|
1
4 package gnu.math;
5
6
7
8 public abstract class RatNum extends RealNum
9 {
10 public abstract IntNum numerator ();
11 public abstract IntNum denominator ();
12
13 public static RatNum make(IntNum num, IntNum den)
14 {
15 IntNum g = IntNum.gcd (num, den);
16 if (den.isNegative ())
17 g = IntNum.neg (g);
18 if (! g.isOne ())
19 {
20 num = IntNum.quotient (num, g);
21 den = IntNum.quotient (den, g);
22 }
23 return den.isOne () ? (RatNum)num : (RatNum)(new IntFraction (num, den));
24 }
25
26 public boolean isExact ()
27 {
28 return true;
29 }
30
31 public boolean isZero ()
32 {
33 return numerator().isZero();
34 }
35
36
38 public static RatNum infinity(int sign)
39 {
40 return new IntFraction (IntNum.make(sign), IntNum.zero());
41 }
42
43 public static int compare (RatNum x, RatNum y)
44 {
45 return IntNum.compare (IntNum.times (x.numerator (), y.denominator ()),
46 IntNum.times (y.numerator (), x.denominator ()));
47 }
48
49
50 public static boolean equals (RatNum x, RatNum y)
51 {
52 return IntNum.equals (x.numerator(), y.numerator())
53 && IntNum.equals (x.denominator(), y.denominator());
54 }
55
56
57 public boolean equals (Object  obj)
58 {
59 if (obj == null || ! (obj instanceof RatNum))
60 return false;
61 return RatNum.equals (this, (RatNum) obj);
62 }
63
64 public static RatNum add (RatNum x, RatNum y, int k)
65 {
66 IntNum x_num = x.numerator();
67 IntNum x_den = x.denominator();
68 IntNum y_num = y.numerator();
69 IntNum y_den = y.denominator();
70 if (IntNum.equals (x_den, y_den))
71 return RatNum.make (IntNum.add (x_num, y_num, k), x_den);
72 return RatNum.make (IntNum.add (IntNum.times (y_den, x_num),
73 IntNum.times (y_num, x_den), k),
74 IntNum.times (x_den, y_den));
75 }
76
77 public static RatNum times (RatNum x, RatNum y)
78 {
79 return RatNum.make (IntNum.times (x.numerator(), y.numerator()),
80 IntNum.times (x.denominator(), y.denominator()));
81 }
82
83 public static RatNum divide (RatNum x, RatNum y)
84 {
85 return RatNum.make (IntNum.times (x.numerator(), y.denominator()),
86 IntNum.times (x.denominator(), y.numerator()));
87 }
88
89 public Numeric power (IntNum y)
90 {
91 boolean inv;
92 if (y.isNegative())
93 {
94 inv = true;
95 y = IntNum.neg(y);
96 }
97 else
98 inv = false;
99 if (y.words == null)
100 {
101 IntNum num = IntNum.power (numerator(), y.ival);
102 IntNum den = IntNum.power (denominator(), y.ival);
103 return inv ? RatNum.make (den, num) : RatNum.make (num, den);
104 }
105 double d = doubleValue();
106 boolean neg = d < 0.0 && y.isOdd();
107 d = Math.pow (d, y.doubleValue());
108 if (inv)
109 d = 1.0/d;
110 return new DFloNum (neg ? -d : d);
111 }
112
113 public final RatNum toExact ()
114 {
115 return this;
116 }
117
118 public RealNum toInt (int rounding_mode)
119 {
120 return IntNum.quotient (numerator(), denominator(), rounding_mode);
121 }
122
123 public IntNum toExactInt (int rounding_mode)
124 {
125 return IntNum.quotient (numerator(), denominator(), rounding_mode);
126 }
127
128
129 public static RealNum rationalize (RealNum x, RealNum y)
130 {
131 if (x.grt (y))
134 return simplest_rational2 (y, x);
135 else if (! (y.grt(x)))
136 return x;
137 else if (x.sign() > 0)
138 return simplest_rational2 (x, y);
139 else if (y.isNegative ())
140 return (RealNum) (simplest_rational2 ((RealNum)y.neg(),
141 (RealNum)x.neg())).neg();
142 else
143 return IntNum.zero ();
144 }
145 private static RealNum simplest_rational2 (RealNum x, RealNum y)
146 {
147 RealNum fx = x.toInt (FLOOR);
148 RealNum fy = y.toInt (FLOOR);
149 if (! x.grt(fx))
150 return fx;
151 else if (fx.equals(fy))
152 {
153 RealNum n = (RealNum) IntNum.one().div(y.sub(fy));
154 RealNum d = (RealNum) IntNum.one().div(x.sub(fx));
155 return (RealNum) fx.add(IntNum.one().div(simplest_rational2 (n, d)),
156 1);
157 }
158 else
159 return (RealNum) fx.add(IntNum.one(), 1);
160 }
161 }
162 |
Popular Tags |
Java API By Example, From Geeks To Geeks.