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1
4 package gnu.math;
5
6 public abstract class Complex extends Quantity
7 {
8 public Complex number() { return this; }
9
10 public boolean isExact ()
11 {
12 return re().isExact() && im().isExact();
14 }
15
16 private static CComplex imOne;
17 private static CComplex imMinusOne;
18
19 public static CComplex imOne()
20 {
21 if (imOne == null)
22 imOne = new CComplex (IntNum.zero(), IntNum.one());
23 return imOne;
24 }
25
26 public static CComplex imMinusOne()
27 {
28 if (imMinusOne == null)
29 imMinusOne = new CComplex (IntNum.zero(), IntNum.minusOne());
30 return imMinusOne;
31 }
32
33 public double doubleValue () { return re().doubleValue (); }
34 public double doubleImagValue () { return im().doubleValue (); }
35 public final double doubleRealValue () { return doubleValue (); }
36 public long longValue () { return re().longValue(); }
37
38 public static Complex make (RealNum re, RealNum im)
39 {
40 if (im.isZero ())
41 return re;
42 if (! re.isExact() || ! im.isExact())
43 return new DComplex(re.doubleValue(), im.doubleValue());
44 return new CComplex (re, im);
45 }
46
47 public static Complex make (double re, double im)
48 {
49 if (im == 0.0)
50 return new DFloNum(re);
51 return new DComplex(re, im);
52 }
53
54 public static DComplex polar (double r, double t)
55 {
56 return new DComplex(r * Math.cos(t), r * Math.sin(t));
57 }
58
59 public static DComplex polar (RealNum r, RealNum t)
60 {
61 return polar(r.doubleValue(), t.doubleValue());
62 }
63
64 public static Complex power (Complex x, Complex y)
65 {
66 if (y instanceof IntNum)
67 return (Complex) x.power((IntNum) y);
68 double x_re = x.doubleRealValue();
69 double x_im = x.doubleImagValue();
70 double y_re = y.doubleRealValue();
71 double y_im = y.doubleImagValue();
72 if (x_im == 0.0 && y_im == 0
73 && (x_re >= 0 || Double.isInfinite(x_re) || Double.isNaN(x_re)))
74 return new DFloNum (Math.pow (x_re, y_re));
75 return DComplex.power (x_re, x_im, y_re, y_im);
76 }
77
78 public Numeric abs ()
79 {
80
81
83 return new DFloNum(DComplex.hypot(doubleRealValue(), doubleImagValue()));
84
85 }
86
87 public RealNum angle()
88 {
89 return new DFloNum(Math.atan2(doubleImagValue(), doubleRealValue()));
90 }
91
92 public static boolean equals (Complex x, Complex y)
93 {
94 return x.re().equals(y.re())
95 && x.im().equals(x.im());
96 }
97
98 public boolean equals (Object  obj)
99 {
100 if (obj == null || ! (obj instanceof Complex))
101 return false;
102 return Complex.equals (this, (Complex) obj);
103 }
104
105 public static int compare (Complex x, Complex y)
106 {
107 int code = x.im().compare(y.im());
108 if (code != 0)
109 return code;
110 return x.re().compare(y.re());
111 }
112
113 public int compare (Object obj)
114 {
115 if (! (obj instanceof Complex))
116 return ((Numeric) obj).compareReversed(this);
117 return compare(this, (Complex) obj);
118 }
119
120 public boolean isZero ()
121 {
122 return re().isZero () && im().isZero();
123 }
124
125
127
131
132
133 public String toString (int radix)
134 {
135 if (im().isZero ())
140 return re().toString(radix);
141 String imString = im().toString(radix) + "i";
142 if (imString.charAt(0) != '-')
143 imString = "+" + imString;
144 if (re().isZero())
145 return imString;
146 return re().toString(radix) + imString;
147 }
148
149 public static Complex neg (Complex x)
150 {
151 return Complex.make (x.re().rneg(), x.im().rneg());
152 }
153
154 public Numeric neg () { return neg (this); }
155
156 public static Complex add (Complex x, Complex y, int k)
157 {
158 return Complex.make (RealNum.add(x.re(), y.re(), k),
159 RealNum.add(x.im(), y.im(), k));
160 }
161
162 public Numeric add (Object y, int k)
163 {
164 if (y instanceof Complex)
165 return add (this, (Complex) y, k);
166 return ((Numeric)y).addReversed(this, k);
167 }
168
169 public Numeric addReversed (Numeric x, int k)
170 {
171 if (x instanceof Complex)
172 return add ((Complex)x, this, k);
173 throw new IllegalArgumentException ();
174 }
175
176 public static Complex times (Complex x, Complex y)
177 {
178 RealNum x_re = x.re();
179 RealNum x_im = x.im();
180 RealNum y_re = y.re();
181 RealNum y_im = y.im();
182 return Complex.make (RealNum.add (RealNum.times(x_re, y_re),
183 RealNum.times(x_im, y_im), -1),
184 RealNum.add (RealNum.times(x_re, y_im),
185 RealNum.times(x_im, y_re), 1));
186 }
187
188 public Numeric mul (Object y)
189 {
190 if (y instanceof Complex)
191 return times(this, (Complex) y);
192 return ((Numeric)y).mulReversed(this);
193 }
194
195 public Numeric mulReversed (Numeric x)
196 {
197 if (x instanceof Complex)
198 return times((Complex)x, this);
199 throw new IllegalArgumentException ();
200 }
201
202 public static Complex divide (Complex x, Complex y)
203 {
204 if (! x.isExact () || ! y.isExact ())
205 return DComplex.div (x.doubleRealValue(), x.doubleImagValue(),
206 y.doubleRealValue(), y.doubleImagValue());
207
208 RealNum x_re = x.re();
209 RealNum x_im = x.im();
210 RealNum y_re = y.re();
211 RealNum y_im = y.im();
212
213 RealNum q = RealNum.add (RealNum.times(y_re, y_re),
214 RealNum.times(y_im, y_im), 1);
215 RealNum n = RealNum.add(RealNum.times(x_re, y_re),
216 RealNum.times(x_im, y_im), 1);
217 RealNum d = RealNum.add(RealNum.times(x_im, y_re),
218 RealNum.times(x_re, y_im), -1);
219 return Complex.make(RealNum.divide(n, q), RealNum.divide(d, q));
220 }
221
222 public Numeric div (Object y)
223 {
224 if (y instanceof Complex)
225 return divide(this, (Complex) y);
226 return ((Numeric)y).divReversed(this);
227 }
228
229 public Numeric divReversed (Numeric x)
230 {
231 if (x instanceof Complex)
232 return divide((Complex)x, this);
233 throw new IllegalArgumentException ();
234 }
235
236 public Complex exp ()
237 {
238 return polar (Math.exp(doubleRealValue()), doubleImagValue());
239 }
240
241
242 public Complex log ()
243 {
244 return DComplex.log(doubleRealValue(), doubleImagValue());
245 }
246
247 public Complex sqrt ()
248 {
249 return DComplex.sqrt(doubleRealValue(), doubleImagValue());
250 }
251 }
252 |
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