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.math3.geometry.partitioning.utilities; 018 019import java.util.Arrays; 020 021import org.apache.commons.math3.util.FastMath; 022 023/** This class implements an ordering operation for T-uples. 024 * 025 * <p>Ordering is done by encoding all components of the T-uple into a 026 * single scalar value and using this value as the sorting 027 * key. Encoding is performed using the method invented by Georg 028 * Cantor in 1877 when he proved it was possible to establish a 029 * bijection between a line and a plane. The binary representations of 030 * the components of the T-uple are mixed together to form a single 031 * scalar. This means that the 2<sup>k</sup> bit of component 0 is 032 * followed by the 2<sup>k</sup> bit of component 1, then by the 033 * 2<sup>k</sup> bit of component 2 up to the 2<sup>k</sup> bit of 034 * component {@code t}, which is followed by the 2<sup>k-1</sup> 035 * bit of component 0, followed by the 2<sup>k-1</sup> bit of 036 * component 1 ... The binary representations are extended as needed 037 * to handle numbers with different scales and a suitable 038 * 2<sup>p</sup> offset is added to the components in order to avoid 039 * negative numbers (this offset is adjusted as needed during the 040 * comparison operations).</p> 041 * 042 * <p>The more interesting property of the encoding method for our 043 * purpose is that it allows to select all the points that are in a 044 * given range. This is depicted in dimension 2 by the following 045 * picture:</p> 046 * 047 * <img src="doc-files/OrderedTuple.png" /> 048 * 049 * <p>This picture shows a set of 100000 random 2-D pairs having their 050 * first component between -50 and +150 and their second component 051 * between -350 and +50. We wanted to extract all pairs having their 052 * first component between +30 and +70 and their second component 053 * between -120 and -30. We built the lower left point at coordinates 054 * (30, -120) and the upper right point at coordinates (70, -30). All 055 * points smaller than the lower left point are drawn in red and all 056 * points larger than the upper right point are drawn in blue. The 057 * green points are between the two limits. This picture shows that 058 * all the desired points are selected, along with spurious points. In 059 * this case, we get 15790 points, 4420 of which really belonging to 060 * the desired rectangle. It is possible to extract very small 061 * subsets. As an example extracting from the same 100000 points set 062 * the points having their first component between +30 and +31 and 063 * their second component between -91 and -90, we get a subset of 11 064 * points, 2 of which really belonging to the desired rectangle.</p> 065 * 066 * <p>the previous selection technique can be applied in all 067 * dimensions, still using two points to define the interval. The 068 * first point will have all its components set to their lower bounds 069 * while the second point will have all its components set to their 070 * upper bounds.</p> 071 * 072 * <p>T-uples with negative infinite or positive infinite components 073 * are sorted logically.</p> 074 * 075 * <p>Since the specification of the {@code Comparator} interface 076 * allows only {@code ClassCastException} errors, some arbitrary 077 * choices have been made to handle specific cases. The rationale for 078 * these choices is to keep <em>regular</em> and consistent T-uples 079 * together.</p> 080 * <ul> 081 * <li>instances with different dimensions are sorted according to 082 * their dimension regardless of their components values</li> 083 * <li>instances with {@code Double.NaN} components are sorted 084 * after all other ones (even after instances with positive infinite 085 * components</li> 086 * <li>instances with both positive and negative infinite components 087 * are considered as if they had {@code Double.NaN} 088 * components</li> 089 * </ul> 090 * 091 * @since 3.0 092 * @deprecated as of 3.4, this class is not used anymore and considered 093 * to be out of scope of Apache Commons Math 094 */ 095@Deprecated 096public class OrderedTuple implements Comparable<OrderedTuple> { 097 098 /** Sign bit mask. */ 099 private static final long SIGN_MASK = 0x8000000000000000L; 100 101 /** Exponent bits mask. */ 102 private static final long EXPONENT_MASK = 0x7ff0000000000000L; 103 104 /** Mantissa bits mask. */ 105 private static final long MANTISSA_MASK = 0x000fffffffffffffL; 106 107 /** Implicit MSB for normalized numbers. */ 108 private static final long IMPLICIT_ONE = 0x0010000000000000L; 109 110 /** Double components of the T-uple. */ 111 private double[] components; 112 113 /** Offset scale. */ 114 private int offset; 115 116 /** Least Significant Bit scale. */ 117 private int lsb; 118 119 /** Ordering encoding of the double components. */ 120 private long[] encoding; 121 122 /** Positive infinity marker. */ 123 private boolean posInf; 124 125 /** Negative infinity marker. */ 126 private boolean negInf; 127 128 /** Not A Number marker. */ 129 private boolean nan; 130 131 /** Build an ordered T-uple from its components. 132 * @param components double components of the T-uple 133 */ 134 public OrderedTuple(final double ... components) { 135 this.components = components.clone(); 136 int msb = Integer.MIN_VALUE; 137 lsb = Integer.MAX_VALUE; 138 posInf = false; 139 negInf = false; 140 nan = false; 141 for (int i = 0; i < components.length; ++i) { 142 if (Double.isInfinite(components[i])) { 143 if (components[i] < 0) { 144 negInf = true; 145 } else { 146 posInf = true; 147 } 148 } else if (Double.isNaN(components[i])) { 149 nan = true; 150 } else { 151 final long b = Double.doubleToLongBits(components[i]); 152 final long m = mantissa(b); 153 if (m != 0) { 154 final int e = exponent(b); 155 msb = FastMath.max(msb, e + computeMSB(m)); 156 lsb = FastMath.min(lsb, e + computeLSB(m)); 157 } 158 } 159 } 160 161 if (posInf && negInf) { 162 // instance cannot be sorted logically 163 posInf = false; 164 negInf = false; 165 nan = true; 166 } 167 168 if (lsb <= msb) { 169 // encode the T-upple with the specified offset 170 encode(msb + 16); 171 } else { 172 encoding = new long[] { 173 0x0L 174 }; 175 } 176 177 } 178 179 /** Encode the T-uple with a given offset. 180 * @param minOffset minimal scale of the offset to add to all 181 * components (must be greater than the MSBs of all components) 182 */ 183 private void encode(final int minOffset) { 184 185 // choose an offset with some margins 186 offset = minOffset + 31; 187 offset -= offset % 32; 188 189 if ((encoding != null) && (encoding.length == 1) && (encoding[0] == 0x0L)) { 190 // the components are all zeroes 191 return; 192 } 193 194 // allocate an integer array to encode the components (we use only 195 // 63 bits per element because there is no unsigned long in Java) 196 final int neededBits = offset + 1 - lsb; 197 final int neededLongs = (neededBits + 62) / 63; 198 encoding = new long[components.length * neededLongs]; 199 200 // mix the bits from all components 201 int eIndex = 0; 202 int shift = 62; 203 long word = 0x0L; 204 for (int k = offset; eIndex < encoding.length; --k) { 205 for (int vIndex = 0; vIndex < components.length; ++vIndex) { 206 if (getBit(vIndex, k) != 0) { 207 word |= 0x1L << shift; 208 } 209 if (shift-- == 0) { 210 encoding[eIndex++] = word; 211 word = 0x0L; 212 shift = 62; 213 } 214 } 215 } 216 217 } 218 219 /** Compares this ordered T-uple with the specified object. 220 221 * <p>The ordering method is detailed in the general description of 222 * the class. Its main property is to be consistent with distance: 223 * geometrically close T-uples stay close to each other when stored 224 * in a sorted collection using this comparison method.</p> 225 226 * <p>T-uples with negative infinite, positive infinite are sorted 227 * logically.</p> 228 229 * <p>Some arbitrary choices have been made to handle specific 230 * cases. The rationale for these choices is to keep 231 * <em>normal</em> and consistent T-uples together.</p> 232 * <ul> 233 * <li>instances with different dimensions are sorted according to 234 * their dimension regardless of their components values</li> 235 * <li>instances with {@code Double.NaN} components are sorted 236 * after all other ones (evan after instances with positive infinite 237 * components</li> 238 * <li>instances with both positive and negative infinite components 239 * are considered as if they had {@code Double.NaN} 240 * components</li> 241 * </ul> 242 243 * @param ot T-uple to compare instance with 244 * @return a negative integer if the instance is less than the 245 * object, zero if they are equal, or a positive integer if the 246 * instance is greater than the object 247 248 */ 249 public int compareTo(final OrderedTuple ot) { 250 if (components.length == ot.components.length) { 251 if (nan) { 252 return +1; 253 } else if (ot.nan) { 254 return -1; 255 } else if (negInf || ot.posInf) { 256 return -1; 257 } else if (posInf || ot.negInf) { 258 return +1; 259 } else { 260 261 if (offset < ot.offset) { 262 encode(ot.offset); 263 } else if (offset > ot.offset) { 264 ot.encode(offset); 265 } 266 267 final int limit = FastMath.min(encoding.length, ot.encoding.length); 268 for (int i = 0; i < limit; ++i) { 269 if (encoding[i] < ot.encoding[i]) { 270 return -1; 271 } else if (encoding[i] > ot.encoding[i]) { 272 return +1; 273 } 274 } 275 276 if (encoding.length < ot.encoding.length) { 277 return -1; 278 } else if (encoding.length > ot.encoding.length) { 279 return +1; 280 } else { 281 return 0; 282 } 283 284 } 285 } 286 287 return components.length - ot.components.length; 288 289 } 290 291 /** {@inheritDoc} */ 292 @Override 293 public boolean equals(final Object other) { 294 if (this == other) { 295 return true; 296 } else if (other instanceof OrderedTuple) { 297 return compareTo((OrderedTuple) other) == 0; 298 } else { 299 return false; 300 } 301 } 302 303 /** {@inheritDoc} */ 304 @Override 305 public int hashCode() { 306 // the following constants are arbitrary small primes 307 final int multiplier = 37; 308 final int trueHash = 97; 309 final int falseHash = 71; 310 311 // hash fields and combine them 312 // (we rely on the multiplier to have different combined weights 313 // for all int fields and all boolean fields) 314 int hash = Arrays.hashCode(components); 315 hash = hash * multiplier + offset; 316 hash = hash * multiplier + lsb; 317 hash = hash * multiplier + (posInf ? trueHash : falseHash); 318 hash = hash * multiplier + (negInf ? trueHash : falseHash); 319 hash = hash * multiplier + (nan ? trueHash : falseHash); 320 321 return hash; 322 323 } 324 325 /** Get the components array. 326 * @return array containing the T-uple components 327 */ 328 public double[] getComponents() { 329 return components.clone(); 330 } 331 332 /** Extract the sign from the bits of a double. 333 * @param bits binary representation of the double 334 * @return sign bit (zero if positive, non zero if negative) 335 */ 336 private static long sign(final long bits) { 337 return bits & SIGN_MASK; 338 } 339 340 /** Extract the exponent from the bits of a double. 341 * @param bits binary representation of the double 342 * @return exponent 343 */ 344 private static int exponent(final long bits) { 345 return ((int) ((bits & EXPONENT_MASK) >> 52)) - 1075; 346 } 347 348 /** Extract the mantissa from the bits of a double. 349 * @param bits binary representation of the double 350 * @return mantissa 351 */ 352 private static long mantissa(final long bits) { 353 return ((bits & EXPONENT_MASK) == 0) ? 354 ((bits & MANTISSA_MASK) << 1) : // subnormal number 355 (IMPLICIT_ONE | (bits & MANTISSA_MASK)); // normal number 356 } 357 358 /** Compute the most significant bit of a long. 359 * @param l long from which the most significant bit is requested 360 * @return scale of the most significant bit of {@code l}, 361 * or 0 if {@code l} is zero 362 * @see #computeLSB 363 */ 364 private static int computeMSB(final long l) { 365 366 long ll = l; 367 long mask = 0xffffffffL; 368 int scale = 32; 369 int msb = 0; 370 371 while (scale != 0) { 372 if ((ll & mask) != ll) { 373 msb |= scale; 374 ll >>= scale; 375 } 376 scale >>= 1; 377 mask >>= scale; 378 } 379 380 return msb; 381 382 } 383 384 /** Compute the least significant bit of a long. 385 * @param l long from which the least significant bit is requested 386 * @return scale of the least significant bit of {@code l}, 387 * or 63 if {@code l} is zero 388 * @see #computeMSB 389 */ 390 private static int computeLSB(final long l) { 391 392 long ll = l; 393 long mask = 0xffffffff00000000L; 394 int scale = 32; 395 int lsb = 0; 396 397 while (scale != 0) { 398 if ((ll & mask) == ll) { 399 lsb |= scale; 400 ll >>= scale; 401 } 402 scale >>= 1; 403 mask >>= scale; 404 } 405 406 return lsb; 407 408 } 409 410 /** Get a bit from the mantissa of a double. 411 * @param i index of the component 412 * @param k scale of the requested bit 413 * @return the specified bit (either 0 or 1), after the offset has 414 * been added to the double 415 */ 416 private int getBit(final int i, final int k) { 417 final long bits = Double.doubleToLongBits(components[i]); 418 final int e = exponent(bits); 419 if ((k < e) || (k > offset)) { 420 return 0; 421 } else if (k == offset) { 422 return (sign(bits) == 0L) ? 1 : 0; 423 } else if (k > (e + 52)) { 424 return (sign(bits) == 0L) ? 0 : 1; 425 } else { 426 final long m = (sign(bits) == 0L) ? mantissa(bits) : -mantissa(bits); 427 return (int) ((m >> (k - e)) & 0x1L); 428 } 429 } 430 431}