1//===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
2//
3//                     The LLVM Compiler Infrastructure
4//
5// This file is distributed under the University of Illinois Open Source
6// License. See LICENSE.TXT for details.
7//
8//===----------------------------------------------------------------------===//
9//
10// This file contains some functions that are useful for math stuff.
11//
12//===----------------------------------------------------------------------===//
13
14#ifndef LLVM_SUPPORT_MATHEXTRAS_H
15#define LLVM_SUPPORT_MATHEXTRAS_H
16
17#include "llvm/Support/Compiler.h"
18#include "llvm/Support/SwapByteOrder.h"
19#include "llvm/Support/type_traits.h"
20
21#include <cstring>
22
23#ifdef _MSC_VER
24# include <intrin.h>
25#endif
26
27namespace llvm {
28/// \brief The behavior an operation has on an input of 0.
29enum ZeroBehavior {
30  /// \brief The returned value is undefined.
31  ZB_Undefined,
32  /// \brief The returned value is numeric_limits<T>::max()
33  ZB_Max,
34  /// \brief The returned value is numeric_limits<T>::digits
35  ZB_Width
36};
37
38/// \brief Count number of 0's from the least significant bit to the most
39///   stopping at the first 1.
40///
41/// Only unsigned integral types are allowed.
42///
43/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
44///   valid arguments.
45template <typename T>
46typename enable_if_c<std::numeric_limits<T>::is_integer &&
47                     !std::numeric_limits<T>::is_signed, std::size_t>::type
48countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
49  (void)ZB;
50
51  if (!Val)
52    return std::numeric_limits<T>::digits;
53  if (Val & 0x1)
54    return 0;
55
56  // Bisection method.
57  std::size_t ZeroBits = 0;
58  T Shift = std::numeric_limits<T>::digits >> 1;
59  T Mask = std::numeric_limits<T>::max() >> Shift;
60  while (Shift) {
61    if ((Val & Mask) == 0) {
62      Val >>= Shift;
63      ZeroBits |= Shift;
64    }
65    Shift >>= 1;
66    Mask >>= Shift;
67  }
68  return ZeroBits;
69}
70
71// Disable signed.
72template <typename T>
73typename enable_if_c<std::numeric_limits<T>::is_integer &&
74                     std::numeric_limits<T>::is_signed, std::size_t>::type
75countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) LLVM_DELETED_FUNCTION;
76
77#if __GNUC__ >= 4 || _MSC_VER
78template <>
79inline std::size_t countTrailingZeros<uint32_t>(uint32_t Val, ZeroBehavior ZB) {
80  if (ZB != ZB_Undefined && Val == 0)
81    return 32;
82
83#if __has_builtin(__builtin_ctz) || __GNUC_PREREQ(4, 0)
84  return __builtin_ctz(Val);
85#elif _MSC_VER
86  unsigned long Index;
87  _BitScanForward(&Index, Val);
88  return Index;
89#endif
90}
91
92#if !defined(_MSC_VER) || defined(_M_X64)
93template <>
94inline std::size_t countTrailingZeros<uint64_t>(uint64_t Val, ZeroBehavior ZB) {
95  if (ZB != ZB_Undefined && Val == 0)
96    return 64;
97
98#if __has_builtin(__builtin_ctzll) || __GNUC_PREREQ(4, 0)
99  return __builtin_ctzll(Val);
100#elif _MSC_VER
101  unsigned long Index;
102  _BitScanForward64(&Index, Val);
103  return Index;
104#endif
105}
106#endif
107#endif
108
109/// \brief Count number of 0's from the most significant bit to the least
110///   stopping at the first 1.
111///
112/// Only unsigned integral types are allowed.
113///
114/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
115///   valid arguments.
116template <typename T>
117typename enable_if_c<std::numeric_limits<T>::is_integer &&
118                     !std::numeric_limits<T>::is_signed, std::size_t>::type
119countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
120  (void)ZB;
121
122  if (!Val)
123    return std::numeric_limits<T>::digits;
124
125  // Bisection method.
126  std::size_t ZeroBits = 0;
127  for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
128    T Tmp = Val >> Shift;
129    if (Tmp)
130      Val = Tmp;
131    else
132      ZeroBits |= Shift;
133  }
134  return ZeroBits;
135}
136
137// Disable signed.
138template <typename T>
139typename enable_if_c<std::numeric_limits<T>::is_integer &&
140                     std::numeric_limits<T>::is_signed, std::size_t>::type
141countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) LLVM_DELETED_FUNCTION;
142
143#if __GNUC__ >= 4 || _MSC_VER
144template <>
145inline std::size_t countLeadingZeros<uint32_t>(uint32_t Val, ZeroBehavior ZB) {
146  if (ZB != ZB_Undefined && Val == 0)
147    return 32;
148
149#if __has_builtin(__builtin_clz) || __GNUC_PREREQ(4, 0)
150  return __builtin_clz(Val);
151#elif _MSC_VER
152  unsigned long Index;
153  _BitScanReverse(&Index, Val);
154  return Index ^ 31;
155#endif
156}
157
158#if !defined(_MSC_VER) || defined(_M_X64)
159template <>
160inline std::size_t countLeadingZeros<uint64_t>(uint64_t Val, ZeroBehavior ZB) {
161  if (ZB != ZB_Undefined && Val == 0)
162    return 64;
163
164#if __has_builtin(__builtin_clzll) || __GNUC_PREREQ(4, 0)
165  return __builtin_clzll(Val);
166#elif _MSC_VER
167  unsigned long Index;
168  _BitScanReverse64(&Index, Val);
169  return Index ^ 63;
170#endif
171}
172#endif
173#endif
174
175/// \brief Get the index of the first set bit starting from the least
176///   significant bit.
177///
178/// Only unsigned integral types are allowed.
179///
180/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
181///   valid arguments.
182template <typename T>
183typename enable_if_c<std::numeric_limits<T>::is_integer &&
184                     !std::numeric_limits<T>::is_signed, T>::type
185findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) {
186  if (ZB == ZB_Max && Val == 0)
187    return std::numeric_limits<T>::max();
188
189  return countTrailingZeros(Val, ZB_Undefined);
190}
191
192// Disable signed.
193template <typename T>
194typename enable_if_c<std::numeric_limits<T>::is_integer &&
195                     std::numeric_limits<T>::is_signed, T>::type
196findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) LLVM_DELETED_FUNCTION;
197
198/// \brief Get the index of the last set bit starting from the least
199///   significant bit.
200///
201/// Only unsigned integral types are allowed.
202///
203/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
204///   valid arguments.
205template <typename T>
206typename enable_if_c<std::numeric_limits<T>::is_integer &&
207                     !std::numeric_limits<T>::is_signed, T>::type
208findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
209  if (ZB == ZB_Max && Val == 0)
210    return std::numeric_limits<T>::max();
211
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);
216}
217
218// Disable signed.
219template <typename T>
220typename enable_if_c<std::numeric_limits<T>::is_integer &&
221                     std::numeric_limits<T>::is_signed, T>::type
222findLastSet(T Val, ZeroBehavior ZB = ZB_Max) LLVM_DELETED_FUNCTION;
223
224/// \brief Macro compressed bit reversal table for 256 bits.
225///
226/// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
227static 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)
232};
233
234/// \brief Reverse the bits in \p Val.
235template <typename T>
236T 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));
243  return Val;
244}
245
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
248// ambiguity.
249
250/// Hi_32 - This function returns the high 32 bits of a 64 bit value.
251inline uint32_t Hi_32(uint64_t Value) {
252  return static_cast<uint32_t>(Value >> 32);
253}
254
255/// Lo_32 - This function returns the low 32 bits of a 64 bit value.
256inline uint32_t Lo_32(uint64_t Value) {
257  return static_cast<uint32_t>(Value);
258}
259
260/// isInt - Checks if an integer fits into the given bit width.
261template<unsigned N>
262inline bool isInt(int64_t x) {
263  return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
264}
265// Template specializations to get better code for common cases.
266template<>
267inline bool isInt<8>(int64_t x) {
268  return static_cast<int8_t>(x) == x;
269}
270template<>
271inline bool isInt<16>(int64_t x) {
272  return static_cast<int16_t>(x) == x;
273}
274template<>
275inline bool isInt<32>(int64_t x) {
276  return static_cast<int32_t>(x) == x;
277}
278
279/// isShiftedInt<N,S> - Checks if a signed integer is an N bit number shifted
280///                     left by S.
281template<unsigned N, unsigned S>
282inline bool isShiftedInt(int64_t x) {
283  return isInt<N+S>(x) && (x % (1<<S) == 0);
284}
285
286/// isUInt - Checks if an unsigned integer fits into the given bit width.
287template<unsigned N>
288inline bool isUInt(uint64_t x) {
289  return N >= 64 || x < (UINT64_C(1)<<(N));
290}
291// Template specializations to get better code for common cases.
292template<>
293inline bool isUInt<8>(uint64_t x) {
294  return static_cast<uint8_t>(x) == x;
295}
296template<>
297inline bool isUInt<16>(uint64_t x) {
298  return static_cast<uint16_t>(x) == x;
299}
300template<>
301inline bool isUInt<32>(uint64_t x) {
302  return static_cast<uint32_t>(x) == x;
303}
304
305/// isShiftedUInt<N,S> - Checks if a unsigned integer is an N bit number shifted
306///                     left by S.
307template<unsigned N, unsigned S>
308inline bool isShiftedUInt(uint64_t x) {
309  return isUInt<N+S>(x) && (x % (1<<S) == 0);
310}
311
312/// isUIntN - Checks if an unsigned integer fits into the given (dynamic)
313/// bit width.
314inline bool isUIntN(unsigned N, uint64_t x) {
315  return x == (x & (~0ULL >> (64 - N)));
316}
317
318/// isIntN - Checks if an signed integer fits into the given (dynamic)
319/// bit width.
320inline bool isIntN(unsigned N, int64_t x) {
321  return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
322}
323
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.
327inline bool isMask_32(uint32_t Value) {
328  return Value && ((Value + 1) & Value) == 0;
329}
330
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
333/// version).
334inline bool isMask_64(uint64_t Value) {
335  return Value && ((Value + 1) & Value) == 0;
336}
337
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.
341inline bool isShiftedMask_32(uint32_t Value) {
342  return isMask_32((Value - 1) | Value);
343}
344
345/// isShiftedMask_64 - This function returns true if the argument contains a
346/// sequence of ones with the remainder zero (64 bit version.)
347inline bool isShiftedMask_64(uint64_t Value) {
348  return isMask_64((Value - 1) | Value);
349}
350
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.)
353inline bool isPowerOf2_32(uint32_t Value) {
354  return Value && !(Value & (Value - 1));
355}
356
357/// isPowerOf2_64 - This function returns true if the argument is a power of two
358/// > 0 (64 bit edition.)
359inline bool isPowerOf2_64(uint64_t Value) {
360  return Value && !(Value & (Value - int64_t(1L)));
361}
362
363/// ByteSwap_16 - This function returns a byte-swapped representation of the
364/// 16-bit argument, Value.
365inline uint16_t ByteSwap_16(uint16_t Value) {
366  return sys::SwapByteOrder_16(Value);
367}
368
369/// ByteSwap_32 - This function returns a byte-swapped representation of the
370/// 32-bit argument, Value.
371inline uint32_t ByteSwap_32(uint32_t Value) {
372  return sys::SwapByteOrder_32(Value);
373}
374
375/// ByteSwap_64 - This function returns a byte-swapped representation of the
376/// 64-bit argument, Value.
377inline uint64_t ByteSwap_64(uint64_t Value) {
378  return sys::SwapByteOrder_64(Value);
379}
380
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.
385inline unsigned CountLeadingOnes_32(uint32_t Value) {
386  return countLeadingZeros(~Value);
387}
388
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.
393inline unsigned CountLeadingOnes_64(uint64_t Value) {
394  return countLeadingZeros(~Value);
395}
396
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.
401inline unsigned CountTrailingOnes_32(uint32_t Value) {
402  return countTrailingZeros(~Value);
403}
404
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.
409inline unsigned CountTrailingOnes_64(uint64_t Value) {
410  return countTrailingZeros(~Value);
411}
412
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.
416inline unsigned CountPopulation_32(uint32_t Value) {
417#if __GNUC__ >= 4
418  return __builtin_popcount(Value);
419#else
420  uint32_t v = Value - ((Value >> 1) & 0x55555555);
421  v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
422  return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
423#endif
424}
425
426/// CountPopulation_64 - this function counts the number of set bits in a value,
427/// (64 bit edition.)
428inline unsigned CountPopulation_64(uint64_t Value) {
429#if __GNUC__ >= 4
430  return __builtin_popcountll(Value);
431#else
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);
436#endif
437}
438
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
442inline unsigned Log2_32(uint32_t Value) {
443  return 31 - countLeadingZeros(Value);
444}
445
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.)
448inline unsigned Log2_64(uint64_t Value) {
449  return 63 - countLeadingZeros(Value);
450}
451
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
455inline unsigned Log2_32_Ceil(uint32_t Value) {
456  return 32 - countLeadingZeros(Value - 1);
457}
458
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.)
461inline unsigned Log2_64_Ceil(uint64_t Value) {
462  return 64 - countLeadingZeros(Value - 1);
463}
464
465/// GreatestCommonDivisor64 - Return the greatest common divisor of the two
466/// values using Euclid's algorithm.
467inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
468  while (B) {
469    uint64_t T = B;
470    B = A % B;
471    A = T;
472  }
473  return A;
474}
475
476/// BitsToDouble - This function takes a 64-bit integer and returns the bit
477/// equivalent double.
478inline double BitsToDouble(uint64_t Bits) {
479  union {
480    uint64_t L;
481    double D;
482  } T;
483  T.L = Bits;
484  return T.D;
485}
486
487/// BitsToFloat - This function takes a 32-bit integer and returns the bit
488/// equivalent float.
489inline float BitsToFloat(uint32_t Bits) {
490  union {
491    uint32_t I;
492    float F;
493  } T;
494  T.I = Bits;
495  return T.F;
496}
497
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.
502inline uint64_t DoubleToBits(double Double) {
503  union {
504    uint64_t L;
505    double D;
506  } T;
507  T.D = Double;
508  return T.L;
509}
510
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.
515inline uint32_t FloatToBits(float Float) {
516  union {
517    uint32_t I;
518    float F;
519  } T;
520  T.F = Float;
521  return T.I;
522}
523
524/// Platform-independent wrappers for the C99 isnan() function.
525int IsNAN(float f);
526int IsNAN(double d);
527
528/// Platform-independent wrappers for the C99 isinf() function.
529int IsInf(float f);
530int IsInf(double d);
531
532/// MinAlign - A and B are either alignments or offsets.  Return the minimum
533/// alignment that may be assumed after adding the two together.
534inline uint64_t MinAlign(uint64_t A, uint64_t B) {
535  // The largest power of 2 that divides both A and B.
536  //
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));
541}
542
543/// NextPowerOf2 - Returns the next power of two (in 64-bits)
544/// that is strictly greater than A.  Returns zero on overflow.
545inline uint64_t NextPowerOf2(uint64_t A) {
546  A |= (A >> 1);
547  A |= (A >> 2);
548  A |= (A >> 4);
549  A |= (A >> 8);
550  A |= (A >> 16);
551  A |= (A >> 32);
552  return A + 1;
553}
554
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.
557///
558/// Examples:
559/// \code
560///   RoundUpToAlignment(5, 8) = 8
561///   RoundUpToAlignment(17, 8) = 24
562///   RoundUpToAlignment(~0LL, 8) = 0
563/// \endcode
564inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
565  return ((Value + Align - 1) / Align) * Align;
566}
567
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
570/// non-zero.
571inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
572  return RoundUpToAlignment(Value, Align) - Value;
573}
574
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".
578inline int64_t abs64(int64_t x) {
579  return (x < 0) ? -x : x;
580}
581
582/// SignExtend32 - Sign extend B-bit number x to 32-bit int.
583/// Usage int32_t r = SignExtend32<5>(x);
584template <unsigned B> inline int32_t SignExtend32(uint32_t x) {
585  return int32_t(x << (32 - B)) >> (32 - B);
586}
587
588/// \brief Sign extend number in the bottom B bits of X to a 32-bit int.
589/// Requires 0 < B <= 32.
590inline int32_t SignExtend32(uint32_t X, unsigned B) {
591  return int32_t(X << (32 - B)) >> (32 - B);
592}
593
594/// SignExtend64 - Sign extend B-bit number x to 64-bit int.
595/// Usage int64_t r = SignExtend64<5>(x);
596template <unsigned B> inline int64_t SignExtend64(uint64_t x) {
597  return int64_t(x << (64 - B)) >> (64 - B);
598}
599
600/// \brief Sign extend number in the bottom B bits of X to a 64-bit int.
601/// Requires 0 < B <= 64.
602inline int64_t SignExtend64(uint64_t X, unsigned B) {
603  return int64_t(X << (64 - B)) >> (64 - B);
604}
605
606} // End llvm namespace
607
608#endif
609