1 //===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains some functions that are useful for math stuff.
12 //===----------------------------------------------------------------------===//
14 #ifndef LLVM_SUPPORT_MATHEXTRAS_H
15 #define LLVM_SUPPORT_MATHEXTRAS_H
17 #include "llvm/Support/Compiler.h"
18 #include "llvm/Support/SwapByteOrder.h"
19 #include "llvm/Support/type_traits.h"
28 /// \brief The behavior an operation has on an input of 0.
30 /// \brief The returned value is undefined.
32 /// \brief The returned value is numeric_limits<T>::max()
34 /// \brief The returned value is numeric_limits<T>::digits
38 /// \brief Count number of 0's from the least significant bit to the most
39 /// stopping at the first 1.
41 /// Only unsigned integral types are allowed.
43 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
46 typename enable_if_c<std::numeric_limits<T>::is_integer &&
47 !std::numeric_limits<T>::is_signed, std::size_t>::type
48 countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
52 return std::numeric_limits<T>::digits;
57 std::size_t ZeroBits = 0;
58 T Shift = std::numeric_limits<T>::digits >> 1;
59 T Mask = std::numeric_limits<T>::max() >> Shift;
61 if ((Val & Mask) == 0) {
73 typename enable_if_c<std::numeric_limits<T>::is_integer &&
74 std::numeric_limits<T>::is_signed, std::size_t>::type
75 countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) LLVM_DELETED_FUNCTION;
77 #if __GNUC__ >= 4 || _MSC_VER
79 inline std::size_t countTrailingZeros<uint32_t>(uint32_t Val, ZeroBehavior ZB) {
80 if (ZB != ZB_Undefined && Val == 0)
84 return __builtin_ctz(Val);
87 _BitScanForward(&Index, Val);
92 #if !defined(_MSC_VER) || defined(_M_X64)
94 inline std::size_t countTrailingZeros<uint64_t>(uint64_t Val, ZeroBehavior ZB) {
95 if (ZB != ZB_Undefined && Val == 0)
99 return __builtin_ctzll(Val);
102 _BitScanForward64(&Index, Val);
109 /// \brief Count number of 0's from the most significant bit to the least
110 /// stopping at the first 1.
112 /// Only unsigned integral types are allowed.
114 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
116 template <typename T>
117 typename enable_if_c<std::numeric_limits<T>::is_integer &&
118 !std::numeric_limits<T>::is_signed, std::size_t>::type
119 countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
123 return std::numeric_limits<T>::digits;
126 std::size_t ZeroBits = 0;
127 for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
128 T Tmp = Val >> Shift;
138 template <typename T>
139 typename enable_if_c<std::numeric_limits<T>::is_integer &&
140 std::numeric_limits<T>::is_signed, std::size_t>::type
141 countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) LLVM_DELETED_FUNCTION;
143 #if __GNUC__ >= 4 || _MSC_VER
145 inline std::size_t countLeadingZeros<uint32_t>(uint32_t Val, ZeroBehavior ZB) {
146 if (ZB != ZB_Undefined && Val == 0)
150 return __builtin_clz(Val);
153 _BitScanReverse(&Index, Val);
158 #if !defined(_MSC_VER) || defined(_M_X64)
160 inline std::size_t countLeadingZeros<uint64_t>(uint64_t Val, ZeroBehavior ZB) {
161 if (ZB != ZB_Undefined && Val == 0)
165 return __builtin_clzll(Val);
168 _BitScanReverse64(&Index, Val);
175 /// \brief Get the index of the first set bit starting from the least
178 /// Only unsigned integral types are allowed.
180 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
182 template <typename T>
183 typename enable_if_c<std::numeric_limits<T>::is_integer &&
184 !std::numeric_limits<T>::is_signed, T>::type
185 findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
186 if (ZB == ZB_Max && Val == 0)
187 return std::numeric_limits<T>::max();
189 return countTrailingZeros(Val, ZB_Undefined);
193 template <typename T>
194 typename enable_if_c<std::numeric_limits<T>::is_integer &&
195 std::numeric_limits<T>::is_signed, T>::type
196 findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) LLVM_DELETED_FUNCTION;
198 /// \brief Get the index of the last set bit starting from the least
201 /// Only unsigned integral types are allowed.
203 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
205 template <typename T>
206 typename enable_if_c<std::numeric_limits<T>::is_integer &&
207 !std::numeric_limits<T>::is_signed, T>::type
208 findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
209 if (ZB == ZB_Max && Val == 0)
210 return std::numeric_limits<T>::max();
212 // Use ^ instead of - because both gcc and llvm can remove the associated ^
213 // in the __builtin_clz intrinsic on x86.
214 return countLeadingZeros(Val, ZB_Undefined) ^
215 (std::numeric_limits<T>::digits - 1);
219 template <typename T>
220 typename enable_if_c<std::numeric_limits<T>::is_integer &&
221 std::numeric_limits<T>::is_signed, T>::type
222 findLastSet(T Val, ZeroBehavior ZB = ZB_Max) LLVM_DELETED_FUNCTION;
224 /// \brief Macro compressed bit reversal table for 256 bits.
226 /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
227 static const unsigned char BitReverseTable256[256] = {
228 #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
229 #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
230 #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
231 R6(0), R6(2), R6(1), R6(3)
234 /// \brief Reverse the bits in \p Val.
235 template <typename T>
236 T reverseBits(T Val) {
237 unsigned char in[sizeof(Val)];
238 unsigned char out[sizeof(Val)];
239 std::memcpy(in, &Val, sizeof(Val));
240 for (unsigned i = 0; i < sizeof(Val); ++i)
241 out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
242 std::memcpy(&Val, out, sizeof(Val));
246 // NOTE: The following support functions use the _32/_64 extensions instead of
247 // type overloading so that signed and unsigned integers can be used without
250 /// Hi_32 - This function returns the high 32 bits of a 64 bit value.
251 inline uint32_t Hi_32(uint64_t Value) {
252 return static_cast<uint32_t>(Value >> 32);
255 /// Lo_32 - This function returns the low 32 bits of a 64 bit value.
256 inline uint32_t Lo_32(uint64_t Value) {
257 return static_cast<uint32_t>(Value);
260 /// isInt - Checks if an integer fits into the given bit width.
262 inline bool isInt(int64_t x) {
263 return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
265 // Template specializations to get better code for common cases.
267 inline bool isInt<8>(int64_t x) {
268 return static_cast<int8_t>(x) == x;
271 inline bool isInt<16>(int64_t x) {
272 return static_cast<int16_t>(x) == x;
275 inline bool isInt<32>(int64_t x) {
276 return static_cast<int32_t>(x) == x;
279 /// isShiftedInt<N,S> - Checks if a signed integer is an N bit number shifted
281 template<unsigned N, unsigned S>
282 inline bool isShiftedInt(int64_t x) {
283 return isInt<N+S>(x) && (x % (1<<S) == 0);
286 /// isUInt - Checks if an unsigned integer fits into the given bit width.
288 inline bool isUInt(uint64_t x) {
289 return N >= 64 || x < (UINT64_C(1)<<(N));
291 // Template specializations to get better code for common cases.
293 inline bool isUInt<8>(uint64_t x) {
294 return static_cast<uint8_t>(x) == x;
297 inline bool isUInt<16>(uint64_t x) {
298 return static_cast<uint16_t>(x) == x;
301 inline bool isUInt<32>(uint64_t x) {
302 return static_cast<uint32_t>(x) == x;
305 /// isShiftedUInt<N,S> - Checks if a unsigned integer is an N bit number shifted
307 template<unsigned N, unsigned S>
308 inline bool isShiftedUInt(uint64_t x) {
309 return isUInt<N+S>(x) && (x % (1<<S) == 0);
312 /// isUIntN - Checks if an unsigned integer fits into the given (dynamic)
314 inline bool isUIntN(unsigned N, uint64_t x) {
315 return x == (x & (~0ULL >> (64 - N)));
318 /// isIntN - Checks if an signed integer fits into the given (dynamic)
320 inline bool isIntN(unsigned N, int64_t x) {
321 return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
324 /// isMask_32 - This function returns true if the argument is a sequence of ones
325 /// starting at the least significant bit with the remainder zero (32 bit
326 /// version). Ex. isMask_32(0x0000FFFFU) == true.
327 inline bool isMask_32(uint32_t Value) {
328 return Value && ((Value + 1) & Value) == 0;
331 /// isMask_64 - This function returns true if the argument is a sequence of ones
332 /// starting at the least significant bit with the remainder zero (64 bit
334 inline bool isMask_64(uint64_t Value) {
335 return Value && ((Value + 1) & Value) == 0;
338 /// isShiftedMask_32 - This function returns true if the argument contains a
339 /// sequence of ones with the remainder zero (32 bit version.)
340 /// Ex. isShiftedMask_32(0x0000FF00U) == true.
341 inline bool isShiftedMask_32(uint32_t Value) {
342 return isMask_32((Value - 1) | Value);
345 /// isShiftedMask_64 - This function returns true if the argument contains a
346 /// sequence of ones with the remainder zero (64 bit version.)
347 inline bool isShiftedMask_64(uint64_t Value) {
348 return isMask_64((Value - 1) | Value);
351 /// isPowerOf2_32 - This function returns true if the argument is a power of
352 /// two > 0. Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
353 inline bool isPowerOf2_32(uint32_t Value) {
354 return Value && !(Value & (Value - 1));
357 /// isPowerOf2_64 - This function returns true if the argument is a power of two
358 /// > 0 (64 bit edition.)
359 inline bool isPowerOf2_64(uint64_t Value) {
360 return Value && !(Value & (Value - int64_t(1L)));
363 /// ByteSwap_16 - This function returns a byte-swapped representation of the
364 /// 16-bit argument, Value.
365 inline uint16_t ByteSwap_16(uint16_t Value) {
366 return sys::SwapByteOrder_16(Value);
369 /// ByteSwap_32 - This function returns a byte-swapped representation of the
370 /// 32-bit argument, Value.
371 inline uint32_t ByteSwap_32(uint32_t Value) {
372 return sys::SwapByteOrder_32(Value);
375 /// ByteSwap_64 - This function returns a byte-swapped representation of the
376 /// 64-bit argument, Value.
377 inline uint64_t ByteSwap_64(uint64_t Value) {
378 return sys::SwapByteOrder_64(Value);
381 /// CountLeadingOnes_32 - this function performs the operation of
382 /// counting the number of ones from the most significant bit to the first zero
383 /// bit. Ex. CountLeadingOnes_32(0xFF0FFF00) == 8.
384 /// Returns 32 if the word is all ones.
385 inline unsigned CountLeadingOnes_32(uint32_t Value) {
386 return countLeadingZeros(~Value);
389 /// CountLeadingOnes_64 - This function performs the operation
390 /// of counting the number of ones from the most significant bit to the first
391 /// zero bit (64 bit edition.)
392 /// Returns 64 if the word is all ones.
393 inline unsigned CountLeadingOnes_64(uint64_t Value) {
394 return countLeadingZeros(~Value);
397 /// CountTrailingOnes_32 - this function performs the operation of
398 /// counting the number of ones from the least significant bit to the first zero
399 /// bit. Ex. CountTrailingOnes_32(0x00FF00FF) == 8.
400 /// Returns 32 if the word is all ones.
401 inline unsigned CountTrailingOnes_32(uint32_t Value) {
402 return countTrailingZeros(~Value);
405 /// CountTrailingOnes_64 - This function performs the operation
406 /// of counting the number of ones from the least significant bit to the first
407 /// zero bit (64 bit edition.)
408 /// Returns 64 if the word is all ones.
409 inline unsigned CountTrailingOnes_64(uint64_t Value) {
410 return countTrailingZeros(~Value);
413 /// CountPopulation_32 - this function counts the number of set bits in a value.
414 /// Ex. CountPopulation(0xF000F000) = 8
415 /// Returns 0 if the word is zero.
416 inline unsigned CountPopulation_32(uint32_t Value) {
418 return __builtin_popcount(Value);
420 uint32_t v = Value - ((Value >> 1) & 0x55555555);
421 v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
422 return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
426 /// CountPopulation_64 - this function counts the number of set bits in a value,
427 /// (64 bit edition.)
428 inline unsigned CountPopulation_64(uint64_t Value) {
430 return __builtin_popcountll(Value);
432 uint64_t v = Value - ((Value >> 1) & 0x5555555555555555ULL);
433 v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
434 v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
435 return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
439 /// Log2_32 - This function returns the floor log base 2 of the specified value,
440 /// -1 if the value is zero. (32 bit edition.)
441 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
442 inline unsigned Log2_32(uint32_t Value) {
443 return 31 - countLeadingZeros(Value);
446 /// Log2_64 - This function returns the floor log base 2 of the specified value,
447 /// -1 if the value is zero. (64 bit edition.)
448 inline unsigned Log2_64(uint64_t Value) {
449 return 63 - countLeadingZeros(Value);
452 /// Log2_32_Ceil - This function returns the ceil log base 2 of the specified
453 /// value, 32 if the value is zero. (32 bit edition).
454 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
455 inline unsigned Log2_32_Ceil(uint32_t Value) {
456 return 32 - countLeadingZeros(Value - 1);
459 /// Log2_64_Ceil - This function returns the ceil log base 2 of the specified
460 /// value, 64 if the value is zero. (64 bit edition.)
461 inline unsigned Log2_64_Ceil(uint64_t Value) {
462 return 64 - countLeadingZeros(Value - 1);
465 /// GreatestCommonDivisor64 - Return the greatest common divisor of the two
466 /// values using Euclid's algorithm.
467 inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
476 /// BitsToDouble - This function takes a 64-bit integer and returns the bit
477 /// equivalent double.
478 inline double BitsToDouble(uint64_t Bits) {
487 /// BitsToFloat - This function takes a 32-bit integer and returns the bit
488 /// equivalent float.
489 inline float BitsToFloat(uint32_t Bits) {
498 /// DoubleToBits - This function takes a double and returns the bit
499 /// equivalent 64-bit integer. Note that copying doubles around
500 /// changes the bits of NaNs on some hosts, notably x86, so this
501 /// routine cannot be used if these bits are needed.
502 inline uint64_t DoubleToBits(double Double) {
511 /// FloatToBits - This function takes a float and returns the bit
512 /// equivalent 32-bit integer. Note that copying floats around
513 /// changes the bits of NaNs on some hosts, notably x86, so this
514 /// routine cannot be used if these bits are needed.
515 inline uint32_t FloatToBits(float Float) {
524 /// Platform-independent wrappers for the C99 isnan() function.
528 /// Platform-independent wrappers for the C99 isinf() function.
532 /// MinAlign - A and B are either alignments or offsets. Return the minimum
533 /// alignment that may be assumed after adding the two together.
534 inline uint64_t MinAlign(uint64_t A, uint64_t B) {
535 // The largest power of 2 that divides both A and B.
537 // Replace "-Value" by "1+~Value" in the following commented code to avoid
538 // MSVC warning C4146
539 // return (A | B) & -(A | B);
540 return (A | B) & (1 + ~(A | B));
543 /// NextPowerOf2 - Returns the next power of two (in 64-bits)
544 /// that is strictly greater than A. Returns zero on overflow.
545 inline uint64_t NextPowerOf2(uint64_t A) {
555 /// Returns the next integer (mod 2**64) that is greater than or equal to
556 /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
560 /// RoundUpToAlignment(5, 8) = 8
561 /// RoundUpToAlignment(17, 8) = 24
562 /// RoundUpToAlignment(~0LL, 8) = 0
564 inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
565 return ((Value + Align - 1) / Align) * Align;
568 /// Returns the offset to the next integer (mod 2**64) that is greater than
569 /// or equal to \p Value and is a multiple of \p Align. \p Align must be
571 inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
572 return RoundUpToAlignment(Value, Align) - Value;
575 /// abs64 - absolute value of a 64-bit int. Not all environments support
576 /// "abs" on whatever their name for the 64-bit int type is. The absolute
577 /// value of the largest negative number is undefined, as with "abs".
578 inline int64_t abs64(int64_t x) {
579 return (x < 0) ? -x : x;
582 /// SignExtend32 - Sign extend B-bit number x to 32-bit int.
583 /// Usage int32_t r = SignExtend32<5>(x);
584 template <unsigned B> inline int32_t SignExtend32(uint32_t x) {
585 return int32_t(x << (32 - B)) >> (32 - B);
588 /// \brief Sign extend number in the bottom B bits of X to a 32-bit int.
589 /// Requires 0 < B <= 32.
590 inline int32_t SignExtend32(uint32_t X, unsigned B) {
591 return int32_t(X << (32 - B)) >> (32 - B);
594 /// SignExtend64 - Sign extend B-bit number x to 64-bit int.
595 /// Usage int64_t r = SignExtend64<5>(x);
596 template <unsigned B> inline int64_t SignExtend64(uint64_t x) {
597 return int64_t(x << (64 - B)) >> (64 - B);
600 /// \brief Sign extend number in the bottom B bits of X to a 64-bit int.
601 /// Requires 0 < B <= 64.
602 inline int64_t SignExtend64(uint64_t X, unsigned B) {
603 return int64_t(X << (64 - B)) >> (64 - B);
606 } // End llvm namespace