001/* 002 * Copyright (C) 2008 The Guava Authors 003 * 004 * Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except 005 * in compliance with the License. You may obtain a copy of the License at 006 * 007 * http://www.apache.org/licenses/LICENSE-2.0 008 * 009 * Unless required by applicable law or agreed to in writing, software distributed under the License 010 * is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express 011 * or implied. See the License for the specific language governing permissions and limitations under 012 * the License. 013 */ 014 015package com.google.common.primitives; 016 017import static com.google.common.base.Preconditions.checkArgument; 018import static com.google.common.base.Preconditions.checkElementIndex; 019import static com.google.common.base.Preconditions.checkNotNull; 020import static com.google.common.base.Preconditions.checkPositionIndexes; 021import static java.lang.Double.NEGATIVE_INFINITY; 022import static java.lang.Double.POSITIVE_INFINITY; 023 024import com.google.common.annotations.Beta; 025import com.google.common.annotations.GwtCompatible; 026import com.google.common.annotations.GwtIncompatible; 027import com.google.common.base.Converter; 028import java.io.Serializable; 029import java.util.AbstractList; 030import java.util.Arrays; 031import java.util.Collection; 032import java.util.Collections; 033import java.util.Comparator; 034import java.util.List; 035import java.util.RandomAccess; 036import org.checkerframework.checker.nullness.compatqual.NullableDecl; 037 038/** 039 * Static utility methods pertaining to {@code double} primitives, that are not already found in 040 * either {@link Double} or {@link Arrays}. 041 * 042 * <p>See the Guava User Guide article on <a 043 * href="https://github.com/google/guava/wiki/PrimitivesExplained">primitive utilities</a>. 044 * 045 * @author Kevin Bourrillion 046 * @since 1.0 047 */ 048@GwtCompatible(emulated = true) 049public final class Doubles { 050 private Doubles() {} 051 052 /** 053 * The number of bytes required to represent a primitive {@code double} value. 054 * 055 * <p><b>Java 8 users:</b> use {@link Double#BYTES} instead. 056 * 057 * @since 10.0 058 */ 059 public static final int BYTES = Double.SIZE / Byte.SIZE; 060 061 /** 062 * Returns a hash code for {@code value}; equal to the result of invoking {@code ((Double) 063 * value).hashCode()}. 064 * 065 * <p><b>Java 8 users:</b> use {@link Double#hashCode(double)} instead. 066 * 067 * @param value a primitive {@code double} value 068 * @return a hash code for the value 069 */ 070 public static int hashCode(double value) { 071 return ((Double) value).hashCode(); 072 // TODO(kevinb): do it this way when we can (GWT problem): 073 // long bits = Double.doubleToLongBits(value); 074 // return (int) (bits ^ (bits >>> 32)); 075 } 076 077 /** 078 * Compares the two specified {@code double} values. The sign of the value returned is the same as 079 * that of <code>((Double) a).{@linkplain Double#compareTo compareTo}(b)</code>. As with that 080 * method, {@code NaN} is treated as greater than all other values, and {@code 0.0 > -0.0}. 081 * 082 * <p><b>Note:</b> this method simply delegates to the JDK method {@link Double#compare}. It is 083 * provided for consistency with the other primitive types, whose compare methods were not added 084 * to the JDK until JDK 7. 085 * 086 * @param a the first {@code double} to compare 087 * @param b the second {@code double} to compare 088 * @return a negative value if {@code a} is less than {@code b}; a positive value if {@code a} is 089 * greater than {@code b}; or zero if they are equal 090 */ 091 public static int compare(double a, double b) { 092 return Double.compare(a, b); 093 } 094 095 /** 096 * Returns {@code true} if {@code value} represents a real number. This is equivalent to, but not 097 * necessarily implemented as, {@code !(Double.isInfinite(value) || Double.isNaN(value))}. 098 * 099 * <p><b>Java 8 users:</b> use {@link Double#isFinite(double)} instead. 100 * 101 * @since 10.0 102 */ 103 public static boolean isFinite(double value) { 104 return NEGATIVE_INFINITY < value && value < POSITIVE_INFINITY; 105 } 106 107 /** 108 * Returns {@code true} if {@code target} is present as an element anywhere in {@code array}. Note 109 * that this always returns {@code false} when {@code target} is {@code NaN}. 110 * 111 * @param array an array of {@code double} values, possibly empty 112 * @param target a primitive {@code double} value 113 * @return {@code true} if {@code array[i] == target} for some value of {@code i} 114 */ 115 public static boolean contains(double[] array, double target) { 116 for (double value : array) { 117 if (value == target) { 118 return true; 119 } 120 } 121 return false; 122 } 123 124 /** 125 * Returns the index of the first appearance of the value {@code target} in {@code array}. Note 126 * that this always returns {@code -1} when {@code target} is {@code NaN}. 127 * 128 * @param array an array of {@code double} values, possibly empty 129 * @param target a primitive {@code double} value 130 * @return the least index {@code i} for which {@code array[i] == target}, or {@code -1} if no 131 * such index exists. 132 */ 133 public static int indexOf(double[] array, double target) { 134 return indexOf(array, target, 0, array.length); 135 } 136 137 // TODO(kevinb): consider making this public 138 private static int indexOf(double[] array, double target, int start, int end) { 139 for (int i = start; i < end; i++) { 140 if (array[i] == target) { 141 return i; 142 } 143 } 144 return -1; 145 } 146 147 /** 148 * Returns the start position of the first occurrence of the specified {@code target} within 149 * {@code array}, or {@code -1} if there is no such occurrence. 150 * 151 * <p>More formally, returns the lowest index {@code i} such that {@code Arrays.copyOfRange(array, 152 * i, i + target.length)} contains exactly the same elements as {@code target}. 153 * 154 * <p>Note that this always returns {@code -1} when {@code target} contains {@code NaN}. 155 * 156 * @param array the array to search for the sequence {@code target} 157 * @param target the array to search for as a sub-sequence of {@code array} 158 */ 159 public static int indexOf(double[] array, double[] target) { 160 checkNotNull(array, "array"); 161 checkNotNull(target, "target"); 162 if (target.length == 0) { 163 return 0; 164 } 165 166 outer: 167 for (int i = 0; i < array.length - target.length + 1; i++) { 168 for (int j = 0; j < target.length; j++) { 169 if (array[i + j] != target[j]) { 170 continue outer; 171 } 172 } 173 return i; 174 } 175 return -1; 176 } 177 178 /** 179 * Returns the index of the last appearance of the value {@code target} in {@code array}. Note 180 * that this always returns {@code -1} when {@code target} is {@code NaN}. 181 * 182 * @param array an array of {@code double} values, possibly empty 183 * @param target a primitive {@code double} value 184 * @return the greatest index {@code i} for which {@code array[i] == target}, or {@code -1} if no 185 * such index exists. 186 */ 187 public static int lastIndexOf(double[] array, double target) { 188 return lastIndexOf(array, target, 0, array.length); 189 } 190 191 // TODO(kevinb): consider making this public 192 private static int lastIndexOf(double[] array, double target, int start, int end) { 193 for (int i = end - 1; i >= start; i--) { 194 if (array[i] == target) { 195 return i; 196 } 197 } 198 return -1; 199 } 200 201 /** 202 * Returns the least value present in {@code array}, using the same rules of comparison as {@link 203 * Math#min(double, double)}. 204 * 205 * @param array a <i>nonempty</i> array of {@code double} values 206 * @return the value present in {@code array} that is less than or equal to every other value in 207 * the array 208 * @throws IllegalArgumentException if {@code array} is empty 209 */ 210 public static double min(double... array) { 211 checkArgument(array.length > 0); 212 double min = array[0]; 213 for (int i = 1; i < array.length; i++) { 214 min = Math.min(min, array[i]); 215 } 216 return min; 217 } 218 219 /** 220 * Returns the greatest value present in {@code array}, using the same rules of comparison as 221 * {@link Math#max(double, double)}. 222 * 223 * @param array a <i>nonempty</i> array of {@code double} values 224 * @return the value present in {@code array} that is greater than or equal to every other value 225 * in the array 226 * @throws IllegalArgumentException if {@code array} is empty 227 */ 228 public static double max(double... array) { 229 checkArgument(array.length > 0); 230 double max = array[0]; 231 for (int i = 1; i < array.length; i++) { 232 max = Math.max(max, array[i]); 233 } 234 return max; 235 } 236 237 /** 238 * Returns the value nearest to {@code value} which is within the closed range {@code [min..max]}. 239 * 240 * <p>If {@code value} is within the range {@code [min..max]}, {@code value} is returned 241 * unchanged. If {@code value} is less than {@code min}, {@code min} is returned, and if {@code 242 * value} is greater than {@code max}, {@code max} is returned. 243 * 244 * @param value the {@code double} value to constrain 245 * @param min the lower bound (inclusive) of the range to constrain {@code value} to 246 * @param max the upper bound (inclusive) of the range to constrain {@code value} to 247 * @throws IllegalArgumentException if {@code min > max} 248 * @since 21.0 249 */ 250 @Beta 251 public static double constrainToRange(double value, double min, double max) { 252 checkArgument(min <= max, "min (%s) must be less than or equal to max (%s)", min, max); 253 return Math.min(Math.max(value, min), max); 254 } 255 256 /** 257 * Returns the values from each provided array combined into a single array. For example, {@code 258 * concat(new double[] {a, b}, new double[] {}, new double[] {c}} returns the array {@code {a, b, 259 * c}}. 260 * 261 * @param arrays zero or more {@code double} arrays 262 * @return a single array containing all the values from the source arrays, in order 263 */ 264 public static double[] concat(double[]... arrays) { 265 int length = 0; 266 for (double[] array : arrays) { 267 length += array.length; 268 } 269 double[] result = new double[length]; 270 int pos = 0; 271 for (double[] array : arrays) { 272 System.arraycopy(array, 0, result, pos, array.length); 273 pos += array.length; 274 } 275 return result; 276 } 277 278 private static final class DoubleConverter extends Converter<String, Double> 279 implements Serializable { 280 static final DoubleConverter INSTANCE = new DoubleConverter(); 281 282 @Override 283 protected Double doForward(String value) { 284 return Double.valueOf(value); 285 } 286 287 @Override 288 protected String doBackward(Double value) { 289 return value.toString(); 290 } 291 292 @Override 293 public String toString() { 294 return "Doubles.stringConverter()"; 295 } 296 297 private Object readResolve() { 298 return INSTANCE; 299 } 300 301 private static final long serialVersionUID = 1; 302 } 303 304 /** 305 * Returns a serializable converter object that converts between strings and doubles using {@link 306 * Double#valueOf} and {@link Double#toString()}. 307 * 308 * @since 16.0 309 */ 310 @Beta 311 public static Converter<String, Double> stringConverter() { 312 return DoubleConverter.INSTANCE; 313 } 314 315 /** 316 * Returns an array containing the same values as {@code array}, but guaranteed to be of a 317 * specified minimum length. If {@code array} already has a length of at least {@code minLength}, 318 * it is returned directly. Otherwise, a new array of size {@code minLength + padding} is 319 * returned, containing the values of {@code array}, and zeroes in the remaining places. 320 * 321 * @param array the source array 322 * @param minLength the minimum length the returned array must guarantee 323 * @param padding an extra amount to "grow" the array by if growth is necessary 324 * @throws IllegalArgumentException if {@code minLength} or {@code padding} is negative 325 * @return an array containing the values of {@code array}, with guaranteed minimum length {@code 326 * minLength} 327 */ 328 public static double[] ensureCapacity(double[] array, int minLength, int padding) { 329 checkArgument(minLength >= 0, "Invalid minLength: %s", minLength); 330 checkArgument(padding >= 0, "Invalid padding: %s", padding); 331 return (array.length < minLength) ? Arrays.copyOf(array, minLength + padding) : array; 332 } 333 334 /** 335 * Returns a string containing the supplied {@code double} values, converted to strings as 336 * specified by {@link Double#toString(double)}, and separated by {@code separator}. For example, 337 * {@code join("-", 1.0, 2.0, 3.0)} returns the string {@code "1.0-2.0-3.0"}. 338 * 339 * <p>Note that {@link Double#toString(double)} formats {@code double} differently in GWT 340 * sometimes. In the previous example, it returns the string {@code "1-2-3"}. 341 * 342 * @param separator the text that should appear between consecutive values in the resulting string 343 * (but not at the start or end) 344 * @param array an array of {@code double} values, possibly empty 345 */ 346 public static String join(String separator, double... array) { 347 checkNotNull(separator); 348 if (array.length == 0) { 349 return ""; 350 } 351 352 // For pre-sizing a builder, just get the right order of magnitude 353 StringBuilder builder = new StringBuilder(array.length * 12); 354 builder.append(array[0]); 355 for (int i = 1; i < array.length; i++) { 356 builder.append(separator).append(array[i]); 357 } 358 return builder.toString(); 359 } 360 361 /** 362 * Returns a comparator that compares two {@code double} arrays <a 363 * href="http://en.wikipedia.org/wiki/Lexicographical_order">lexicographically</a>. That is, it 364 * compares, using {@link #compare(double, double)}), the first pair of values that follow any 365 * common prefix, or when one array is a prefix of the other, treats the shorter array as the 366 * lesser. For example, {@code [] < [1.0] < [1.0, 2.0] < [2.0]}. 367 * 368 * <p>The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays 369 * support only identity equality), but it is consistent with {@link Arrays#equals(double[], 370 * double[])}. 371 * 372 * @since 2.0 373 */ 374 public static Comparator<double[]> lexicographicalComparator() { 375 return LexicographicalComparator.INSTANCE; 376 } 377 378 private enum LexicographicalComparator implements Comparator<double[]> { 379 INSTANCE; 380 381 @Override 382 public int compare(double[] left, double[] right) { 383 int minLength = Math.min(left.length, right.length); 384 for (int i = 0; i < minLength; i++) { 385 int result = Double.compare(left[i], right[i]); 386 if (result != 0) { 387 return result; 388 } 389 } 390 return left.length - right.length; 391 } 392 393 @Override 394 public String toString() { 395 return "Doubles.lexicographicalComparator()"; 396 } 397 } 398 399 /** 400 * Sorts the elements of {@code array} in descending order. 401 * 402 * <p>Note that this method uses the total order imposed by {@link Double#compare}, which treats 403 * all NaN values as equal and 0.0 as greater than -0.0. 404 * 405 * @since 23.1 406 */ 407 public static void sortDescending(double[] array) { 408 checkNotNull(array); 409 sortDescending(array, 0, array.length); 410 } 411 412 /** 413 * Sorts the elements of {@code array} between {@code fromIndex} inclusive and {@code toIndex} 414 * exclusive in descending order. 415 * 416 * <p>Note that this method uses the total order imposed by {@link Double#compare}, which treats 417 * all NaN values as equal and 0.0 as greater than -0.0. 418 * 419 * @since 23.1 420 */ 421 public static void sortDescending(double[] array, int fromIndex, int toIndex) { 422 checkNotNull(array); 423 checkPositionIndexes(fromIndex, toIndex, array.length); 424 Arrays.sort(array, fromIndex, toIndex); 425 reverse(array, fromIndex, toIndex); 426 } 427 428 /** 429 * Reverses the elements of {@code array}. This is equivalent to {@code 430 * Collections.reverse(Doubles.asList(array))}, but is likely to be more efficient. 431 * 432 * @since 23.1 433 */ 434 public static void reverse(double[] array) { 435 checkNotNull(array); 436 reverse(array, 0, array.length); 437 } 438 439 /** 440 * Reverses the elements of {@code array} between {@code fromIndex} inclusive and {@code toIndex} 441 * exclusive. This is equivalent to {@code 442 * Collections.reverse(Doubles.asList(array).subList(fromIndex, toIndex))}, but is likely to be 443 * more efficient. 444 * 445 * @throws IndexOutOfBoundsException if {@code fromIndex < 0}, {@code toIndex > array.length}, or 446 * {@code toIndex > fromIndex} 447 * @since 23.1 448 */ 449 public static void reverse(double[] array, int fromIndex, int toIndex) { 450 checkNotNull(array); 451 checkPositionIndexes(fromIndex, toIndex, array.length); 452 for (int i = fromIndex, j = toIndex - 1; i < j; i++, j--) { 453 double tmp = array[i]; 454 array[i] = array[j]; 455 array[j] = tmp; 456 } 457 } 458 459 /** 460 * Returns an array containing each value of {@code collection}, converted to a {@code double} 461 * value in the manner of {@link Number#doubleValue}. 462 * 463 * <p>Elements are copied from the argument collection as if by {@code collection.toArray()}. 464 * Calling this method is as thread-safe as calling that method. 465 * 466 * @param collection a collection of {@code Number} instances 467 * @return an array containing the same values as {@code collection}, in the same order, converted 468 * to primitives 469 * @throws NullPointerException if {@code collection} or any of its elements is null 470 * @since 1.0 (parameter was {@code Collection<Double>} before 12.0) 471 */ 472 public static double[] toArray(Collection<? extends Number> collection) { 473 if (collection instanceof DoubleArrayAsList) { 474 return ((DoubleArrayAsList) collection).toDoubleArray(); 475 } 476 477 Object[] boxedArray = collection.toArray(); 478 int len = boxedArray.length; 479 double[] array = new double[len]; 480 for (int i = 0; i < len; i++) { 481 // checkNotNull for GWT (do not optimize) 482 array[i] = ((Number) checkNotNull(boxedArray[i])).doubleValue(); 483 } 484 return array; 485 } 486 487 /** 488 * Returns a fixed-size list backed by the specified array, similar to {@link 489 * Arrays#asList(Object[])}. The list supports {@link List#set(int, Object)}, but any attempt to 490 * set a value to {@code null} will result in a {@link NullPointerException}. 491 * 492 * <p>The returned list maintains the values, but not the identities, of {@code Double} objects 493 * written to or read from it. For example, whether {@code list.get(0) == list.get(0)} is true for 494 * the returned list is unspecified. 495 * 496 * <p>The returned list may have unexpected behavior if it contains {@code NaN}, or if {@code NaN} 497 * is used as a parameter to any of its methods. 498 * 499 * <p><b>Note:</b> when possible, you should represent your data as an {@link 500 * ImmutableDoubleArray} instead, which has an {@link ImmutableDoubleArray#asList asList} view. 501 * 502 * @param backingArray the array to back the list 503 * @return a list view of the array 504 */ 505 public static List<Double> asList(double... backingArray) { 506 if (backingArray.length == 0) { 507 return Collections.emptyList(); 508 } 509 return new DoubleArrayAsList(backingArray); 510 } 511 512 @GwtCompatible 513 private static class DoubleArrayAsList extends AbstractList<Double> 514 implements RandomAccess, Serializable { 515 final double[] array; 516 final int start; 517 final int end; 518 519 DoubleArrayAsList(double[] array) { 520 this(array, 0, array.length); 521 } 522 523 DoubleArrayAsList(double[] array, int start, int end) { 524 this.array = array; 525 this.start = start; 526 this.end = end; 527 } 528 529 @Override 530 public int size() { 531 return end - start; 532 } 533 534 @Override 535 public boolean isEmpty() { 536 return false; 537 } 538 539 @Override 540 public Double get(int index) { 541 checkElementIndex(index, size()); 542 return array[start + index]; 543 } 544 545 @Override 546 public boolean contains(Object target) { 547 // Overridden to prevent a ton of boxing 548 return (target instanceof Double) 549 && Doubles.indexOf(array, (Double) target, start, end) != -1; 550 } 551 552 @Override 553 public int indexOf(Object target) { 554 // Overridden to prevent a ton of boxing 555 if (target instanceof Double) { 556 int i = Doubles.indexOf(array, (Double) target, start, end); 557 if (i >= 0) { 558 return i - start; 559 } 560 } 561 return -1; 562 } 563 564 @Override 565 public int lastIndexOf(Object target) { 566 // Overridden to prevent a ton of boxing 567 if (target instanceof Double) { 568 int i = Doubles.lastIndexOf(array, (Double) target, start, end); 569 if (i >= 0) { 570 return i - start; 571 } 572 } 573 return -1; 574 } 575 576 @Override 577 public Double set(int index, Double element) { 578 checkElementIndex(index, size()); 579 double oldValue = array[start + index]; 580 // checkNotNull for GWT (do not optimize) 581 array[start + index] = checkNotNull(element); 582 return oldValue; 583 } 584 585 @Override 586 public List<Double> subList(int fromIndex, int toIndex) { 587 int size = size(); 588 checkPositionIndexes(fromIndex, toIndex, size); 589 if (fromIndex == toIndex) { 590 return Collections.emptyList(); 591 } 592 return new DoubleArrayAsList(array, start + fromIndex, start + toIndex); 593 } 594 595 @Override 596 public boolean equals(@NullableDecl Object object) { 597 if (object == this) { 598 return true; 599 } 600 if (object instanceof DoubleArrayAsList) { 601 DoubleArrayAsList that = (DoubleArrayAsList) object; 602 int size = size(); 603 if (that.size() != size) { 604 return false; 605 } 606 for (int i = 0; i < size; i++) { 607 if (array[start + i] != that.array[that.start + i]) { 608 return false; 609 } 610 } 611 return true; 612 } 613 return super.equals(object); 614 } 615 616 @Override 617 public int hashCode() { 618 int result = 1; 619 for (int i = start; i < end; i++) { 620 result = 31 * result + Doubles.hashCode(array[i]); 621 } 622 return result; 623 } 624 625 @Override 626 public String toString() { 627 StringBuilder builder = new StringBuilder(size() * 12); 628 builder.append('[').append(array[start]); 629 for (int i = start + 1; i < end; i++) { 630 builder.append(", ").append(array[i]); 631 } 632 return builder.append(']').toString(); 633 } 634 635 double[] toDoubleArray() { 636 return Arrays.copyOfRange(array, start, end); 637 } 638 639 private static final long serialVersionUID = 0; 640 } 641 642 /** 643 * This is adapted from the regex suggested by {@link Double#valueOf(String)} for prevalidating 644 * inputs. All valid inputs must pass this regex, but it's semantically fine if not all inputs 645 * that pass this regex are valid -- only a performance hit is incurred, not a semantics bug. 646 */ 647 @GwtIncompatible // regular expressions 648 static final 649 java.util.regex.Pattern 650 FLOATING_POINT_PATTERN = fpPattern(); 651 652 @GwtIncompatible // regular expressions 653 private static 654 java.util.regex.Pattern 655 fpPattern() { 656 /* 657 * We use # instead of * for possessive quantifiers. This lets us strip them out when building 658 * the regex for RE2 (which doesn't support them) but leave them in when building it for 659 * java.util.regex (where we want them in order to avoid catastrophic backtracking). 660 */ 661 String decimal = "(?:\\d+#(?:\\.\\d*#)?|\\.\\d+#)"; 662 String completeDec = decimal + "(?:[eE][+-]?\\d+#)?[fFdD]?"; 663 String hex = "(?:[0-9a-fA-F]+#(?:\\.[0-9a-fA-F]*#)?|\\.[0-9a-fA-F]+#)"; 664 String completeHex = "0[xX]" + hex + "[pP][+-]?\\d+#[fFdD]?"; 665 String fpPattern = "[+-]?(?:NaN|Infinity|" + completeDec + "|" + completeHex + ")"; 666 fpPattern = 667 fpPattern.replace( 668 "#", 669 "+" 670 ); 671 return 672 java.util.regex.Pattern 673 .compile(fpPattern); 674 } 675 676 /** 677 * Parses the specified string as a double-precision floating point value. The ASCII character 678 * {@code '-'} (<code>'\u002D'</code>) is recognized as the minus sign. 679 * 680 * <p>Unlike {@link Double#parseDouble(String)}, this method returns {@code null} instead of 681 * throwing an exception if parsing fails. Valid inputs are exactly those accepted by {@link 682 * Double#valueOf(String)}, except that leading and trailing whitespace is not permitted. 683 * 684 * <p>This implementation is likely to be faster than {@code Double.parseDouble} if many failures 685 * are expected. 686 * 687 * @param string the string representation of a {@code double} value 688 * @return the floating point value represented by {@code string}, or {@code null} if {@code 689 * string} has a length of zero or cannot be parsed as a {@code double} value 690 * @since 14.0 691 */ 692 @Beta 693 @GwtIncompatible // regular expressions 694 @NullableDecl 695 public static Double tryParse(String string) { 696 if (FLOATING_POINT_PATTERN.matcher(string).matches()) { 697 // TODO(lowasser): could be potentially optimized, but only with 698 // extensive testing 699 try { 700 return Double.parseDouble(string); 701 } catch (NumberFormatException e) { 702 // Double.parseDouble has changed specs several times, so fall through 703 // gracefully 704 } 705 } 706 return null; 707 } 708}