APInt.cpp revision 218893
1//===-- APInt.cpp - Implement APInt class ---------------------------------===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file is distributed under the University of Illinois Open Source 6// License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file implements a class to represent arbitrary precision integer 11// constant values and provide a variety of arithmetic operations on them. 12// 13//===----------------------------------------------------------------------===// 14 15#define DEBUG_TYPE "apint" 16#include "llvm/ADT/APInt.h" 17#include "llvm/ADT/StringRef.h" 18#include "llvm/ADT/FoldingSet.h" 19#include "llvm/ADT/SmallString.h" 20#include "llvm/Support/Debug.h" 21#include "llvm/Support/ErrorHandling.h" 22#include "llvm/Support/MathExtras.h" 23#include "llvm/Support/raw_ostream.h" 24#include <cmath> 25#include <limits> 26#include <cstring> 27#include <cstdlib> 28using namespace llvm; 29 30/// A utility function for allocating memory, checking for allocation failures, 31/// and ensuring the contents are zeroed. 32inline static uint64_t* getClearedMemory(unsigned numWords) { 33 uint64_t * result = new uint64_t[numWords]; 34 assert(result && "APInt memory allocation fails!"); 35 memset(result, 0, numWords * sizeof(uint64_t)); 36 return result; 37} 38 39/// A utility function for allocating memory and checking for allocation 40/// failure. The content is not zeroed. 41inline static uint64_t* getMemory(unsigned numWords) { 42 uint64_t * result = new uint64_t[numWords]; 43 assert(result && "APInt memory allocation fails!"); 44 return result; 45} 46 47/// A utility function that converts a character to a digit. 48inline static unsigned getDigit(char cdigit, uint8_t radix) { 49 unsigned r; 50 51 if (radix == 16) { 52 r = cdigit - '0'; 53 if (r <= 9) 54 return r; 55 56 r = cdigit - 'A'; 57 if (r <= 5) 58 return r + 10; 59 60 r = cdigit - 'a'; 61 if (r <= 5) 62 return r + 10; 63 } 64 65 r = cdigit - '0'; 66 if (r < radix) 67 return r; 68 69 return -1U; 70} 71 72 73void APInt::initSlowCase(unsigned numBits, uint64_t val, bool isSigned) { 74 pVal = getClearedMemory(getNumWords()); 75 pVal[0] = val; 76 if (isSigned && int64_t(val) < 0) 77 for (unsigned i = 1; i < getNumWords(); ++i) 78 pVal[i] = -1ULL; 79} 80 81void APInt::initSlowCase(const APInt& that) { 82 pVal = getMemory(getNumWords()); 83 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE); 84} 85 86 87APInt::APInt(unsigned numBits, unsigned numWords, const uint64_t bigVal[]) 88 : BitWidth(numBits), VAL(0) { 89 assert(BitWidth && "Bitwidth too small"); 90 assert(bigVal && "Null pointer detected!"); 91 if (isSingleWord()) 92 VAL = bigVal[0]; 93 else { 94 // Get memory, cleared to 0 95 pVal = getClearedMemory(getNumWords()); 96 // Calculate the number of words to copy 97 unsigned words = std::min<unsigned>(numWords, getNumWords()); 98 // Copy the words from bigVal to pVal 99 memcpy(pVal, bigVal, words * APINT_WORD_SIZE); 100 } 101 // Make sure unused high bits are cleared 102 clearUnusedBits(); 103} 104 105APInt::APInt(unsigned numbits, StringRef Str, uint8_t radix) 106 : BitWidth(numbits), VAL(0) { 107 assert(BitWidth && "Bitwidth too small"); 108 fromString(numbits, Str, radix); 109} 110 111APInt& APInt::AssignSlowCase(const APInt& RHS) { 112 // Don't do anything for X = X 113 if (this == &RHS) 114 return *this; 115 116 if (BitWidth == RHS.getBitWidth()) { 117 // assume same bit-width single-word case is already handled 118 assert(!isSingleWord()); 119 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE); 120 return *this; 121 } 122 123 if (isSingleWord()) { 124 // assume case where both are single words is already handled 125 assert(!RHS.isSingleWord()); 126 VAL = 0; 127 pVal = getMemory(RHS.getNumWords()); 128 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 129 } else if (getNumWords() == RHS.getNumWords()) 130 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 131 else if (RHS.isSingleWord()) { 132 delete [] pVal; 133 VAL = RHS.VAL; 134 } else { 135 delete [] pVal; 136 pVal = getMemory(RHS.getNumWords()); 137 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 138 } 139 BitWidth = RHS.BitWidth; 140 return clearUnusedBits(); 141} 142 143APInt& APInt::operator=(uint64_t RHS) { 144 if (isSingleWord()) 145 VAL = RHS; 146 else { 147 pVal[0] = RHS; 148 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE); 149 } 150 return clearUnusedBits(); 151} 152 153/// Profile - This method 'profiles' an APInt for use with FoldingSet. 154void APInt::Profile(FoldingSetNodeID& ID) const { 155 ID.AddInteger(BitWidth); 156 157 if (isSingleWord()) { 158 ID.AddInteger(VAL); 159 return; 160 } 161 162 unsigned NumWords = getNumWords(); 163 for (unsigned i = 0; i < NumWords; ++i) 164 ID.AddInteger(pVal[i]); 165} 166 167/// add_1 - This function adds a single "digit" integer, y, to the multiple 168/// "digit" integer array, x[]. x[] is modified to reflect the addition and 169/// 1 is returned if there is a carry out, otherwise 0 is returned. 170/// @returns the carry of the addition. 171static bool add_1(uint64_t dest[], uint64_t x[], unsigned len, uint64_t y) { 172 for (unsigned i = 0; i < len; ++i) { 173 dest[i] = y + x[i]; 174 if (dest[i] < y) 175 y = 1; // Carry one to next digit. 176 else { 177 y = 0; // No need to carry so exit early 178 break; 179 } 180 } 181 return y; 182} 183 184/// @brief Prefix increment operator. Increments the APInt by one. 185APInt& APInt::operator++() { 186 if (isSingleWord()) 187 ++VAL; 188 else 189 add_1(pVal, pVal, getNumWords(), 1); 190 return clearUnusedBits(); 191} 192 193/// sub_1 - This function subtracts a single "digit" (64-bit word), y, from 194/// the multi-digit integer array, x[], propagating the borrowed 1 value until 195/// no further borrowing is neeeded or it runs out of "digits" in x. The result 196/// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted. 197/// In other words, if y > x then this function returns 1, otherwise 0. 198/// @returns the borrow out of the subtraction 199static bool sub_1(uint64_t x[], unsigned len, uint64_t y) { 200 for (unsigned i = 0; i < len; ++i) { 201 uint64_t X = x[i]; 202 x[i] -= y; 203 if (y > X) 204 y = 1; // We have to "borrow 1" from next "digit" 205 else { 206 y = 0; // No need to borrow 207 break; // Remaining digits are unchanged so exit early 208 } 209 } 210 return bool(y); 211} 212 213/// @brief Prefix decrement operator. Decrements the APInt by one. 214APInt& APInt::operator--() { 215 if (isSingleWord()) 216 --VAL; 217 else 218 sub_1(pVal, getNumWords(), 1); 219 return clearUnusedBits(); 220} 221 222/// add - This function adds the integer array x to the integer array Y and 223/// places the result in dest. 224/// @returns the carry out from the addition 225/// @brief General addition of 64-bit integer arrays 226static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y, 227 unsigned len) { 228 bool carry = false; 229 for (unsigned i = 0; i< len; ++i) { 230 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x 231 dest[i] = x[i] + y[i] + carry; 232 carry = dest[i] < limit || (carry && dest[i] == limit); 233 } 234 return carry; 235} 236 237/// Adds the RHS APint to this APInt. 238/// @returns this, after addition of RHS. 239/// @brief Addition assignment operator. 240APInt& APInt::operator+=(const APInt& RHS) { 241 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 242 if (isSingleWord()) 243 VAL += RHS.VAL; 244 else { 245 add(pVal, pVal, RHS.pVal, getNumWords()); 246 } 247 return clearUnusedBits(); 248} 249 250/// Subtracts the integer array y from the integer array x 251/// @returns returns the borrow out. 252/// @brief Generalized subtraction of 64-bit integer arrays. 253static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y, 254 unsigned len) { 255 bool borrow = false; 256 for (unsigned i = 0; i < len; ++i) { 257 uint64_t x_tmp = borrow ? x[i] - 1 : x[i]; 258 borrow = y[i] > x_tmp || (borrow && x[i] == 0); 259 dest[i] = x_tmp - y[i]; 260 } 261 return borrow; 262} 263 264/// Subtracts the RHS APInt from this APInt 265/// @returns this, after subtraction 266/// @brief Subtraction assignment operator. 267APInt& APInt::operator-=(const APInt& RHS) { 268 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 269 if (isSingleWord()) 270 VAL -= RHS.VAL; 271 else 272 sub(pVal, pVal, RHS.pVal, getNumWords()); 273 return clearUnusedBits(); 274} 275 276/// Multiplies an integer array, x, by a uint64_t integer and places the result 277/// into dest. 278/// @returns the carry out of the multiplication. 279/// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer. 280static uint64_t mul_1(uint64_t dest[], uint64_t x[], unsigned len, uint64_t y) { 281 // Split y into high 32-bit part (hy) and low 32-bit part (ly) 282 uint64_t ly = y & 0xffffffffULL, hy = y >> 32; 283 uint64_t carry = 0; 284 285 // For each digit of x. 286 for (unsigned i = 0; i < len; ++i) { 287 // Split x into high and low words 288 uint64_t lx = x[i] & 0xffffffffULL; 289 uint64_t hx = x[i] >> 32; 290 // hasCarry - A flag to indicate if there is a carry to the next digit. 291 // hasCarry == 0, no carry 292 // hasCarry == 1, has carry 293 // hasCarry == 2, no carry and the calculation result == 0. 294 uint8_t hasCarry = 0; 295 dest[i] = carry + lx * ly; 296 // Determine if the add above introduces carry. 297 hasCarry = (dest[i] < carry) ? 1 : 0; 298 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0); 299 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) + 300 // (2^32 - 1) + 2^32 = 2^64. 301 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0); 302 303 carry += (lx * hy) & 0xffffffffULL; 304 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL); 305 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) + 306 (carry >> 32) + ((lx * hy) >> 32) + hx * hy; 307 } 308 return carry; 309} 310 311/// Multiplies integer array x by integer array y and stores the result into 312/// the integer array dest. Note that dest's size must be >= xlen + ylen. 313/// @brief Generalized multiplicate of integer arrays. 314static void mul(uint64_t dest[], uint64_t x[], unsigned xlen, uint64_t y[], 315 unsigned ylen) { 316 dest[xlen] = mul_1(dest, x, xlen, y[0]); 317 for (unsigned i = 1; i < ylen; ++i) { 318 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32; 319 uint64_t carry = 0, lx = 0, hx = 0; 320 for (unsigned j = 0; j < xlen; ++j) { 321 lx = x[j] & 0xffffffffULL; 322 hx = x[j] >> 32; 323 // hasCarry - A flag to indicate if has carry. 324 // hasCarry == 0, no carry 325 // hasCarry == 1, has carry 326 // hasCarry == 2, no carry and the calculation result == 0. 327 uint8_t hasCarry = 0; 328 uint64_t resul = carry + lx * ly; 329 hasCarry = (resul < carry) ? 1 : 0; 330 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32); 331 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0); 332 333 carry += (lx * hy) & 0xffffffffULL; 334 resul = (carry << 32) | (resul & 0xffffffffULL); 335 dest[i+j] += resul; 336 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+ 337 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) + 338 ((lx * hy) >> 32) + hx * hy; 339 } 340 dest[i+xlen] = carry; 341 } 342} 343 344APInt& APInt::operator*=(const APInt& RHS) { 345 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 346 if (isSingleWord()) { 347 VAL *= RHS.VAL; 348 clearUnusedBits(); 349 return *this; 350 } 351 352 // Get some bit facts about LHS and check for zero 353 unsigned lhsBits = getActiveBits(); 354 unsigned lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1; 355 if (!lhsWords) 356 // 0 * X ===> 0 357 return *this; 358 359 // Get some bit facts about RHS and check for zero 360 unsigned rhsBits = RHS.getActiveBits(); 361 unsigned rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1; 362 if (!rhsWords) { 363 // X * 0 ===> 0 364 clearAllBits(); 365 return *this; 366 } 367 368 // Allocate space for the result 369 unsigned destWords = rhsWords + lhsWords; 370 uint64_t *dest = getMemory(destWords); 371 372 // Perform the long multiply 373 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords); 374 375 // Copy result back into *this 376 clearAllBits(); 377 unsigned wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords; 378 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE); 379 380 // delete dest array and return 381 delete[] dest; 382 return *this; 383} 384 385APInt& APInt::operator&=(const APInt& RHS) { 386 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 387 if (isSingleWord()) { 388 VAL &= RHS.VAL; 389 return *this; 390 } 391 unsigned numWords = getNumWords(); 392 for (unsigned i = 0; i < numWords; ++i) 393 pVal[i] &= RHS.pVal[i]; 394 return *this; 395} 396 397APInt& APInt::operator|=(const APInt& RHS) { 398 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 399 if (isSingleWord()) { 400 VAL |= RHS.VAL; 401 return *this; 402 } 403 unsigned numWords = getNumWords(); 404 for (unsigned i = 0; i < numWords; ++i) 405 pVal[i] |= RHS.pVal[i]; 406 return *this; 407} 408 409APInt& APInt::operator^=(const APInt& RHS) { 410 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 411 if (isSingleWord()) { 412 VAL ^= RHS.VAL; 413 this->clearUnusedBits(); 414 return *this; 415 } 416 unsigned numWords = getNumWords(); 417 for (unsigned i = 0; i < numWords; ++i) 418 pVal[i] ^= RHS.pVal[i]; 419 return clearUnusedBits(); 420} 421 422APInt APInt::AndSlowCase(const APInt& RHS) const { 423 unsigned numWords = getNumWords(); 424 uint64_t* val = getMemory(numWords); 425 for (unsigned i = 0; i < numWords; ++i) 426 val[i] = pVal[i] & RHS.pVal[i]; 427 return APInt(val, getBitWidth()); 428} 429 430APInt APInt::OrSlowCase(const APInt& RHS) const { 431 unsigned numWords = getNumWords(); 432 uint64_t *val = getMemory(numWords); 433 for (unsigned i = 0; i < numWords; ++i) 434 val[i] = pVal[i] | RHS.pVal[i]; 435 return APInt(val, getBitWidth()); 436} 437 438APInt APInt::XorSlowCase(const APInt& RHS) const { 439 unsigned numWords = getNumWords(); 440 uint64_t *val = getMemory(numWords); 441 for (unsigned i = 0; i < numWords; ++i) 442 val[i] = pVal[i] ^ RHS.pVal[i]; 443 444 // 0^0==1 so clear the high bits in case they got set. 445 return APInt(val, getBitWidth()).clearUnusedBits(); 446} 447 448bool APInt::operator !() const { 449 if (isSingleWord()) 450 return !VAL; 451 452 for (unsigned i = 0; i < getNumWords(); ++i) 453 if (pVal[i]) 454 return false; 455 return true; 456} 457 458APInt APInt::operator*(const APInt& RHS) const { 459 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 460 if (isSingleWord()) 461 return APInt(BitWidth, VAL * RHS.VAL); 462 APInt Result(*this); 463 Result *= RHS; 464 return Result.clearUnusedBits(); 465} 466 467APInt APInt::operator+(const APInt& RHS) const { 468 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 469 if (isSingleWord()) 470 return APInt(BitWidth, VAL + RHS.VAL); 471 APInt Result(BitWidth, 0); 472 add(Result.pVal, this->pVal, RHS.pVal, getNumWords()); 473 return Result.clearUnusedBits(); 474} 475 476APInt APInt::operator-(const APInt& RHS) const { 477 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 478 if (isSingleWord()) 479 return APInt(BitWidth, VAL - RHS.VAL); 480 APInt Result(BitWidth, 0); 481 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords()); 482 return Result.clearUnusedBits(); 483} 484 485bool APInt::operator[](unsigned bitPosition) const { 486 assert(bitPosition < getBitWidth() && "Bit position out of bounds!"); 487 return (maskBit(bitPosition) & 488 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0; 489} 490 491bool APInt::EqualSlowCase(const APInt& RHS) const { 492 // Get some facts about the number of bits used in the two operands. 493 unsigned n1 = getActiveBits(); 494 unsigned n2 = RHS.getActiveBits(); 495 496 // If the number of bits isn't the same, they aren't equal 497 if (n1 != n2) 498 return false; 499 500 // If the number of bits fits in a word, we only need to compare the low word. 501 if (n1 <= APINT_BITS_PER_WORD) 502 return pVal[0] == RHS.pVal[0]; 503 504 // Otherwise, compare everything 505 for (int i = whichWord(n1 - 1); i >= 0; --i) 506 if (pVal[i] != RHS.pVal[i]) 507 return false; 508 return true; 509} 510 511bool APInt::EqualSlowCase(uint64_t Val) const { 512 unsigned n = getActiveBits(); 513 if (n <= APINT_BITS_PER_WORD) 514 return pVal[0] == Val; 515 else 516 return false; 517} 518 519bool APInt::ult(const APInt& RHS) const { 520 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); 521 if (isSingleWord()) 522 return VAL < RHS.VAL; 523 524 // Get active bit length of both operands 525 unsigned n1 = getActiveBits(); 526 unsigned n2 = RHS.getActiveBits(); 527 528 // If magnitude of LHS is less than RHS, return true. 529 if (n1 < n2) 530 return true; 531 532 // If magnitude of RHS is greather than LHS, return false. 533 if (n2 < n1) 534 return false; 535 536 // If they bot fit in a word, just compare the low order word 537 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD) 538 return pVal[0] < RHS.pVal[0]; 539 540 // Otherwise, compare all words 541 unsigned topWord = whichWord(std::max(n1,n2)-1); 542 for (int i = topWord; i >= 0; --i) { 543 if (pVal[i] > RHS.pVal[i]) 544 return false; 545 if (pVal[i] < RHS.pVal[i]) 546 return true; 547 } 548 return false; 549} 550 551bool APInt::slt(const APInt& RHS) const { 552 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); 553 if (isSingleWord()) { 554 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth); 555 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth); 556 return lhsSext < rhsSext; 557 } 558 559 APInt lhs(*this); 560 APInt rhs(RHS); 561 bool lhsNeg = isNegative(); 562 bool rhsNeg = rhs.isNegative(); 563 if (lhsNeg) { 564 // Sign bit is set so perform two's complement to make it positive 565 lhs.flipAllBits(); 566 lhs++; 567 } 568 if (rhsNeg) { 569 // Sign bit is set so perform two's complement to make it positive 570 rhs.flipAllBits(); 571 rhs++; 572 } 573 574 // Now we have unsigned values to compare so do the comparison if necessary 575 // based on the negativeness of the values. 576 if (lhsNeg) 577 if (rhsNeg) 578 return lhs.ugt(rhs); 579 else 580 return true; 581 else if (rhsNeg) 582 return false; 583 else 584 return lhs.ult(rhs); 585} 586 587void APInt::setBit(unsigned bitPosition) { 588 if (isSingleWord()) 589 VAL |= maskBit(bitPosition); 590 else 591 pVal[whichWord(bitPosition)] |= maskBit(bitPosition); 592} 593 594/// Set the given bit to 0 whose position is given as "bitPosition". 595/// @brief Set a given bit to 0. 596void APInt::clearBit(unsigned bitPosition) { 597 if (isSingleWord()) 598 VAL &= ~maskBit(bitPosition); 599 else 600 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition); 601} 602 603/// @brief Toggle every bit to its opposite value. 604 605/// Toggle a given bit to its opposite value whose position is given 606/// as "bitPosition". 607/// @brief Toggles a given bit to its opposite value. 608void APInt::flipBit(unsigned bitPosition) { 609 assert(bitPosition < BitWidth && "Out of the bit-width range!"); 610 if ((*this)[bitPosition]) clearBit(bitPosition); 611 else setBit(bitPosition); 612} 613 614unsigned APInt::getBitsNeeded(StringRef str, uint8_t radix) { 615 assert(!str.empty() && "Invalid string length"); 616 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) && 617 "Radix should be 2, 8, 10, or 16!"); 618 619 size_t slen = str.size(); 620 621 // Each computation below needs to know if it's negative. 622 StringRef::iterator p = str.begin(); 623 unsigned isNegative = *p == '-'; 624 if (*p == '-' || *p == '+') { 625 p++; 626 slen--; 627 assert(slen && "String is only a sign, needs a value."); 628 } 629 630 // For radixes of power-of-two values, the bits required is accurately and 631 // easily computed 632 if (radix == 2) 633 return slen + isNegative; 634 if (radix == 8) 635 return slen * 3 + isNegative; 636 if (radix == 16) 637 return slen * 4 + isNegative; 638 639 // This is grossly inefficient but accurate. We could probably do something 640 // with a computation of roughly slen*64/20 and then adjust by the value of 641 // the first few digits. But, I'm not sure how accurate that could be. 642 643 // Compute a sufficient number of bits that is always large enough but might 644 // be too large. This avoids the assertion in the constructor. This 645 // calculation doesn't work appropriately for the numbers 0-9, so just use 4 646 // bits in that case. 647 unsigned sufficient = slen == 1 ? 4 : slen * 64/18; 648 649 // Convert to the actual binary value. 650 APInt tmp(sufficient, StringRef(p, slen), radix); 651 652 // Compute how many bits are required. If the log is infinite, assume we need 653 // just bit. 654 unsigned log = tmp.logBase2(); 655 if (log == (unsigned)-1) { 656 return isNegative + 1; 657 } else { 658 return isNegative + log + 1; 659 } 660} 661 662// From http://www.burtleburtle.net, byBob Jenkins. 663// When targeting x86, both GCC and LLVM seem to recognize this as a 664// rotate instruction. 665#define rot(x,k) (((x)<<(k)) | ((x)>>(32-(k)))) 666 667// From http://www.burtleburtle.net, by Bob Jenkins. 668#define mix(a,b,c) \ 669 { \ 670 a -= c; a ^= rot(c, 4); c += b; \ 671 b -= a; b ^= rot(a, 6); a += c; \ 672 c -= b; c ^= rot(b, 8); b += a; \ 673 a -= c; a ^= rot(c,16); c += b; \ 674 b -= a; b ^= rot(a,19); a += c; \ 675 c -= b; c ^= rot(b, 4); b += a; \ 676 } 677 678// From http://www.burtleburtle.net, by Bob Jenkins. 679#define final(a,b,c) \ 680 { \ 681 c ^= b; c -= rot(b,14); \ 682 a ^= c; a -= rot(c,11); \ 683 b ^= a; b -= rot(a,25); \ 684 c ^= b; c -= rot(b,16); \ 685 a ^= c; a -= rot(c,4); \ 686 b ^= a; b -= rot(a,14); \ 687 c ^= b; c -= rot(b,24); \ 688 } 689 690// hashword() was adapted from http://www.burtleburtle.net, by Bob 691// Jenkins. k is a pointer to an array of uint32_t values; length is 692// the length of the key, in 32-bit chunks. This version only handles 693// keys that are a multiple of 32 bits in size. 694static inline uint32_t hashword(const uint64_t *k64, size_t length) 695{ 696 const uint32_t *k = reinterpret_cast<const uint32_t *>(k64); 697 uint32_t a,b,c; 698 699 /* Set up the internal state */ 700 a = b = c = 0xdeadbeef + (((uint32_t)length)<<2); 701 702 /*------------------------------------------------- handle most of the key */ 703 while (length > 3) { 704 a += k[0]; 705 b += k[1]; 706 c += k[2]; 707 mix(a,b,c); 708 length -= 3; 709 k += 3; 710 } 711 712 /*------------------------------------------- handle the last 3 uint32_t's */ 713 switch (length) { /* all the case statements fall through */ 714 case 3 : c+=k[2]; 715 case 2 : b+=k[1]; 716 case 1 : a+=k[0]; 717 final(a,b,c); 718 case 0: /* case 0: nothing left to add */ 719 break; 720 } 721 /*------------------------------------------------------ report the result */ 722 return c; 723} 724 725// hashword8() was adapted from http://www.burtleburtle.net, by Bob 726// Jenkins. This computes a 32-bit hash from one 64-bit word. When 727// targeting x86 (32 or 64 bit), both LLVM and GCC compile this 728// function into about 35 instructions when inlined. 729static inline uint32_t hashword8(const uint64_t k64) 730{ 731 uint32_t a,b,c; 732 a = b = c = 0xdeadbeef + 4; 733 b += k64 >> 32; 734 a += k64 & 0xffffffff; 735 final(a,b,c); 736 return c; 737} 738#undef final 739#undef mix 740#undef rot 741 742uint64_t APInt::getHashValue() const { 743 uint64_t hash; 744 if (isSingleWord()) 745 hash = hashword8(VAL); 746 else 747 hash = hashword(pVal, getNumWords()*2); 748 return hash; 749} 750 751/// HiBits - This function returns the high "numBits" bits of this APInt. 752APInt APInt::getHiBits(unsigned numBits) const { 753 return APIntOps::lshr(*this, BitWidth - numBits); 754} 755 756/// LoBits - This function returns the low "numBits" bits of this APInt. 757APInt APInt::getLoBits(unsigned numBits) const { 758 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits), 759 BitWidth - numBits); 760} 761 762unsigned APInt::countLeadingZerosSlowCase() const { 763 // Treat the most significand word differently because it might have 764 // meaningless bits set beyond the precision. 765 unsigned BitsInMSW = BitWidth % APINT_BITS_PER_WORD; 766 integerPart MSWMask; 767 if (BitsInMSW) MSWMask = (integerPart(1) << BitsInMSW) - 1; 768 else { 769 MSWMask = ~integerPart(0); 770 BitsInMSW = APINT_BITS_PER_WORD; 771 } 772 773 unsigned i = getNumWords(); 774 integerPart MSW = pVal[i-1] & MSWMask; 775 if (MSW) 776 return CountLeadingZeros_64(MSW) - (APINT_BITS_PER_WORD - BitsInMSW); 777 778 unsigned Count = BitsInMSW; 779 for (--i; i > 0u; --i) { 780 if (pVal[i-1] == 0) 781 Count += APINT_BITS_PER_WORD; 782 else { 783 Count += CountLeadingZeros_64(pVal[i-1]); 784 break; 785 } 786 } 787 return Count; 788} 789 790static unsigned countLeadingOnes_64(uint64_t V, unsigned skip) { 791 unsigned Count = 0; 792 if (skip) 793 V <<= skip; 794 while (V && (V & (1ULL << 63))) { 795 Count++; 796 V <<= 1; 797 } 798 return Count; 799} 800 801unsigned APInt::countLeadingOnes() const { 802 if (isSingleWord()) 803 return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth); 804 805 unsigned highWordBits = BitWidth % APINT_BITS_PER_WORD; 806 unsigned shift; 807 if (!highWordBits) { 808 highWordBits = APINT_BITS_PER_WORD; 809 shift = 0; 810 } else { 811 shift = APINT_BITS_PER_WORD - highWordBits; 812 } 813 int i = getNumWords() - 1; 814 unsigned Count = countLeadingOnes_64(pVal[i], shift); 815 if (Count == highWordBits) { 816 for (i--; i >= 0; --i) { 817 if (pVal[i] == -1ULL) 818 Count += APINT_BITS_PER_WORD; 819 else { 820 Count += countLeadingOnes_64(pVal[i], 0); 821 break; 822 } 823 } 824 } 825 return Count; 826} 827 828unsigned APInt::countTrailingZeros() const { 829 if (isSingleWord()) 830 return std::min(unsigned(CountTrailingZeros_64(VAL)), BitWidth); 831 unsigned Count = 0; 832 unsigned i = 0; 833 for (; i < getNumWords() && pVal[i] == 0; ++i) 834 Count += APINT_BITS_PER_WORD; 835 if (i < getNumWords()) 836 Count += CountTrailingZeros_64(pVal[i]); 837 return std::min(Count, BitWidth); 838} 839 840unsigned APInt::countTrailingOnesSlowCase() const { 841 unsigned Count = 0; 842 unsigned i = 0; 843 for (; i < getNumWords() && pVal[i] == -1ULL; ++i) 844 Count += APINT_BITS_PER_WORD; 845 if (i < getNumWords()) 846 Count += CountTrailingOnes_64(pVal[i]); 847 return std::min(Count, BitWidth); 848} 849 850unsigned APInt::countPopulationSlowCase() const { 851 unsigned Count = 0; 852 for (unsigned i = 0; i < getNumWords(); ++i) 853 Count += CountPopulation_64(pVal[i]); 854 return Count; 855} 856 857APInt APInt::byteSwap() const { 858 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!"); 859 if (BitWidth == 16) 860 return APInt(BitWidth, ByteSwap_16(uint16_t(VAL))); 861 else if (BitWidth == 32) 862 return APInt(BitWidth, ByteSwap_32(unsigned(VAL))); 863 else if (BitWidth == 48) { 864 unsigned Tmp1 = unsigned(VAL >> 16); 865 Tmp1 = ByteSwap_32(Tmp1); 866 uint16_t Tmp2 = uint16_t(VAL); 867 Tmp2 = ByteSwap_16(Tmp2); 868 return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1); 869 } else if (BitWidth == 64) 870 return APInt(BitWidth, ByteSwap_64(VAL)); 871 else { 872 APInt Result(BitWidth, 0); 873 char *pByte = (char*)Result.pVal; 874 for (unsigned i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) { 875 char Tmp = pByte[i]; 876 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i]; 877 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp; 878 } 879 return Result; 880 } 881} 882 883APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1, 884 const APInt& API2) { 885 APInt A = API1, B = API2; 886 while (!!B) { 887 APInt T = B; 888 B = APIntOps::urem(A, B); 889 A = T; 890 } 891 return A; 892} 893 894APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, unsigned width) { 895 union { 896 double D; 897 uint64_t I; 898 } T; 899 T.D = Double; 900 901 // Get the sign bit from the highest order bit 902 bool isNeg = T.I >> 63; 903 904 // Get the 11-bit exponent and adjust for the 1023 bit bias 905 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023; 906 907 // If the exponent is negative, the value is < 0 so just return 0. 908 if (exp < 0) 909 return APInt(width, 0u); 910 911 // Extract the mantissa by clearing the top 12 bits (sign + exponent). 912 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52; 913 914 // If the exponent doesn't shift all bits out of the mantissa 915 if (exp < 52) 916 return isNeg ? -APInt(width, mantissa >> (52 - exp)) : 917 APInt(width, mantissa >> (52 - exp)); 918 919 // If the client didn't provide enough bits for us to shift the mantissa into 920 // then the result is undefined, just return 0 921 if (width <= exp - 52) 922 return APInt(width, 0); 923 924 // Otherwise, we have to shift the mantissa bits up to the right location 925 APInt Tmp(width, mantissa); 926 Tmp = Tmp.shl((unsigned)exp - 52); 927 return isNeg ? -Tmp : Tmp; 928} 929 930/// RoundToDouble - This function converts this APInt to a double. 931/// The layout for double is as following (IEEE Standard 754): 932/// -------------------------------------- 933/// | Sign Exponent Fraction Bias | 934/// |-------------------------------------- | 935/// | 1[63] 11[62-52] 52[51-00] 1023 | 936/// -------------------------------------- 937double APInt::roundToDouble(bool isSigned) const { 938 939 // Handle the simple case where the value is contained in one uint64_t. 940 // It is wrong to optimize getWord(0) to VAL; there might be more than one word. 941 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) { 942 if (isSigned) { 943 int64_t sext = (int64_t(getWord(0)) << (64-BitWidth)) >> (64-BitWidth); 944 return double(sext); 945 } else 946 return double(getWord(0)); 947 } 948 949 // Determine if the value is negative. 950 bool isNeg = isSigned ? (*this)[BitWidth-1] : false; 951 952 // Construct the absolute value if we're negative. 953 APInt Tmp(isNeg ? -(*this) : (*this)); 954 955 // Figure out how many bits we're using. 956 unsigned n = Tmp.getActiveBits(); 957 958 // The exponent (without bias normalization) is just the number of bits 959 // we are using. Note that the sign bit is gone since we constructed the 960 // absolute value. 961 uint64_t exp = n; 962 963 // Return infinity for exponent overflow 964 if (exp > 1023) { 965 if (!isSigned || !isNeg) 966 return std::numeric_limits<double>::infinity(); 967 else 968 return -std::numeric_limits<double>::infinity(); 969 } 970 exp += 1023; // Increment for 1023 bias 971 972 // Number of bits in mantissa is 52. To obtain the mantissa value, we must 973 // extract the high 52 bits from the correct words in pVal. 974 uint64_t mantissa; 975 unsigned hiWord = whichWord(n-1); 976 if (hiWord == 0) { 977 mantissa = Tmp.pVal[0]; 978 if (n > 52) 979 mantissa >>= n - 52; // shift down, we want the top 52 bits. 980 } else { 981 assert(hiWord > 0 && "huh?"); 982 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD); 983 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD); 984 mantissa = hibits | lobits; 985 } 986 987 // The leading bit of mantissa is implicit, so get rid of it. 988 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0; 989 union { 990 double D; 991 uint64_t I; 992 } T; 993 T.I = sign | (exp << 52) | mantissa; 994 return T.D; 995} 996 997// Truncate to new width. 998APInt APInt::trunc(unsigned width) const { 999 assert(width < BitWidth && "Invalid APInt Truncate request"); 1000 assert(width && "Can't truncate to 0 bits"); 1001 1002 if (width <= APINT_BITS_PER_WORD) 1003 return APInt(width, getRawData()[0]); 1004 1005 APInt Result(getMemory(getNumWords(width)), width); 1006 1007 // Copy full words. 1008 unsigned i; 1009 for (i = 0; i != width / APINT_BITS_PER_WORD; i++) 1010 Result.pVal[i] = pVal[i]; 1011 1012 // Truncate and copy any partial word. 1013 unsigned bits = (0 - width) % APINT_BITS_PER_WORD; 1014 if (bits != 0) 1015 Result.pVal[i] = pVal[i] << bits >> bits; 1016 1017 return Result; 1018} 1019 1020// Sign extend to a new width. 1021APInt APInt::sext(unsigned width) const { 1022 assert(width > BitWidth && "Invalid APInt SignExtend request"); 1023 1024 if (width <= APINT_BITS_PER_WORD) { 1025 uint64_t val = VAL << (APINT_BITS_PER_WORD - BitWidth); 1026 val = (int64_t)val >> (width - BitWidth); 1027 return APInt(width, val >> (APINT_BITS_PER_WORD - width)); 1028 } 1029 1030 APInt Result(getMemory(getNumWords(width)), width); 1031 1032 // Copy full words. 1033 unsigned i; 1034 uint64_t word = 0; 1035 for (i = 0; i != BitWidth / APINT_BITS_PER_WORD; i++) { 1036 word = getRawData()[i]; 1037 Result.pVal[i] = word; 1038 } 1039 1040 // Read and sign-extend any partial word. 1041 unsigned bits = (0 - BitWidth) % APINT_BITS_PER_WORD; 1042 if (bits != 0) 1043 word = (int64_t)getRawData()[i] << bits >> bits; 1044 else 1045 word = (int64_t)word >> (APINT_BITS_PER_WORD - 1); 1046 1047 // Write remaining full words. 1048 for (; i != width / APINT_BITS_PER_WORD; i++) { 1049 Result.pVal[i] = word; 1050 word = (int64_t)word >> (APINT_BITS_PER_WORD - 1); 1051 } 1052 1053 // Write any partial word. 1054 bits = (0 - width) % APINT_BITS_PER_WORD; 1055 if (bits != 0) 1056 Result.pVal[i] = word << bits >> bits; 1057 1058 return Result; 1059} 1060 1061// Zero extend to a new width. 1062APInt APInt::zext(unsigned width) const { 1063 assert(width > BitWidth && "Invalid APInt ZeroExtend request"); 1064 1065 if (width <= APINT_BITS_PER_WORD) 1066 return APInt(width, VAL); 1067 1068 APInt Result(getMemory(getNumWords(width)), width); 1069 1070 // Copy words. 1071 unsigned i; 1072 for (i = 0; i != getNumWords(); i++) 1073 Result.pVal[i] = getRawData()[i]; 1074 1075 // Zero remaining words. 1076 memset(&Result.pVal[i], 0, (Result.getNumWords() - i) * APINT_WORD_SIZE); 1077 1078 return Result; 1079} 1080 1081APInt APInt::zextOrTrunc(unsigned width) const { 1082 if (BitWidth < width) 1083 return zext(width); 1084 if (BitWidth > width) 1085 return trunc(width); 1086 return *this; 1087} 1088 1089APInt APInt::sextOrTrunc(unsigned width) const { 1090 if (BitWidth < width) 1091 return sext(width); 1092 if (BitWidth > width) 1093 return trunc(width); 1094 return *this; 1095} 1096 1097/// Arithmetic right-shift this APInt by shiftAmt. 1098/// @brief Arithmetic right-shift function. 1099APInt APInt::ashr(const APInt &shiftAmt) const { 1100 return ashr((unsigned)shiftAmt.getLimitedValue(BitWidth)); 1101} 1102 1103/// Arithmetic right-shift this APInt by shiftAmt. 1104/// @brief Arithmetic right-shift function. 1105APInt APInt::ashr(unsigned shiftAmt) const { 1106 assert(shiftAmt <= BitWidth && "Invalid shift amount"); 1107 // Handle a degenerate case 1108 if (shiftAmt == 0) 1109 return *this; 1110 1111 // Handle single word shifts with built-in ashr 1112 if (isSingleWord()) { 1113 if (shiftAmt == BitWidth) 1114 return APInt(BitWidth, 0); // undefined 1115 else { 1116 unsigned SignBit = APINT_BITS_PER_WORD - BitWidth; 1117 return APInt(BitWidth, 1118 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt)); 1119 } 1120 } 1121 1122 // If all the bits were shifted out, the result is, technically, undefined. 1123 // We return -1 if it was negative, 0 otherwise. We check this early to avoid 1124 // issues in the algorithm below. 1125 if (shiftAmt == BitWidth) { 1126 if (isNegative()) 1127 return APInt(BitWidth, -1ULL, true); 1128 else 1129 return APInt(BitWidth, 0); 1130 } 1131 1132 // Create some space for the result. 1133 uint64_t * val = new uint64_t[getNumWords()]; 1134 1135 // Compute some values needed by the following shift algorithms 1136 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word 1137 unsigned offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift 1138 unsigned breakWord = getNumWords() - 1 - offset; // last word affected 1139 unsigned bitsInWord = whichBit(BitWidth); // how many bits in last word? 1140 if (bitsInWord == 0) 1141 bitsInWord = APINT_BITS_PER_WORD; 1142 1143 // If we are shifting whole words, just move whole words 1144 if (wordShift == 0) { 1145 // Move the words containing significant bits 1146 for (unsigned i = 0; i <= breakWord; ++i) 1147 val[i] = pVal[i+offset]; // move whole word 1148 1149 // Adjust the top significant word for sign bit fill, if negative 1150 if (isNegative()) 1151 if (bitsInWord < APINT_BITS_PER_WORD) 1152 val[breakWord] |= ~0ULL << bitsInWord; // set high bits 1153 } else { 1154 // Shift the low order words 1155 for (unsigned i = 0; i < breakWord; ++i) { 1156 // This combines the shifted corresponding word with the low bits from 1157 // the next word (shifted into this word's high bits). 1158 val[i] = (pVal[i+offset] >> wordShift) | 1159 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift)); 1160 } 1161 1162 // Shift the break word. In this case there are no bits from the next word 1163 // to include in this word. 1164 val[breakWord] = pVal[breakWord+offset] >> wordShift; 1165 1166 // Deal with sign extenstion in the break word, and possibly the word before 1167 // it. 1168 if (isNegative()) { 1169 if (wordShift > bitsInWord) { 1170 if (breakWord > 0) 1171 val[breakWord-1] |= 1172 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord)); 1173 val[breakWord] |= ~0ULL; 1174 } else 1175 val[breakWord] |= (~0ULL << (bitsInWord - wordShift)); 1176 } 1177 } 1178 1179 // Remaining words are 0 or -1, just assign them. 1180 uint64_t fillValue = (isNegative() ? -1ULL : 0); 1181 for (unsigned i = breakWord+1; i < getNumWords(); ++i) 1182 val[i] = fillValue; 1183 return APInt(val, BitWidth).clearUnusedBits(); 1184} 1185 1186/// Logical right-shift this APInt by shiftAmt. 1187/// @brief Logical right-shift function. 1188APInt APInt::lshr(const APInt &shiftAmt) const { 1189 return lshr((unsigned)shiftAmt.getLimitedValue(BitWidth)); 1190} 1191 1192/// Logical right-shift this APInt by shiftAmt. 1193/// @brief Logical right-shift function. 1194APInt APInt::lshr(unsigned shiftAmt) const { 1195 if (isSingleWord()) { 1196 if (shiftAmt == BitWidth) 1197 return APInt(BitWidth, 0); 1198 else 1199 return APInt(BitWidth, this->VAL >> shiftAmt); 1200 } 1201 1202 // If all the bits were shifted out, the result is 0. This avoids issues 1203 // with shifting by the size of the integer type, which produces undefined 1204 // results. We define these "undefined results" to always be 0. 1205 if (shiftAmt == BitWidth) 1206 return APInt(BitWidth, 0); 1207 1208 // If none of the bits are shifted out, the result is *this. This avoids 1209 // issues with shifting by the size of the integer type, which produces 1210 // undefined results in the code below. This is also an optimization. 1211 if (shiftAmt == 0) 1212 return *this; 1213 1214 // Create some space for the result. 1215 uint64_t * val = new uint64_t[getNumWords()]; 1216 1217 // If we are shifting less than a word, compute the shift with a simple carry 1218 if (shiftAmt < APINT_BITS_PER_WORD) { 1219 uint64_t carry = 0; 1220 for (int i = getNumWords()-1; i >= 0; --i) { 1221 val[i] = (pVal[i] >> shiftAmt) | carry; 1222 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt); 1223 } 1224 return APInt(val, BitWidth).clearUnusedBits(); 1225 } 1226 1227 // Compute some values needed by the remaining shift algorithms 1228 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; 1229 unsigned offset = shiftAmt / APINT_BITS_PER_WORD; 1230 1231 // If we are shifting whole words, just move whole words 1232 if (wordShift == 0) { 1233 for (unsigned i = 0; i < getNumWords() - offset; ++i) 1234 val[i] = pVal[i+offset]; 1235 for (unsigned i = getNumWords()-offset; i < getNumWords(); i++) 1236 val[i] = 0; 1237 return APInt(val,BitWidth).clearUnusedBits(); 1238 } 1239 1240 // Shift the low order words 1241 unsigned breakWord = getNumWords() - offset -1; 1242 for (unsigned i = 0; i < breakWord; ++i) 1243 val[i] = (pVal[i+offset] >> wordShift) | 1244 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift)); 1245 // Shift the break word. 1246 val[breakWord] = pVal[breakWord+offset] >> wordShift; 1247 1248 // Remaining words are 0 1249 for (unsigned i = breakWord+1; i < getNumWords(); ++i) 1250 val[i] = 0; 1251 return APInt(val, BitWidth).clearUnusedBits(); 1252} 1253 1254/// Left-shift this APInt by shiftAmt. 1255/// @brief Left-shift function. 1256APInt APInt::shl(const APInt &shiftAmt) const { 1257 // It's undefined behavior in C to shift by BitWidth or greater. 1258 return shl((unsigned)shiftAmt.getLimitedValue(BitWidth)); 1259} 1260 1261APInt APInt::shlSlowCase(unsigned shiftAmt) const { 1262 // If all the bits were shifted out, the result is 0. This avoids issues 1263 // with shifting by the size of the integer type, which produces undefined 1264 // results. We define these "undefined results" to always be 0. 1265 if (shiftAmt == BitWidth) 1266 return APInt(BitWidth, 0); 1267 1268 // If none of the bits are shifted out, the result is *this. This avoids a 1269 // lshr by the words size in the loop below which can produce incorrect 1270 // results. It also avoids the expensive computation below for a common case. 1271 if (shiftAmt == 0) 1272 return *this; 1273 1274 // Create some space for the result. 1275 uint64_t * val = new uint64_t[getNumWords()]; 1276 1277 // If we are shifting less than a word, do it the easy way 1278 if (shiftAmt < APINT_BITS_PER_WORD) { 1279 uint64_t carry = 0; 1280 for (unsigned i = 0; i < getNumWords(); i++) { 1281 val[i] = pVal[i] << shiftAmt | carry; 1282 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt); 1283 } 1284 return APInt(val, BitWidth).clearUnusedBits(); 1285 } 1286 1287 // Compute some values needed by the remaining shift algorithms 1288 unsigned wordShift = shiftAmt % APINT_BITS_PER_WORD; 1289 unsigned offset = shiftAmt / APINT_BITS_PER_WORD; 1290 1291 // If we are shifting whole words, just move whole words 1292 if (wordShift == 0) { 1293 for (unsigned i = 0; i < offset; i++) 1294 val[i] = 0; 1295 for (unsigned i = offset; i < getNumWords(); i++) 1296 val[i] = pVal[i-offset]; 1297 return APInt(val,BitWidth).clearUnusedBits(); 1298 } 1299 1300 // Copy whole words from this to Result. 1301 unsigned i = getNumWords() - 1; 1302 for (; i > offset; --i) 1303 val[i] = pVal[i-offset] << wordShift | 1304 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift); 1305 val[offset] = pVal[0] << wordShift; 1306 for (i = 0; i < offset; ++i) 1307 val[i] = 0; 1308 return APInt(val, BitWidth).clearUnusedBits(); 1309} 1310 1311APInt APInt::rotl(const APInt &rotateAmt) const { 1312 return rotl((unsigned)rotateAmt.getLimitedValue(BitWidth)); 1313} 1314 1315APInt APInt::rotl(unsigned rotateAmt) const { 1316 if (rotateAmt == 0) 1317 return *this; 1318 // Don't get too fancy, just use existing shift/or facilities 1319 APInt hi(*this); 1320 APInt lo(*this); 1321 hi.shl(rotateAmt); 1322 lo.lshr(BitWidth - rotateAmt); 1323 return hi | lo; 1324} 1325 1326APInt APInt::rotr(const APInt &rotateAmt) const { 1327 return rotr((unsigned)rotateAmt.getLimitedValue(BitWidth)); 1328} 1329 1330APInt APInt::rotr(unsigned rotateAmt) const { 1331 if (rotateAmt == 0) 1332 return *this; 1333 // Don't get too fancy, just use existing shift/or facilities 1334 APInt hi(*this); 1335 APInt lo(*this); 1336 lo.lshr(rotateAmt); 1337 hi.shl(BitWidth - rotateAmt); 1338 return hi | lo; 1339} 1340 1341// Square Root - this method computes and returns the square root of "this". 1342// Three mechanisms are used for computation. For small values (<= 5 bits), 1343// a table lookup is done. This gets some performance for common cases. For 1344// values using less than 52 bits, the value is converted to double and then 1345// the libc sqrt function is called. The result is rounded and then converted 1346// back to a uint64_t which is then used to construct the result. Finally, 1347// the Babylonian method for computing square roots is used. 1348APInt APInt::sqrt() const { 1349 1350 // Determine the magnitude of the value. 1351 unsigned magnitude = getActiveBits(); 1352 1353 // Use a fast table for some small values. This also gets rid of some 1354 // rounding errors in libc sqrt for small values. 1355 if (magnitude <= 5) { 1356 static const uint8_t results[32] = { 1357 /* 0 */ 0, 1358 /* 1- 2 */ 1, 1, 1359 /* 3- 6 */ 2, 2, 2, 2, 1360 /* 7-12 */ 3, 3, 3, 3, 3, 3, 1361 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4, 1362 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1363 /* 31 */ 6 1364 }; 1365 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]); 1366 } 1367 1368 // If the magnitude of the value fits in less than 52 bits (the precision of 1369 // an IEEE double precision floating point value), then we can use the 1370 // libc sqrt function which will probably use a hardware sqrt computation. 1371 // This should be faster than the algorithm below. 1372 if (magnitude < 52) { 1373#if HAVE_ROUND 1374 return APInt(BitWidth, 1375 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0]))))); 1376#else 1377 return APInt(BitWidth, 1378 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5); 1379#endif 1380 } 1381 1382 // Okay, all the short cuts are exhausted. We must compute it. The following 1383 // is a classical Babylonian method for computing the square root. This code 1384 // was adapted to APINt from a wikipedia article on such computations. 1385 // See http://www.wikipedia.org/ and go to the page named 1386 // Calculate_an_integer_square_root. 1387 unsigned nbits = BitWidth, i = 4; 1388 APInt testy(BitWidth, 16); 1389 APInt x_old(BitWidth, 1); 1390 APInt x_new(BitWidth, 0); 1391 APInt two(BitWidth, 2); 1392 1393 // Select a good starting value using binary logarithms. 1394 for (;; i += 2, testy = testy.shl(2)) 1395 if (i >= nbits || this->ule(testy)) { 1396 x_old = x_old.shl(i / 2); 1397 break; 1398 } 1399 1400 // Use the Babylonian method to arrive at the integer square root: 1401 for (;;) { 1402 x_new = (this->udiv(x_old) + x_old).udiv(two); 1403 if (x_old.ule(x_new)) 1404 break; 1405 x_old = x_new; 1406 } 1407 1408 // Make sure we return the closest approximation 1409 // NOTE: The rounding calculation below is correct. It will produce an 1410 // off-by-one discrepancy with results from pari/gp. That discrepancy has been 1411 // determined to be a rounding issue with pari/gp as it begins to use a 1412 // floating point representation after 192 bits. There are no discrepancies 1413 // between this algorithm and pari/gp for bit widths < 192 bits. 1414 APInt square(x_old * x_old); 1415 APInt nextSquare((x_old + 1) * (x_old +1)); 1416 if (this->ult(square)) 1417 return x_old; 1418 else if (this->ule(nextSquare)) { 1419 APInt midpoint((nextSquare - square).udiv(two)); 1420 APInt offset(*this - square); 1421 if (offset.ult(midpoint)) 1422 return x_old; 1423 else 1424 return x_old + 1; 1425 } else 1426 llvm_unreachable("Error in APInt::sqrt computation"); 1427 return x_old + 1; 1428} 1429 1430/// Computes the multiplicative inverse of this APInt for a given modulo. The 1431/// iterative extended Euclidean algorithm is used to solve for this value, 1432/// however we simplify it to speed up calculating only the inverse, and take 1433/// advantage of div+rem calculations. We also use some tricks to avoid copying 1434/// (potentially large) APInts around. 1435APInt APInt::multiplicativeInverse(const APInt& modulo) const { 1436 assert(ult(modulo) && "This APInt must be smaller than the modulo"); 1437 1438 // Using the properties listed at the following web page (accessed 06/21/08): 1439 // http://www.numbertheory.org/php/euclid.html 1440 // (especially the properties numbered 3, 4 and 9) it can be proved that 1441 // BitWidth bits suffice for all the computations in the algorithm implemented 1442 // below. More precisely, this number of bits suffice if the multiplicative 1443 // inverse exists, but may not suffice for the general extended Euclidean 1444 // algorithm. 1445 1446 APInt r[2] = { modulo, *this }; 1447 APInt t[2] = { APInt(BitWidth, 0), APInt(BitWidth, 1) }; 1448 APInt q(BitWidth, 0); 1449 1450 unsigned i; 1451 for (i = 0; r[i^1] != 0; i ^= 1) { 1452 // An overview of the math without the confusing bit-flipping: 1453 // q = r[i-2] / r[i-1] 1454 // r[i] = r[i-2] % r[i-1] 1455 // t[i] = t[i-2] - t[i-1] * q 1456 udivrem(r[i], r[i^1], q, r[i]); 1457 t[i] -= t[i^1] * q; 1458 } 1459 1460 // If this APInt and the modulo are not coprime, there is no multiplicative 1461 // inverse, so return 0. We check this by looking at the next-to-last 1462 // remainder, which is the gcd(*this,modulo) as calculated by the Euclidean 1463 // algorithm. 1464 if (r[i] != 1) 1465 return APInt(BitWidth, 0); 1466 1467 // The next-to-last t is the multiplicative inverse. However, we are 1468 // interested in a positive inverse. Calcuate a positive one from a negative 1469 // one if necessary. A simple addition of the modulo suffices because 1470 // abs(t[i]) is known to be less than *this/2 (see the link above). 1471 return t[i].isNegative() ? t[i] + modulo : t[i]; 1472} 1473 1474/// Calculate the magic numbers required to implement a signed integer division 1475/// by a constant as a sequence of multiplies, adds and shifts. Requires that 1476/// the divisor not be 0, 1, or -1. Taken from "Hacker's Delight", Henry S. 1477/// Warren, Jr., chapter 10. 1478APInt::ms APInt::magic() const { 1479 const APInt& d = *this; 1480 unsigned p; 1481 APInt ad, anc, delta, q1, r1, q2, r2, t; 1482 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth()); 1483 struct ms mag; 1484 1485 ad = d.abs(); 1486 t = signedMin + (d.lshr(d.getBitWidth() - 1)); 1487 anc = t - 1 - t.urem(ad); // absolute value of nc 1488 p = d.getBitWidth() - 1; // initialize p 1489 q1 = signedMin.udiv(anc); // initialize q1 = 2p/abs(nc) 1490 r1 = signedMin - q1*anc; // initialize r1 = rem(2p,abs(nc)) 1491 q2 = signedMin.udiv(ad); // initialize q2 = 2p/abs(d) 1492 r2 = signedMin - q2*ad; // initialize r2 = rem(2p,abs(d)) 1493 do { 1494 p = p + 1; 1495 q1 = q1<<1; // update q1 = 2p/abs(nc) 1496 r1 = r1<<1; // update r1 = rem(2p/abs(nc)) 1497 if (r1.uge(anc)) { // must be unsigned comparison 1498 q1 = q1 + 1; 1499 r1 = r1 - anc; 1500 } 1501 q2 = q2<<1; // update q2 = 2p/abs(d) 1502 r2 = r2<<1; // update r2 = rem(2p/abs(d)) 1503 if (r2.uge(ad)) { // must be unsigned comparison 1504 q2 = q2 + 1; 1505 r2 = r2 - ad; 1506 } 1507 delta = ad - r2; 1508 } while (q1.ule(delta) || (q1 == delta && r1 == 0)); 1509 1510 mag.m = q2 + 1; 1511 if (d.isNegative()) mag.m = -mag.m; // resulting magic number 1512 mag.s = p - d.getBitWidth(); // resulting shift 1513 return mag; 1514} 1515 1516/// Calculate the magic numbers required to implement an unsigned integer 1517/// division by a constant as a sequence of multiplies, adds and shifts. 1518/// Requires that the divisor not be 0. Taken from "Hacker's Delight", Henry 1519/// S. Warren, Jr., chapter 10. 1520APInt::mu APInt::magicu() const { 1521 const APInt& d = *this; 1522 unsigned p; 1523 APInt nc, delta, q1, r1, q2, r2; 1524 struct mu magu; 1525 magu.a = 0; // initialize "add" indicator 1526 APInt allOnes = APInt::getAllOnesValue(d.getBitWidth()); 1527 APInt signedMin = APInt::getSignedMinValue(d.getBitWidth()); 1528 APInt signedMax = APInt::getSignedMaxValue(d.getBitWidth()); 1529 1530 nc = allOnes - (-d).urem(d); 1531 p = d.getBitWidth() - 1; // initialize p 1532 q1 = signedMin.udiv(nc); // initialize q1 = 2p/nc 1533 r1 = signedMin - q1*nc; // initialize r1 = rem(2p,nc) 1534 q2 = signedMax.udiv(d); // initialize q2 = (2p-1)/d 1535 r2 = signedMax - q2*d; // initialize r2 = rem((2p-1),d) 1536 do { 1537 p = p + 1; 1538 if (r1.uge(nc - r1)) { 1539 q1 = q1 + q1 + 1; // update q1 1540 r1 = r1 + r1 - nc; // update r1 1541 } 1542 else { 1543 q1 = q1+q1; // update q1 1544 r1 = r1+r1; // update r1 1545 } 1546 if ((r2 + 1).uge(d - r2)) { 1547 if (q2.uge(signedMax)) magu.a = 1; 1548 q2 = q2+q2 + 1; // update q2 1549 r2 = r2+r2 + 1 - d; // update r2 1550 } 1551 else { 1552 if (q2.uge(signedMin)) magu.a = 1; 1553 q2 = q2+q2; // update q2 1554 r2 = r2+r2 + 1; // update r2 1555 } 1556 delta = d - 1 - r2; 1557 } while (p < d.getBitWidth()*2 && 1558 (q1.ult(delta) || (q1 == delta && r1 == 0))); 1559 magu.m = q2 + 1; // resulting magic number 1560 magu.s = p - d.getBitWidth(); // resulting shift 1561 return magu; 1562} 1563 1564/// Implementation of Knuth's Algorithm D (Division of nonnegative integers) 1565/// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The 1566/// variables here have the same names as in the algorithm. Comments explain 1567/// the algorithm and any deviation from it. 1568static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r, 1569 unsigned m, unsigned n) { 1570 assert(u && "Must provide dividend"); 1571 assert(v && "Must provide divisor"); 1572 assert(q && "Must provide quotient"); 1573 assert(u != v && u != q && v != q && "Must us different memory"); 1574 assert(n>1 && "n must be > 1"); 1575 1576 // Knuth uses the value b as the base of the number system. In our case b 1577 // is 2^31 so we just set it to -1u. 1578 uint64_t b = uint64_t(1) << 32; 1579 1580#if 0 1581 DEBUG(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n'); 1582 DEBUG(dbgs() << "KnuthDiv: original:"); 1583 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); 1584 DEBUG(dbgs() << " by"); 1585 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]); 1586 DEBUG(dbgs() << '\n'); 1587#endif 1588 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of 1589 // u and v by d. Note that we have taken Knuth's advice here to use a power 1590 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of 1591 // 2 allows us to shift instead of multiply and it is easy to determine the 1592 // shift amount from the leading zeros. We are basically normalizing the u 1593 // and v so that its high bits are shifted to the top of v's range without 1594 // overflow. Note that this can require an extra word in u so that u must 1595 // be of length m+n+1. 1596 unsigned shift = CountLeadingZeros_32(v[n-1]); 1597 unsigned v_carry = 0; 1598 unsigned u_carry = 0; 1599 if (shift) { 1600 for (unsigned i = 0; i < m+n; ++i) { 1601 unsigned u_tmp = u[i] >> (32 - shift); 1602 u[i] = (u[i] << shift) | u_carry; 1603 u_carry = u_tmp; 1604 } 1605 for (unsigned i = 0; i < n; ++i) { 1606 unsigned v_tmp = v[i] >> (32 - shift); 1607 v[i] = (v[i] << shift) | v_carry; 1608 v_carry = v_tmp; 1609 } 1610 } 1611 u[m+n] = u_carry; 1612#if 0 1613 DEBUG(dbgs() << "KnuthDiv: normal:"); 1614 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); 1615 DEBUG(dbgs() << " by"); 1616 DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]); 1617 DEBUG(dbgs() << '\n'); 1618#endif 1619 1620 // D2. [Initialize j.] Set j to m. This is the loop counter over the places. 1621 int j = m; 1622 do { 1623 DEBUG(dbgs() << "KnuthDiv: quotient digit #" << j << '\n'); 1624 // D3. [Calculate q'.]. 1625 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q') 1626 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r') 1627 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease 1628 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test 1629 // on v[n-2] determines at high speed most of the cases in which the trial 1630 // value qp is one too large, and it eliminates all cases where qp is two 1631 // too large. 1632 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]); 1633 DEBUG(dbgs() << "KnuthDiv: dividend == " << dividend << '\n'); 1634 uint64_t qp = dividend / v[n-1]; 1635 uint64_t rp = dividend % v[n-1]; 1636 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) { 1637 qp--; 1638 rp += v[n-1]; 1639 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2])) 1640 qp--; 1641 } 1642 DEBUG(dbgs() << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n'); 1643 1644 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with 1645 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation 1646 // consists of a simple multiplication by a one-place number, combined with 1647 // a subtraction. 1648 bool isNeg = false; 1649 for (unsigned i = 0; i < n; ++i) { 1650 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32); 1651 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]); 1652 bool borrow = subtrahend > u_tmp; 1653 DEBUG(dbgs() << "KnuthDiv: u_tmp == " << u_tmp 1654 << ", subtrahend == " << subtrahend 1655 << ", borrow = " << borrow << '\n'); 1656 1657 uint64_t result = u_tmp - subtrahend; 1658 unsigned k = j + i; 1659 u[k++] = (unsigned)(result & (b-1)); // subtract low word 1660 u[k++] = (unsigned)(result >> 32); // subtract high word 1661 while (borrow && k <= m+n) { // deal with borrow to the left 1662 borrow = u[k] == 0; 1663 u[k]--; 1664 k++; 1665 } 1666 isNeg |= borrow; 1667 DEBUG(dbgs() << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " << 1668 u[j+i+1] << '\n'); 1669 } 1670 DEBUG(dbgs() << "KnuthDiv: after subtraction:"); 1671 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); 1672 DEBUG(dbgs() << '\n'); 1673 // The digits (u[j+n]...u[j]) should be kept positive; if the result of 1674 // this step is actually negative, (u[j+n]...u[j]) should be left as the 1675 // true value plus b**(n+1), namely as the b's complement of 1676 // the true value, and a "borrow" to the left should be remembered. 1677 // 1678 if (isNeg) { 1679 bool carry = true; // true because b's complement is "complement + 1" 1680 for (unsigned i = 0; i <= m+n; ++i) { 1681 u[i] = ~u[i] + carry; // b's complement 1682 carry = carry && u[i] == 0; 1683 } 1684 } 1685 DEBUG(dbgs() << "KnuthDiv: after complement:"); 1686 DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]); 1687 DEBUG(dbgs() << '\n'); 1688 1689 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was 1690 // negative, go to step D6; otherwise go on to step D7. 1691 q[j] = (unsigned)qp; 1692 if (isNeg) { 1693 // D6. [Add back]. The probability that this step is necessary is very 1694 // small, on the order of only 2/b. Make sure that test data accounts for 1695 // this possibility. Decrease q[j] by 1 1696 q[j]--; 1697 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]). 1698 // A carry will occur to the left of u[j+n], and it should be ignored 1699 // since it cancels with the borrow that occurred in D4. 1700 bool carry = false; 1701 for (unsigned i = 0; i < n; i++) { 1702 unsigned limit = std::min(u[j+i],v[i]); 1703 u[j+i] += v[i] + carry; 1704 carry = u[j+i] < limit || (carry && u[j+i] == limit); 1705 } 1706 u[j+n] += carry; 1707 } 1708 DEBUG(dbgs() << "KnuthDiv: after correction:"); 1709 DEBUG(for (int i = m+n; i >=0; i--) dbgs() <<" " << u[i]); 1710 DEBUG(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n'); 1711 1712 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3. 1713 } while (--j >= 0); 1714 1715 DEBUG(dbgs() << "KnuthDiv: quotient:"); 1716 DEBUG(for (int i = m; i >=0; i--) dbgs() <<" " << q[i]); 1717 DEBUG(dbgs() << '\n'); 1718 1719 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired 1720 // remainder may be obtained by dividing u[...] by d. If r is non-null we 1721 // compute the remainder (urem uses this). 1722 if (r) { 1723 // The value d is expressed by the "shift" value above since we avoided 1724 // multiplication by d by using a shift left. So, all we have to do is 1725 // shift right here. In order to mak 1726 if (shift) { 1727 unsigned carry = 0; 1728 DEBUG(dbgs() << "KnuthDiv: remainder:"); 1729 for (int i = n-1; i >= 0; i--) { 1730 r[i] = (u[i] >> shift) | carry; 1731 carry = u[i] << (32 - shift); 1732 DEBUG(dbgs() << " " << r[i]); 1733 } 1734 } else { 1735 for (int i = n-1; i >= 0; i--) { 1736 r[i] = u[i]; 1737 DEBUG(dbgs() << " " << r[i]); 1738 } 1739 } 1740 DEBUG(dbgs() << '\n'); 1741 } 1742#if 0 1743 DEBUG(dbgs() << '\n'); 1744#endif 1745} 1746 1747void APInt::divide(const APInt LHS, unsigned lhsWords, 1748 const APInt &RHS, unsigned rhsWords, 1749 APInt *Quotient, APInt *Remainder) 1750{ 1751 assert(lhsWords >= rhsWords && "Fractional result"); 1752 1753 // First, compose the values into an array of 32-bit words instead of 1754 // 64-bit words. This is a necessity of both the "short division" algorithm 1755 // and the Knuth "classical algorithm" which requires there to be native 1756 // operations for +, -, and * on an m bit value with an m*2 bit result. We 1757 // can't use 64-bit operands here because we don't have native results of 1758 // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't 1759 // work on large-endian machines. 1760 uint64_t mask = ~0ull >> (sizeof(unsigned)*CHAR_BIT); 1761 unsigned n = rhsWords * 2; 1762 unsigned m = (lhsWords * 2) - n; 1763 1764 // Allocate space for the temporary values we need either on the stack, if 1765 // it will fit, or on the heap if it won't. 1766 unsigned SPACE[128]; 1767 unsigned *U = 0; 1768 unsigned *V = 0; 1769 unsigned *Q = 0; 1770 unsigned *R = 0; 1771 if ((Remainder?4:3)*n+2*m+1 <= 128) { 1772 U = &SPACE[0]; 1773 V = &SPACE[m+n+1]; 1774 Q = &SPACE[(m+n+1) + n]; 1775 if (Remainder) 1776 R = &SPACE[(m+n+1) + n + (m+n)]; 1777 } else { 1778 U = new unsigned[m + n + 1]; 1779 V = new unsigned[n]; 1780 Q = new unsigned[m+n]; 1781 if (Remainder) 1782 R = new unsigned[n]; 1783 } 1784 1785 // Initialize the dividend 1786 memset(U, 0, (m+n+1)*sizeof(unsigned)); 1787 for (unsigned i = 0; i < lhsWords; ++i) { 1788 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]); 1789 U[i * 2] = (unsigned)(tmp & mask); 1790 U[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT)); 1791 } 1792 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm. 1793 1794 // Initialize the divisor 1795 memset(V, 0, (n)*sizeof(unsigned)); 1796 for (unsigned i = 0; i < rhsWords; ++i) { 1797 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]); 1798 V[i * 2] = (unsigned)(tmp & mask); 1799 V[i * 2 + 1] = (unsigned)(tmp >> (sizeof(unsigned)*CHAR_BIT)); 1800 } 1801 1802 // initialize the quotient and remainder 1803 memset(Q, 0, (m+n) * sizeof(unsigned)); 1804 if (Remainder) 1805 memset(R, 0, n * sizeof(unsigned)); 1806 1807 // Now, adjust m and n for the Knuth division. n is the number of words in 1808 // the divisor. m is the number of words by which the dividend exceeds the 1809 // divisor (i.e. m+n is the length of the dividend). These sizes must not 1810 // contain any zero words or the Knuth algorithm fails. 1811 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) { 1812 n--; 1813 m++; 1814 } 1815 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--) 1816 m--; 1817 1818 // If we're left with only a single word for the divisor, Knuth doesn't work 1819 // so we implement the short division algorithm here. This is much simpler 1820 // and faster because we are certain that we can divide a 64-bit quantity 1821 // by a 32-bit quantity at hardware speed and short division is simply a 1822 // series of such operations. This is just like doing short division but we 1823 // are using base 2^32 instead of base 10. 1824 assert(n != 0 && "Divide by zero?"); 1825 if (n == 1) { 1826 unsigned divisor = V[0]; 1827 unsigned remainder = 0; 1828 for (int i = m+n-1; i >= 0; i--) { 1829 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i]; 1830 if (partial_dividend == 0) { 1831 Q[i] = 0; 1832 remainder = 0; 1833 } else if (partial_dividend < divisor) { 1834 Q[i] = 0; 1835 remainder = (unsigned)partial_dividend; 1836 } else if (partial_dividend == divisor) { 1837 Q[i] = 1; 1838 remainder = 0; 1839 } else { 1840 Q[i] = (unsigned)(partial_dividend / divisor); 1841 remainder = (unsigned)(partial_dividend - (Q[i] * divisor)); 1842 } 1843 } 1844 if (R) 1845 R[0] = remainder; 1846 } else { 1847 // Now we're ready to invoke the Knuth classical divide algorithm. In this 1848 // case n > 1. 1849 KnuthDiv(U, V, Q, R, m, n); 1850 } 1851 1852 // If the caller wants the quotient 1853 if (Quotient) { 1854 // Set up the Quotient value's memory. 1855 if (Quotient->BitWidth != LHS.BitWidth) { 1856 if (Quotient->isSingleWord()) 1857 Quotient->VAL = 0; 1858 else 1859 delete [] Quotient->pVal; 1860 Quotient->BitWidth = LHS.BitWidth; 1861 if (!Quotient->isSingleWord()) 1862 Quotient->pVal = getClearedMemory(Quotient->getNumWords()); 1863 } else 1864 Quotient->clearAllBits(); 1865 1866 // The quotient is in Q. Reconstitute the quotient into Quotient's low 1867 // order words. 1868 if (lhsWords == 1) { 1869 uint64_t tmp = 1870 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2)); 1871 if (Quotient->isSingleWord()) 1872 Quotient->VAL = tmp; 1873 else 1874 Quotient->pVal[0] = tmp; 1875 } else { 1876 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough"); 1877 for (unsigned i = 0; i < lhsWords; ++i) 1878 Quotient->pVal[i] = 1879 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2)); 1880 } 1881 } 1882 1883 // If the caller wants the remainder 1884 if (Remainder) { 1885 // Set up the Remainder value's memory. 1886 if (Remainder->BitWidth != RHS.BitWidth) { 1887 if (Remainder->isSingleWord()) 1888 Remainder->VAL = 0; 1889 else 1890 delete [] Remainder->pVal; 1891 Remainder->BitWidth = RHS.BitWidth; 1892 if (!Remainder->isSingleWord()) 1893 Remainder->pVal = getClearedMemory(Remainder->getNumWords()); 1894 } else 1895 Remainder->clearAllBits(); 1896 1897 // The remainder is in R. Reconstitute the remainder into Remainder's low 1898 // order words. 1899 if (rhsWords == 1) { 1900 uint64_t tmp = 1901 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2)); 1902 if (Remainder->isSingleWord()) 1903 Remainder->VAL = tmp; 1904 else 1905 Remainder->pVal[0] = tmp; 1906 } else { 1907 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough"); 1908 for (unsigned i = 0; i < rhsWords; ++i) 1909 Remainder->pVal[i] = 1910 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2)); 1911 } 1912 } 1913 1914 // Clean up the memory we allocated. 1915 if (U != &SPACE[0]) { 1916 delete [] U; 1917 delete [] V; 1918 delete [] Q; 1919 delete [] R; 1920 } 1921} 1922 1923APInt APInt::udiv(const APInt& RHS) const { 1924 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 1925 1926 // First, deal with the easy case 1927 if (isSingleWord()) { 1928 assert(RHS.VAL != 0 && "Divide by zero?"); 1929 return APInt(BitWidth, VAL / RHS.VAL); 1930 } 1931 1932 // Get some facts about the LHS and RHS number of bits and words 1933 unsigned rhsBits = RHS.getActiveBits(); 1934 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); 1935 assert(rhsWords && "Divided by zero???"); 1936 unsigned lhsBits = this->getActiveBits(); 1937 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1); 1938 1939 // Deal with some degenerate cases 1940 if (!lhsWords) 1941 // 0 / X ===> 0 1942 return APInt(BitWidth, 0); 1943 else if (lhsWords < rhsWords || this->ult(RHS)) { 1944 // X / Y ===> 0, iff X < Y 1945 return APInt(BitWidth, 0); 1946 } else if (*this == RHS) { 1947 // X / X ===> 1 1948 return APInt(BitWidth, 1); 1949 } else if (lhsWords == 1 && rhsWords == 1) { 1950 // All high words are zero, just use native divide 1951 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]); 1952 } 1953 1954 // We have to compute it the hard way. Invoke the Knuth divide algorithm. 1955 APInt Quotient(1,0); // to hold result. 1956 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0); 1957 return Quotient; 1958} 1959 1960APInt APInt::urem(const APInt& RHS) const { 1961 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 1962 if (isSingleWord()) { 1963 assert(RHS.VAL != 0 && "Remainder by zero?"); 1964 return APInt(BitWidth, VAL % RHS.VAL); 1965 } 1966 1967 // Get some facts about the LHS 1968 unsigned lhsBits = getActiveBits(); 1969 unsigned lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1); 1970 1971 // Get some facts about the RHS 1972 unsigned rhsBits = RHS.getActiveBits(); 1973 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); 1974 assert(rhsWords && "Performing remainder operation by zero ???"); 1975 1976 // Check the degenerate cases 1977 if (lhsWords == 0) { 1978 // 0 % Y ===> 0 1979 return APInt(BitWidth, 0); 1980 } else if (lhsWords < rhsWords || this->ult(RHS)) { 1981 // X % Y ===> X, iff X < Y 1982 return *this; 1983 } else if (*this == RHS) { 1984 // X % X == 0; 1985 return APInt(BitWidth, 0); 1986 } else if (lhsWords == 1) { 1987 // All high words are zero, just use native remainder 1988 return APInt(BitWidth, pVal[0] % RHS.pVal[0]); 1989 } 1990 1991 // We have to compute it the hard way. Invoke the Knuth divide algorithm. 1992 APInt Remainder(1,0); 1993 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder); 1994 return Remainder; 1995} 1996 1997void APInt::udivrem(const APInt &LHS, const APInt &RHS, 1998 APInt &Quotient, APInt &Remainder) { 1999 // Get some size facts about the dividend and divisor 2000 unsigned lhsBits = LHS.getActiveBits(); 2001 unsigned lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1); 2002 unsigned rhsBits = RHS.getActiveBits(); 2003 unsigned rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); 2004 2005 // Check the degenerate cases 2006 if (lhsWords == 0) { 2007 Quotient = 0; // 0 / Y ===> 0 2008 Remainder = 0; // 0 % Y ===> 0 2009 return; 2010 } 2011 2012 if (lhsWords < rhsWords || LHS.ult(RHS)) { 2013 Remainder = LHS; // X % Y ===> X, iff X < Y 2014 Quotient = 0; // X / Y ===> 0, iff X < Y 2015 return; 2016 } 2017 2018 if (LHS == RHS) { 2019 Quotient = 1; // X / X ===> 1 2020 Remainder = 0; // X % X ===> 0; 2021 return; 2022 } 2023 2024 if (lhsWords == 1 && rhsWords == 1) { 2025 // There is only one word to consider so use the native versions. 2026 uint64_t lhsValue = LHS.isSingleWord() ? LHS.VAL : LHS.pVal[0]; 2027 uint64_t rhsValue = RHS.isSingleWord() ? RHS.VAL : RHS.pVal[0]; 2028 Quotient = APInt(LHS.getBitWidth(), lhsValue / rhsValue); 2029 Remainder = APInt(LHS.getBitWidth(), lhsValue % rhsValue); 2030 return; 2031 } 2032 2033 // Okay, lets do it the long way 2034 divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder); 2035} 2036 2037APInt APInt::sadd_ov(const APInt &RHS, bool &Overflow) const { 2038 APInt Res = *this+RHS; 2039 Overflow = isNonNegative() == RHS.isNonNegative() && 2040 Res.isNonNegative() != isNonNegative(); 2041 return Res; 2042} 2043 2044APInt APInt::uadd_ov(const APInt &RHS, bool &Overflow) const { 2045 APInt Res = *this+RHS; 2046 Overflow = Res.ult(RHS); 2047 return Res; 2048} 2049 2050APInt APInt::ssub_ov(const APInt &RHS, bool &Overflow) const { 2051 APInt Res = *this - RHS; 2052 Overflow = isNonNegative() != RHS.isNonNegative() && 2053 Res.isNonNegative() != isNonNegative(); 2054 return Res; 2055} 2056 2057APInt APInt::usub_ov(const APInt &RHS, bool &Overflow) const { 2058 APInt Res = *this-RHS; 2059 Overflow = Res.ugt(*this); 2060 return Res; 2061} 2062 2063APInt APInt::sdiv_ov(const APInt &RHS, bool &Overflow) const { 2064 // MININT/-1 --> overflow. 2065 Overflow = isMinSignedValue() && RHS.isAllOnesValue(); 2066 return sdiv(RHS); 2067} 2068 2069APInt APInt::smul_ov(const APInt &RHS, bool &Overflow) const { 2070 APInt Res = *this * RHS; 2071 2072 if (*this != 0 && RHS != 0) 2073 Overflow = Res.sdiv(RHS) != *this || Res.sdiv(*this) != RHS; 2074 else 2075 Overflow = false; 2076 return Res; 2077} 2078 2079APInt APInt::sshl_ov(unsigned ShAmt, bool &Overflow) const { 2080 Overflow = ShAmt >= getBitWidth(); 2081 if (Overflow) 2082 ShAmt = getBitWidth()-1; 2083 2084 if (isNonNegative()) // Don't allow sign change. 2085 Overflow = ShAmt >= countLeadingZeros(); 2086 else 2087 Overflow = ShAmt >= countLeadingOnes(); 2088 2089 return *this << ShAmt; 2090} 2091 2092 2093 2094 2095void APInt::fromString(unsigned numbits, StringRef str, uint8_t radix) { 2096 // Check our assumptions here 2097 assert(!str.empty() && "Invalid string length"); 2098 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) && 2099 "Radix should be 2, 8, 10, or 16!"); 2100 2101 StringRef::iterator p = str.begin(); 2102 size_t slen = str.size(); 2103 bool isNeg = *p == '-'; 2104 if (*p == '-' || *p == '+') { 2105 p++; 2106 slen--; 2107 assert(slen && "String is only a sign, needs a value."); 2108 } 2109 assert((slen <= numbits || radix != 2) && "Insufficient bit width"); 2110 assert(((slen-1)*3 <= numbits || radix != 8) && "Insufficient bit width"); 2111 assert(((slen-1)*4 <= numbits || radix != 16) && "Insufficient bit width"); 2112 assert((((slen-1)*64)/22 <= numbits || radix != 10) && 2113 "Insufficient bit width"); 2114 2115 // Allocate memory 2116 if (!isSingleWord()) 2117 pVal = getClearedMemory(getNumWords()); 2118 2119 // Figure out if we can shift instead of multiply 2120 unsigned shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0); 2121 2122 // Set up an APInt for the digit to add outside the loop so we don't 2123 // constantly construct/destruct it. 2124 APInt apdigit(getBitWidth(), 0); 2125 APInt apradix(getBitWidth(), radix); 2126 2127 // Enter digit traversal loop 2128 for (StringRef::iterator e = str.end(); p != e; ++p) { 2129 unsigned digit = getDigit(*p, radix); 2130 assert(digit < radix && "Invalid character in digit string"); 2131 2132 // Shift or multiply the value by the radix 2133 if (slen > 1) { 2134 if (shift) 2135 *this <<= shift; 2136 else 2137 *this *= apradix; 2138 } 2139 2140 // Add in the digit we just interpreted 2141 if (apdigit.isSingleWord()) 2142 apdigit.VAL = digit; 2143 else 2144 apdigit.pVal[0] = digit; 2145 *this += apdigit; 2146 } 2147 // If its negative, put it in two's complement form 2148 if (isNeg) { 2149 (*this)--; 2150 this->flipAllBits(); 2151 } 2152} 2153 2154void APInt::toString(SmallVectorImpl<char> &Str, unsigned Radix, 2155 bool Signed) const { 2156 assert((Radix == 10 || Radix == 8 || Radix == 16 || Radix == 2) && 2157 "Radix should be 2, 8, 10, or 16!"); 2158 2159 // First, check for a zero value and just short circuit the logic below. 2160 if (*this == 0) { 2161 Str.push_back('0'); 2162 return; 2163 } 2164 2165 static const char Digits[] = "0123456789ABCDEF"; 2166 2167 if (isSingleWord()) { 2168 char Buffer[65]; 2169 char *BufPtr = Buffer+65; 2170 2171 uint64_t N; 2172 if (!Signed) { 2173 N = getZExtValue(); 2174 } else { 2175 int64_t I = getSExtValue(); 2176 if (I >= 0) { 2177 N = I; 2178 } else { 2179 Str.push_back('-'); 2180 N = -(uint64_t)I; 2181 } 2182 } 2183 2184 while (N) { 2185 *--BufPtr = Digits[N % Radix]; 2186 N /= Radix; 2187 } 2188 Str.append(BufPtr, Buffer+65); 2189 return; 2190 } 2191 2192 APInt Tmp(*this); 2193 2194 if (Signed && isNegative()) { 2195 // They want to print the signed version and it is a negative value 2196 // Flip the bits and add one to turn it into the equivalent positive 2197 // value and put a '-' in the result. 2198 Tmp.flipAllBits(); 2199 Tmp++; 2200 Str.push_back('-'); 2201 } 2202 2203 // We insert the digits backward, then reverse them to get the right order. 2204 unsigned StartDig = Str.size(); 2205 2206 // For the 2, 8 and 16 bit cases, we can just shift instead of divide 2207 // because the number of bits per digit (1, 3 and 4 respectively) divides 2208 // equaly. We just shift until the value is zero. 2209 if (Radix != 10) { 2210 // Just shift tmp right for each digit width until it becomes zero 2211 unsigned ShiftAmt = (Radix == 16 ? 4 : (Radix == 8 ? 3 : 1)); 2212 unsigned MaskAmt = Radix - 1; 2213 2214 while (Tmp != 0) { 2215 unsigned Digit = unsigned(Tmp.getRawData()[0]) & MaskAmt; 2216 Str.push_back(Digits[Digit]); 2217 Tmp = Tmp.lshr(ShiftAmt); 2218 } 2219 } else { 2220 APInt divisor(4, 10); 2221 while (Tmp != 0) { 2222 APInt APdigit(1, 0); 2223 APInt tmp2(Tmp.getBitWidth(), 0); 2224 divide(Tmp, Tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2, 2225 &APdigit); 2226 unsigned Digit = (unsigned)APdigit.getZExtValue(); 2227 assert(Digit < Radix && "divide failed"); 2228 Str.push_back(Digits[Digit]); 2229 Tmp = tmp2; 2230 } 2231 } 2232 2233 // Reverse the digits before returning. 2234 std::reverse(Str.begin()+StartDig, Str.end()); 2235} 2236 2237/// toString - This returns the APInt as a std::string. Note that this is an 2238/// inefficient method. It is better to pass in a SmallVector/SmallString 2239/// to the methods above. 2240std::string APInt::toString(unsigned Radix = 10, bool Signed = true) const { 2241 SmallString<40> S; 2242 toString(S, Radix, Signed); 2243 return S.str(); 2244} 2245 2246 2247void APInt::dump() const { 2248 SmallString<40> S, U; 2249 this->toStringUnsigned(U); 2250 this->toStringSigned(S); 2251 dbgs() << "APInt(" << BitWidth << "b, " 2252 << U.str() << "u " << S.str() << "s)"; 2253} 2254 2255void APInt::print(raw_ostream &OS, bool isSigned) const { 2256 SmallString<40> S; 2257 this->toString(S, 10, isSigned); 2258 OS << S.str(); 2259} 2260 2261// This implements a variety of operations on a representation of 2262// arbitrary precision, two's-complement, bignum integer values. 2263 2264// Assumed by lowHalf, highHalf, partMSB and partLSB. A fairly safe 2265// and unrestricting assumption. 2266#define COMPILE_TIME_ASSERT(cond) extern int CTAssert[(cond) ? 1 : -1] 2267COMPILE_TIME_ASSERT(integerPartWidth % 2 == 0); 2268 2269/* Some handy functions local to this file. */ 2270namespace { 2271 2272 /* Returns the integer part with the least significant BITS set. 2273 BITS cannot be zero. */ 2274 static inline integerPart 2275 lowBitMask(unsigned int bits) 2276 { 2277 assert(bits != 0 && bits <= integerPartWidth); 2278 2279 return ~(integerPart) 0 >> (integerPartWidth - bits); 2280 } 2281 2282 /* Returns the value of the lower half of PART. */ 2283 static inline integerPart 2284 lowHalf(integerPart part) 2285 { 2286 return part & lowBitMask(integerPartWidth / 2); 2287 } 2288 2289 /* Returns the value of the upper half of PART. */ 2290 static inline integerPart 2291 highHalf(integerPart part) 2292 { 2293 return part >> (integerPartWidth / 2); 2294 } 2295 2296 /* Returns the bit number of the most significant set bit of a part. 2297 If the input number has no bits set -1U is returned. */ 2298 static unsigned int 2299 partMSB(integerPart value) 2300 { 2301 unsigned int n, msb; 2302 2303 if (value == 0) 2304 return -1U; 2305 2306 n = integerPartWidth / 2; 2307 2308 msb = 0; 2309 do { 2310 if (value >> n) { 2311 value >>= n; 2312 msb += n; 2313 } 2314 2315 n >>= 1; 2316 } while (n); 2317 2318 return msb; 2319 } 2320 2321 /* Returns the bit number of the least significant set bit of a 2322 part. If the input number has no bits set -1U is returned. */ 2323 static unsigned int 2324 partLSB(integerPart value) 2325 { 2326 unsigned int n, lsb; 2327 2328 if (value == 0) 2329 return -1U; 2330 2331 lsb = integerPartWidth - 1; 2332 n = integerPartWidth / 2; 2333 2334 do { 2335 if (value << n) { 2336 value <<= n; 2337 lsb -= n; 2338 } 2339 2340 n >>= 1; 2341 } while (n); 2342 2343 return lsb; 2344 } 2345} 2346 2347/* Sets the least significant part of a bignum to the input value, and 2348 zeroes out higher parts. */ 2349void 2350APInt::tcSet(integerPart *dst, integerPart part, unsigned int parts) 2351{ 2352 unsigned int i; 2353 2354 assert(parts > 0); 2355 2356 dst[0] = part; 2357 for (i = 1; i < parts; i++) 2358 dst[i] = 0; 2359} 2360 2361/* Assign one bignum to another. */ 2362void 2363APInt::tcAssign(integerPart *dst, const integerPart *src, unsigned int parts) 2364{ 2365 unsigned int i; 2366 2367 for (i = 0; i < parts; i++) 2368 dst[i] = src[i]; 2369} 2370 2371/* Returns true if a bignum is zero, false otherwise. */ 2372bool 2373APInt::tcIsZero(const integerPart *src, unsigned int parts) 2374{ 2375 unsigned int i; 2376 2377 for (i = 0; i < parts; i++) 2378 if (src[i]) 2379 return false; 2380 2381 return true; 2382} 2383 2384/* Extract the given bit of a bignum; returns 0 or 1. */ 2385int 2386APInt::tcExtractBit(const integerPart *parts, unsigned int bit) 2387{ 2388 return (parts[bit / integerPartWidth] & 2389 ((integerPart) 1 << bit % integerPartWidth)) != 0; 2390} 2391 2392/* Set the given bit of a bignum. */ 2393void 2394APInt::tcSetBit(integerPart *parts, unsigned int bit) 2395{ 2396 parts[bit / integerPartWidth] |= (integerPart) 1 << (bit % integerPartWidth); 2397} 2398 2399/* Clears the given bit of a bignum. */ 2400void 2401APInt::tcClearBit(integerPart *parts, unsigned int bit) 2402{ 2403 parts[bit / integerPartWidth] &= 2404 ~((integerPart) 1 << (bit % integerPartWidth)); 2405} 2406 2407/* Returns the bit number of the least significant set bit of a 2408 number. If the input number has no bits set -1U is returned. */ 2409unsigned int 2410APInt::tcLSB(const integerPart *parts, unsigned int n) 2411{ 2412 unsigned int i, lsb; 2413 2414 for (i = 0; i < n; i++) { 2415 if (parts[i] != 0) { 2416 lsb = partLSB(parts[i]); 2417 2418 return lsb + i * integerPartWidth; 2419 } 2420 } 2421 2422 return -1U; 2423} 2424 2425/* Returns the bit number of the most significant set bit of a number. 2426 If the input number has no bits set -1U is returned. */ 2427unsigned int 2428APInt::tcMSB(const integerPart *parts, unsigned int n) 2429{ 2430 unsigned int msb; 2431 2432 do { 2433 --n; 2434 2435 if (parts[n] != 0) { 2436 msb = partMSB(parts[n]); 2437 2438 return msb + n * integerPartWidth; 2439 } 2440 } while (n); 2441 2442 return -1U; 2443} 2444 2445/* Copy the bit vector of width srcBITS from SRC, starting at bit 2446 srcLSB, to DST, of dstCOUNT parts, such that the bit srcLSB becomes 2447 the least significant bit of DST. All high bits above srcBITS in 2448 DST are zero-filled. */ 2449void 2450APInt::tcExtract(integerPart *dst, unsigned int dstCount,const integerPart *src, 2451 unsigned int srcBits, unsigned int srcLSB) 2452{ 2453 unsigned int firstSrcPart, dstParts, shift, n; 2454 2455 dstParts = (srcBits + integerPartWidth - 1) / integerPartWidth; 2456 assert(dstParts <= dstCount); 2457 2458 firstSrcPart = srcLSB / integerPartWidth; 2459 tcAssign (dst, src + firstSrcPart, dstParts); 2460 2461 shift = srcLSB % integerPartWidth; 2462 tcShiftRight (dst, dstParts, shift); 2463 2464 /* We now have (dstParts * integerPartWidth - shift) bits from SRC 2465 in DST. If this is less that srcBits, append the rest, else 2466 clear the high bits. */ 2467 n = dstParts * integerPartWidth - shift; 2468 if (n < srcBits) { 2469 integerPart mask = lowBitMask (srcBits - n); 2470 dst[dstParts - 1] |= ((src[firstSrcPart + dstParts] & mask) 2471 << n % integerPartWidth); 2472 } else if (n > srcBits) { 2473 if (srcBits % integerPartWidth) 2474 dst[dstParts - 1] &= lowBitMask (srcBits % integerPartWidth); 2475 } 2476 2477 /* Clear high parts. */ 2478 while (dstParts < dstCount) 2479 dst[dstParts++] = 0; 2480} 2481 2482/* DST += RHS + C where C is zero or one. Returns the carry flag. */ 2483integerPart 2484APInt::tcAdd(integerPart *dst, const integerPart *rhs, 2485 integerPart c, unsigned int parts) 2486{ 2487 unsigned int i; 2488 2489 assert(c <= 1); 2490 2491 for (i = 0; i < parts; i++) { 2492 integerPart l; 2493 2494 l = dst[i]; 2495 if (c) { 2496 dst[i] += rhs[i] + 1; 2497 c = (dst[i] <= l); 2498 } else { 2499 dst[i] += rhs[i]; 2500 c = (dst[i] < l); 2501 } 2502 } 2503 2504 return c; 2505} 2506 2507/* DST -= RHS + C where C is zero or one. Returns the carry flag. */ 2508integerPart 2509APInt::tcSubtract(integerPart *dst, const integerPart *rhs, 2510 integerPart c, unsigned int parts) 2511{ 2512 unsigned int i; 2513 2514 assert(c <= 1); 2515 2516 for (i = 0; i < parts; i++) { 2517 integerPart l; 2518 2519 l = dst[i]; 2520 if (c) { 2521 dst[i] -= rhs[i] + 1; 2522 c = (dst[i] >= l); 2523 } else { 2524 dst[i] -= rhs[i]; 2525 c = (dst[i] > l); 2526 } 2527 } 2528 2529 return c; 2530} 2531 2532/* Negate a bignum in-place. */ 2533void 2534APInt::tcNegate(integerPart *dst, unsigned int parts) 2535{ 2536 tcComplement(dst, parts); 2537 tcIncrement(dst, parts); 2538} 2539 2540/* DST += SRC * MULTIPLIER + CARRY if add is true 2541 DST = SRC * MULTIPLIER + CARRY if add is false 2542 2543 Requires 0 <= DSTPARTS <= SRCPARTS + 1. If DST overlaps SRC 2544 they must start at the same point, i.e. DST == SRC. 2545 2546 If DSTPARTS == SRCPARTS + 1 no overflow occurs and zero is 2547 returned. Otherwise DST is filled with the least significant 2548 DSTPARTS parts of the result, and if all of the omitted higher 2549 parts were zero return zero, otherwise overflow occurred and 2550 return one. */ 2551int 2552APInt::tcMultiplyPart(integerPart *dst, const integerPart *src, 2553 integerPart multiplier, integerPart carry, 2554 unsigned int srcParts, unsigned int dstParts, 2555 bool add) 2556{ 2557 unsigned int i, n; 2558 2559 /* Otherwise our writes of DST kill our later reads of SRC. */ 2560 assert(dst <= src || dst >= src + srcParts); 2561 assert(dstParts <= srcParts + 1); 2562 2563 /* N loops; minimum of dstParts and srcParts. */ 2564 n = dstParts < srcParts ? dstParts: srcParts; 2565 2566 for (i = 0; i < n; i++) { 2567 integerPart low, mid, high, srcPart; 2568 2569 /* [ LOW, HIGH ] = MULTIPLIER * SRC[i] + DST[i] + CARRY. 2570 2571 This cannot overflow, because 2572 2573 (n - 1) * (n - 1) + 2 (n - 1) = (n - 1) * (n + 1) 2574 2575 which is less than n^2. */ 2576 2577 srcPart = src[i]; 2578 2579 if (multiplier == 0 || srcPart == 0) { 2580 low = carry; 2581 high = 0; 2582 } else { 2583 low = lowHalf(srcPart) * lowHalf(multiplier); 2584 high = highHalf(srcPart) * highHalf(multiplier); 2585 2586 mid = lowHalf(srcPart) * highHalf(multiplier); 2587 high += highHalf(mid); 2588 mid <<= integerPartWidth / 2; 2589 if (low + mid < low) 2590 high++; 2591 low += mid; 2592 2593 mid = highHalf(srcPart) * lowHalf(multiplier); 2594 high += highHalf(mid); 2595 mid <<= integerPartWidth / 2; 2596 if (low + mid < low) 2597 high++; 2598 low += mid; 2599 2600 /* Now add carry. */ 2601 if (low + carry < low) 2602 high++; 2603 low += carry; 2604 } 2605 2606 if (add) { 2607 /* And now DST[i], and store the new low part there. */ 2608 if (low + dst[i] < low) 2609 high++; 2610 dst[i] += low; 2611 } else 2612 dst[i] = low; 2613 2614 carry = high; 2615 } 2616 2617 if (i < dstParts) { 2618 /* Full multiplication, there is no overflow. */ 2619 assert(i + 1 == dstParts); 2620 dst[i] = carry; 2621 return 0; 2622 } else { 2623 /* We overflowed if there is carry. */ 2624 if (carry) 2625 return 1; 2626 2627 /* We would overflow if any significant unwritten parts would be 2628 non-zero. This is true if any remaining src parts are non-zero 2629 and the multiplier is non-zero. */ 2630 if (multiplier) 2631 for (; i < srcParts; i++) 2632 if (src[i]) 2633 return 1; 2634 2635 /* We fitted in the narrow destination. */ 2636 return 0; 2637 } 2638} 2639 2640/* DST = LHS * RHS, where DST has the same width as the operands and 2641 is filled with the least significant parts of the result. Returns 2642 one if overflow occurred, otherwise zero. DST must be disjoint 2643 from both operands. */ 2644int 2645APInt::tcMultiply(integerPart *dst, const integerPart *lhs, 2646 const integerPart *rhs, unsigned int parts) 2647{ 2648 unsigned int i; 2649 int overflow; 2650 2651 assert(dst != lhs && dst != rhs); 2652 2653 overflow = 0; 2654 tcSet(dst, 0, parts); 2655 2656 for (i = 0; i < parts; i++) 2657 overflow |= tcMultiplyPart(&dst[i], lhs, rhs[i], 0, parts, 2658 parts - i, true); 2659 2660 return overflow; 2661} 2662 2663/* DST = LHS * RHS, where DST has width the sum of the widths of the 2664 operands. No overflow occurs. DST must be disjoint from both 2665 operands. Returns the number of parts required to hold the 2666 result. */ 2667unsigned int 2668APInt::tcFullMultiply(integerPart *dst, const integerPart *lhs, 2669 const integerPart *rhs, unsigned int lhsParts, 2670 unsigned int rhsParts) 2671{ 2672 /* Put the narrower number on the LHS for less loops below. */ 2673 if (lhsParts > rhsParts) { 2674 return tcFullMultiply (dst, rhs, lhs, rhsParts, lhsParts); 2675 } else { 2676 unsigned int n; 2677 2678 assert(dst != lhs && dst != rhs); 2679 2680 tcSet(dst, 0, rhsParts); 2681 2682 for (n = 0; n < lhsParts; n++) 2683 tcMultiplyPart(&dst[n], rhs, lhs[n], 0, rhsParts, rhsParts + 1, true); 2684 2685 n = lhsParts + rhsParts; 2686 2687 return n - (dst[n - 1] == 0); 2688 } 2689} 2690 2691/* If RHS is zero LHS and REMAINDER are left unchanged, return one. 2692 Otherwise set LHS to LHS / RHS with the fractional part discarded, 2693 set REMAINDER to the remainder, return zero. i.e. 2694 2695 OLD_LHS = RHS * LHS + REMAINDER 2696 2697 SCRATCH is a bignum of the same size as the operands and result for 2698 use by the routine; its contents need not be initialized and are 2699 destroyed. LHS, REMAINDER and SCRATCH must be distinct. 2700*/ 2701int 2702APInt::tcDivide(integerPart *lhs, const integerPart *rhs, 2703 integerPart *remainder, integerPart *srhs, 2704 unsigned int parts) 2705{ 2706 unsigned int n, shiftCount; 2707 integerPart mask; 2708 2709 assert(lhs != remainder && lhs != srhs && remainder != srhs); 2710 2711 shiftCount = tcMSB(rhs, parts) + 1; 2712 if (shiftCount == 0) 2713 return true; 2714 2715 shiftCount = parts * integerPartWidth - shiftCount; 2716 n = shiftCount / integerPartWidth; 2717 mask = (integerPart) 1 << (shiftCount % integerPartWidth); 2718 2719 tcAssign(srhs, rhs, parts); 2720 tcShiftLeft(srhs, parts, shiftCount); 2721 tcAssign(remainder, lhs, parts); 2722 tcSet(lhs, 0, parts); 2723 2724 /* Loop, subtracting SRHS if REMAINDER is greater and adding that to 2725 the total. */ 2726 for (;;) { 2727 int compare; 2728 2729 compare = tcCompare(remainder, srhs, parts); 2730 if (compare >= 0) { 2731 tcSubtract(remainder, srhs, 0, parts); 2732 lhs[n] |= mask; 2733 } 2734 2735 if (shiftCount == 0) 2736 break; 2737 shiftCount--; 2738 tcShiftRight(srhs, parts, 1); 2739 if ((mask >>= 1) == 0) 2740 mask = (integerPart) 1 << (integerPartWidth - 1), n--; 2741 } 2742 2743 return false; 2744} 2745 2746/* Shift a bignum left COUNT bits in-place. Shifted in bits are zero. 2747 There are no restrictions on COUNT. */ 2748void 2749APInt::tcShiftLeft(integerPart *dst, unsigned int parts, unsigned int count) 2750{ 2751 if (count) { 2752 unsigned int jump, shift; 2753 2754 /* Jump is the inter-part jump; shift is is intra-part shift. */ 2755 jump = count / integerPartWidth; 2756 shift = count % integerPartWidth; 2757 2758 while (parts > jump) { 2759 integerPart part; 2760 2761 parts--; 2762 2763 /* dst[i] comes from the two parts src[i - jump] and, if we have 2764 an intra-part shift, src[i - jump - 1]. */ 2765 part = dst[parts - jump]; 2766 if (shift) { 2767 part <<= shift; 2768 if (parts >= jump + 1) 2769 part |= dst[parts - jump - 1] >> (integerPartWidth - shift); 2770 } 2771 2772 dst[parts] = part; 2773 } 2774 2775 while (parts > 0) 2776 dst[--parts] = 0; 2777 } 2778} 2779 2780/* Shift a bignum right COUNT bits in-place. Shifted in bits are 2781 zero. There are no restrictions on COUNT. */ 2782void 2783APInt::tcShiftRight(integerPart *dst, unsigned int parts, unsigned int count) 2784{ 2785 if (count) { 2786 unsigned int i, jump, shift; 2787 2788 /* Jump is the inter-part jump; shift is is intra-part shift. */ 2789 jump = count / integerPartWidth; 2790 shift = count % integerPartWidth; 2791 2792 /* Perform the shift. This leaves the most significant COUNT bits 2793 of the result at zero. */ 2794 for (i = 0; i < parts; i++) { 2795 integerPart part; 2796 2797 if (i + jump >= parts) { 2798 part = 0; 2799 } else { 2800 part = dst[i + jump]; 2801 if (shift) { 2802 part >>= shift; 2803 if (i + jump + 1 < parts) 2804 part |= dst[i + jump + 1] << (integerPartWidth - shift); 2805 } 2806 } 2807 2808 dst[i] = part; 2809 } 2810 } 2811} 2812 2813/* Bitwise and of two bignums. */ 2814void 2815APInt::tcAnd(integerPart *dst, const integerPart *rhs, unsigned int parts) 2816{ 2817 unsigned int i; 2818 2819 for (i = 0; i < parts; i++) 2820 dst[i] &= rhs[i]; 2821} 2822 2823/* Bitwise inclusive or of two bignums. */ 2824void 2825APInt::tcOr(integerPart *dst, const integerPart *rhs, unsigned int parts) 2826{ 2827 unsigned int i; 2828 2829 for (i = 0; i < parts; i++) 2830 dst[i] |= rhs[i]; 2831} 2832 2833/* Bitwise exclusive or of two bignums. */ 2834void 2835APInt::tcXor(integerPart *dst, const integerPart *rhs, unsigned int parts) 2836{ 2837 unsigned int i; 2838 2839 for (i = 0; i < parts; i++) 2840 dst[i] ^= rhs[i]; 2841} 2842 2843/* Complement a bignum in-place. */ 2844void 2845APInt::tcComplement(integerPart *dst, unsigned int parts) 2846{ 2847 unsigned int i; 2848 2849 for (i = 0; i < parts; i++) 2850 dst[i] = ~dst[i]; 2851} 2852 2853/* Comparison (unsigned) of two bignums. */ 2854int 2855APInt::tcCompare(const integerPart *lhs, const integerPart *rhs, 2856 unsigned int parts) 2857{ 2858 while (parts) { 2859 parts--; 2860 if (lhs[parts] == rhs[parts]) 2861 continue; 2862 2863 if (lhs[parts] > rhs[parts]) 2864 return 1; 2865 else 2866 return -1; 2867 } 2868 2869 return 0; 2870} 2871 2872/* Increment a bignum in-place, return the carry flag. */ 2873integerPart 2874APInt::tcIncrement(integerPart *dst, unsigned int parts) 2875{ 2876 unsigned int i; 2877 2878 for (i = 0; i < parts; i++) 2879 if (++dst[i] != 0) 2880 break; 2881 2882 return i == parts; 2883} 2884 2885/* Set the least significant BITS bits of a bignum, clear the 2886 rest. */ 2887void 2888APInt::tcSetLeastSignificantBits(integerPart *dst, unsigned int parts, 2889 unsigned int bits) 2890{ 2891 unsigned int i; 2892 2893 i = 0; 2894 while (bits > integerPartWidth) { 2895 dst[i++] = ~(integerPart) 0; 2896 bits -= integerPartWidth; 2897 } 2898 2899 if (bits) 2900 dst[i++] = ~(integerPart) 0 >> (integerPartWidth - bits); 2901 2902 while (i < parts) 2903 dst[i++] = 0; 2904} 2905