Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 1 | /* |
| 2 | * Copyright (C) 2015 The Android Open Source Project |
| 3 | * |
| 4 | * Licensed under the Apache License, Version 2.0 (the "License"); |
| 5 | * you may not use this file except in compliance with the License. |
| 6 | * You may obtain a copy of the License at |
| 7 | * |
| 8 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 9 | * |
| 10 | * Unless required by applicable law or agreed to in writing, software |
| 11 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 12 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 13 | * See the License for the specific language governing permissions and |
| 14 | * limitations under the License. |
| 15 | */ |
| 16 | |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 17 | package com.android.calculator2; |
| 18 | |
| 19 | // We implement rational numbers of bounded size. |
| 20 | // If the length of the nuumerator plus the length of the denominator |
| 21 | // exceeds a maximum size, we simply return null, and rely on our caller |
| 22 | // do something else. |
| 23 | // We currently never return null for a pure integer. |
| 24 | // TODO: Reconsider that. With some care, large factorials might |
| 25 | // become much faster. |
| 26 | // |
| 27 | // We also implement a number of irrational functions. These return |
| 28 | // a non-null result only when the result is known to be rational. |
| 29 | |
| 30 | import java.math.BigInteger; |
| 31 | import com.hp.creals.CR; |
Hans Boehm | c023b73 | 2015-04-29 11:30:47 -0700 | [diff] [blame] | 32 | import com.hp.creals.AbortedError; |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 33 | |
| 34 | public class BoundedRational { |
| 35 | // TODO: Maybe eventually make this extend Number? |
Hans Boehm | 50ed320 | 2015-06-09 14:35:49 -0700 | [diff] [blame] | 36 | private static final int MAX_SIZE = 800; // total, in bits |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 37 | |
| 38 | private final BigInteger mNum; |
| 39 | private final BigInteger mDen; |
| 40 | |
| 41 | public BoundedRational(BigInteger n, BigInteger d) { |
| 42 | mNum = n; |
| 43 | mDen = d; |
| 44 | } |
| 45 | |
| 46 | public BoundedRational(BigInteger n) { |
| 47 | mNum = n; |
| 48 | mDen = BigInteger.ONE; |
| 49 | } |
| 50 | |
| 51 | public BoundedRational(long n, long d) { |
| 52 | mNum = BigInteger.valueOf(n); |
| 53 | mDen = BigInteger.valueOf(d); |
| 54 | } |
| 55 | |
| 56 | public BoundedRational(long n) { |
| 57 | mNum = BigInteger.valueOf(n); |
| 58 | mDen = BigInteger.valueOf(1); |
| 59 | } |
| 60 | |
| 61 | // Debug or log messages only, not pretty. |
Hans Boehm | 75ca21c | 2015-03-11 18:43:24 -0700 | [diff] [blame] | 62 | public String toString() { |
| 63 | return mNum.toString() + "/" + mDen.toString(); |
| 64 | } |
| 65 | |
Hans Boehm | 4a6b7cb | 2015-04-03 18:41:52 -0700 | [diff] [blame] | 66 | // Output to user, more expensive, less useful for debugging |
Hans Boehm | 013969e | 2015-04-13 20:29:47 -0700 | [diff] [blame] | 67 | // Not internationalized. |
Hans Boehm | 4a6b7cb | 2015-04-03 18:41:52 -0700 | [diff] [blame] | 68 | public String toNiceString() { |
Hans Boehm | 9e855e8 | 2015-04-22 18:03:28 -0700 | [diff] [blame] | 69 | BoundedRational nicer = reduce().positiveDen(); |
Hans Boehm | 4a6b7cb | 2015-04-03 18:41:52 -0700 | [diff] [blame] | 70 | String result = nicer.mNum.toString(); |
| 71 | if (!nicer.mDen.equals(BigInteger.ONE)) { |
| 72 | result += "/" + nicer.mDen; |
| 73 | } |
| 74 | return result; |
| 75 | } |
| 76 | |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 77 | public static String toString(BoundedRational r) { |
| 78 | if (r == null) return "not a small rational"; |
Hans Boehm | 75ca21c | 2015-03-11 18:43:24 -0700 | [diff] [blame] | 79 | return r.toString(); |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 80 | } |
| 81 | |
| 82 | // Primarily for debugging; clearly not exact |
| 83 | public double doubleValue() { |
| 84 | return mNum.doubleValue() / mDen.doubleValue(); |
| 85 | } |
| 86 | |
| 87 | public CR CRValue() { |
| 88 | return CR.valueOf(mNum).divide(CR.valueOf(mDen)); |
| 89 | } |
| 90 | |
| 91 | private boolean tooBig() { |
| 92 | if (mDen.equals(BigInteger.ONE)) return false; |
| 93 | return (mNum.bitLength() + mDen.bitLength() > MAX_SIZE); |
| 94 | } |
| 95 | |
| 96 | // return an equivalent fraction with a positive denominator. |
Hans Boehm | 9e855e8 | 2015-04-22 18:03:28 -0700 | [diff] [blame] | 97 | private BoundedRational positiveDen() { |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 98 | if (mDen.compareTo(BigInteger.ZERO) > 0) return this; |
| 99 | return new BoundedRational(mNum.negate(), mDen.negate()); |
| 100 | } |
| 101 | |
| 102 | // Return an equivalent fraction in lowest terms. |
| 103 | private BoundedRational reduce() { |
| 104 | if (mDen.equals(BigInteger.ONE)) return this; // Optimization only |
| 105 | BigInteger divisor = mNum.gcd(mDen); |
| 106 | return new BoundedRational(mNum.divide(divisor), mDen.divide(divisor)); |
| 107 | } |
| 108 | |
| 109 | // Return a possibly reduced version of this that's not tooBig. |
| 110 | // Return null if none exists. |
| 111 | private BoundedRational maybeReduce() { |
| 112 | if (!tooBig()) return this; |
Hans Boehm | 9e855e8 | 2015-04-22 18:03:28 -0700 | [diff] [blame] | 113 | BoundedRational result = positiveDen(); |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 114 | if (!result.tooBig()) return this; |
| 115 | result = result.reduce(); |
| 116 | if (!result.tooBig()) return this; |
| 117 | return null; |
| 118 | } |
| 119 | |
| 120 | public int compareTo(BoundedRational r) { |
| 121 | // Compare by multiplying both sides by denominators, |
| 122 | // invert result if denominator product was negative. |
| 123 | return mNum.multiply(r.mDen).compareTo(r.mNum.multiply(mDen)) |
| 124 | * mDen.signum() * r.mDen.signum(); |
| 125 | } |
| 126 | |
| 127 | public int signum() { |
Hans Boehm | 75ca21c | 2015-03-11 18:43:24 -0700 | [diff] [blame] | 128 | return mNum.signum() * mDen.signum(); |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 129 | } |
| 130 | |
| 131 | public boolean equals(BoundedRational r) { |
| 132 | return compareTo(r) == 0; |
| 133 | } |
| 134 | |
| 135 | // We use static methods for arithmetic, so that we can |
| 136 | // easily handle the null case. |
| 137 | // We try to catch domain errors whenever possible, sometimes even when |
| 138 | // one of the arguments is null, but not relevant. |
| 139 | |
| 140 | // Returns equivalent BigInteger result if it exists, null if not. |
| 141 | public static BigInteger asBigInteger(BoundedRational r) { |
| 142 | if (r == null) return null; |
| 143 | if (!r.mDen.equals(BigInteger.ONE)) r = r.reduce(); |
| 144 | if (!r.mDen.equals(BigInteger.ONE)) return null; |
| 145 | return r.mNum; |
| 146 | } |
| 147 | public static BoundedRational add(BoundedRational r1, BoundedRational r2) { |
| 148 | if (r1 == null || r2 == null) return null; |
| 149 | final BigInteger den = r1.mDen.multiply(r2.mDen); |
| 150 | final BigInteger num = r1.mNum.multiply(r2.mDen) |
| 151 | .add(r2.mNum.multiply(r1.mDen)); |
| 152 | return new BoundedRational(num,den).maybeReduce(); |
| 153 | } |
| 154 | |
| 155 | public static BoundedRational negate(BoundedRational r) { |
| 156 | if (r == null) return null; |
| 157 | return new BoundedRational(r.mNum.negate(), r.mDen); |
| 158 | } |
| 159 | |
| 160 | static BoundedRational subtract(BoundedRational r1, BoundedRational r2) { |
| 161 | return add(r1, negate(r2)); |
| 162 | } |
| 163 | |
| 164 | static BoundedRational multiply(BoundedRational r1, BoundedRational r2) { |
| 165 | // It's tempting but marginally unsound to reduce 0 * null to zero. |
| 166 | // The null could represent an infinite value, for which we |
| 167 | // failed to throw an exception because it was too big. |
| 168 | if (r1 == null || r2 == null) return null; |
| 169 | final BigInteger num = r1.mNum.multiply(r2.mNum); |
| 170 | final BigInteger den = r1.mDen.multiply(r2.mDen); |
| 171 | return new BoundedRational(num,den).maybeReduce(); |
| 172 | } |
| 173 | |
Hans Boehm | fbcef70 | 2015-04-27 18:07:47 -0700 | [diff] [blame] | 174 | public static class ZeroDivisionException extends ArithmeticException { |
| 175 | public ZeroDivisionException() { |
| 176 | super("Division by zero"); |
| 177 | } |
| 178 | } |
| 179 | |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 180 | static BoundedRational inverse(BoundedRational r) { |
| 181 | if (r == null) return null; |
| 182 | if (r.mNum.equals(BigInteger.ZERO)) { |
Hans Boehm | fbcef70 | 2015-04-27 18:07:47 -0700 | [diff] [blame] | 183 | throw new ZeroDivisionException(); |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 184 | } |
| 185 | return new BoundedRational(r.mDen, r.mNum); |
| 186 | } |
| 187 | |
| 188 | static BoundedRational divide(BoundedRational r1, BoundedRational r2) { |
| 189 | return multiply(r1, inverse(r2)); |
| 190 | } |
| 191 | |
| 192 | static BoundedRational sqrt(BoundedRational r) { |
| 193 | // Return non-null if numerator and denominator are small perfect |
| 194 | // squares. |
| 195 | if (r == null) return null; |
Hans Boehm | 9e855e8 | 2015-04-22 18:03:28 -0700 | [diff] [blame] | 196 | r = r.positiveDen().reduce(); |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 197 | if (r.mNum.compareTo(BigInteger.ZERO) < 0) { |
| 198 | throw new ArithmeticException("sqrt(negative)"); |
| 199 | } |
| 200 | final BigInteger num_sqrt = BigInteger.valueOf(Math.round(Math.sqrt( |
| 201 | r.mNum.doubleValue()))); |
| 202 | if (!num_sqrt.multiply(num_sqrt).equals(r.mNum)) return null; |
| 203 | final BigInteger den_sqrt = BigInteger.valueOf(Math.round(Math.sqrt( |
| 204 | r.mDen.doubleValue()))); |
Hans Boehm | 75ca21c | 2015-03-11 18:43:24 -0700 | [diff] [blame] | 205 | if (!den_sqrt.multiply(den_sqrt).equals(r.mDen)) return null; |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 206 | return new BoundedRational(num_sqrt, den_sqrt); |
| 207 | } |
| 208 | |
| 209 | public final static BoundedRational ZERO = new BoundedRational(0); |
| 210 | public final static BoundedRational HALF = new BoundedRational(1,2); |
| 211 | public final static BoundedRational MINUS_HALF = new BoundedRational(-1,2); |
| 212 | public final static BoundedRational ONE = new BoundedRational(1); |
| 213 | public final static BoundedRational MINUS_ONE = new BoundedRational(-1); |
| 214 | public final static BoundedRational TWO = new BoundedRational(2); |
| 215 | public final static BoundedRational MINUS_TWO = new BoundedRational(-2); |
| 216 | public final static BoundedRational THIRTY = new BoundedRational(30); |
| 217 | public final static BoundedRational MINUS_THIRTY = new BoundedRational(-30); |
| 218 | public final static BoundedRational FORTY_FIVE = new BoundedRational(45); |
| 219 | public final static BoundedRational MINUS_FORTY_FIVE = |
| 220 | new BoundedRational(-45); |
| 221 | public final static BoundedRational NINETY = new BoundedRational(90); |
| 222 | public final static BoundedRational MINUS_NINETY = new BoundedRational(-90); |
| 223 | |
| 224 | private static BoundedRational map0to0(BoundedRational r) { |
| 225 | if (r == null) return null; |
| 226 | if (r.mNum.equals(BigInteger.ZERO)) { |
| 227 | return ZERO; |
| 228 | } |
| 229 | return null; |
| 230 | } |
| 231 | |
Hans Boehm | 4db31b4 | 2015-05-31 12:19:05 -0700 | [diff] [blame] | 232 | private static BoundedRational map0to1(BoundedRational r) { |
| 233 | if (r == null) return null; |
| 234 | if (r.mNum.equals(BigInteger.ZERO)) { |
| 235 | return ONE; |
| 236 | } |
| 237 | return null; |
| 238 | } |
| 239 | |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 240 | private static BoundedRational map1to0(BoundedRational r) { |
| 241 | if (r == null) return null; |
| 242 | if (r.mNum.equals(r.mDen)) { |
| 243 | return ZERO; |
| 244 | } |
| 245 | return null; |
| 246 | } |
| 247 | |
| 248 | // Throw an exception if the argument is definitely out of bounds for asin |
| 249 | // or acos. |
| 250 | private static void checkAsinDomain(BoundedRational r) { |
| 251 | if (r == null) return; |
| 252 | if (r.mNum.abs().compareTo(r.mDen.abs()) > 0) { |
| 253 | throw new ArithmeticException("inverse trig argument out of range"); |
| 254 | } |
| 255 | } |
| 256 | |
| 257 | public static BoundedRational sin(BoundedRational r) { |
| 258 | return map0to0(r); |
| 259 | } |
| 260 | |
| 261 | private final static BigInteger BIG360 = BigInteger.valueOf(360); |
| 262 | |
| 263 | public static BoundedRational degreeSin(BoundedRational r) { |
| 264 | final BigInteger r_BI = asBigInteger(r); |
| 265 | if (r_BI == null) return null; |
| 266 | final int r_int = r_BI.mod(BIG360).intValue(); |
| 267 | if (r_int % 30 != 0) return null; |
| 268 | switch (r_int / 10) { |
| 269 | case 0: |
| 270 | return ZERO; |
| 271 | case 3: // 30 degrees |
| 272 | return HALF; |
| 273 | case 9: |
| 274 | return ONE; |
| 275 | case 15: |
| 276 | return HALF; |
| 277 | case 18: // 180 degrees |
| 278 | return ZERO; |
| 279 | case 21: |
| 280 | return MINUS_HALF; |
| 281 | case 27: |
| 282 | return MINUS_ONE; |
| 283 | case 33: |
| 284 | return MINUS_HALF; |
| 285 | default: |
| 286 | return null; |
| 287 | } |
| 288 | } |
| 289 | |
| 290 | public static BoundedRational asin(BoundedRational r) { |
| 291 | checkAsinDomain(r); |
| 292 | return map0to0(r); |
| 293 | } |
| 294 | |
| 295 | public static BoundedRational degreeAsin(BoundedRational r) { |
| 296 | checkAsinDomain(r); |
| 297 | final BigInteger r2_BI = asBigInteger(multiply(r, TWO)); |
| 298 | if (r2_BI == null) return null; |
| 299 | final int r2_int = r2_BI.intValue(); |
| 300 | // Somewhat surprisingly, it seems to be the case that the following |
| 301 | // covers all rational cases: |
| 302 | switch (r2_int) { |
| 303 | case -2: // Corresponding to -1 argument |
| 304 | return MINUS_NINETY; |
| 305 | case -1: // Corresponding to -1/2 argument |
| 306 | return MINUS_THIRTY; |
| 307 | case 0: |
| 308 | return ZERO; |
| 309 | case 1: |
| 310 | return THIRTY; |
| 311 | case 2: |
| 312 | return NINETY; |
| 313 | default: |
| 314 | throw new AssertionError("Impossible asin arg"); |
| 315 | } |
| 316 | } |
| 317 | |
| 318 | public static BoundedRational tan(BoundedRational r) { |
| 319 | // Unlike the degree case, we cannot check for the singularity, |
| 320 | // since it occurs at an irrational argument. |
| 321 | return map0to0(r); |
| 322 | } |
| 323 | |
| 324 | public static BoundedRational degreeTan(BoundedRational r) { |
| 325 | final BoundedRational degree_sin = degreeSin(r); |
| 326 | final BoundedRational degree_cos = degreeCos(r); |
| 327 | if (degree_cos != null && degree_cos.mNum.equals(BigInteger.ZERO)) { |
| 328 | throw new ArithmeticException("Tangent undefined"); |
| 329 | } |
| 330 | return divide(degree_sin, degree_cos); |
| 331 | } |
| 332 | |
| 333 | public static BoundedRational atan(BoundedRational r) { |
| 334 | return map0to0(r); |
| 335 | } |
| 336 | |
| 337 | public static BoundedRational degreeAtan(BoundedRational r) { |
| 338 | final BigInteger r_BI = asBigInteger(r); |
| 339 | if (r_BI == null) return null; |
| 340 | if (r_BI.abs().compareTo(BigInteger.ONE) > 0) return null; |
| 341 | final int r_int = r_BI.intValue(); |
| 342 | // Again, these seem to be all rational cases: |
| 343 | switch (r_int) { |
| 344 | case -1: |
| 345 | return MINUS_FORTY_FIVE; |
| 346 | case 0: |
| 347 | return ZERO; |
| 348 | case 1: |
| 349 | return FORTY_FIVE; |
| 350 | default: |
| 351 | throw new AssertionError("Impossible atan arg"); |
| 352 | } |
| 353 | } |
| 354 | |
| 355 | public static BoundedRational cos(BoundedRational r) { |
Hans Boehm | 4db31b4 | 2015-05-31 12:19:05 -0700 | [diff] [blame] | 356 | return map0to1(r); |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 357 | } |
| 358 | |
| 359 | public static BoundedRational degreeCos(BoundedRational r) { |
| 360 | return degreeSin(add(r, NINETY)); |
| 361 | } |
| 362 | |
| 363 | public static BoundedRational acos(BoundedRational r) { |
| 364 | checkAsinDomain(r); |
| 365 | return map1to0(r); |
| 366 | } |
| 367 | |
| 368 | public static BoundedRational degreeAcos(BoundedRational r) { |
| 369 | final BoundedRational asin_r = degreeAsin(r); |
| 370 | return subtract(NINETY, asin_r); |
| 371 | } |
| 372 | |
| 373 | private static final BigInteger BIG_TWO = BigInteger.valueOf(2); |
| 374 | |
| 375 | // Compute an integral power of this |
| 376 | private BoundedRational pow(BigInteger exp) { |
| 377 | if (exp.compareTo(BigInteger.ZERO) < 0) { |
| 378 | return inverse(pow(exp.negate())); |
| 379 | } |
| 380 | if (exp.equals(BigInteger.ONE)) return this; |
| 381 | if (exp.and(BigInteger.ONE).intValue() == 1) { |
| 382 | return multiply(pow(exp.subtract(BigInteger.ONE)), this); |
| 383 | } |
| 384 | if (exp.equals(BigInteger.ZERO)) { |
| 385 | return ONE; |
| 386 | } |
| 387 | BoundedRational tmp = pow(exp.shiftRight(1)); |
| 388 | return multiply(tmp, tmp); |
| 389 | } |
| 390 | |
| 391 | public static BoundedRational pow(BoundedRational base, BoundedRational exp) { |
| 392 | if (exp == null) return null; |
| 393 | if (exp.mNum.equals(BigInteger.ZERO)) { |
| 394 | return new BoundedRational(1); |
| 395 | } |
| 396 | if (base == null) return null; |
Hans Boehm | 9e855e8 | 2015-04-22 18:03:28 -0700 | [diff] [blame] | 397 | exp = exp.reduce().positiveDen(); |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 398 | if (!exp.mDen.equals(BigInteger.ONE)) return null; |
| 399 | return base.pow(exp.mNum); |
| 400 | } |
| 401 | |
| 402 | public static BoundedRational ln(BoundedRational r) { |
Hans Boehm | 9e855e8 | 2015-04-22 18:03:28 -0700 | [diff] [blame] | 403 | if (r != null && r.signum() <= 0) { |
| 404 | throw new ArithmeticException("log(non-positive)"); |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 405 | } |
| 406 | return map1to0(r); |
| 407 | } |
| 408 | |
Hans Boehm | 4db31b4 | 2015-05-31 12:19:05 -0700 | [diff] [blame] | 409 | public static BoundedRational exp(BoundedRational r) { |
| 410 | return map0to1(r); |
| 411 | } |
| 412 | |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 413 | // Return the base 10 log of n, if n is a power of 10, -1 otherwise. |
Hans Boehm | 9e855e8 | 2015-04-22 18:03:28 -0700 | [diff] [blame] | 414 | // n must be positive. |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 415 | private static long b10Log(BigInteger n) { |
| 416 | // This algorithm is very naive, but we doubt it matters. |
| 417 | long count = 0; |
| 418 | while (n.mod(BigInteger.TEN).equals(BigInteger.ZERO)) { |
| 419 | n = n.divide(BigInteger.TEN); |
| 420 | ++count; |
| 421 | } |
| 422 | if (n.equals(BigInteger.ONE)) { |
| 423 | return count; |
| 424 | } |
| 425 | return -1; |
| 426 | } |
| 427 | |
| 428 | public static BoundedRational log(BoundedRational r) { |
| 429 | if (r == null) return null; |
Hans Boehm | 9e855e8 | 2015-04-22 18:03:28 -0700 | [diff] [blame] | 430 | if (r.signum() <= 0) { |
| 431 | throw new ArithmeticException("log(non-positive)"); |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 432 | } |
Hans Boehm | 9e855e8 | 2015-04-22 18:03:28 -0700 | [diff] [blame] | 433 | r = r.reduce().positiveDen(); |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 434 | if (r == null) return null; |
| 435 | if (r.mDen.equals(BigInteger.ONE)) { |
| 436 | long log = b10Log(r.mNum); |
| 437 | if (log != -1) return new BoundedRational(log); |
| 438 | } else if (r.mNum.equals(BigInteger.ONE)) { |
| 439 | long log = b10Log(r.mDen); |
| 440 | if (log != -1) return new BoundedRational(-log); |
| 441 | } |
| 442 | return null; |
| 443 | } |
| 444 | |
| 445 | // Generalized factorial. |
| 446 | // Compute n * (n - step) * (n - 2 * step) * ... |
| 447 | // This can be used to compute factorial a bit faster, especially |
| 448 | // if BigInteger uses sub-quadratic multiplication. |
| 449 | private static BigInteger genFactorial(long n, long step) { |
| 450 | if (n > 4 * step) { |
| 451 | BigInteger prod1 = genFactorial(n, 2 * step); |
Hans Boehm | c023b73 | 2015-04-29 11:30:47 -0700 | [diff] [blame] | 452 | if (Thread.interrupted()) { |
| 453 | throw new AbortedError(); |
| 454 | } |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 455 | BigInteger prod2 = genFactorial(n - step, 2 * step); |
Hans Boehm | c023b73 | 2015-04-29 11:30:47 -0700 | [diff] [blame] | 456 | if (Thread.interrupted()) { |
| 457 | throw new AbortedError(); |
| 458 | } |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 459 | return prod1.multiply(prod2); |
| 460 | } else { |
| 461 | BigInteger res = BigInteger.valueOf(n); |
| 462 | for (long i = n - step; i > 1; i -= step) { |
| 463 | res = res.multiply(BigInteger.valueOf(i)); |
| 464 | } |
| 465 | return res; |
| 466 | } |
| 467 | } |
| 468 | |
| 469 | // Factorial; |
| 470 | // always produces non-null (or exception) when called on non-null r. |
| 471 | public static BoundedRational fact(BoundedRational r) { |
| 472 | if (r == null) return null; // Caller should probably preclude this case. |
| 473 | final BigInteger r_BI = asBigInteger(r); |
| 474 | if (r_BI == null) { |
| 475 | throw new ArithmeticException("Non-integral factorial argument"); |
| 476 | } |
| 477 | if (r_BI.signum() < 0) { |
| 478 | throw new ArithmeticException("Negative factorial argument"); |
| 479 | } |
| 480 | if (r_BI.bitLength() > 30) { |
| 481 | // Will fail. LongValue() may not work. Punt now. |
| 482 | throw new ArithmeticException("Factorial argument too big"); |
| 483 | } |
| 484 | return new BoundedRational(genFactorial(r_BI.longValue(), 1)); |
| 485 | } |
| 486 | |
| 487 | private static final BigInteger BIG_FIVE = BigInteger.valueOf(5); |
Hans Boehm | cd74059 | 2015-06-13 21:12:23 -0700 | [diff] [blame^] | 488 | private static final BigInteger BIG_MINUS_ONE = BigInteger.valueOf(-1); |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 489 | |
| 490 | // Return the number of decimal digits to the right of the |
| 491 | // decimal point required to represent the argument exactly, |
| 492 | // or Integer.MAX_VALUE if it's not possible. |
| 493 | // Never returns a value les than zero, even if r is |
| 494 | // a power of ten. |
| 495 | static int digitsRequired(BoundedRational r) { |
| 496 | if (r == null) return Integer.MAX_VALUE; |
| 497 | int powers_of_two = 0; // Max power of 2 that divides denominator |
| 498 | int powers_of_five = 0; // Max power of 5 that divides denominator |
| 499 | // Try the easy case first to speed things up. |
| 500 | if (r.mDen.equals(BigInteger.ONE)) return 0; |
| 501 | r = r.reduce(); |
| 502 | BigInteger den = r.mDen; |
| 503 | while (!den.testBit(0)) { |
| 504 | ++powers_of_two; |
| 505 | den = den.shiftRight(1); |
| 506 | } |
| 507 | while (den.mod(BIG_FIVE).equals(BigInteger.ZERO)) { |
| 508 | ++powers_of_five; |
| 509 | den = den.divide(BIG_FIVE); |
| 510 | } |
| 511 | // If the denominator has a factor of other than 2 or 5 |
| 512 | // (the divisors of 10), the decimal expansion does not |
| 513 | // terminate. Multiplying the fraction by any number of |
| 514 | // powers of 10 will not cancel the demoniator. |
| 515 | // (Recall the fraction was in lowest terms to start with.) |
| 516 | // Otherwise the powers of 10 we need to cancel the denominator |
| 517 | // is the larger of powers_of_two and powers_of_five. |
Hans Boehm | cd74059 | 2015-06-13 21:12:23 -0700 | [diff] [blame^] | 518 | if (!den.equals(BigInteger.ONE) && !den.equals(BIG_MINUS_ONE)) { |
| 519 | return Integer.MAX_VALUE; |
| 520 | } |
Hans Boehm | 682ff5e | 2015-03-09 14:40:25 -0700 | [diff] [blame] | 521 | return Math.max(powers_of_two, powers_of_five); |
| 522 | } |
| 523 | } |