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/System/DataTypes.h"
18 #include "llvm/System/SwapByteOrder.h"
22 // NOTE: The following support functions use the _32/_64 extensions instead of
23 // type overloading so that signed and unsigned integers can be used without
26 /// Hi_32 - This function returns the high 32 bits of a 64 bit value.
27 inline uint32_t Hi_32(uint64_t Value) {
28 return static_cast<uint32_t>(Value >> 32);
31 /// Lo_32 - This function returns the low 32 bits of a 64 bit value.
32 inline uint32_t Lo_32(uint64_t Value) {
33 return static_cast<uint32_t>(Value);
36 /// isInt - Checks if an integer fits into the given bit width.
38 inline bool isInt(int64_t x) {
39 return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
41 // Template specializations to get better code for common cases.
43 inline bool isInt<8>(int64_t x) {
44 return static_cast<int8_t>(x) == x;
47 inline bool isInt<16>(int64_t x) {
48 return static_cast<int16_t>(x) == x;
51 inline bool isInt<32>(int64_t x) {
52 return static_cast<int32_t>(x) == x;
55 /// isUInt - Checks if an unsigned integer fits into the given bit width.
57 inline bool isUInt(uint64_t x) {
58 return N >= 64 || x < (UINT64_C(1)<<N);
60 // Template specializations to get better code for common cases.
62 inline bool isUInt<8>(uint64_t x) {
63 return static_cast<uint8_t>(x) == x;
66 inline bool isUInt<16>(uint64_t x) {
67 return static_cast<uint16_t>(x) == x;
70 inline bool isUInt<32>(uint64_t x) {
71 return static_cast<uint32_t>(x) == x;
74 /// isMask_32 - This function returns true if the argument is a sequence of ones
75 /// starting at the least significant bit with the remainder zero (32 bit
76 /// version). Ex. isMask_32(0x0000FFFFU) == true.
77 inline bool isMask_32(uint32_t Value) {
78 return Value && ((Value + 1) & Value) == 0;
81 /// isMask_64 - This function returns true if the argument is a sequence of ones
82 /// starting at the least significant bit with the remainder zero (64 bit
84 inline bool isMask_64(uint64_t Value) {
85 return Value && ((Value + 1) & Value) == 0;
88 /// isShiftedMask_32 - This function returns true if the argument contains a
89 /// sequence of ones with the remainder zero (32 bit version.)
90 /// Ex. isShiftedMask_32(0x0000FF00U) == true.
91 inline bool isShiftedMask_32(uint32_t Value) {
92 return isMask_32((Value - 1) | Value);
95 /// isShiftedMask_64 - This function returns true if the argument contains a
96 /// sequence of ones with the remainder zero (64 bit version.)
97 inline bool isShiftedMask_64(uint64_t Value) {
98 return isMask_64((Value - 1) | Value);
101 /// isPowerOf2_32 - This function returns true if the argument is a power of
102 /// two > 0. Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
103 inline bool isPowerOf2_32(uint32_t Value) {
104 return Value && !(Value & (Value - 1));
107 /// isPowerOf2_64 - This function returns true if the argument is a power of two
108 /// > 0 (64 bit edition.)
109 inline bool isPowerOf2_64(uint64_t Value) {
110 return Value && !(Value & (Value - int64_t(1L)));
113 /// ByteSwap_16 - This function returns a byte-swapped representation of the
114 /// 16-bit argument, Value.
115 inline uint16_t ByteSwap_16(uint16_t Value) {
116 return sys::SwapByteOrder(Value);
119 /// ByteSwap_32 - This function returns a byte-swapped representation of the
120 /// 32-bit argument, Value.
121 inline uint32_t ByteSwap_32(uint32_t Value) {
122 return sys::SwapByteOrder(Value);
125 /// ByteSwap_64 - This function returns a byte-swapped representation of the
126 /// 64-bit argument, Value.
127 inline uint64_t ByteSwap_64(uint64_t Value) {
128 return sys::SwapByteOrder(Value);
131 /// CountLeadingZeros_32 - this function performs the platform optimal form of
132 /// counting the number of zeros from the most significant bit to the first one
133 /// bit. Ex. CountLeadingZeros_32(0x00F000FF) == 8.
134 /// Returns 32 if the word is zero.
135 inline unsigned CountLeadingZeros_32(uint32_t Value) {
136 unsigned Count; // result
138 // PowerPC is defined for __builtin_clz(0)
139 #if !defined(__ppc__) && !defined(__ppc64__)
140 if (!Value) return 32;
142 Count = __builtin_clz(Value);
144 if (!Value) return 32;
146 // bisection method for count leading zeros
147 for (unsigned Shift = 32 >> 1; Shift; Shift >>= 1) {
148 uint32_t Tmp = Value >> Shift;
159 /// CountLeadingOnes_32 - this function performs the operation of
160 /// counting the number of ones from the most significant bit to the first zero
161 /// bit. Ex. CountLeadingOnes_32(0xFF0FFF00) == 8.
162 /// Returns 32 if the word is all ones.
163 inline unsigned CountLeadingOnes_32(uint32_t Value) {
164 return CountLeadingZeros_32(~Value);
167 /// CountLeadingZeros_64 - This function performs the platform optimal form
168 /// of counting the number of zeros from the most significant bit to the first
169 /// one bit (64 bit edition.)
170 /// Returns 64 if the word is zero.
171 inline unsigned CountLeadingZeros_64(uint64_t Value) {
172 unsigned Count; // result
174 // PowerPC is defined for __builtin_clzll(0)
175 #if !defined(__ppc__) && !defined(__ppc64__)
176 if (!Value) return 64;
178 Count = __builtin_clzll(Value);
180 if (sizeof(long) == sizeof(int64_t)) {
181 if (!Value) return 64;
183 // bisection method for count leading zeros
184 for (unsigned Shift = 64 >> 1; Shift; Shift >>= 1) {
185 uint64_t Tmp = Value >> Shift;
194 uint32_t Hi = Hi_32(Value);
196 // if some bits in hi portion
198 // leading zeros in hi portion plus all bits in lo portion
199 Count = CountLeadingZeros_32(Hi);
202 uint32_t Lo = Lo_32(Value);
203 // same as 32 bit value
204 Count = CountLeadingZeros_32(Lo)+32;
211 /// CountLeadingOnes_64 - This function performs the operation
212 /// of counting the number of ones from the most significant bit to the first
213 /// zero bit (64 bit edition.)
214 /// Returns 64 if the word is all ones.
215 inline unsigned CountLeadingOnes_64(uint64_t Value) {
216 return CountLeadingZeros_64(~Value);
219 /// CountTrailingZeros_32 - this function performs the platform optimal form of
220 /// counting the number of zeros from the least significant bit to the first one
221 /// bit. Ex. CountTrailingZeros_32(0xFF00FF00) == 8.
222 /// Returns 32 if the word is zero.
223 inline unsigned CountTrailingZeros_32(uint32_t Value) {
225 return Value ? __builtin_ctz(Value) : 32;
227 static const unsigned Mod37BitPosition[] = {
228 32, 0, 1, 26, 2, 23, 27, 0, 3, 16, 24, 30, 28, 11, 0, 13,
229 4, 7, 17, 0, 25, 22, 31, 15, 29, 10, 12, 6, 0, 21, 14, 9,
232 return Mod37BitPosition[(-Value & Value) % 37];
236 /// CountTrailingOnes_32 - this function performs the operation of
237 /// counting the number of ones from the least significant bit to the first zero
238 /// bit. Ex. CountTrailingOnes_32(0x00FF00FF) == 8.
239 /// Returns 32 if the word is all ones.
240 inline unsigned CountTrailingOnes_32(uint32_t Value) {
241 return CountTrailingZeros_32(~Value);
244 /// CountTrailingZeros_64 - This function performs the platform optimal form
245 /// of counting the number of zeros from the least significant bit to the first
246 /// one bit (64 bit edition.)
247 /// Returns 64 if the word is zero.
248 inline unsigned CountTrailingZeros_64(uint64_t Value) {
250 return Value ? __builtin_ctzll(Value) : 64;
252 static const unsigned Mod67Position[] = {
253 64, 0, 1, 39, 2, 15, 40, 23, 3, 12, 16, 59, 41, 19, 24, 54,
254 4, 64, 13, 10, 17, 62, 60, 28, 42, 30, 20, 51, 25, 44, 55,
255 47, 5, 32, 65, 38, 14, 22, 11, 58, 18, 53, 63, 9, 61, 27,
256 29, 50, 43, 46, 31, 37, 21, 57, 52, 8, 26, 49, 45, 36, 56,
257 7, 48, 35, 6, 34, 33, 0
259 return Mod67Position[(-Value & Value) % 67];
263 /// CountTrailingOnes_64 - This function performs the operation
264 /// of counting the number of ones from the least significant bit to the first
265 /// zero bit (64 bit edition.)
266 /// Returns 64 if the word is all ones.
267 inline unsigned CountTrailingOnes_64(uint64_t Value) {
268 return CountTrailingZeros_64(~Value);
271 /// CountPopulation_32 - this function counts the number of set bits in a value.
272 /// Ex. CountPopulation(0xF000F000) = 8
273 /// Returns 0 if the word is zero.
274 inline unsigned CountPopulation_32(uint32_t Value) {
276 return __builtin_popcount(Value);
278 uint32_t v = Value - ((Value >> 1) & 0x55555555);
279 v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
280 return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
284 /// CountPopulation_64 - this function counts the number of set bits in a value,
285 /// (64 bit edition.)
286 inline unsigned CountPopulation_64(uint64_t Value) {
288 return __builtin_popcountll(Value);
290 uint64_t v = Value - ((Value >> 1) & 0x5555555555555555ULL);
291 v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
292 v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
293 return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
297 /// Log2_32 - This function returns the floor log base 2 of the specified value,
298 /// -1 if the value is zero. (32 bit edition.)
299 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
300 inline unsigned Log2_32(uint32_t Value) {
301 return 31 - CountLeadingZeros_32(Value);
304 /// Log2_64 - This function returns the floor log base 2 of the specified value,
305 /// -1 if the value is zero. (64 bit edition.)
306 inline unsigned Log2_64(uint64_t Value) {
307 return 63 - CountLeadingZeros_64(Value);
310 /// Log2_32_Ceil - This function returns the ceil log base 2 of the specified
311 /// value, 32 if the value is zero. (32 bit edition).
312 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
313 inline unsigned Log2_32_Ceil(uint32_t Value) {
314 return 32-CountLeadingZeros_32(Value-1);
317 /// Log2_64_Ceil - This function returns the ceil log base 2 of the specified
318 /// value, 64 if the value is zero. (64 bit edition.)
319 inline unsigned Log2_64_Ceil(uint64_t Value) {
320 return 64-CountLeadingZeros_64(Value-1);
323 /// GreatestCommonDivisor64 - Return the greatest common divisor of the two
324 /// values using Euclid's algorithm.
325 inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
334 /// BitsToDouble - This function takes a 64-bit integer and returns the bit
335 /// equivalent double.
336 inline double BitsToDouble(uint64_t Bits) {
345 /// BitsToFloat - This function takes a 32-bit integer and returns the bit
346 /// equivalent float.
347 inline float BitsToFloat(uint32_t Bits) {
356 /// DoubleToBits - This function takes a double and returns the bit
357 /// equivalent 64-bit integer. Note that copying doubles around
358 /// changes the bits of NaNs on some hosts, notably x86, so this
359 /// routine cannot be used if these bits are needed.
360 inline uint64_t DoubleToBits(double Double) {
369 /// FloatToBits - This function takes a float and returns the bit
370 /// equivalent 32-bit integer. Note that copying floats around
371 /// changes the bits of NaNs on some hosts, notably x86, so this
372 /// routine cannot be used if these bits are needed.
373 inline uint32_t FloatToBits(float Float) {
382 /// Platform-independent wrappers for the C99 isnan() function.
386 /// Platform-independent wrappers for the C99 isinf() function.
390 /// MinAlign - A and B are either alignments or offsets. Return the minimum
391 /// alignment that may be assumed after adding the two together.
392 static inline uint64_t MinAlign(uint64_t A, uint64_t B) {
393 // The largest power of 2 that divides both A and B.
394 return (A | B) & -(A | B);
397 /// NextPowerOf2 - Returns the next power of two (in 64-bits)
398 /// that is strictly greater than A. Returns zero on overflow.
399 static inline uint64_t NextPowerOf2(uint64_t A) {
409 /// RoundUpToAlignment - Returns the next integer (mod 2**64) that is
410 /// greater than or equal to \arg Value and is a multiple of \arg
411 /// Align. Align must be non-zero.
414 /// RoundUpToAlignment(5, 8) = 8
415 /// RoundUpToAlignment(17, 8) = 24
416 /// RoundUpToAlignment(~0LL, 8) = 0
417 inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
418 return ((Value + Align - 1) / Align) * Align;
421 /// OffsetToAlignment - Return the offset to the next integer (mod 2**64) that
422 /// is greater than or equal to \arg Value and is a multiple of \arg
423 /// Align. Align must be non-zero.
424 inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
425 return RoundUpToAlignment(Value, Align) - Value;
428 /// abs64 - absolute value of a 64-bit int. Not all environments support
429 /// "abs" on whatever their name for the 64-bit int type is. The absolute
430 /// value of the largest negative number is undefined, as with "abs".
431 inline int64_t abs64(int64_t x) {
432 return (x < 0) ? -x : x;
435 /// SignExtend32 - Sign extend B-bit number x to 32-bit int.
436 /// Usage int32_t r = SignExtend32<5>(x);
437 template <unsigned B> inline int32_t SignExtend32(uint32_t x) {
438 return int32_t(x << (32 - B)) >> (32 - B);
441 /// SignExtend64 - Sign extend B-bit number x to 64-bit int.
442 /// Usage int64_t r = SignExtend64<5>(x);
443 template <unsigned B> inline int64_t SignExtend64(uint64_t x) {
444 return int64_t(x << (64 - B)) >> (64 - B);
447 } // End llvm namespace