1 //===-- llvm/Support/APInt.h - For Arbitrary Precision Integer -*- C++ -*--===//
3 // The LLVM Compiler Infrastructure
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.
8 //===----------------------------------------------------------------------===//
10 // This file implements a class to represent arbitrary precision integral
13 //===----------------------------------------------------------------------===//
18 #include "llvm/Support/DataTypes.h"
24 /// Forward declaration.
27 APInt udiv(const APInt& LHS, const APInt& RHS);
28 APInt urem(const APInt& LHS, const APInt& RHS);
31 //===----------------------------------------------------------------------===//
33 //===----------------------------------------------------------------------===//
35 /// APInt - This class represents arbitrary precision constant integral values.
36 /// It is a functional replacement for common case unsigned integer type like
37 /// "unsigned", "unsigned long" or "uint64_t", but also allows non-byte-width
38 /// integer sizes and large integer value types such as 3-bits, 15-bits, or more
39 /// than 64-bits of precision. APInt provides a variety of arithmetic operators
40 /// and methods to manipulate integer values of any bit-width. It supports both
41 /// the typical integer arithmetic and comparison operations as well as bitwise
44 /// The class has several invariants worth noting:
45 /// * All bit, byte, and word positions are zero-based.
46 /// * Once the bit width is set, it doesn't change except by the Truncate,
47 /// SignExtend, or ZeroExtend operations.
48 /// * All binary operators must be on APInt instances of the same bit width.
49 /// Attempting to use these operators on instances with different bit
50 /// widths will yield an assertion.
51 /// * The value is stored canonically as an unsigned value. For operations
52 /// where it makes a difference, there are both signed and unsigned variants
53 /// of the operation. For example, sdiv and udiv. However, because the bit
54 /// widths must be the same, operations such as Mul and Add produce the same
55 /// results regardless of whether the values are interpreted as signed or
57 /// * In general, the class tries to follow the style of computation that LLVM
58 /// uses in its IR. This simplifies its use for LLVM.
60 /// @brief Class for arbitrary precision integers.
64 uint32_t BitWidth; ///< The number of bits in this APInt.
66 /// This union is used to store the integer value. When the
67 /// integer bit-width <= 64, it uses VAL;
68 /// otherwise it uses the pVal.
70 uint64_t VAL; ///< Used to store the <= 64 bits integer value.
71 uint64_t *pVal; ///< Used to store the >64 bits integer value.
74 /// This enum is just used to hold a constant we needed for APInt.
76 APINT_BITS_PER_WORD = sizeof(uint64_t) * 8,
77 APINT_WORD_SIZE = sizeof(uint64_t)
80 // Fast internal constructor
81 APInt(uint64_t* val, uint32_t bits) : BitWidth(bits), pVal(val) { }
83 /// Here one word's bitwidth equals to that of uint64_t.
84 /// @returns the number of words to hold the integer value of this APInt.
85 /// @brief Get the number of words.
86 inline uint32_t getNumWords() const {
87 return (BitWidth + APINT_BITS_PER_WORD - 1) / APINT_BITS_PER_WORD;
90 /// @returns true if the number of bits <= 64, false otherwise.
91 /// @brief Determine if this APInt just has one word to store value.
92 inline bool isSingleWord() const {
93 return BitWidth <= APINT_BITS_PER_WORD;
96 /// @returns the word position for the specified bit position.
97 static inline uint32_t whichWord(uint32_t bitPosition) {
98 return bitPosition / APINT_BITS_PER_WORD;
101 /// @returns the bit position in a word for the specified bit position
103 static inline uint32_t whichBit(uint32_t bitPosition) {
104 return bitPosition % APINT_BITS_PER_WORD;
107 /// @returns a uint64_t type integer with just bit position at
108 /// "whichBit(bitPosition)" setting, others zero.
109 static inline uint64_t maskBit(uint32_t bitPosition) {
110 return (static_cast<uint64_t>(1)) << whichBit(bitPosition);
113 /// This method is used internally to clear the to "N" bits that are not used
114 /// by the APInt. This is needed after the most significant word is assigned
115 /// a value to ensure that those bits are zero'd out.
116 /// @brief Clear high order bits
117 inline APInt& clearUnusedBits() {
118 // Compute how many bits are used in the final word
119 uint32_t wordBits = BitWidth % APINT_BITS_PER_WORD;
121 // If all bits are used, we want to leave the value alone. This also
122 // avoids the undefined behavior of >> when the shfit is the same size as
123 // the word size (64).
126 // Mask out the hight bits.
127 uint64_t mask = ~uint64_t(0ULL) >> (APINT_BITS_PER_WORD - wordBits);
131 pVal[getNumWords() - 1] &= mask;
135 /// @returns the corresponding word for the specified bit position.
136 /// @brief Get the word corresponding to a bit position
137 inline uint64_t getWord(uint32_t bitPosition) const {
138 return isSingleWord() ? VAL : pVal[whichWord(bitPosition)];
141 /// This is used by the constructors that take string arguments.
142 /// @brief Converts a char array into an APInt
143 void fromString(uint32_t numBits, const char *StrStart, uint32_t slen,
146 /// This is used by the toString method to divide by the radix. It simply
147 /// provides a more convenient form of divide for internal use since KnuthDiv
148 /// has specific constraints on its inputs. If those constraints are not met
149 /// then it provides a simpler form of divide.
150 /// @brief An internal division function for dividing APInts.
151 static void divide(const APInt LHS, uint32_t lhsWords,
152 const APInt &RHS, uint32_t rhsWords,
153 APInt *Quotient, APInt *Remainder);
156 /// @brief debug method
161 /// @brief Create a new APInt of numBits width, initialized as val.
162 APInt(uint32_t numBits, uint64_t val);
164 /// Note that numWords can be smaller or larger than the corresponding bit
165 /// width but any extraneous bits will be dropped.
166 /// @brief Create a new APInt of numBits width, initialized as bigVal[].
167 APInt(uint32_t numBits, uint32_t numWords, uint64_t bigVal[]);
169 /// @brief Create a new APInt by translating the string represented
171 APInt(uint32_t numBits, const std::string& Val, uint8_t radix);
173 /// @brief Create a new APInt by translating the char array represented
175 APInt(uint32_t numBits, const char StrStart[], uint32_t slen, uint8_t radix);
177 /// @brief Copy Constructor.
178 APInt(const APInt& API);
180 /// @brief Destructor.
183 /// @brief Copy assignment operator.
184 APInt& operator=(const APInt& RHS);
186 /// Assigns an integer value to the APInt.
187 /// @brief Assignment operator.
188 APInt& operator=(uint64_t RHS);
190 /// Increments the APInt by one.
191 /// @brief Postfix increment operator.
192 inline const APInt operator++(int) {
198 /// Increments the APInt by one.
199 /// @brief Prefix increment operator.
202 /// Decrements the APInt by one.
203 /// @brief Postfix decrement operator.
204 inline const APInt operator--(int) {
210 /// Decrements the APInt by one.
211 /// @brief Prefix decrement operator.
214 /// Performs bitwise AND operation on this APInt and the given APInt& RHS,
215 /// assigns the result to this APInt.
216 /// @brief Bitwise AND assignment operator.
217 APInt& operator&=(const APInt& RHS);
219 /// Performs bitwise OR operation on this APInt and the given APInt& RHS,
220 /// assigns the result to this APInt.
221 /// @brief Bitwise OR assignment operator.
222 APInt& operator|=(const APInt& RHS);
224 /// Performs bitwise XOR operation on this APInt and the given APInt& RHS,
225 /// assigns the result to this APInt.
226 /// @brief Bitwise XOR assignment operator.
227 APInt& operator^=(const APInt& RHS);
229 /// Performs a bitwise complement operation on this APInt.
230 /// @brief Bitwise complement operator.
231 APInt operator~() const;
233 /// Multiplies this APInt by the given APInt& RHS and
234 /// assigns the result to this APInt.
235 /// @brief Multiplication assignment operator.
236 APInt& operator*=(const APInt& RHS);
238 /// Adds this APInt by the given APInt& RHS and
239 /// assigns the result to this APInt.
240 /// @brief Addition assignment operator.
241 APInt& operator+=(const APInt& RHS);
243 /// Subtracts this APInt by the given APInt &RHS and
244 /// assigns the result to this APInt.
245 /// @brief Subtraction assignment operator.
246 APInt& operator-=(const APInt& RHS);
248 /// Performs bitwise AND operation on this APInt and
249 /// the given APInt& RHS.
250 /// @brief Bitwise AND operator.
251 APInt operator&(const APInt& RHS) const;
253 /// Performs bitwise OR operation on this APInt and the given APInt& RHS.
254 /// @brief Bitwise OR operator.
255 APInt operator|(const APInt& RHS) const;
257 /// Performs bitwise XOR operation on this APInt and the given APInt& RHS.
258 /// @brief Bitwise XOR operator.
259 APInt operator^(const APInt& RHS) const;
261 /// Performs logical negation operation on this APInt.
262 /// @brief Logical negation operator.
263 bool operator !() const;
265 /// Multiplies this APInt by the given APInt& RHS.
266 /// @brief Multiplication operator.
267 APInt operator*(const APInt& RHS) const;
269 /// Adds this APInt by the given APInt& RHS.
270 /// @brief Addition operator.
271 APInt operator+(const APInt& RHS) const;
273 /// Subtracts this APInt by the given APInt& RHS
274 /// @brief Subtraction operator.
275 APInt operator-(const APInt& RHS) const;
277 /// @brief Unary negation operator
278 inline APInt operator-() const {
279 return APInt(BitWidth, 0) - (*this);
282 /// @brief Array-indexing support.
283 bool operator[](uint32_t bitPosition) const;
285 /// Compare this APInt with the given APInt& RHS
286 /// for the validity of the equality relationship.
287 /// @brief Equality operator.
288 bool operator==(const APInt& RHS) const;
290 /// Compare this APInt with the given uint64_t value
291 /// for the validity of the equality relationship.
292 /// @brief Equality operator.
293 bool operator==(uint64_t Val) const;
295 /// Compare this APInt with the given APInt& RHS
296 /// for the validity of the inequality relationship.
297 /// @brief Inequality operator.
298 inline bool operator!=(const APInt& RHS) const {
299 return !((*this) == RHS);
302 /// Compare this APInt with the given uint64_t value
303 /// for the validity of the inequality relationship.
304 /// @brief Inequality operator.
305 inline bool operator!=(uint64_t Val) const {
306 return !((*this) == Val);
309 /// @brief Equality comparison
310 bool eq(const APInt &RHS) const {
311 return (*this) == RHS;
314 /// @brief Inequality comparison
315 bool ne(const APInt &RHS) const {
316 return !((*this) == RHS);
319 /// @brief Unsigned less than comparison
320 bool ult(const APInt& RHS) const;
322 /// @brief Signed less than comparison
323 bool slt(const APInt& RHS) const;
325 /// @brief Unsigned less or equal comparison
326 bool ule(const APInt& RHS) const {
327 return ult(RHS) || eq(RHS);
330 /// @brief Signed less or equal comparison
331 bool sle(const APInt& RHS) const {
332 return slt(RHS) || eq(RHS);
335 /// @brief Unsigned greather than comparison
336 bool ugt(const APInt& RHS) const {
337 return !ult(RHS) && !eq(RHS);
340 /// @brief Signed greather than comparison
341 bool sgt(const APInt& RHS) const {
342 return !slt(RHS) && !eq(RHS);
345 /// @brief Unsigned greater or equal comparison
346 bool uge(const APInt& RHS) const {
350 /// @brief Signed greather or equal comparison
351 bool sge(const APInt& RHS) const {
355 /// Arithmetic right-shift this APInt by shiftAmt.
356 /// @brief Arithmetic right-shift function.
357 APInt ashr(uint32_t shiftAmt) const;
359 /// Logical right-shift this APInt by shiftAmt.
360 /// @brief Logical right-shift function.
361 APInt lshr(uint32_t shiftAmt) const;
363 /// Left-shift this APInt by shiftAmt.
364 /// @brief Left-shift function.
365 APInt shl(uint32_t shiftAmt) const;
367 /// Signed divide this APInt by APInt RHS.
368 /// @brief Signed division function for APInt.
369 inline APInt sdiv(const APInt& RHS) const {
370 bool isNegativeLHS = (*this)[BitWidth - 1];
371 bool isNegativeRHS = RHS[RHS.BitWidth - 1];
372 APInt Result = APIntOps::udiv(
373 isNegativeLHS ? -(*this) : (*this), isNegativeRHS ? -RHS : RHS);
374 return isNegativeLHS != isNegativeRHS ? -Result : Result;
377 /// Unsigned divide this APInt by APInt RHS.
378 /// @brief Unsigned division function for APInt.
379 APInt udiv(const APInt& RHS) const;
381 /// Signed remainder operation on APInt.
382 /// @brief Function for signed remainder operation.
383 inline APInt srem(const APInt& RHS) const {
384 bool isNegativeLHS = (*this)[BitWidth - 1];
385 bool isNegativeRHS = RHS[RHS.BitWidth - 1];
386 APInt Result = APIntOps::urem(
387 isNegativeLHS ? -(*this) : (*this), isNegativeRHS ? -RHS : RHS);
388 return isNegativeLHS ? -Result : Result;
391 /// Unsigned remainder operation on APInt.
392 /// @brief Function for unsigned remainder operation.
393 APInt urem(const APInt& RHS) const;
395 /// Truncate the APInt to a specified width. It is an error to specify a width
396 /// that is greater than or equal to the current width.
397 /// @brief Truncate to new width.
398 void trunc(uint32_t width);
400 /// This operation sign extends the APInt to a new width. If the high order
401 /// bit is set, the fill on the left will be done with 1 bits, otherwise zero.
402 /// It is an error to specify a width that is less than or equal to the
404 /// @brief Sign extend to a new width.
405 void sext(uint32_t width);
407 /// This operation zero extends the APInt to a new width. Thie high order bits
408 /// are filled with 0 bits. It is an error to specify a width that is less
409 /// than or equal to the current width.
410 /// @brief Zero extend to a new width.
411 void zext(uint32_t width);
413 /// @brief Set every bit to 1.
416 /// Set the given bit to 1 whose position is given as "bitPosition".
417 /// @brief Set a given bit to 1.
418 APInt& set(uint32_t bitPosition);
420 /// @brief Set every bit to 0.
423 /// Set the given bit to 0 whose position is given as "bitPosition".
424 /// @brief Set a given bit to 0.
425 APInt& clear(uint32_t bitPosition);
427 /// @brief Toggle every bit to its opposite value.
430 /// Toggle a given bit to its opposite value whose position is given
431 /// as "bitPosition".
432 /// @brief Toggles a given bit to its opposite value.
433 APInt& flip(uint32_t bitPosition);
435 /// This function returns the number of active bits which is defined as the
436 /// bit width minus the number of leading zeros. This is used in several
437 /// computations to see how "wide" the value is.
438 /// @brief Compute the number of active bits in the value
439 inline uint32_t getActiveBits() const {
440 return BitWidth - countLeadingZeros();
443 /// @returns a uint64_t value from this APInt. If this APInt contains a single
444 /// word, just returns VAL, otherwise pVal[0].
445 inline uint64_t getValue(bool isSigned = false) const {
447 return isSigned ? int64_t(VAL << (64 - BitWidth)) >>
448 (64 - BitWidth) : VAL;
449 uint32_t n = getActiveBits();
452 assert(0 && "This APInt's bitwidth > 64");
455 /// @returns the largest value for an APInt of the specified bit-width and
456 /// if isSign == true, it should be largest signed value, otherwise largest
458 /// @brief Gets max value of the APInt with bitwidth <= 64.
459 static APInt getMaxValue(uint32_t numBits, bool isSign);
461 /// @returns the smallest value for an APInt of the given bit-width and
462 /// if isSign == true, it should be smallest signed value, otherwise zero.
463 /// @brief Gets min value of the APInt with bitwidth <= 64.
464 static APInt getMinValue(uint32_t numBits, bool isSign);
466 /// @returns the all-ones value for an APInt of the specified bit-width.
467 /// @brief Get the all-ones value.
468 static APInt getAllOnesValue(uint32_t numBits);
470 /// @returns the '0' value for an APInt of the specified bit-width.
471 /// @brief Get the '0' value.
472 static APInt getNullValue(uint32_t numBits);
474 /// This converts the APInt to a boolean valy as a test against zero.
475 /// @brief Boolean conversion function.
476 inline bool getBoolValue() const {
477 return countLeadingZeros() != BitWidth;
480 /// @returns a character interpretation of the APInt.
481 std::string toString(uint8_t radix = 10, bool wantSigned = true) const;
483 /// Get an APInt with the same BitWidth as this APInt, just zero mask
484 /// the low bits and right shift to the least significant bit.
485 /// @returns the high "numBits" bits of this APInt.
486 APInt getHiBits(uint32_t numBits) const;
488 /// Get an APInt with the same BitWidth as this APInt, just zero mask
490 /// @returns the low "numBits" bits of this APInt.
491 APInt getLoBits(uint32_t numBits) const;
493 /// @returns true if the argument APInt value is a power of two > 0.
494 bool isPowerOf2() const;
496 /// countLeadingZeros - This function is an APInt version of the
497 /// countLeadingZeros_{32,64} functions in MathExtras.h. It counts the number
498 /// of zeros from the most significant bit to the first one bit.
499 /// @returns getNumWords() * APINT_BITS_PER_WORD if the value is zero.
500 /// @returns the number of zeros from the most significant bit to the first
502 /// @brief Count the number of trailing one bits.
503 uint32_t countLeadingZeros() const;
505 /// countTrailingZeros - This function is an APInt version of the
506 /// countTrailingZoers_{32,64} functions in MathExtras.h. It counts
507 /// the number of zeros from the least significant bit to the first one bit.
508 /// @returns getNumWords() * APINT_BITS_PER_WORD if the value is zero.
509 /// @returns the number of zeros from the least significant bit to the first
511 /// @brief Count the number of trailing zero bits.
512 uint32_t countTrailingZeros() const;
514 /// countPopulation - This function is an APInt version of the
515 /// countPopulation_{32,64} functions in MathExtras.h. It counts the number
516 /// of 1 bits in the APInt value.
517 /// @returns 0 if the value is zero.
518 /// @returns the number of set bits.
519 /// @brief Count the number of bits set.
520 uint32_t countPopulation() const;
522 /// @returns the total number of bits.
523 inline uint32_t getBitWidth() const {
527 /// @brief Check if this APInt has a N-bits integer value.
528 inline bool isIntN(uint32_t N) const {
529 assert(N && "N == 0 ???");
530 if (isSingleWord()) {
531 return VAL == (VAL & (~0ULL >> (64 - N)));
533 APInt Tmp(N, getNumWords(), pVal);
534 return Tmp == (*this);
538 /// @returns a byte-swapped representation of this APInt Value.
539 APInt byteSwap() const;
541 /// @returns the floor log base 2 of this APInt.
542 inline uint32_t logBase2() const {
543 return getNumWords() * APINT_BITS_PER_WORD - 1 - countLeadingZeros();
546 /// @brief Converts this APInt to a double value.
547 double roundToDouble(bool isSigned = false) const;
553 /// @brief Check if the specified APInt has a N-bits integer value.
554 inline bool isIntN(uint32_t N, const APInt& APIVal) {
555 return APIVal.isIntN(N);
558 /// @returns true if the argument APInt value is a sequence of ones
559 /// starting at the least significant bit with the remainder zero.
560 inline const bool isMask(uint32_t numBits, const APInt& APIVal) {
561 return APIVal.getBoolValue() && ((APIVal + APInt(numBits,1)) & APIVal) == 0;
564 /// @returns true if the argument APInt value contains a sequence of ones
565 /// with the remainder zero.
566 inline const bool isShiftedMask(uint32_t numBits, const APInt& APIVal) {
567 return isMask(numBits, (APIVal - APInt(numBits,1)) | APIVal);
570 /// @returns a byte-swapped representation of the specified APInt Value.
571 inline APInt byteSwap(const APInt& APIVal) {
572 return APIVal.byteSwap();
575 /// @returns the floor log base 2 of the specified APInt value.
576 inline uint32_t logBase2(const APInt& APIVal) {
577 return APIVal.logBase2();
580 /// GreatestCommonDivisor - This function returns the greatest common
581 /// divisor of the two APInt values using Enclid's algorithm.
582 /// @returns the greatest common divisor of Val1 and Val2
583 /// @brief Compute GCD of two APInt values.
584 APInt GreatestCommonDivisor(const APInt& Val1, const APInt& Val2);
586 /// @brief Converts the given APInt to a double value.
587 inline double RoundAPIntToDouble(const APInt& APIVal, bool isSigned = false) {
588 return APIVal.roundToDouble(isSigned);
591 /// @brief Converts the given APInt to a float vlalue.
592 inline float RoundAPIntToFloat(const APInt& APIVal) {
593 return float(RoundAPIntToDouble(APIVal));
596 /// RoundDoubleToAPInt - This function convert a double value to an APInt value.
597 /// @brief Converts the given double value into a APInt.
598 APInt RoundDoubleToAPInt(double Double);
600 /// RoundFloatToAPInt - Converts a float value into an APInt value.
601 /// @brief Converts a float value into a APInt.
602 inline APInt RoundFloatToAPInt(float Float) {
603 return RoundDoubleToAPInt(double(Float));
606 /// Arithmetic right-shift the APInt by shiftAmt.
607 /// @brief Arithmetic right-shift function.
608 inline APInt ashr(const APInt& LHS, uint32_t shiftAmt) {
609 return LHS.ashr(shiftAmt);
612 /// Logical right-shift the APInt by shiftAmt.
613 /// @brief Logical right-shift function.
614 inline APInt lshr(const APInt& LHS, uint32_t shiftAmt) {
615 return LHS.lshr(shiftAmt);
618 /// Left-shift the APInt by shiftAmt.
619 /// @brief Left-shift function.
620 inline APInt shl(const APInt& LHS, uint32_t shiftAmt) {
621 return LHS.shl(shiftAmt);
624 /// Signed divide APInt LHS by APInt RHS.
625 /// @brief Signed division function for APInt.
626 inline APInt sdiv(const APInt& LHS, const APInt& RHS) {
627 return LHS.sdiv(RHS);
630 /// Unsigned divide APInt LHS by APInt RHS.
631 /// @brief Unsigned division function for APInt.
632 inline APInt udiv(const APInt& LHS, const APInt& RHS) {
633 return LHS.udiv(RHS);
636 /// Signed remainder operation on APInt.
637 /// @brief Function for signed remainder operation.
638 inline APInt srem(const APInt& LHS, const APInt& RHS) {
639 return LHS.srem(RHS);
642 /// Unsigned remainder operation on APInt.
643 /// @brief Function for unsigned remainder operation.
644 inline APInt urem(const APInt& LHS, const APInt& RHS) {
645 return LHS.urem(RHS);
648 /// Performs multiplication on APInt values.
649 /// @brief Function for multiplication operation.
650 inline APInt mul(const APInt& LHS, const APInt& RHS) {
654 /// Performs addition on APInt values.
655 /// @brief Function for addition operation.
656 inline APInt add(const APInt& LHS, const APInt& RHS) {
660 /// Performs subtraction on APInt values.
661 /// @brief Function for subtraction operation.
662 inline APInt sub(const APInt& LHS, const APInt& RHS) {
666 /// Performs bitwise AND operation on APInt LHS and
668 /// @brief Bitwise AND function for APInt.
669 inline APInt And(const APInt& LHS, const APInt& RHS) {
673 /// Performs bitwise OR operation on APInt LHS and APInt RHS.
674 /// @brief Bitwise OR function for APInt.
675 inline APInt Or(const APInt& LHS, const APInt& RHS) {
679 /// Performs bitwise XOR operation on APInt.
680 /// @brief Bitwise XOR function for APInt.
681 inline APInt Xor(const APInt& LHS, const APInt& RHS) {
685 /// Performs a bitwise complement operation on APInt.
686 /// @brief Bitwise complement function.
687 inline APInt Not(const APInt& APIVal) {
691 } // End of APIntOps namespace
693 } // End of llvm namespace