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178
Task/Imaginary-base-numbers/Java/imaginary-base-numbers.java
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178
Task/Imaginary-base-numbers/Java/imaginary-base-numbers.java
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public class ImaginaryBaseNumber {
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private static class Complex {
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private Double real, imag;
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public Complex(double r, double i) {
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this.real = r;
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this.imag = i;
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}
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public Complex(int r, int i) {
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this.real = (double) r;
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this.imag = (double) i;
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}
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public Complex add(Complex rhs) {
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return new Complex(
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real + rhs.real,
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imag + rhs.imag
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);
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}
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public Complex times(Complex rhs) {
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return new Complex(
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real * rhs.real - imag * rhs.imag,
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real * rhs.imag + imag * rhs.real
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);
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}
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public Complex times(double rhs) {
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return new Complex(
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real * rhs,
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imag * rhs
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);
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}
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public Complex inv() {
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double denom = real * real + imag * imag;
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return new Complex(
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real / denom,
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-imag / denom
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);
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}
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public Complex unaryMinus() {
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return new Complex(-real, -imag);
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}
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public Complex divide(Complex rhs) {
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return this.times(rhs.inv());
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}
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// only works properly if 'real' and 'imag' are both integral
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public QuaterImaginary toQuaterImaginary() {
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if (real == 0.0 && imag == 0.0) return new QuaterImaginary("0");
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int re = real.intValue();
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int im = imag.intValue();
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int fi = -1;
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StringBuilder sb = new StringBuilder();
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while (re != 0) {
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int rem = re % -4;
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re /= -4;
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if (rem < 0) {
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rem += 4;
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re++;
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}
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sb.append(rem);
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sb.append(0);
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}
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if (im != 0) {
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Double f = new Complex(0.0, imag).divide(new Complex(0.0, 2.0)).real;
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im = ((Double) Math.ceil(f)).intValue();
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f = -4.0 * (f - im);
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int index = 1;
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while (im != 0) {
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int rem = im % -4;
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im /= -4;
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if (rem < 0) {
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rem += 4;
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im++;
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}
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if (index < sb.length()) {
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sb.setCharAt(index, (char) (rem + 48));
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} else {
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sb.append(0);
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sb.append(rem);
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}
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index += 2;
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}
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fi = f.intValue();
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}
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sb.reverse();
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if (fi != -1) sb.append(".").append(fi);
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while (sb.charAt(0) == '0') sb.deleteCharAt(0);
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if (sb.charAt(0) == '.') sb.insert(0, '0');
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return new QuaterImaginary(sb.toString());
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}
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@Override
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public String toString() {
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double real2 = real == -0.0 ? 0.0 : real; // get rid of negative zero
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double imag2 = imag == -0.0 ? 0.0 : imag; // ditto
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String result = imag2 >= 0.0 ? String.format("%.0f + %.0fi", real2, imag2) : String.format("%.0f - %.0fi", real2, -imag2);
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result = result.replace(".0 ", " ").replace(".0i", "i").replace(" + 0i", "");
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if (result.startsWith("0 + ")) result = result.substring(4);
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if (result.startsWith("0 - ")) result = result.substring(4);
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return result;
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}
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}
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private static class QuaterImaginary {
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private static final Complex TWOI = new Complex(0.0, 2.0);
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private static final Complex INVTWOI = TWOI.inv();
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private String b2i;
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public QuaterImaginary(String b2i) {
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if (b2i.equals("") || !b2i.chars().allMatch(c -> "0123.".indexOf(c) > -1) || b2i.chars().filter(c -> c == '.').count() > 1) {
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throw new RuntimeException("Invalid Base 2i number");
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}
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this.b2i = b2i;
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}
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public Complex toComplex() {
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int pointPos = b2i.indexOf(".");
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int posLen = pointPos != -1 ? pointPos : b2i.length();
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Complex sum = new Complex(0, 0);
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Complex prod = new Complex(1, 0);
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for (int j = 0; j < posLen; ++j) {
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double k = b2i.charAt(posLen - 1 - j) - '0';
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if (k > 0.0) sum = sum.add(prod.times(k));
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prod = prod.times(TWOI);
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}
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if (pointPos != -1) {
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prod = INVTWOI;
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for (int j = posLen + 1; j < b2i.length(); ++j) {
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double k = b2i.charAt(j) - '0';
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if (k > 0.0) sum = sum.add(prod.times(k));
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prod = prod.times(INVTWOI);
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}
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}
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return sum;
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}
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@Override
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public String toString() {
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return b2i;
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}
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}
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public static void main(String[] args) {
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String fmt = "%4s -> %8s -> %4s";
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for (int i = 1; i <= 16; ++i) {
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Complex c1 = new Complex(i, 0);
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QuaterImaginary qi = c1.toQuaterImaginary();
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Complex c2 = qi.toComplex();
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System.out.printf(fmt + " ", c1, qi, c2);
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c1 = c2.unaryMinus();
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qi = c1.toQuaterImaginary();
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c2 = qi.toComplex();
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System.out.printf(fmt, c1, qi, c2);
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System.out.println();
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}
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System.out.println();
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for (int i = 1; i <= 16; ++i) {
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Complex c1 = new Complex(0, i);
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QuaterImaginary qi = c1.toQuaterImaginary();
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Complex c2 = qi.toComplex();
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System.out.printf(fmt + " ", c1, qi, c2);
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c1 = c2.unaryMinus();
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qi = c1.toQuaterImaginary();
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c2 = qi.toComplex();
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System.out.printf(fmt, c1, qi, c2);
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System.out.println();
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}
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}
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}
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