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;
}

Go: package main

import (
    "fmt"
    "math"
    "strconv"
    "strings"
)

const (
    twoI    = 2.0i
    invTwoI = 1.0 / twoI
)

type quaterImaginary struct {
    b2i string
}

func reverse(s string) string {
    r := []rune(s)
    for i, j := 0, len(r)-1; i < len(r)/2; i, j = i+1, j-1 {
        r[i], r[j] = r[j], r[i]
    }
    return string(r)
}

func newQuaterImaginary(b2i string) quaterImaginary {
    b2i = strings.TrimSpace(b2i)
    _, err := strconv.ParseFloat(b2i, 64)
    if err != nil {
        panic("invalid Base 2i number")
    }
    return quaterImaginary{b2i}
}

func toComplex(q quaterImaginary) complex128 {
    pointPos := strings.Index(q.b2i, ".")
    var posLen int
    if pointPos != -1 {
        posLen = pointPos
    } else {
        posLen = len(q.b2i)
    }
    sum := 0.0i
    prod := complex(1.0, 0.0)
    for j := 0; j < posLen; j++ {
        k := float64(q.b2i[posLen-1-j] - '0')
        if k > 0.0 {
            sum += prod * complex(k, 0.0)
        }
        prod *= twoI
    }
    if pointPos != -1 {
        prod = invTwoI
        for j := posLen + 1; j < len(q.b2i); j++ {
            k := float64(q.b2i[j] - '0')
            if k > 0.0 {
                sum += prod * complex(k, 0.0)
            }
            prod *= invTwoI
        }
    }
    return sum
}

func (q quaterImaginary) String() string {
    return q.b2i
}


func toQuaterImaginary(c complex128) quaterImaginary {
    if c == 0i {
        return quaterImaginary{"0"}
    }
    re := int(real(c))
    im := int(imag(c))
    fi := -1
    var sb strings.Builder
    for re != 0 {
        rem := re % -4
        re /= -4
        if rem < 0 {
            rem += 4
            re++
        }
        sb.WriteString(strconv.Itoa(rem))
        sb.WriteString("0")
    }
    if im != 0 {
        f := real(complex(0.0, imag(c)) / 2.0i)
        im = int(math.Ceil(f))
        f = -4.0 * (f - float64(im))
        index := 1
        for im != 0 {
            rem := im % -4
            im /= -4
            if rem < 0 {
                rem += 4
                im++
            }
            if index < sb.Len() {
                bs := []byte(sb.String())
                bs[index] = byte(rem + 48)
                sb.Reset()
                sb.Write(bs)
            } else {
                sb.WriteString("0")
                sb.WriteString(strconv.Itoa(rem))
            }
            index += 2
        }
        fi = int(f)
    }
    s := reverse(sb.String())
    if fi != -1 {
        s = fmt.Sprintf("%s.%d", s, fi)
    }
    s = strings.TrimLeft(s, "0")
    if s[0] == '.' {
        s = "0" + s
    }
    return newQuaterImaginary(s)
}

func main() {
    for i := 1; i <= 16; i++ {
        c1 := complex(float64(i), 0.0)
        qi := toQuaterImaginary(c1)
        c2 := toComplex(qi)
        fmt.Printf("%4.0f -> %8s -> %4.0f     ", real(c1), qi, real(c2))
        c1 = -c1
        qi = toQuaterImaginary(c1)
        c2 = toComplex(qi)
        fmt.Printf("%4.0f -> %8s -> %4.0f\n", real(c1), qi, real(c2))
    }
    fmt.Println()
    for i := 1; i <= 16; i++ {
        c1 := complex(0.0, float64(i))
        qi := toQuaterImaginary(c1)
        c2 := toComplex(qi)
        fmt.Printf("%3.0fi -> %8s -> %3.0fi     ", imag(c1), qi, imag(c2))
        c1 = -c1
        qi = toQuaterImaginary(c1)
        c2 = toComplex(qi)
        fmt.Printf("%3.0fi -> %8s -> %3.0fi\n", imag(c1), qi, imag(c2))
    }
}