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;
}

Java: public class ImaginaryBaseNumber {
    private static class Complex {
        private Double real, imag;

        public Complex(double r, double i) {
            this.real = r;
            this.imag = i;
        }

        public Complex(int r, int i) {
            this.real = (double) r;
            this.imag = (double) i;
        }

        public Complex add(Complex rhs) {
            return new Complex(
                real + rhs.real,
                imag + rhs.imag
            );
        }

        public Complex times(Complex rhs) {
            return new Complex(
                real * rhs.real - imag * rhs.imag,
                real * rhs.imag + imag * rhs.real
            );
        }

        public Complex times(double rhs) {
            return new Complex(
                real * rhs,
                imag * rhs
            );
        }

        public Complex inv() {
            double denom = real * real + imag * imag;
            return new Complex(
                real / denom,
                -imag / denom
            );
        }

        public Complex unaryMinus() {
            return new Complex(-real, -imag);
        }

        public Complex divide(Complex rhs) {
            return this.times(rhs.inv());
        }

        
        public QuaterImaginary toQuaterImaginary() {
            if (real == 0.0 && imag == 0.0) return new QuaterImaginary("0");
            int re = real.intValue();
            int im = imag.intValue();
            int fi = -1;
            StringBuilder sb = new StringBuilder();
            while (re != 0) {
                int rem = re % -4;
                re /= -4;
                if (rem < 0) {
                    rem += 4;
                    re++;
                }
                sb.append(rem);
                sb.append(0);
            }
            if (im != 0) {
                Double f = new Complex(0.0, imag).divide(new Complex(0.0, 2.0)).real;
                im = ((Double) Math.ceil(f)).intValue();
                f = -4.0 * (f - im);
                int index = 1;
                while (im != 0) {
                    int rem = im % -4;
                    im /= -4;
                    if (rem < 0) {
                        rem += 4;
                        im++;
                    }
                    if (index < sb.length()) {
                        sb.setCharAt(index, (char) (rem + 48));
                    } else {
                        sb.append(0);
                        sb.append(rem);
                    }
                    index += 2;
                }
                fi = f.intValue();
            }
            sb.reverse();
            if (fi != -1) sb.append(".").append(fi);
            while (sb.charAt(0) == '0') sb.deleteCharAt(0);
            if (sb.charAt(0) == '.') sb.insert(0, '0');
            return new QuaterImaginary(sb.toString());
        }

        @Override
        public String toString() {
            double real2 = real == -0.0 ? 0.0 : real;  
            double imag2 = imag == -0.0 ? 0.0 : imag;  
            String result = imag2 >= 0.0 ? String.format("%.0f + %.0fi", real2, imag2) : String.format("%.0f - %.0fi", real2, -imag2);
            result = result.replace(".0 ", " ").replace(".0i", "i").replace(" + 0i", "");
            if (result.startsWith("0 + ")) result = result.substring(4);
            if (result.startsWith("0 - ")) result = result.substring(4);
            return result;
        }
    }

    private static class QuaterImaginary {
        private static final Complex TWOI = new Complex(0.0, 2.0);
        private static final Complex INVTWOI = TWOI.inv();

        private String b2i;

        public QuaterImaginary(String b2i) {
            if (b2i.equals("") || !b2i.chars().allMatch(c -> "0123.".indexOf(c) > -1) || b2i.chars().filter(c -> c == '.').count() > 1) {
                throw new RuntimeException("Invalid Base 2i number");
            }
            this.b2i = b2i;
        }

        public Complex toComplex() {
            int pointPos = b2i.indexOf(".");
            int posLen = pointPos != -1 ? pointPos : b2i.length();
            Complex sum = new Complex(0, 0);
            Complex prod = new Complex(1, 0);

            for (int j = 0; j < posLen; ++j) {
                double k = b2i.charAt(posLen - 1 - j) - '0';
                if (k > 0.0) sum = sum.add(prod.times(k));
                prod = prod.times(TWOI);
            }
            if (pointPos != -1) {
                prod = INVTWOI;
                for (int j = posLen + 1; j < b2i.length(); ++j) {
                    double k = b2i.charAt(j) - '0';
                    if (k > 0.0) sum = sum.add(prod.times(k));
                    prod = prod.times(INVTWOI);
                }
            }

            return sum;
        }

        @Override
        public String toString() {
            return b2i;
        }
    }

    public static void main(String[] args) {
        String fmt = "%4s -> %8s -> %4s";
        for (int i = 1; i <= 16; ++i) {
            Complex c1 = new Complex(i, 0);
            QuaterImaginary qi = c1.toQuaterImaginary();
            Complex c2 = qi.toComplex();
            System.out.printf(fmt + "     ", c1, qi, c2);
            c1 = c2.unaryMinus();
            qi = c1.toQuaterImaginary();
            c2 = qi.toComplex();
            System.out.printf(fmt, c1, qi, c2);
            System.out.println();
        }
        System.out.println();
        for (int i = 1; i <= 16; ++i) {
            Complex c1 = new Complex(0, i);
            QuaterImaginary qi = c1.toQuaterImaginary();
            Complex c2 = qi.toComplex();
            System.out.printf(fmt + "     ", c1, qi, c2);
            c1 = c2.unaryMinus();
            qi = c1.toQuaterImaginary();
            c2 = qi.toComplex();
            System.out.printf(fmt, c1, qi, c2);
            System.out.println();
        }
    }
}