
            }
            index += 2;
        }
        fi = (int)f;
    }

    auto r = ss.str();
    std::reverse(r.begin(), r.end());
    ss.str("");
    ss.clear();
    ss << r;
    if (fi != -1) ss << '.' << fi;
    r = ss.str();
    r.erase(r.begin(), std::find_if(r.begin(), r.end(), [](char c) { return c != '0'; }));
    if (r[0] == '.')r = "0" + r;
    return QuaterImaginary(r);
}

int main() {
    using namespace std;

    for (int i = 1; i <= 16; i++) {
        complex<double> c1(i, 0);
        QuaterImaginary qi = toQuaterImaginary(c1);
        complex<double> c2 = qi.toComplex();
        cout << setw(8) << c1 << " -> " << setw(8) << qi << " -> " << setw(8) << c2 << "     ";
        c1 = -c1;
        qi = toQuaterImaginary(c1);
        c2 = qi.toComplex();
        cout << setw(8) << c1 << " -> " << setw(8) << qi << " -> " << setw(8) << c2 << endl;
    }
    cout << endl;

    for (int i = 1; i <= 16; i++) {
        complex<double> c1(0, i);
        QuaterImaginary qi = toQuaterImaginary(c1);
        complex<double> c2 = qi.toComplex();
        cout << setw(8) << c1 << " -> " << setw(8) << qi << " -> " << setw(8) << c2 << "     ";
        c1 = -c1;
        qi = toQuaterImaginary(c1);
        c2 = qi.toComplex();
        cout << setw(8) << c1 << " -> " << setw(8) << qi << " -> " << setw(8) << c2 << endl;
    }

    return 0;
}