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"
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 /// isMask_32 - This function returns true if the argument is a sequence of ones
74 /// starting at the least significant bit with the remainder zero (32 bit
75 /// version). Ex. isMask_32(0x0000FFFFU) == true.
76 inline bool isMask_32(uint32_t Value) {
77 return Value && ((Value + 1) & Value) == 0;
80 /// isMask_64 - This function returns true if the argument is a sequence of ones
81 /// starting at the least significant bit with the remainder zero (64 bit
83 inline bool isMask_64(uint64_t Value) {
84 return Value && ((Value + 1) & Value) == 0;
87 /// isShiftedMask_32 - This function returns true if the argument contains a
88 /// sequence of ones with the remainder zero (32 bit version.)
89 /// Ex. isShiftedMask_32(0x0000FF00U) == true.
90 inline bool isShiftedMask_32(uint32_t Value) {
91 return isMask_32((Value - 1) | Value);
94 /// isShiftedMask_64 - This function returns true if the argument contains a
95 /// sequence of ones with the remainder zero (64 bit version.)
96 inline bool isShiftedMask_64(uint64_t Value) {
97 return isMask_64((Value - 1) | Value);
100 /// isPowerOf2_32 - This function returns true if the argument is a power of
101 /// two > 0. Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
102 inline bool isPowerOf2_32(uint32_t Value) {
103 return Value && !(Value & (Value - 1));
106 /// isPowerOf2_64 - This function returns true if the argument is a power of two
107 /// > 0 (64 bit edition.)
108 inline bool isPowerOf2_64(uint64_t Value) {
109 return Value && !(Value & (Value - int64_t(1L)));
112 /// ByteSwap_16 - This function returns a byte-swapped representation of the
113 /// 16-bit argument, Value.
114 inline uint16_t ByteSwap_16(uint16_t Value) {
115 #if defined(_MSC_VER) && !defined(_DEBUG)
116 // The DLL version of the runtime lacks these functions (bug!?), but in a
117 // release build they're replaced with BSWAP instructions anyway.
118 return _byteswap_ushort(Value);
120 uint16_t Hi = Value << 8;
121 uint16_t Lo = Value >> 8;
126 /// ByteSwap_32 - This function returns a byte-swapped representation of the
127 /// 32-bit argument, Value.
128 inline uint32_t ByteSwap_32(uint32_t Value) {
129 #if defined(__llvm__) || \
130 (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3)) && !defined(__ICC)
131 return __builtin_bswap32(Value);
132 #elif defined(_MSC_VER) && !defined(_DEBUG)
133 return _byteswap_ulong(Value);
135 uint32_t Byte0 = Value & 0x000000FF;
136 uint32_t Byte1 = Value & 0x0000FF00;
137 uint32_t Byte2 = Value & 0x00FF0000;
138 uint32_t Byte3 = Value & 0xFF000000;
139 return (Byte0 << 24) | (Byte1 << 8) | (Byte2 >> 8) | (Byte3 >> 24);
143 /// ByteSwap_64 - This function returns a byte-swapped representation of the
144 /// 64-bit argument, Value.
145 inline uint64_t ByteSwap_64(uint64_t Value) {
146 #if defined(__llvm__) || \
147 (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 3)) && !defined(__ICC)
148 return __builtin_bswap64(Value);
149 #elif defined(_MSC_VER) && !defined(_DEBUG)
150 return _byteswap_uint64(Value);
152 uint64_t Hi = ByteSwap_32(uint32_t(Value));
153 uint32_t Lo = ByteSwap_32(uint32_t(Value >> 32));
154 return (Hi << 32) | Lo;
158 /// CountLeadingZeros_32 - this function performs the platform optimal form of
159 /// counting the number of zeros from the most significant bit to the first one
160 /// bit. Ex. CountLeadingZeros_32(0x00F000FF) == 8.
161 /// Returns 32 if the word is zero.
162 inline unsigned CountLeadingZeros_32(uint32_t Value) {
163 unsigned Count; // result
165 // PowerPC is defined for __builtin_clz(0)
166 #if !defined(__ppc__) && !defined(__ppc64__)
167 if (!Value) return 32;
169 Count = __builtin_clz(Value);
171 if (!Value) return 32;
173 // bisection method for count leading zeros
174 for (unsigned Shift = 32 >> 1; Shift; Shift >>= 1) {
175 uint32_t Tmp = Value >> Shift;
186 /// CountLeadingOnes_32 - this function performs the operation of
187 /// counting the number of ones from the most significant bit to the first zero
188 /// bit. Ex. CountLeadingOnes_32(0xFF0FFF00) == 8.
189 /// Returns 32 if the word is all ones.
190 inline unsigned CountLeadingOnes_32(uint32_t Value) {
191 return CountLeadingZeros_32(~Value);
194 /// CountLeadingZeros_64 - This function performs the platform optimal form
195 /// of counting the number of zeros from the most significant bit to the first
196 /// one bit (64 bit edition.)
197 /// Returns 64 if the word is zero.
198 inline unsigned CountLeadingZeros_64(uint64_t Value) {
199 unsigned Count; // result
201 // PowerPC is defined for __builtin_clzll(0)
202 #if !defined(__ppc__) && !defined(__ppc64__)
203 if (!Value) return 64;
205 Count = __builtin_clzll(Value);
207 if (sizeof(long) == sizeof(int64_t)) {
208 if (!Value) return 64;
210 // bisection method for count leading zeros
211 for (unsigned Shift = 64 >> 1; Shift; Shift >>= 1) {
212 uint64_t Tmp = Value >> Shift;
221 uint32_t Hi = Hi_32(Value);
223 // if some bits in hi portion
225 // leading zeros in hi portion plus all bits in lo portion
226 Count = CountLeadingZeros_32(Hi);
229 uint32_t Lo = Lo_32(Value);
230 // same as 32 bit value
231 Count = CountLeadingZeros_32(Lo)+32;
238 /// CountLeadingOnes_64 - This function performs the operation
239 /// of counting the number of ones from the most significant bit to the first
240 /// zero bit (64 bit edition.)
241 /// Returns 64 if the word is all ones.
242 inline unsigned CountLeadingOnes_64(uint64_t Value) {
243 return CountLeadingZeros_64(~Value);
246 /// CountTrailingZeros_32 - this function performs the platform optimal form of
247 /// counting the number of zeros from the least significant bit to the first one
248 /// bit. Ex. CountTrailingZeros_32(0xFF00FF00) == 8.
249 /// Returns 32 if the word is zero.
250 inline unsigned CountTrailingZeros_32(uint32_t Value) {
252 return Value ? __builtin_ctz(Value) : 32;
254 static const unsigned Mod37BitPosition[] = {
255 32, 0, 1, 26, 2, 23, 27, 0, 3, 16, 24, 30, 28, 11, 0, 13,
256 4, 7, 17, 0, 25, 22, 31, 15, 29, 10, 12, 6, 0, 21, 14, 9,
259 return Mod37BitPosition[(-Value & Value) % 37];
263 /// CountTrailingOnes_32 - this function performs the operation of
264 /// counting the number of ones from the least significant bit to the first zero
265 /// bit. Ex. CountTrailingOnes_32(0x00FF00FF) == 8.
266 /// Returns 32 if the word is all ones.
267 inline unsigned CountTrailingOnes_32(uint32_t Value) {
268 return CountTrailingZeros_32(~Value);
271 /// CountTrailingZeros_64 - This function performs the platform optimal form
272 /// of counting the number of zeros from the least significant bit to the first
273 /// one bit (64 bit edition.)
274 /// Returns 64 if the word is zero.
275 inline unsigned CountTrailingZeros_64(uint64_t Value) {
277 return Value ? __builtin_ctzll(Value) : 64;
279 static const unsigned Mod67Position[] = {
280 64, 0, 1, 39, 2, 15, 40, 23, 3, 12, 16, 59, 41, 19, 24, 54,
281 4, 64, 13, 10, 17, 62, 60, 28, 42, 30, 20, 51, 25, 44, 55,
282 47, 5, 32, 65, 38, 14, 22, 11, 58, 18, 53, 63, 9, 61, 27,
283 29, 50, 43, 46, 31, 37, 21, 57, 52, 8, 26, 49, 45, 36, 56,
284 7, 48, 35, 6, 34, 33, 0
286 return Mod67Position[(-Value & Value) % 67];
290 /// CountTrailingOnes_64 - This function performs the operation
291 /// of counting the number of ones from the least significant bit to the first
292 /// zero bit (64 bit edition.)
293 /// Returns 64 if the word is all ones.
294 inline unsigned CountTrailingOnes_64(uint64_t Value) {
295 return CountTrailingZeros_64(~Value);
298 /// CountPopulation_32 - this function counts the number of set bits in a value.
299 /// Ex. CountPopulation(0xF000F000) = 8
300 /// Returns 0 if the word is zero.
301 inline unsigned CountPopulation_32(uint32_t Value) {
303 return __builtin_popcount(Value);
305 uint32_t v = Value - ((Value >> 1) & 0x55555555);
306 v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
307 return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
311 /// CountPopulation_64 - this function counts the number of set bits in a value,
312 /// (64 bit edition.)
313 inline unsigned CountPopulation_64(uint64_t Value) {
315 return __builtin_popcountll(Value);
317 uint64_t v = Value - ((Value >> 1) & 0x5555555555555555ULL);
318 v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
319 v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
320 return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
324 /// Log2_32 - This function returns the floor log base 2 of the specified value,
325 /// -1 if the value is zero. (32 bit edition.)
326 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
327 inline unsigned Log2_32(uint32_t Value) {
328 return 31 - CountLeadingZeros_32(Value);
331 /// Log2_64 - This function returns the floor log base 2 of the specified value,
332 /// -1 if the value is zero. (64 bit edition.)
333 inline unsigned Log2_64(uint64_t Value) {
334 return 63 - CountLeadingZeros_64(Value);
337 /// Log2_32_Ceil - This function returns the ceil log base 2 of the specified
338 /// value, 32 if the value is zero. (32 bit edition).
339 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
340 inline unsigned Log2_32_Ceil(uint32_t Value) {
341 return 32-CountLeadingZeros_32(Value-1);
344 /// Log2_64_Ceil - This function returns the ceil log base 2 of the specified
345 /// value, 64 if the value is zero. (64 bit edition.)
346 inline unsigned Log2_64_Ceil(uint64_t Value) {
347 return 64-CountLeadingZeros_64(Value-1);
350 /// GreatestCommonDivisor64 - Return the greatest common divisor of the two
351 /// values using Euclid's algorithm.
352 inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
361 /// BitsToDouble - This function takes a 64-bit integer and returns the bit
362 /// equivalent double.
363 inline double BitsToDouble(uint64_t Bits) {
372 /// BitsToFloat - This function takes a 32-bit integer and returns the bit
373 /// equivalent float.
374 inline float BitsToFloat(uint32_t Bits) {
383 /// DoubleToBits - This function takes a double and returns the bit
384 /// equivalent 64-bit integer. Note that copying doubles around
385 /// changes the bits of NaNs on some hosts, notably x86, so this
386 /// routine cannot be used if these bits are needed.
387 inline uint64_t DoubleToBits(double Double) {
396 /// FloatToBits - This function takes a float and returns the bit
397 /// equivalent 32-bit integer. Note that copying floats around
398 /// changes the bits of NaNs on some hosts, notably x86, so this
399 /// routine cannot be used if these bits are needed.
400 inline uint32_t FloatToBits(float Float) {
409 /// Platform-independent wrappers for the C99 isnan() function.
413 /// Platform-independent wrappers for the C99 isinf() function.
417 /// MinAlign - A and B are either alignments or offsets. Return the minimum
418 /// alignment that may be assumed after adding the two together.
419 static inline uint64_t MinAlign(uint64_t A, uint64_t B) {
420 // The largest power of 2 that divides both A and B.
421 return (A | B) & -(A | B);
424 /// NextPowerOf2 - Returns the next power of two (in 64-bits)
425 /// that is strictly greater than A. Returns zero on overflow.
426 static inline uint64_t NextPowerOf2(uint64_t A) {
436 /// RoundUpToAlignment - Returns the next integer (mod 2**64) that is
437 /// greater than or equal to \arg Value and is a multiple of \arg
438 /// Align. Align must be non-zero.
441 /// RoundUpToAlignment(5, 8) = 8
442 /// RoundUpToAlignment(17, 8) = 24
443 /// RoundUpToAlignment(~0LL, 8) = 0
444 inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
445 return ((Value + Align - 1) / Align) * Align;
448 /// OffsetToAlignment - Return the offset to the next integer (mod 2**64) that
449 /// is greater than or equal to \arg Value and is a multiple of \arg
450 /// Align. Align must be non-zero.
451 inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
452 return RoundUpToAlignment(Value, Align) - Value;
455 /// abs64 - absolute value of a 64-bit int. Not all environments support
456 /// "abs" on whatever their name for the 64-bit int type is. The absolute
457 /// value of the largest negative number is undefined, as with "abs".
458 inline int64_t abs64(int64_t x) {
459 return (x < 0) ? -x : x;
462 /// SignExtend32 - Sign extend B-bit number x to 32-bit int.
463 /// Usage int32_t r = SignExtend32<5>(x);
464 template <unsigned B> inline int32_t SignExtend32(uint32_t x) {
465 return int32_t(x << (32 - B)) >> (32 - B);
468 /// SignExtend64 - Sign extend B-bit number x to 64-bit int.
469 /// Usage int64_t r = SignExtend64<5>(x);
470 template <unsigned B> inline int64_t SignExtend64(uint64_t x) {
471 return int64_t(x << (64 - B)) >> (64 - B);
474 } // End llvm namespace