Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 1 | /* |
| 2 | * Licensed to the Apache Software Foundation (ASF) under one or more |
| 3 | * contributor license agreements. See the NOTICE file distributed with |
| 4 | * this work for additional information regarding copyright ownership. |
| 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 |
| 6 | * (the "License"); you may not use this file except in compliance with |
| 7 | * the License. You may obtain a copy of the License at |
| 8 | * |
| 9 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 10 | * |
| 11 | * Unless required by applicable law or agreed to in writing, software |
| 12 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 14 | * See the License for the specific language governing permissions and |
| 15 | * limitations under the License. |
| 16 | */ |
| 17 | |
| 18 | package org.apache.commons.math.util; |
| 19 | |
| 20 | import java.math.BigDecimal; |
| 21 | import java.math.BigInteger; |
| 22 | import java.util.Arrays; |
| 23 | |
| 24 | import org.apache.commons.math.MathRuntimeException; |
| 25 | import org.apache.commons.math.exception.util.Localizable; |
| 26 | import org.apache.commons.math.exception.util.LocalizedFormats; |
| 27 | import org.apache.commons.math.exception.NonMonotonousSequenceException; |
| 28 | |
| 29 | /** |
| 30 | * Some useful additions to the built-in functions in {@link Math}. |
| 31 | * @version $Revision: 1073472 $ $Date: 2011-02-22 20:49:07 +0100 (mar. 22 févr. 2011) $ |
| 32 | */ |
| 33 | public final class MathUtils { |
| 34 | |
| 35 | /** Smallest positive number such that 1 - EPSILON is not numerically equal to 1. */ |
| 36 | public static final double EPSILON = 0x1.0p-53; |
| 37 | |
| 38 | /** Safe minimum, such that 1 / SAFE_MIN does not overflow. |
| 39 | * <p>In IEEE 754 arithmetic, this is also the smallest normalized |
| 40 | * number 2<sup>-1022</sup>.</p> |
| 41 | */ |
| 42 | public static final double SAFE_MIN = 0x1.0p-1022; |
| 43 | |
| 44 | /** |
| 45 | * 2 π. |
| 46 | * @since 2.1 |
| 47 | */ |
| 48 | public static final double TWO_PI = 2 * FastMath.PI; |
| 49 | |
| 50 | /** -1.0 cast as a byte. */ |
| 51 | private static final byte NB = (byte)-1; |
| 52 | |
| 53 | /** -1.0 cast as a short. */ |
| 54 | private static final short NS = (short)-1; |
| 55 | |
| 56 | /** 1.0 cast as a byte. */ |
| 57 | private static final byte PB = (byte)1; |
| 58 | |
| 59 | /** 1.0 cast as a short. */ |
| 60 | private static final short PS = (short)1; |
| 61 | |
| 62 | /** 0.0 cast as a byte. */ |
| 63 | private static final byte ZB = (byte)0; |
| 64 | |
| 65 | /** 0.0 cast as a short. */ |
| 66 | private static final short ZS = (short)0; |
| 67 | |
| 68 | /** Gap between NaN and regular numbers. */ |
| 69 | private static final int NAN_GAP = 4 * 1024 * 1024; |
| 70 | |
| 71 | /** Offset to order signed double numbers lexicographically. */ |
| 72 | private static final long SGN_MASK = 0x8000000000000000L; |
| 73 | |
| 74 | /** Offset to order signed double numbers lexicographically. */ |
| 75 | private static final int SGN_MASK_FLOAT = 0x80000000; |
| 76 | |
| 77 | /** All long-representable factorials */ |
| 78 | private static final long[] FACTORIALS = new long[] { |
| 79 | 1l, 1l, 2l, |
| 80 | 6l, 24l, 120l, |
| 81 | 720l, 5040l, 40320l, |
| 82 | 362880l, 3628800l, 39916800l, |
| 83 | 479001600l, 6227020800l, 87178291200l, |
| 84 | 1307674368000l, 20922789888000l, 355687428096000l, |
| 85 | 6402373705728000l, 121645100408832000l, 2432902008176640000l }; |
| 86 | |
| 87 | /** |
| 88 | * Private Constructor |
| 89 | */ |
| 90 | private MathUtils() { |
| 91 | super(); |
| 92 | } |
| 93 | |
| 94 | /** |
| 95 | * Add two integers, checking for overflow. |
| 96 | * |
| 97 | * @param x an addend |
| 98 | * @param y an addend |
| 99 | * @return the sum <code>x+y</code> |
| 100 | * @throws ArithmeticException if the result can not be represented as an |
| 101 | * int |
| 102 | * @since 1.1 |
| 103 | */ |
| 104 | public static int addAndCheck(int x, int y) { |
| 105 | long s = (long)x + (long)y; |
| 106 | if (s < Integer.MIN_VALUE || s > Integer.MAX_VALUE) { |
| 107 | throw MathRuntimeException.createArithmeticException(LocalizedFormats.OVERFLOW_IN_ADDITION, x, y); |
| 108 | } |
| 109 | return (int)s; |
| 110 | } |
| 111 | |
| 112 | /** |
| 113 | * Add two long integers, checking for overflow. |
| 114 | * |
| 115 | * @param a an addend |
| 116 | * @param b an addend |
| 117 | * @return the sum <code>a+b</code> |
| 118 | * @throws ArithmeticException if the result can not be represented as an |
| 119 | * long |
| 120 | * @since 1.2 |
| 121 | */ |
| 122 | public static long addAndCheck(long a, long b) { |
| 123 | return addAndCheck(a, b, LocalizedFormats.OVERFLOW_IN_ADDITION); |
| 124 | } |
| 125 | |
| 126 | /** |
| 127 | * Add two long integers, checking for overflow. |
| 128 | * |
| 129 | * @param a an addend |
| 130 | * @param b an addend |
| 131 | * @param pattern the pattern to use for any thrown exception. |
| 132 | * @return the sum <code>a+b</code> |
| 133 | * @throws ArithmeticException if the result can not be represented as an |
| 134 | * long |
| 135 | * @since 1.2 |
| 136 | */ |
| 137 | private static long addAndCheck(long a, long b, Localizable pattern) { |
| 138 | long ret; |
| 139 | if (a > b) { |
| 140 | // use symmetry to reduce boundary cases |
| 141 | ret = addAndCheck(b, a, pattern); |
| 142 | } else { |
| 143 | // assert a <= b |
| 144 | |
| 145 | if (a < 0) { |
| 146 | if (b < 0) { |
| 147 | // check for negative overflow |
| 148 | if (Long.MIN_VALUE - b <= a) { |
| 149 | ret = a + b; |
| 150 | } else { |
| 151 | throw MathRuntimeException.createArithmeticException(pattern, a, b); |
| 152 | } |
| 153 | } else { |
| 154 | // opposite sign addition is always safe |
| 155 | ret = a + b; |
| 156 | } |
| 157 | } else { |
| 158 | // assert a >= 0 |
| 159 | // assert b >= 0 |
| 160 | |
| 161 | // check for positive overflow |
| 162 | if (a <= Long.MAX_VALUE - b) { |
| 163 | ret = a + b; |
| 164 | } else { |
| 165 | throw MathRuntimeException.createArithmeticException(pattern, a, b); |
| 166 | } |
| 167 | } |
| 168 | } |
| 169 | return ret; |
| 170 | } |
| 171 | |
| 172 | /** |
| 173 | * Returns an exact representation of the <a |
| 174 | * href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial |
| 175 | * Coefficient</a>, "<code>n choose k</code>", the number of |
| 176 | * <code>k</code>-element subsets that can be selected from an |
| 177 | * <code>n</code>-element set. |
| 178 | * <p> |
| 179 | * <Strong>Preconditions</strong>: |
| 180 | * <ul> |
| 181 | * <li> <code>0 <= k <= n </code> (otherwise |
| 182 | * <code>IllegalArgumentException</code> is thrown)</li> |
| 183 | * <li> The result is small enough to fit into a <code>long</code>. The |
| 184 | * largest value of <code>n</code> for which all coefficients are |
| 185 | * <code> < Long.MAX_VALUE</code> is 66. If the computed value exceeds |
| 186 | * <code>Long.MAX_VALUE</code> an <code>ArithMeticException</code> is |
| 187 | * thrown.</li> |
| 188 | * </ul></p> |
| 189 | * |
| 190 | * @param n the size of the set |
| 191 | * @param k the size of the subsets to be counted |
| 192 | * @return <code>n choose k</code> |
| 193 | * @throws IllegalArgumentException if preconditions are not met. |
| 194 | * @throws ArithmeticException if the result is too large to be represented |
| 195 | * by a long integer. |
| 196 | */ |
| 197 | public static long binomialCoefficient(final int n, final int k) { |
| 198 | checkBinomial(n, k); |
| 199 | if ((n == k) || (k == 0)) { |
| 200 | return 1; |
| 201 | } |
| 202 | if ((k == 1) || (k == n - 1)) { |
| 203 | return n; |
| 204 | } |
| 205 | // Use symmetry for large k |
| 206 | if (k > n / 2) |
| 207 | return binomialCoefficient(n, n - k); |
| 208 | |
| 209 | // We use the formula |
| 210 | // (n choose k) = n! / (n-k)! / k! |
| 211 | // (n choose k) == ((n-k+1)*...*n) / (1*...*k) |
| 212 | // which could be written |
| 213 | // (n choose k) == (n-1 choose k-1) * n / k |
| 214 | long result = 1; |
| 215 | if (n <= 61) { |
| 216 | // For n <= 61, the naive implementation cannot overflow. |
| 217 | int i = n - k + 1; |
| 218 | for (int j = 1; j <= k; j++) { |
| 219 | result = result * i / j; |
| 220 | i++; |
| 221 | } |
| 222 | } else if (n <= 66) { |
| 223 | // For n > 61 but n <= 66, the result cannot overflow, |
| 224 | // but we must take care not to overflow intermediate values. |
| 225 | int i = n - k + 1; |
| 226 | for (int j = 1; j <= k; j++) { |
| 227 | // We know that (result * i) is divisible by j, |
| 228 | // but (result * i) may overflow, so we split j: |
| 229 | // Filter out the gcd, d, so j/d and i/d are integer. |
| 230 | // result is divisible by (j/d) because (j/d) |
| 231 | // is relative prime to (i/d) and is a divisor of |
| 232 | // result * (i/d). |
| 233 | final long d = gcd(i, j); |
| 234 | result = (result / (j / d)) * (i / d); |
| 235 | i++; |
| 236 | } |
| 237 | } else { |
| 238 | // For n > 66, a result overflow might occur, so we check |
| 239 | // the multiplication, taking care to not overflow |
| 240 | // unnecessary. |
| 241 | int i = n - k + 1; |
| 242 | for (int j = 1; j <= k; j++) { |
| 243 | final long d = gcd(i, j); |
| 244 | result = mulAndCheck(result / (j / d), i / d); |
| 245 | i++; |
| 246 | } |
| 247 | } |
| 248 | return result; |
| 249 | } |
| 250 | |
| 251 | /** |
| 252 | * Returns a <code>double</code> representation of the <a |
| 253 | * href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial |
| 254 | * Coefficient</a>, "<code>n choose k</code>", the number of |
| 255 | * <code>k</code>-element subsets that can be selected from an |
| 256 | * <code>n</code>-element set. |
| 257 | * <p> |
| 258 | * <Strong>Preconditions</strong>: |
| 259 | * <ul> |
| 260 | * <li> <code>0 <= k <= n </code> (otherwise |
| 261 | * <code>IllegalArgumentException</code> is thrown)</li> |
| 262 | * <li> The result is small enough to fit into a <code>double</code>. The |
| 263 | * largest value of <code>n</code> for which all coefficients are < |
| 264 | * Double.MAX_VALUE is 1029. If the computed value exceeds Double.MAX_VALUE, |
| 265 | * Double.POSITIVE_INFINITY is returned</li> |
| 266 | * </ul></p> |
| 267 | * |
| 268 | * @param n the size of the set |
| 269 | * @param k the size of the subsets to be counted |
| 270 | * @return <code>n choose k</code> |
| 271 | * @throws IllegalArgumentException if preconditions are not met. |
| 272 | */ |
| 273 | public static double binomialCoefficientDouble(final int n, final int k) { |
| 274 | checkBinomial(n, k); |
| 275 | if ((n == k) || (k == 0)) { |
| 276 | return 1d; |
| 277 | } |
| 278 | if ((k == 1) || (k == n - 1)) { |
| 279 | return n; |
| 280 | } |
| 281 | if (k > n/2) { |
| 282 | return binomialCoefficientDouble(n, n - k); |
| 283 | } |
| 284 | if (n < 67) { |
| 285 | return binomialCoefficient(n,k); |
| 286 | } |
| 287 | |
| 288 | double result = 1d; |
| 289 | for (int i = 1; i <= k; i++) { |
| 290 | result *= (double)(n - k + i) / (double)i; |
| 291 | } |
| 292 | |
| 293 | return FastMath.floor(result + 0.5); |
| 294 | } |
| 295 | |
| 296 | /** |
| 297 | * Returns the natural <code>log</code> of the <a |
| 298 | * href="http://mathworld.wolfram.com/BinomialCoefficient.html"> Binomial |
| 299 | * Coefficient</a>, "<code>n choose k</code>", the number of |
| 300 | * <code>k</code>-element subsets that can be selected from an |
| 301 | * <code>n</code>-element set. |
| 302 | * <p> |
| 303 | * <Strong>Preconditions</strong>: |
| 304 | * <ul> |
| 305 | * <li> <code>0 <= k <= n </code> (otherwise |
| 306 | * <code>IllegalArgumentException</code> is thrown)</li> |
| 307 | * </ul></p> |
| 308 | * |
| 309 | * @param n the size of the set |
| 310 | * @param k the size of the subsets to be counted |
| 311 | * @return <code>n choose k</code> |
| 312 | * @throws IllegalArgumentException if preconditions are not met. |
| 313 | */ |
| 314 | public static double binomialCoefficientLog(final int n, final int k) { |
| 315 | checkBinomial(n, k); |
| 316 | if ((n == k) || (k == 0)) { |
| 317 | return 0; |
| 318 | } |
| 319 | if ((k == 1) || (k == n - 1)) { |
| 320 | return FastMath.log(n); |
| 321 | } |
| 322 | |
| 323 | /* |
| 324 | * For values small enough to do exact integer computation, |
| 325 | * return the log of the exact value |
| 326 | */ |
| 327 | if (n < 67) { |
| 328 | return FastMath.log(binomialCoefficient(n,k)); |
| 329 | } |
| 330 | |
| 331 | /* |
| 332 | * Return the log of binomialCoefficientDouble for values that will not |
| 333 | * overflow binomialCoefficientDouble |
| 334 | */ |
| 335 | if (n < 1030) { |
| 336 | return FastMath.log(binomialCoefficientDouble(n, k)); |
| 337 | } |
| 338 | |
| 339 | if (k > n / 2) { |
| 340 | return binomialCoefficientLog(n, n - k); |
| 341 | } |
| 342 | |
| 343 | /* |
| 344 | * Sum logs for values that could overflow |
| 345 | */ |
| 346 | double logSum = 0; |
| 347 | |
| 348 | // n!/(n-k)! |
| 349 | for (int i = n - k + 1; i <= n; i++) { |
| 350 | logSum += FastMath.log(i); |
| 351 | } |
| 352 | |
| 353 | // divide by k! |
| 354 | for (int i = 2; i <= k; i++) { |
| 355 | logSum -= FastMath.log(i); |
| 356 | } |
| 357 | |
| 358 | return logSum; |
| 359 | } |
| 360 | |
| 361 | /** |
| 362 | * Check binomial preconditions. |
| 363 | * @param n the size of the set |
| 364 | * @param k the size of the subsets to be counted |
| 365 | * @exception IllegalArgumentException if preconditions are not met. |
| 366 | */ |
| 367 | private static void checkBinomial(final int n, final int k) |
| 368 | throws IllegalArgumentException { |
| 369 | if (n < k) { |
| 370 | throw MathRuntimeException.createIllegalArgumentException( |
| 371 | LocalizedFormats.BINOMIAL_INVALID_PARAMETERS_ORDER, |
| 372 | n, k); |
| 373 | } |
| 374 | if (n < 0) { |
| 375 | throw MathRuntimeException.createIllegalArgumentException( |
| 376 | LocalizedFormats.BINOMIAL_NEGATIVE_PARAMETER, |
| 377 | n); |
| 378 | } |
| 379 | } |
| 380 | |
| 381 | /** |
| 382 | * Compares two numbers given some amount of allowed error. |
| 383 | * |
| 384 | * @param x the first number |
| 385 | * @param y the second number |
| 386 | * @param eps the amount of error to allow when checking for equality |
| 387 | * @return <ul><li>0 if {@link #equals(double, double, double) equals(x, y, eps)}</li> |
| 388 | * <li>< 0 if !{@link #equals(double, double, double) equals(x, y, eps)} && x < y</li> |
| 389 | * <li>> 0 if !{@link #equals(double, double, double) equals(x, y, eps)} && x > y</li></ul> |
| 390 | */ |
| 391 | public static int compareTo(double x, double y, double eps) { |
| 392 | if (equals(x, y, eps)) { |
| 393 | return 0; |
| 394 | } else if (x < y) { |
| 395 | return -1; |
| 396 | } |
| 397 | return 1; |
| 398 | } |
| 399 | |
| 400 | /** |
| 401 | * Returns the <a href="http://mathworld.wolfram.com/HyperbolicCosine.html"> |
| 402 | * hyperbolic cosine</a> of x. |
| 403 | * |
| 404 | * @param x double value for which to find the hyperbolic cosine |
| 405 | * @return hyperbolic cosine of x |
| 406 | */ |
| 407 | public static double cosh(double x) { |
| 408 | return (FastMath.exp(x) + FastMath.exp(-x)) / 2.0; |
| 409 | } |
| 410 | |
| 411 | /** |
| 412 | * Returns true iff they are strictly equal. |
| 413 | * |
| 414 | * @param x first value |
| 415 | * @param y second value |
| 416 | * @return {@code true} if the values are equal. |
| 417 | * @deprecated as of 2.2 his method considers that {@code NaN == NaN}. In release |
| 418 | * 3.0, the semantics will change in order to comply with IEEE754 where it |
| 419 | * is specified that {@code NaN != NaN}. |
| 420 | * New methods have been added for those cases wher the old semantics is |
| 421 | * useful (see e.g. {@link #equalsIncludingNaN(float,float) |
| 422 | * equalsIncludingNaN}. |
| 423 | */ |
| 424 | @Deprecated |
| 425 | public static boolean equals(float x, float y) { |
| 426 | return (Float.isNaN(x) && Float.isNaN(y)) || x == y; |
| 427 | } |
| 428 | |
| 429 | /** |
| 430 | * Returns true if both arguments are NaN or neither is NaN and they are |
| 431 | * equal as defined by {@link #equals(float,float,int) equals(x, y, 1)}. |
| 432 | * |
| 433 | * @param x first value |
| 434 | * @param y second value |
| 435 | * @return {@code true} if the values are equal or both are NaN. |
| 436 | * @since 2.2 |
| 437 | */ |
| 438 | public static boolean equalsIncludingNaN(float x, float y) { |
| 439 | return (Float.isNaN(x) && Float.isNaN(y)) || equals(x, y, 1); |
| 440 | } |
| 441 | |
| 442 | /** |
| 443 | * Returns true if both arguments are equal or within the range of allowed |
| 444 | * error (inclusive). |
| 445 | * |
| 446 | * @param x first value |
| 447 | * @param y second value |
| 448 | * @param eps the amount of absolute error to allow. |
| 449 | * @return {@code true} if the values are equal or within range of each other. |
| 450 | * @since 2.2 |
| 451 | */ |
| 452 | public static boolean equals(float x, float y, float eps) { |
| 453 | return equals(x, y, 1) || FastMath.abs(y - x) <= eps; |
| 454 | } |
| 455 | |
| 456 | /** |
| 457 | * Returns true if both arguments are NaN or are equal or within the range |
| 458 | * of allowed error (inclusive). |
| 459 | * |
| 460 | * @param x first value |
| 461 | * @param y second value |
| 462 | * @param eps the amount of absolute error to allow. |
| 463 | * @return {@code true} if the values are equal or within range of each other, |
| 464 | * or both are NaN. |
| 465 | * @since 2.2 |
| 466 | */ |
| 467 | public static boolean equalsIncludingNaN(float x, float y, float eps) { |
| 468 | return equalsIncludingNaN(x, y) || (FastMath.abs(y - x) <= eps); |
| 469 | } |
| 470 | |
| 471 | /** |
| 472 | * Returns true if both arguments are equal or within the range of allowed |
| 473 | * error (inclusive). |
| 474 | * Two float numbers are considered equal if there are {@code (maxUlps - 1)} |
| 475 | * (or fewer) floating point numbers between them, i.e. two adjacent floating |
| 476 | * point numbers are considered equal. |
| 477 | * Adapted from <a |
| 478 | * href="http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm"> |
| 479 | * Bruce Dawson</a> |
| 480 | * |
| 481 | * @param x first value |
| 482 | * @param y second value |
| 483 | * @param maxUlps {@code (maxUlps - 1)} is the number of floating point |
| 484 | * values between {@code x} and {@code y}. |
| 485 | * @return {@code true} if there are fewer than {@code maxUlps} floating |
| 486 | * point values between {@code x} and {@code y}. |
| 487 | * @since 2.2 |
| 488 | */ |
| 489 | public static boolean equals(float x, float y, int maxUlps) { |
| 490 | // Check that "maxUlps" is non-negative and small enough so that |
| 491 | // NaN won't compare as equal to anything (except another NaN). |
| 492 | assert maxUlps > 0 && maxUlps < NAN_GAP; |
| 493 | |
| 494 | int xInt = Float.floatToIntBits(x); |
| 495 | int yInt = Float.floatToIntBits(y); |
| 496 | |
| 497 | // Make lexicographically ordered as a two's-complement integer. |
| 498 | if (xInt < 0) { |
| 499 | xInt = SGN_MASK_FLOAT - xInt; |
| 500 | } |
| 501 | if (yInt < 0) { |
| 502 | yInt = SGN_MASK_FLOAT - yInt; |
| 503 | } |
| 504 | |
| 505 | final boolean isEqual = FastMath.abs(xInt - yInt) <= maxUlps; |
| 506 | |
| 507 | return isEqual && !Float.isNaN(x) && !Float.isNaN(y); |
| 508 | } |
| 509 | |
| 510 | /** |
| 511 | * Returns true if both arguments are NaN or if they are equal as defined |
| 512 | * by {@link #equals(float,float,int) equals(x, y, maxUlps)}. |
| 513 | * |
| 514 | * @param x first value |
| 515 | * @param y second value |
| 516 | * @param maxUlps {@code (maxUlps - 1)} is the number of floating point |
| 517 | * values between {@code x} and {@code y}. |
| 518 | * @return {@code true} if both arguments are NaN or if there are less than |
| 519 | * {@code maxUlps} floating point values between {@code x} and {@code y}. |
| 520 | * @since 2.2 |
| 521 | */ |
| 522 | public static boolean equalsIncludingNaN(float x, float y, int maxUlps) { |
| 523 | return (Float.isNaN(x) && Float.isNaN(y)) || equals(x, y, maxUlps); |
| 524 | } |
| 525 | |
| 526 | /** |
| 527 | * Returns true iff both arguments are null or have same dimensions and all |
| 528 | * their elements are equal as defined by |
| 529 | * {@link #equals(float,float)}. |
| 530 | * |
| 531 | * @param x first array |
| 532 | * @param y second array |
| 533 | * @return true if the values are both null or have same dimension |
| 534 | * and equal elements. |
| 535 | * @deprecated as of 2.2 this method considers that {@code NaN == NaN}. In release |
| 536 | * 3.0, the semantics will change in order to comply with IEEE754 where it |
| 537 | * is specified that {@code NaN != NaN}. |
| 538 | * New methods have been added for those cases where the old semantics is |
| 539 | * useful (see e.g. {@link #equalsIncludingNaN(float[],float[]) |
| 540 | * equalsIncludingNaN}. |
| 541 | */ |
| 542 | @Deprecated |
| 543 | public static boolean equals(float[] x, float[] y) { |
| 544 | if ((x == null) || (y == null)) { |
| 545 | return !((x == null) ^ (y == null)); |
| 546 | } |
| 547 | if (x.length != y.length) { |
| 548 | return false; |
| 549 | } |
| 550 | for (int i = 0; i < x.length; ++i) { |
| 551 | if (!equals(x[i], y[i])) { |
| 552 | return false; |
| 553 | } |
| 554 | } |
| 555 | return true; |
| 556 | } |
| 557 | |
| 558 | /** |
| 559 | * Returns true iff both arguments are null or have same dimensions and all |
| 560 | * their elements are equal as defined by |
| 561 | * {@link #equalsIncludingNaN(float,float)}. |
| 562 | * |
| 563 | * @param x first array |
| 564 | * @param y second array |
| 565 | * @return true if the values are both null or have same dimension and |
| 566 | * equal elements |
| 567 | * @since 2.2 |
| 568 | */ |
| 569 | public static boolean equalsIncludingNaN(float[] x, float[] y) { |
| 570 | if ((x == null) || (y == null)) { |
| 571 | return !((x == null) ^ (y == null)); |
| 572 | } |
| 573 | if (x.length != y.length) { |
| 574 | return false; |
| 575 | } |
| 576 | for (int i = 0; i < x.length; ++i) { |
| 577 | if (!equalsIncludingNaN(x[i], y[i])) { |
| 578 | return false; |
| 579 | } |
| 580 | } |
| 581 | return true; |
| 582 | } |
| 583 | |
| 584 | /** |
| 585 | * Returns true iff both arguments are NaN or neither is NaN and they are |
| 586 | * equal |
| 587 | * |
| 588 | * <p>This method considers that {@code NaN == NaN}. In release |
| 589 | * 3.0, the semantics will change in order to comply with IEEE754 where it |
| 590 | * is specified that {@code NaN != NaN}. |
| 591 | * New methods have been added for those cases where the old semantics |
| 592 | * (w.r.t. NaN) is useful (see e.g. |
| 593 | * {@link #equalsIncludingNaN(double,double, double) equalsIncludingNaN}. |
| 594 | * </p> |
| 595 | * |
| 596 | * @param x first value |
| 597 | * @param y second value |
| 598 | * @return {@code true} if the values are equal. |
| 599 | */ |
| 600 | public static boolean equals(double x, double y) { |
| 601 | return (Double.isNaN(x) && Double.isNaN(y)) || x == y; |
| 602 | } |
| 603 | |
| 604 | /** |
| 605 | * Returns true if both arguments are NaN or neither is NaN and they are |
| 606 | * equal as defined by {@link #equals(double,double,int) equals(x, y, 1)}. |
| 607 | * |
| 608 | * @param x first value |
| 609 | * @param y second value |
| 610 | * @return {@code true} if the values are equal or both are NaN. |
| 611 | * @since 2.2 |
| 612 | */ |
| 613 | public static boolean equalsIncludingNaN(double x, double y) { |
| 614 | return (Double.isNaN(x) && Double.isNaN(y)) || equals(x, y, 1); |
| 615 | } |
| 616 | |
| 617 | /** |
| 618 | * Returns true if both arguments are equal or within the range of allowed |
| 619 | * error (inclusive). |
| 620 | * <p> |
| 621 | * Two NaNs are considered equals, as are two infinities with same sign. |
| 622 | * </p> |
| 623 | * <p>This method considers that {@code NaN == NaN}. In release |
| 624 | * 3.0, the semantics will change in order to comply with IEEE754 where it |
| 625 | * is specified that {@code NaN != NaN}. |
| 626 | * New methods have been added for those cases where the old semantics |
| 627 | * (w.r.t. NaN) is useful (see e.g. |
| 628 | * {@link #equalsIncludingNaN(double,double, double) equalsIncludingNaN}. |
| 629 | * </p> |
| 630 | * @param x first value |
| 631 | * @param y second value |
| 632 | * @param eps the amount of absolute error to allow. |
| 633 | * @return {@code true} if the values are equal or within range of each other. |
| 634 | */ |
| 635 | public static boolean equals(double x, double y, double eps) { |
| 636 | return equals(x, y) || FastMath.abs(y - x) <= eps; |
| 637 | } |
| 638 | |
| 639 | /** |
| 640 | * Returns true if both arguments are NaN or are equal or within the range |
| 641 | * of allowed error (inclusive). |
| 642 | * |
| 643 | * @param x first value |
| 644 | * @param y second value |
| 645 | * @param eps the amount of absolute error to allow. |
| 646 | * @return {@code true} if the values are equal or within range of each other, |
| 647 | * or both are NaN. |
| 648 | * @since 2.2 |
| 649 | */ |
| 650 | public static boolean equalsIncludingNaN(double x, double y, double eps) { |
| 651 | return equalsIncludingNaN(x, y) || (FastMath.abs(y - x) <= eps); |
| 652 | } |
| 653 | |
| 654 | /** |
| 655 | * Returns true if both arguments are equal or within the range of allowed |
| 656 | * error (inclusive). |
| 657 | * Two float numbers are considered equal if there are {@code (maxUlps - 1)} |
| 658 | * (or fewer) floating point numbers between them, i.e. two adjacent floating |
| 659 | * point numbers are considered equal. |
| 660 | * Adapted from <a |
| 661 | * href="http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm"> |
| 662 | * Bruce Dawson</a> |
| 663 | * |
| 664 | * <p>This method considers that {@code NaN == NaN}. In release |
| 665 | * 3.0, the semantics will change in order to comply with IEEE754 where it |
| 666 | * is specified that {@code NaN != NaN}. |
| 667 | * New methods have been added for those cases where the old semantics |
| 668 | * (w.r.t. NaN) is useful (see e.g. |
| 669 | * {@link #equalsIncludingNaN(double,double, int) equalsIncludingNaN}. |
| 670 | * </p> |
| 671 | * |
| 672 | * @param x first value |
| 673 | * @param y second value |
| 674 | * @param maxUlps {@code (maxUlps - 1)} is the number of floating point |
| 675 | * values between {@code x} and {@code y}. |
| 676 | * @return {@code true} if there are fewer than {@code maxUlps} floating |
| 677 | * point values between {@code x} and {@code y}. |
| 678 | */ |
| 679 | public static boolean equals(double x, double y, int maxUlps) { |
| 680 | // Check that "maxUlps" is non-negative and small enough so that |
| 681 | // NaN won't compare as equal to anything (except another NaN). |
| 682 | assert maxUlps > 0 && maxUlps < NAN_GAP; |
| 683 | |
| 684 | long xInt = Double.doubleToLongBits(x); |
| 685 | long yInt = Double.doubleToLongBits(y); |
| 686 | |
| 687 | // Make lexicographically ordered as a two's-complement integer. |
| 688 | if (xInt < 0) { |
| 689 | xInt = SGN_MASK - xInt; |
| 690 | } |
| 691 | if (yInt < 0) { |
| 692 | yInt = SGN_MASK - yInt; |
| 693 | } |
| 694 | |
| 695 | return FastMath.abs(xInt - yInt) <= maxUlps; |
| 696 | } |
| 697 | |
| 698 | /** |
| 699 | * Returns true if both arguments are NaN or if they are equal as defined |
| 700 | * by {@link #equals(double,double,int) equals(x, y, maxUlps}. |
| 701 | * |
| 702 | * @param x first value |
| 703 | * @param y second value |
| 704 | * @param maxUlps {@code (maxUlps - 1)} is the number of floating point |
| 705 | * values between {@code x} and {@code y}. |
| 706 | * @return {@code true} if both arguments are NaN or if there are less than |
| 707 | * {@code maxUlps} floating point values between {@code x} and {@code y}. |
| 708 | * @since 2.2 |
| 709 | */ |
| 710 | public static boolean equalsIncludingNaN(double x, double y, int maxUlps) { |
| 711 | return (Double.isNaN(x) && Double.isNaN(y)) || equals(x, y, maxUlps); |
| 712 | } |
| 713 | |
| 714 | /** |
| 715 | * Returns true iff both arguments are null or have same dimensions and all |
| 716 | * their elements are equal as defined by |
| 717 | * {@link #equals(double,double)}. |
| 718 | * |
| 719 | * <p>This method considers that {@code NaN == NaN}. In release |
| 720 | * 3.0, the semantics will change in order to comply with IEEE754 where it |
| 721 | * is specified that {@code NaN != NaN}. |
| 722 | * New methods have been added for those cases wher the old semantics is |
| 723 | * useful (see e.g. {@link #equalsIncludingNaN(double[],double[]) |
| 724 | * equalsIncludingNaN}. |
| 725 | * </p> |
| 726 | * @param x first array |
| 727 | * @param y second array |
| 728 | * @return true if the values are both null or have same dimension |
| 729 | * and equal elements. |
| 730 | */ |
| 731 | public static boolean equals(double[] x, double[] y) { |
| 732 | if ((x == null) || (y == null)) { |
| 733 | return !((x == null) ^ (y == null)); |
| 734 | } |
| 735 | if (x.length != y.length) { |
| 736 | return false; |
| 737 | } |
| 738 | for (int i = 0; i < x.length; ++i) { |
| 739 | if (!equals(x[i], y[i])) { |
| 740 | return false; |
| 741 | } |
| 742 | } |
| 743 | return true; |
| 744 | } |
| 745 | |
| 746 | /** |
| 747 | * Returns true iff both arguments are null or have same dimensions and all |
| 748 | * their elements are equal as defined by |
| 749 | * {@link #equalsIncludingNaN(double,double)}. |
| 750 | * |
| 751 | * @param x first array |
| 752 | * @param y second array |
| 753 | * @return true if the values are both null or have same dimension and |
| 754 | * equal elements |
| 755 | * @since 2.2 |
| 756 | */ |
| 757 | public static boolean equalsIncludingNaN(double[] x, double[] y) { |
| 758 | if ((x == null) || (y == null)) { |
| 759 | return !((x == null) ^ (y == null)); |
| 760 | } |
| 761 | if (x.length != y.length) { |
| 762 | return false; |
| 763 | } |
| 764 | for (int i = 0; i < x.length; ++i) { |
| 765 | if (!equalsIncludingNaN(x[i], y[i])) { |
| 766 | return false; |
| 767 | } |
| 768 | } |
| 769 | return true; |
| 770 | } |
| 771 | |
| 772 | /** |
| 773 | * Returns n!. Shorthand for <code>n</code> <a |
| 774 | * href="http://mathworld.wolfram.com/Factorial.html"> Factorial</a>, the |
| 775 | * product of the numbers <code>1,...,n</code>. |
| 776 | * <p> |
| 777 | * <Strong>Preconditions</strong>: |
| 778 | * <ul> |
| 779 | * <li> <code>n >= 0</code> (otherwise |
| 780 | * <code>IllegalArgumentException</code> is thrown)</li> |
| 781 | * <li> The result is small enough to fit into a <code>long</code>. The |
| 782 | * largest value of <code>n</code> for which <code>n!</code> < |
| 783 | * Long.MAX_VALUE</code> is 20. If the computed value exceeds <code>Long.MAX_VALUE</code> |
| 784 | * an <code>ArithMeticException </code> is thrown.</li> |
| 785 | * </ul> |
| 786 | * </p> |
| 787 | * |
| 788 | * @param n argument |
| 789 | * @return <code>n!</code> |
| 790 | * @throws ArithmeticException if the result is too large to be represented |
| 791 | * by a long integer. |
| 792 | * @throws IllegalArgumentException if n < 0 |
| 793 | */ |
| 794 | public static long factorial(final int n) { |
| 795 | if (n < 0) { |
| 796 | throw MathRuntimeException.createIllegalArgumentException( |
| 797 | LocalizedFormats.FACTORIAL_NEGATIVE_PARAMETER, |
| 798 | n); |
| 799 | } |
| 800 | if (n > 20) { |
| 801 | throw new ArithmeticException( |
| 802 | "factorial value is too large to fit in a long"); |
| 803 | } |
| 804 | return FACTORIALS[n]; |
| 805 | } |
| 806 | |
| 807 | /** |
| 808 | * Returns n!. Shorthand for <code>n</code> <a |
| 809 | * href="http://mathworld.wolfram.com/Factorial.html"> Factorial</a>, the |
| 810 | * product of the numbers <code>1,...,n</code> as a <code>double</code>. |
| 811 | * <p> |
| 812 | * <Strong>Preconditions</strong>: |
| 813 | * <ul> |
| 814 | * <li> <code>n >= 0</code> (otherwise |
| 815 | * <code>IllegalArgumentException</code> is thrown)</li> |
| 816 | * <li> The result is small enough to fit into a <code>double</code>. The |
| 817 | * largest value of <code>n</code> for which <code>n!</code> < |
| 818 | * Double.MAX_VALUE</code> is 170. If the computed value exceeds |
| 819 | * Double.MAX_VALUE, Double.POSITIVE_INFINITY is returned</li> |
| 820 | * </ul> |
| 821 | * </p> |
| 822 | * |
| 823 | * @param n argument |
| 824 | * @return <code>n!</code> |
| 825 | * @throws IllegalArgumentException if n < 0 |
| 826 | */ |
| 827 | public static double factorialDouble(final int n) { |
| 828 | if (n < 0) { |
| 829 | throw MathRuntimeException.createIllegalArgumentException( |
| 830 | LocalizedFormats.FACTORIAL_NEGATIVE_PARAMETER, |
| 831 | n); |
| 832 | } |
| 833 | if (n < 21) { |
| 834 | return factorial(n); |
| 835 | } |
| 836 | return FastMath.floor(FastMath.exp(factorialLog(n)) + 0.5); |
| 837 | } |
| 838 | |
| 839 | /** |
| 840 | * Returns the natural logarithm of n!. |
| 841 | * <p> |
| 842 | * <Strong>Preconditions</strong>: |
| 843 | * <ul> |
| 844 | * <li> <code>n >= 0</code> (otherwise |
| 845 | * <code>IllegalArgumentException</code> is thrown)</li> |
| 846 | * </ul></p> |
| 847 | * |
| 848 | * @param n argument |
| 849 | * @return <code>n!</code> |
| 850 | * @throws IllegalArgumentException if preconditions are not met. |
| 851 | */ |
| 852 | public static double factorialLog(final int n) { |
| 853 | if (n < 0) { |
| 854 | throw MathRuntimeException.createIllegalArgumentException( |
| 855 | LocalizedFormats.FACTORIAL_NEGATIVE_PARAMETER, |
| 856 | n); |
| 857 | } |
| 858 | if (n < 21) { |
| 859 | return FastMath.log(factorial(n)); |
| 860 | } |
| 861 | double logSum = 0; |
| 862 | for (int i = 2; i <= n; i++) { |
| 863 | logSum += FastMath.log(i); |
| 864 | } |
| 865 | return logSum; |
| 866 | } |
| 867 | |
| 868 | /** |
| 869 | * <p> |
| 870 | * Gets the greatest common divisor of the absolute value of two numbers, |
| 871 | * using the "binary gcd" method which avoids division and modulo |
| 872 | * operations. See Knuth 4.5.2 algorithm B. This algorithm is due to Josef |
| 873 | * Stein (1961). |
| 874 | * </p> |
| 875 | * Special cases: |
| 876 | * <ul> |
| 877 | * <li>The invocations |
| 878 | * <code>gcd(Integer.MIN_VALUE, Integer.MIN_VALUE)</code>, |
| 879 | * <code>gcd(Integer.MIN_VALUE, 0)</code> and |
| 880 | * <code>gcd(0, Integer.MIN_VALUE)</code> throw an |
| 881 | * <code>ArithmeticException</code>, because the result would be 2^31, which |
| 882 | * is too large for an int value.</li> |
| 883 | * <li>The result of <code>gcd(x, x)</code>, <code>gcd(0, x)</code> and |
| 884 | * <code>gcd(x, 0)</code> is the absolute value of <code>x</code>, except |
| 885 | * for the special cases above. |
| 886 | * <li>The invocation <code>gcd(0, 0)</code> is the only one which returns |
| 887 | * <code>0</code>.</li> |
| 888 | * </ul> |
| 889 | * |
| 890 | * @param p any number |
| 891 | * @param q any number |
| 892 | * @return the greatest common divisor, never negative |
| 893 | * @throws ArithmeticException if the result cannot be represented as a |
| 894 | * nonnegative int value |
| 895 | * @since 1.1 |
| 896 | */ |
| 897 | public static int gcd(final int p, final int q) { |
| 898 | int u = p; |
| 899 | int v = q; |
| 900 | if ((u == 0) || (v == 0)) { |
| 901 | if ((u == Integer.MIN_VALUE) || (v == Integer.MIN_VALUE)) { |
| 902 | throw MathRuntimeException.createArithmeticException( |
| 903 | LocalizedFormats.GCD_OVERFLOW_32_BITS, |
| 904 | p, q); |
| 905 | } |
| 906 | return FastMath.abs(u) + FastMath.abs(v); |
| 907 | } |
| 908 | // keep u and v negative, as negative integers range down to |
| 909 | // -2^31, while positive numbers can only be as large as 2^31-1 |
| 910 | // (i.e. we can't necessarily negate a negative number without |
| 911 | // overflow) |
| 912 | /* assert u!=0 && v!=0; */ |
| 913 | if (u > 0) { |
| 914 | u = -u; |
| 915 | } // make u negative |
| 916 | if (v > 0) { |
| 917 | v = -v; |
| 918 | } // make v negative |
| 919 | // B1. [Find power of 2] |
| 920 | int k = 0; |
| 921 | while ((u & 1) == 0 && (v & 1) == 0 && k < 31) { // while u and v are |
| 922 | // both even... |
| 923 | u /= 2; |
| 924 | v /= 2; |
| 925 | k++; // cast out twos. |
| 926 | } |
| 927 | if (k == 31) { |
| 928 | throw MathRuntimeException.createArithmeticException( |
| 929 | LocalizedFormats.GCD_OVERFLOW_32_BITS, |
| 930 | p, q); |
| 931 | } |
| 932 | // B2. Initialize: u and v have been divided by 2^k and at least |
| 933 | // one is odd. |
| 934 | int t = ((u & 1) == 1) ? v : -(u / 2)/* B3 */; |
| 935 | // t negative: u was odd, v may be even (t replaces v) |
| 936 | // t positive: u was even, v is odd (t replaces u) |
| 937 | do { |
| 938 | /* assert u<0 && v<0; */ |
| 939 | // B4/B3: cast out twos from t. |
| 940 | while ((t & 1) == 0) { // while t is even.. |
| 941 | t /= 2; // cast out twos |
| 942 | } |
| 943 | // B5 [reset max(u,v)] |
| 944 | if (t > 0) { |
| 945 | u = -t; |
| 946 | } else { |
| 947 | v = t; |
| 948 | } |
| 949 | // B6/B3. at this point both u and v should be odd. |
| 950 | t = (v - u) / 2; |
| 951 | // |u| larger: t positive (replace u) |
| 952 | // |v| larger: t negative (replace v) |
| 953 | } while (t != 0); |
| 954 | return -u * (1 << k); // gcd is u*2^k |
| 955 | } |
| 956 | |
| 957 | /** |
| 958 | * <p> |
| 959 | * Gets the greatest common divisor of the absolute value of two numbers, |
| 960 | * using the "binary gcd" method which avoids division and modulo |
| 961 | * operations. See Knuth 4.5.2 algorithm B. This algorithm is due to Josef |
| 962 | * Stein (1961). |
| 963 | * </p> |
| 964 | * Special cases: |
| 965 | * <ul> |
| 966 | * <li>The invocations |
| 967 | * <code>gcd(Long.MIN_VALUE, Long.MIN_VALUE)</code>, |
| 968 | * <code>gcd(Long.MIN_VALUE, 0L)</code> and |
| 969 | * <code>gcd(0L, Long.MIN_VALUE)</code> throw an |
| 970 | * <code>ArithmeticException</code>, because the result would be 2^63, which |
| 971 | * is too large for a long value.</li> |
| 972 | * <li>The result of <code>gcd(x, x)</code>, <code>gcd(0L, x)</code> and |
| 973 | * <code>gcd(x, 0L)</code> is the absolute value of <code>x</code>, except |
| 974 | * for the special cases above. |
| 975 | * <li>The invocation <code>gcd(0L, 0L)</code> is the only one which returns |
| 976 | * <code>0L</code>.</li> |
| 977 | * </ul> |
| 978 | * |
| 979 | * @param p any number |
| 980 | * @param q any number |
| 981 | * @return the greatest common divisor, never negative |
| 982 | * @throws ArithmeticException if the result cannot be represented as a nonnegative long |
| 983 | * value |
| 984 | * @since 2.1 |
| 985 | */ |
| 986 | public static long gcd(final long p, final long q) { |
| 987 | long u = p; |
| 988 | long v = q; |
| 989 | if ((u == 0) || (v == 0)) { |
| 990 | if ((u == Long.MIN_VALUE) || (v == Long.MIN_VALUE)){ |
| 991 | throw MathRuntimeException.createArithmeticException( |
| 992 | LocalizedFormats.GCD_OVERFLOW_64_BITS, |
| 993 | p, q); |
| 994 | } |
| 995 | return FastMath.abs(u) + FastMath.abs(v); |
| 996 | } |
| 997 | // keep u and v negative, as negative integers range down to |
| 998 | // -2^63, while positive numbers can only be as large as 2^63-1 |
| 999 | // (i.e. we can't necessarily negate a negative number without |
| 1000 | // overflow) |
| 1001 | /* assert u!=0 && v!=0; */ |
| 1002 | if (u > 0) { |
| 1003 | u = -u; |
| 1004 | } // make u negative |
| 1005 | if (v > 0) { |
| 1006 | v = -v; |
| 1007 | } // make v negative |
| 1008 | // B1. [Find power of 2] |
| 1009 | int k = 0; |
| 1010 | while ((u & 1) == 0 && (v & 1) == 0 && k < 63) { // while u and v are |
| 1011 | // both even... |
| 1012 | u /= 2; |
| 1013 | v /= 2; |
| 1014 | k++; // cast out twos. |
| 1015 | } |
| 1016 | if (k == 63) { |
| 1017 | throw MathRuntimeException.createArithmeticException( |
| 1018 | LocalizedFormats.GCD_OVERFLOW_64_BITS, |
| 1019 | p, q); |
| 1020 | } |
| 1021 | // B2. Initialize: u and v have been divided by 2^k and at least |
| 1022 | // one is odd. |
| 1023 | long t = ((u & 1) == 1) ? v : -(u / 2)/* B3 */; |
| 1024 | // t negative: u was odd, v may be even (t replaces v) |
| 1025 | // t positive: u was even, v is odd (t replaces u) |
| 1026 | do { |
| 1027 | /* assert u<0 && v<0; */ |
| 1028 | // B4/B3: cast out twos from t. |
| 1029 | while ((t & 1) == 0) { // while t is even.. |
| 1030 | t /= 2; // cast out twos |
| 1031 | } |
| 1032 | // B5 [reset max(u,v)] |
| 1033 | if (t > 0) { |
| 1034 | u = -t; |
| 1035 | } else { |
| 1036 | v = t; |
| 1037 | } |
| 1038 | // B6/B3. at this point both u and v should be odd. |
| 1039 | t = (v - u) / 2; |
| 1040 | // |u| larger: t positive (replace u) |
| 1041 | // |v| larger: t negative (replace v) |
| 1042 | } while (t != 0); |
| 1043 | return -u * (1L << k); // gcd is u*2^k |
| 1044 | } |
| 1045 | |
| 1046 | /** |
| 1047 | * Returns an integer hash code representing the given double value. |
| 1048 | * |
| 1049 | * @param value the value to be hashed |
| 1050 | * @return the hash code |
| 1051 | */ |
| 1052 | public static int hash(double value) { |
| 1053 | return new Double(value).hashCode(); |
| 1054 | } |
| 1055 | |
| 1056 | /** |
| 1057 | * Returns an integer hash code representing the given double array. |
| 1058 | * |
| 1059 | * @param value the value to be hashed (may be null) |
| 1060 | * @return the hash code |
| 1061 | * @since 1.2 |
| 1062 | */ |
| 1063 | public static int hash(double[] value) { |
| 1064 | return Arrays.hashCode(value); |
| 1065 | } |
| 1066 | |
| 1067 | /** |
| 1068 | * For a byte value x, this method returns (byte)(+1) if x >= 0 and |
| 1069 | * (byte)(-1) if x < 0. |
| 1070 | * |
| 1071 | * @param x the value, a byte |
| 1072 | * @return (byte)(+1) or (byte)(-1), depending on the sign of x |
| 1073 | */ |
| 1074 | public static byte indicator(final byte x) { |
| 1075 | return (x >= ZB) ? PB : NB; |
| 1076 | } |
| 1077 | |
| 1078 | /** |
| 1079 | * For a double precision value x, this method returns +1.0 if x >= 0 and |
| 1080 | * -1.0 if x < 0. Returns <code>NaN</code> if <code>x</code> is |
| 1081 | * <code>NaN</code>. |
| 1082 | * |
| 1083 | * @param x the value, a double |
| 1084 | * @return +1.0 or -1.0, depending on the sign of x |
| 1085 | */ |
| 1086 | public static double indicator(final double x) { |
| 1087 | if (Double.isNaN(x)) { |
| 1088 | return Double.NaN; |
| 1089 | } |
| 1090 | return (x >= 0.0) ? 1.0 : -1.0; |
| 1091 | } |
| 1092 | |
| 1093 | /** |
| 1094 | * For a float value x, this method returns +1.0F if x >= 0 and -1.0F if x < |
| 1095 | * 0. Returns <code>NaN</code> if <code>x</code> is <code>NaN</code>. |
| 1096 | * |
| 1097 | * @param x the value, a float |
| 1098 | * @return +1.0F or -1.0F, depending on the sign of x |
| 1099 | */ |
| 1100 | public static float indicator(final float x) { |
| 1101 | if (Float.isNaN(x)) { |
| 1102 | return Float.NaN; |
| 1103 | } |
| 1104 | return (x >= 0.0F) ? 1.0F : -1.0F; |
| 1105 | } |
| 1106 | |
| 1107 | /** |
| 1108 | * For an int value x, this method returns +1 if x >= 0 and -1 if x < 0. |
| 1109 | * |
| 1110 | * @param x the value, an int |
| 1111 | * @return +1 or -1, depending on the sign of x |
| 1112 | */ |
| 1113 | public static int indicator(final int x) { |
| 1114 | return (x >= 0) ? 1 : -1; |
| 1115 | } |
| 1116 | |
| 1117 | /** |
| 1118 | * For a long value x, this method returns +1L if x >= 0 and -1L if x < 0. |
| 1119 | * |
| 1120 | * @param x the value, a long |
| 1121 | * @return +1L or -1L, depending on the sign of x |
| 1122 | */ |
| 1123 | public static long indicator(final long x) { |
| 1124 | return (x >= 0L) ? 1L : -1L; |
| 1125 | } |
| 1126 | |
| 1127 | /** |
| 1128 | * For a short value x, this method returns (short)(+1) if x >= 0 and |
| 1129 | * (short)(-1) if x < 0. |
| 1130 | * |
| 1131 | * @param x the value, a short |
| 1132 | * @return (short)(+1) or (short)(-1), depending on the sign of x |
| 1133 | */ |
| 1134 | public static short indicator(final short x) { |
| 1135 | return (x >= ZS) ? PS : NS; |
| 1136 | } |
| 1137 | |
| 1138 | /** |
| 1139 | * <p> |
| 1140 | * Returns the least common multiple of the absolute value of two numbers, |
| 1141 | * using the formula <code>lcm(a,b) = (a / gcd(a,b)) * b</code>. |
| 1142 | * </p> |
| 1143 | * Special cases: |
| 1144 | * <ul> |
| 1145 | * <li>The invocations <code>lcm(Integer.MIN_VALUE, n)</code> and |
| 1146 | * <code>lcm(n, Integer.MIN_VALUE)</code>, where <code>abs(n)</code> is a |
| 1147 | * power of 2, throw an <code>ArithmeticException</code>, because the result |
| 1148 | * would be 2^31, which is too large for an int value.</li> |
| 1149 | * <li>The result of <code>lcm(0, x)</code> and <code>lcm(x, 0)</code> is |
| 1150 | * <code>0</code> for any <code>x</code>. |
| 1151 | * </ul> |
| 1152 | * |
| 1153 | * @param a any number |
| 1154 | * @param b any number |
| 1155 | * @return the least common multiple, never negative |
| 1156 | * @throws ArithmeticException |
| 1157 | * if the result cannot be represented as a nonnegative int |
| 1158 | * value |
| 1159 | * @since 1.1 |
| 1160 | */ |
| 1161 | public static int lcm(int a, int b) { |
| 1162 | if (a==0 || b==0){ |
| 1163 | return 0; |
| 1164 | } |
| 1165 | int lcm = FastMath.abs(mulAndCheck(a / gcd(a, b), b)); |
| 1166 | if (lcm == Integer.MIN_VALUE) { |
| 1167 | throw MathRuntimeException.createArithmeticException( |
| 1168 | LocalizedFormats.LCM_OVERFLOW_32_BITS, |
| 1169 | a, b); |
| 1170 | } |
| 1171 | return lcm; |
| 1172 | } |
| 1173 | |
| 1174 | /** |
| 1175 | * <p> |
| 1176 | * Returns the least common multiple of the absolute value of two numbers, |
| 1177 | * using the formula <code>lcm(a,b) = (a / gcd(a,b)) * b</code>. |
| 1178 | * </p> |
| 1179 | * Special cases: |
| 1180 | * <ul> |
| 1181 | * <li>The invocations <code>lcm(Long.MIN_VALUE, n)</code> and |
| 1182 | * <code>lcm(n, Long.MIN_VALUE)</code>, where <code>abs(n)</code> is a |
| 1183 | * power of 2, throw an <code>ArithmeticException</code>, because the result |
| 1184 | * would be 2^63, which is too large for an int value.</li> |
| 1185 | * <li>The result of <code>lcm(0L, x)</code> and <code>lcm(x, 0L)</code> is |
| 1186 | * <code>0L</code> for any <code>x</code>. |
| 1187 | * </ul> |
| 1188 | * |
| 1189 | * @param a any number |
| 1190 | * @param b any number |
| 1191 | * @return the least common multiple, never negative |
| 1192 | * @throws ArithmeticException if the result cannot be represented as a nonnegative long |
| 1193 | * value |
| 1194 | * @since 2.1 |
| 1195 | */ |
| 1196 | public static long lcm(long a, long b) { |
| 1197 | if (a==0 || b==0){ |
| 1198 | return 0; |
| 1199 | } |
| 1200 | long lcm = FastMath.abs(mulAndCheck(a / gcd(a, b), b)); |
| 1201 | if (lcm == Long.MIN_VALUE){ |
| 1202 | throw MathRuntimeException.createArithmeticException( |
| 1203 | LocalizedFormats.LCM_OVERFLOW_64_BITS, |
| 1204 | a, b); |
| 1205 | } |
| 1206 | return lcm; |
| 1207 | } |
| 1208 | |
| 1209 | /** |
| 1210 | * <p>Returns the |
| 1211 | * <a href="http://mathworld.wolfram.com/Logarithm.html">logarithm</a> |
| 1212 | * for base <code>b</code> of <code>x</code>. |
| 1213 | * </p> |
| 1214 | * <p>Returns <code>NaN<code> if either argument is negative. If |
| 1215 | * <code>base</code> is 0 and <code>x</code> is positive, 0 is returned. |
| 1216 | * If <code>base</code> is positive and <code>x</code> is 0, |
| 1217 | * <code>Double.NEGATIVE_INFINITY</code> is returned. If both arguments |
| 1218 | * are 0, the result is <code>NaN</code>.</p> |
| 1219 | * |
| 1220 | * @param base the base of the logarithm, must be greater than 0 |
| 1221 | * @param x argument, must be greater than 0 |
| 1222 | * @return the value of the logarithm - the number y such that base^y = x. |
| 1223 | * @since 1.2 |
| 1224 | */ |
| 1225 | public static double log(double base, double x) { |
| 1226 | return FastMath.log(x)/FastMath.log(base); |
| 1227 | } |
| 1228 | |
| 1229 | /** |
| 1230 | * Multiply two integers, checking for overflow. |
| 1231 | * |
| 1232 | * @param x a factor |
| 1233 | * @param y a factor |
| 1234 | * @return the product <code>x*y</code> |
| 1235 | * @throws ArithmeticException if the result can not be represented as an |
| 1236 | * int |
| 1237 | * @since 1.1 |
| 1238 | */ |
| 1239 | public static int mulAndCheck(int x, int y) { |
| 1240 | long m = ((long)x) * ((long)y); |
| 1241 | if (m < Integer.MIN_VALUE || m > Integer.MAX_VALUE) { |
| 1242 | throw new ArithmeticException("overflow: mul"); |
| 1243 | } |
| 1244 | return (int)m; |
| 1245 | } |
| 1246 | |
| 1247 | /** |
| 1248 | * Multiply two long integers, checking for overflow. |
| 1249 | * |
| 1250 | * @param a first value |
| 1251 | * @param b second value |
| 1252 | * @return the product <code>a * b</code> |
| 1253 | * @throws ArithmeticException if the result can not be represented as an |
| 1254 | * long |
| 1255 | * @since 1.2 |
| 1256 | */ |
| 1257 | public static long mulAndCheck(long a, long b) { |
| 1258 | long ret; |
| 1259 | String msg = "overflow: multiply"; |
| 1260 | if (a > b) { |
| 1261 | // use symmetry to reduce boundary cases |
| 1262 | ret = mulAndCheck(b, a); |
| 1263 | } else { |
| 1264 | if (a < 0) { |
| 1265 | if (b < 0) { |
| 1266 | // check for positive overflow with negative a, negative b |
| 1267 | if (a >= Long.MAX_VALUE / b) { |
| 1268 | ret = a * b; |
| 1269 | } else { |
| 1270 | throw new ArithmeticException(msg); |
| 1271 | } |
| 1272 | } else if (b > 0) { |
| 1273 | // check for negative overflow with negative a, positive b |
| 1274 | if (Long.MIN_VALUE / b <= a) { |
| 1275 | ret = a * b; |
| 1276 | } else { |
| 1277 | throw new ArithmeticException(msg); |
| 1278 | |
| 1279 | } |
| 1280 | } else { |
| 1281 | // assert b == 0 |
| 1282 | ret = 0; |
| 1283 | } |
| 1284 | } else if (a > 0) { |
| 1285 | // assert a > 0 |
| 1286 | // assert b > 0 |
| 1287 | |
| 1288 | // check for positive overflow with positive a, positive b |
| 1289 | if (a <= Long.MAX_VALUE / b) { |
| 1290 | ret = a * b; |
| 1291 | } else { |
| 1292 | throw new ArithmeticException(msg); |
| 1293 | } |
| 1294 | } else { |
| 1295 | // assert a == 0 |
| 1296 | ret = 0; |
| 1297 | } |
| 1298 | } |
| 1299 | return ret; |
| 1300 | } |
| 1301 | |
| 1302 | /** |
| 1303 | * Get the next machine representable number after a number, moving |
| 1304 | * in the direction of another number. |
| 1305 | * <p> |
| 1306 | * If <code>direction</code> is greater than or equal to<code>d</code>, |
| 1307 | * the smallest machine representable number strictly greater than |
| 1308 | * <code>d</code> is returned; otherwise the largest representable number |
| 1309 | * strictly less than <code>d</code> is returned.</p> |
| 1310 | * <p> |
| 1311 | * If <code>d</code> is NaN or Infinite, it is returned unchanged.</p> |
| 1312 | * |
| 1313 | * @param d base number |
| 1314 | * @param direction (the only important thing is whether |
| 1315 | * direction is greater or smaller than d) |
| 1316 | * @return the next machine representable number in the specified direction |
| 1317 | * @since 1.2 |
| 1318 | * @deprecated as of 2.2, replaced by {@link FastMath#nextAfter(double, double)} |
| 1319 | * which handles Infinities differently, and returns direction if d and direction compare equal. |
| 1320 | */ |
| 1321 | @Deprecated |
| 1322 | public static double nextAfter(double d, double direction) { |
| 1323 | |
| 1324 | // handling of some important special cases |
| 1325 | if (Double.isNaN(d) || Double.isInfinite(d)) { |
| 1326 | return d; |
| 1327 | } else if (d == 0) { |
| 1328 | return (direction < 0) ? -Double.MIN_VALUE : Double.MIN_VALUE; |
| 1329 | } |
| 1330 | // special cases MAX_VALUE to infinity and MIN_VALUE to 0 |
| 1331 | // are handled just as normal numbers |
| 1332 | |
| 1333 | // split the double in raw components |
| 1334 | long bits = Double.doubleToLongBits(d); |
| 1335 | long sign = bits & 0x8000000000000000L; |
| 1336 | long exponent = bits & 0x7ff0000000000000L; |
| 1337 | long mantissa = bits & 0x000fffffffffffffL; |
| 1338 | |
| 1339 | if (d * (direction - d) >= 0) { |
| 1340 | // we should increase the mantissa |
| 1341 | if (mantissa == 0x000fffffffffffffL) { |
| 1342 | return Double.longBitsToDouble(sign | |
| 1343 | (exponent + 0x0010000000000000L)); |
| 1344 | } else { |
| 1345 | return Double.longBitsToDouble(sign | |
| 1346 | exponent | (mantissa + 1)); |
| 1347 | } |
| 1348 | } else { |
| 1349 | // we should decrease the mantissa |
| 1350 | if (mantissa == 0L) { |
| 1351 | return Double.longBitsToDouble(sign | |
| 1352 | (exponent - 0x0010000000000000L) | |
| 1353 | 0x000fffffffffffffL); |
| 1354 | } else { |
| 1355 | return Double.longBitsToDouble(sign | |
| 1356 | exponent | (mantissa - 1)); |
| 1357 | } |
| 1358 | } |
| 1359 | } |
| 1360 | |
| 1361 | /** |
| 1362 | * Scale a number by 2<sup>scaleFactor</sup>. |
| 1363 | * <p>If <code>d</code> is 0 or NaN or Infinite, it is returned unchanged.</p> |
| 1364 | * |
| 1365 | * @param d base number |
| 1366 | * @param scaleFactor power of two by which d should be multiplied |
| 1367 | * @return d × 2<sup>scaleFactor</sup> |
| 1368 | * @since 2.0 |
| 1369 | * @deprecated as of 2.2, replaced by {@link FastMath#scalb(double, int)} |
| 1370 | */ |
| 1371 | @Deprecated |
| 1372 | public static double scalb(final double d, final int scaleFactor) { |
| 1373 | return FastMath.scalb(d, scaleFactor); |
| 1374 | } |
| 1375 | |
| 1376 | /** |
| 1377 | * Normalize an angle in a 2&pi wide interval around a center value. |
| 1378 | * <p>This method has three main uses:</p> |
| 1379 | * <ul> |
| 1380 | * <li>normalize an angle between 0 and 2π:<br/> |
| 1381 | * <code>a = MathUtils.normalizeAngle(a, FastMath.PI);</code></li> |
| 1382 | * <li>normalize an angle between -π and +π<br/> |
| 1383 | * <code>a = MathUtils.normalizeAngle(a, 0.0);</code></li> |
| 1384 | * <li>compute the angle between two defining angular positions:<br> |
| 1385 | * <code>angle = MathUtils.normalizeAngle(end, start) - start;</code></li> |
| 1386 | * </ul> |
| 1387 | * <p>Note that due to numerical accuracy and since π cannot be represented |
| 1388 | * exactly, the result interval is <em>closed</em>, it cannot be half-closed |
| 1389 | * as would be more satisfactory in a purely mathematical view.</p> |
| 1390 | * @param a angle to normalize |
| 1391 | * @param center center of the desired 2π interval for the result |
| 1392 | * @return a-2kπ with integer k and center-π <= a-2kπ <= center+π |
| 1393 | * @since 1.2 |
| 1394 | */ |
| 1395 | public static double normalizeAngle(double a, double center) { |
| 1396 | return a - TWO_PI * FastMath.floor((a + FastMath.PI - center) / TWO_PI); |
| 1397 | } |
| 1398 | |
| 1399 | /** |
| 1400 | * <p>Normalizes an array to make it sum to a specified value. |
| 1401 | * Returns the result of the transformation <pre> |
| 1402 | * x |-> x * normalizedSum / sum |
| 1403 | * </pre> |
| 1404 | * applied to each non-NaN element x of the input array, where sum is the |
| 1405 | * sum of the non-NaN entries in the input array.</p> |
| 1406 | * |
| 1407 | * <p>Throws IllegalArgumentException if <code>normalizedSum</code> is infinite |
| 1408 | * or NaN and ArithmeticException if the input array contains any infinite elements |
| 1409 | * or sums to 0</p> |
| 1410 | * |
| 1411 | * <p>Ignores (i.e., copies unchanged to the output array) NaNs in the input array.</p> |
| 1412 | * |
| 1413 | * @param values input array to be normalized |
| 1414 | * @param normalizedSum target sum for the normalized array |
| 1415 | * @return normalized array |
| 1416 | * @throws ArithmeticException if the input array contains infinite elements or sums to zero |
| 1417 | * @throws IllegalArgumentException if the target sum is infinite or NaN |
| 1418 | * @since 2.1 |
| 1419 | */ |
| 1420 | public static double[] normalizeArray(double[] values, double normalizedSum) |
| 1421 | throws ArithmeticException, IllegalArgumentException { |
| 1422 | if (Double.isInfinite(normalizedSum)) { |
| 1423 | throw MathRuntimeException.createIllegalArgumentException( |
| 1424 | LocalizedFormats.NORMALIZE_INFINITE); |
| 1425 | } |
| 1426 | if (Double.isNaN(normalizedSum)) { |
| 1427 | throw MathRuntimeException.createIllegalArgumentException( |
| 1428 | LocalizedFormats.NORMALIZE_NAN); |
| 1429 | } |
| 1430 | double sum = 0d; |
| 1431 | final int len = values.length; |
| 1432 | double[] out = new double[len]; |
| 1433 | for (int i = 0; i < len; i++) { |
| 1434 | if (Double.isInfinite(values[i])) { |
| 1435 | throw MathRuntimeException.createArithmeticException( |
| 1436 | LocalizedFormats.INFINITE_ARRAY_ELEMENT, values[i], i); |
| 1437 | } |
| 1438 | if (!Double.isNaN(values[i])) { |
| 1439 | sum += values[i]; |
| 1440 | } |
| 1441 | } |
| 1442 | if (sum == 0) { |
| 1443 | throw MathRuntimeException.createArithmeticException(LocalizedFormats.ARRAY_SUMS_TO_ZERO); |
| 1444 | } |
| 1445 | for (int i = 0; i < len; i++) { |
| 1446 | if (Double.isNaN(values[i])) { |
| 1447 | out[i] = Double.NaN; |
| 1448 | } else { |
| 1449 | out[i] = values[i] * normalizedSum / sum; |
| 1450 | } |
| 1451 | } |
| 1452 | return out; |
| 1453 | } |
| 1454 | |
| 1455 | /** |
| 1456 | * Round the given value to the specified number of decimal places. The |
| 1457 | * value is rounded using the {@link BigDecimal#ROUND_HALF_UP} method. |
| 1458 | * |
| 1459 | * @param x the value to round. |
| 1460 | * @param scale the number of digits to the right of the decimal point. |
| 1461 | * @return the rounded value. |
| 1462 | * @since 1.1 |
| 1463 | */ |
| 1464 | public static double round(double x, int scale) { |
| 1465 | return round(x, scale, BigDecimal.ROUND_HALF_UP); |
| 1466 | } |
| 1467 | |
| 1468 | /** |
| 1469 | * Round the given value to the specified number of decimal places. The |
| 1470 | * value is rounded using the given method which is any method defined in |
| 1471 | * {@link BigDecimal}. |
| 1472 | * |
| 1473 | * @param x the value to round. |
| 1474 | * @param scale the number of digits to the right of the decimal point. |
| 1475 | * @param roundingMethod the rounding method as defined in |
| 1476 | * {@link BigDecimal}. |
| 1477 | * @return the rounded value. |
| 1478 | * @since 1.1 |
| 1479 | */ |
| 1480 | public static double round(double x, int scale, int roundingMethod) { |
| 1481 | try { |
| 1482 | return (new BigDecimal |
| 1483 | (Double.toString(x)) |
| 1484 | .setScale(scale, roundingMethod)) |
| 1485 | .doubleValue(); |
| 1486 | } catch (NumberFormatException ex) { |
| 1487 | if (Double.isInfinite(x)) { |
| 1488 | return x; |
| 1489 | } else { |
| 1490 | return Double.NaN; |
| 1491 | } |
| 1492 | } |
| 1493 | } |
| 1494 | |
| 1495 | /** |
| 1496 | * Round the given value to the specified number of decimal places. The |
| 1497 | * value is rounding using the {@link BigDecimal#ROUND_HALF_UP} method. |
| 1498 | * |
| 1499 | * @param x the value to round. |
| 1500 | * @param scale the number of digits to the right of the decimal point. |
| 1501 | * @return the rounded value. |
| 1502 | * @since 1.1 |
| 1503 | */ |
| 1504 | public static float round(float x, int scale) { |
| 1505 | return round(x, scale, BigDecimal.ROUND_HALF_UP); |
| 1506 | } |
| 1507 | |
| 1508 | /** |
| 1509 | * Round the given value to the specified number of decimal places. The |
| 1510 | * value is rounded using the given method which is any method defined in |
| 1511 | * {@link BigDecimal}. |
| 1512 | * |
| 1513 | * @param x the value to round. |
| 1514 | * @param scale the number of digits to the right of the decimal point. |
| 1515 | * @param roundingMethod the rounding method as defined in |
| 1516 | * {@link BigDecimal}. |
| 1517 | * @return the rounded value. |
| 1518 | * @since 1.1 |
| 1519 | */ |
| 1520 | public static float round(float x, int scale, int roundingMethod) { |
| 1521 | float sign = indicator(x); |
| 1522 | float factor = (float)FastMath.pow(10.0f, scale) * sign; |
| 1523 | return (float)roundUnscaled(x * factor, sign, roundingMethod) / factor; |
| 1524 | } |
| 1525 | |
| 1526 | /** |
| 1527 | * Round the given non-negative, value to the "nearest" integer. Nearest is |
| 1528 | * determined by the rounding method specified. Rounding methods are defined |
| 1529 | * in {@link BigDecimal}. |
| 1530 | * |
| 1531 | * @param unscaled the value to round. |
| 1532 | * @param sign the sign of the original, scaled value. |
| 1533 | * @param roundingMethod the rounding method as defined in |
| 1534 | * {@link BigDecimal}. |
| 1535 | * @return the rounded value. |
| 1536 | * @since 1.1 |
| 1537 | */ |
| 1538 | private static double roundUnscaled(double unscaled, double sign, |
| 1539 | int roundingMethod) { |
| 1540 | switch (roundingMethod) { |
| 1541 | case BigDecimal.ROUND_CEILING : |
| 1542 | if (sign == -1) { |
| 1543 | unscaled = FastMath.floor(nextAfter(unscaled, Double.NEGATIVE_INFINITY)); |
| 1544 | } else { |
| 1545 | unscaled = FastMath.ceil(nextAfter(unscaled, Double.POSITIVE_INFINITY)); |
| 1546 | } |
| 1547 | break; |
| 1548 | case BigDecimal.ROUND_DOWN : |
| 1549 | unscaled = FastMath.floor(nextAfter(unscaled, Double.NEGATIVE_INFINITY)); |
| 1550 | break; |
| 1551 | case BigDecimal.ROUND_FLOOR : |
| 1552 | if (sign == -1) { |
| 1553 | unscaled = FastMath.ceil(nextAfter(unscaled, Double.POSITIVE_INFINITY)); |
| 1554 | } else { |
| 1555 | unscaled = FastMath.floor(nextAfter(unscaled, Double.NEGATIVE_INFINITY)); |
| 1556 | } |
| 1557 | break; |
| 1558 | case BigDecimal.ROUND_HALF_DOWN : { |
| 1559 | unscaled = nextAfter(unscaled, Double.NEGATIVE_INFINITY); |
| 1560 | double fraction = unscaled - FastMath.floor(unscaled); |
| 1561 | if (fraction > 0.5) { |
| 1562 | unscaled = FastMath.ceil(unscaled); |
| 1563 | } else { |
| 1564 | unscaled = FastMath.floor(unscaled); |
| 1565 | } |
| 1566 | break; |
| 1567 | } |
| 1568 | case BigDecimal.ROUND_HALF_EVEN : { |
| 1569 | double fraction = unscaled - FastMath.floor(unscaled); |
| 1570 | if (fraction > 0.5) { |
| 1571 | unscaled = FastMath.ceil(unscaled); |
| 1572 | } else if (fraction < 0.5) { |
| 1573 | unscaled = FastMath.floor(unscaled); |
| 1574 | } else { |
| 1575 | // The following equality test is intentional and needed for rounding purposes |
| 1576 | if (FastMath.floor(unscaled) / 2.0 == FastMath.floor(Math |
| 1577 | .floor(unscaled) / 2.0)) { // even |
| 1578 | unscaled = FastMath.floor(unscaled); |
| 1579 | } else { // odd |
| 1580 | unscaled = FastMath.ceil(unscaled); |
| 1581 | } |
| 1582 | } |
| 1583 | break; |
| 1584 | } |
| 1585 | case BigDecimal.ROUND_HALF_UP : { |
| 1586 | unscaled = nextAfter(unscaled, Double.POSITIVE_INFINITY); |
| 1587 | double fraction = unscaled - FastMath.floor(unscaled); |
| 1588 | if (fraction >= 0.5) { |
| 1589 | unscaled = FastMath.ceil(unscaled); |
| 1590 | } else { |
| 1591 | unscaled = FastMath.floor(unscaled); |
| 1592 | } |
| 1593 | break; |
| 1594 | } |
| 1595 | case BigDecimal.ROUND_UNNECESSARY : |
| 1596 | if (unscaled != FastMath.floor(unscaled)) { |
| 1597 | throw new ArithmeticException("Inexact result from rounding"); |
| 1598 | } |
| 1599 | break; |
| 1600 | case BigDecimal.ROUND_UP : |
| 1601 | unscaled = FastMath.ceil(nextAfter(unscaled, Double.POSITIVE_INFINITY)); |
| 1602 | break; |
| 1603 | default : |
| 1604 | throw MathRuntimeException.createIllegalArgumentException( |
| 1605 | LocalizedFormats.INVALID_ROUNDING_METHOD, |
| 1606 | roundingMethod, |
| 1607 | "ROUND_CEILING", BigDecimal.ROUND_CEILING, |
| 1608 | "ROUND_DOWN", BigDecimal.ROUND_DOWN, |
| 1609 | "ROUND_FLOOR", BigDecimal.ROUND_FLOOR, |
| 1610 | "ROUND_HALF_DOWN", BigDecimal.ROUND_HALF_DOWN, |
| 1611 | "ROUND_HALF_EVEN", BigDecimal.ROUND_HALF_EVEN, |
| 1612 | "ROUND_HALF_UP", BigDecimal.ROUND_HALF_UP, |
| 1613 | "ROUND_UNNECESSARY", BigDecimal.ROUND_UNNECESSARY, |
| 1614 | "ROUND_UP", BigDecimal.ROUND_UP); |
| 1615 | } |
| 1616 | return unscaled; |
| 1617 | } |
| 1618 | |
| 1619 | /** |
| 1620 | * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a> |
| 1621 | * for byte value <code>x</code>. |
| 1622 | * <p> |
| 1623 | * For a byte value x, this method returns (byte)(+1) if x > 0, (byte)(0) if |
| 1624 | * x = 0, and (byte)(-1) if x < 0.</p> |
| 1625 | * |
| 1626 | * @param x the value, a byte |
| 1627 | * @return (byte)(+1), (byte)(0), or (byte)(-1), depending on the sign of x |
| 1628 | */ |
| 1629 | public static byte sign(final byte x) { |
| 1630 | return (x == ZB) ? ZB : (x > ZB) ? PB : NB; |
| 1631 | } |
| 1632 | |
| 1633 | /** |
| 1634 | * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a> |
| 1635 | * for double precision <code>x</code>. |
| 1636 | * <p> |
| 1637 | * For a double value <code>x</code>, this method returns |
| 1638 | * <code>+1.0</code> if <code>x > 0</code>, <code>0.0</code> if |
| 1639 | * <code>x = 0.0</code>, and <code>-1.0</code> if <code>x < 0</code>. |
| 1640 | * Returns <code>NaN</code> if <code>x</code> is <code>NaN</code>.</p> |
| 1641 | * |
| 1642 | * @param x the value, a double |
| 1643 | * @return +1.0, 0.0, or -1.0, depending on the sign of x |
| 1644 | */ |
| 1645 | public static double sign(final double x) { |
| 1646 | if (Double.isNaN(x)) { |
| 1647 | return Double.NaN; |
| 1648 | } |
| 1649 | return (x == 0.0) ? 0.0 : (x > 0.0) ? 1.0 : -1.0; |
| 1650 | } |
| 1651 | |
| 1652 | /** |
| 1653 | * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a> |
| 1654 | * for float value <code>x</code>. |
| 1655 | * <p> |
| 1656 | * For a float value x, this method returns +1.0F if x > 0, 0.0F if x = |
| 1657 | * 0.0F, and -1.0F if x < 0. Returns <code>NaN</code> if <code>x</code> |
| 1658 | * is <code>NaN</code>.</p> |
| 1659 | * |
| 1660 | * @param x the value, a float |
| 1661 | * @return +1.0F, 0.0F, or -1.0F, depending on the sign of x |
| 1662 | */ |
| 1663 | public static float sign(final float x) { |
| 1664 | if (Float.isNaN(x)) { |
| 1665 | return Float.NaN; |
| 1666 | } |
| 1667 | return (x == 0.0F) ? 0.0F : (x > 0.0F) ? 1.0F : -1.0F; |
| 1668 | } |
| 1669 | |
| 1670 | /** |
| 1671 | * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a> |
| 1672 | * for int value <code>x</code>. |
| 1673 | * <p> |
| 1674 | * For an int value x, this method returns +1 if x > 0, 0 if x = 0, and -1 |
| 1675 | * if x < 0.</p> |
| 1676 | * |
| 1677 | * @param x the value, an int |
| 1678 | * @return +1, 0, or -1, depending on the sign of x |
| 1679 | */ |
| 1680 | public static int sign(final int x) { |
| 1681 | return (x == 0) ? 0 : (x > 0) ? 1 : -1; |
| 1682 | } |
| 1683 | |
| 1684 | /** |
| 1685 | * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a> |
| 1686 | * for long value <code>x</code>. |
| 1687 | * <p> |
| 1688 | * For a long value x, this method returns +1L if x > 0, 0L if x = 0, and |
| 1689 | * -1L if x < 0.</p> |
| 1690 | * |
| 1691 | * @param x the value, a long |
| 1692 | * @return +1L, 0L, or -1L, depending on the sign of x |
| 1693 | */ |
| 1694 | public static long sign(final long x) { |
| 1695 | return (x == 0L) ? 0L : (x > 0L) ? 1L : -1L; |
| 1696 | } |
| 1697 | |
| 1698 | /** |
| 1699 | * Returns the <a href="http://mathworld.wolfram.com/Sign.html"> sign</a> |
| 1700 | * for short value <code>x</code>. |
| 1701 | * <p> |
| 1702 | * For a short value x, this method returns (short)(+1) if x > 0, (short)(0) |
| 1703 | * if x = 0, and (short)(-1) if x < 0.</p> |
| 1704 | * |
| 1705 | * @param x the value, a short |
| 1706 | * @return (short)(+1), (short)(0), or (short)(-1), depending on the sign of |
| 1707 | * x |
| 1708 | */ |
| 1709 | public static short sign(final short x) { |
| 1710 | return (x == ZS) ? ZS : (x > ZS) ? PS : NS; |
| 1711 | } |
| 1712 | |
| 1713 | /** |
| 1714 | * Returns the <a href="http://mathworld.wolfram.com/HyperbolicSine.html"> |
| 1715 | * hyperbolic sine</a> of x. |
| 1716 | * |
| 1717 | * @param x double value for which to find the hyperbolic sine |
| 1718 | * @return hyperbolic sine of x |
| 1719 | */ |
| 1720 | public static double sinh(double x) { |
| 1721 | return (FastMath.exp(x) - FastMath.exp(-x)) / 2.0; |
| 1722 | } |
| 1723 | |
| 1724 | /** |
| 1725 | * Subtract two integers, checking for overflow. |
| 1726 | * |
| 1727 | * @param x the minuend |
| 1728 | * @param y the subtrahend |
| 1729 | * @return the difference <code>x-y</code> |
| 1730 | * @throws ArithmeticException if the result can not be represented as an |
| 1731 | * int |
| 1732 | * @since 1.1 |
| 1733 | */ |
| 1734 | public static int subAndCheck(int x, int y) { |
| 1735 | long s = (long)x - (long)y; |
| 1736 | if (s < Integer.MIN_VALUE || s > Integer.MAX_VALUE) { |
| 1737 | throw MathRuntimeException.createArithmeticException(LocalizedFormats.OVERFLOW_IN_SUBTRACTION, x, y); |
| 1738 | } |
| 1739 | return (int)s; |
| 1740 | } |
| 1741 | |
| 1742 | /** |
| 1743 | * Subtract two long integers, checking for overflow. |
| 1744 | * |
| 1745 | * @param a first value |
| 1746 | * @param b second value |
| 1747 | * @return the difference <code>a-b</code> |
| 1748 | * @throws ArithmeticException if the result can not be represented as an |
| 1749 | * long |
| 1750 | * @since 1.2 |
| 1751 | */ |
| 1752 | public static long subAndCheck(long a, long b) { |
| 1753 | long ret; |
| 1754 | String msg = "overflow: subtract"; |
| 1755 | if (b == Long.MIN_VALUE) { |
| 1756 | if (a < 0) { |
| 1757 | ret = a - b; |
| 1758 | } else { |
| 1759 | throw new ArithmeticException(msg); |
| 1760 | } |
| 1761 | } else { |
| 1762 | // use additive inverse |
| 1763 | ret = addAndCheck(a, -b, LocalizedFormats.OVERFLOW_IN_ADDITION); |
| 1764 | } |
| 1765 | return ret; |
| 1766 | } |
| 1767 | |
| 1768 | /** |
| 1769 | * Raise an int to an int power. |
| 1770 | * @param k number to raise |
| 1771 | * @param e exponent (must be positive or null) |
| 1772 | * @return k<sup>e</sup> |
| 1773 | * @exception IllegalArgumentException if e is negative |
| 1774 | */ |
| 1775 | public static int pow(final int k, int e) |
| 1776 | throws IllegalArgumentException { |
| 1777 | |
| 1778 | if (e < 0) { |
| 1779 | throw MathRuntimeException.createIllegalArgumentException( |
| 1780 | LocalizedFormats.POWER_NEGATIVE_PARAMETERS, |
| 1781 | k, e); |
| 1782 | } |
| 1783 | |
| 1784 | int result = 1; |
| 1785 | int k2p = k; |
| 1786 | while (e != 0) { |
| 1787 | if ((e & 0x1) != 0) { |
| 1788 | result *= k2p; |
| 1789 | } |
| 1790 | k2p *= k2p; |
| 1791 | e = e >> 1; |
| 1792 | } |
| 1793 | |
| 1794 | return result; |
| 1795 | |
| 1796 | } |
| 1797 | |
| 1798 | /** |
| 1799 | * Raise an int to a long power. |
| 1800 | * @param k number to raise |
| 1801 | * @param e exponent (must be positive or null) |
| 1802 | * @return k<sup>e</sup> |
| 1803 | * @exception IllegalArgumentException if e is negative |
| 1804 | */ |
| 1805 | public static int pow(final int k, long e) |
| 1806 | throws IllegalArgumentException { |
| 1807 | |
| 1808 | if (e < 0) { |
| 1809 | throw MathRuntimeException.createIllegalArgumentException( |
| 1810 | LocalizedFormats.POWER_NEGATIVE_PARAMETERS, |
| 1811 | k, e); |
| 1812 | } |
| 1813 | |
| 1814 | int result = 1; |
| 1815 | int k2p = k; |
| 1816 | while (e != 0) { |
| 1817 | if ((e & 0x1) != 0) { |
| 1818 | result *= k2p; |
| 1819 | } |
| 1820 | k2p *= k2p; |
| 1821 | e = e >> 1; |
| 1822 | } |
| 1823 | |
| 1824 | return result; |
| 1825 | |
| 1826 | } |
| 1827 | |
| 1828 | /** |
| 1829 | * Raise a long to an int power. |
| 1830 | * @param k number to raise |
| 1831 | * @param e exponent (must be positive or null) |
| 1832 | * @return k<sup>e</sup> |
| 1833 | * @exception IllegalArgumentException if e is negative |
| 1834 | */ |
| 1835 | public static long pow(final long k, int e) |
| 1836 | throws IllegalArgumentException { |
| 1837 | |
| 1838 | if (e < 0) { |
| 1839 | throw MathRuntimeException.createIllegalArgumentException( |
| 1840 | LocalizedFormats.POWER_NEGATIVE_PARAMETERS, |
| 1841 | k, e); |
| 1842 | } |
| 1843 | |
| 1844 | long result = 1l; |
| 1845 | long k2p = k; |
| 1846 | while (e != 0) { |
| 1847 | if ((e & 0x1) != 0) { |
| 1848 | result *= k2p; |
| 1849 | } |
| 1850 | k2p *= k2p; |
| 1851 | e = e >> 1; |
| 1852 | } |
| 1853 | |
| 1854 | return result; |
| 1855 | |
| 1856 | } |
| 1857 | |
| 1858 | /** |
| 1859 | * Raise a long to a long power. |
| 1860 | * @param k number to raise |
| 1861 | * @param e exponent (must be positive or null) |
| 1862 | * @return k<sup>e</sup> |
| 1863 | * @exception IllegalArgumentException if e is negative |
| 1864 | */ |
| 1865 | public static long pow(final long k, long e) |
| 1866 | throws IllegalArgumentException { |
| 1867 | |
| 1868 | if (e < 0) { |
| 1869 | throw MathRuntimeException.createIllegalArgumentException( |
| 1870 | LocalizedFormats.POWER_NEGATIVE_PARAMETERS, |
| 1871 | k, e); |
| 1872 | } |
| 1873 | |
| 1874 | long result = 1l; |
| 1875 | long k2p = k; |
| 1876 | while (e != 0) { |
| 1877 | if ((e & 0x1) != 0) { |
| 1878 | result *= k2p; |
| 1879 | } |
| 1880 | k2p *= k2p; |
| 1881 | e = e >> 1; |
| 1882 | } |
| 1883 | |
| 1884 | return result; |
| 1885 | |
| 1886 | } |
| 1887 | |
| 1888 | /** |
| 1889 | * Raise a BigInteger to an int power. |
| 1890 | * @param k number to raise |
| 1891 | * @param e exponent (must be positive or null) |
| 1892 | * @return k<sup>e</sup> |
| 1893 | * @exception IllegalArgumentException if e is negative |
| 1894 | */ |
| 1895 | public static BigInteger pow(final BigInteger k, int e) |
| 1896 | throws IllegalArgumentException { |
| 1897 | |
| 1898 | if (e < 0) { |
| 1899 | throw MathRuntimeException.createIllegalArgumentException( |
| 1900 | LocalizedFormats.POWER_NEGATIVE_PARAMETERS, |
| 1901 | k, e); |
| 1902 | } |
| 1903 | |
| 1904 | return k.pow(e); |
| 1905 | |
| 1906 | } |
| 1907 | |
| 1908 | /** |
| 1909 | * Raise a BigInteger to a long power. |
| 1910 | * @param k number to raise |
| 1911 | * @param e exponent (must be positive or null) |
| 1912 | * @return k<sup>e</sup> |
| 1913 | * @exception IllegalArgumentException if e is negative |
| 1914 | */ |
| 1915 | public static BigInteger pow(final BigInteger k, long e) |
| 1916 | throws IllegalArgumentException { |
| 1917 | |
| 1918 | if (e < 0) { |
| 1919 | throw MathRuntimeException.createIllegalArgumentException( |
| 1920 | LocalizedFormats.POWER_NEGATIVE_PARAMETERS, |
| 1921 | k, e); |
| 1922 | } |
| 1923 | |
| 1924 | BigInteger result = BigInteger.ONE; |
| 1925 | BigInteger k2p = k; |
| 1926 | while (e != 0) { |
| 1927 | if ((e & 0x1) != 0) { |
| 1928 | result = result.multiply(k2p); |
| 1929 | } |
| 1930 | k2p = k2p.multiply(k2p); |
| 1931 | e = e >> 1; |
| 1932 | } |
| 1933 | |
| 1934 | return result; |
| 1935 | |
| 1936 | } |
| 1937 | |
| 1938 | /** |
| 1939 | * Raise a BigInteger to a BigInteger power. |
| 1940 | * @param k number to raise |
| 1941 | * @param e exponent (must be positive or null) |
| 1942 | * @return k<sup>e</sup> |
| 1943 | * @exception IllegalArgumentException if e is negative |
| 1944 | */ |
| 1945 | public static BigInteger pow(final BigInteger k, BigInteger e) |
| 1946 | throws IllegalArgumentException { |
| 1947 | |
| 1948 | if (e.compareTo(BigInteger.ZERO) < 0) { |
| 1949 | throw MathRuntimeException.createIllegalArgumentException( |
| 1950 | LocalizedFormats.POWER_NEGATIVE_PARAMETERS, |
| 1951 | k, e); |
| 1952 | } |
| 1953 | |
| 1954 | BigInteger result = BigInteger.ONE; |
| 1955 | BigInteger k2p = k; |
| 1956 | while (!BigInteger.ZERO.equals(e)) { |
| 1957 | if (e.testBit(0)) { |
| 1958 | result = result.multiply(k2p); |
| 1959 | } |
| 1960 | k2p = k2p.multiply(k2p); |
| 1961 | e = e.shiftRight(1); |
| 1962 | } |
| 1963 | |
| 1964 | return result; |
| 1965 | |
| 1966 | } |
| 1967 | |
| 1968 | /** |
| 1969 | * Calculates the L<sub>1</sub> (sum of abs) distance between two points. |
| 1970 | * |
| 1971 | * @param p1 the first point |
| 1972 | * @param p2 the second point |
| 1973 | * @return the L<sub>1</sub> distance between the two points |
| 1974 | */ |
| 1975 | public static double distance1(double[] p1, double[] p2) { |
| 1976 | double sum = 0; |
| 1977 | for (int i = 0; i < p1.length; i++) { |
| 1978 | sum += FastMath.abs(p1[i] - p2[i]); |
| 1979 | } |
| 1980 | return sum; |
| 1981 | } |
| 1982 | |
| 1983 | /** |
| 1984 | * Calculates the L<sub>1</sub> (sum of abs) distance between two points. |
| 1985 | * |
| 1986 | * @param p1 the first point |
| 1987 | * @param p2 the second point |
| 1988 | * @return the L<sub>1</sub> distance between the two points |
| 1989 | */ |
| 1990 | public static int distance1(int[] p1, int[] p2) { |
| 1991 | int sum = 0; |
| 1992 | for (int i = 0; i < p1.length; i++) { |
| 1993 | sum += FastMath.abs(p1[i] - p2[i]); |
| 1994 | } |
| 1995 | return sum; |
| 1996 | } |
| 1997 | |
| 1998 | /** |
| 1999 | * Calculates the L<sub>2</sub> (Euclidean) distance between two points. |
| 2000 | * |
| 2001 | * @param p1 the first point |
| 2002 | * @param p2 the second point |
| 2003 | * @return the L<sub>2</sub> distance between the two points |
| 2004 | */ |
| 2005 | public static double distance(double[] p1, double[] p2) { |
| 2006 | double sum = 0; |
| 2007 | for (int i = 0; i < p1.length; i++) { |
| 2008 | final double dp = p1[i] - p2[i]; |
| 2009 | sum += dp * dp; |
| 2010 | } |
| 2011 | return FastMath.sqrt(sum); |
| 2012 | } |
| 2013 | |
| 2014 | /** |
| 2015 | * Calculates the L<sub>2</sub> (Euclidean) distance between two points. |
| 2016 | * |
| 2017 | * @param p1 the first point |
| 2018 | * @param p2 the second point |
| 2019 | * @return the L<sub>2</sub> distance between the two points |
| 2020 | */ |
| 2021 | public static double distance(int[] p1, int[] p2) { |
| 2022 | double sum = 0; |
| 2023 | for (int i = 0; i < p1.length; i++) { |
| 2024 | final double dp = p1[i] - p2[i]; |
| 2025 | sum += dp * dp; |
| 2026 | } |
| 2027 | return FastMath.sqrt(sum); |
| 2028 | } |
| 2029 | |
| 2030 | /** |
| 2031 | * Calculates the L<sub>∞</sub> (max of abs) distance between two points. |
| 2032 | * |
| 2033 | * @param p1 the first point |
| 2034 | * @param p2 the second point |
| 2035 | * @return the L<sub>∞</sub> distance between the two points |
| 2036 | */ |
| 2037 | public static double distanceInf(double[] p1, double[] p2) { |
| 2038 | double max = 0; |
| 2039 | for (int i = 0; i < p1.length; i++) { |
| 2040 | max = FastMath.max(max, FastMath.abs(p1[i] - p2[i])); |
| 2041 | } |
| 2042 | return max; |
| 2043 | } |
| 2044 | |
| 2045 | /** |
| 2046 | * Calculates the L<sub>∞</sub> (max of abs) distance between two points. |
| 2047 | * |
| 2048 | * @param p1 the first point |
| 2049 | * @param p2 the second point |
| 2050 | * @return the L<sub>∞</sub> distance between the two points |
| 2051 | */ |
| 2052 | public static int distanceInf(int[] p1, int[] p2) { |
| 2053 | int max = 0; |
| 2054 | for (int i = 0; i < p1.length; i++) { |
| 2055 | max = FastMath.max(max, FastMath.abs(p1[i] - p2[i])); |
| 2056 | } |
| 2057 | return max; |
| 2058 | } |
| 2059 | |
| 2060 | /** |
| 2061 | * Specification of ordering direction. |
| 2062 | */ |
| 2063 | public static enum OrderDirection { |
| 2064 | /** Constant for increasing direction. */ |
| 2065 | INCREASING, |
| 2066 | /** Constant for decreasing direction. */ |
| 2067 | DECREASING |
| 2068 | } |
| 2069 | |
| 2070 | /** |
| 2071 | * Checks that the given array is sorted. |
| 2072 | * |
| 2073 | * @param val Values. |
| 2074 | * @param dir Ordering direction. |
| 2075 | * @param strict Whether the order should be strict. |
| 2076 | * @throws NonMonotonousSequenceException if the array is not sorted. |
| 2077 | * @since 2.2 |
| 2078 | */ |
| 2079 | public static void checkOrder(double[] val, OrderDirection dir, boolean strict) { |
| 2080 | double previous = val[0]; |
| 2081 | boolean ok = true; |
| 2082 | |
| 2083 | int max = val.length; |
| 2084 | for (int i = 1; i < max; i++) { |
| 2085 | switch (dir) { |
| 2086 | case INCREASING: |
| 2087 | if (strict) { |
| 2088 | if (val[i] <= previous) { |
| 2089 | ok = false; |
| 2090 | } |
| 2091 | } else { |
| 2092 | if (val[i] < previous) { |
| 2093 | ok = false; |
| 2094 | } |
| 2095 | } |
| 2096 | break; |
| 2097 | case DECREASING: |
| 2098 | if (strict) { |
| 2099 | if (val[i] >= previous) { |
| 2100 | ok = false; |
| 2101 | } |
| 2102 | } else { |
| 2103 | if (val[i] > previous) { |
| 2104 | ok = false; |
| 2105 | } |
| 2106 | } |
| 2107 | break; |
| 2108 | default: |
| 2109 | // Should never happen. |
| 2110 | throw new IllegalArgumentException(); |
| 2111 | } |
| 2112 | |
| 2113 | if (!ok) { |
| 2114 | throw new NonMonotonousSequenceException(val[i], previous, i, dir, strict); |
| 2115 | } |
| 2116 | previous = val[i]; |
| 2117 | } |
| 2118 | } |
| 2119 | |
| 2120 | /** |
| 2121 | * Checks that the given array is sorted in strictly increasing order. |
| 2122 | * |
| 2123 | * @param val Values. |
| 2124 | * @throws NonMonotonousSequenceException if the array is not sorted. |
| 2125 | * @since 2.2 |
| 2126 | */ |
| 2127 | public static void checkOrder(double[] val) { |
| 2128 | checkOrder(val, OrderDirection.INCREASING, true); |
| 2129 | } |
| 2130 | |
| 2131 | /** |
| 2132 | * Checks that the given array is sorted. |
| 2133 | * |
| 2134 | * @param val Values |
| 2135 | * @param dir Order direction (-1 for decreasing, 1 for increasing) |
| 2136 | * @param strict Whether the order should be strict |
| 2137 | * @throws NonMonotonousSequenceException if the array is not sorted. |
| 2138 | * @deprecated as of 2.2 (please use the new {@link #checkOrder(double[],OrderDirection,boolean) |
| 2139 | * checkOrder} method). To be removed in 3.0. |
| 2140 | */ |
| 2141 | @Deprecated |
| 2142 | public static void checkOrder(double[] val, int dir, boolean strict) { |
| 2143 | if (dir > 0) { |
| 2144 | checkOrder(val, OrderDirection.INCREASING, strict); |
| 2145 | } else { |
| 2146 | checkOrder(val, OrderDirection.DECREASING, strict); |
| 2147 | } |
| 2148 | } |
| 2149 | |
| 2150 | /** |
| 2151 | * Returns the Cartesian norm (2-norm), handling both overflow and underflow. |
| 2152 | * Translation of the minpack enorm subroutine. |
| 2153 | * |
| 2154 | * The redistribution policy for MINPACK is available <a |
| 2155 | * href="http://www.netlib.org/minpack/disclaimer">here</a>, for convenience, it |
| 2156 | * is reproduced below.</p> |
| 2157 | * |
| 2158 | * <table border="0" width="80%" cellpadding="10" align="center" bgcolor="#E0E0E0"> |
| 2159 | * <tr><td> |
| 2160 | * Minpack Copyright Notice (1999) University of Chicago. |
| 2161 | * All rights reserved |
| 2162 | * </td></tr> |
| 2163 | * <tr><td> |
| 2164 | * Redistribution and use in source and binary forms, with or without |
| 2165 | * modification, are permitted provided that the following conditions |
| 2166 | * are met: |
| 2167 | * <ol> |
| 2168 | * <li>Redistributions of source code must retain the above copyright |
| 2169 | * notice, this list of conditions and the following disclaimer.</li> |
| 2170 | * <li>Redistributions in binary form must reproduce the above |
| 2171 | * copyright notice, this list of conditions and the following |
| 2172 | * disclaimer in the documentation and/or other materials provided |
| 2173 | * with the distribution.</li> |
| 2174 | * <li>The end-user documentation included with the redistribution, if any, |
| 2175 | * must include the following acknowledgment: |
| 2176 | * <code>This product includes software developed by the University of |
| 2177 | * Chicago, as Operator of Argonne National Laboratory.</code> |
| 2178 | * Alternately, this acknowledgment may appear in the software itself, |
| 2179 | * if and wherever such third-party acknowledgments normally appear.</li> |
| 2180 | * <li><strong>WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS" |
| 2181 | * WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE |
| 2182 | * UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND |
| 2183 | * THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR |
| 2184 | * IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES |
| 2185 | * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE |
| 2186 | * OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY |
| 2187 | * OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR |
| 2188 | * USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF |
| 2189 | * THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4) |
| 2190 | * DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION |
| 2191 | * UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL |
| 2192 | * BE CORRECTED.</strong></li> |
| 2193 | * <li><strong>LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT |
| 2194 | * HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF |
| 2195 | * ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT, |
| 2196 | * INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF |
| 2197 | * ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF |
| 2198 | * PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER |
| 2199 | * SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT |
| 2200 | * (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE, |
| 2201 | * EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE |
| 2202 | * POSSIBILITY OF SUCH LOSS OR DAMAGES.</strong></li> |
| 2203 | * <ol></td></tr> |
| 2204 | * </table> |
| 2205 | * |
| 2206 | * @param v vector of doubles |
| 2207 | * @return the 2-norm of the vector |
| 2208 | * @since 2.2 |
| 2209 | */ |
| 2210 | public static double safeNorm(double[] v) { |
| 2211 | double rdwarf = 3.834e-20; |
| 2212 | double rgiant = 1.304e+19; |
| 2213 | double s1=0.0; |
| 2214 | double s2=0.0; |
| 2215 | double s3=0.0; |
| 2216 | double x1max = 0.0; |
| 2217 | double x3max = 0.0; |
| 2218 | double floatn = (double)v.length; |
| 2219 | double agiant = rgiant/floatn; |
| 2220 | for (int i=0;i<v.length;i++) { |
| 2221 | double xabs = Math.abs(v[i]); |
| 2222 | if (xabs<rdwarf || xabs>agiant) { |
| 2223 | if (xabs>rdwarf) { |
| 2224 | if (xabs>x1max) { |
| 2225 | double r=x1max/xabs; |
| 2226 | s1=1.0+s1*r*r; |
| 2227 | x1max=xabs; |
| 2228 | } else { |
| 2229 | double r=xabs/x1max; |
| 2230 | s1+=r*r; |
| 2231 | } |
| 2232 | } else { |
| 2233 | if (xabs>x3max) { |
| 2234 | double r=x3max/xabs; |
| 2235 | s3=1.0+s3*r*r; |
| 2236 | x3max=xabs; |
| 2237 | } else { |
| 2238 | if (xabs!=0.0) { |
| 2239 | double r=xabs/x3max; |
| 2240 | s3+=r*r; |
| 2241 | } |
| 2242 | } |
| 2243 | } |
| 2244 | } else { |
| 2245 | s2+=xabs*xabs; |
| 2246 | } |
| 2247 | } |
| 2248 | double norm; |
| 2249 | if (s1!=0.0) { |
| 2250 | norm = x1max*Math.sqrt(s1+(s2/x1max)/x1max); |
| 2251 | } else { |
| 2252 | if (s2==0.0) { |
| 2253 | norm = x3max*Math.sqrt(s3); |
| 2254 | } else { |
| 2255 | if (s2>=x3max) { |
| 2256 | norm = Math.sqrt(s2*(1.0+(x3max/s2)*(x3max*s3))); |
| 2257 | } else { |
| 2258 | norm = Math.sqrt(x3max*((s2/x3max)+(x3max*s3))); |
| 2259 | } |
| 2260 | } |
| 2261 | } |
| 2262 | return norm; |
| 2263 | } |
| 2264 | |
| 2265 | } |