APInt.cpp revision 4fd8606791e0ff67a9dd13a21d95cda7e114c0e0
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 <cstring> 22#include <cstdlib> 23#ifndef NDEBUG 24#include <iomanip> 25#endif 26 27using namespace llvm; 28 29/// A utility function for allocating memory, checking for allocation failures, 30/// and ensuring the contents are zeroed. 31inline static uint64_t* getClearedMemory(uint32_t numWords) { 32 uint64_t * result = new uint64_t[numWords]; 33 assert(result && "APInt memory allocation fails!"); 34 memset(result, 0, numWords * sizeof(uint64_t)); 35 return result; 36} 37 38/// A utility function for allocating memory and checking for allocation 39/// failure. The content is not zeroed. 40inline static uint64_t* getMemory(uint32_t numWords) { 41 uint64_t * result = new uint64_t[numWords]; 42 assert(result && "APInt memory allocation fails!"); 43 return result; 44} 45 46APInt::APInt(uint32_t numBits, uint64_t val) : BitWidth(numBits), VAL(0) { 47 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small"); 48 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large"); 49 if (isSingleWord()) 50 VAL = val; 51 else { 52 pVal = getClearedMemory(getNumWords()); 53 pVal[0] = val; 54 } 55 clearUnusedBits(); 56} 57 58APInt::APInt(uint32_t numBits, uint32_t numWords, uint64_t bigVal[]) 59 : BitWidth(numBits), VAL(0) { 60 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small"); 61 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large"); 62 assert(bigVal && "Null pointer detected!"); 63 if (isSingleWord()) 64 VAL = bigVal[0]; 65 else { 66 // Get memory, cleared to 0 67 pVal = getClearedMemory(getNumWords()); 68 // Calculate the number of words to copy 69 uint32_t words = std::min<uint32_t>(numWords, getNumWords()); 70 // Copy the words from bigVal to pVal 71 memcpy(pVal, bigVal, words * APINT_WORD_SIZE); 72 } 73 // Make sure unused high bits are cleared 74 clearUnusedBits(); 75} 76 77APInt::APInt(uint32_t numbits, const char StrStart[], uint32_t slen, 78 uint8_t radix) 79 : BitWidth(numbits), VAL(0) { 80 fromString(numbits, StrStart, slen, radix); 81} 82 83APInt::APInt(uint32_t numbits, const std::string& Val, uint8_t radix) 84 : BitWidth(numbits), VAL(0) { 85 assert(!Val.empty() && "String empty?"); 86 fromString(numbits, Val.c_str(), Val.size(), radix); 87} 88 89APInt::APInt(const APInt& that) 90 : BitWidth(that.BitWidth), VAL(0) { 91 if (isSingleWord()) 92 VAL = that.VAL; 93 else { 94 pVal = getMemory(getNumWords()); 95 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE); 96 } 97} 98 99APInt::~APInt() { 100 if (!isSingleWord() && pVal) 101 delete [] pVal; 102} 103 104APInt& APInt::operator=(const APInt& RHS) { 105 // Don't do anything for X = X 106 if (this == &RHS) 107 return *this; 108 109 // If the bitwidths are the same, we can avoid mucking with memory 110 if (BitWidth == RHS.getBitWidth()) { 111 if (isSingleWord()) 112 VAL = RHS.VAL; 113 else 114 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE); 115 return *this; 116 } 117 118 if (isSingleWord()) 119 if (RHS.isSingleWord()) 120 VAL = RHS.VAL; 121 else { 122 VAL = 0; 123 pVal = getMemory(RHS.getNumWords()); 124 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 125 } 126 else if (getNumWords() == RHS.getNumWords()) 127 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 128 else if (RHS.isSingleWord()) { 129 delete [] pVal; 130 VAL = RHS.VAL; 131 } else { 132 delete [] pVal; 133 pVal = getMemory(RHS.getNumWords()); 134 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 135 } 136 BitWidth = RHS.BitWidth; 137 return clearUnusedBits(); 138} 139 140APInt& APInt::operator=(uint64_t RHS) { 141 if (isSingleWord()) 142 VAL = RHS; 143 else { 144 pVal[0] = RHS; 145 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE); 146 } 147 return clearUnusedBits(); 148} 149 150/// add_1 - This function adds a single "digit" integer, y, to the multiple 151/// "digit" integer array, x[]. x[] is modified to reflect the addition and 152/// 1 is returned if there is a carry out, otherwise 0 is returned. 153/// @returns the carry of the addition. 154static bool add_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) { 155 for (uint32_t i = 0; i < len; ++i) { 156 dest[i] = y + x[i]; 157 if (dest[i] < y) 158 y = 1; // Carry one to next digit. 159 else { 160 y = 0; // No need to carry so exit early 161 break; 162 } 163 } 164 return y; 165} 166 167/// @brief Prefix increment operator. Increments the APInt by one. 168APInt& APInt::operator++() { 169 if (isSingleWord()) 170 ++VAL; 171 else 172 add_1(pVal, pVal, getNumWords(), 1); 173 return clearUnusedBits(); 174} 175 176/// sub_1 - This function subtracts a single "digit" (64-bit word), y, from 177/// the multi-digit integer array, x[], propagating the borrowed 1 value until 178/// no further borrowing is neeeded or it runs out of "digits" in x. The result 179/// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted. 180/// In other words, if y > x then this function returns 1, otherwise 0. 181/// @returns the borrow out of the subtraction 182static bool sub_1(uint64_t x[], uint32_t len, uint64_t y) { 183 for (uint32_t i = 0; i < len; ++i) { 184 uint64_t X = x[i]; 185 x[i] -= y; 186 if (y > X) 187 y = 1; // We have to "borrow 1" from next "digit" 188 else { 189 y = 0; // No need to borrow 190 break; // Remaining digits are unchanged so exit early 191 } 192 } 193 return bool(y); 194} 195 196/// @brief Prefix decrement operator. Decrements the APInt by one. 197APInt& APInt::operator--() { 198 if (isSingleWord()) 199 --VAL; 200 else 201 sub_1(pVal, getNumWords(), 1); 202 return clearUnusedBits(); 203} 204 205/// add - This function adds the integer array x to the integer array Y and 206/// places the result in dest. 207/// @returns the carry out from the addition 208/// @brief General addition of 64-bit integer arrays 209static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y, 210 uint32_t len) { 211 bool carry = false; 212 for (uint32_t i = 0; i< len; ++i) { 213 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x 214 dest[i] = x[i] + y[i] + carry; 215 carry = dest[i] < limit || (carry && dest[i] == limit); 216 } 217 return carry; 218} 219 220/// Adds the RHS APint to this APInt. 221/// @returns this, after addition of RHS. 222/// @brief Addition assignment operator. 223APInt& APInt::operator+=(const APInt& RHS) { 224 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 225 if (isSingleWord()) 226 VAL += RHS.VAL; 227 else { 228 add(pVal, pVal, RHS.pVal, getNumWords()); 229 } 230 return clearUnusedBits(); 231} 232 233/// Subtracts the integer array y from the integer array x 234/// @returns returns the borrow out. 235/// @brief Generalized subtraction of 64-bit integer arrays. 236static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y, 237 uint32_t len) { 238 bool borrow = false; 239 for (uint32_t i = 0; i < len; ++i) { 240 uint64_t x_tmp = borrow ? x[i] - 1 : x[i]; 241 borrow = y[i] > x_tmp || (borrow && x[i] == 0); 242 dest[i] = x_tmp - y[i]; 243 } 244 return borrow; 245} 246 247/// Subtracts the RHS APInt from this APInt 248/// @returns this, after subtraction 249/// @brief Subtraction assignment operator. 250APInt& APInt::operator-=(const APInt& RHS) { 251 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 252 if (isSingleWord()) 253 VAL -= RHS.VAL; 254 else 255 sub(pVal, pVal, RHS.pVal, getNumWords()); 256 return clearUnusedBits(); 257} 258 259/// Multiplies an integer array, x by a a uint64_t integer and places the result 260/// into dest. 261/// @returns the carry out of the multiplication. 262/// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer. 263static uint64_t mul_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) { 264 // Split y into high 32-bit part (hy) and low 32-bit part (ly) 265 uint64_t ly = y & 0xffffffffULL, hy = y >> 32; 266 uint64_t carry = 0; 267 268 // For each digit of x. 269 for (uint32_t i = 0; i < len; ++i) { 270 // Split x into high and low words 271 uint64_t lx = x[i] & 0xffffffffULL; 272 uint64_t hx = x[i] >> 32; 273 // hasCarry - A flag to indicate if there is a carry to the next digit. 274 // hasCarry == 0, no carry 275 // hasCarry == 1, has carry 276 // hasCarry == 2, no carry and the calculation result == 0. 277 uint8_t hasCarry = 0; 278 dest[i] = carry + lx * ly; 279 // Determine if the add above introduces carry. 280 hasCarry = (dest[i] < carry) ? 1 : 0; 281 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0); 282 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) + 283 // (2^32 - 1) + 2^32 = 2^64. 284 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0); 285 286 carry += (lx * hy) & 0xffffffffULL; 287 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL); 288 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) + 289 (carry >> 32) + ((lx * hy) >> 32) + hx * hy; 290 } 291 return carry; 292} 293 294/// Multiplies integer array x by integer array y and stores the result into 295/// the integer array dest. Note that dest's size must be >= xlen + ylen. 296/// @brief Generalized multiplicate of integer arrays. 297static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, uint64_t y[], 298 uint32_t ylen) { 299 dest[xlen] = mul_1(dest, x, xlen, y[0]); 300 for (uint32_t i = 1; i < ylen; ++i) { 301 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32; 302 uint64_t carry = 0, lx = 0, hx = 0; 303 for (uint32_t j = 0; j < xlen; ++j) { 304 lx = x[j] & 0xffffffffULL; 305 hx = x[j] >> 32; 306 // hasCarry - A flag to indicate if has carry. 307 // hasCarry == 0, no carry 308 // hasCarry == 1, has carry 309 // hasCarry == 2, no carry and the calculation result == 0. 310 uint8_t hasCarry = 0; 311 uint64_t resul = carry + lx * ly; 312 hasCarry = (resul < carry) ? 1 : 0; 313 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32); 314 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0); 315 316 carry += (lx * hy) & 0xffffffffULL; 317 resul = (carry << 32) | (resul & 0xffffffffULL); 318 dest[i+j] += resul; 319 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+ 320 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) + 321 ((lx * hy) >> 32) + hx * hy; 322 } 323 dest[i+xlen] = carry; 324 } 325} 326 327APInt& APInt::operator*=(const APInt& RHS) { 328 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 329 if (isSingleWord()) { 330 VAL *= RHS.VAL; 331 clearUnusedBits(); 332 return *this; 333 } 334 335 // Get some bit facts about LHS and check for zero 336 uint32_t lhsBits = getActiveBits(); 337 uint32_t lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1; 338 if (!lhsWords) 339 // 0 * X ===> 0 340 return *this; 341 342 // Get some bit facts about RHS and check for zero 343 uint32_t rhsBits = RHS.getActiveBits(); 344 uint32_t rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1; 345 if (!rhsWords) { 346 // X * 0 ===> 0 347 clear(); 348 return *this; 349 } 350 351 // Allocate space for the result 352 uint32_t destWords = rhsWords + lhsWords; 353 uint64_t *dest = getMemory(destWords); 354 355 // Perform the long multiply 356 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords); 357 358 // Copy result back into *this 359 clear(); 360 uint32_t wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords; 361 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE); 362 363 // delete dest array and return 364 delete[] dest; 365 return *this; 366} 367 368APInt& APInt::operator&=(const APInt& RHS) { 369 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 370 if (isSingleWord()) { 371 VAL &= RHS.VAL; 372 return *this; 373 } 374 uint32_t numWords = getNumWords(); 375 for (uint32_t i = 0; i < numWords; ++i) 376 pVal[i] &= RHS.pVal[i]; 377 return *this; 378} 379 380APInt& APInt::operator|=(const APInt& RHS) { 381 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 382 if (isSingleWord()) { 383 VAL |= RHS.VAL; 384 return *this; 385 } 386 uint32_t numWords = getNumWords(); 387 for (uint32_t i = 0; i < numWords; ++i) 388 pVal[i] |= RHS.pVal[i]; 389 return *this; 390} 391 392APInt& APInt::operator^=(const APInt& RHS) { 393 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 394 if (isSingleWord()) { 395 VAL ^= RHS.VAL; 396 this->clearUnusedBits(); 397 return *this; 398 } 399 uint32_t numWords = getNumWords(); 400 for (uint32_t i = 0; i < numWords; ++i) 401 pVal[i] ^= RHS.pVal[i]; 402 return clearUnusedBits(); 403} 404 405APInt APInt::operator&(const APInt& RHS) const { 406 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 407 if (isSingleWord()) 408 return APInt(getBitWidth(), VAL & RHS.VAL); 409 410 uint32_t numWords = getNumWords(); 411 uint64_t* val = getMemory(numWords); 412 for (uint32_t i = 0; i < numWords; ++i) 413 val[i] = pVal[i] & RHS.pVal[i]; 414 return APInt(val, getBitWidth()); 415} 416 417APInt APInt::operator|(const APInt& RHS) const { 418 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 419 if (isSingleWord()) 420 return APInt(getBitWidth(), VAL | RHS.VAL); 421 422 uint32_t numWords = getNumWords(); 423 uint64_t *val = getMemory(numWords); 424 for (uint32_t i = 0; i < numWords; ++i) 425 val[i] = pVal[i] | RHS.pVal[i]; 426 return APInt(val, getBitWidth()); 427} 428 429APInt APInt::operator^(const APInt& RHS) const { 430 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 431 if (isSingleWord()) 432 return APInt(BitWidth, VAL ^ RHS.VAL); 433 434 uint32_t numWords = getNumWords(); 435 uint64_t *val = getMemory(numWords); 436 for (uint32_t i = 0; i < numWords; ++i) 437 val[i] = pVal[i] ^ RHS.pVal[i]; 438 439 // 0^0==1 so clear the high bits in case they got set. 440 return APInt(val, getBitWidth()).clearUnusedBits(); 441} 442 443bool APInt::operator !() const { 444 if (isSingleWord()) 445 return !VAL; 446 447 for (uint32_t i = 0; i < getNumWords(); ++i) 448 if (pVal[i]) 449 return false; 450 return true; 451} 452 453APInt APInt::operator*(const APInt& RHS) const { 454 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 455 if (isSingleWord()) 456 return APInt(BitWidth, VAL * RHS.VAL); 457 APInt Result(*this); 458 Result *= RHS; 459 return Result.clearUnusedBits(); 460} 461 462APInt APInt::operator+(const APInt& RHS) const { 463 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 464 if (isSingleWord()) 465 return APInt(BitWidth, VAL + RHS.VAL); 466 APInt Result(BitWidth, 0); 467 add(Result.pVal, this->pVal, RHS.pVal, getNumWords()); 468 return Result.clearUnusedBits(); 469} 470 471APInt APInt::operator-(const APInt& RHS) const { 472 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 473 if (isSingleWord()) 474 return APInt(BitWidth, VAL - RHS.VAL); 475 APInt Result(BitWidth, 0); 476 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords()); 477 return Result.clearUnusedBits(); 478} 479 480bool APInt::operator[](uint32_t bitPosition) const { 481 return (maskBit(bitPosition) & 482 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0; 483} 484 485bool APInt::operator==(const APInt& RHS) const { 486 assert(BitWidth == RHS.BitWidth && "Comparison requires equal bit widths"); 487 if (isSingleWord()) 488 return VAL == RHS.VAL; 489 490 // Get some facts about the number of bits used in the two operands. 491 uint32_t n1 = getActiveBits(); 492 uint32_t n2 = RHS.getActiveBits(); 493 494 // If the number of bits isn't the same, they aren't equal 495 if (n1 != n2) 496 return false; 497 498 // If the number of bits fits in a word, we only need to compare the low word. 499 if (n1 <= APINT_BITS_PER_WORD) 500 return pVal[0] == RHS.pVal[0]; 501 502 // Otherwise, compare everything 503 for (int i = whichWord(n1 - 1); i >= 0; --i) 504 if (pVal[i] != RHS.pVal[i]) 505 return false; 506 return true; 507} 508 509bool APInt::operator==(uint64_t Val) const { 510 if (isSingleWord()) 511 return VAL == Val; 512 513 uint32_t n = getActiveBits(); 514 if (n <= APINT_BITS_PER_WORD) 515 return pVal[0] == Val; 516 else 517 return false; 518} 519 520bool APInt::ult(const APInt& RHS) const { 521 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); 522 if (isSingleWord()) 523 return VAL < RHS.VAL; 524 525 // Get active bit length of both operands 526 uint32_t n1 = getActiveBits(); 527 uint32_t n2 = RHS.getActiveBits(); 528 529 // If magnitude of LHS is less than RHS, return true. 530 if (n1 < n2) 531 return true; 532 533 // If magnitude of RHS is greather than LHS, return false. 534 if (n2 < n1) 535 return false; 536 537 // If they bot fit in a word, just compare the low order word 538 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD) 539 return pVal[0] < RHS.pVal[0]; 540 541 // Otherwise, compare all words 542 uint32_t topWord = whichWord(std::max(n1,n2)-1); 543 for (int i = topWord; i >= 0; --i) { 544 if (pVal[i] > RHS.pVal[i]) 545 return false; 546 if (pVal[i] < RHS.pVal[i]) 547 return true; 548 } 549 return false; 550} 551 552bool APInt::slt(const APInt& RHS) const { 553 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); 554 if (isSingleWord()) { 555 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth); 556 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth); 557 return lhsSext < rhsSext; 558 } 559 560 APInt lhs(*this); 561 APInt rhs(RHS); 562 bool lhsNeg = isNegative(); 563 bool rhsNeg = rhs.isNegative(); 564 if (lhsNeg) { 565 // Sign bit is set so perform two's complement to make it positive 566 lhs.flip(); 567 lhs++; 568 } 569 if (rhsNeg) { 570 // Sign bit is set so perform two's complement to make it positive 571 rhs.flip(); 572 rhs++; 573 } 574 575 // Now we have unsigned values to compare so do the comparison if necessary 576 // based on the negativeness of the values. 577 if (lhsNeg) 578 if (rhsNeg) 579 return lhs.ugt(rhs); 580 else 581 return true; 582 else if (rhsNeg) 583 return false; 584 else 585 return lhs.ult(rhs); 586} 587 588APInt& APInt::set(uint32_t bitPosition) { 589 if (isSingleWord()) 590 VAL |= maskBit(bitPosition); 591 else 592 pVal[whichWord(bitPosition)] |= maskBit(bitPosition); 593 return *this; 594} 595 596APInt& APInt::set() { 597 if (isSingleWord()) { 598 VAL = -1ULL; 599 return clearUnusedBits(); 600 } 601 602 // Set all the bits in all the words. 603 for (uint32_t i = 0; i < getNumWords() - 1; ++i) 604 pVal[i] = -1ULL; 605 // Clear the unused ones 606 return clearUnusedBits(); 607} 608 609/// Set the given bit to 0 whose position is given as "bitPosition". 610/// @brief Set a given bit to 0. 611APInt& APInt::clear(uint32_t bitPosition) { 612 if (isSingleWord()) 613 VAL &= ~maskBit(bitPosition); 614 else 615 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition); 616 return *this; 617} 618 619/// @brief Set every bit to 0. 620APInt& APInt::clear() { 621 if (isSingleWord()) 622 VAL = 0; 623 else 624 memset(pVal, 0, getNumWords() * APINT_WORD_SIZE); 625 return *this; 626} 627 628/// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on 629/// this APInt. 630APInt APInt::operator~() const { 631 APInt Result(*this); 632 Result.flip(); 633 return Result; 634} 635 636/// @brief Toggle every bit to its opposite value. 637APInt& APInt::flip() { 638 if (isSingleWord()) { 639 VAL ^= -1ULL; 640 return clearUnusedBits(); 641 } 642 for (uint32_t i = 0; i < getNumWords(); ++i) 643 pVal[i] ^= -1ULL; 644 return clearUnusedBits(); 645} 646 647/// Toggle a given bit to its opposite value whose position is given 648/// as "bitPosition". 649/// @brief Toggles a given bit to its opposite value. 650APInt& APInt::flip(uint32_t bitPosition) { 651 assert(bitPosition < BitWidth && "Out of the bit-width range!"); 652 if ((*this)[bitPosition]) clear(bitPosition); 653 else set(bitPosition); 654 return *this; 655} 656 657uint64_t APInt::getHashValue() const { 658 // Put the bit width into the low order bits. 659 uint64_t hash = BitWidth; 660 661 // Add the sum of the words to the hash. 662 if (isSingleWord()) 663 hash += VAL << 6; // clear separation of up to 64 bits 664 else 665 for (uint32_t i = 0; i < getNumWords(); ++i) 666 hash += pVal[i] << 6; // clear sepration of up to 64 bits 667 return hash; 668} 669 670/// HiBits - This function returns the high "numBits" bits of this APInt. 671APInt APInt::getHiBits(uint32_t numBits) const { 672 return APIntOps::lshr(*this, BitWidth - numBits); 673} 674 675/// LoBits - This function returns the low "numBits" bits of this APInt. 676APInt APInt::getLoBits(uint32_t numBits) const { 677 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits), 678 BitWidth - numBits); 679} 680 681bool APInt::isPowerOf2() const { 682 return (!!*this) && !(*this & (*this - APInt(BitWidth,1))); 683} 684 685uint32_t APInt::countLeadingZeros() const { 686 uint32_t Count = 0; 687 if (isSingleWord()) 688 Count = CountLeadingZeros_64(VAL); 689 else { 690 for (uint32_t i = getNumWords(); i > 0u; --i) { 691 if (pVal[i-1] == 0) 692 Count += APINT_BITS_PER_WORD; 693 else { 694 Count += CountLeadingZeros_64(pVal[i-1]); 695 break; 696 } 697 } 698 } 699 uint32_t remainder = BitWidth % APINT_BITS_PER_WORD; 700 if (remainder) 701 Count -= APINT_BITS_PER_WORD - remainder; 702 return Count; 703} 704 705static uint32_t countLeadingOnes_64(uint64_t V, uint32_t skip) { 706 uint32_t Count = 0; 707 if (skip) 708 V <<= skip; 709 while (V && (V & (1ULL << 63))) { 710 Count++; 711 V <<= 1; 712 } 713 return Count; 714} 715 716uint32_t APInt::countLeadingOnes() const { 717 if (isSingleWord()) 718 return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth); 719 720 uint32_t highWordBits = BitWidth % APINT_BITS_PER_WORD; 721 uint32_t shift = (highWordBits == 0 ? 0 : APINT_BITS_PER_WORD - highWordBits); 722 int i = getNumWords() - 1; 723 uint32_t Count = countLeadingOnes_64(pVal[i], shift); 724 if (Count == highWordBits) { 725 for (i--; i >= 0; --i) { 726 if (pVal[i] == -1ULL) 727 Count += APINT_BITS_PER_WORD; 728 else { 729 Count += countLeadingOnes_64(pVal[i], 0); 730 break; 731 } 732 } 733 } 734 return Count; 735} 736 737uint32_t APInt::countTrailingZeros() const { 738 if (isSingleWord()) 739 return CountTrailingZeros_64(VAL); 740 uint32_t Count = 0; 741 uint32_t i = 0; 742 for (; i < getNumWords() && pVal[i] == 0; ++i) 743 Count += APINT_BITS_PER_WORD; 744 if (i < getNumWords()) 745 Count += CountTrailingZeros_64(pVal[i]); 746 return Count; 747} 748 749uint32_t APInt::countPopulation() const { 750 if (isSingleWord()) 751 return CountPopulation_64(VAL); 752 uint32_t Count = 0; 753 for (uint32_t i = 0; i < getNumWords(); ++i) 754 Count += CountPopulation_64(pVal[i]); 755 return Count; 756} 757 758APInt APInt::byteSwap() const { 759 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!"); 760 if (BitWidth == 16) 761 return APInt(BitWidth, ByteSwap_16(VAL)); 762 else if (BitWidth == 32) 763 return APInt(BitWidth, ByteSwap_32(VAL)); 764 else if (BitWidth == 48) { 765 uint64_t Tmp1 = ((VAL >> 32) << 16) | (VAL & 0xFFFF); 766 Tmp1 = ByteSwap_32(Tmp1); 767 uint64_t Tmp2 = (VAL >> 16) & 0xFFFF; 768 Tmp2 = ByteSwap_16(Tmp2); 769 return 770 APInt(BitWidth, 771 (Tmp1 & 0xff) | ((Tmp1<<16) & 0xffff00000000ULL) | (Tmp2 << 16)); 772 } else if (BitWidth == 64) 773 return APInt(BitWidth, ByteSwap_64(VAL)); 774 else { 775 APInt Result(BitWidth, 0); 776 char *pByte = (char*)Result.pVal; 777 for (uint32_t i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) { 778 char Tmp = pByte[i]; 779 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i]; 780 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp; 781 } 782 return Result; 783 } 784} 785 786APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1, 787 const APInt& API2) { 788 APInt A = API1, B = API2; 789 while (!!B) { 790 APInt T = B; 791 B = APIntOps::urem(A, B); 792 A = T; 793 } 794 return A; 795} 796 797APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, uint32_t width) { 798 union { 799 double D; 800 uint64_t I; 801 } T; 802 T.D = Double; 803 804 // Get the sign bit from the highest order bit 805 bool isNeg = T.I >> 63; 806 807 // Get the 11-bit exponent and adjust for the 1023 bit bias 808 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023; 809 810 // If the exponent is negative, the value is < 0 so just return 0. 811 if (exp < 0) 812 return APInt(width, 0u); 813 814 // Extract the mantissa by clearing the top 12 bits (sign + exponent). 815 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52; 816 817 // If the exponent doesn't shift all bits out of the mantissa 818 if (exp < 52) 819 return isNeg ? -APInt(width, mantissa >> (52 - exp)) : 820 APInt(width, mantissa >> (52 - exp)); 821 822 // If the client didn't provide enough bits for us to shift the mantissa into 823 // then the result is undefined, just return 0 824 if (width <= exp - 52) 825 return APInt(width, 0); 826 827 // Otherwise, we have to shift the mantissa bits up to the right location 828 APInt Tmp(width, mantissa); 829 Tmp = Tmp.shl(exp - 52); 830 return isNeg ? -Tmp : Tmp; 831} 832 833/// RoundToDouble - This function convert this APInt to a double. 834/// The layout for double is as following (IEEE Standard 754): 835/// -------------------------------------- 836/// | Sign Exponent Fraction Bias | 837/// |-------------------------------------- | 838/// | 1[63] 11[62-52] 52[51-00] 1023 | 839/// -------------------------------------- 840double APInt::roundToDouble(bool isSigned) const { 841 842 // Handle the simple case where the value is contained in one uint64_t. 843 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) { 844 if (isSigned) { 845 int64_t sext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth); 846 return double(sext); 847 } else 848 return double(VAL); 849 } 850 851 // Determine if the value is negative. 852 bool isNeg = isSigned ? (*this)[BitWidth-1] : false; 853 854 // Construct the absolute value if we're negative. 855 APInt Tmp(isNeg ? -(*this) : (*this)); 856 857 // Figure out how many bits we're using. 858 uint32_t n = Tmp.getActiveBits(); 859 860 // The exponent (without bias normalization) is just the number of bits 861 // we are using. Note that the sign bit is gone since we constructed the 862 // absolute value. 863 uint64_t exp = n; 864 865 // Return infinity for exponent overflow 866 if (exp > 1023) { 867 if (!isSigned || !isNeg) 868 return double(1.0E300 * 1.0E300); // positive infinity 869 else 870 return double(-1.0E300 * 1.0E300); // negative infinity 871 } 872 exp += 1023; // Increment for 1023 bias 873 874 // Number of bits in mantissa is 52. To obtain the mantissa value, we must 875 // extract the high 52 bits from the correct words in pVal. 876 uint64_t mantissa; 877 unsigned hiWord = whichWord(n-1); 878 if (hiWord == 0) { 879 mantissa = Tmp.pVal[0]; 880 if (n > 52) 881 mantissa >>= n - 52; // shift down, we want the top 52 bits. 882 } else { 883 assert(hiWord > 0 && "huh?"); 884 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD); 885 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD); 886 mantissa = hibits | lobits; 887 } 888 889 // The leading bit of mantissa is implicit, so get rid of it. 890 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0; 891 union { 892 double D; 893 uint64_t I; 894 } T; 895 T.I = sign | (exp << 52) | mantissa; 896 return T.D; 897} 898 899// Truncate to new width. 900APInt &APInt::trunc(uint32_t width) { 901 assert(width < BitWidth && "Invalid APInt Truncate request"); 902 assert(width >= IntegerType::MIN_INT_BITS && "Can't truncate to 0 bits"); 903 uint32_t wordsBefore = getNumWords(); 904 BitWidth = width; 905 uint32_t wordsAfter = getNumWords(); 906 if (wordsBefore != wordsAfter) { 907 if (wordsAfter == 1) { 908 uint64_t *tmp = pVal; 909 VAL = pVal[0]; 910 delete [] tmp; 911 } else { 912 uint64_t *newVal = getClearedMemory(wordsAfter); 913 for (uint32_t i = 0; i < wordsAfter; ++i) 914 newVal[i] = pVal[i]; 915 delete [] pVal; 916 pVal = newVal; 917 } 918 } 919 return clearUnusedBits(); 920} 921 922// Sign extend to a new width. 923APInt &APInt::sext(uint32_t width) { 924 assert(width > BitWidth && "Invalid APInt SignExtend request"); 925 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits"); 926 // If the sign bit isn't set, this is the same as zext. 927 if (!isNegative()) { 928 zext(width); 929 return *this; 930 } 931 932 // The sign bit is set. First, get some facts 933 uint32_t wordsBefore = getNumWords(); 934 uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD; 935 BitWidth = width; 936 uint32_t wordsAfter = getNumWords(); 937 938 // Mask the high order word appropriately 939 if (wordsBefore == wordsAfter) { 940 uint32_t newWordBits = width % APINT_BITS_PER_WORD; 941 // The extension is contained to the wordsBefore-1th word. 942 uint64_t mask = ~0ULL; 943 if (newWordBits) 944 mask >>= APINT_BITS_PER_WORD - newWordBits; 945 mask <<= wordBits; 946 if (wordsBefore == 1) 947 VAL |= mask; 948 else 949 pVal[wordsBefore-1] |= mask; 950 return clearUnusedBits(); 951 } 952 953 uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits; 954 uint64_t *newVal = getMemory(wordsAfter); 955 if (wordsBefore == 1) 956 newVal[0] = VAL | mask; 957 else { 958 for (uint32_t i = 0; i < wordsBefore; ++i) 959 newVal[i] = pVal[i]; 960 newVal[wordsBefore-1] |= mask; 961 } 962 for (uint32_t i = wordsBefore; i < wordsAfter; i++) 963 newVal[i] = -1ULL; 964 if (wordsBefore != 1) 965 delete [] pVal; 966 pVal = newVal; 967 return clearUnusedBits(); 968} 969 970// Zero extend to a new width. 971APInt &APInt::zext(uint32_t width) { 972 assert(width > BitWidth && "Invalid APInt ZeroExtend request"); 973 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits"); 974 uint32_t wordsBefore = getNumWords(); 975 BitWidth = width; 976 uint32_t wordsAfter = getNumWords(); 977 if (wordsBefore != wordsAfter) { 978 uint64_t *newVal = getClearedMemory(wordsAfter); 979 if (wordsBefore == 1) 980 newVal[0] = VAL; 981 else 982 for (uint32_t i = 0; i < wordsBefore; ++i) 983 newVal[i] = pVal[i]; 984 if (wordsBefore != 1) 985 delete [] pVal; 986 pVal = newVal; 987 } 988 return *this; 989} 990 991APInt &APInt::zextOrTrunc(uint32_t width) { 992 if (BitWidth < width) 993 return zext(width); 994 if (BitWidth > width) 995 return trunc(width); 996 return *this; 997} 998 999APInt &APInt::sextOrTrunc(uint32_t width) { 1000 if (BitWidth < width) 1001 return sext(width); 1002 if (BitWidth > width) 1003 return trunc(width); 1004 return *this; 1005} 1006 1007/// Arithmetic right-shift this APInt by shiftAmt. 1008/// @brief Arithmetic right-shift function. 1009APInt APInt::ashr(uint32_t shiftAmt) const { 1010 assert(shiftAmt <= BitWidth && "Invalid shift amount"); 1011 // Handle a degenerate case 1012 if (shiftAmt == 0) 1013 return *this; 1014 1015 // Handle single word shifts with built-in ashr 1016 if (isSingleWord()) { 1017 if (shiftAmt == BitWidth) 1018 return APInt(BitWidth, 0); // undefined 1019 else { 1020 uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth; 1021 return APInt(BitWidth, 1022 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt)); 1023 } 1024 } 1025 1026 // If all the bits were shifted out, the result is, technically, undefined. 1027 // We return -1 if it was negative, 0 otherwise. We check this early to avoid 1028 // issues in the algorithm below. 1029 if (shiftAmt == BitWidth) 1030 if (isNegative()) 1031 return APInt(BitWidth, -1ULL); 1032 else 1033 return APInt(BitWidth, 0); 1034 1035 // Create some space for the result. 1036 uint64_t * val = new uint64_t[getNumWords()]; 1037 1038 // Compute some values needed by the following shift algorithms 1039 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word 1040 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift 1041 uint32_t breakWord = getNumWords() - 1 - offset; // last word affected 1042 uint32_t bitsInWord = whichBit(BitWidth); // how many bits in last word? 1043 if (bitsInWord == 0) 1044 bitsInWord = APINT_BITS_PER_WORD; 1045 1046 // If we are shifting whole words, just move whole words 1047 if (wordShift == 0) { 1048 // Move the words containing significant bits 1049 for (uint32_t i = 0; i <= breakWord; ++i) 1050 val[i] = pVal[i+offset]; // move whole word 1051 1052 // Adjust the top significant word for sign bit fill, if negative 1053 if (isNegative()) 1054 if (bitsInWord < APINT_BITS_PER_WORD) 1055 val[breakWord] |= ~0ULL << bitsInWord; // set high bits 1056 } else { 1057 // Shift the low order words 1058 for (uint32_t i = 0; i < breakWord; ++i) { 1059 // This combines the shifted corresponding word with the low bits from 1060 // the next word (shifted into this word's high bits). 1061 val[i] = (pVal[i+offset] >> wordShift) | 1062 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift)); 1063 } 1064 1065 // Shift the break word. In this case there are no bits from the next word 1066 // to include in this word. 1067 val[breakWord] = pVal[breakWord+offset] >> wordShift; 1068 1069 // Deal with sign extenstion in the break word, and possibly the word before 1070 // it. 1071 if (isNegative()) 1072 if (wordShift > bitsInWord) { 1073 if (breakWord > 0) 1074 val[breakWord-1] |= 1075 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord)); 1076 val[breakWord] |= ~0ULL; 1077 } else 1078 val[breakWord] |= (~0ULL << (bitsInWord - wordShift)); 1079 } 1080 1081 // Remaining words are 0 or -1, just assign them. 1082 uint64_t fillValue = (isNegative() ? -1ULL : 0); 1083 for (uint32_t i = breakWord+1; i < getNumWords(); ++i) 1084 val[i] = fillValue; 1085 return APInt(val, BitWidth).clearUnusedBits(); 1086} 1087 1088/// Logical right-shift this APInt by shiftAmt. 1089/// @brief Logical right-shift function. 1090APInt APInt::lshr(uint32_t shiftAmt) const { 1091 if (isSingleWord()) 1092 if (shiftAmt == BitWidth) 1093 return APInt(BitWidth, 0); 1094 else 1095 return APInt(BitWidth, this->VAL >> shiftAmt); 1096 1097 // If all the bits were shifted out, the result is 0. This avoids issues 1098 // with shifting by the size of the integer type, which produces undefined 1099 // results. We define these "undefined results" to always be 0. 1100 if (shiftAmt == BitWidth) 1101 return APInt(BitWidth, 0); 1102 1103 // Create some space for the result. 1104 uint64_t * val = new uint64_t[getNumWords()]; 1105 1106 // If we are shifting less than a word, compute the shift with a simple carry 1107 if (shiftAmt < APINT_BITS_PER_WORD) { 1108 uint64_t carry = 0; 1109 for (int i = getNumWords()-1; i >= 0; --i) { 1110 val[i] = (pVal[i] >> shiftAmt) | carry; 1111 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt); 1112 } 1113 return APInt(val, BitWidth).clearUnusedBits(); 1114 } 1115 1116 // Compute some values needed by the remaining shift algorithms 1117 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; 1118 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; 1119 1120 // If we are shifting whole words, just move whole words 1121 if (wordShift == 0) { 1122 for (uint32_t i = 0; i < getNumWords() - offset; ++i) 1123 val[i] = pVal[i+offset]; 1124 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++) 1125 val[i] = 0; 1126 return APInt(val,BitWidth).clearUnusedBits(); 1127 } 1128 1129 // Shift the low order words 1130 uint32_t breakWord = getNumWords() - offset -1; 1131 for (uint32_t i = 0; i < breakWord; ++i) 1132 val[i] = (pVal[i+offset] >> wordShift) | 1133 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift)); 1134 // Shift the break word. 1135 val[breakWord] = pVal[breakWord+offset] >> wordShift; 1136 1137 // Remaining words are 0 1138 for (uint32_t i = breakWord+1; i < getNumWords(); ++i) 1139 val[i] = 0; 1140 return APInt(val, BitWidth).clearUnusedBits(); 1141} 1142 1143/// Left-shift this APInt by shiftAmt. 1144/// @brief Left-shift function. 1145APInt APInt::shl(uint32_t shiftAmt) const { 1146 assert(shiftAmt <= BitWidth && "Invalid shift amount"); 1147 if (isSingleWord()) { 1148 if (shiftAmt == BitWidth) 1149 return APInt(BitWidth, 0); // avoid undefined shift results 1150 return APInt(BitWidth, VAL << shiftAmt); 1151 } 1152 1153 // If all the bits were shifted out, the result is 0. This avoids issues 1154 // with shifting by the size of the integer type, which produces undefined 1155 // results. We define these "undefined results" to always be 0. 1156 if (shiftAmt == BitWidth) 1157 return APInt(BitWidth, 0); 1158 1159 // Create some space for the result. 1160 uint64_t * val = new uint64_t[getNumWords()]; 1161 1162 // If we are shifting less than a word, do it the easy way 1163 if (shiftAmt < APINT_BITS_PER_WORD) { 1164 uint64_t carry = 0; 1165 for (uint32_t i = 0; i < getNumWords(); i++) { 1166 val[i] = pVal[i] << shiftAmt | carry; 1167 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt); 1168 } 1169 return APInt(val, BitWidth).clearUnusedBits(); 1170 } 1171 1172 // Compute some values needed by the remaining shift algorithms 1173 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; 1174 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; 1175 1176 // If we are shifting whole words, just move whole words 1177 if (wordShift == 0) { 1178 for (uint32_t i = 0; i < offset; i++) 1179 val[i] = 0; 1180 for (uint32_t i = offset; i < getNumWords(); i++) 1181 val[i] = pVal[i-offset]; 1182 return APInt(val,BitWidth).clearUnusedBits(); 1183 } 1184 1185 // Copy whole words from this to Result. 1186 uint32_t i = getNumWords() - 1; 1187 for (; i > offset; --i) 1188 val[i] = pVal[i-offset] << wordShift | 1189 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift); 1190 val[offset] = pVal[0] << wordShift; 1191 for (i = 0; i < offset; ++i) 1192 val[i] = 0; 1193 return APInt(val, BitWidth).clearUnusedBits(); 1194} 1195 1196 1197// Square Root - this method computes and returns the square root of "this". 1198// Three mechanisms are used for computation. For small values (<= 5 bits), 1199// a table lookup is done. This gets some performance for common cases. For 1200// values using less than 52 bits, the value is converted to double and then 1201// the libc sqrt function is called. The result is rounded and then converted 1202// back to a uint64_t which is then used to construct the result. Finally, 1203// the Babylonian method for computing square roots is used. 1204APInt APInt::sqrt() const { 1205 1206 // Determine the magnitude of the value. 1207 uint32_t magnitude = getActiveBits(); 1208 1209 // Use a fast table for some small values. This also gets rid of some 1210 // rounding errors in libc sqrt for small values. 1211 if (magnitude <= 5) { 1212 static const uint8_t results[32] = { 1213 /* 0 */ 0, 1214 /* 1- 2 */ 1, 1, 1215 /* 3- 6 */ 2, 2, 2, 2, 1216 /* 7-12 */ 3, 3, 3, 3, 3, 3, 1217 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4, 1218 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1219 /* 31 */ 6 1220 }; 1221 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]); 1222 } 1223 1224 // If the magnitude of the value fits in less than 52 bits (the precision of 1225 // an IEEE double precision floating point value), then we can use the 1226 // libc sqrt function which will probably use a hardware sqrt computation. 1227 // This should be faster than the algorithm below. 1228 if (magnitude < 52) { 1229#ifdef _MSC_VER 1230 // Amazingly, VC++ doesn't have round(). 1231 return APInt(BitWidth, 1232 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5); 1233#else 1234 return APInt(BitWidth, 1235 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0]))))); 1236#endif 1237 } 1238 1239 // Okay, all the short cuts are exhausted. We must compute it. The following 1240 // is a classical Babylonian method for computing the square root. This code 1241 // was adapted to APINt from a wikipedia article on such computations. 1242 // See http://www.wikipedia.org/ and go to the page named 1243 // Calculate_an_integer_square_root. 1244 uint32_t nbits = BitWidth, i = 4; 1245 APInt testy(BitWidth, 16); 1246 APInt x_old(BitWidth, 1); 1247 APInt x_new(BitWidth, 0); 1248 APInt two(BitWidth, 2); 1249 1250 // Select a good starting value using binary logarithms. 1251 for (;; i += 2, testy = testy.shl(2)) 1252 if (i >= nbits || this->ule(testy)) { 1253 x_old = x_old.shl(i / 2); 1254 break; 1255 } 1256 1257 // Use the Babylonian method to arrive at the integer square root: 1258 for (;;) { 1259 x_new = (this->udiv(x_old) + x_old).udiv(two); 1260 if (x_old.ule(x_new)) 1261 break; 1262 x_old = x_new; 1263 } 1264 1265 // Make sure we return the closest approximation 1266 // NOTE: The rounding calculation below is correct. It will produce an 1267 // off-by-one discrepancy with results from pari/gp. That discrepancy has been 1268 // determined to be a rounding issue with pari/gp as it begins to use a 1269 // floating point representation after 192 bits. There are no discrepancies 1270 // between this algorithm and pari/gp for bit widths < 192 bits. 1271 APInt square(x_old * x_old); 1272 APInt nextSquare((x_old + 1) * (x_old +1)); 1273 if (this->ult(square)) 1274 return x_old; 1275 else if (this->ule(nextSquare)) { 1276 APInt midpoint((nextSquare - square).udiv(two)); 1277 APInt offset(*this - square); 1278 if (offset.ult(midpoint)) 1279 return x_old; 1280 else 1281 return x_old + 1; 1282 } else 1283 assert(0 && "Error in APInt::sqrt computation"); 1284 return x_old + 1; 1285} 1286 1287/// Implementation of Knuth's Algorithm D (Division of nonnegative integers) 1288/// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The 1289/// variables here have the same names as in the algorithm. Comments explain 1290/// the algorithm and any deviation from it. 1291static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r, 1292 uint32_t m, uint32_t n) { 1293 assert(u && "Must provide dividend"); 1294 assert(v && "Must provide divisor"); 1295 assert(q && "Must provide quotient"); 1296 assert(u != v && u != q && v != q && "Must us different memory"); 1297 assert(n>1 && "n must be > 1"); 1298 1299 // Knuth uses the value b as the base of the number system. In our case b 1300 // is 2^31 so we just set it to -1u. 1301 uint64_t b = uint64_t(1) << 32; 1302 1303 DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n'); 1304 DEBUG(cerr << "KnuthDiv: original:"); 1305 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]); 1306 DEBUG(cerr << " by"); 1307 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]); 1308 DEBUG(cerr << '\n'); 1309 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of 1310 // u and v by d. Note that we have taken Knuth's advice here to use a power 1311 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of 1312 // 2 allows us to shift instead of multiply and it is easy to determine the 1313 // shift amount from the leading zeros. We are basically normalizing the u 1314 // and v so that its high bits are shifted to the top of v's range without 1315 // overflow. Note that this can require an extra word in u so that u must 1316 // be of length m+n+1. 1317 uint32_t shift = CountLeadingZeros_32(v[n-1]); 1318 uint32_t v_carry = 0; 1319 uint32_t u_carry = 0; 1320 if (shift) { 1321 for (uint32_t i = 0; i < m+n; ++i) { 1322 uint32_t u_tmp = u[i] >> (32 - shift); 1323 u[i] = (u[i] << shift) | u_carry; 1324 u_carry = u_tmp; 1325 } 1326 for (uint32_t i = 0; i < n; ++i) { 1327 uint32_t v_tmp = v[i] >> (32 - shift); 1328 v[i] = (v[i] << shift) | v_carry; 1329 v_carry = v_tmp; 1330 } 1331 } 1332 u[m+n] = u_carry; 1333 DEBUG(cerr << "KnuthDiv: normal:"); 1334 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]); 1335 DEBUG(cerr << " by"); 1336 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]); 1337 DEBUG(cerr << '\n'); 1338 1339 // D2. [Initialize j.] Set j to m. This is the loop counter over the places. 1340 int j = m; 1341 do { 1342 DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n'); 1343 // D3. [Calculate q'.]. 1344 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q') 1345 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r') 1346 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease 1347 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test 1348 // on v[n-2] determines at high speed most of the cases in which the trial 1349 // value qp is one too large, and it eliminates all cases where qp is two 1350 // too large. 1351 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]); 1352 DEBUG(cerr << "KnuthDiv: dividend == " << dividend << '\n'); 1353 uint64_t qp = dividend / v[n-1]; 1354 uint64_t rp = dividend % v[n-1]; 1355 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) { 1356 qp--; 1357 rp += v[n-1]; 1358 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2])) 1359 qp--; 1360 } 1361 DEBUG(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n'); 1362 1363 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with 1364 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation 1365 // consists of a simple multiplication by a one-place number, combined with 1366 // a subtraction. 1367 bool isNeg = false; 1368 for (uint32_t i = 0; i < n; ++i) { 1369 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32); 1370 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]); 1371 bool borrow = subtrahend > u_tmp; 1372 DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp 1373 << ", subtrahend == " << subtrahend 1374 << ", borrow = " << borrow << '\n'); 1375 1376 uint64_t result = u_tmp - subtrahend; 1377 uint32_t k = j + i; 1378 u[k++] = result & (b-1); // subtract low word 1379 u[k++] = result >> 32; // subtract high word 1380 while (borrow && k <= m+n) { // deal with borrow to the left 1381 borrow = u[k] == 0; 1382 u[k]--; 1383 k++; 1384 } 1385 isNeg |= borrow; 1386 DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " << 1387 u[j+i+1] << '\n'); 1388 } 1389 DEBUG(cerr << "KnuthDiv: after subtraction:"); 1390 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]); 1391 DEBUG(cerr << '\n'); 1392 // The digits (u[j+n]...u[j]) should be kept positive; if the result of 1393 // this step is actually negative, (u[j+n]...u[j]) should be left as the 1394 // true value plus b**(n+1), namely as the b's complement of 1395 // the true value, and a "borrow" to the left should be remembered. 1396 // 1397 if (isNeg) { 1398 bool carry = true; // true because b's complement is "complement + 1" 1399 for (uint32_t i = 0; i <= m+n; ++i) { 1400 u[i] = ~u[i] + carry; // b's complement 1401 carry = carry && u[i] == 0; 1402 } 1403 } 1404 DEBUG(cerr << "KnuthDiv: after complement:"); 1405 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]); 1406 DEBUG(cerr << '\n'); 1407 1408 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was 1409 // negative, go to step D6; otherwise go on to step D7. 1410 q[j] = qp; 1411 if (isNeg) { 1412 // D6. [Add back]. The probability that this step is necessary is very 1413 // small, on the order of only 2/b. Make sure that test data accounts for 1414 // this possibility. Decrease q[j] by 1 1415 q[j]--; 1416 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]). 1417 // A carry will occur to the left of u[j+n], and it should be ignored 1418 // since it cancels with the borrow that occurred in D4. 1419 bool carry = false; 1420 for (uint32_t i = 0; i < n; i++) { 1421 uint32_t limit = std::min(u[j+i],v[i]); 1422 u[j+i] += v[i] + carry; 1423 carry = u[j+i] < limit || (carry && u[j+i] == limit); 1424 } 1425 u[j+n] += carry; 1426 } 1427 DEBUG(cerr << "KnuthDiv: after correction:"); 1428 DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]); 1429 DEBUG(cerr << "\nKnuthDiv: digit result = " << q[j] << '\n'); 1430 1431 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3. 1432 } while (--j >= 0); 1433 1434 DEBUG(cerr << "KnuthDiv: quotient:"); 1435 DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]); 1436 DEBUG(cerr << '\n'); 1437 1438 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired 1439 // remainder may be obtained by dividing u[...] by d. If r is non-null we 1440 // compute the remainder (urem uses this). 1441 if (r) { 1442 // The value d is expressed by the "shift" value above since we avoided 1443 // multiplication by d by using a shift left. So, all we have to do is 1444 // shift right here. In order to mak 1445 if (shift) { 1446 uint32_t carry = 0; 1447 DEBUG(cerr << "KnuthDiv: remainder:"); 1448 for (int i = n-1; i >= 0; i--) { 1449 r[i] = (u[i] >> shift) | carry; 1450 carry = u[i] << (32 - shift); 1451 DEBUG(cerr << " " << r[i]); 1452 } 1453 } else { 1454 for (int i = n-1; i >= 0; i--) { 1455 r[i] = u[i]; 1456 DEBUG(cerr << " " << r[i]); 1457 } 1458 } 1459 DEBUG(cerr << '\n'); 1460 } 1461 DEBUG(cerr << std::setbase(10) << '\n'); 1462} 1463 1464void APInt::divide(const APInt LHS, uint32_t lhsWords, 1465 const APInt &RHS, uint32_t rhsWords, 1466 APInt *Quotient, APInt *Remainder) 1467{ 1468 assert(lhsWords >= rhsWords && "Fractional result"); 1469 1470 // First, compose the values into an array of 32-bit words instead of 1471 // 64-bit words. This is a necessity of both the "short division" algorithm 1472 // and the the Knuth "classical algorithm" which requires there to be native 1473 // operations for +, -, and * on an m bit value with an m*2 bit result. We 1474 // can't use 64-bit operands here because we don't have native results of 1475 // 128-bits. Furthremore, casting the 64-bit values to 32-bit values won't 1476 // work on large-endian machines. 1477 uint64_t mask = ~0ull >> (sizeof(uint32_t)*8); 1478 uint32_t n = rhsWords * 2; 1479 uint32_t m = (lhsWords * 2) - n; 1480 1481 // Allocate space for the temporary values we need either on the stack, if 1482 // it will fit, or on the heap if it won't. 1483 uint32_t SPACE[128]; 1484 uint32_t *U = 0; 1485 uint32_t *V = 0; 1486 uint32_t *Q = 0; 1487 uint32_t *R = 0; 1488 if ((Remainder?4:3)*n+2*m+1 <= 128) { 1489 U = &SPACE[0]; 1490 V = &SPACE[m+n+1]; 1491 Q = &SPACE[(m+n+1) + n]; 1492 if (Remainder) 1493 R = &SPACE[(m+n+1) + n + (m+n)]; 1494 } else { 1495 U = new uint32_t[m + n + 1]; 1496 V = new uint32_t[n]; 1497 Q = new uint32_t[m+n]; 1498 if (Remainder) 1499 R = new uint32_t[n]; 1500 } 1501 1502 // Initialize the dividend 1503 memset(U, 0, (m+n+1)*sizeof(uint32_t)); 1504 for (unsigned i = 0; i < lhsWords; ++i) { 1505 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]); 1506 U[i * 2] = tmp & mask; 1507 U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8); 1508 } 1509 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm. 1510 1511 // Initialize the divisor 1512 memset(V, 0, (n)*sizeof(uint32_t)); 1513 for (unsigned i = 0; i < rhsWords; ++i) { 1514 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]); 1515 V[i * 2] = tmp & mask; 1516 V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8); 1517 } 1518 1519 // initialize the quotient and remainder 1520 memset(Q, 0, (m+n) * sizeof(uint32_t)); 1521 if (Remainder) 1522 memset(R, 0, n * sizeof(uint32_t)); 1523 1524 // Now, adjust m and n for the Knuth division. n is the number of words in 1525 // the divisor. m is the number of words by which the dividend exceeds the 1526 // divisor (i.e. m+n is the length of the dividend). These sizes must not 1527 // contain any zero words or the Knuth algorithm fails. 1528 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) { 1529 n--; 1530 m++; 1531 } 1532 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--) 1533 m--; 1534 1535 // If we're left with only a single word for the divisor, Knuth doesn't work 1536 // so we implement the short division algorithm here. This is much simpler 1537 // and faster because we are certain that we can divide a 64-bit quantity 1538 // by a 32-bit quantity at hardware speed and short division is simply a 1539 // series of such operations. This is just like doing short division but we 1540 // are using base 2^32 instead of base 10. 1541 assert(n != 0 && "Divide by zero?"); 1542 if (n == 1) { 1543 uint32_t divisor = V[0]; 1544 uint32_t remainder = 0; 1545 for (int i = m+n-1; i >= 0; i--) { 1546 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i]; 1547 if (partial_dividend == 0) { 1548 Q[i] = 0; 1549 remainder = 0; 1550 } else if (partial_dividend < divisor) { 1551 Q[i] = 0; 1552 remainder = partial_dividend; 1553 } else if (partial_dividend == divisor) { 1554 Q[i] = 1; 1555 remainder = 0; 1556 } else { 1557 Q[i] = partial_dividend / divisor; 1558 remainder = partial_dividend - (Q[i] * divisor); 1559 } 1560 } 1561 if (R) 1562 R[0] = remainder; 1563 } else { 1564 // Now we're ready to invoke the Knuth classical divide algorithm. In this 1565 // case n > 1. 1566 KnuthDiv(U, V, Q, R, m, n); 1567 } 1568 1569 // If the caller wants the quotient 1570 if (Quotient) { 1571 // Set up the Quotient value's memory. 1572 if (Quotient->BitWidth != LHS.BitWidth) { 1573 if (Quotient->isSingleWord()) 1574 Quotient->VAL = 0; 1575 else 1576 delete [] Quotient->pVal; 1577 Quotient->BitWidth = LHS.BitWidth; 1578 if (!Quotient->isSingleWord()) 1579 Quotient->pVal = getClearedMemory(Quotient->getNumWords()); 1580 } else 1581 Quotient->clear(); 1582 1583 // The quotient is in Q. Reconstitute the quotient into Quotient's low 1584 // order words. 1585 if (lhsWords == 1) { 1586 uint64_t tmp = 1587 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2)); 1588 if (Quotient->isSingleWord()) 1589 Quotient->VAL = tmp; 1590 else 1591 Quotient->pVal[0] = tmp; 1592 } else { 1593 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough"); 1594 for (unsigned i = 0; i < lhsWords; ++i) 1595 Quotient->pVal[i] = 1596 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2)); 1597 } 1598 } 1599 1600 // If the caller wants the remainder 1601 if (Remainder) { 1602 // Set up the Remainder value's memory. 1603 if (Remainder->BitWidth != RHS.BitWidth) { 1604 if (Remainder->isSingleWord()) 1605 Remainder->VAL = 0; 1606 else 1607 delete [] Remainder->pVal; 1608 Remainder->BitWidth = RHS.BitWidth; 1609 if (!Remainder->isSingleWord()) 1610 Remainder->pVal = getClearedMemory(Remainder->getNumWords()); 1611 } else 1612 Remainder->clear(); 1613 1614 // The remainder is in R. Reconstitute the remainder into Remainder's low 1615 // order words. 1616 if (rhsWords == 1) { 1617 uint64_t tmp = 1618 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2)); 1619 if (Remainder->isSingleWord()) 1620 Remainder->VAL = tmp; 1621 else 1622 Remainder->pVal[0] = tmp; 1623 } else { 1624 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough"); 1625 for (unsigned i = 0; i < rhsWords; ++i) 1626 Remainder->pVal[i] = 1627 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2)); 1628 } 1629 } 1630 1631 // Clean up the memory we allocated. 1632 if (U != &SPACE[0]) { 1633 delete [] U; 1634 delete [] V; 1635 delete [] Q; 1636 delete [] R; 1637 } 1638} 1639 1640APInt APInt::udiv(const APInt& RHS) const { 1641 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 1642 1643 // First, deal with the easy case 1644 if (isSingleWord()) { 1645 assert(RHS.VAL != 0 && "Divide by zero?"); 1646 return APInt(BitWidth, VAL / RHS.VAL); 1647 } 1648 1649 // Get some facts about the LHS and RHS number of bits and words 1650 uint32_t rhsBits = RHS.getActiveBits(); 1651 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); 1652 assert(rhsWords && "Divided by zero???"); 1653 uint32_t lhsBits = this->getActiveBits(); 1654 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1); 1655 1656 // Deal with some degenerate cases 1657 if (!lhsWords) 1658 // 0 / X ===> 0 1659 return APInt(BitWidth, 0); 1660 else if (lhsWords < rhsWords || this->ult(RHS)) { 1661 // X / Y ===> 0, iff X < Y 1662 return APInt(BitWidth, 0); 1663 } else if (*this == RHS) { 1664 // X / X ===> 1 1665 return APInt(BitWidth, 1); 1666 } else if (lhsWords == 1 && rhsWords == 1) { 1667 // All high words are zero, just use native divide 1668 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]); 1669 } 1670 1671 // We have to compute it the hard way. Invoke the Knuth divide algorithm. 1672 APInt Quotient(1,0); // to hold result. 1673 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0); 1674 return Quotient; 1675} 1676 1677APInt APInt::urem(const APInt& RHS) const { 1678 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 1679 if (isSingleWord()) { 1680 assert(RHS.VAL != 0 && "Remainder by zero?"); 1681 return APInt(BitWidth, VAL % RHS.VAL); 1682 } 1683 1684 // Get some facts about the LHS 1685 uint32_t lhsBits = getActiveBits(); 1686 uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1); 1687 1688 // Get some facts about the RHS 1689 uint32_t rhsBits = RHS.getActiveBits(); 1690 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); 1691 assert(rhsWords && "Performing remainder operation by zero ???"); 1692 1693 // Check the degenerate cases 1694 if (lhsWords == 0) { 1695 // 0 % Y ===> 0 1696 return APInt(BitWidth, 0); 1697 } else if (lhsWords < rhsWords || this->ult(RHS)) { 1698 // X % Y ===> X, iff X < Y 1699 return *this; 1700 } else if (*this == RHS) { 1701 // X % X == 0; 1702 return APInt(BitWidth, 0); 1703 } else if (lhsWords == 1) { 1704 // All high words are zero, just use native remainder 1705 return APInt(BitWidth, pVal[0] % RHS.pVal[0]); 1706 } 1707 1708 // We have to compute it the hard way. Invoke the Knute divide algorithm. 1709 APInt Remainder(1,0); 1710 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder); 1711 return Remainder; 1712} 1713 1714void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen, 1715 uint8_t radix) { 1716 // Check our assumptions here 1717 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) && 1718 "Radix should be 2, 8, 10, or 16!"); 1719 assert(str && "String is null?"); 1720 bool isNeg = str[0] == '-'; 1721 if (isNeg) 1722 str++, slen--; 1723 assert(slen <= numbits || radix != 2 && "Insufficient bit width"); 1724 assert(slen*3 <= numbits || radix != 8 && "Insufficient bit width"); 1725 assert(slen*4 <= numbits || radix != 16 && "Insufficient bit width"); 1726 assert((slen*64)/20 <= numbits || radix != 10 && "Insufficient bit width"); 1727 1728 // Allocate memory 1729 if (!isSingleWord()) 1730 pVal = getClearedMemory(getNumWords()); 1731 1732 // Figure out if we can shift instead of multiply 1733 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0); 1734 1735 // Set up an APInt for the digit to add outside the loop so we don't 1736 // constantly construct/destruct it. 1737 APInt apdigit(getBitWidth(), 0); 1738 APInt apradix(getBitWidth(), radix); 1739 1740 // Enter digit traversal loop 1741 for (unsigned i = 0; i < slen; i++) { 1742 // Get a digit 1743 uint32_t digit = 0; 1744 char cdigit = str[i]; 1745 if (isdigit(cdigit)) 1746 digit = cdigit - '0'; 1747 else if (isxdigit(cdigit)) 1748 if (cdigit >= 'a') 1749 digit = cdigit - 'a' + 10; 1750 else if (cdigit >= 'A') 1751 digit = cdigit - 'A' + 10; 1752 else 1753 assert(0 && "huh?"); 1754 else 1755 assert(0 && "Invalid character in digit string"); 1756 1757 // Shift or multiple the value by the radix 1758 if (shift) 1759 this->shl(shift); 1760 else 1761 *this *= apradix; 1762 1763 // Add in the digit we just interpreted 1764 if (apdigit.isSingleWord()) 1765 apdigit.VAL = digit; 1766 else 1767 apdigit.pVal[0] = digit; 1768 *this += apdigit; 1769 } 1770 // If its negative, put it in two's complement form 1771 if (isNeg) { 1772 (*this)--; 1773 this->flip(); 1774 } 1775} 1776 1777std::string APInt::toString(uint8_t radix, bool wantSigned) const { 1778 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) && 1779 "Radix should be 2, 8, 10, or 16!"); 1780 static const char *digits[] = { 1781 "0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F" 1782 }; 1783 std::string result; 1784 uint32_t bits_used = getActiveBits(); 1785 if (isSingleWord()) { 1786 char buf[65]; 1787 const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") : 1788 (radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0))); 1789 if (format) { 1790 if (wantSigned) { 1791 int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >> 1792 (APINT_BITS_PER_WORD-BitWidth); 1793 sprintf(buf, format, sextVal); 1794 } else 1795 sprintf(buf, format, VAL); 1796 } else { 1797 memset(buf, 0, 65); 1798 uint64_t v = VAL; 1799 while (bits_used) { 1800 uint32_t bit = v & 1; 1801 bits_used--; 1802 buf[bits_used] = digits[bit][0]; 1803 v >>=1; 1804 } 1805 } 1806 result = buf; 1807 return result; 1808 } 1809 1810 if (radix != 10) { 1811 uint64_t mask = radix - 1; 1812 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : 1); 1813 uint32_t nibbles = APINT_BITS_PER_WORD / shift; 1814 for (uint32_t i = 0; i < getNumWords(); ++i) { 1815 uint64_t value = pVal[i]; 1816 for (uint32_t j = 0; j < nibbles; ++j) { 1817 result.insert(0, digits[ value & mask ]); 1818 value >>= shift; 1819 } 1820 } 1821 return result; 1822 } 1823 1824 APInt tmp(*this); 1825 APInt divisor(4, radix); 1826 APInt zero(tmp.getBitWidth(), 0); 1827 size_t insert_at = 0; 1828 if (wantSigned && tmp[BitWidth-1]) { 1829 // They want to print the signed version and it is a negative value 1830 // Flip the bits and add one to turn it into the equivalent positive 1831 // value and put a '-' in the result. 1832 tmp.flip(); 1833 tmp++; 1834 result = "-"; 1835 insert_at = 1; 1836 } 1837 if (tmp == APInt(tmp.getBitWidth(), 0)) 1838 result = "0"; 1839 else while (tmp.ne(zero)) { 1840 APInt APdigit(1,0); 1841 APInt tmp2(tmp.getBitWidth(), 0); 1842 divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2, 1843 &APdigit); 1844 uint32_t digit = APdigit.getZExtValue(); 1845 assert(digit < radix && "divide failed"); 1846 result.insert(insert_at,digits[digit]); 1847 tmp = tmp2; 1848 } 1849 1850 return result; 1851} 1852 1853#ifndef NDEBUG 1854void APInt::dump() const 1855{ 1856 cerr << "APInt(" << BitWidth << ")=" << std::setbase(16); 1857 if (isSingleWord()) 1858 cerr << VAL; 1859 else for (unsigned i = getNumWords(); i > 0; i--) { 1860 cerr << pVal[i-1] << " "; 1861 } 1862 cerr << " U(" << this->toString(10) << ") S(" << this->toStringSigned(10) 1863 << ")\n" << std::setbase(10); 1864} 1865#endif 1866