001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.imaging.common;
018
019import java.text.NumberFormat;
020
021/**
022 * Rational number, as used by the TIFF image format.
023 */
024public class RationalNumber extends Number {
025
026    private static final long serialVersionUID = -8412262656468158691L;
027
028    // int-precision tolerance
029    private static final double TOLERANCE = 1E-8;
030
031    public final int numerator;
032    public final int divisor;
033
034    public RationalNumber(final int numerator, final int divisor) {
035        this.numerator = numerator;
036        this.divisor = divisor;
037    }
038
039    static RationalNumber factoryMethod(long n, long d) {
040        // safer than constructor - handles values outside min/max range.
041        // also does some simple finding of common denominators.
042
043        if (n > Integer.MAX_VALUE || n < Integer.MIN_VALUE
044                || d > Integer.MAX_VALUE || d < Integer.MIN_VALUE) {
045            while ((n > Integer.MAX_VALUE || n < Integer.MIN_VALUE
046                    || d > Integer.MAX_VALUE || d < Integer.MIN_VALUE)
047                    && (Math.abs(n) > 1) && (Math.abs(d) > 1)) {
048                // brutal, inprecise truncation =(
049                // use the sign-preserving right shift operator.
050                n >>= 1;
051                d >>= 1;
052            }
053
054            if (d == 0) {
055                throw new NumberFormatException("Invalid value, numerator: " + n + ", divisor: " + d);
056            }
057        }
058
059        final long gcd = gcd(n, d);
060        d = d / gcd;
061        n = n / gcd;
062
063        return new RationalNumber((int) n, (int) d);
064    }
065
066    /**
067     * Return the greatest common divisor
068     */
069    private static long gcd(final long a, final long b) {
070        if (b == 0) {
071            return a;
072        } else {
073            return gcd(b, a % b);
074        }
075    }
076
077    public RationalNumber negate() {
078        return new RationalNumber(-numerator, divisor);
079    }
080
081    @Override
082    public double doubleValue() {
083        return (double) numerator / (double) divisor;
084    }
085
086    @Override
087    public float floatValue() {
088        return (float) numerator / (float) divisor;
089    }
090
091    @Override
092    public int intValue() {
093        return numerator / divisor;
094    }
095
096    @Override
097    public long longValue() {
098        return (long) numerator / (long) divisor;
099    }
100
101    @Override
102    public String toString() {
103        if (divisor == 0) {
104            return "Invalid rational (" + numerator + "/" + divisor + ")";
105        }
106        final NumberFormat nf = NumberFormat.getInstance();
107
108        if ((numerator % divisor) == 0) {
109            return nf.format(numerator / divisor);
110        }
111        return numerator + "/" + divisor + " (" + nf.format((double) numerator / divisor) + ")";
112    }
113
114    public String toDisplayString() {
115        if ((numerator % divisor) == 0) {
116            return Integer.toString(numerator / divisor);
117        }
118        final NumberFormat nf = NumberFormat.getInstance();
119        nf.setMaximumFractionDigits(3);
120        return nf.format((double) numerator / (double) divisor);
121    }
122
123    private static final class Option {
124        public final RationalNumber rationalNumber;
125        public final double error;
126
127        private Option(final RationalNumber rationalNumber, final double error) {
128            this.rationalNumber = rationalNumber;
129            this.error = error;
130        }
131
132        public static Option factory(final RationalNumber rationalNumber, final double value) {
133            return new Option(rationalNumber, Math.abs(rationalNumber .doubleValue() - value));
134        }
135
136        @Override
137        public String toString() {
138            return rationalNumber.toString();
139        }
140    }
141
142    /**
143     * Calculate rational number using successive approximations.
144     */
145    public static RationalNumber valueOf(double value) {
146        if (value >= Integer.MAX_VALUE) {
147            return new RationalNumber(Integer.MAX_VALUE, 1);
148        } else if (value <= -Integer.MAX_VALUE) {
149            return new RationalNumber(-Integer.MAX_VALUE, 1);
150        }
151
152        boolean negative = false;
153        if (value < 0) {
154            negative = true;
155            value = Math.abs(value);
156        }
157
158        RationalNumber l;
159        RationalNumber h;
160
161        if (value == 0) {
162            return new RationalNumber(0, 1);
163        } else if (value >= 1) {
164            final int approx = (int) value;
165            if (approx < value) {
166                l = new RationalNumber(approx, 1);
167                h = new RationalNumber(approx + 1, 1);
168            } else {
169                l = new RationalNumber(approx - 1, 1);
170                h = new RationalNumber(approx, 1);
171            }
172        } else {
173            final int approx = (int) (1.0 / value);
174            if ((1.0 / approx) < value) {
175                l = new RationalNumber(1, approx);
176                h = new RationalNumber(1, approx - 1);
177            } else {
178                l = new RationalNumber(1, approx + 1);
179                h = new RationalNumber(1, approx);
180            }
181        }
182        Option low = Option.factory(l, value);
183        Option high = Option.factory(h, value);
184
185        Option bestOption = (low.error < high.error) ? low : high;
186
187        final int maxIterations = 100; // value is quite high, actually.
188                                       // shouldn't matter.
189        for (int count = 0; bestOption.error > TOLERANCE
190                && count < maxIterations; count++) {
191            final RationalNumber mediant = RationalNumber.factoryMethod(
192                    (long) low.rationalNumber.numerator
193                            + (long) high.rationalNumber.numerator,
194                    (long) low.rationalNumber.divisor
195                            + (long) high.rationalNumber.divisor);
196            final Option mediantOption = Option.factory(mediant, value);
197
198            if (value < mediant.doubleValue()) {
199                if (high.error <= mediantOption.error) {
200                    break;
201                }
202
203                high = mediantOption;
204            } else {
205                if (low.error <= mediantOption.error) {
206                    break;
207                }
208
209                low = mediantOption;
210            }
211
212            if (mediantOption.error < bestOption.error) {
213                bestOption = mediantOption;
214            }
215        }
216
217        return negative ? bestOption.rationalNumber.negate()
218                : bestOption.rationalNumber;
219    }
220
221}