APInt.cpp revision 6dbe233959eed02971f3075e0c48234238ff6fa3
1//===-- APInt.cpp - Implement APInt class ---------------------------------===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file was developed by Sheng Zhou and is distributed under the 6// University of Illinois Open Source 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/DerivedTypes.h" 18#include "llvm/Support/Debug.h" 19#include "llvm/Support/MathExtras.h" 20#include <math.h> 21#include <limits> 22#include <cstring> 23#include <cstdlib> 24#ifndef NDEBUG 25#include <iomanip> 26#endif 27 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(uint32_t 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(uint32_t numWords) { 42 uint64_t * result = new uint64_t[numWords]; 43 assert(result && "APInt memory allocation fails!"); 44 return result; 45} 46 47APInt::APInt(uint32_t numBits, uint64_t val, bool isSigned) 48 : BitWidth(numBits), VAL(0) { 49 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small"); 50 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large"); 51 if (isSingleWord()) 52 VAL = val; 53 else { 54 pVal = getClearedMemory(getNumWords()); 55 pVal[0] = val; 56 if (isSigned && int64_t(val) < 0) 57 for (unsigned i = 1; i < getNumWords(); ++i) 58 pVal[i] = -1ULL; 59 } 60 clearUnusedBits(); 61} 62 63APInt::APInt(uint32_t numBits, uint32_t numWords, uint64_t bigVal[]) 64 : BitWidth(numBits), VAL(0) { 65 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small"); 66 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large"); 67 assert(bigVal && "Null pointer detected!"); 68 if (isSingleWord()) 69 VAL = bigVal[0]; 70 else { 71 // Get memory, cleared to 0 72 pVal = getClearedMemory(getNumWords()); 73 // Calculate the number of words to copy 74 uint32_t words = std::min<uint32_t>(numWords, getNumWords()); 75 // Copy the words from bigVal to pVal 76 memcpy(pVal, bigVal, words * APINT_WORD_SIZE); 77 } 78 // Make sure unused high bits are cleared 79 clearUnusedBits(); 80} 81 82APInt::APInt(uint32_t numbits, const char StrStart[], uint32_t slen, 83 uint8_t radix) 84 : BitWidth(numbits), VAL(0) { 85 fromString(numbits, StrStart, slen, radix); 86} 87 88APInt::APInt(uint32_t numbits, const std::string& Val, uint8_t radix) 89 : BitWidth(numbits), VAL(0) { 90 assert(!Val.empty() && "String empty?"); 91 fromString(numbits, Val.c_str(), Val.size(), radix); 92} 93 94APInt::APInt(const APInt& that) 95 : BitWidth(that.BitWidth), VAL(0) { 96 if (isSingleWord()) 97 VAL = that.VAL; 98 else { 99 pVal = getMemory(getNumWords()); 100 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE); 101 } 102} 103 104APInt::~APInt() { 105 if (!isSingleWord() && pVal) 106 delete [] pVal; 107} 108 109APInt& APInt::operator=(const APInt& RHS) { 110 // Don't do anything for X = X 111 if (this == &RHS) 112 return *this; 113 114 // If the bitwidths are the same, we can avoid mucking with memory 115 if (BitWidth == RHS.getBitWidth()) { 116 if (isSingleWord()) 117 VAL = RHS.VAL; 118 else 119 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE); 120 return *this; 121 } 122 123 if (isSingleWord()) 124 if (RHS.isSingleWord()) 125 VAL = RHS.VAL; 126 else { 127 VAL = 0; 128 pVal = getMemory(RHS.getNumWords()); 129 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 130 } 131 else if (getNumWords() == RHS.getNumWords()) 132 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 133 else if (RHS.isSingleWord()) { 134 delete [] pVal; 135 VAL = RHS.VAL; 136 } else { 137 delete [] pVal; 138 pVal = getMemory(RHS.getNumWords()); 139 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 140 } 141 BitWidth = RHS.BitWidth; 142 return clearUnusedBits(); 143} 144 145APInt& APInt::operator=(uint64_t RHS) { 146 if (isSingleWord()) 147 VAL = RHS; 148 else { 149 pVal[0] = RHS; 150 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE); 151 } 152 return clearUnusedBits(); 153} 154 155/// add_1 - This function adds a single "digit" integer, y, to the multiple 156/// "digit" integer array, x[]. x[] is modified to reflect the addition and 157/// 1 is returned if there is a carry out, otherwise 0 is returned. 158/// @returns the carry of the addition. 159static bool add_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) { 160 for (uint32_t i = 0; i < len; ++i) { 161 dest[i] = y + x[i]; 162 if (dest[i] < y) 163 y = 1; // Carry one to next digit. 164 else { 165 y = 0; // No need to carry so exit early 166 break; 167 } 168 } 169 return y; 170} 171 172/// @brief Prefix increment operator. Increments the APInt by one. 173APInt& APInt::operator++() { 174 if (isSingleWord()) 175 ++VAL; 176 else 177 add_1(pVal, pVal, getNumWords(), 1); 178 return clearUnusedBits(); 179} 180 181/// sub_1 - This function subtracts a single "digit" (64-bit word), y, from 182/// the multi-digit integer array, x[], propagating the borrowed 1 value until 183/// no further borrowing is neeeded or it runs out of "digits" in x. The result 184/// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted. 185/// In other words, if y > x then this function returns 1, otherwise 0. 186/// @returns the borrow out of the subtraction 187static bool sub_1(uint64_t x[], uint32_t len, uint64_t y) { 188 for (uint32_t i = 0; i < len; ++i) { 189 uint64_t X = x[i]; 190 x[i] -= y; 191 if (y > X) 192 y = 1; // We have to "borrow 1" from next "digit" 193 else { 194 y = 0; // No need to borrow 195 break; // Remaining digits are unchanged so exit early 196 } 197 } 198 return bool(y); 199} 200 201/// @brief Prefix decrement operator. Decrements the APInt by one. 202APInt& APInt::operator--() { 203 if (isSingleWord()) 204 --VAL; 205 else 206 sub_1(pVal, getNumWords(), 1); 207 return clearUnusedBits(); 208} 209 210/// add - This function adds the integer array x to the integer array Y and 211/// places the result in dest. 212/// @returns the carry out from the addition 213/// @brief General addition of 64-bit integer arrays 214static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y, 215 uint32_t len) { 216 bool carry = false; 217 for (uint32_t i = 0; i< len; ++i) { 218 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x 219 dest[i] = x[i] + y[i] + carry; 220 carry = dest[i] < limit || (carry && dest[i] == limit); 221 } 222 return carry; 223} 224 225/// Adds the RHS APint to this APInt. 226/// @returns this, after addition of RHS. 227/// @brief Addition assignment operator. 228APInt& APInt::operator+=(const APInt& RHS) { 229 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 230 if (isSingleWord()) 231 VAL += RHS.VAL; 232 else { 233 add(pVal, pVal, RHS.pVal, getNumWords()); 234 } 235 return clearUnusedBits(); 236} 237 238/// Subtracts the integer array y from the integer array x 239/// @returns returns the borrow out. 240/// @brief Generalized subtraction of 64-bit integer arrays. 241static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y, 242 uint32_t len) { 243 bool borrow = false; 244 for (uint32_t i = 0; i < len; ++i) { 245 uint64_t x_tmp = borrow ? x[i] - 1 : x[i]; 246 borrow = y[i] > x_tmp || (borrow && x[i] == 0); 247 dest[i] = x_tmp - y[i]; 248 } 249 return borrow; 250} 251 252/// Subtracts the RHS APInt from this APInt 253/// @returns this, after subtraction 254/// @brief Subtraction assignment operator. 255APInt& APInt::operator-=(const APInt& RHS) { 256 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 257 if (isSingleWord()) 258 VAL -= RHS.VAL; 259 else 260 sub(pVal, pVal, RHS.pVal, getNumWords()); 261 return clearUnusedBits(); 262} 263 264/// Multiplies an integer array, x by a a uint64_t integer and places the result 265/// into dest. 266/// @returns the carry out of the multiplication. 267/// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer. 268static uint64_t mul_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) { 269 // Split y into high 32-bit part (hy) and low 32-bit part (ly) 270 uint64_t ly = y & 0xffffffffULL, hy = y >> 32; 271 uint64_t carry = 0; 272 273 // For each digit of x. 274 for (uint32_t i = 0; i < len; ++i) { 275 // Split x into high and low words 276 uint64_t lx = x[i] & 0xffffffffULL; 277 uint64_t hx = x[i] >> 32; 278 // hasCarry - A flag to indicate if there is a carry to the next digit. 279 // hasCarry == 0, no carry 280 // hasCarry == 1, has carry 281 // hasCarry == 2, no carry and the calculation result == 0. 282 uint8_t hasCarry = 0; 283 dest[i] = carry + lx * ly; 284 // Determine if the add above introduces carry. 285 hasCarry = (dest[i] < carry) ? 1 : 0; 286 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0); 287 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) + 288 // (2^32 - 1) + 2^32 = 2^64. 289 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0); 290 291 carry += (lx * hy) & 0xffffffffULL; 292 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL); 293 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) + 294 (carry >> 32) + ((lx * hy) >> 32) + hx * hy; 295 } 296 return carry; 297} 298 299/// Multiplies integer array x by integer array y and stores the result into 300/// the integer array dest. Note that dest's size must be >= xlen + ylen. 301/// @brief Generalized multiplicate of integer arrays. 302static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, uint64_t y[], 303 uint32_t ylen) { 304 dest[xlen] = mul_1(dest, x, xlen, y[0]); 305 for (uint32_t i = 1; i < ylen; ++i) { 306 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32; 307 uint64_t carry = 0, lx = 0, hx = 0; 308 for (uint32_t j = 0; j < xlen; ++j) { 309 lx = x[j] & 0xffffffffULL; 310 hx = x[j] >> 32; 311 // hasCarry - A flag to indicate if has carry. 312 // hasCarry == 0, no carry 313 // hasCarry == 1, has carry 314 // hasCarry == 2, no carry and the calculation result == 0. 315 uint8_t hasCarry = 0; 316 uint64_t resul = carry + lx * ly; 317 hasCarry = (resul < carry) ? 1 : 0; 318 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32); 319 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0); 320 321 carry += (lx * hy) & 0xffffffffULL; 322 resul = (carry << 32) | (resul & 0xffffffffULL); 323 dest[i+j] += resul; 324 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+ 325 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) + 326 ((lx * hy) >> 32) + hx * hy; 327 } 328 dest[i+xlen] = carry; 329 } 330} 331 332APInt& APInt::operator*=(const APInt& RHS) { 333 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 334 if (isSingleWord()) { 335 VAL *= RHS.VAL; 336 clearUnusedBits(); 337 return *this; 338 } 339 340 // Get some bit facts about LHS and check for zero 341 uint32_t lhsBits = getActiveBits(); 342 uint32_t lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1; 343 if (!lhsWords) 344 // 0 * X ===> 0 345 return *this; 346 347 // Get some bit facts about RHS and check for zero 348 uint32_t rhsBits = RHS.getActiveBits(); 349 uint32_t rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1; 350 if (!rhsWords) { 351 // X * 0 ===> 0 352 clear(); 353 return *this; 354 } 355 356 // Allocate space for the result 357 uint32_t destWords = rhsWords + lhsWords; 358 uint64_t *dest = getMemory(destWords); 359 360 // Perform the long multiply 361 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords); 362 363 // Copy result back into *this 364 clear(); 365 uint32_t wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords; 366 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE); 367 368 // delete dest array and return 369 delete[] dest; 370 return *this; 371} 372 373APInt& APInt::operator&=(const APInt& RHS) { 374 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 375 if (isSingleWord()) { 376 VAL &= RHS.VAL; 377 return *this; 378 } 379 uint32_t numWords = getNumWords(); 380 for (uint32_t i = 0; i < numWords; ++i) 381 pVal[i] &= RHS.pVal[i]; 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 uint32_t numWords = getNumWords(); 392 for (uint32_t 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 this->clearUnusedBits(); 402 return *this; 403 } 404 uint32_t numWords = getNumWords(); 405 for (uint32_t i = 0; i < numWords; ++i) 406 pVal[i] ^= RHS.pVal[i]; 407 return clearUnusedBits(); 408} 409 410APInt APInt::operator&(const APInt& RHS) const { 411 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 412 if (isSingleWord()) 413 return APInt(getBitWidth(), VAL & RHS.VAL); 414 415 uint32_t numWords = getNumWords(); 416 uint64_t* val = getMemory(numWords); 417 for (uint32_t i = 0; i < numWords; ++i) 418 val[i] = pVal[i] & RHS.pVal[i]; 419 return APInt(val, getBitWidth()); 420} 421 422APInt APInt::operator|(const APInt& RHS) const { 423 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 424 if (isSingleWord()) 425 return APInt(getBitWidth(), VAL | RHS.VAL); 426 427 uint32_t numWords = getNumWords(); 428 uint64_t *val = getMemory(numWords); 429 for (uint32_t i = 0; i < numWords; ++i) 430 val[i] = pVal[i] | RHS.pVal[i]; 431 return APInt(val, getBitWidth()); 432} 433 434APInt APInt::operator^(const APInt& RHS) const { 435 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 436 if (isSingleWord()) 437 return APInt(BitWidth, VAL ^ RHS.VAL); 438 439 uint32_t numWords = getNumWords(); 440 uint64_t *val = getMemory(numWords); 441 for (uint32_t 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 (uint32_t 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[](uint32_t bitPosition) const { 486 return (maskBit(bitPosition) & 487 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0; 488} 489 490bool APInt::operator==(const APInt& RHS) const { 491 assert(BitWidth == RHS.BitWidth && "Comparison requires equal bit widths"); 492 if (isSingleWord()) 493 return VAL == RHS.VAL; 494 495 // Get some facts about the number of bits used in the two operands. 496 uint32_t n1 = getActiveBits(); 497 uint32_t n2 = RHS.getActiveBits(); 498 499 // If the number of bits isn't the same, they aren't equal 500 if (n1 != n2) 501 return false; 502 503 // If the number of bits fits in a word, we only need to compare the low word. 504 if (n1 <= APINT_BITS_PER_WORD) 505 return pVal[0] == RHS.pVal[0]; 506 507 // Otherwise, compare everything 508 for (int i = whichWord(n1 - 1); i >= 0; --i) 509 if (pVal[i] != RHS.pVal[i]) 510 return false; 511 return true; 512} 513 514bool APInt::operator==(uint64_t Val) const { 515 if (isSingleWord()) 516 return VAL == Val; 517 518 uint32_t n = getActiveBits(); 519 if (n <= APINT_BITS_PER_WORD) 520 return pVal[0] == Val; 521 else 522 return false; 523} 524 525bool APInt::ult(const APInt& RHS) const { 526 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); 527 if (isSingleWord()) 528 return VAL < RHS.VAL; 529 530 // Get active bit length of both operands 531 uint32_t n1 = getActiveBits(); 532 uint32_t n2 = RHS.getActiveBits(); 533 534 // If magnitude of LHS is less than RHS, return true. 535 if (n1 < n2) 536 return true; 537 538 // If magnitude of RHS is greather than LHS, return false. 539 if (n2 < n1) 540 return false; 541 542 // If they bot fit in a word, just compare the low order word 543 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD) 544 return pVal[0] < RHS.pVal[0]; 545 546 // Otherwise, compare all words 547 uint32_t topWord = whichWord(std::max(n1,n2)-1); 548 for (int i = topWord; i >= 0; --i) { 549 if (pVal[i] > RHS.pVal[i]) 550 return false; 551 if (pVal[i] < RHS.pVal[i]) 552 return true; 553 } 554 return false; 555} 556 557bool APInt::slt(const APInt& RHS) const { 558 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); 559 if (isSingleWord()) { 560 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth); 561 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth); 562 return lhsSext < rhsSext; 563 } 564 565 APInt lhs(*this); 566 APInt rhs(RHS); 567 bool lhsNeg = isNegative(); 568 bool rhsNeg = rhs.isNegative(); 569 if (lhsNeg) { 570 // Sign bit is set so perform two's complement to make it positive 571 lhs.flip(); 572 lhs++; 573 } 574 if (rhsNeg) { 575 // Sign bit is set so perform two's complement to make it positive 576 rhs.flip(); 577 rhs++; 578 } 579 580 // Now we have unsigned values to compare so do the comparison if necessary 581 // based on the negativeness of the values. 582 if (lhsNeg) 583 if (rhsNeg) 584 return lhs.ugt(rhs); 585 else 586 return true; 587 else if (rhsNeg) 588 return false; 589 else 590 return lhs.ult(rhs); 591} 592 593APInt& APInt::set(uint32_t bitPosition) { 594 if (isSingleWord()) 595 VAL |= maskBit(bitPosition); 596 else 597 pVal[whichWord(bitPosition)] |= maskBit(bitPosition); 598 return *this; 599} 600 601APInt& APInt::set() { 602 if (isSingleWord()) { 603 VAL = -1ULL; 604 return clearUnusedBits(); 605 } 606 607 // Set all the bits in all the words. 608 for (uint32_t i = 0; i < getNumWords(); ++i) 609 pVal[i] = -1ULL; 610 // Clear the unused ones 611 return clearUnusedBits(); 612} 613 614/// Set the given bit to 0 whose position is given as "bitPosition". 615/// @brief Set a given bit to 0. 616APInt& APInt::clear(uint32_t bitPosition) { 617 if (isSingleWord()) 618 VAL &= ~maskBit(bitPosition); 619 else 620 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition); 621 return *this; 622} 623 624/// @brief Set every bit to 0. 625APInt& APInt::clear() { 626 if (isSingleWord()) 627 VAL = 0; 628 else 629 memset(pVal, 0, getNumWords() * APINT_WORD_SIZE); 630 return *this; 631} 632 633/// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on 634/// this APInt. 635APInt APInt::operator~() const { 636 APInt Result(*this); 637 Result.flip(); 638 return Result; 639} 640 641/// @brief Toggle every bit to its opposite value. 642APInt& APInt::flip() { 643 if (isSingleWord()) { 644 VAL ^= -1ULL; 645 return clearUnusedBits(); 646 } 647 for (uint32_t i = 0; i < getNumWords(); ++i) 648 pVal[i] ^= -1ULL; 649 return clearUnusedBits(); 650} 651 652/// Toggle a given bit to its opposite value whose position is given 653/// as "bitPosition". 654/// @brief Toggles a given bit to its opposite value. 655APInt& APInt::flip(uint32_t bitPosition) { 656 assert(bitPosition < BitWidth && "Out of the bit-width range!"); 657 if ((*this)[bitPosition]) clear(bitPosition); 658 else set(bitPosition); 659 return *this; 660} 661 662uint64_t APInt::getHashValue() const { 663 // Put the bit width into the low order bits. 664 uint64_t hash = BitWidth; 665 666 // Add the sum of the words to the hash. 667 if (isSingleWord()) 668 hash += VAL << 6; // clear separation of up to 64 bits 669 else 670 for (uint32_t i = 0; i < getNumWords(); ++i) 671 hash += pVal[i] << 6; // clear sepration of up to 64 bits 672 return hash; 673} 674 675/// HiBits - This function returns the high "numBits" bits of this APInt. 676APInt APInt::getHiBits(uint32_t numBits) const { 677 return APIntOps::lshr(*this, BitWidth - numBits); 678} 679 680/// LoBits - This function returns the low "numBits" bits of this APInt. 681APInt APInt::getLoBits(uint32_t numBits) const { 682 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits), 683 BitWidth - numBits); 684} 685 686bool APInt::isPowerOf2() const { 687 return (!!*this) && !(*this & (*this - APInt(BitWidth,1))); 688} 689 690uint32_t APInt::countLeadingZeros() const { 691 uint32_t Count = 0; 692 if (isSingleWord()) 693 Count = CountLeadingZeros_64(VAL); 694 else { 695 for (uint32_t i = getNumWords(); i > 0u; --i) { 696 if (pVal[i-1] == 0) 697 Count += APINT_BITS_PER_WORD; 698 else { 699 Count += CountLeadingZeros_64(pVal[i-1]); 700 break; 701 } 702 } 703 } 704 uint32_t remainder = BitWidth % APINT_BITS_PER_WORD; 705 if (remainder) 706 Count -= APINT_BITS_PER_WORD - remainder; 707 return Count; 708} 709 710static uint32_t countLeadingOnes_64(uint64_t V, uint32_t skip) { 711 uint32_t Count = 0; 712 if (skip) 713 V <<= skip; 714 while (V && (V & (1ULL << 63))) { 715 Count++; 716 V <<= 1; 717 } 718 return Count; 719} 720 721uint32_t APInt::countLeadingOnes() const { 722 if (isSingleWord()) 723 return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth); 724 725 uint32_t highWordBits = BitWidth % APINT_BITS_PER_WORD; 726 uint32_t shift = (highWordBits == 0 ? 0 : APINT_BITS_PER_WORD - highWordBits); 727 int i = getNumWords() - 1; 728 uint32_t Count = countLeadingOnes_64(pVal[i], shift); 729 if (Count == highWordBits) { 730 for (i--; i >= 0; --i) { 731 if (pVal[i] == -1ULL) 732 Count += APINT_BITS_PER_WORD; 733 else { 734 Count += countLeadingOnes_64(pVal[i], 0); 735 break; 736 } 737 } 738 } 739 return Count; 740} 741 742uint32_t APInt::countTrailingZeros() const { 743 if (isSingleWord()) 744 return CountTrailingZeros_64(VAL); 745 uint32_t Count = 0; 746 uint32_t i = 0; 747 for (; i < getNumWords() && pVal[i] == 0; ++i) 748 Count += APINT_BITS_PER_WORD; 749 if (i < getNumWords()) 750 Count += CountTrailingZeros_64(pVal[i]); 751 return Count; 752} 753 754uint32_t APInt::countPopulation() const { 755 if (isSingleWord()) 756 return CountPopulation_64(VAL); 757 uint32_t Count = 0; 758 for (uint32_t i = 0; i < getNumWords(); ++i) 759 Count += CountPopulation_64(pVal[i]); 760 return Count; 761} 762 763APInt APInt::byteSwap() const { 764 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!"); 765 if (BitWidth == 16) 766 return APInt(BitWidth, ByteSwap_16(uint16_t(VAL))); 767 else if (BitWidth == 32) 768 return APInt(BitWidth, ByteSwap_32(uint32_t(VAL))); 769 else if (BitWidth == 48) { 770 uint32_t Tmp1 = uint32_t(VAL >> 16); 771 Tmp1 = ByteSwap_32(Tmp1); 772 uint16_t Tmp2 = uint16_t(VAL); 773 Tmp2 = ByteSwap_16(Tmp2); 774 return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1); 775 } else if (BitWidth == 64) 776 return APInt(BitWidth, ByteSwap_64(VAL)); 777 else { 778 APInt Result(BitWidth, 0); 779 char *pByte = (char*)Result.pVal; 780 for (uint32_t i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) { 781 char Tmp = pByte[i]; 782 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i]; 783 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp; 784 } 785 return Result; 786 } 787} 788 789APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1, 790 const APInt& API2) { 791 APInt A = API1, B = API2; 792 while (!!B) { 793 APInt T = B; 794 B = APIntOps::urem(A, B); 795 A = T; 796 } 797 return A; 798} 799 800APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, uint32_t width) { 801 union { 802 double D; 803 uint64_t I; 804 } T; 805 T.D = Double; 806 807 // Get the sign bit from the highest order bit 808 bool isNeg = T.I >> 63; 809 810 // Get the 11-bit exponent and adjust for the 1023 bit bias 811 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023; 812 813 // If the exponent is negative, the value is < 0 so just return 0. 814 if (exp < 0) 815 return APInt(width, 0u); 816 817 // Extract the mantissa by clearing the top 12 bits (sign + exponent). 818 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52; 819 820 // If the exponent doesn't shift all bits out of the mantissa 821 if (exp < 52) 822 return isNeg ? -APInt(width, mantissa >> (52 - exp)) : 823 APInt(width, mantissa >> (52 - exp)); 824 825 // If the client didn't provide enough bits for us to shift the mantissa into 826 // then the result is undefined, just return 0 827 if (width <= exp - 52) 828 return APInt(width, 0); 829 830 // Otherwise, we have to shift the mantissa bits up to the right location 831 APInt Tmp(width, mantissa); 832 Tmp = Tmp.shl(exp - 52); 833 return isNeg ? -Tmp : Tmp; 834} 835 836/// RoundToDouble - This function convert this APInt to a double. 837/// The layout for double is as following (IEEE Standard 754): 838/// -------------------------------------- 839/// | Sign Exponent Fraction Bias | 840/// |-------------------------------------- | 841/// | 1[63] 11[62-52] 52[51-00] 1023 | 842/// -------------------------------------- 843double APInt::roundToDouble(bool isSigned) const { 844 845 // Handle the simple case where the value is contained in one uint64_t. 846 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) { 847 if (isSigned) { 848 int64_t sext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth); 849 return double(sext); 850 } else 851 return double(VAL); 852 } 853 854 // Determine if the value is negative. 855 bool isNeg = isSigned ? (*this)[BitWidth-1] : false; 856 857 // Construct the absolute value if we're negative. 858 APInt Tmp(isNeg ? -(*this) : (*this)); 859 860 // Figure out how many bits we're using. 861 uint32_t n = Tmp.getActiveBits(); 862 863 // The exponent (without bias normalization) is just the number of bits 864 // we are using. Note that the sign bit is gone since we constructed the 865 // absolute value. 866 uint64_t exp = n; 867 868 // Return infinity for exponent overflow 869 if (exp > 1023) { 870 if (!isSigned || !isNeg) 871 return std::numeric_limits<double>::infinity(); 872 else 873 return -std::numeric_limits<double>::infinity(); 874 } 875 exp += 1023; // Increment for 1023 bias 876 877 // Number of bits in mantissa is 52. To obtain the mantissa value, we must 878 // extract the high 52 bits from the correct words in pVal. 879 uint64_t mantissa; 880 unsigned hiWord = whichWord(n-1); 881 if (hiWord == 0) { 882 mantissa = Tmp.pVal[0]; 883 if (n > 52) 884 mantissa >>= n - 52; // shift down, we want the top 52 bits. 885 } else { 886 assert(hiWord > 0 && "huh?"); 887 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD); 888 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD); 889 mantissa = hibits | lobits; 890 } 891 892 // The leading bit of mantissa is implicit, so get rid of it. 893 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0; 894 union { 895 double D; 896 uint64_t I; 897 } T; 898 T.I = sign | (exp << 52) | mantissa; 899 return T.D; 900} 901 902// Truncate to new width. 903APInt &APInt::trunc(uint32_t width) { 904 assert(width < BitWidth && "Invalid APInt Truncate request"); 905 assert(width >= IntegerType::MIN_INT_BITS && "Can't truncate to 0 bits"); 906 uint32_t wordsBefore = getNumWords(); 907 BitWidth = width; 908 uint32_t wordsAfter = getNumWords(); 909 if (wordsBefore != wordsAfter) { 910 if (wordsAfter == 1) { 911 uint64_t *tmp = pVal; 912 VAL = pVal[0]; 913 delete [] tmp; 914 } else { 915 uint64_t *newVal = getClearedMemory(wordsAfter); 916 for (uint32_t i = 0; i < wordsAfter; ++i) 917 newVal[i] = pVal[i]; 918 delete [] pVal; 919 pVal = newVal; 920 } 921 } 922 return clearUnusedBits(); 923} 924 925// Sign extend to a new width. 926APInt &APInt::sext(uint32_t width) { 927 assert(width > BitWidth && "Invalid APInt SignExtend request"); 928 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits"); 929 // If the sign bit isn't set, this is the same as zext. 930 if (!isNegative()) { 931 zext(width); 932 return *this; 933 } 934 935 // The sign bit is set. First, get some facts 936 uint32_t wordsBefore = getNumWords(); 937 uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD; 938 BitWidth = width; 939 uint32_t wordsAfter = getNumWords(); 940 941 // Mask the high order word appropriately 942 if (wordsBefore == wordsAfter) { 943 uint32_t newWordBits = width % APINT_BITS_PER_WORD; 944 // The extension is contained to the wordsBefore-1th word. 945 uint64_t mask = ~0ULL; 946 if (newWordBits) 947 mask >>= APINT_BITS_PER_WORD - newWordBits; 948 mask <<= wordBits; 949 if (wordsBefore == 1) 950 VAL |= mask; 951 else 952 pVal[wordsBefore-1] |= mask; 953 return clearUnusedBits(); 954 } 955 956 uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits; 957 uint64_t *newVal = getMemory(wordsAfter); 958 if (wordsBefore == 1) 959 newVal[0] = VAL | mask; 960 else { 961 for (uint32_t i = 0; i < wordsBefore; ++i) 962 newVal[i] = pVal[i]; 963 newVal[wordsBefore-1] |= mask; 964 } 965 for (uint32_t i = wordsBefore; i < wordsAfter; i++) 966 newVal[i] = -1ULL; 967 if (wordsBefore != 1) 968 delete [] pVal; 969 pVal = newVal; 970 return clearUnusedBits(); 971} 972 973// Zero extend to a new width. 974APInt &APInt::zext(uint32_t width) { 975 assert(width > BitWidth && "Invalid APInt ZeroExtend request"); 976 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits"); 977 uint32_t wordsBefore = getNumWords(); 978 BitWidth = width; 979 uint32_t wordsAfter = getNumWords(); 980 if (wordsBefore != wordsAfter) { 981 uint64_t *newVal = getClearedMemory(wordsAfter); 982 if (wordsBefore == 1) 983 newVal[0] = VAL; 984 else 985 for (uint32_t i = 0; i < wordsBefore; ++i) 986 newVal[i] = pVal[i]; 987 if (wordsBefore != 1) 988 delete [] pVal; 989 pVal = newVal; 990 } 991 return *this; 992} 993 994APInt &APInt::zextOrTrunc(uint32_t width) { 995 if (BitWidth < width) 996 return zext(width); 997 if (BitWidth > width) 998 return trunc(width); 999 return *this; 1000} 1001 1002APInt &APInt::sextOrTrunc(uint32_t width) { 1003 if (BitWidth < width) 1004 return sext(width); 1005 if (BitWidth > width) 1006 return trunc(width); 1007 return *this; 1008} 1009 1010/// Arithmetic right-shift this APInt by shiftAmt. 1011/// @brief Arithmetic right-shift function. 1012APInt APInt::ashr(uint32_t shiftAmt) const { 1013 assert(shiftAmt <= BitWidth && "Invalid shift amount"); 1014 // Handle a degenerate case 1015 if (shiftAmt == 0) 1016 return *this; 1017 1018 // Handle single word shifts with built-in ashr 1019 if (isSingleWord()) { 1020 if (shiftAmt == BitWidth) 1021 return APInt(BitWidth, 0); // undefined 1022 else { 1023 uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth; 1024 return APInt(BitWidth, 1025 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt)); 1026 } 1027 } 1028 1029 // If all the bits were shifted out, the result is, technically, undefined. 1030 // We return -1 if it was negative, 0 otherwise. We check this early to avoid 1031 // issues in the algorithm below. 1032 if (shiftAmt == BitWidth) 1033 if (isNegative()) 1034 return APInt(BitWidth, -1ULL); 1035 else 1036 return APInt(BitWidth, 0); 1037 1038 // Create some space for the result. 1039 uint64_t * val = new uint64_t[getNumWords()]; 1040 1041 // Compute some values needed by the following shift algorithms 1042 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word 1043 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift 1044 uint32_t breakWord = getNumWords() - 1 - offset; // last word affected 1045 uint32_t bitsInWord = whichBit(BitWidth); // how many bits in last word? 1046 if (bitsInWord == 0) 1047 bitsInWord = APINT_BITS_PER_WORD; 1048 1049 // If we are shifting whole words, just move whole words 1050 if (wordShift == 0) { 1051 // Move the words containing significant bits 1052 for (uint32_t i = 0; i <= breakWord; ++i) 1053 val[i] = pVal[i+offset]; // move whole word 1054 1055 // Adjust the top significant word for sign bit fill, if negative 1056 if (isNegative()) 1057 if (bitsInWord < APINT_BITS_PER_WORD) 1058 val[breakWord] |= ~0ULL << bitsInWord; // set high bits 1059 } else { 1060 // Shift the low order words 1061 for (uint32_t i = 0; i < breakWord; ++i) { 1062 // This combines the shifted corresponding word with the low bits from 1063 // the next word (shifted into this word's high bits). 1064 val[i] = (pVal[i+offset] >> wordShift) | 1065 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift)); 1066 } 1067 1068 // Shift the break word. In this case there are no bits from the next word 1069 // to include in this word. 1070 val[breakWord] = pVal[breakWord+offset] >> wordShift; 1071 1072 // Deal with sign extenstion in the break word, and possibly the word before 1073 // it. 1074 if (isNegative()) 1075 if (wordShift > bitsInWord) { 1076 if (breakWord > 0) 1077 val[breakWord-1] |= 1078 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord)); 1079 val[breakWord] |= ~0ULL; 1080 } else 1081 val[breakWord] |= (~0ULL << (bitsInWord - wordShift)); 1082 } 1083 1084 // Remaining words are 0 or -1, just assign them. 1085 uint64_t fillValue = (isNegative() ? -1ULL : 0); 1086 for (uint32_t i = breakWord+1; i < getNumWords(); ++i) 1087 val[i] = fillValue; 1088 return APInt(val, BitWidth).clearUnusedBits(); 1089} 1090 1091/// Logical right-shift this APInt by shiftAmt. 1092/// @brief Logical right-shift function. 1093APInt APInt::lshr(uint32_t shiftAmt) const { 1094 if (isSingleWord()) 1095 if (shiftAmt == BitWidth) 1096 return APInt(BitWidth, 0); 1097 else 1098 return APInt(BitWidth, this->VAL >> shiftAmt); 1099 1100 // If all the bits were shifted out, the result is 0. This avoids issues 1101 // with shifting by the size of the integer type, which produces undefined 1102 // results. We define these "undefined results" to always be 0. 1103 if (shiftAmt == BitWidth) 1104 return APInt(BitWidth, 0); 1105 1106 // Create some space for the result. 1107 uint64_t * val = new uint64_t[getNumWords()]; 1108 1109 // If we are shifting less than a word, compute the shift with a simple carry 1110 if (shiftAmt < APINT_BITS_PER_WORD) { 1111 uint64_t carry = 0; 1112 for (int i = getNumWords()-1; i >= 0; --i) { 1113 val[i] = (pVal[i] >> shiftAmt) | carry; 1114 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt); 1115 } 1116 return APInt(val, BitWidth).clearUnusedBits(); 1117 } 1118 1119 // Compute some values needed by the remaining shift algorithms 1120 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; 1121 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; 1122 1123 // If we are shifting whole words, just move whole words 1124 if (wordShift == 0) { 1125 for (uint32_t i = 0; i < getNumWords() - offset; ++i) 1126 val[i] = pVal[i+offset]; 1127 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++) 1128 val[i] = 0; 1129 return APInt(val,BitWidth).clearUnusedBits(); 1130 } 1131 1132 // Shift the low order words 1133 uint32_t breakWord = getNumWords() - offset -1; 1134 for (uint32_t i = 0; i < breakWord; ++i) 1135 val[i] = (pVal[i+offset] >> wordShift) | 1136 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift)); 1137 // Shift the break word. 1138 val[breakWord] = pVal[breakWord+offset] >> wordShift; 1139 1140 // Remaining words are 0 1141 for (uint32_t i = breakWord+1; i < getNumWords(); ++i) 1142 val[i] = 0; 1143 return APInt(val, BitWidth).clearUnusedBits(); 1144} 1145 1146/// Left-shift this APInt by shiftAmt. 1147/// @brief Left-shift function. 1148APInt APInt::shl(uint32_t shiftAmt) const { 1149 assert(shiftAmt <= BitWidth && "Invalid shift amount"); 1150 if (isSingleWord()) { 1151 if (shiftAmt == BitWidth) 1152 return APInt(BitWidth, 0); // avoid undefined shift results 1153 return APInt(BitWidth, VAL << shiftAmt); 1154 } 1155 1156 // If all the bits were shifted out, the result is 0. This avoids issues 1157 // with shifting by the size of the integer type, which produces undefined 1158 // results. We define these "undefined results" to always be 0. 1159 if (shiftAmt == BitWidth) 1160 return APInt(BitWidth, 0); 1161 1162 // Create some space for the result. 1163 uint64_t * val = new uint64_t[getNumWords()]; 1164 1165 // If we are shifting less than a word, do it the easy way 1166 if (shiftAmt < APINT_BITS_PER_WORD) { 1167 uint64_t carry = 0; 1168 for (uint32_t i = 0; i < getNumWords(); i++) { 1169 val[i] = pVal[i] << shiftAmt | carry; 1170 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt); 1171 } 1172 return APInt(val, BitWidth).clearUnusedBits(); 1173 } 1174 1175 // Compute some values needed by the remaining shift algorithms 1176 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; 1177 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; 1178 1179 // If we are shifting whole words, just move whole words 1180 if (wordShift == 0) { 1181 for (uint32_t i = 0; i < offset; i++) 1182 val[i] = 0; 1183 for (uint32_t i = offset; i < getNumWords(); i++) 1184 val[i] = pVal[i-offset]; 1185 return APInt(val,BitWidth).clearUnusedBits(); 1186 } 1187 1188 // Copy whole words from this to Result. 1189 uint32_t i = getNumWords() - 1; 1190 for (; i > offset; --i) 1191 val[i] = pVal[i-offset] << wordShift | 1192 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift); 1193 val[offset] = pVal[0] << wordShift; 1194 for (i = 0; i < offset; ++i) 1195 val[i] = 0; 1196 return APInt(val, BitWidth).clearUnusedBits(); 1197} 1198 1199 1200// Square Root - this method computes and returns the square root of "this". 1201// Three mechanisms are used for computation. For small values (<= 5 bits), 1202// a table lookup is done. This gets some performance for common cases. For 1203// values using less than 52 bits, the value is converted to double and then 1204// the libc sqrt function is called. The result is rounded and then converted 1205// back to a uint64_t which is then used to construct the result. Finally, 1206// the Babylonian method for computing square roots is used. 1207APInt APInt::sqrt() const { 1208 1209 // Determine the magnitude of the value. 1210 uint32_t magnitude = getActiveBits(); 1211 1212 // Use a fast table for some small values. This also gets rid of some 1213 // rounding errors in libc sqrt for small values. 1214 if (magnitude <= 5) { 1215 static const uint8_t results[32] = { 1216 /* 0 */ 0, 1217 /* 1- 2 */ 1, 1, 1218 /* 3- 6 */ 2, 2, 2, 2, 1219 /* 7-12 */ 3, 3, 3, 3, 3, 3, 1220 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4, 1221 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1222 /* 31 */ 6 1223 }; 1224 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]); 1225 } 1226 1227 // If the magnitude of the value fits in less than 52 bits (the precision of 1228 // an IEEE double precision floating point value), then we can use the 1229 // libc sqrt function which will probably use a hardware sqrt computation. 1230 // This should be faster than the algorithm below. 1231 if (magnitude < 52) { 1232#ifdef _MSC_VER 1233 // Amazingly, VC++ doesn't have round(). 1234 return APInt(BitWidth, 1235 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5); 1236#else 1237 return APInt(BitWidth, 1238 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0]))))); 1239#endif 1240 } 1241 1242 // Okay, all the short cuts are exhausted. We must compute it. The following 1243 // is a classical Babylonian method for computing the square root. This code 1244 // was adapted to APINt from a wikipedia article on such computations. 1245 // See http://www.wikipedia.org/ and go to the page named 1246 // Calculate_an_integer_square_root. 1247 uint32_t nbits = BitWidth, i = 4; 1248 APInt testy(BitWidth, 16); 1249 APInt x_old(BitWidth, 1); 1250 APInt x_new(BitWidth, 0); 1251 APInt two(BitWidth, 2); 1252 1253 // Select a good starting value using binary logarithms. 1254 for (;; i += 2, testy = testy.shl(2)) 1255 if (i >= nbits || this->ule(testy)) { 1256 x_old = x_old.shl(i / 2); 1257 break; 1258 } 1259 1260 // Use the Babylonian method to arrive at the integer square root: 1261 for (;;) { 1262 x_new = (this->udiv(x_old) + x_old).udiv(two); 1263 if (x_old.ule(x_new)) 1264 break; 1265 x_old = x_new; 1266 } 1267 1268 // Make sure we return the closest approximation 1269 // NOTE: The rounding calculation below is correct. It will produce an 1270 // off-by-one discrepancy with results from pari/gp. That discrepancy has been 1271 // determined to be a rounding issue with pari/gp as it begins to use a 1272 // floating point representation after 192 bits. There are no discrepancies 1273 // between this algorithm and pari/gp for bit widths < 192 bits. 1274 APInt square(x_old * x_old); 1275 APInt nextSquare((x_old + 1) * (x_old +1)); 1276 if (this->ult(square)) 1277 return x_old; 1278 else if (this->ule(nextSquare)) { 1279 APInt midpoint((nextSquare - square).udiv(two)); 1280 APInt offset(*this - square); 1281 if (offset.ult(midpoint)) 1282 return x_old; 1283 else 1284 return x_old + 1; 1285 } else 1286 assert(0 && "Error in APInt::sqrt computation"); 1287 return x_old + 1; 1288} 1289 1290/// Implementation of Knuth's Algorithm D (Division of nonnegative integers) 1291/// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The 1292/// variables here have the same names as in the algorithm. Comments explain 1293/// the algorithm and any deviation from it. 1294static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r, 1295 uint32_t m, uint32_t n) { 1296 assert(u && "Must provide dividend"); 1297 assert(v && "Must provide divisor"); 1298 assert(q && "Must provide quotient"); 1299 assert(u != v && u != q && v != q && "Must us different memory"); 1300 assert(n>1 && "n must be > 1"); 1301 1302 // Knuth uses the value b as the base of the number system. In our case b 1303 // is 2^31 so we just set it to -1u. 1304 uint64_t b = uint64_t(1) << 32; 1305 1306 DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n'); 1307 DEBUG(cerr << "KnuthDiv: original:"); 1308 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]); 1309 DEBUG(cerr << " by"); 1310 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]); 1311 DEBUG(cerr << '\n'); 1312 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of 1313 // u and v by d. Note that we have taken Knuth's advice here to use a power 1314 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of 1315 // 2 allows us to shift instead of multiply and it is easy to determine the 1316 // shift amount from the leading zeros. We are basically normalizing the u 1317 // and v so that its high bits are shifted to the top of v's range without 1318 // overflow. Note that this can require an extra word in u so that u must 1319 // be of length m+n+1. 1320 uint32_t shift = CountLeadingZeros_32(v[n-1]); 1321 uint32_t v_carry = 0; 1322 uint32_t u_carry = 0; 1323 if (shift) { 1324 for (uint32_t i = 0; i < m+n; ++i) { 1325 uint32_t u_tmp = u[i] >> (32 - shift); 1326 u[i] = (u[i] << shift) | u_carry; 1327 u_carry = u_tmp; 1328 } 1329 for (uint32_t i = 0; i < n; ++i) { 1330 uint32_t v_tmp = v[i] >> (32 - shift); 1331 v[i] = (v[i] << shift) | v_carry; 1332 v_carry = v_tmp; 1333 } 1334 } 1335 u[m+n] = u_carry; 1336 DEBUG(cerr << "KnuthDiv: normal:"); 1337 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]); 1338 DEBUG(cerr << " by"); 1339 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]); 1340 DEBUG(cerr << '\n'); 1341 1342 // D2. [Initialize j.] Set j to m. This is the loop counter over the places. 1343 int j = m; 1344 do { 1345 DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n'); 1346 // D3. [Calculate q'.]. 1347 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q') 1348 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r') 1349 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease 1350 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test 1351 // on v[n-2] determines at high speed most of the cases in which the trial 1352 // value qp is one too large, and it eliminates all cases where qp is two 1353 // too large. 1354 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]); 1355 DEBUG(cerr << "KnuthDiv: dividend == " << dividend << '\n'); 1356 uint64_t qp = dividend / v[n-1]; 1357 uint64_t rp = dividend % v[n-1]; 1358 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) { 1359 qp--; 1360 rp += v[n-1]; 1361 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2])) 1362 qp--; 1363 } 1364 DEBUG(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n'); 1365 1366 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with 1367 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation 1368 // consists of a simple multiplication by a one-place number, combined with 1369 // a subtraction. 1370 bool isNeg = false; 1371 for (uint32_t i = 0; i < n; ++i) { 1372 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32); 1373 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]); 1374 bool borrow = subtrahend > u_tmp; 1375 DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp 1376 << ", subtrahend == " << subtrahend 1377 << ", borrow = " << borrow << '\n'); 1378 1379 uint64_t result = u_tmp - subtrahend; 1380 uint32_t k = j + i; 1381 u[k++] = result & (b-1); // subtract low word 1382 u[k++] = result >> 32; // subtract high word 1383 while (borrow && k <= m+n) { // deal with borrow to the left 1384 borrow = u[k] == 0; 1385 u[k]--; 1386 k++; 1387 } 1388 isNeg |= borrow; 1389 DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " << 1390 u[j+i+1] << '\n'); 1391 } 1392 DEBUG(cerr << "KnuthDiv: after subtraction:"); 1393 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]); 1394 DEBUG(cerr << '\n'); 1395 // The digits (u[j+n]...u[j]) should be kept positive; if the result of 1396 // this step is actually negative, (u[j+n]...u[j]) should be left as the 1397 // true value plus b**(n+1), namely as the b's complement of 1398 // the true value, and a "borrow" to the left should be remembered. 1399 // 1400 if (isNeg) { 1401 bool carry = true; // true because b's complement is "complement + 1" 1402 for (uint32_t i = 0; i <= m+n; ++i) { 1403 u[i] = ~u[i] + carry; // b's complement 1404 carry = carry && u[i] == 0; 1405 } 1406 } 1407 DEBUG(cerr << "KnuthDiv: after complement:"); 1408 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]); 1409 DEBUG(cerr << '\n'); 1410 1411 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was 1412 // negative, go to step D6; otherwise go on to step D7. 1413 q[j] = qp; 1414 if (isNeg) { 1415 // D6. [Add back]. The probability that this step is necessary is very 1416 // small, on the order of only 2/b. Make sure that test data accounts for 1417 // this possibility. Decrease q[j] by 1 1418 q[j]--; 1419 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]). 1420 // A carry will occur to the left of u[j+n], and it should be ignored 1421 // since it cancels with the borrow that occurred in D4. 1422 bool carry = false; 1423 for (uint32_t i = 0; i < n; i++) { 1424 uint32_t limit = std::min(u[j+i],v[i]); 1425 u[j+i] += v[i] + carry; 1426 carry = u[j+i] < limit || (carry && u[j+i] == limit); 1427 } 1428 u[j+n] += carry; 1429 } 1430 DEBUG(cerr << "KnuthDiv: after correction:"); 1431 DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]); 1432 DEBUG(cerr << "\nKnuthDiv: digit result = " << q[j] << '\n'); 1433 1434 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3. 1435 } while (--j >= 0); 1436 1437 DEBUG(cerr << "KnuthDiv: quotient:"); 1438 DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]); 1439 DEBUG(cerr << '\n'); 1440 1441 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired 1442 // remainder may be obtained by dividing u[...] by d. If r is non-null we 1443 // compute the remainder (urem uses this). 1444 if (r) { 1445 // The value d is expressed by the "shift" value above since we avoided 1446 // multiplication by d by using a shift left. So, all we have to do is 1447 // shift right here. In order to mak 1448 if (shift) { 1449 uint32_t carry = 0; 1450 DEBUG(cerr << "KnuthDiv: remainder:"); 1451 for (int i = n-1; i >= 0; i--) { 1452 r[i] = (u[i] >> shift) | carry; 1453 carry = u[i] << (32 - shift); 1454 DEBUG(cerr << " " << r[i]); 1455 } 1456 } else { 1457 for (int i = n-1; i >= 0; i--) { 1458 r[i] = u[i]; 1459 DEBUG(cerr << " " << r[i]); 1460 } 1461 } 1462 DEBUG(cerr << '\n'); 1463 } 1464 DEBUG(cerr << std::setbase(10) << '\n'); 1465} 1466 1467void APInt::divide(const APInt LHS, uint32_t lhsWords, 1468 const APInt &RHS, uint32_t rhsWords, 1469 APInt *Quotient, APInt *Remainder) 1470{ 1471 assert(lhsWords >= rhsWords && "Fractional result"); 1472 1473 // First, compose the values into an array of 32-bit words instead of 1474 // 64-bit words. This is a necessity of both the "short division" algorithm 1475 // and the the Knuth "classical algorithm" which requires there to be native 1476 // operations for +, -, and * on an m bit value with an m*2 bit result. We 1477 // can't use 64-bit operands here because we don't have native results of 1478 // 128-bits. Furthremore, casting the 64-bit values to 32-bit values won't 1479 // work on large-endian machines. 1480 uint64_t mask = ~0ull >> (sizeof(uint32_t)*8); 1481 uint32_t n = rhsWords * 2; 1482 uint32_t m = (lhsWords * 2) - n; 1483 1484 // Allocate space for the temporary values we need either on the stack, if 1485 // it will fit, or on the heap if it won't. 1486 uint32_t SPACE[128]; 1487 uint32_t *U = 0; 1488 uint32_t *V = 0; 1489 uint32_t *Q = 0; 1490 uint32_t *R = 0; 1491 if ((Remainder?4:3)*n+2*m+1 <= 128) { 1492 U = &SPACE[0]; 1493 V = &SPACE[m+n+1]; 1494 Q = &SPACE[(m+n+1) + n]; 1495 if (Remainder) 1496 R = &SPACE[(m+n+1) + n + (m+n)]; 1497 } else { 1498 U = new uint32_t[m + n + 1]; 1499 V = new uint32_t[n]; 1500 Q = new uint32_t[m+n]; 1501 if (Remainder) 1502 R = new uint32_t[n]; 1503 } 1504 1505 // Initialize the dividend 1506 memset(U, 0, (m+n+1)*sizeof(uint32_t)); 1507 for (unsigned i = 0; i < lhsWords; ++i) { 1508 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]); 1509 U[i * 2] = tmp & mask; 1510 U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8); 1511 } 1512 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm. 1513 1514 // Initialize the divisor 1515 memset(V, 0, (n)*sizeof(uint32_t)); 1516 for (unsigned i = 0; i < rhsWords; ++i) { 1517 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]); 1518 V[i * 2] = tmp & mask; 1519 V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8); 1520 } 1521 1522 // initialize the quotient and remainder 1523 memset(Q, 0, (m+n) * sizeof(uint32_t)); 1524 if (Remainder) 1525 memset(R, 0, n * sizeof(uint32_t)); 1526 1527 // Now, adjust m and n for the Knuth division. n is the number of words in 1528 // the divisor. m is the number of words by which the dividend exceeds the 1529 // divisor (i.e. m+n is the length of the dividend). These sizes must not 1530 // contain any zero words or the Knuth algorithm fails. 1531 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) { 1532 n--; 1533 m++; 1534 } 1535 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--) 1536 m--; 1537 1538 // If we're left with only a single word for the divisor, Knuth doesn't work 1539 // so we implement the short division algorithm here. This is much simpler 1540 // and faster because we are certain that we can divide a 64-bit quantity 1541 // by a 32-bit quantity at hardware speed and short division is simply a 1542 // series of such operations. This is just like doing short division but we 1543 // are using base 2^32 instead of base 10. 1544 assert(n != 0 && "Divide by zero?"); 1545 if (n == 1) { 1546 uint32_t divisor = V[0]; 1547 uint32_t remainder = 0; 1548 for (int i = m+n-1; i >= 0; i--) { 1549 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i]; 1550 if (partial_dividend == 0) { 1551 Q[i] = 0; 1552 remainder = 0; 1553 } else if (partial_dividend < divisor) { 1554 Q[i] = 0; 1555 remainder = partial_dividend; 1556 } else if (partial_dividend == divisor) { 1557 Q[i] = 1; 1558 remainder = 0; 1559 } else { 1560 Q[i] = partial_dividend / divisor; 1561 remainder = partial_dividend - (Q[i] * divisor); 1562 } 1563 } 1564 if (R) 1565 R[0] = remainder; 1566 } else { 1567 // Now we're ready to invoke the Knuth classical divide algorithm. In this 1568 // case n > 1. 1569 KnuthDiv(U, V, Q, R, m, n); 1570 } 1571 1572 // If the caller wants the quotient 1573 if (Quotient) { 1574 // Set up the Quotient value's memory. 1575 if (Quotient->BitWidth != LHS.BitWidth) { 1576 if (Quotient->isSingleWord()) 1577 Quotient->VAL = 0; 1578 else 1579 delete [] Quotient->pVal; 1580 Quotient->BitWidth = LHS.BitWidth; 1581 if (!Quotient->isSingleWord()) 1582 Quotient->pVal = getClearedMemory(Quotient->getNumWords()); 1583 } else 1584 Quotient->clear(); 1585 1586 // The quotient is in Q. Reconstitute the quotient into Quotient's low 1587 // order words. 1588 if (lhsWords == 1) { 1589 uint64_t tmp = 1590 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2)); 1591 if (Quotient->isSingleWord()) 1592 Quotient->VAL = tmp; 1593 else 1594 Quotient->pVal[0] = tmp; 1595 } else { 1596 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough"); 1597 for (unsigned i = 0; i < lhsWords; ++i) 1598 Quotient->pVal[i] = 1599 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2)); 1600 } 1601 } 1602 1603 // If the caller wants the remainder 1604 if (Remainder) { 1605 // Set up the Remainder value's memory. 1606 if (Remainder->BitWidth != RHS.BitWidth) { 1607 if (Remainder->isSingleWord()) 1608 Remainder->VAL = 0; 1609 else 1610 delete [] Remainder->pVal; 1611 Remainder->BitWidth = RHS.BitWidth; 1612 if (!Remainder->isSingleWord()) 1613 Remainder->pVal = getClearedMemory(Remainder->getNumWords()); 1614 } else 1615 Remainder->clear(); 1616 1617 // The remainder is in R. Reconstitute the remainder into Remainder's low 1618 // order words. 1619 if (rhsWords == 1) { 1620 uint64_t tmp = 1621 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2)); 1622 if (Remainder->isSingleWord()) 1623 Remainder->VAL = tmp; 1624 else 1625 Remainder->pVal[0] = tmp; 1626 } else { 1627 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough"); 1628 for (unsigned i = 0; i < rhsWords; ++i) 1629 Remainder->pVal[i] = 1630 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2)); 1631 } 1632 } 1633 1634 // Clean up the memory we allocated. 1635 if (U != &SPACE[0]) { 1636 delete [] U; 1637 delete [] V; 1638 delete [] Q; 1639 delete [] R; 1640 } 1641} 1642 1643APInt APInt::udiv(const APInt& RHS) const { 1644 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 1645 1646 // First, deal with the easy case 1647 if (isSingleWord()) { 1648 assert(RHS.VAL != 0 && "Divide by zero?"); 1649 return APInt(BitWidth, VAL / RHS.VAL); 1650 } 1651 1652 // Get some facts about the LHS and RHS number of bits and words 1653 uint32_t rhsBits = RHS.getActiveBits(); 1654 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); 1655 assert(rhsWords && "Divided by zero???"); 1656 uint32_t lhsBits = this->getActiveBits(); 1657 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1); 1658 1659 // Deal with some degenerate cases 1660 if (!lhsWords) 1661 // 0 / X ===> 0 1662 return APInt(BitWidth, 0); 1663 else if (lhsWords < rhsWords || this->ult(RHS)) { 1664 // X / Y ===> 0, iff X < Y 1665 return APInt(BitWidth, 0); 1666 } else if (*this == RHS) { 1667 // X / X ===> 1 1668 return APInt(BitWidth, 1); 1669 } else if (lhsWords == 1 && rhsWords == 1) { 1670 // All high words are zero, just use native divide 1671 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]); 1672 } 1673 1674 // We have to compute it the hard way. Invoke the Knuth divide algorithm. 1675 APInt Quotient(1,0); // to hold result. 1676 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0); 1677 return Quotient; 1678} 1679 1680APInt APInt::urem(const APInt& RHS) const { 1681 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 1682 if (isSingleWord()) { 1683 assert(RHS.VAL != 0 && "Remainder by zero?"); 1684 return APInt(BitWidth, VAL % RHS.VAL); 1685 } 1686 1687 // Get some facts about the LHS 1688 uint32_t lhsBits = getActiveBits(); 1689 uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1); 1690 1691 // Get some facts about the RHS 1692 uint32_t rhsBits = RHS.getActiveBits(); 1693 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); 1694 assert(rhsWords && "Performing remainder operation by zero ???"); 1695 1696 // Check the degenerate cases 1697 if (lhsWords == 0) { 1698 // 0 % Y ===> 0 1699 return APInt(BitWidth, 0); 1700 } else if (lhsWords < rhsWords || this->ult(RHS)) { 1701 // X % Y ===> X, iff X < Y 1702 return *this; 1703 } else if (*this == RHS) { 1704 // X % X == 0; 1705 return APInt(BitWidth, 0); 1706 } else if (lhsWords == 1) { 1707 // All high words are zero, just use native remainder 1708 return APInt(BitWidth, pVal[0] % RHS.pVal[0]); 1709 } 1710 1711 // We have to compute it the hard way. Invoke the Knute divide algorithm. 1712 APInt Remainder(1,0); 1713 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder); 1714 return Remainder; 1715} 1716 1717void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen, 1718 uint8_t radix) { 1719 // Check our assumptions here 1720 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) && 1721 "Radix should be 2, 8, 10, or 16!"); 1722 assert(str && "String is null?"); 1723 bool isNeg = str[0] == '-'; 1724 if (isNeg) 1725 str++, slen--; 1726 assert(slen <= numbits || radix != 2 && "Insufficient bit width"); 1727 assert(slen*3 <= numbits || radix != 8 && "Insufficient bit width"); 1728 assert(slen*4 <= numbits || radix != 16 && "Insufficient bit width"); 1729 assert((slen*64)/20 <= numbits || radix != 10 && "Insufficient bit width"); 1730 1731 // Allocate memory 1732 if (!isSingleWord()) 1733 pVal = getClearedMemory(getNumWords()); 1734 1735 // Figure out if we can shift instead of multiply 1736 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0); 1737 1738 // Set up an APInt for the digit to add outside the loop so we don't 1739 // constantly construct/destruct it. 1740 APInt apdigit(getBitWidth(), 0); 1741 APInt apradix(getBitWidth(), radix); 1742 1743 // Enter digit traversal loop 1744 for (unsigned i = 0; i < slen; i++) { 1745 // Get a digit 1746 uint32_t digit = 0; 1747 char cdigit = str[i]; 1748 if (isdigit(cdigit)) 1749 digit = cdigit - '0'; 1750 else if (isxdigit(cdigit)) 1751 if (cdigit >= 'a') 1752 digit = cdigit - 'a' + 10; 1753 else if (cdigit >= 'A') 1754 digit = cdigit - 'A' + 10; 1755 else 1756 assert(0 && "huh?"); 1757 else 1758 assert(0 && "Invalid character in digit string"); 1759 1760 // Shift or multiple the value by the radix 1761 if (shift) 1762 this->shl(shift); 1763 else 1764 *this *= apradix; 1765 1766 // Add in the digit we just interpreted 1767 if (apdigit.isSingleWord()) 1768 apdigit.VAL = digit; 1769 else 1770 apdigit.pVal[0] = digit; 1771 *this += apdigit; 1772 } 1773 // If its negative, put it in two's complement form 1774 if (isNeg) { 1775 (*this)--; 1776 this->flip(); 1777 } 1778} 1779 1780std::string APInt::toString(uint8_t radix, bool wantSigned) const { 1781 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) && 1782 "Radix should be 2, 8, 10, or 16!"); 1783 static const char *digits[] = { 1784 "0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F" 1785 }; 1786 std::string result; 1787 uint32_t bits_used = getActiveBits(); 1788 if (isSingleWord()) { 1789 char buf[65]; 1790 const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") : 1791 (radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0))); 1792 if (format) { 1793 if (wantSigned) { 1794 int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >> 1795 (APINT_BITS_PER_WORD-BitWidth); 1796 sprintf(buf, format, sextVal); 1797 } else 1798 sprintf(buf, format, VAL); 1799 } else { 1800 memset(buf, 0, 65); 1801 uint64_t v = VAL; 1802 while (bits_used) { 1803 uint32_t bit = v & 1; 1804 bits_used--; 1805 buf[bits_used] = digits[bit][0]; 1806 v >>=1; 1807 } 1808 } 1809 result = buf; 1810 return result; 1811 } 1812 1813 if (radix != 10) { 1814 uint64_t mask = radix - 1; 1815 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : 1); 1816 uint32_t nibbles = APINT_BITS_PER_WORD / shift; 1817 for (uint32_t i = 0; i < getNumWords(); ++i) { 1818 uint64_t value = pVal[i]; 1819 for (uint32_t j = 0; j < nibbles; ++j) { 1820 result.insert(0, digits[ value & mask ]); 1821 value >>= shift; 1822 } 1823 } 1824 return result; 1825 } 1826 1827 APInt tmp(*this); 1828 APInt divisor(4, radix); 1829 APInt zero(tmp.getBitWidth(), 0); 1830 size_t insert_at = 0; 1831 if (wantSigned && tmp[BitWidth-1]) { 1832 // They want to print the signed version and it is a negative value 1833 // Flip the bits and add one to turn it into the equivalent positive 1834 // value and put a '-' in the result. 1835 tmp.flip(); 1836 tmp++; 1837 result = "-"; 1838 insert_at = 1; 1839 } 1840 if (tmp == APInt(tmp.getBitWidth(), 0)) 1841 result = "0"; 1842 else while (tmp.ne(zero)) { 1843 APInt APdigit(1,0); 1844 APInt tmp2(tmp.getBitWidth(), 0); 1845 divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2, 1846 &APdigit); 1847 uint32_t digit = APdigit.getZExtValue(); 1848 assert(digit < radix && "divide failed"); 1849 result.insert(insert_at,digits[digit]); 1850 tmp = tmp2; 1851 } 1852 1853 return result; 1854} 1855 1856#ifndef NDEBUG 1857void APInt::dump() const 1858{ 1859 cerr << "APInt(" << BitWidth << ")=" << std::setbase(16); 1860 if (isSingleWord()) 1861 cerr << VAL; 1862 else for (unsigned i = getNumWords(); i > 0; i--) { 1863 cerr << pVal[i-1] << " "; 1864 } 1865 cerr << " U(" << this->toString(10) << ") S(" << this->toStringSigned(10) 1866 << ")\n" << std::setbase(10); 1867} 1868#endif 1869