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/SwapByteOrder.h"
21 // NOTE: The following support functions use the _32/_64 extensions instead of
22 // type overloading so that signed and unsigned integers can be used without
25 /// Hi_32 - This function returns the high 32 bits of a 64 bit value.
26 inline uint32_t Hi_32(uint64_t Value) {
27 return static_cast<uint32_t>(Value >> 32);
30 /// Lo_32 - This function returns the low 32 bits of a 64 bit value.
31 inline uint32_t Lo_32(uint64_t Value) {
32 return static_cast<uint32_t>(Value);
35 /// isInt - Checks if an integer fits into the given bit width.
37 inline bool isInt(int64_t x) {
38 return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
40 // Template specializations to get better code for common cases.
42 inline bool isInt<8>(int64_t x) {
43 return static_cast<int8_t>(x) == x;
46 inline bool isInt<16>(int64_t x) {
47 return static_cast<int16_t>(x) == x;
50 inline bool isInt<32>(int64_t x) {
51 return static_cast<int32_t>(x) == x;
54 /// isUInt - Checks if an unsigned integer fits into the given bit width.
56 inline bool isUInt(uint64_t x) {
57 return N >= 64 || x < (UINT64_C(1)<<N);
59 // Template specializations to get better code for common cases.
61 inline bool isUInt<8>(uint64_t x) {
62 return static_cast<uint8_t>(x) == x;
65 inline bool isUInt<16>(uint64_t x) {
66 return static_cast<uint16_t>(x) == x;
69 inline bool isUInt<32>(uint64_t x) {
70 return static_cast<uint32_t>(x) == x;
73 /// isUIntN - Checks if an unsigned integer fits into the given (dynamic)
75 inline bool isUIntN(unsigned N, uint64_t x) {
76 return x == (x & (~0ULL >> (64 - N)));
79 /// isIntN - Checks if an signed integer fits into the given (dynamic)
81 inline bool isIntN(unsigned N, int64_t x) {
82 return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
85 /// isMask_32 - This function returns true if the argument is a sequence of ones
86 /// starting at the least significant bit with the remainder zero (32 bit
87 /// version). Ex. isMask_32(0x0000FFFFU) == true.
88 inline bool isMask_32(uint32_t Value) {
89 return Value && ((Value + 1) & Value) == 0;
92 /// isMask_64 - This function returns true if the argument is a sequence of ones
93 /// starting at the least significant bit with the remainder zero (64 bit
95 inline bool isMask_64(uint64_t Value) {
96 return Value && ((Value + 1) & Value) == 0;
99 /// isShiftedMask_32 - This function returns true if the argument contains a
100 /// sequence of ones with the remainder zero (32 bit version.)
101 /// Ex. isShiftedMask_32(0x0000FF00U) == true.
102 inline bool isShiftedMask_32(uint32_t Value) {
103 return isMask_32((Value - 1) | Value);
106 /// isShiftedMask_64 - This function returns true if the argument contains a
107 /// sequence of ones with the remainder zero (64 bit version.)
108 inline bool isShiftedMask_64(uint64_t Value) {
109 return isMask_64((Value - 1) | Value);
112 /// isPowerOf2_32 - This function returns true if the argument is a power of
113 /// two > 0. Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
114 inline bool isPowerOf2_32(uint32_t Value) {
115 return Value && !(Value & (Value - 1));
118 /// isPowerOf2_64 - This function returns true if the argument is a power of two
119 /// > 0 (64 bit edition.)
120 inline bool isPowerOf2_64(uint64_t Value) {
121 return Value && !(Value & (Value - int64_t(1L)));
124 /// ByteSwap_16 - This function returns a byte-swapped representation of the
125 /// 16-bit argument, Value.
126 inline uint16_t ByteSwap_16(uint16_t Value) {
127 return sys::SwapByteOrder_16(Value);
130 /// ByteSwap_32 - This function returns a byte-swapped representation of the
131 /// 32-bit argument, Value.
132 inline uint32_t ByteSwap_32(uint32_t Value) {
133 return sys::SwapByteOrder_32(Value);
136 /// ByteSwap_64 - This function returns a byte-swapped representation of the
137 /// 64-bit argument, Value.
138 inline uint64_t ByteSwap_64(uint64_t Value) {
139 return sys::SwapByteOrder_64(Value);
142 /// CountLeadingZeros_32 - this function performs the platform optimal form of
143 /// counting the number of zeros from the most significant bit to the first one
144 /// bit. Ex. CountLeadingZeros_32(0x00F000FF) == 8.
145 /// Returns 32 if the word is zero.
146 inline unsigned CountLeadingZeros_32(uint32_t Value) {
147 unsigned Count; // result
149 // PowerPC is defined for __builtin_clz(0)
150 #if !defined(__ppc__) && !defined(__ppc64__)
151 if (!Value) return 32;
153 Count = __builtin_clz(Value);
155 if (!Value) return 32;
157 // bisection method for count leading zeros
158 for (unsigned Shift = 32 >> 1; Shift; Shift >>= 1) {
159 uint32_t Tmp = Value >> Shift;
170 /// CountLeadingOnes_32 - this function performs the operation of
171 /// counting the number of ones from the most significant bit to the first zero
172 /// bit. Ex. CountLeadingOnes_32(0xFF0FFF00) == 8.
173 /// Returns 32 if the word is all ones.
174 inline unsigned CountLeadingOnes_32(uint32_t Value) {
175 return CountLeadingZeros_32(~Value);
178 /// CountLeadingZeros_64 - This function performs the platform optimal form
179 /// of counting the number of zeros from the most significant bit to the first
180 /// one bit (64 bit edition.)
181 /// Returns 64 if the word is zero.
182 inline unsigned CountLeadingZeros_64(uint64_t Value) {
183 unsigned Count; // result
185 // PowerPC is defined for __builtin_clzll(0)
186 #if !defined(__ppc__) && !defined(__ppc64__)
187 if (!Value) return 64;
189 Count = __builtin_clzll(Value);
191 if (sizeof(long) == sizeof(int64_t)) {
192 if (!Value) return 64;
194 // bisection method for count leading zeros
195 for (unsigned Shift = 64 >> 1; Shift; Shift >>= 1) {
196 uint64_t Tmp = Value >> Shift;
205 uint32_t Hi = Hi_32(Value);
207 // if some bits in hi portion
209 // leading zeros in hi portion plus all bits in lo portion
210 Count = CountLeadingZeros_32(Hi);
213 uint32_t Lo = Lo_32(Value);
214 // same as 32 bit value
215 Count = CountLeadingZeros_32(Lo)+32;
222 /// CountLeadingOnes_64 - This function performs the operation
223 /// of counting the number of ones from the most significant bit to the first
224 /// zero bit (64 bit edition.)
225 /// Returns 64 if the word is all ones.
226 inline unsigned CountLeadingOnes_64(uint64_t Value) {
227 return CountLeadingZeros_64(~Value);
230 /// CountTrailingZeros_32 - this function performs the platform optimal form of
231 /// counting the number of zeros from the least significant bit to the first one
232 /// bit. Ex. CountTrailingZeros_32(0xFF00FF00) == 8.
233 /// Returns 32 if the word is zero.
234 inline unsigned CountTrailingZeros_32(uint32_t Value) {
236 return Value ? __builtin_ctz(Value) : 32;
238 static const unsigned Mod37BitPosition[] = {
239 32, 0, 1, 26, 2, 23, 27, 0, 3, 16, 24, 30, 28, 11, 0, 13,
240 4, 7, 17, 0, 25, 22, 31, 15, 29, 10, 12, 6, 0, 21, 14, 9,
243 return Mod37BitPosition[(-Value & Value) % 37];
247 /// CountTrailingOnes_32 - this function performs the operation of
248 /// counting the number of ones from the least significant bit to the first zero
249 /// bit. Ex. CountTrailingOnes_32(0x00FF00FF) == 8.
250 /// Returns 32 if the word is all ones.
251 inline unsigned CountTrailingOnes_32(uint32_t Value) {
252 return CountTrailingZeros_32(~Value);
255 /// CountTrailingZeros_64 - This function performs the platform optimal form
256 /// of counting the number of zeros from the least significant bit to the first
257 /// one bit (64 bit edition.)
258 /// Returns 64 if the word is zero.
259 inline unsigned CountTrailingZeros_64(uint64_t Value) {
261 return Value ? __builtin_ctzll(Value) : 64;
263 static const unsigned Mod67Position[] = {
264 64, 0, 1, 39, 2, 15, 40, 23, 3, 12, 16, 59, 41, 19, 24, 54,
265 4, 64, 13, 10, 17, 62, 60, 28, 42, 30, 20, 51, 25, 44, 55,
266 47, 5, 32, 65, 38, 14, 22, 11, 58, 18, 53, 63, 9, 61, 27,
267 29, 50, 43, 46, 31, 37, 21, 57, 52, 8, 26, 49, 45, 36, 56,
268 7, 48, 35, 6, 34, 33, 0
270 return Mod67Position[(-Value & Value) % 67];
274 /// CountTrailingOnes_64 - This function performs the operation
275 /// of counting the number of ones from the least significant bit to the first
276 /// zero bit (64 bit edition.)
277 /// Returns 64 if the word is all ones.
278 inline unsigned CountTrailingOnes_64(uint64_t Value) {
279 return CountTrailingZeros_64(~Value);
282 /// CountPopulation_32 - this function counts the number of set bits in a value.
283 /// Ex. CountPopulation(0xF000F000) = 8
284 /// Returns 0 if the word is zero.
285 inline unsigned CountPopulation_32(uint32_t Value) {
287 return __builtin_popcount(Value);
289 uint32_t v = Value - ((Value >> 1) & 0x55555555);
290 v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
291 return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
295 /// CountPopulation_64 - this function counts the number of set bits in a value,
296 /// (64 bit edition.)
297 inline unsigned CountPopulation_64(uint64_t Value) {
299 return __builtin_popcountll(Value);
301 uint64_t v = Value - ((Value >> 1) & 0x5555555555555555ULL);
302 v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
303 v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
304 return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
308 /// Log2_32 - This function returns the floor log base 2 of the specified value,
309 /// -1 if the value is zero. (32 bit edition.)
310 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
311 inline unsigned Log2_32(uint32_t Value) {
312 return 31 - CountLeadingZeros_32(Value);
315 /// Log2_64 - This function returns the floor log base 2 of the specified value,
316 /// -1 if the value is zero. (64 bit edition.)
317 inline unsigned Log2_64(uint64_t Value) {
318 return 63 - CountLeadingZeros_64(Value);
321 /// Log2_32_Ceil - This function returns the ceil log base 2 of the specified
322 /// value, 32 if the value is zero. (32 bit edition).
323 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
324 inline unsigned Log2_32_Ceil(uint32_t Value) {
325 return 32-CountLeadingZeros_32(Value-1);
328 /// Log2_64_Ceil - This function returns the ceil log base 2 of the specified
329 /// value, 64 if the value is zero. (64 bit edition.)
330 inline unsigned Log2_64_Ceil(uint64_t Value) {
331 return 64-CountLeadingZeros_64(Value-1);
334 /// GreatestCommonDivisor64 - Return the greatest common divisor of the two
335 /// values using Euclid's algorithm.
336 inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
345 /// BitsToDouble - This function takes a 64-bit integer and returns the bit
346 /// equivalent double.
347 inline double BitsToDouble(uint64_t Bits) {
356 /// BitsToFloat - This function takes a 32-bit integer and returns the bit
357 /// equivalent float.
358 inline float BitsToFloat(uint32_t Bits) {
367 /// DoubleToBits - This function takes a double and returns the bit
368 /// equivalent 64-bit integer. Note that copying doubles around
369 /// changes the bits of NaNs on some hosts, notably x86, so this
370 /// routine cannot be used if these bits are needed.
371 inline uint64_t DoubleToBits(double Double) {
380 /// FloatToBits - This function takes a float and returns the bit
381 /// equivalent 32-bit integer. Note that copying floats around
382 /// changes the bits of NaNs on some hosts, notably x86, so this
383 /// routine cannot be used if these bits are needed.
384 inline uint32_t FloatToBits(float Float) {
393 /// Platform-independent wrappers for the C99 isnan() function.
397 /// Platform-independent wrappers for the C99 isinf() function.
401 /// MinAlign - A and B are either alignments or offsets. Return the minimum
402 /// alignment that may be assumed after adding the two together.
403 static inline uint64_t MinAlign(uint64_t A, uint64_t B) {
404 // The largest power of 2 that divides both A and B.
405 return (A | B) & -(A | B);
408 /// NextPowerOf2 - Returns the next power of two (in 64-bits)
409 /// that is strictly greater than A. Returns zero on overflow.
410 static inline uint64_t NextPowerOf2(uint64_t A) {
420 /// RoundUpToAlignment - Returns the next integer (mod 2**64) that is
421 /// greater than or equal to \arg Value and is a multiple of \arg
422 /// Align. Align must be non-zero.
425 /// RoundUpToAlignment(5, 8) = 8
426 /// RoundUpToAlignment(17, 8) = 24
427 /// RoundUpToAlignment(~0LL, 8) = 0
428 inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
429 return ((Value + Align - 1) / Align) * Align;
432 /// OffsetToAlignment - Return the offset to the next integer (mod 2**64) that
433 /// is greater than or equal to \arg Value and is a multiple of \arg
434 /// Align. Align must be non-zero.
435 inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
436 return RoundUpToAlignment(Value, Align) - Value;
439 /// abs64 - absolute value of a 64-bit int. Not all environments support
440 /// "abs" on whatever their name for the 64-bit int type is. The absolute
441 /// value of the largest negative number is undefined, as with "abs".
442 inline int64_t abs64(int64_t x) {
443 return (x < 0) ? -x : x;
446 /// SignExtend32 - Sign extend B-bit number x to 32-bit int.
447 /// Usage int32_t r = SignExtend32<5>(x);
448 template <unsigned B> inline int32_t SignExtend32(uint32_t x) {
449 return int32_t(x << (32 - B)) >> (32 - B);
452 /// SignExtend64 - Sign extend B-bit number x to 64-bit int.
453 /// Usage int64_t r = SignExtend64<5>(x);
454 template <unsigned B> inline int64_t SignExtend64(uint64_t x) {
455 return int64_t(x << (64 - B)) >> (64 - B);
458 } // End llvm namespace