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"
29 /// \brief The behavior an operation has on an input of 0.
31 /// \brief The returned value is undefined.
33 /// \brief The returned value is numeric_limits<T>::max()
35 /// \brief The returned value is numeric_limits<T>::digits
39 /// \brief Count number of 0's from the least significant bit to the most
40 /// stopping at the first 1.
42 /// Only unsigned integral types are allowed.
44 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
47 typename enable_if_c<std::numeric_limits<T>::is_integer &&
48 !std::numeric_limits<T>::is_signed, std::size_t>::type
49 countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
53 return std::numeric_limits<T>::digits;
58 std::size_t ZeroBits = 0;
59 T Shift = std::numeric_limits<T>::digits >> 1;
60 T Mask = std::numeric_limits<T>::max() >> Shift;
62 if ((Val & Mask) == 0) {
74 typename enable_if_c<std::numeric_limits<T>::is_integer &&
75 std::numeric_limits<T>::is_signed, std::size_t>::type
76 countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) LLVM_DELETED_FUNCTION;
78 #if __GNUC__ >= 4 || _MSC_VER
80 inline std::size_t countTrailingZeros<uint32_t>(uint32_t Val, ZeroBehavior ZB) {
81 if (ZB != ZB_Undefined && Val == 0)
84 #if __has_builtin(__builtin_ctz) || __GNUC_PREREQ(4, 0)
85 return __builtin_ctz(Val);
88 _BitScanForward(&Index, Val);
93 #if !defined(_MSC_VER) || defined(_M_X64)
95 inline std::size_t countTrailingZeros<uint64_t>(uint64_t Val, ZeroBehavior ZB) {
96 if (ZB != ZB_Undefined && Val == 0)
99 #if __has_builtin(__builtin_ctzll) || __GNUC_PREREQ(4, 0)
100 return __builtin_ctzll(Val);
103 _BitScanForward64(&Index, Val);
110 /// \brief Count number of 0's from the most significant bit to the least
111 /// stopping at the first 1.
113 /// Only unsigned integral types are allowed.
115 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
117 template <typename T>
118 typename enable_if_c<std::numeric_limits<T>::is_integer &&
119 !std::numeric_limits<T>::is_signed, std::size_t>::type
120 countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
124 return std::numeric_limits<T>::digits;
127 std::size_t ZeroBits = 0;
128 for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
129 T Tmp = Val >> Shift;
139 template <typename T>
140 typename enable_if_c<std::numeric_limits<T>::is_integer &&
141 std::numeric_limits<T>::is_signed, std::size_t>::type
142 countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) LLVM_DELETED_FUNCTION;
144 #if __GNUC__ >= 4 || _MSC_VER
146 inline std::size_t countLeadingZeros<uint32_t>(uint32_t Val, ZeroBehavior ZB) {
147 if (ZB != ZB_Undefined && Val == 0)
150 #if __has_builtin(__builtin_clz) || __GNUC_PREREQ(4, 0)
151 return __builtin_clz(Val);
154 _BitScanReverse(&Index, Val);
159 #if !defined(_MSC_VER) || defined(_M_X64)
161 inline std::size_t countLeadingZeros<uint64_t>(uint64_t Val, ZeroBehavior ZB) {
162 if (ZB != ZB_Undefined && Val == 0)
165 #if __has_builtin(__builtin_clzll) || __GNUC_PREREQ(4, 0)
166 return __builtin_clzll(Val);
169 _BitScanReverse64(&Index, Val);
176 /// \brief Get the index of the first set bit starting from the least
179 /// Only unsigned integral types are allowed.
181 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
183 template <typename T>
184 typename enable_if_c<std::numeric_limits<T>::is_integer &&
185 !std::numeric_limits<T>::is_signed, T>::type
186 findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
187 if (ZB == ZB_Max && Val == 0)
188 return std::numeric_limits<T>::max();
190 return countTrailingZeros(Val, ZB_Undefined);
194 template <typename T>
195 typename enable_if_c<std::numeric_limits<T>::is_integer &&
196 std::numeric_limits<T>::is_signed, T>::type
197 findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) LLVM_DELETED_FUNCTION;
199 /// \brief Get the index of the last set bit starting from the least
202 /// Only unsigned integral types are allowed.
204 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
206 template <typename T>
207 typename enable_if_c<std::numeric_limits<T>::is_integer &&
208 !std::numeric_limits<T>::is_signed, T>::type
209 findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
210 if (ZB == ZB_Max && Val == 0)
211 return std::numeric_limits<T>::max();
213 // Use ^ instead of - because both gcc and llvm can remove the associated ^
214 // in the __builtin_clz intrinsic on x86.
215 return countLeadingZeros(Val, ZB_Undefined) ^
216 (std::numeric_limits<T>::digits - 1);
220 template <typename T>
221 typename enable_if_c<std::numeric_limits<T>::is_integer &&
222 std::numeric_limits<T>::is_signed, T>::type
223 findLastSet(T Val, ZeroBehavior ZB = ZB_Max) LLVM_DELETED_FUNCTION;
225 /// \brief Macro compressed bit reversal table for 256 bits.
227 /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
228 static const unsigned char BitReverseTable256[256] = {
229 #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
230 #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
231 #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
232 R6(0), R6(2), R6(1), R6(3)
235 /// \brief Reverse the bits in \p Val.
236 template <typename T>
237 T reverseBits(T Val) {
238 unsigned char in[sizeof(Val)];
239 unsigned char out[sizeof(Val)];
240 std::memcpy(in, &Val, sizeof(Val));
241 for (unsigned i = 0; i < sizeof(Val); ++i)
242 out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
243 std::memcpy(&Val, out, sizeof(Val));
247 // NOTE: The following support functions use the _32/_64 extensions instead of
248 // type overloading so that signed and unsigned integers can be used without
251 /// Hi_32 - This function returns the high 32 bits of a 64 bit value.
252 inline uint32_t Hi_32(uint64_t Value) {
253 return static_cast<uint32_t>(Value >> 32);
256 /// Lo_32 - This function returns the low 32 bits of a 64 bit value.
257 inline uint32_t Lo_32(uint64_t Value) {
258 return static_cast<uint32_t>(Value);
261 /// isInt - Checks if an integer fits into the given bit width.
263 inline bool isInt(int64_t x) {
264 return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
266 // Template specializations to get better code for common cases.
268 inline bool isInt<8>(int64_t x) {
269 return static_cast<int8_t>(x) == x;
272 inline bool isInt<16>(int64_t x) {
273 return static_cast<int16_t>(x) == x;
276 inline bool isInt<32>(int64_t x) {
277 return static_cast<int32_t>(x) == x;
280 /// isShiftedInt<N,S> - Checks if a signed integer is an N bit number shifted
282 template<unsigned N, unsigned S>
283 inline bool isShiftedInt(int64_t x) {
284 return isInt<N+S>(x) && (x % (1<<S) == 0);
287 /// isUInt - Checks if an unsigned integer fits into the given bit width.
289 inline bool isUInt(uint64_t x) {
290 return N >= 64 || x < (UINT64_C(1)<<(N));
292 // Template specializations to get better code for common cases.
294 inline bool isUInt<8>(uint64_t x) {
295 return static_cast<uint8_t>(x) == x;
298 inline bool isUInt<16>(uint64_t x) {
299 return static_cast<uint16_t>(x) == x;
302 inline bool isUInt<32>(uint64_t x) {
303 return static_cast<uint32_t>(x) == x;
306 /// isShiftedUInt<N,S> - Checks if a unsigned integer is an N bit number shifted
308 template<unsigned N, unsigned S>
309 inline bool isShiftedUInt(uint64_t x) {
310 return isUInt<N+S>(x) && (x % (1<<S) == 0);
313 /// isUIntN - Checks if an unsigned integer fits into the given (dynamic)
315 inline bool isUIntN(unsigned N, uint64_t x) {
316 return x == (x & (~0ULL >> (64 - N)));
319 /// isIntN - Checks if an signed integer fits into the given (dynamic)
321 inline bool isIntN(unsigned N, int64_t x) {
322 return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
325 /// isMask_32 - This function returns true if the argument is a sequence of ones
326 /// starting at the least significant bit with the remainder zero (32 bit
327 /// version). Ex. isMask_32(0x0000FFFFU) == true.
328 inline bool isMask_32(uint32_t Value) {
329 return Value && ((Value + 1) & Value) == 0;
332 /// isMask_64 - This function returns true if the argument is a sequence of ones
333 /// starting at the least significant bit with the remainder zero (64 bit
335 inline bool isMask_64(uint64_t Value) {
336 return Value && ((Value + 1) & Value) == 0;
339 /// isShiftedMask_32 - This function returns true if the argument contains a
340 /// sequence of ones with the remainder zero (32 bit version.)
341 /// Ex. isShiftedMask_32(0x0000FF00U) == true.
342 inline bool isShiftedMask_32(uint32_t Value) {
343 return isMask_32((Value - 1) | Value);
346 /// isShiftedMask_64 - This function returns true if the argument contains a
347 /// sequence of ones with the remainder zero (64 bit version.)
348 inline bool isShiftedMask_64(uint64_t Value) {
349 return isMask_64((Value - 1) | Value);
352 /// isPowerOf2_32 - This function returns true if the argument is a power of
353 /// two > 0. Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
354 inline bool isPowerOf2_32(uint32_t Value) {
355 return Value && !(Value & (Value - 1));
358 /// isPowerOf2_64 - This function returns true if the argument is a power of two
359 /// > 0 (64 bit edition.)
360 inline bool isPowerOf2_64(uint64_t Value) {
361 return Value && !(Value & (Value - int64_t(1L)));
364 /// ByteSwap_16 - This function returns a byte-swapped representation of the
365 /// 16-bit argument, Value.
366 inline uint16_t ByteSwap_16(uint16_t Value) {
367 return sys::SwapByteOrder_16(Value);
370 /// ByteSwap_32 - This function returns a byte-swapped representation of the
371 /// 32-bit argument, Value.
372 inline uint32_t ByteSwap_32(uint32_t Value) {
373 return sys::SwapByteOrder_32(Value);
376 /// ByteSwap_64 - This function returns a byte-swapped representation of the
377 /// 64-bit argument, Value.
378 inline uint64_t ByteSwap_64(uint64_t Value) {
379 return sys::SwapByteOrder_64(Value);
382 /// CountLeadingOnes_32 - this function performs the operation of
383 /// counting the number of ones from the most significant bit to the first zero
384 /// bit. Ex. CountLeadingOnes_32(0xFF0FFF00) == 8.
385 /// Returns 32 if the word is all ones.
386 inline unsigned CountLeadingOnes_32(uint32_t Value) {
387 return countLeadingZeros(~Value);
390 /// CountLeadingOnes_64 - This function performs the operation
391 /// of counting the number of ones from the most significant bit to the first
392 /// zero bit (64 bit edition.)
393 /// Returns 64 if the word is all ones.
394 inline unsigned CountLeadingOnes_64(uint64_t Value) {
395 return countLeadingZeros(~Value);
398 /// CountTrailingOnes_32 - this function performs the operation of
399 /// counting the number of ones from the least significant bit to the first zero
400 /// bit. Ex. CountTrailingOnes_32(0x00FF00FF) == 8.
401 /// Returns 32 if the word is all ones.
402 inline unsigned CountTrailingOnes_32(uint32_t Value) {
403 return countTrailingZeros(~Value);
406 /// CountTrailingOnes_64 - This function performs the operation
407 /// of counting the number of ones from the least significant bit to the first
408 /// zero bit (64 bit edition.)
409 /// Returns 64 if the word is all ones.
410 inline unsigned CountTrailingOnes_64(uint64_t Value) {
411 return countTrailingZeros(~Value);
414 /// CountPopulation_32 - this function counts the number of set bits in a value.
415 /// Ex. CountPopulation(0xF000F000) = 8
416 /// Returns 0 if the word is zero.
417 inline unsigned CountPopulation_32(uint32_t Value) {
419 return __builtin_popcount(Value);
421 uint32_t v = Value - ((Value >> 1) & 0x55555555);
422 v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
423 return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
427 /// CountPopulation_64 - this function counts the number of set bits in a value,
428 /// (64 bit edition.)
429 inline unsigned CountPopulation_64(uint64_t Value) {
431 return __builtin_popcountll(Value);
433 uint64_t v = Value - ((Value >> 1) & 0x5555555555555555ULL);
434 v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
435 v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
436 return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
440 /// Log2_32 - This function returns the floor log base 2 of the specified value,
441 /// -1 if the value is zero. (32 bit edition.)
442 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
443 inline unsigned Log2_32(uint32_t Value) {
444 return 31 - countLeadingZeros(Value);
447 /// Log2_64 - This function returns the floor log base 2 of the specified value,
448 /// -1 if the value is zero. (64 bit edition.)
449 inline unsigned Log2_64(uint64_t Value) {
450 return 63 - countLeadingZeros(Value);
453 /// Log2_32_Ceil - This function returns the ceil log base 2 of the specified
454 /// value, 32 if the value is zero. (32 bit edition).
455 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
456 inline unsigned Log2_32_Ceil(uint32_t Value) {
457 return 32 - countLeadingZeros(Value - 1);
460 /// Log2_64_Ceil - This function returns the ceil log base 2 of the specified
461 /// value, 64 if the value is zero. (64 bit edition.)
462 inline unsigned Log2_64_Ceil(uint64_t Value) {
463 return 64 - countLeadingZeros(Value - 1);
466 /// GreatestCommonDivisor64 - Return the greatest common divisor of the two
467 /// values using Euclid's algorithm.
468 inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
477 /// BitsToDouble - This function takes a 64-bit integer and returns the bit
478 /// equivalent double.
479 inline double BitsToDouble(uint64_t Bits) {
488 /// BitsToFloat - This function takes a 32-bit integer and returns the bit
489 /// equivalent float.
490 inline float BitsToFloat(uint32_t Bits) {
499 /// DoubleToBits - This function takes a double and returns the bit
500 /// equivalent 64-bit integer. Note that copying doubles around
501 /// changes the bits of NaNs on some hosts, notably x86, so this
502 /// routine cannot be used if these bits are needed.
503 inline uint64_t DoubleToBits(double Double) {
512 /// FloatToBits - This function takes a float and returns the bit
513 /// equivalent 32-bit integer. Note that copying floats around
514 /// changes the bits of NaNs on some hosts, notably x86, so this
515 /// routine cannot be used if these bits are needed.
516 inline uint32_t FloatToBits(float Float) {
525 /// Platform-independent wrappers for the C99 isnan() function.
529 /// Platform-independent wrappers for the C99 isinf() function.
533 /// MinAlign - A and B are either alignments or offsets. Return the minimum
534 /// alignment that may be assumed after adding the two together.
535 inline uint64_t MinAlign(uint64_t A, uint64_t B) {
536 // The largest power of 2 that divides both A and B.
538 // Replace "-Value" by "1+~Value" in the following commented code to avoid
539 // MSVC warning C4146
540 // return (A | B) & -(A | B);
541 return (A | B) & (1 + ~(A | B));
544 /// NextPowerOf2 - Returns the next power of two (in 64-bits)
545 /// that is strictly greater than A. Returns zero on overflow.
546 inline uint64_t NextPowerOf2(uint64_t A) {
556 /// Returns the next integer (mod 2**64) that is greater than or equal to
557 /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
561 /// RoundUpToAlignment(5, 8) = 8
562 /// RoundUpToAlignment(17, 8) = 24
563 /// RoundUpToAlignment(~0LL, 8) = 0
565 inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
566 return ((Value + Align - 1) / Align) * Align;
569 /// Returns the offset to the next integer (mod 2**64) that is greater than
570 /// or equal to \p Value and is a multiple of \p Align. \p Align must be
572 inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
573 return RoundUpToAlignment(Value, Align) - Value;
576 /// abs64 - absolute value of a 64-bit int. Not all environments support
577 /// "abs" on whatever their name for the 64-bit int type is. The absolute
578 /// value of the largest negative number is undefined, as with "abs".
579 inline int64_t abs64(int64_t x) {
580 return (x < 0) ? -x : x;
583 /// SignExtend32 - Sign extend B-bit number x to 32-bit int.
584 /// Usage int32_t r = SignExtend32<5>(x);
585 template <unsigned B> inline int32_t SignExtend32(uint32_t x) {
586 return int32_t(x << (32 - B)) >> (32 - B);
589 /// \brief Sign extend number in the bottom B bits of X to a 32-bit int.
590 /// Requires 0 < B <= 32.
591 inline int32_t SignExtend32(uint32_t X, unsigned B) {
592 return int32_t(X << (32 - B)) >> (32 - B);
595 /// SignExtend64 - Sign extend B-bit number x to 64-bit int.
596 /// Usage int64_t r = SignExtend64<5>(x);
597 template <unsigned B> inline int64_t SignExtend64(uint64_t x) {
598 return int64_t(x << (64 - B)) >> (64 - B);
601 /// \brief Sign extend number in the bottom B bits of X to a 64-bit int.
602 /// Requires 0 < B <= 64.
603 inline int64_t SignExtend64(uint64_t X, unsigned B) {
604 return int64_t(X << (64 - B)) >> (64 - B);
607 #if defined(_MSC_VER)
608 // Visual Studio defines the HUGE_VAL class of macros using purposeful
609 // constant arithmetic overflow, which it then warns on when encountered.
610 const float huge_valf = std::numeric_limits<float>::infinity();
612 const float huge_valf = HUGE_VALF;
614 } // End llvm namespace