154 lines
4.0 KiB
D
154 lines
4.0 KiB
D
import std.algorithm;
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import std.array;
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import std.complex;
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import std.conv;
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import std.format;
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import std.math;
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import std.stdio;
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import std.string;
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Complex!double inv(Complex!double v) {
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auto denom = v.re*v.re + v.im*v.im;
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return v.conj / denom;
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}
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QuaterImaginary toQuaterImaginary(Complex!double v) {
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if (v.re == 0.0 && v.im == 0.0) return QuaterImaginary("0");
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auto re = v.re.to!int;
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auto im = v.im.to!int;
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auto fi = -1;
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auto sb = appender!(char[]);
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while (re != 0) {
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auto rem = re % -4;
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re /= -4;
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if (rem < 0) {
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rem = 4 + rem;
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re++;
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}
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sb.formattedWrite("%d", rem);
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sb.put("0");
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}
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if (im != 0) {
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auto f = (complex(0.0, v.im) / complex(0.0, 2.0)).re;
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im = f.ceil.to!int;
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f = -4.0 * (f - im.to!double);
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auto index = 1;
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while (im != 0) {
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auto rem = im % -4;
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im /= -4;
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if (rem < 0) {
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rem = 4 + rem;
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im++;
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}
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if (index < sb.data.length) {
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sb.data[index] = cast(char)(rem + '0');
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} else {
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sb.put("0");
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sb.formattedWrite("%d", rem);
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}
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index += 2;
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}
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fi = f.to!int;
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}
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sb.data.reverse;
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if (fi != -1) sb.formattedWrite(".%d", fi);
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int i;
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while (i < sb.data.length && sb.data[i] == '0') {
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i++;
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}
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auto s = sb.data[i..$].idup;
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if (s[0] == '.') s = "0" ~ s;
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return QuaterImaginary(s);
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}
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struct QuaterImaginary {
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private string b2i;
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this(string b2i) {
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if (b2i == "" || b2i.count('.') > 1) {
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throw new Exception("Invalid Base 2i number");
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}
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foreach (c; b2i) {
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if (!canFind("0123.", c)) {
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throw new Exception("Invalid Base 2i number");
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}
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}
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this.b2i = b2i;
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}
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T opCast(T : Complex!double)() {
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auto pointPos = b2i.indexOf('.');
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size_t posLen;
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if (pointPos != -1) {
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posLen = pointPos;
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} else {
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posLen = b2i.length;
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}
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auto sum = complex(0.0, 0.0);
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auto prod = complex(1.0, 0.0);
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foreach (j; 0..posLen) {
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auto k = (b2i[posLen - 1 - j] - '0').to!double;
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if (k > 0.0) {
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sum += prod * k;
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}
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prod *= twoI;
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}
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if (pointPos != -1) {
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prod = invTwoI;
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foreach (j; posLen+1..b2i.length) {
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auto k = (b2i[j] - '0').to!double;
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if (k > 0.0) {
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sum += prod * k;
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}
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prod *= invTwoI;
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}
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}
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return sum;
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}
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void toString(scope void delegate(const(char)[]) sink, FormatSpec!char fmt) const {
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if (fmt.spec == 's') {
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for (int i=0; i<fmt.width-b2i.length; ++i) {
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sink(" ");
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}
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}
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sink(b2i);
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}
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enum twoI = complex(0.0, 2.0);
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enum invTwoI = twoI.inv;
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}
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unittest {
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import std.exception;
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assertThrown!Exception(QuaterImaginary(""));
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assertThrown!Exception(QuaterImaginary("1.2.3"));
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assertThrown!Exception(QuaterImaginary("a"));
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assertThrown!Exception(QuaterImaginary("4"));
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assertThrown!Exception(QuaterImaginary(" "));
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}
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void main() {
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foreach (i; 1..17) {
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auto c1 = complex(i, 0);
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auto qi = c1.toQuaterImaginary;
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auto c2 = cast(Complex!double) qi;
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writef("%4s -> %8s -> %4s ", c1.re, qi, c2.re);
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c1 = -c1;
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qi = c1.toQuaterImaginary();
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c2 = cast(Complex!double) qi;
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writefln("%4s -> %8s -> %4s", c1.re, qi, c2.re);
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}
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writeln;
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foreach (i; 1..17) {
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auto c1 = complex(0, i);
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auto qi = c1.toQuaterImaginary;
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auto c2 = qi.to!(Complex!double);
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writef("%4si -> %8s -> %4si ", c1.im, qi, c2.im);
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c1 = -c1;
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qi = c1.toQuaterImaginary();
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c2 = cast(Complex!double) qi;
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writefln("%4si -> %8s -> %4si", c1.im, qi, c2.im);
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}
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}
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