Hans Boehm | 8461495 | 2014-11-25 18:46:17 -0800 | [diff] [blame^] | 1 | /* |
| 2 | * Copyright (C) 2014 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 | |
| 17 | package com.android.calculator2; |
| 18 | |
| 19 | import java.util.ArrayList; |
| 20 | import java.util.HashMap; |
| 21 | import java.util.IdentityHashMap; |
| 22 | import java.math.BigInteger; |
| 23 | import java.io.DataInput; |
| 24 | import java.io.DataOutput; |
| 25 | import java.io.IOException; |
| 26 | |
| 27 | import com.hp.creals.CR; |
| 28 | import com.hp.creals.UnaryCRFunction; |
| 29 | import com.hp.creals.PrecisionOverflowError; |
| 30 | import com.hp.creals.AbortedError; |
| 31 | |
| 32 | import android.content.Context; |
| 33 | |
| 34 | // A mathematical expression represented as a sequence of "tokens". |
| 35 | // Many tokes are represented by button ids for the corresponding operator. |
| 36 | // Parsed only when we evaluate the expression using the "eval" method. |
| 37 | class CalculatorExpr { |
| 38 | private ArrayList<Token> mExpr; // The actual representation |
| 39 | // as a list of tokens. Constant |
| 40 | // tokens are always nonempty. |
| 41 | |
| 42 | private static enum TokenKind { CONSTANT, OPERATOR, PRE_EVAL }; |
| 43 | private static TokenKind[] tokenKindValues = TokenKind.values(); |
| 44 | private final static BigInteger BIG_MILLION = BigInteger.valueOf(1000000); |
| 45 | private final static BigInteger BIG_BILLION = BigInteger.valueOf(1000000000); |
| 46 | |
| 47 | private static abstract class Token { |
| 48 | abstract TokenKind kind(); |
| 49 | abstract void write(DataOutput out) throws IOException; |
| 50 | // Implementation writes kind as Byte followed by |
| 51 | // data read by constructor. |
| 52 | abstract String toString(Context context); |
| 53 | // We need the context to convert button ids to strings. |
| 54 | } |
| 55 | |
| 56 | // An operator token |
| 57 | private static class Operator extends Token { |
| 58 | final int mId; // We use the button resource id |
| 59 | Operator(int resId) { |
| 60 | mId = resId; |
| 61 | } |
| 62 | Operator(DataInput in) throws IOException { |
| 63 | mId = in.readInt(); |
| 64 | } |
| 65 | @Override |
| 66 | void write(DataOutput out) throws IOException { |
| 67 | out.writeByte(TokenKind.OPERATOR.ordinal()); |
| 68 | out.writeInt(mId); |
| 69 | } |
| 70 | @Override |
| 71 | public String toString(Context context) { |
| 72 | return KeyMaps.toString(mId, context); |
| 73 | } |
| 74 | @Override |
| 75 | TokenKind kind() { return TokenKind.OPERATOR; } |
| 76 | } |
| 77 | |
| 78 | // A (possibly incomplete) numerical constant |
| 79 | private static class Constant extends Token implements Cloneable { |
| 80 | private boolean mSawDecimal; |
| 81 | String mWhole; // part before decimal point |
| 82 | private String mFraction; // part after decimal point |
| 83 | |
| 84 | Constant() { |
| 85 | mWhole = ""; |
| 86 | mFraction = ""; |
| 87 | mSawDecimal = false; |
| 88 | }; |
| 89 | |
| 90 | Constant(DataInput in) throws IOException { |
| 91 | mWhole = in.readUTF(); |
| 92 | mSawDecimal = in.readBoolean(); |
| 93 | mFraction = in.readUTF(); |
| 94 | } |
| 95 | |
| 96 | @Override |
| 97 | void write(DataOutput out) throws IOException { |
| 98 | out.writeByte(TokenKind.CONSTANT.ordinal()); |
| 99 | out.writeUTF(mWhole); |
| 100 | out.writeBoolean(mSawDecimal); |
| 101 | out.writeUTF(mFraction); |
| 102 | } |
| 103 | |
| 104 | // Given a button press, append corresponding digit. |
| 105 | // We assume id is a digit or decimal point. |
| 106 | // Just return false if this was the second (or later) decimal point |
| 107 | // in this constant. |
| 108 | boolean add(int id) { |
| 109 | if (id == R.id.dec_point) { |
| 110 | if (mSawDecimal) return false; |
| 111 | mSawDecimal = true; |
| 112 | return true; |
| 113 | } |
| 114 | int val = KeyMaps.digVal(id); |
| 115 | if (mSawDecimal) { |
| 116 | mFraction += val; |
| 117 | } else { |
| 118 | mWhole += val; |
| 119 | } |
| 120 | return true; |
| 121 | } |
| 122 | |
| 123 | // Undo the last add. |
| 124 | // Assumes the constant is nonempty. |
| 125 | void delete() { |
| 126 | if (!mFraction.isEmpty()) { |
| 127 | mFraction = mFraction.substring(0, mFraction.length() - 1); |
| 128 | } else if (mSawDecimal) { |
| 129 | mSawDecimal = false; |
| 130 | } else { |
| 131 | mWhole = mWhole.substring(0, mWhole.length() - 1); |
| 132 | } |
| 133 | } |
| 134 | |
| 135 | boolean isEmpty() { |
| 136 | return (mSawDecimal == false && mWhole.isEmpty()); |
| 137 | } |
| 138 | |
| 139 | boolean isInt() { |
| 140 | return !mSawDecimal || mFraction.isEmpty() |
| 141 | || new BigInteger(mFraction).equals(BigInteger.ZERO); |
| 142 | } |
| 143 | |
| 144 | @Override |
| 145 | public String toString() { |
| 146 | String result = mWhole; |
| 147 | if (mSawDecimal) { |
| 148 | result += '.'; |
| 149 | result += mFraction; |
| 150 | } |
| 151 | return result; |
| 152 | } |
| 153 | |
| 154 | @Override |
| 155 | String toString(Context context) { |
| 156 | return toString(); |
| 157 | } |
| 158 | |
| 159 | @Override |
| 160 | TokenKind kind() { return TokenKind.CONSTANT; } |
| 161 | |
| 162 | // Override clone to make it public |
| 163 | @Override |
| 164 | public Object clone() { |
| 165 | Constant res = new Constant(); |
| 166 | res.mWhole = mWhole; |
| 167 | res.mFraction = mFraction; |
| 168 | res.mSawDecimal = mSawDecimal; |
| 169 | return res; |
| 170 | } |
| 171 | } |
| 172 | |
| 173 | // Hash maps used to detect duplicate subexpressions when |
| 174 | // we write out CalculatorExprs and read them back in. |
| 175 | private static final ThreadLocal<IdentityHashMap<CR,Integer>>outMap = |
| 176 | new ThreadLocal<IdentityHashMap<CR,Integer>>(); |
| 177 | // Maps expressions to indices on output |
| 178 | private static final ThreadLocal<HashMap<Integer,PreEval>>inMap = |
| 179 | new ThreadLocal<HashMap<Integer,PreEval>>(); |
| 180 | // Maps expressions to indices on output |
| 181 | private static final ThreadLocal<Integer> exprIndex = |
| 182 | new ThreadLocal<Integer>(); |
| 183 | |
| 184 | static void initExprOutput() { |
| 185 | outMap.set(new IdentityHashMap<CR,Integer>()); |
| 186 | exprIndex.set(Integer.valueOf(0)); |
| 187 | } |
| 188 | |
| 189 | static void initExprInput() { |
| 190 | inMap.set(new HashMap<Integer,PreEval>()); |
| 191 | } |
| 192 | |
| 193 | // We treat previously evaluated subexpressions as tokens |
| 194 | // These are inserted when either: |
| 195 | // - We continue an expression after evaluating some of it. |
| 196 | // - TODO: When we copy/paste expressions. |
| 197 | // The representation includes three different representations |
| 198 | // of the expression: |
| 199 | // 1) The CR value for use in computation. |
| 200 | // 2) The integer value for use in the computations, |
| 201 | // if the expression evaluates to an integer. |
| 202 | // 3a) The corresponding CalculatorExpr, together with |
| 203 | // 3b) The context (currently just deg/rad mode) used to evaluate |
| 204 | // the expression. |
| 205 | // 4) A short string representation that is used to |
| 206 | // Display the expression. |
| 207 | // |
| 208 | // (3) is present only so that we can persist the object. |
| 209 | // (4) is stored explicitly to avoid waiting for recomputation in the UI |
| 210 | // thread. |
| 211 | private static class PreEval extends Token { |
| 212 | final CR mValue; |
| 213 | final BigInteger mIntValue; |
| 214 | private final CalculatorExpr mExpr; |
| 215 | private final EvalContext mContext; |
| 216 | private final String mShortRep; |
| 217 | PreEval(CR val, BigInteger intVal, CalculatorExpr expr, EvalContext ec, |
| 218 | String shortRep) { |
| 219 | mValue = val; |
| 220 | mIntValue = intVal; |
| 221 | mExpr = expr; |
| 222 | mContext = ec; |
| 223 | mShortRep = shortRep; |
| 224 | } |
| 225 | // In writing out PreEvals, we are careful to avoid writing |
| 226 | // out duplicates. We assume that two expressions are |
| 227 | // duplicates if they have the same mVal. This avoids a |
| 228 | // potential exponential blow up in certain off cases and |
| 229 | // redundant evaluation after reading them back in. |
| 230 | // The parameter hash map maps expressions we've seen |
| 231 | // before to their index. |
| 232 | @Override |
| 233 | void write(DataOutput out) throws IOException { |
| 234 | out.writeByte(TokenKind.PRE_EVAL.ordinal()); |
| 235 | Integer index = outMap.get().get(mValue); |
| 236 | if (index == null) { |
| 237 | int nextIndex = exprIndex.get() + 1; |
| 238 | exprIndex.set(nextIndex); |
| 239 | outMap.get().put(mValue, nextIndex); |
| 240 | out.writeInt(nextIndex); |
| 241 | mExpr.write(out); |
| 242 | mContext.write(out); |
| 243 | out.writeUTF(mShortRep); |
| 244 | } else { |
| 245 | // Just write out the index |
| 246 | out.writeInt(index); |
| 247 | } |
| 248 | } |
| 249 | PreEval(DataInput in) throws IOException { |
| 250 | int index = in.readInt(); |
| 251 | PreEval prev = inMap.get().get(index); |
| 252 | if (prev == null) { |
| 253 | mExpr = new CalculatorExpr(in); |
| 254 | mContext = new EvalContext(in); |
| 255 | // Recompute other fields |
| 256 | // We currently do this in the UI thread, but we |
| 257 | // only create PreEval expressions that were |
| 258 | // previously successfully evaluated, and thus |
| 259 | // don't diverge. We also only evaluate to a |
| 260 | // constructive real, which involves substantial |
| 261 | // work only in fairly contrived circumstances. |
| 262 | // TODO: Deal better with slow evaluations. |
| 263 | EvalRet res = mExpr.evalExpr(0,mContext); |
| 264 | mValue = res.mVal; |
| 265 | mIntValue = res.mIntVal; |
| 266 | mShortRep = in.readUTF(); |
| 267 | inMap.get().put(index, this); |
| 268 | } else { |
| 269 | mValue = prev.mValue; |
| 270 | mIntValue = prev.mIntValue; |
| 271 | mExpr = prev.mExpr; |
| 272 | mContext = prev.mContext; |
| 273 | mShortRep = prev.mShortRep; |
| 274 | } |
| 275 | } |
| 276 | @Override |
| 277 | String toString(Context context) { |
| 278 | return mShortRep; |
| 279 | } |
| 280 | @Override |
| 281 | TokenKind kind() { return TokenKind.PRE_EVAL; } |
| 282 | } |
| 283 | |
| 284 | static Token newToken(DataInput in) throws IOException { |
| 285 | TokenKind kind = tokenKindValues[in.readByte()]; |
| 286 | switch(kind) { |
| 287 | case CONSTANT: |
| 288 | return new Constant(in); |
| 289 | case OPERATOR: |
| 290 | return new Operator(in); |
| 291 | case PRE_EVAL: |
| 292 | return new PreEval(in); |
| 293 | default: throw new IOException("Bad save file format"); |
| 294 | } |
| 295 | } |
| 296 | |
| 297 | CalculatorExpr() { |
| 298 | mExpr = new ArrayList<Token>(); |
| 299 | } |
| 300 | |
| 301 | private CalculatorExpr(ArrayList<Token> expr) { |
| 302 | mExpr = expr; |
| 303 | } |
| 304 | |
| 305 | CalculatorExpr(DataInput in) throws IOException { |
| 306 | mExpr = new ArrayList<Token>(); |
| 307 | int size = in.readInt(); |
| 308 | for (int i = 0; i < size; ++i) { |
| 309 | mExpr.add(newToken(in)); |
| 310 | } |
| 311 | } |
| 312 | |
| 313 | void write(DataOutput out) throws IOException { |
| 314 | int size = mExpr.size(); |
| 315 | out.writeInt(size); |
| 316 | for (int i = 0; i < size; ++i) { |
| 317 | mExpr.get(i).write(out); |
| 318 | } |
| 319 | } |
| 320 | |
| 321 | private boolean hasTrailingBinary() { |
| 322 | int s = mExpr.size(); |
| 323 | if (s == 0) return false; |
| 324 | Token t = mExpr.get(s-1); |
| 325 | if (!(t instanceof Operator)) return false; |
| 326 | Operator o = (Operator)t; |
| 327 | return (KeyMaps.isBinary(o.mId)); |
| 328 | } |
| 329 | |
| 330 | // Append press of button with given id to expression. |
| 331 | // Returns false and does nothing if this would clearly |
| 332 | // result in a syntax error. |
| 333 | boolean add(int id) { |
| 334 | int s = mExpr.size(); |
| 335 | int d = KeyMaps.digVal(id); |
| 336 | boolean binary = KeyMaps.isBinary(id); |
| 337 | if (s == 0 && binary && id != R.id.op_sub) return false; |
| 338 | if (binary && hasTrailingBinary() |
| 339 | && (id != R.id.op_sub || isOperator(s-1, R.id.op_sub))) { |
| 340 | return false; |
| 341 | } |
| 342 | boolean isConstPiece = (d != KeyMaps.NOT_DIGIT || id == R.id.dec_point); |
| 343 | if (isConstPiece) { |
| 344 | if (s == 0) { |
| 345 | mExpr.add(new Constant()); |
| 346 | s++; |
| 347 | } else { |
| 348 | Token last = mExpr.get(s-1); |
| 349 | if(!(last instanceof Constant)) { |
| 350 | if (!(last instanceof Operator)) { |
| 351 | return false; |
| 352 | } |
| 353 | int lastOp = ((Operator)last).mId; |
| 354 | if (lastOp == R.id.const_e || lastOp == R.id.const_pi |
| 355 | || lastOp == R.id.op_fact |
| 356 | || lastOp == R.id.rparen) { |
| 357 | // Constant cannot possibly follow; reject immediately |
| 358 | return false; |
| 359 | } |
| 360 | mExpr.add(new Constant()); |
| 361 | s++; |
| 362 | } |
| 363 | } |
| 364 | return ((Constant)(mExpr.get(s-1))).add(id); |
| 365 | } else { |
| 366 | mExpr.add(new Operator(id)); |
| 367 | return true; |
| 368 | } |
| 369 | } |
| 370 | |
| 371 | // Append the contents of the argument expression. |
| 372 | // It is assumed that the argument expression will not change, |
| 373 | // and thus its pieces can be reused directly. |
| 374 | // TODO: We probably only need this for expressions consisting of |
| 375 | // a single PreEval "token", and may want to check that. |
| 376 | void append(CalculatorExpr expr2) { |
| 377 | int s2 = expr2.mExpr.size(); |
| 378 | for (int i = 0; i < s2; ++i) { |
| 379 | mExpr.add(expr2.mExpr.get(i)); |
| 380 | } |
| 381 | } |
| 382 | |
| 383 | // Undo the last key addition, if any. |
| 384 | void delete() { |
| 385 | int s = mExpr.size(); |
| 386 | if (s == 0) return; |
| 387 | Token last = mExpr.get(s-1); |
| 388 | if (last instanceof Constant) { |
| 389 | Constant c = (Constant)last; |
| 390 | c.delete(); |
| 391 | if (!c.isEmpty()) return; |
| 392 | } |
| 393 | mExpr.remove(s-1); |
| 394 | } |
| 395 | |
| 396 | void clear() { |
| 397 | mExpr.clear(); |
| 398 | } |
| 399 | |
| 400 | boolean isEmpty() { |
| 401 | return mExpr.isEmpty(); |
| 402 | } |
| 403 | |
| 404 | // Returns a logical deep copy of the CalculatorExpr. |
| 405 | // Operator and PreEval tokens are immutable, and thus |
| 406 | // aren't really copied. |
| 407 | public Object clone() { |
| 408 | CalculatorExpr res = new CalculatorExpr(); |
| 409 | for (Token t: mExpr) { |
| 410 | if (t instanceof Constant) { |
| 411 | res.mExpr.add((Token)(((Constant)t).clone())); |
| 412 | } else { |
| 413 | res.mExpr.add(t); |
| 414 | } |
| 415 | } |
| 416 | return res; |
| 417 | } |
| 418 | |
| 419 | // Am I just a constant? |
| 420 | boolean isConstant() { |
| 421 | if (mExpr.size() != 1) return false; |
| 422 | return mExpr.get(0) instanceof Constant; |
| 423 | } |
| 424 | |
| 425 | // Return a new expression consisting of a single PreEval token |
| 426 | // representing the current expression. |
| 427 | // The caller supplies the value, degree mode, and short |
| 428 | // string representation, which must have been previously computed. |
| 429 | // Thus this is guaranteed to terminate reasonably quickly. |
| 430 | CalculatorExpr abbreviate(CR val, BigInteger intVal, |
| 431 | boolean dm, String sr) { |
| 432 | CalculatorExpr result = new CalculatorExpr(); |
| 433 | Token t = new PreEval(val, intVal, |
| 434 | new CalculatorExpr( |
| 435 | (ArrayList<Token>)mExpr.clone()), |
| 436 | new EvalContext(dm), sr); |
| 437 | result.mExpr.add(t); |
| 438 | return result; |
| 439 | } |
| 440 | |
| 441 | // Internal evaluation functions return an EvalRet triple. |
| 442 | // We compute integer (BigInteger) results when possible, both as |
| 443 | // a performance optimization, and to detect errors exactly when we can. |
| 444 | private class EvalRet { |
| 445 | int mPos; // Next position (expression index) to be parsed |
| 446 | final CR mVal; // Constructive Real result of evaluating subexpression |
| 447 | final BigInteger mIntVal; // Exact Integer value or null if not integer |
| 448 | EvalRet(int p, CR v, BigInteger i) { |
| 449 | mPos = p; |
| 450 | mVal = v; |
| 451 | mIntVal = i; |
| 452 | } |
| 453 | } |
| 454 | |
| 455 | // And take a context argument: |
| 456 | private static class EvalContext { |
| 457 | // Memory register contents are not included here, |
| 458 | // since we now make that an explicit part of the expression |
| 459 | // If we add any other kinds of evaluation modes, they go here. |
| 460 | boolean mDegreeMode; |
| 461 | EvalContext(boolean degreeMode) { |
| 462 | mDegreeMode = degreeMode; |
| 463 | } |
| 464 | EvalContext(DataInput in) throws IOException { |
| 465 | mDegreeMode = in.readBoolean(); |
| 466 | } |
| 467 | void write(DataOutput out) throws IOException { |
| 468 | out.writeBoolean(mDegreeMode); |
| 469 | } |
| 470 | } |
| 471 | |
| 472 | private final CR RADIANS_PER_DEGREE = CR.PI.divide(CR.valueOf(180)); |
| 473 | |
| 474 | private final CR DEGREES_PER_RADIAN = CR.valueOf(180).divide(CR.PI); |
| 475 | |
| 476 | private CR toRadians(CR x, EvalContext ec) { |
| 477 | if (ec.mDegreeMode) { |
| 478 | return x.multiply(RADIANS_PER_DEGREE); |
| 479 | } else { |
| 480 | return x; |
| 481 | } |
| 482 | } |
| 483 | |
| 484 | private CR fromRadians(CR x, EvalContext ec) { |
| 485 | if (ec.mDegreeMode) { |
| 486 | return x.multiply(DEGREES_PER_RADIAN); |
| 487 | } else { |
| 488 | return x; |
| 489 | } |
| 490 | } |
| 491 | |
| 492 | // The following methods can all throw IndexOutOfBoundsException |
| 493 | // in the event of a syntax error. We expect that to be caught in |
| 494 | // eval below. |
| 495 | |
| 496 | private boolean isOperator(int i, int op) { |
| 497 | if (i >= mExpr.size()) return false; |
| 498 | Token t = mExpr.get(i); |
| 499 | if (!(t instanceof Operator)) return false; |
| 500 | return ((Operator)(t)).mId == op; |
| 501 | } |
| 502 | |
| 503 | static class SyntaxError extends Error { |
| 504 | public SyntaxError() { |
| 505 | super(); |
| 506 | } |
| 507 | public SyntaxError(String s) { |
| 508 | super(s); |
| 509 | } |
| 510 | } |
| 511 | |
| 512 | // The following functions all evaluate some kind of expression |
| 513 | // starting at position i in mExpr in a specified evaluation context. |
| 514 | // They return both the expression value (as constructive real and, |
| 515 | // if applicable, as BigInteger) and the position of the next token |
| 516 | // that was not used as part of the evaluation. |
| 517 | private EvalRet evalUnary(int i, EvalContext ec) |
| 518 | throws ArithmeticException { |
| 519 | Token t = mExpr.get(i); |
| 520 | CR value; |
| 521 | if (t instanceof Constant) { |
| 522 | Constant c = (Constant)t; |
| 523 | value = CR.valueOf(c.toString(),10); |
| 524 | return new EvalRet(i+1, value, |
| 525 | c.isInt()? new BigInteger(c.mWhole) : null); |
| 526 | } |
| 527 | if (t instanceof PreEval) { |
| 528 | PreEval p = (PreEval)t; |
| 529 | return new EvalRet(i+1, p.mValue, p.mIntValue); |
| 530 | } |
| 531 | EvalRet argVal; |
| 532 | switch(((Operator)(t)).mId) { |
| 533 | case R.id.const_pi: |
| 534 | return new EvalRet(i+1, CR.PI, null); |
| 535 | case R.id.const_e: |
| 536 | return new EvalRet(i+1, CR.valueOf(1).exp(), null); |
| 537 | case R.id.op_sqrt: |
| 538 | // Seems to have highest precedence |
| 539 | // Does not add implicit paren |
| 540 | argVal = evalUnary(i+1, ec); |
| 541 | return new EvalRet(argVal.mPos, argVal.mVal.sqrt(), null); |
| 542 | case R.id.lparen: |
| 543 | argVal = evalExpr(i+1, ec); |
| 544 | if (isOperator(argVal.mPos, R.id.rparen)) argVal.mPos++; |
| 545 | return new EvalRet(argVal.mPos, argVal.mVal, argVal.mIntVal); |
| 546 | case R.id.fun_sin: |
| 547 | argVal = evalExpr(i+1, ec); |
| 548 | if (isOperator(argVal.mPos, R.id.rparen)) argVal.mPos++; |
| 549 | return new EvalRet(argVal.mPos, |
| 550 | toRadians(argVal.mVal,ec).sin(), null); |
| 551 | case R.id.fun_cos: |
| 552 | argVal = evalExpr(i+1, ec); |
| 553 | if (isOperator(argVal.mPos, R.id.rparen)) argVal.mPos++; |
| 554 | return new EvalRet(argVal.mPos, |
| 555 | toRadians(argVal.mVal,ec).cos(), null); |
| 556 | case R.id.fun_tan: |
| 557 | argVal = evalExpr(i+1, ec); |
| 558 | if (isOperator(argVal.mPos, R.id.rparen)) argVal.mPos++; |
| 559 | CR argCR = toRadians(argVal.mVal, ec); |
| 560 | return new EvalRet(argVal.mPos, |
| 561 | argCR.sin().divide(argCR.cos()), null); |
| 562 | case R.id.fun_ln: |
| 563 | argVal = evalExpr(i+1, ec); |
| 564 | if (isOperator(argVal.mPos, R.id.rparen)) argVal.mPos++; |
| 565 | return new EvalRet(argVal.mPos, argVal.mVal.ln(), null); |
| 566 | case R.id.fun_log: |
| 567 | argVal = evalExpr(i+1, ec); |
| 568 | if (isOperator(argVal.mPos, R.id.rparen)) argVal.mPos++; |
| 569 | // FIXME: Heuristically test argument sign |
| 570 | return new EvalRet(argVal.mPos, |
| 571 | argVal.mVal.ln().divide(CR.valueOf(10).ln()), |
| 572 | null); |
| 573 | case R.id.fun_arcsin: |
| 574 | argVal = evalExpr(i+1, ec); |
| 575 | if (isOperator(argVal.mPos, R.id.rparen)) argVal.mPos++; |
| 576 | // FIXME: Heuristically test argument in range |
| 577 | return new EvalRet(argVal.mPos, |
| 578 | fromRadians(UnaryCRFunction |
| 579 | .asinFunction.execute(argVal.mVal),ec), |
| 580 | null); |
| 581 | case R.id.fun_arccos: |
| 582 | argVal = evalExpr(i+1, ec); |
| 583 | if (isOperator(argVal.mPos, R.id.rparen)) argVal.mPos++; |
| 584 | // FIXME: Heuristically test argument in range |
| 585 | return new EvalRet(argVal.mPos, |
| 586 | fromRadians(UnaryCRFunction |
| 587 | .acosFunction.execute(argVal.mVal),ec), |
| 588 | null); |
| 589 | case R.id.fun_arctan: |
| 590 | argVal = evalExpr(i+1, ec); |
| 591 | if (isOperator(argVal.mPos, R.id.rparen)) argVal.mPos++; |
| 592 | return new EvalRet(argVal.mPos, |
| 593 | fromRadians(UnaryCRFunction |
| 594 | .atanFunction.execute(argVal.mVal),ec), |
| 595 | null); |
| 596 | default: |
| 597 | throw new SyntaxError("Unrecognized token in expression"); |
| 598 | } |
| 599 | } |
| 600 | |
| 601 | // Generalized factorial. |
| 602 | // Compute n * (n - step) * (n - 2 * step) * ... |
| 603 | // This can be used to compute factorial a bit faster, especially |
| 604 | // if BigInteger uses sub-quadratic multiplication. |
| 605 | private static BigInteger genFactorial(long n, long step) { |
| 606 | if (n > 4 * step) { |
| 607 | BigInteger prod1 = genFactorial(n, 2 * step); |
| 608 | BigInteger prod2 = genFactorial(n - step, 2 * step); |
| 609 | return prod1.multiply(prod2); |
| 610 | } else { |
| 611 | BigInteger res = BigInteger.valueOf(n); |
| 612 | for (long i = n - step; i > 1; i -= step) { |
| 613 | res = res.multiply(BigInteger.valueOf(i)); |
| 614 | } |
| 615 | return res; |
| 616 | } |
| 617 | } |
| 618 | |
| 619 | // Compute an integral power of a constructive real. |
| 620 | // Unlike the "general" case using logarithms, this handles a negative |
| 621 | // base. |
| 622 | private static CR pow(CR base, BigInteger exp) { |
| 623 | if (exp.compareTo(BigInteger.ZERO) < 0) { |
| 624 | return pow(base, exp.negate()).inverse(); |
| 625 | } |
| 626 | if (exp.equals(BigInteger.ONE)) return base; |
| 627 | if (exp.and(BigInteger.ONE).intValue() == 1) { |
| 628 | return pow(base, exp.subtract(BigInteger.ONE)).multiply(base); |
| 629 | } |
| 630 | if (exp.equals(BigInteger.ZERO)) { |
| 631 | return CR.valueOf(1); |
| 632 | } |
| 633 | CR tmp = pow(base, exp.shiftRight(1)); |
| 634 | return tmp.multiply(tmp); |
| 635 | } |
| 636 | |
| 637 | private EvalRet evalFactorial(int i, EvalContext ec) { |
| 638 | EvalRet tmp = evalUnary(i, ec); |
| 639 | int cpos = tmp.mPos; |
| 640 | CR cval = tmp.mVal; |
| 641 | BigInteger ival = tmp.mIntVal; |
| 642 | while (isOperator(cpos, R.id.op_fact)) { |
| 643 | if (ival == null) { |
| 644 | // Assume it was an integer, but we |
| 645 | // didn't figure it out. |
| 646 | // Calculator2 may have used the Gamma function. |
| 647 | ival = cval.BigIntegerValue(); |
| 648 | } |
| 649 | if (ival.compareTo(BigInteger.ZERO) <= 0 |
| 650 | || ival.compareTo(BIG_BILLION) > 0) { |
| 651 | throw new ArithmeticException("Bad factorial argument"); |
| 652 | } |
| 653 | ival = genFactorial(ival.longValue(), 1); |
| 654 | ++cpos; |
| 655 | } |
| 656 | if (ival != null) cval = CR.valueOf(ival); |
| 657 | return new EvalRet(cpos, cval, ival); |
| 658 | } |
| 659 | |
| 660 | private EvalRet evalFactor(int i, EvalContext ec) |
| 661 | throws ArithmeticException { |
| 662 | final EvalRet result1 = evalFactorial(i, ec); |
| 663 | int cpos = result1.mPos; // current position |
| 664 | CR cval = result1.mVal; // value so far |
| 665 | BigInteger ival = result1.mIntVal; // int value so far |
| 666 | if (isOperator(cpos, R.id.op_pow)) { |
| 667 | final EvalRet exp = evalSignedFactor(cpos+1, ec); |
| 668 | cpos = exp.mPos; |
| 669 | if (ival != null && ival.equals(BigInteger.ONE)) { |
| 670 | // 1^x = 1 |
| 671 | return new EvalRet(cpos, cval, ival); |
| 672 | } |
| 673 | if (exp.mIntVal != null) { |
| 674 | if (ival != null |
| 675 | && exp.mIntVal.compareTo(BigInteger.ZERO) >= 0 |
| 676 | && exp.mIntVal.compareTo(BIG_MILLION) < 0 |
| 677 | && ival.abs().compareTo(BIG_MILLION) < 0) { |
| 678 | // Use pure integer exponentiation |
| 679 | ival = ival.pow(exp.mIntVal.intValue()); |
| 680 | cval = CR.valueOf(ival); |
| 681 | } else { |
| 682 | // Integer exponent, cval may be negative; |
| 683 | // use repeated squaring. Unsafe to use ln(). |
| 684 | ival = null; |
| 685 | cval = pow(cval, exp.mIntVal); |
| 686 | } |
| 687 | } else { |
| 688 | ival = null; |
| 689 | cval = cval.ln().multiply(exp.mVal).exp(); |
| 690 | } |
| 691 | } |
| 692 | return new EvalRet(cpos, cval, ival); |
| 693 | } |
| 694 | |
| 695 | private EvalRet evalSignedFactor(int i, EvalContext ec) |
| 696 | throws ArithmeticException { |
| 697 | final boolean negative = isOperator(i, R.id.op_sub); |
| 698 | int cpos = negative? i + 1 : i; |
| 699 | EvalRet tmp = evalFactor(cpos, ec); |
| 700 | cpos = tmp.mPos; |
| 701 | CR cval = negative? tmp.mVal.negate() : tmp.mVal; |
| 702 | BigInteger ival = (negative && tmp.mIntVal != null)? |
| 703 | tmp.mIntVal.negate() |
| 704 | : tmp.mIntVal; |
| 705 | return new EvalRet(cpos, cval, ival); |
| 706 | } |
| 707 | |
| 708 | private boolean canStartFactor(int i) { |
| 709 | if (i >= mExpr.size()) return false; |
| 710 | Token t = mExpr.get(i); |
| 711 | if (!(t instanceof Operator)) return true; |
| 712 | int id = ((Operator)(t)).mId; |
| 713 | if (KeyMaps.isBinary(id)) return false; |
| 714 | switch (id) { |
| 715 | case R.id.op_fact: |
| 716 | case R.id.rparen: |
| 717 | return false; |
| 718 | default: |
| 719 | return true; |
| 720 | } |
| 721 | } |
| 722 | |
| 723 | private EvalRet evalTerm(int i, EvalContext ec) |
| 724 | throws ArithmeticException { |
| 725 | EvalRet tmp = evalSignedFactor(i, ec); |
| 726 | boolean is_mul = false; |
| 727 | boolean is_div = false; |
| 728 | int cpos = tmp.mPos; // Current position in expression. |
| 729 | CR cval = tmp.mVal; // Current value. |
| 730 | BigInteger ival = tmp.mIntVal; |
| 731 | while ((is_mul = isOperator(cpos, R.id.op_mul)) |
| 732 | || (is_div = isOperator(cpos, R.id.op_div)) |
| 733 | || canStartFactor(cpos)) { |
| 734 | if (is_mul || is_div) ++cpos; |
| 735 | tmp = evalTerm(cpos, ec); |
| 736 | if (is_div) { |
| 737 | if (ival != null && tmp.mIntVal != null |
| 738 | && ival.mod(tmp.mIntVal) == BigInteger.ZERO) { |
| 739 | ival = ival.divide(tmp.mIntVal); |
| 740 | cval = CR.valueOf(ival); |
| 741 | } else { |
| 742 | cval = cval.divide(tmp.mVal); |
| 743 | ival = null; |
| 744 | } |
| 745 | } else { |
| 746 | if (ival != null && tmp.mIntVal != null) { |
| 747 | ival = ival.multiply(tmp.mIntVal); |
| 748 | cval = CR.valueOf(ival); |
| 749 | } else { |
| 750 | cval = cval.multiply(tmp.mVal); |
| 751 | ival = null; |
| 752 | } |
| 753 | } |
| 754 | cpos = tmp.mPos; |
| 755 | is_mul = is_div = false; |
| 756 | } |
| 757 | return new EvalRet(cpos, cval, ival); |
| 758 | } |
| 759 | |
| 760 | private EvalRet evalExpr(int i, EvalContext ec) throws ArithmeticException { |
| 761 | EvalRet tmp = evalTerm(i, ec); |
| 762 | boolean is_plus; |
| 763 | int cpos = tmp.mPos; |
| 764 | CR cval = tmp.mVal; |
| 765 | BigInteger ival = tmp.mIntVal; |
| 766 | while ((is_plus = isOperator(cpos, R.id.op_add)) |
| 767 | || isOperator(cpos, R.id.op_sub)) { |
| 768 | tmp = evalTerm(cpos+1, ec); |
| 769 | if (is_plus) { |
| 770 | if (ival != null && tmp.mIntVal != null) { |
| 771 | ival = ival.add(tmp.mIntVal); |
| 772 | cval = CR.valueOf(ival); |
| 773 | } else { |
| 774 | cval = cval.add(tmp.mVal); |
| 775 | ival = null; |
| 776 | } |
| 777 | } else { |
| 778 | if (ival != null && tmp.mIntVal != null) { |
| 779 | ival = ival.subtract(tmp.mIntVal); |
| 780 | cval = CR.valueOf(ival); |
| 781 | } else { |
| 782 | cval = cval.subtract(tmp.mVal); |
| 783 | ival = null; |
| 784 | } |
| 785 | } |
| 786 | cpos = tmp.mPos; |
| 787 | } |
| 788 | return new EvalRet(cpos, cval, ival); |
| 789 | } |
| 790 | |
| 791 | // Externally visible evaluation result. |
| 792 | public class EvalResult { |
| 793 | EvalResult (CR val, BigInteger intVal) { |
| 794 | mVal = val; |
| 795 | mIntVal = intVal; |
| 796 | } |
| 797 | final CR mVal; |
| 798 | final BigInteger mIntVal; |
| 799 | } |
| 800 | |
| 801 | // Evaluate the entire expression, returning null in the event |
| 802 | // of an error. |
| 803 | // Not called from the UI thread, but should not be called |
| 804 | // concurrently with modifications to the expression. |
| 805 | EvalResult eval(boolean degreeMode) throws SyntaxError, |
| 806 | ArithmeticException, PrecisionOverflowError |
| 807 | { |
| 808 | try { |
| 809 | EvalContext ec = new EvalContext(degreeMode); |
| 810 | EvalRet res = evalExpr(0, ec); |
| 811 | if (res.mPos != mExpr.size()) return null; |
| 812 | return new EvalResult(res.mVal, res.mIntVal); |
| 813 | } catch (IndexOutOfBoundsException e) { |
| 814 | throw new SyntaxError("Unexpected expression end"); |
| 815 | } |
| 816 | } |
| 817 | |
| 818 | // Produce a string representation of the expression itself |
| 819 | String toString(Context context) { |
| 820 | StringBuilder sb = new StringBuilder(); |
| 821 | for (Token t: mExpr) { |
| 822 | sb.append(t.toString(context)); |
| 823 | } |
| 824 | return sb.toString(); |
| 825 | } |
| 826 | } |