APInt.cpp revision fb0709a180e55325f8b13754df4c9d9671b7b285
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 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small"); 86 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large"); 87 fromString(numbits, StrStart, slen, radix); 88} 89 90APInt::APInt(uint32_t numbits, const std::string& Val, uint8_t radix) 91 : BitWidth(numbits), VAL(0) { 92 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small"); 93 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large"); 94 assert(!Val.empty() && "String empty?"); 95 fromString(numbits, Val.c_str(), Val.size(), radix); 96} 97 98APInt::APInt(const APInt& that) 99 : BitWidth(that.BitWidth), VAL(0) { 100 assert(BitWidth >= IntegerType::MIN_INT_BITS && "bitwidth too small"); 101 assert(BitWidth <= IntegerType::MAX_INT_BITS && "bitwidth too large"); 102 if (isSingleWord()) 103 VAL = that.VAL; 104 else { 105 pVal = getMemory(getNumWords()); 106 memcpy(pVal, that.pVal, getNumWords() * APINT_WORD_SIZE); 107 } 108} 109 110APInt::~APInt() { 111 if (!isSingleWord() && pVal) 112 delete [] pVal; 113} 114 115APInt& APInt::operator=(const APInt& RHS) { 116 // Don't do anything for X = X 117 if (this == &RHS) 118 return *this; 119 120 // If the bitwidths are the same, we can avoid mucking with memory 121 if (BitWidth == RHS.getBitWidth()) { 122 if (isSingleWord()) 123 VAL = RHS.VAL; 124 else 125 memcpy(pVal, RHS.pVal, getNumWords() * APINT_WORD_SIZE); 126 return *this; 127 } 128 129 if (isSingleWord()) 130 if (RHS.isSingleWord()) 131 VAL = RHS.VAL; 132 else { 133 VAL = 0; 134 pVal = getMemory(RHS.getNumWords()); 135 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 136 } 137 else if (getNumWords() == RHS.getNumWords()) 138 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 139 else if (RHS.isSingleWord()) { 140 delete [] pVal; 141 VAL = RHS.VAL; 142 } else { 143 delete [] pVal; 144 pVal = getMemory(RHS.getNumWords()); 145 memcpy(pVal, RHS.pVal, RHS.getNumWords() * APINT_WORD_SIZE); 146 } 147 BitWidth = RHS.BitWidth; 148 return clearUnusedBits(); 149} 150 151APInt& APInt::operator=(uint64_t RHS) { 152 if (isSingleWord()) 153 VAL = RHS; 154 else { 155 pVal[0] = RHS; 156 memset(pVal+1, 0, (getNumWords() - 1) * APINT_WORD_SIZE); 157 } 158 return clearUnusedBits(); 159} 160 161/// add_1 - This function adds a single "digit" integer, y, to the multiple 162/// "digit" integer array, x[]. x[] is modified to reflect the addition and 163/// 1 is returned if there is a carry out, otherwise 0 is returned. 164/// @returns the carry of the addition. 165static bool add_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) { 166 for (uint32_t i = 0; i < len; ++i) { 167 dest[i] = y + x[i]; 168 if (dest[i] < y) 169 y = 1; // Carry one to next digit. 170 else { 171 y = 0; // No need to carry so exit early 172 break; 173 } 174 } 175 return y; 176} 177 178/// @brief Prefix increment operator. Increments the APInt by one. 179APInt& APInt::operator++() { 180 if (isSingleWord()) 181 ++VAL; 182 else 183 add_1(pVal, pVal, getNumWords(), 1); 184 return clearUnusedBits(); 185} 186 187/// sub_1 - This function subtracts a single "digit" (64-bit word), y, from 188/// the multi-digit integer array, x[], propagating the borrowed 1 value until 189/// no further borrowing is neeeded or it runs out of "digits" in x. The result 190/// is 1 if "borrowing" exhausted the digits in x, or 0 if x was not exhausted. 191/// In other words, if y > x then this function returns 1, otherwise 0. 192/// @returns the borrow out of the subtraction 193static bool sub_1(uint64_t x[], uint32_t len, uint64_t y) { 194 for (uint32_t i = 0; i < len; ++i) { 195 uint64_t X = x[i]; 196 x[i] -= y; 197 if (y > X) 198 y = 1; // We have to "borrow 1" from next "digit" 199 else { 200 y = 0; // No need to borrow 201 break; // Remaining digits are unchanged so exit early 202 } 203 } 204 return bool(y); 205} 206 207/// @brief Prefix decrement operator. Decrements the APInt by one. 208APInt& APInt::operator--() { 209 if (isSingleWord()) 210 --VAL; 211 else 212 sub_1(pVal, getNumWords(), 1); 213 return clearUnusedBits(); 214} 215 216/// add - This function adds the integer array x to the integer array Y and 217/// places the result in dest. 218/// @returns the carry out from the addition 219/// @brief General addition of 64-bit integer arrays 220static bool add(uint64_t *dest, const uint64_t *x, const uint64_t *y, 221 uint32_t len) { 222 bool carry = false; 223 for (uint32_t i = 0; i< len; ++i) { 224 uint64_t limit = std::min(x[i],y[i]); // must come first in case dest == x 225 dest[i] = x[i] + y[i] + carry; 226 carry = dest[i] < limit || (carry && dest[i] == limit); 227 } 228 return carry; 229} 230 231/// Adds the RHS APint to this APInt. 232/// @returns this, after addition of RHS. 233/// @brief Addition assignment operator. 234APInt& APInt::operator+=(const APInt& RHS) { 235 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 236 if (isSingleWord()) 237 VAL += RHS.VAL; 238 else { 239 add(pVal, pVal, RHS.pVal, getNumWords()); 240 } 241 return clearUnusedBits(); 242} 243 244/// Subtracts the integer array y from the integer array x 245/// @returns returns the borrow out. 246/// @brief Generalized subtraction of 64-bit integer arrays. 247static bool sub(uint64_t *dest, const uint64_t *x, const uint64_t *y, 248 uint32_t len) { 249 bool borrow = false; 250 for (uint32_t i = 0; i < len; ++i) { 251 uint64_t x_tmp = borrow ? x[i] - 1 : x[i]; 252 borrow = y[i] > x_tmp || (borrow && x[i] == 0); 253 dest[i] = x_tmp - y[i]; 254 } 255 return borrow; 256} 257 258/// Subtracts the RHS APInt from this APInt 259/// @returns this, after subtraction 260/// @brief Subtraction assignment operator. 261APInt& APInt::operator-=(const APInt& RHS) { 262 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 263 if (isSingleWord()) 264 VAL -= RHS.VAL; 265 else 266 sub(pVal, pVal, RHS.pVal, getNumWords()); 267 return clearUnusedBits(); 268} 269 270/// Multiplies an integer array, x by a a uint64_t integer and places the result 271/// into dest. 272/// @returns the carry out of the multiplication. 273/// @brief Multiply a multi-digit APInt by a single digit (64-bit) integer. 274static uint64_t mul_1(uint64_t dest[], uint64_t x[], uint32_t len, uint64_t y) { 275 // Split y into high 32-bit part (hy) and low 32-bit part (ly) 276 uint64_t ly = y & 0xffffffffULL, hy = y >> 32; 277 uint64_t carry = 0; 278 279 // For each digit of x. 280 for (uint32_t i = 0; i < len; ++i) { 281 // Split x into high and low words 282 uint64_t lx = x[i] & 0xffffffffULL; 283 uint64_t hx = x[i] >> 32; 284 // hasCarry - A flag to indicate if there is a carry to the next digit. 285 // hasCarry == 0, no carry 286 // hasCarry == 1, has carry 287 // hasCarry == 2, no carry and the calculation result == 0. 288 uint8_t hasCarry = 0; 289 dest[i] = carry + lx * ly; 290 // Determine if the add above introduces carry. 291 hasCarry = (dest[i] < carry) ? 1 : 0; 292 carry = hx * ly + (dest[i] >> 32) + (hasCarry ? (1ULL << 32) : 0); 293 // The upper limit of carry can be (2^32 - 1)(2^32 - 1) + 294 // (2^32 - 1) + 2^32 = 2^64. 295 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0); 296 297 carry += (lx * hy) & 0xffffffffULL; 298 dest[i] = (carry << 32) | (dest[i] & 0xffffffffULL); 299 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0) + 300 (carry >> 32) + ((lx * hy) >> 32) + hx * hy; 301 } 302 return carry; 303} 304 305/// Multiplies integer array x by integer array y and stores the result into 306/// the integer array dest. Note that dest's size must be >= xlen + ylen. 307/// @brief Generalized multiplicate of integer arrays. 308static void mul(uint64_t dest[], uint64_t x[], uint32_t xlen, uint64_t y[], 309 uint32_t ylen) { 310 dest[xlen] = mul_1(dest, x, xlen, y[0]); 311 for (uint32_t i = 1; i < ylen; ++i) { 312 uint64_t ly = y[i] & 0xffffffffULL, hy = y[i] >> 32; 313 uint64_t carry = 0, lx = 0, hx = 0; 314 for (uint32_t j = 0; j < xlen; ++j) { 315 lx = x[j] & 0xffffffffULL; 316 hx = x[j] >> 32; 317 // hasCarry - A flag to indicate if has carry. 318 // hasCarry == 0, no carry 319 // hasCarry == 1, has carry 320 // hasCarry == 2, no carry and the calculation result == 0. 321 uint8_t hasCarry = 0; 322 uint64_t resul = carry + lx * ly; 323 hasCarry = (resul < carry) ? 1 : 0; 324 carry = (hasCarry ? (1ULL << 32) : 0) + hx * ly + (resul >> 32); 325 hasCarry = (!carry && hasCarry) ? 1 : (!carry ? 2 : 0); 326 327 carry += (lx * hy) & 0xffffffffULL; 328 resul = (carry << 32) | (resul & 0xffffffffULL); 329 dest[i+j] += resul; 330 carry = (((!carry && hasCarry != 2) || hasCarry == 1) ? (1ULL << 32) : 0)+ 331 (carry >> 32) + (dest[i+j] < resul ? 1 : 0) + 332 ((lx * hy) >> 32) + hx * hy; 333 } 334 dest[i+xlen] = carry; 335 } 336} 337 338APInt& APInt::operator*=(const APInt& RHS) { 339 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 340 if (isSingleWord()) { 341 VAL *= RHS.VAL; 342 clearUnusedBits(); 343 return *this; 344 } 345 346 // Get some bit facts about LHS and check for zero 347 uint32_t lhsBits = getActiveBits(); 348 uint32_t lhsWords = !lhsBits ? 0 : whichWord(lhsBits - 1) + 1; 349 if (!lhsWords) 350 // 0 * X ===> 0 351 return *this; 352 353 // Get some bit facts about RHS and check for zero 354 uint32_t rhsBits = RHS.getActiveBits(); 355 uint32_t rhsWords = !rhsBits ? 0 : whichWord(rhsBits - 1) + 1; 356 if (!rhsWords) { 357 // X * 0 ===> 0 358 clear(); 359 return *this; 360 } 361 362 // Allocate space for the result 363 uint32_t destWords = rhsWords + lhsWords; 364 uint64_t *dest = getMemory(destWords); 365 366 // Perform the long multiply 367 mul(dest, pVal, lhsWords, RHS.pVal, rhsWords); 368 369 // Copy result back into *this 370 clear(); 371 uint32_t wordsToCopy = destWords >= getNumWords() ? getNumWords() : destWords; 372 memcpy(pVal, dest, wordsToCopy * APINT_WORD_SIZE); 373 374 // delete dest array and return 375 delete[] dest; 376 return *this; 377} 378 379APInt& APInt::operator&=(const APInt& RHS) { 380 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 381 if (isSingleWord()) { 382 VAL &= RHS.VAL; 383 return *this; 384 } 385 uint32_t numWords = getNumWords(); 386 for (uint32_t i = 0; i < numWords; ++i) 387 pVal[i] &= RHS.pVal[i]; 388 return *this; 389} 390 391APInt& APInt::operator|=(const APInt& RHS) { 392 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 393 if (isSingleWord()) { 394 VAL |= RHS.VAL; 395 return *this; 396 } 397 uint32_t numWords = getNumWords(); 398 for (uint32_t i = 0; i < numWords; ++i) 399 pVal[i] |= RHS.pVal[i]; 400 return *this; 401} 402 403APInt& APInt::operator^=(const APInt& RHS) { 404 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 405 if (isSingleWord()) { 406 VAL ^= RHS.VAL; 407 this->clearUnusedBits(); 408 return *this; 409 } 410 uint32_t numWords = getNumWords(); 411 for (uint32_t i = 0; i < numWords; ++i) 412 pVal[i] ^= RHS.pVal[i]; 413 return clearUnusedBits(); 414} 415 416APInt APInt::operator&(const APInt& RHS) const { 417 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 418 if (isSingleWord()) 419 return APInt(getBitWidth(), VAL & RHS.VAL); 420 421 uint32_t numWords = getNumWords(); 422 uint64_t* val = getMemory(numWords); 423 for (uint32_t i = 0; i < numWords; ++i) 424 val[i] = pVal[i] & RHS.pVal[i]; 425 return APInt(val, getBitWidth()); 426} 427 428APInt APInt::operator|(const APInt& RHS) const { 429 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 430 if (isSingleWord()) 431 return APInt(getBitWidth(), VAL | RHS.VAL); 432 433 uint32_t numWords = getNumWords(); 434 uint64_t *val = getMemory(numWords); 435 for (uint32_t i = 0; i < numWords; ++i) 436 val[i] = pVal[i] | RHS.pVal[i]; 437 return APInt(val, getBitWidth()); 438} 439 440APInt APInt::operator^(const APInt& RHS) const { 441 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 442 if (isSingleWord()) 443 return APInt(BitWidth, VAL ^ RHS.VAL); 444 445 uint32_t numWords = getNumWords(); 446 uint64_t *val = getMemory(numWords); 447 for (uint32_t i = 0; i < numWords; ++i) 448 val[i] = pVal[i] ^ RHS.pVal[i]; 449 450 // 0^0==1 so clear the high bits in case they got set. 451 return APInt(val, getBitWidth()).clearUnusedBits(); 452} 453 454bool APInt::operator !() const { 455 if (isSingleWord()) 456 return !VAL; 457 458 for (uint32_t i = 0; i < getNumWords(); ++i) 459 if (pVal[i]) 460 return false; 461 return true; 462} 463 464APInt APInt::operator*(const APInt& RHS) const { 465 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 466 if (isSingleWord()) 467 return APInt(BitWidth, VAL * RHS.VAL); 468 APInt Result(*this); 469 Result *= RHS; 470 return Result.clearUnusedBits(); 471} 472 473APInt APInt::operator+(const APInt& RHS) const { 474 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 475 if (isSingleWord()) 476 return APInt(BitWidth, VAL + RHS.VAL); 477 APInt Result(BitWidth, 0); 478 add(Result.pVal, this->pVal, RHS.pVal, getNumWords()); 479 return Result.clearUnusedBits(); 480} 481 482APInt APInt::operator-(const APInt& RHS) const { 483 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 484 if (isSingleWord()) 485 return APInt(BitWidth, VAL - RHS.VAL); 486 APInt Result(BitWidth, 0); 487 sub(Result.pVal, this->pVal, RHS.pVal, getNumWords()); 488 return Result.clearUnusedBits(); 489} 490 491bool APInt::operator[](uint32_t bitPosition) const { 492 return (maskBit(bitPosition) & 493 (isSingleWord() ? VAL : pVal[whichWord(bitPosition)])) != 0; 494} 495 496bool APInt::operator==(const APInt& RHS) const { 497 assert(BitWidth == RHS.BitWidth && "Comparison requires equal bit widths"); 498 if (isSingleWord()) 499 return VAL == RHS.VAL; 500 501 // Get some facts about the number of bits used in the two operands. 502 uint32_t n1 = getActiveBits(); 503 uint32_t n2 = RHS.getActiveBits(); 504 505 // If the number of bits isn't the same, they aren't equal 506 if (n1 != n2) 507 return false; 508 509 // If the number of bits fits in a word, we only need to compare the low word. 510 if (n1 <= APINT_BITS_PER_WORD) 511 return pVal[0] == RHS.pVal[0]; 512 513 // Otherwise, compare everything 514 for (int i = whichWord(n1 - 1); i >= 0; --i) 515 if (pVal[i] != RHS.pVal[i]) 516 return false; 517 return true; 518} 519 520bool APInt::operator==(uint64_t Val) const { 521 if (isSingleWord()) 522 return VAL == Val; 523 524 uint32_t n = getActiveBits(); 525 if (n <= APINT_BITS_PER_WORD) 526 return pVal[0] == Val; 527 else 528 return false; 529} 530 531bool APInt::ult(const APInt& RHS) const { 532 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); 533 if (isSingleWord()) 534 return VAL < RHS.VAL; 535 536 // Get active bit length of both operands 537 uint32_t n1 = getActiveBits(); 538 uint32_t n2 = RHS.getActiveBits(); 539 540 // If magnitude of LHS is less than RHS, return true. 541 if (n1 < n2) 542 return true; 543 544 // If magnitude of RHS is greather than LHS, return false. 545 if (n2 < n1) 546 return false; 547 548 // If they bot fit in a word, just compare the low order word 549 if (n1 <= APINT_BITS_PER_WORD && n2 <= APINT_BITS_PER_WORD) 550 return pVal[0] < RHS.pVal[0]; 551 552 // Otherwise, compare all words 553 uint32_t topWord = whichWord(std::max(n1,n2)-1); 554 for (int i = topWord; i >= 0; --i) { 555 if (pVal[i] > RHS.pVal[i]) 556 return false; 557 if (pVal[i] < RHS.pVal[i]) 558 return true; 559 } 560 return false; 561} 562 563bool APInt::slt(const APInt& RHS) const { 564 assert(BitWidth == RHS.BitWidth && "Bit widths must be same for comparison"); 565 if (isSingleWord()) { 566 int64_t lhsSext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth); 567 int64_t rhsSext = (int64_t(RHS.VAL) << (64-BitWidth)) >> (64-BitWidth); 568 return lhsSext < rhsSext; 569 } 570 571 APInt lhs(*this); 572 APInt rhs(RHS); 573 bool lhsNeg = isNegative(); 574 bool rhsNeg = rhs.isNegative(); 575 if (lhsNeg) { 576 // Sign bit is set so perform two's complement to make it positive 577 lhs.flip(); 578 lhs++; 579 } 580 if (rhsNeg) { 581 // Sign bit is set so perform two's complement to make it positive 582 rhs.flip(); 583 rhs++; 584 } 585 586 // Now we have unsigned values to compare so do the comparison if necessary 587 // based on the negativeness of the values. 588 if (lhsNeg) 589 if (rhsNeg) 590 return lhs.ugt(rhs); 591 else 592 return true; 593 else if (rhsNeg) 594 return false; 595 else 596 return lhs.ult(rhs); 597} 598 599APInt& APInt::set(uint32_t bitPosition) { 600 if (isSingleWord()) 601 VAL |= maskBit(bitPosition); 602 else 603 pVal[whichWord(bitPosition)] |= maskBit(bitPosition); 604 return *this; 605} 606 607APInt& APInt::set() { 608 if (isSingleWord()) { 609 VAL = -1ULL; 610 return clearUnusedBits(); 611 } 612 613 // Set all the bits in all the words. 614 for (uint32_t i = 0; i < getNumWords(); ++i) 615 pVal[i] = -1ULL; 616 // Clear the unused ones 617 return clearUnusedBits(); 618} 619 620/// Set the given bit to 0 whose position is given as "bitPosition". 621/// @brief Set a given bit to 0. 622APInt& APInt::clear(uint32_t bitPosition) { 623 if (isSingleWord()) 624 VAL &= ~maskBit(bitPosition); 625 else 626 pVal[whichWord(bitPosition)] &= ~maskBit(bitPosition); 627 return *this; 628} 629 630/// @brief Set every bit to 0. 631APInt& APInt::clear() { 632 if (isSingleWord()) 633 VAL = 0; 634 else 635 memset(pVal, 0, getNumWords() * APINT_WORD_SIZE); 636 return *this; 637} 638 639/// @brief Bitwise NOT operator. Performs a bitwise logical NOT operation on 640/// this APInt. 641APInt APInt::operator~() const { 642 APInt Result(*this); 643 Result.flip(); 644 return Result; 645} 646 647/// @brief Toggle every bit to its opposite value. 648APInt& APInt::flip() { 649 if (isSingleWord()) { 650 VAL ^= -1ULL; 651 return clearUnusedBits(); 652 } 653 for (uint32_t i = 0; i < getNumWords(); ++i) 654 pVal[i] ^= -1ULL; 655 return clearUnusedBits(); 656} 657 658/// Toggle a given bit to its opposite value whose position is given 659/// as "bitPosition". 660/// @brief Toggles a given bit to its opposite value. 661APInt& APInt::flip(uint32_t bitPosition) { 662 assert(bitPosition < BitWidth && "Out of the bit-width range!"); 663 if ((*this)[bitPosition]) clear(bitPosition); 664 else set(bitPosition); 665 return *this; 666} 667 668uint32_t APInt::getBitsNeeded(const char* str, uint32_t slen, uint8_t radix) { 669 assert(str != 0 && "Invalid value string"); 670 assert(slen > 0 && "Invalid string length"); 671 672 // Each computation below needs to know if its negative 673 uint32_t isNegative = str[0] == '-'; 674 if (isNegative) { 675 slen--; 676 str++; 677 } 678 // For radixes of power-of-two values, the bits required is accurately and 679 // easily computed 680 if (radix == 2) 681 return slen + isNegative; 682 if (radix == 8) 683 return slen * 3 + isNegative; 684 if (radix == 16) 685 return slen * 4 + isNegative; 686 687 // Otherwise it must be radix == 10, the hard case 688 assert(radix == 10 && "Invalid radix"); 689 690 // This is grossly inefficient but accurate. We could probably do something 691 // with a computation of roughly slen*64/20 and then adjust by the value of 692 // the first few digits. But, I'm not sure how accurate that could be. 693 694 // Compute a sufficient number of bits that is always large enough but might 695 // be too large. This avoids the assertion in the constructor. 696 uint32_t sufficient = slen*64/18; 697 698 // Convert to the actual binary value. 699 APInt tmp(sufficient, str, slen, radix); 700 701 // Compute how many bits are required. 702 return isNegative + tmp.logBase2() + 1; 703} 704 705uint64_t APInt::getHashValue() const { 706 // Put the bit width into the low order bits. 707 uint64_t hash = BitWidth; 708 709 // Add the sum of the words to the hash. 710 if (isSingleWord()) 711 hash += VAL << 6; // clear separation of up to 64 bits 712 else 713 for (uint32_t i = 0; i < getNumWords(); ++i) 714 hash += pVal[i] << 6; // clear sepration of up to 64 bits 715 return hash; 716} 717 718/// HiBits - This function returns the high "numBits" bits of this APInt. 719APInt APInt::getHiBits(uint32_t numBits) const { 720 return APIntOps::lshr(*this, BitWidth - numBits); 721} 722 723/// LoBits - This function returns the low "numBits" bits of this APInt. 724APInt APInt::getLoBits(uint32_t numBits) const { 725 return APIntOps::lshr(APIntOps::shl(*this, BitWidth - numBits), 726 BitWidth - numBits); 727} 728 729bool APInt::isPowerOf2() const { 730 return (!!*this) && !(*this & (*this - APInt(BitWidth,1))); 731} 732 733uint32_t APInt::countLeadingZeros() const { 734 uint32_t Count = 0; 735 if (isSingleWord()) 736 Count = CountLeadingZeros_64(VAL); 737 else { 738 for (uint32_t i = getNumWords(); i > 0u; --i) { 739 if (pVal[i-1] == 0) 740 Count += APINT_BITS_PER_WORD; 741 else { 742 Count += CountLeadingZeros_64(pVal[i-1]); 743 break; 744 } 745 } 746 } 747 uint32_t remainder = BitWidth % APINT_BITS_PER_WORD; 748 if (remainder) 749 Count -= APINT_BITS_PER_WORD - remainder; 750 return Count; 751} 752 753static uint32_t countLeadingOnes_64(uint64_t V, uint32_t skip) { 754 uint32_t Count = 0; 755 if (skip) 756 V <<= skip; 757 while (V && (V & (1ULL << 63))) { 758 Count++; 759 V <<= 1; 760 } 761 return Count; 762} 763 764uint32_t APInt::countLeadingOnes() const { 765 if (isSingleWord()) 766 return countLeadingOnes_64(VAL, APINT_BITS_PER_WORD - BitWidth); 767 768 uint32_t highWordBits = BitWidth % APINT_BITS_PER_WORD; 769 uint32_t shift = (highWordBits == 0 ? 0 : APINT_BITS_PER_WORD - highWordBits); 770 int i = getNumWords() - 1; 771 uint32_t Count = countLeadingOnes_64(pVal[i], shift); 772 if (Count == highWordBits) { 773 for (i--; i >= 0; --i) { 774 if (pVal[i] == -1ULL) 775 Count += APINT_BITS_PER_WORD; 776 else { 777 Count += countLeadingOnes_64(pVal[i], 0); 778 break; 779 } 780 } 781 } 782 return Count; 783} 784 785uint32_t APInt::countTrailingZeros() const { 786 if (isSingleWord()) 787 return CountTrailingZeros_64(VAL); 788 uint32_t Count = 0; 789 uint32_t i = 0; 790 for (; i < getNumWords() && pVal[i] == 0; ++i) 791 Count += APINT_BITS_PER_WORD; 792 if (i < getNumWords()) 793 Count += CountTrailingZeros_64(pVal[i]); 794 return Count; 795} 796 797uint32_t APInt::countPopulation() const { 798 if (isSingleWord()) 799 return CountPopulation_64(VAL); 800 uint32_t Count = 0; 801 for (uint32_t i = 0; i < getNumWords(); ++i) 802 Count += CountPopulation_64(pVal[i]); 803 return Count; 804} 805 806APInt APInt::byteSwap() const { 807 assert(BitWidth >= 16 && BitWidth % 16 == 0 && "Cannot byteswap!"); 808 if (BitWidth == 16) 809 return APInt(BitWidth, ByteSwap_16(uint16_t(VAL))); 810 else if (BitWidth == 32) 811 return APInt(BitWidth, ByteSwap_32(uint32_t(VAL))); 812 else if (BitWidth == 48) { 813 uint32_t Tmp1 = uint32_t(VAL >> 16); 814 Tmp1 = ByteSwap_32(Tmp1); 815 uint16_t Tmp2 = uint16_t(VAL); 816 Tmp2 = ByteSwap_16(Tmp2); 817 return APInt(BitWidth, (uint64_t(Tmp2) << 32) | Tmp1); 818 } else if (BitWidth == 64) 819 return APInt(BitWidth, ByteSwap_64(VAL)); 820 else { 821 APInt Result(BitWidth, 0); 822 char *pByte = (char*)Result.pVal; 823 for (uint32_t i = 0; i < BitWidth / APINT_WORD_SIZE / 2; ++i) { 824 char Tmp = pByte[i]; 825 pByte[i] = pByte[BitWidth / APINT_WORD_SIZE - 1 - i]; 826 pByte[BitWidth / APINT_WORD_SIZE - i - 1] = Tmp; 827 } 828 return Result; 829 } 830} 831 832APInt llvm::APIntOps::GreatestCommonDivisor(const APInt& API1, 833 const APInt& API2) { 834 APInt A = API1, B = API2; 835 while (!!B) { 836 APInt T = B; 837 B = APIntOps::urem(A, B); 838 A = T; 839 } 840 return A; 841} 842 843APInt llvm::APIntOps::RoundDoubleToAPInt(double Double, uint32_t width) { 844 union { 845 double D; 846 uint64_t I; 847 } T; 848 T.D = Double; 849 850 // Get the sign bit from the highest order bit 851 bool isNeg = T.I >> 63; 852 853 // Get the 11-bit exponent and adjust for the 1023 bit bias 854 int64_t exp = ((T.I >> 52) & 0x7ff) - 1023; 855 856 // If the exponent is negative, the value is < 0 so just return 0. 857 if (exp < 0) 858 return APInt(width, 0u); 859 860 // Extract the mantissa by clearing the top 12 bits (sign + exponent). 861 uint64_t mantissa = (T.I & (~0ULL >> 12)) | 1ULL << 52; 862 863 // If the exponent doesn't shift all bits out of the mantissa 864 if (exp < 52) 865 return isNeg ? -APInt(width, mantissa >> (52 - exp)) : 866 APInt(width, mantissa >> (52 - exp)); 867 868 // If the client didn't provide enough bits for us to shift the mantissa into 869 // then the result is undefined, just return 0 870 if (width <= exp - 52) 871 return APInt(width, 0); 872 873 // Otherwise, we have to shift the mantissa bits up to the right location 874 APInt Tmp(width, mantissa); 875 Tmp = Tmp.shl(exp - 52); 876 return isNeg ? -Tmp : Tmp; 877} 878 879/// RoundToDouble - This function convert this APInt to a double. 880/// The layout for double is as following (IEEE Standard 754): 881/// -------------------------------------- 882/// | Sign Exponent Fraction Bias | 883/// |-------------------------------------- | 884/// | 1[63] 11[62-52] 52[51-00] 1023 | 885/// -------------------------------------- 886double APInt::roundToDouble(bool isSigned) const { 887 888 // Handle the simple case where the value is contained in one uint64_t. 889 if (isSingleWord() || getActiveBits() <= APINT_BITS_PER_WORD) { 890 if (isSigned) { 891 int64_t sext = (int64_t(VAL) << (64-BitWidth)) >> (64-BitWidth); 892 return double(sext); 893 } else 894 return double(VAL); 895 } 896 897 // Determine if the value is negative. 898 bool isNeg = isSigned ? (*this)[BitWidth-1] : false; 899 900 // Construct the absolute value if we're negative. 901 APInt Tmp(isNeg ? -(*this) : (*this)); 902 903 // Figure out how many bits we're using. 904 uint32_t n = Tmp.getActiveBits(); 905 906 // The exponent (without bias normalization) is just the number of bits 907 // we are using. Note that the sign bit is gone since we constructed the 908 // absolute value. 909 uint64_t exp = n; 910 911 // Return infinity for exponent overflow 912 if (exp > 1023) { 913 if (!isSigned || !isNeg) 914 return std::numeric_limits<double>::infinity(); 915 else 916 return -std::numeric_limits<double>::infinity(); 917 } 918 exp += 1023; // Increment for 1023 bias 919 920 // Number of bits in mantissa is 52. To obtain the mantissa value, we must 921 // extract the high 52 bits from the correct words in pVal. 922 uint64_t mantissa; 923 unsigned hiWord = whichWord(n-1); 924 if (hiWord == 0) { 925 mantissa = Tmp.pVal[0]; 926 if (n > 52) 927 mantissa >>= n - 52; // shift down, we want the top 52 bits. 928 } else { 929 assert(hiWord > 0 && "huh?"); 930 uint64_t hibits = Tmp.pVal[hiWord] << (52 - n % APINT_BITS_PER_WORD); 931 uint64_t lobits = Tmp.pVal[hiWord-1] >> (11 + n % APINT_BITS_PER_WORD); 932 mantissa = hibits | lobits; 933 } 934 935 // The leading bit of mantissa is implicit, so get rid of it. 936 uint64_t sign = isNeg ? (1ULL << (APINT_BITS_PER_WORD - 1)) : 0; 937 union { 938 double D; 939 uint64_t I; 940 } T; 941 T.I = sign | (exp << 52) | mantissa; 942 return T.D; 943} 944 945// Truncate to new width. 946APInt &APInt::trunc(uint32_t width) { 947 assert(width < BitWidth && "Invalid APInt Truncate request"); 948 assert(width >= IntegerType::MIN_INT_BITS && "Can't truncate to 0 bits"); 949 uint32_t wordsBefore = getNumWords(); 950 BitWidth = width; 951 uint32_t wordsAfter = getNumWords(); 952 if (wordsBefore != wordsAfter) { 953 if (wordsAfter == 1) { 954 uint64_t *tmp = pVal; 955 VAL = pVal[0]; 956 delete [] tmp; 957 } else { 958 uint64_t *newVal = getClearedMemory(wordsAfter); 959 for (uint32_t i = 0; i < wordsAfter; ++i) 960 newVal[i] = pVal[i]; 961 delete [] pVal; 962 pVal = newVal; 963 } 964 } 965 return clearUnusedBits(); 966} 967 968// Sign extend to a new width. 969APInt &APInt::sext(uint32_t width) { 970 assert(width > BitWidth && "Invalid APInt SignExtend request"); 971 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits"); 972 // If the sign bit isn't set, this is the same as zext. 973 if (!isNegative()) { 974 zext(width); 975 return *this; 976 } 977 978 // The sign bit is set. First, get some facts 979 uint32_t wordsBefore = getNumWords(); 980 uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD; 981 BitWidth = width; 982 uint32_t wordsAfter = getNumWords(); 983 984 // Mask the high order word appropriately 985 if (wordsBefore == wordsAfter) { 986 uint32_t newWordBits = width % APINT_BITS_PER_WORD; 987 // The extension is contained to the wordsBefore-1th word. 988 uint64_t mask = ~0ULL; 989 if (newWordBits) 990 mask >>= APINT_BITS_PER_WORD - newWordBits; 991 mask <<= wordBits; 992 if (wordsBefore == 1) 993 VAL |= mask; 994 else 995 pVal[wordsBefore-1] |= mask; 996 return clearUnusedBits(); 997 } 998 999 uint64_t mask = wordBits == 0 ? 0 : ~0ULL << wordBits; 1000 uint64_t *newVal = getMemory(wordsAfter); 1001 if (wordsBefore == 1) 1002 newVal[0] = VAL | mask; 1003 else { 1004 for (uint32_t i = 0; i < wordsBefore; ++i) 1005 newVal[i] = pVal[i]; 1006 newVal[wordsBefore-1] |= mask; 1007 } 1008 for (uint32_t i = wordsBefore; i < wordsAfter; i++) 1009 newVal[i] = -1ULL; 1010 if (wordsBefore != 1) 1011 delete [] pVal; 1012 pVal = newVal; 1013 return clearUnusedBits(); 1014} 1015 1016// Zero extend to a new width. 1017APInt &APInt::zext(uint32_t width) { 1018 assert(width > BitWidth && "Invalid APInt ZeroExtend request"); 1019 assert(width <= IntegerType::MAX_INT_BITS && "Too many bits"); 1020 uint32_t wordsBefore = getNumWords(); 1021 BitWidth = width; 1022 uint32_t wordsAfter = getNumWords(); 1023 if (wordsBefore != wordsAfter) { 1024 uint64_t *newVal = getClearedMemory(wordsAfter); 1025 if (wordsBefore == 1) 1026 newVal[0] = VAL; 1027 else 1028 for (uint32_t i = 0; i < wordsBefore; ++i) 1029 newVal[i] = pVal[i]; 1030 if (wordsBefore != 1) 1031 delete [] pVal; 1032 pVal = newVal; 1033 } 1034 return *this; 1035} 1036 1037APInt &APInt::zextOrTrunc(uint32_t width) { 1038 if (BitWidth < width) 1039 return zext(width); 1040 if (BitWidth > width) 1041 return trunc(width); 1042 return *this; 1043} 1044 1045APInt &APInt::sextOrTrunc(uint32_t width) { 1046 if (BitWidth < width) 1047 return sext(width); 1048 if (BitWidth > width) 1049 return trunc(width); 1050 return *this; 1051} 1052 1053/// Arithmetic right-shift this APInt by shiftAmt. 1054/// @brief Arithmetic right-shift function. 1055APInt APInt::ashr(uint32_t shiftAmt) const { 1056 assert(shiftAmt <= BitWidth && "Invalid shift amount"); 1057 // Handle a degenerate case 1058 if (shiftAmt == 0) 1059 return *this; 1060 1061 // Handle single word shifts with built-in ashr 1062 if (isSingleWord()) { 1063 if (shiftAmt == BitWidth) 1064 return APInt(BitWidth, 0); // undefined 1065 else { 1066 uint32_t SignBit = APINT_BITS_PER_WORD - BitWidth; 1067 return APInt(BitWidth, 1068 (((int64_t(VAL) << SignBit) >> SignBit) >> shiftAmt)); 1069 } 1070 } 1071 1072 // If all the bits were shifted out, the result is, technically, undefined. 1073 // We return -1 if it was negative, 0 otherwise. We check this early to avoid 1074 // issues in the algorithm below. 1075 if (shiftAmt == BitWidth) { 1076 if (isNegative()) 1077 return APInt(BitWidth, -1ULL); 1078 else 1079 return APInt(BitWidth, 0); 1080 } 1081 1082 // Create some space for the result. 1083 uint64_t * val = new uint64_t[getNumWords()]; 1084 1085 // Compute some values needed by the following shift algorithms 1086 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; // bits to shift per word 1087 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; // word offset for shift 1088 uint32_t breakWord = getNumWords() - 1 - offset; // last word affected 1089 uint32_t bitsInWord = whichBit(BitWidth); // how many bits in last word? 1090 if (bitsInWord == 0) 1091 bitsInWord = APINT_BITS_PER_WORD; 1092 1093 // If we are shifting whole words, just move whole words 1094 if (wordShift == 0) { 1095 // Move the words containing significant bits 1096 for (uint32_t i = 0; i <= breakWord; ++i) 1097 val[i] = pVal[i+offset]; // move whole word 1098 1099 // Adjust the top significant word for sign bit fill, if negative 1100 if (isNegative()) 1101 if (bitsInWord < APINT_BITS_PER_WORD) 1102 val[breakWord] |= ~0ULL << bitsInWord; // set high bits 1103 } else { 1104 // Shift the low order words 1105 for (uint32_t i = 0; i < breakWord; ++i) { 1106 // This combines the shifted corresponding word with the low bits from 1107 // the next word (shifted into this word's high bits). 1108 val[i] = (pVal[i+offset] >> wordShift) | 1109 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift)); 1110 } 1111 1112 // Shift the break word. In this case there are no bits from the next word 1113 // to include in this word. 1114 val[breakWord] = pVal[breakWord+offset] >> wordShift; 1115 1116 // Deal with sign extenstion in the break word, and possibly the word before 1117 // it. 1118 if (isNegative()) { 1119 if (wordShift > bitsInWord) { 1120 if (breakWord > 0) 1121 val[breakWord-1] |= 1122 ~0ULL << (APINT_BITS_PER_WORD - (wordShift - bitsInWord)); 1123 val[breakWord] |= ~0ULL; 1124 } else 1125 val[breakWord] |= (~0ULL << (bitsInWord - wordShift)); 1126 } 1127 } 1128 1129 // Remaining words are 0 or -1, just assign them. 1130 uint64_t fillValue = (isNegative() ? -1ULL : 0); 1131 for (uint32_t i = breakWord+1; i < getNumWords(); ++i) 1132 val[i] = fillValue; 1133 return APInt(val, BitWidth).clearUnusedBits(); 1134} 1135 1136/// Logical right-shift this APInt by shiftAmt. 1137/// @brief Logical right-shift function. 1138APInt APInt::lshr(uint32_t shiftAmt) const { 1139 if (isSingleWord()) { 1140 if (shiftAmt == BitWidth) 1141 return APInt(BitWidth, 0); 1142 else 1143 return APInt(BitWidth, this->VAL >> shiftAmt); 1144 } 1145 1146 // If all the bits were shifted out, the result is 0. This avoids issues 1147 // with shifting by the size of the integer type, which produces undefined 1148 // results. We define these "undefined results" to always be 0. 1149 if (shiftAmt == BitWidth) 1150 return APInt(BitWidth, 0); 1151 1152 // If none of the bits are shifted out, the result is *this. This avoids 1153 // issues with shifting byt he size of the integer type, which produces 1154 // undefined results in the code below. This is also an optimization. 1155 if (shiftAmt == 0) 1156 return *this; 1157 1158 // Create some space for the result. 1159 uint64_t * val = new uint64_t[getNumWords()]; 1160 1161 // If we are shifting less than a word, compute the shift with a simple carry 1162 if (shiftAmt < APINT_BITS_PER_WORD) { 1163 uint64_t carry = 0; 1164 for (int i = getNumWords()-1; i >= 0; --i) { 1165 val[i] = (pVal[i] >> shiftAmt) | carry; 1166 carry = pVal[i] << (APINT_BITS_PER_WORD - shiftAmt); 1167 } 1168 return APInt(val, BitWidth).clearUnusedBits(); 1169 } 1170 1171 // Compute some values needed by the remaining shift algorithms 1172 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; 1173 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; 1174 1175 // If we are shifting whole words, just move whole words 1176 if (wordShift == 0) { 1177 for (uint32_t i = 0; i < getNumWords() - offset; ++i) 1178 val[i] = pVal[i+offset]; 1179 for (uint32_t i = getNumWords()-offset; i < getNumWords(); i++) 1180 val[i] = 0; 1181 return APInt(val,BitWidth).clearUnusedBits(); 1182 } 1183 1184 // Shift the low order words 1185 uint32_t breakWord = getNumWords() - offset -1; 1186 for (uint32_t i = 0; i < breakWord; ++i) 1187 val[i] = (pVal[i+offset] >> wordShift) | 1188 (pVal[i+offset+1] << (APINT_BITS_PER_WORD - wordShift)); 1189 // Shift the break word. 1190 val[breakWord] = pVal[breakWord+offset] >> wordShift; 1191 1192 // Remaining words are 0 1193 for (uint32_t i = breakWord+1; i < getNumWords(); ++i) 1194 val[i] = 0; 1195 return APInt(val, BitWidth).clearUnusedBits(); 1196} 1197 1198/// Left-shift this APInt by shiftAmt. 1199/// @brief Left-shift function. 1200APInt APInt::shl(uint32_t shiftAmt) const { 1201 assert(shiftAmt <= BitWidth && "Invalid shift amount"); 1202 if (isSingleWord()) { 1203 if (shiftAmt == BitWidth) 1204 return APInt(BitWidth, 0); // avoid undefined shift results 1205 return APInt(BitWidth, VAL << shiftAmt); 1206 } 1207 1208 // If all the bits were shifted out, the result is 0. This avoids issues 1209 // with shifting by the size of the integer type, which produces undefined 1210 // results. We define these "undefined results" to always be 0. 1211 if (shiftAmt == BitWidth) 1212 return APInt(BitWidth, 0); 1213 1214 // If none of the bits are shifted out, the result is *this. This avoids a 1215 // lshr by the words size in the loop below which can produce incorrect 1216 // results. It also avoids the expensive computation below for a common case. 1217 if (shiftAmt == 0) 1218 return *this; 1219 1220 // Create some space for the result. 1221 uint64_t * val = new uint64_t[getNumWords()]; 1222 1223 // If we are shifting less than a word, do it the easy way 1224 if (shiftAmt < APINT_BITS_PER_WORD) { 1225 uint64_t carry = 0; 1226 for (uint32_t i = 0; i < getNumWords(); i++) { 1227 val[i] = pVal[i] << shiftAmt | carry; 1228 carry = pVal[i] >> (APINT_BITS_PER_WORD - shiftAmt); 1229 } 1230 return APInt(val, BitWidth).clearUnusedBits(); 1231 } 1232 1233 // Compute some values needed by the remaining shift algorithms 1234 uint32_t wordShift = shiftAmt % APINT_BITS_PER_WORD; 1235 uint32_t offset = shiftAmt / APINT_BITS_PER_WORD; 1236 1237 // If we are shifting whole words, just move whole words 1238 if (wordShift == 0) { 1239 for (uint32_t i = 0; i < offset; i++) 1240 val[i] = 0; 1241 for (uint32_t i = offset; i < getNumWords(); i++) 1242 val[i] = pVal[i-offset]; 1243 return APInt(val,BitWidth).clearUnusedBits(); 1244 } 1245 1246 // Copy whole words from this to Result. 1247 uint32_t i = getNumWords() - 1; 1248 for (; i > offset; --i) 1249 val[i] = pVal[i-offset] << wordShift | 1250 pVal[i-offset-1] >> (APINT_BITS_PER_WORD - wordShift); 1251 val[offset] = pVal[0] << wordShift; 1252 for (i = 0; i < offset; ++i) 1253 val[i] = 0; 1254 return APInt(val, BitWidth).clearUnusedBits(); 1255} 1256 1257APInt APInt::rotl(uint32_t rotateAmt) const { 1258 if (rotateAmt == 0) 1259 return *this; 1260 // Don't get too fancy, just use existing shift/or facilities 1261 APInt hi(*this); 1262 APInt lo(*this); 1263 hi.shl(rotateAmt); 1264 lo.lshr(BitWidth - rotateAmt); 1265 return hi | lo; 1266} 1267 1268APInt APInt::rotr(uint32_t rotateAmt) const { 1269 if (rotateAmt == 0) 1270 return *this; 1271 // Don't get too fancy, just use existing shift/or facilities 1272 APInt hi(*this); 1273 APInt lo(*this); 1274 lo.lshr(rotateAmt); 1275 hi.shl(BitWidth - rotateAmt); 1276 return hi | lo; 1277} 1278 1279// Square Root - this method computes and returns the square root of "this". 1280// Three mechanisms are used for computation. For small values (<= 5 bits), 1281// a table lookup is done. This gets some performance for common cases. For 1282// values using less than 52 bits, the value is converted to double and then 1283// the libc sqrt function is called. The result is rounded and then converted 1284// back to a uint64_t which is then used to construct the result. Finally, 1285// the Babylonian method for computing square roots is used. 1286APInt APInt::sqrt() const { 1287 1288 // Determine the magnitude of the value. 1289 uint32_t magnitude = getActiveBits(); 1290 1291 // Use a fast table for some small values. This also gets rid of some 1292 // rounding errors in libc sqrt for small values. 1293 if (magnitude <= 5) { 1294 static const uint8_t results[32] = { 1295 /* 0 */ 0, 1296 /* 1- 2 */ 1, 1, 1297 /* 3- 6 */ 2, 2, 2, 2, 1298 /* 7-12 */ 3, 3, 3, 3, 3, 3, 1299 /* 13-20 */ 4, 4, 4, 4, 4, 4, 4, 4, 1300 /* 21-30 */ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1301 /* 31 */ 6 1302 }; 1303 return APInt(BitWidth, results[ (isSingleWord() ? VAL : pVal[0]) ]); 1304 } 1305 1306 // If the magnitude of the value fits in less than 52 bits (the precision of 1307 // an IEEE double precision floating point value), then we can use the 1308 // libc sqrt function which will probably use a hardware sqrt computation. 1309 // This should be faster than the algorithm below. 1310 if (magnitude < 52) { 1311#ifdef _MSC_VER 1312 // Amazingly, VC++ doesn't have round(). 1313 return APInt(BitWidth, 1314 uint64_t(::sqrt(double(isSingleWord()?VAL:pVal[0]))) + 0.5); 1315#else 1316 return APInt(BitWidth, 1317 uint64_t(::round(::sqrt(double(isSingleWord()?VAL:pVal[0]))))); 1318#endif 1319 } 1320 1321 // Okay, all the short cuts are exhausted. We must compute it. The following 1322 // is a classical Babylonian method for computing the square root. This code 1323 // was adapted to APINt from a wikipedia article on such computations. 1324 // See http://www.wikipedia.org/ and go to the page named 1325 // Calculate_an_integer_square_root. 1326 uint32_t nbits = BitWidth, i = 4; 1327 APInt testy(BitWidth, 16); 1328 APInt x_old(BitWidth, 1); 1329 APInt x_new(BitWidth, 0); 1330 APInt two(BitWidth, 2); 1331 1332 // Select a good starting value using binary logarithms. 1333 for (;; i += 2, testy = testy.shl(2)) 1334 if (i >= nbits || this->ule(testy)) { 1335 x_old = x_old.shl(i / 2); 1336 break; 1337 } 1338 1339 // Use the Babylonian method to arrive at the integer square root: 1340 for (;;) { 1341 x_new = (this->udiv(x_old) + x_old).udiv(two); 1342 if (x_old.ule(x_new)) 1343 break; 1344 x_old = x_new; 1345 } 1346 1347 // Make sure we return the closest approximation 1348 // NOTE: The rounding calculation below is correct. It will produce an 1349 // off-by-one discrepancy with results from pari/gp. That discrepancy has been 1350 // determined to be a rounding issue with pari/gp as it begins to use a 1351 // floating point representation after 192 bits. There are no discrepancies 1352 // between this algorithm and pari/gp for bit widths < 192 bits. 1353 APInt square(x_old * x_old); 1354 APInt nextSquare((x_old + 1) * (x_old +1)); 1355 if (this->ult(square)) 1356 return x_old; 1357 else if (this->ule(nextSquare)) { 1358 APInt midpoint((nextSquare - square).udiv(two)); 1359 APInt offset(*this - square); 1360 if (offset.ult(midpoint)) 1361 return x_old; 1362 else 1363 return x_old + 1; 1364 } else 1365 assert(0 && "Error in APInt::sqrt computation"); 1366 return x_old + 1; 1367} 1368 1369/// Implementation of Knuth's Algorithm D (Division of nonnegative integers) 1370/// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The 1371/// variables here have the same names as in the algorithm. Comments explain 1372/// the algorithm and any deviation from it. 1373static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r, 1374 uint32_t m, uint32_t n) { 1375 assert(u && "Must provide dividend"); 1376 assert(v && "Must provide divisor"); 1377 assert(q && "Must provide quotient"); 1378 assert(u != v && u != q && v != q && "Must us different memory"); 1379 assert(n>1 && "n must be > 1"); 1380 1381 // Knuth uses the value b as the base of the number system. In our case b 1382 // is 2^31 so we just set it to -1u. 1383 uint64_t b = uint64_t(1) << 32; 1384 1385 DEBUG(cerr << "KnuthDiv: m=" << m << " n=" << n << '\n'); 1386 DEBUG(cerr << "KnuthDiv: original:"); 1387 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]); 1388 DEBUG(cerr << " by"); 1389 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]); 1390 DEBUG(cerr << '\n'); 1391 // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of 1392 // u and v by d. Note that we have taken Knuth's advice here to use a power 1393 // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of 1394 // 2 allows us to shift instead of multiply and it is easy to determine the 1395 // shift amount from the leading zeros. We are basically normalizing the u 1396 // and v so that its high bits are shifted to the top of v's range without 1397 // overflow. Note that this can require an extra word in u so that u must 1398 // be of length m+n+1. 1399 uint32_t shift = CountLeadingZeros_32(v[n-1]); 1400 uint32_t v_carry = 0; 1401 uint32_t u_carry = 0; 1402 if (shift) { 1403 for (uint32_t i = 0; i < m+n; ++i) { 1404 uint32_t u_tmp = u[i] >> (32 - shift); 1405 u[i] = (u[i] << shift) | u_carry; 1406 u_carry = u_tmp; 1407 } 1408 for (uint32_t i = 0; i < n; ++i) { 1409 uint32_t v_tmp = v[i] >> (32 - shift); 1410 v[i] = (v[i] << shift) | v_carry; 1411 v_carry = v_tmp; 1412 } 1413 } 1414 u[m+n] = u_carry; 1415 DEBUG(cerr << "KnuthDiv: normal:"); 1416 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << std::setbase(16) << u[i]); 1417 DEBUG(cerr << " by"); 1418 DEBUG(for (int i = n; i >0; i--) cerr << " " << std::setbase(16) << v[i-1]); 1419 DEBUG(cerr << '\n'); 1420 1421 // D2. [Initialize j.] Set j to m. This is the loop counter over the places. 1422 int j = m; 1423 do { 1424 DEBUG(cerr << "KnuthDiv: quotient digit #" << j << '\n'); 1425 // D3. [Calculate q'.]. 1426 // Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q') 1427 // Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r') 1428 // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease 1429 // qp by 1, inrease rp by v[n-1], and repeat this test if rp < b. The test 1430 // on v[n-2] determines at high speed most of the cases in which the trial 1431 // value qp is one too large, and it eliminates all cases where qp is two 1432 // too large. 1433 uint64_t dividend = ((uint64_t(u[j+n]) << 32) + u[j+n-1]); 1434 DEBUG(cerr << "KnuthDiv: dividend == " << dividend << '\n'); 1435 uint64_t qp = dividend / v[n-1]; 1436 uint64_t rp = dividend % v[n-1]; 1437 if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) { 1438 qp--; 1439 rp += v[n-1]; 1440 if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2])) 1441 qp--; 1442 } 1443 DEBUG(cerr << "KnuthDiv: qp == " << qp << ", rp == " << rp << '\n'); 1444 1445 // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with 1446 // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation 1447 // consists of a simple multiplication by a one-place number, combined with 1448 // a subtraction. 1449 bool isNeg = false; 1450 for (uint32_t i = 0; i < n; ++i) { 1451 uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32); 1452 uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]); 1453 bool borrow = subtrahend > u_tmp; 1454 DEBUG(cerr << "KnuthDiv: u_tmp == " << u_tmp 1455 << ", subtrahend == " << subtrahend 1456 << ", borrow = " << borrow << '\n'); 1457 1458 uint64_t result = u_tmp - subtrahend; 1459 uint32_t k = j + i; 1460 u[k++] = result & (b-1); // subtract low word 1461 u[k++] = result >> 32; // subtract high word 1462 while (borrow && k <= m+n) { // deal with borrow to the left 1463 borrow = u[k] == 0; 1464 u[k]--; 1465 k++; 1466 } 1467 isNeg |= borrow; 1468 DEBUG(cerr << "KnuthDiv: u[j+i] == " << u[j+i] << ", u[j+i+1] == " << 1469 u[j+i+1] << '\n'); 1470 } 1471 DEBUG(cerr << "KnuthDiv: after subtraction:"); 1472 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]); 1473 DEBUG(cerr << '\n'); 1474 // The digits (u[j+n]...u[j]) should be kept positive; if the result of 1475 // this step is actually negative, (u[j+n]...u[j]) should be left as the 1476 // true value plus b**(n+1), namely as the b's complement of 1477 // the true value, and a "borrow" to the left should be remembered. 1478 // 1479 if (isNeg) { 1480 bool carry = true; // true because b's complement is "complement + 1" 1481 for (uint32_t i = 0; i <= m+n; ++i) { 1482 u[i] = ~u[i] + carry; // b's complement 1483 carry = carry && u[i] == 0; 1484 } 1485 } 1486 DEBUG(cerr << "KnuthDiv: after complement:"); 1487 DEBUG(for (int i = m+n; i >=0; i--) cerr << " " << u[i]); 1488 DEBUG(cerr << '\n'); 1489 1490 // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was 1491 // negative, go to step D6; otherwise go on to step D7. 1492 q[j] = qp; 1493 if (isNeg) { 1494 // D6. [Add back]. The probability that this step is necessary is very 1495 // small, on the order of only 2/b. Make sure that test data accounts for 1496 // this possibility. Decrease q[j] by 1 1497 q[j]--; 1498 // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]). 1499 // A carry will occur to the left of u[j+n], and it should be ignored 1500 // since it cancels with the borrow that occurred in D4. 1501 bool carry = false; 1502 for (uint32_t i = 0; i < n; i++) { 1503 uint32_t limit = std::min(u[j+i],v[i]); 1504 u[j+i] += v[i] + carry; 1505 carry = u[j+i] < limit || (carry && u[j+i] == limit); 1506 } 1507 u[j+n] += carry; 1508 } 1509 DEBUG(cerr << "KnuthDiv: after correction:"); 1510 DEBUG(for (int i = m+n; i >=0; i--) cerr <<" " << u[i]); 1511 DEBUG(cerr << "\nKnuthDiv: digit result = " << q[j] << '\n'); 1512 1513 // D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3. 1514 } while (--j >= 0); 1515 1516 DEBUG(cerr << "KnuthDiv: quotient:"); 1517 DEBUG(for (int i = m; i >=0; i--) cerr <<" " << q[i]); 1518 DEBUG(cerr << '\n'); 1519 1520 // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired 1521 // remainder may be obtained by dividing u[...] by d. If r is non-null we 1522 // compute the remainder (urem uses this). 1523 if (r) { 1524 // The value d is expressed by the "shift" value above since we avoided 1525 // multiplication by d by using a shift left. So, all we have to do is 1526 // shift right here. In order to mak 1527 if (shift) { 1528 uint32_t carry = 0; 1529 DEBUG(cerr << "KnuthDiv: remainder:"); 1530 for (int i = n-1; i >= 0; i--) { 1531 r[i] = (u[i] >> shift) | carry; 1532 carry = u[i] << (32 - shift); 1533 DEBUG(cerr << " " << r[i]); 1534 } 1535 } else { 1536 for (int i = n-1; i >= 0; i--) { 1537 r[i] = u[i]; 1538 DEBUG(cerr << " " << r[i]); 1539 } 1540 } 1541 DEBUG(cerr << '\n'); 1542 } 1543 DEBUG(cerr << std::setbase(10) << '\n'); 1544} 1545 1546void APInt::divide(const APInt LHS, uint32_t lhsWords, 1547 const APInt &RHS, uint32_t rhsWords, 1548 APInt *Quotient, APInt *Remainder) 1549{ 1550 assert(lhsWords >= rhsWords && "Fractional result"); 1551 1552 // First, compose the values into an array of 32-bit words instead of 1553 // 64-bit words. This is a necessity of both the "short division" algorithm 1554 // and the the Knuth "classical algorithm" which requires there to be native 1555 // operations for +, -, and * on an m bit value with an m*2 bit result. We 1556 // can't use 64-bit operands here because we don't have native results of 1557 // 128-bits. Furthremore, casting the 64-bit values to 32-bit values won't 1558 // work on large-endian machines. 1559 uint64_t mask = ~0ull >> (sizeof(uint32_t)*8); 1560 uint32_t n = rhsWords * 2; 1561 uint32_t m = (lhsWords * 2) - n; 1562 1563 // Allocate space for the temporary values we need either on the stack, if 1564 // it will fit, or on the heap if it won't. 1565 uint32_t SPACE[128]; 1566 uint32_t *U = 0; 1567 uint32_t *V = 0; 1568 uint32_t *Q = 0; 1569 uint32_t *R = 0; 1570 if ((Remainder?4:3)*n+2*m+1 <= 128) { 1571 U = &SPACE[0]; 1572 V = &SPACE[m+n+1]; 1573 Q = &SPACE[(m+n+1) + n]; 1574 if (Remainder) 1575 R = &SPACE[(m+n+1) + n + (m+n)]; 1576 } else { 1577 U = new uint32_t[m + n + 1]; 1578 V = new uint32_t[n]; 1579 Q = new uint32_t[m+n]; 1580 if (Remainder) 1581 R = new uint32_t[n]; 1582 } 1583 1584 // Initialize the dividend 1585 memset(U, 0, (m+n+1)*sizeof(uint32_t)); 1586 for (unsigned i = 0; i < lhsWords; ++i) { 1587 uint64_t tmp = (LHS.getNumWords() == 1 ? LHS.VAL : LHS.pVal[i]); 1588 U[i * 2] = tmp & mask; 1589 U[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8); 1590 } 1591 U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm. 1592 1593 // Initialize the divisor 1594 memset(V, 0, (n)*sizeof(uint32_t)); 1595 for (unsigned i = 0; i < rhsWords; ++i) { 1596 uint64_t tmp = (RHS.getNumWords() == 1 ? RHS.VAL : RHS.pVal[i]); 1597 V[i * 2] = tmp & mask; 1598 V[i * 2 + 1] = tmp >> (sizeof(uint32_t)*8); 1599 } 1600 1601 // initialize the quotient and remainder 1602 memset(Q, 0, (m+n) * sizeof(uint32_t)); 1603 if (Remainder) 1604 memset(R, 0, n * sizeof(uint32_t)); 1605 1606 // Now, adjust m and n for the Knuth division. n is the number of words in 1607 // the divisor. m is the number of words by which the dividend exceeds the 1608 // divisor (i.e. m+n is the length of the dividend). These sizes must not 1609 // contain any zero words or the Knuth algorithm fails. 1610 for (unsigned i = n; i > 0 && V[i-1] == 0; i--) { 1611 n--; 1612 m++; 1613 } 1614 for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--) 1615 m--; 1616 1617 // If we're left with only a single word for the divisor, Knuth doesn't work 1618 // so we implement the short division algorithm here. This is much simpler 1619 // and faster because we are certain that we can divide a 64-bit quantity 1620 // by a 32-bit quantity at hardware speed and short division is simply a 1621 // series of such operations. This is just like doing short division but we 1622 // are using base 2^32 instead of base 10. 1623 assert(n != 0 && "Divide by zero?"); 1624 if (n == 1) { 1625 uint32_t divisor = V[0]; 1626 uint32_t remainder = 0; 1627 for (int i = m+n-1; i >= 0; i--) { 1628 uint64_t partial_dividend = uint64_t(remainder) << 32 | U[i]; 1629 if (partial_dividend == 0) { 1630 Q[i] = 0; 1631 remainder = 0; 1632 } else if (partial_dividend < divisor) { 1633 Q[i] = 0; 1634 remainder = partial_dividend; 1635 } else if (partial_dividend == divisor) { 1636 Q[i] = 1; 1637 remainder = 0; 1638 } else { 1639 Q[i] = partial_dividend / divisor; 1640 remainder = partial_dividend - (Q[i] * divisor); 1641 } 1642 } 1643 if (R) 1644 R[0] = remainder; 1645 } else { 1646 // Now we're ready to invoke the Knuth classical divide algorithm. In this 1647 // case n > 1. 1648 KnuthDiv(U, V, Q, R, m, n); 1649 } 1650 1651 // If the caller wants the quotient 1652 if (Quotient) { 1653 // Set up the Quotient value's memory. 1654 if (Quotient->BitWidth != LHS.BitWidth) { 1655 if (Quotient->isSingleWord()) 1656 Quotient->VAL = 0; 1657 else 1658 delete [] Quotient->pVal; 1659 Quotient->BitWidth = LHS.BitWidth; 1660 if (!Quotient->isSingleWord()) 1661 Quotient->pVal = getClearedMemory(Quotient->getNumWords()); 1662 } else 1663 Quotient->clear(); 1664 1665 // The quotient is in Q. Reconstitute the quotient into Quotient's low 1666 // order words. 1667 if (lhsWords == 1) { 1668 uint64_t tmp = 1669 uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2)); 1670 if (Quotient->isSingleWord()) 1671 Quotient->VAL = tmp; 1672 else 1673 Quotient->pVal[0] = tmp; 1674 } else { 1675 assert(!Quotient->isSingleWord() && "Quotient APInt not large enough"); 1676 for (unsigned i = 0; i < lhsWords; ++i) 1677 Quotient->pVal[i] = 1678 uint64_t(Q[i*2]) | (uint64_t(Q[i*2+1]) << (APINT_BITS_PER_WORD / 2)); 1679 } 1680 } 1681 1682 // If the caller wants the remainder 1683 if (Remainder) { 1684 // Set up the Remainder value's memory. 1685 if (Remainder->BitWidth != RHS.BitWidth) { 1686 if (Remainder->isSingleWord()) 1687 Remainder->VAL = 0; 1688 else 1689 delete [] Remainder->pVal; 1690 Remainder->BitWidth = RHS.BitWidth; 1691 if (!Remainder->isSingleWord()) 1692 Remainder->pVal = getClearedMemory(Remainder->getNumWords()); 1693 } else 1694 Remainder->clear(); 1695 1696 // The remainder is in R. Reconstitute the remainder into Remainder's low 1697 // order words. 1698 if (rhsWords == 1) { 1699 uint64_t tmp = 1700 uint64_t(R[0]) | (uint64_t(R[1]) << (APINT_BITS_PER_WORD / 2)); 1701 if (Remainder->isSingleWord()) 1702 Remainder->VAL = tmp; 1703 else 1704 Remainder->pVal[0] = tmp; 1705 } else { 1706 assert(!Remainder->isSingleWord() && "Remainder APInt not large enough"); 1707 for (unsigned i = 0; i < rhsWords; ++i) 1708 Remainder->pVal[i] = 1709 uint64_t(R[i*2]) | (uint64_t(R[i*2+1]) << (APINT_BITS_PER_WORD / 2)); 1710 } 1711 } 1712 1713 // Clean up the memory we allocated. 1714 if (U != &SPACE[0]) { 1715 delete [] U; 1716 delete [] V; 1717 delete [] Q; 1718 delete [] R; 1719 } 1720} 1721 1722APInt APInt::udiv(const APInt& RHS) const { 1723 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 1724 1725 // First, deal with the easy case 1726 if (isSingleWord()) { 1727 assert(RHS.VAL != 0 && "Divide by zero?"); 1728 return APInt(BitWidth, VAL / RHS.VAL); 1729 } 1730 1731 // Get some facts about the LHS and RHS number of bits and words 1732 uint32_t rhsBits = RHS.getActiveBits(); 1733 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); 1734 assert(rhsWords && "Divided by zero???"); 1735 uint32_t lhsBits = this->getActiveBits(); 1736 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1); 1737 1738 // Deal with some degenerate cases 1739 if (!lhsWords) 1740 // 0 / X ===> 0 1741 return APInt(BitWidth, 0); 1742 else if (lhsWords < rhsWords || this->ult(RHS)) { 1743 // X / Y ===> 0, iff X < Y 1744 return APInt(BitWidth, 0); 1745 } else if (*this == RHS) { 1746 // X / X ===> 1 1747 return APInt(BitWidth, 1); 1748 } else if (lhsWords == 1 && rhsWords == 1) { 1749 // All high words are zero, just use native divide 1750 return APInt(BitWidth, this->pVal[0] / RHS.pVal[0]); 1751 } 1752 1753 // We have to compute it the hard way. Invoke the Knuth divide algorithm. 1754 APInt Quotient(1,0); // to hold result. 1755 divide(*this, lhsWords, RHS, rhsWords, &Quotient, 0); 1756 return Quotient; 1757} 1758 1759APInt APInt::urem(const APInt& RHS) const { 1760 assert(BitWidth == RHS.BitWidth && "Bit widths must be the same"); 1761 if (isSingleWord()) { 1762 assert(RHS.VAL != 0 && "Remainder by zero?"); 1763 return APInt(BitWidth, VAL % RHS.VAL); 1764 } 1765 1766 // Get some facts about the LHS 1767 uint32_t lhsBits = getActiveBits(); 1768 uint32_t lhsWords = !lhsBits ? 0 : (whichWord(lhsBits - 1) + 1); 1769 1770 // Get some facts about the RHS 1771 uint32_t rhsBits = RHS.getActiveBits(); 1772 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); 1773 assert(rhsWords && "Performing remainder operation by zero ???"); 1774 1775 // Check the degenerate cases 1776 if (lhsWords == 0) { 1777 // 0 % Y ===> 0 1778 return APInt(BitWidth, 0); 1779 } else if (lhsWords < rhsWords || this->ult(RHS)) { 1780 // X % Y ===> X, iff X < Y 1781 return *this; 1782 } else if (*this == RHS) { 1783 // X % X == 0; 1784 return APInt(BitWidth, 0); 1785 } else if (lhsWords == 1) { 1786 // All high words are zero, just use native remainder 1787 return APInt(BitWidth, pVal[0] % RHS.pVal[0]); 1788 } 1789 1790 // We have to compute it the hard way. Invoke the Knuth divide algorithm. 1791 APInt Remainder(1,0); 1792 divide(*this, lhsWords, RHS, rhsWords, 0, &Remainder); 1793 return Remainder; 1794} 1795 1796void APInt::udivrem(const APInt &LHS, const APInt &RHS, 1797 APInt &Quotient, APInt &Remainder) { 1798 // Get some size facts about the dividend and divisor 1799 uint32_t lhsBits = LHS.getActiveBits(); 1800 uint32_t lhsWords = !lhsBits ? 0 : (APInt::whichWord(lhsBits - 1) + 1); 1801 uint32_t rhsBits = RHS.getActiveBits(); 1802 uint32_t rhsWords = !rhsBits ? 0 : (APInt::whichWord(rhsBits - 1) + 1); 1803 1804 // Check the degenerate cases 1805 if (lhsWords == 0) { 1806 Quotient = 0; // 0 / Y ===> 0 1807 Remainder = 0; // 0 % Y ===> 0 1808 return; 1809 } 1810 1811 if (lhsWords < rhsWords || LHS.ult(RHS)) { 1812 Quotient = 0; // X / Y ===> 0, iff X < Y 1813 Remainder = LHS; // X % Y ===> X, iff X < Y 1814 return; 1815 } 1816 1817 if (LHS == RHS) { 1818 Quotient = 1; // X / X ===> 1 1819 Remainder = 0; // X % X ===> 0; 1820 return; 1821 } 1822 1823 if (lhsWords == 1 && rhsWords == 1) { 1824 // There is only one word to consider so use the native versions. 1825 if (LHS.isSingleWord()) { 1826 Quotient = APInt(LHS.getBitWidth(), LHS.VAL / RHS.VAL); 1827 Remainder = APInt(LHS.getBitWidth(), LHS.VAL % RHS.VAL); 1828 } else { 1829 Quotient = APInt(LHS.getBitWidth(), LHS.pVal[0] / RHS.pVal[0]); 1830 Remainder = APInt(LHS.getBitWidth(), LHS.pVal[0] % RHS.pVal[0]); 1831 } 1832 return; 1833 } 1834 1835 // Okay, lets do it the long way 1836 divide(LHS, lhsWords, RHS, rhsWords, &Quotient, &Remainder); 1837} 1838 1839void APInt::fromString(uint32_t numbits, const char *str, uint32_t slen, 1840 uint8_t radix) { 1841 // Check our assumptions here 1842 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) && 1843 "Radix should be 2, 8, 10, or 16!"); 1844 assert(str && "String is null?"); 1845 bool isNeg = str[0] == '-'; 1846 if (isNeg) 1847 str++, slen--; 1848 assert((slen <= numbits || radix != 2) && "Insufficient bit width"); 1849 assert((slen*3 <= numbits || radix != 8) && "Insufficient bit width"); 1850 assert((slen*4 <= numbits || radix != 16) && "Insufficient bit width"); 1851 assert(((slen*64)/22 <= numbits || radix != 10) && "Insufficient bit width"); 1852 1853 // Allocate memory 1854 if (!isSingleWord()) 1855 pVal = getClearedMemory(getNumWords()); 1856 1857 // Figure out if we can shift instead of multiply 1858 uint32_t shift = (radix == 16 ? 4 : radix == 8 ? 3 : radix == 2 ? 1 : 0); 1859 1860 // Set up an APInt for the digit to add outside the loop so we don't 1861 // constantly construct/destruct it. 1862 APInt apdigit(getBitWidth(), 0); 1863 APInt apradix(getBitWidth(), radix); 1864 1865 // Enter digit traversal loop 1866 for (unsigned i = 0; i < slen; i++) { 1867 // Get a digit 1868 uint32_t digit = 0; 1869 char cdigit = str[i]; 1870 if (radix == 16) { 1871 if (!isxdigit(cdigit)) 1872 assert(0 && "Invalid hex digit in string"); 1873 if (isdigit(cdigit)) 1874 digit = cdigit - '0'; 1875 else if (cdigit >= 'a') 1876 digit = cdigit - 'a' + 10; 1877 else if (cdigit >= 'A') 1878 digit = cdigit - 'A' + 10; 1879 else 1880 assert(0 && "huh? we shouldn't get here"); 1881 } else if (isdigit(cdigit)) { 1882 digit = cdigit - '0'; 1883 } else { 1884 assert(0 && "Invalid character in digit string"); 1885 } 1886 1887 // Shift or multiply the value by the radix 1888 if (shift) 1889 *this <<= shift; 1890 else 1891 *this *= apradix; 1892 1893 // Add in the digit we just interpreted 1894 if (apdigit.isSingleWord()) 1895 apdigit.VAL = digit; 1896 else 1897 apdigit.pVal[0] = digit; 1898 *this += apdigit; 1899 } 1900 // If its negative, put it in two's complement form 1901 if (isNeg) { 1902 (*this)--; 1903 this->flip(); 1904 } 1905} 1906 1907std::string APInt::toString(uint8_t radix, bool wantSigned) const { 1908 assert((radix == 10 || radix == 8 || radix == 16 || radix == 2) && 1909 "Radix should be 2, 8, 10, or 16!"); 1910 static const char *digits[] = { 1911 "0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F" 1912 }; 1913 std::string result; 1914 uint32_t bits_used = getActiveBits(); 1915 if (isSingleWord()) { 1916 char buf[65]; 1917 const char *format = (radix == 10 ? (wantSigned ? "%lld" : "%llu") : 1918 (radix == 16 ? "%llX" : (radix == 8 ? "%llo" : 0))); 1919 if (format) { 1920 if (wantSigned) { 1921 int64_t sextVal = (int64_t(VAL) << (APINT_BITS_PER_WORD-BitWidth)) >> 1922 (APINT_BITS_PER_WORD-BitWidth); 1923 sprintf(buf, format, sextVal); 1924 } else 1925 sprintf(buf, format, VAL); 1926 } else { 1927 memset(buf, 0, 65); 1928 uint64_t v = VAL; 1929 while (bits_used) { 1930 uint32_t bit = v & 1; 1931 bits_used--; 1932 buf[bits_used] = digits[bit][0]; 1933 v >>=1; 1934 } 1935 } 1936 result = buf; 1937 return result; 1938 } 1939 1940 if (radix != 10) { 1941 // For the 2, 8 and 16 bit cases, we can just shift instead of divide 1942 // because the number of bits per digit (1,3 and 4 respectively) divides 1943 // equaly. We just shift until there value is zero. 1944 1945 // First, check for a zero value and just short circuit the logic below. 1946 if (*this == 0) 1947 result = "0"; 1948 else { 1949 APInt tmp(*this); 1950 size_t insert_at = 0; 1951 if (wantSigned && this->isNegative()) { 1952 // They want to print the signed version and it is a negative value 1953 // Flip the bits and add one to turn it into the equivalent positive 1954 // value and put a '-' in the result. 1955 tmp.flip(); 1956 tmp++; 1957 result = "-"; 1958 insert_at = 1; 1959 } 1960 // Just shift tmp right for each digit width until it becomes zero 1961 uint32_t shift = (radix == 16 ? 4 : (radix == 8 ? 3 : 1)); 1962 uint64_t mask = radix - 1; 1963 APInt zero(tmp.getBitWidth(), 0); 1964 while (tmp.ne(zero)) { 1965 unsigned digit = tmp.getZExtValue() & mask; 1966 tmp = tmp.lshr(shift); 1967 result.insert(insert_at, digits[digit]); 1968 } 1969 } 1970 return result; 1971 } 1972 1973 APInt tmp(*this); 1974 APInt divisor(4, radix); 1975 APInt zero(tmp.getBitWidth(), 0); 1976 size_t insert_at = 0; 1977 if (wantSigned && tmp[BitWidth-1]) { 1978 // They want to print the signed version and it is a negative value 1979 // Flip the bits and add one to turn it into the equivalent positive 1980 // value and put a '-' in the result. 1981 tmp.flip(); 1982 tmp++; 1983 result = "-"; 1984 insert_at = 1; 1985 } 1986 if (tmp == APInt(tmp.getBitWidth(), 0)) 1987 result = "0"; 1988 else while (tmp.ne(zero)) { 1989 APInt APdigit(1,0); 1990 APInt tmp2(tmp.getBitWidth(), 0); 1991 divide(tmp, tmp.getNumWords(), divisor, divisor.getNumWords(), &tmp2, 1992 &APdigit); 1993 uint32_t digit = APdigit.getZExtValue(); 1994 assert(digit < radix && "divide failed"); 1995 result.insert(insert_at,digits[digit]); 1996 tmp = tmp2; 1997 } 1998 1999 return result; 2000} 2001 2002#ifndef NDEBUG 2003void APInt::dump() const 2004{ 2005 cerr << "APInt(" << BitWidth << ")=" << std::setbase(16); 2006 if (isSingleWord()) 2007 cerr << VAL; 2008 else for (unsigned i = getNumWords(); i > 0; i--) { 2009 cerr << pVal[i-1] << " "; 2010 } 2011 cerr << " U(" << this->toString(10) << ") S(" << this->toStringSigned(10) 2012 << ")\n" << std::setbase(10); 2013} 2014#endif 2015