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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 /* Capstone Disassembly Engine */
15 /* By Nguyen Anh Quynh <aquynh@gmail.com>, 2013-2014 */
16 
17 #ifndef CS_LLVM_SUPPORT_MATHEXTRAS_H
18 #define CS_LLVM_SUPPORT_MATHEXTRAS_H
19 
20 #if !defined(_MSC_VER) || !defined(_KERNEL_MODE)
21 #include <stdint.h>
22 #endif
23 
24 #ifdef _MSC_VER
25 # include <intrin.h>
26 #endif
27 
28 #ifndef __cplusplus
29 #if defined (WIN32) || defined (WIN64) || defined (_WIN32) || defined (_WIN64)
30 #define inline /* inline */
31 #endif
32 #endif
33 
34 // NOTE: The following support functions use the _32/_64 extensions instead of
35 // type overloading so that signed and unsigned integers can be used without
36 // ambiguity.
37 
38 /// Hi_32 - This function returns the high 32 bits of a 64 bit value.
Hi_32(uint64_t Value)39 static inline uint32_t Hi_32(uint64_t Value) {
40 	return (uint32_t)(Value >> 32);
41 }
42 
43 /// Lo_32 - This function returns the low 32 bits of a 64 bit value.
Lo_32(uint64_t Value)44 static inline uint32_t Lo_32(uint64_t Value) {
45 	return (uint32_t)(Value);
46 }
47 
48 /// isUIntN - Checks if an unsigned integer fits into the given (dynamic)
49 /// bit width.
isUIntN(unsigned N,uint64_t x)50 static inline bool isUIntN(unsigned N, uint64_t x) {
51 	return x == (x & (~0ULL >> (64 - N)));
52 }
53 
54 /// isIntN - Checks if an signed integer fits into the given (dynamic)
55 /// bit width.
56 //static inline bool isIntN(unsigned N, int64_t x) {
57 //  return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
58 //}
59 
60 /// isMask_32 - This function returns true if the argument is a sequence of ones
61 /// starting at the least significant bit with the remainder zero (32 bit
62 /// version).   Ex. isMask_32(0x0000FFFFU) == true.
isMask_32(uint32_t Value)63 static inline bool isMask_32(uint32_t Value) {
64 	return Value && ((Value + 1) & Value) == 0;
65 }
66 
67 /// isMask_64 - This function returns true if the argument is a sequence of ones
68 /// starting at the least significant bit with the remainder zero (64 bit
69 /// version).
isMask_64(uint64_t Value)70 static inline bool isMask_64(uint64_t Value) {
71 	return Value && ((Value + 1) & Value) == 0;
72 }
73 
74 /// isShiftedMask_32 - This function returns true if the argument contains a
75 /// sequence of ones with the remainder zero (32 bit version.)
76 /// Ex. isShiftedMask_32(0x0000FF00U) == true.
isShiftedMask_32(uint32_t Value)77 static inline bool isShiftedMask_32(uint32_t Value) {
78 	return isMask_32((Value - 1) | Value);
79 }
80 
81 /// isShiftedMask_64 - This function returns true if the argument contains a
82 /// sequence of ones with the remainder zero (64 bit version.)
isShiftedMask_64(uint64_t Value)83 static inline bool isShiftedMask_64(uint64_t Value) {
84 	return isMask_64((Value - 1) | Value);
85 }
86 
87 /// isPowerOf2_32 - This function returns true if the argument is a power of
88 /// two > 0. Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
isPowerOf2_32(uint32_t Value)89 static inline bool isPowerOf2_32(uint32_t Value) {
90 	return Value && !(Value & (Value - 1));
91 }
92 
93 /// CountLeadingZeros_32 - this function performs the platform optimal form of
94 /// counting the number of zeros from the most significant bit to the first one
95 /// bit.  Ex. CountLeadingZeros_32(0x00F000FF) == 8.
96 /// Returns 32 if the word is zero.
CountLeadingZeros_32(uint32_t Value)97 static inline unsigned CountLeadingZeros_32(uint32_t Value) {
98 	unsigned Count; // result
99 #if __GNUC__ >= 4
100 	// PowerPC is defined for __builtin_clz(0)
101 #if !defined(__ppc__) && !defined(__ppc64__)
102 	if (!Value) return 32;
103 #endif
104 	Count = __builtin_clz(Value);
105 #else
106 	unsigned Shift;
107 	if (!Value) return 32;
108 	Count = 0;
109 	// bisection method for count leading zeros
110 	for (Shift = 32 >> 1; Shift; Shift >>= 1) {
111 		uint32_t Tmp = Value >> Shift;
112 		if (Tmp) {
113 			Value = Tmp;
114 		} else {
115 			Count |= Shift;
116 		}
117 	}
118 #endif
119 	return Count;
120 }
121 
122 /// CountLeadingOnes_32 - this function performs the operation of
123 /// counting the number of ones from the most significant bit to the first zero
124 /// bit.  Ex. CountLeadingOnes_32(0xFF0FFF00) == 8.
125 /// Returns 32 if the word is all ones.
CountLeadingOnes_32(uint32_t Value)126 static inline unsigned CountLeadingOnes_32(uint32_t Value) {
127 	return CountLeadingZeros_32(~Value);
128 }
129 
130 /// CountLeadingZeros_64 - This function performs the platform optimal form
131 /// of counting the number of zeros from the most significant bit to the first
132 /// one bit (64 bit edition.)
133 /// Returns 64 if the word is zero.
CountLeadingZeros_64(uint64_t Value)134 static inline unsigned CountLeadingZeros_64(uint64_t Value) {
135 	unsigned Count; // result
136 #if __GNUC__ >= 4
137 	// PowerPC is defined for __builtin_clzll(0)
138 #if !defined(__ppc__) && !defined(__ppc64__)
139 	if (!Value) return 64;
140 #endif
141 	Count = __builtin_clzll(Value);
142 #else
143 #ifndef _MSC_VER
144 	unsigned Shift;
145 	if (sizeof(long) == sizeof(int64_t))
146 	{
147 		if (!Value) return 64;
148 		Count = 0;
149 		// bisection method for count leading zeros
150 		for (Shift = 64 >> 1; Shift; Shift >>= 1) {
151 			uint64_t Tmp = Value >> Shift;
152 			if (Tmp) {
153 				Value = Tmp;
154 			} else {
155 				Count |= Shift;
156 			}
157 		}
158 	}
159 	else
160 #endif
161 	{
162 		// get hi portion
163 		uint32_t Hi = Hi_32(Value);
164 
165 		// if some bits in hi portion
166 		if (Hi) {
167 			// leading zeros in hi portion plus all bits in lo portion
168 			Count = CountLeadingZeros_32(Hi);
169 		} else {
170 			// get lo portion
171 			uint32_t Lo = Lo_32(Value);
172 			// same as 32 bit value
173 			Count = CountLeadingZeros_32(Lo)+32;
174 		}
175 	}
176 #endif
177 	return Count;
178 }
179 
180 /// CountLeadingOnes_64 - This function performs the operation
181 /// of counting the number of ones from the most significant bit to the first
182 /// zero bit (64 bit edition.)
183 /// Returns 64 if the word is all ones.
CountLeadingOnes_64(uint64_t Value)184 static inline unsigned CountLeadingOnes_64(uint64_t Value) {
185 	return CountLeadingZeros_64(~Value);
186 }
187 
188 /// CountTrailingZeros_32 - this function performs the platform optimal form of
189 /// counting the number of zeros from the least significant bit to the first one
190 /// bit.  Ex. CountTrailingZeros_32(0xFF00FF00) == 8.
191 /// Returns 32 if the word is zero.
CountTrailingZeros_32(uint32_t Value)192 static inline unsigned CountTrailingZeros_32(uint32_t Value) {
193 #if __GNUC__ >= 4
194 	return Value ? __builtin_ctz(Value) : 32;
195 #else
196 	static const unsigned Mod37BitPosition[] = {
197 		32, 0, 1, 26, 2, 23, 27, 0, 3, 16, 24, 30, 28, 11, 0, 13,
198 		4, 7, 17, 0, 25, 22, 31, 15, 29, 10, 12, 6, 0, 21, 14, 9,
199 		5, 20, 8, 19, 18
200 	};
201 	// Replace "-Value" by "1+~Value" in the following commented code to avoid
202 	// MSVC warning C4146
203 	//    return Mod37BitPosition[(-Value & Value) % 37];
204 	return Mod37BitPosition[((1 + ~Value) & Value) % 37];
205 #endif
206 }
207 
208 /// CountTrailingOnes_32 - this function performs the operation of
209 /// counting the number of ones from the least significant bit to the first zero
210 /// bit.  Ex. CountTrailingOnes_32(0x00FF00FF) == 8.
211 /// Returns 32 if the word is all ones.
CountTrailingOnes_32(uint32_t Value)212 static inline unsigned CountTrailingOnes_32(uint32_t Value) {
213 	return CountTrailingZeros_32(~Value);
214 }
215 
216 /// CountTrailingZeros_64 - This function performs the platform optimal form
217 /// of counting the number of zeros from the least significant bit to the first
218 /// one bit (64 bit edition.)
219 /// Returns 64 if the word is zero.
CountTrailingZeros_64(uint64_t Value)220 static inline unsigned CountTrailingZeros_64(uint64_t Value) {
221 #if __GNUC__ >= 4
222 	return Value ? __builtin_ctzll(Value) : 64;
223 #else
224 	static const unsigned Mod67Position[] = {
225 		64, 0, 1, 39, 2, 15, 40, 23, 3, 12, 16, 59, 41, 19, 24, 54,
226 		4, 64, 13, 10, 17, 62, 60, 28, 42, 30, 20, 51, 25, 44, 55,
227 		47, 5, 32, 65, 38, 14, 22, 11, 58, 18, 53, 63, 9, 61, 27,
228 		29, 50, 43, 46, 31, 37, 21, 57, 52, 8, 26, 49, 45, 36, 56,
229 		7, 48, 35, 6, 34, 33, 0
230 	};
231 	// Replace "-Value" by "1+~Value" in the following commented code to avoid
232 	// MSVC warning C4146
233 	//    return Mod67Position[(-Value & Value) % 67];
234 	return Mod67Position[((1 + ~Value) & Value) % 67];
235 #endif
236 }
237 
238 /// CountTrailingOnes_64 - This function performs the operation
239 /// of counting the number of ones from the least significant bit to the first
240 /// zero bit (64 bit edition.)
241 /// Returns 64 if the word is all ones.
CountTrailingOnes_64(uint64_t Value)242 static inline unsigned CountTrailingOnes_64(uint64_t Value) {
243 	return CountTrailingZeros_64(~Value);
244 }
245 
246 /// CountPopulation_32 - this function counts the number of set bits in a value.
247 /// Ex. CountPopulation(0xF000F000) = 8
248 /// Returns 0 if the word is zero.
CountPopulation_32(uint32_t Value)249 static inline unsigned CountPopulation_32(uint32_t Value) {
250 #if __GNUC__ >= 4
251 	return __builtin_popcount(Value);
252 #else
253 	uint32_t v = Value - ((Value >> 1) & 0x55555555);
254 	v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
255 	return (((v + (v >> 4)) & 0xF0F0F0F) * 0x1010101) >> 24;
256 #endif
257 }
258 
259 /// CountPopulation_64 - this function counts the number of set bits in a value,
260 /// (64 bit edition.)
CountPopulation_64(uint64_t Value)261 static inline unsigned CountPopulation_64(uint64_t Value) {
262 #if __GNUC__ >= 4
263 	return __builtin_popcountll(Value);
264 #else
265 	uint64_t v = Value - ((Value >> 1) & 0x5555555555555555ULL);
266 	v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
267 	v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
268 	return (uint64_t)((v * 0x0101010101010101ULL) >> 56);
269 #endif
270 }
271 
272 /// Log2_32 - This function returns the floor log base 2 of the specified value,
273 /// -1 if the value is zero. (32 bit edition.)
274 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
Log2_32(uint32_t Value)275 static inline unsigned Log2_32(uint32_t Value) {
276 	return 31 - CountLeadingZeros_32(Value);
277 }
278 
279 /// Log2_64 - This function returns the floor log base 2 of the specified value,
280 /// -1 if the value is zero. (64 bit edition.)
Log2_64(uint64_t Value)281 static inline unsigned Log2_64(uint64_t Value) {
282 	return 63 - CountLeadingZeros_64(Value);
283 }
284 
285 /// Log2_32_Ceil - This function returns the ceil log base 2 of the specified
286 /// value, 32 if the value is zero. (32 bit edition).
287 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
Log2_32_Ceil(uint32_t Value)288 static inline unsigned Log2_32_Ceil(uint32_t Value) {
289 	return 32-CountLeadingZeros_32(Value-1);
290 }
291 
292 /// Log2_64_Ceil - This function returns the ceil log base 2 of the specified
293 /// value, 64 if the value is zero. (64 bit edition.)
Log2_64_Ceil(uint64_t Value)294 static inline unsigned Log2_64_Ceil(uint64_t Value) {
295 	return 64-CountLeadingZeros_64(Value-1);
296 }
297 
298 /// GreatestCommonDivisor64 - Return the greatest common divisor of the two
299 /// values using Euclid's algorithm.
GreatestCommonDivisor64(uint64_t A,uint64_t B)300 static inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
301 	while (B) {
302 		uint64_t T = B;
303 		B = A % B;
304 		A = T;
305 	}
306 	return A;
307 }
308 
309 /// BitsToDouble - This function takes a 64-bit integer and returns the bit
310 /// equivalent double.
BitsToDouble(uint64_t Bits)311 static inline double BitsToDouble(uint64_t Bits) {
312 	union {
313 		uint64_t L;
314 		double D;
315 	} T;
316 	T.L = Bits;
317 	return T.D;
318 }
319 
320 /// BitsToFloat - This function takes a 32-bit integer and returns the bit
321 /// equivalent float.
BitsToFloat(uint32_t Bits)322 static inline float BitsToFloat(uint32_t Bits) {
323 	union {
324 		uint32_t I;
325 		float F;
326 	} T;
327 	T.I = Bits;
328 	return T.F;
329 }
330 
331 /// DoubleToBits - This function takes a double and returns the bit
332 /// equivalent 64-bit integer.  Note that copying doubles around
333 /// changes the bits of NaNs on some hosts, notably x86, so this
334 /// routine cannot be used if these bits are needed.
DoubleToBits(double Double)335 static inline uint64_t DoubleToBits(double Double) {
336 	union {
337 		uint64_t L;
338 		double D;
339 	} T;
340 	T.D = Double;
341 	return T.L;
342 }
343 
344 /// FloatToBits - This function takes a float and returns the bit
345 /// equivalent 32-bit integer.  Note that copying floats around
346 /// changes the bits of NaNs on some hosts, notably x86, so this
347 /// routine cannot be used if these bits are needed.
FloatToBits(float Float)348 static inline uint32_t FloatToBits(float Float) {
349 	union {
350 		uint32_t I;
351 		float F;
352 	} T;
353 	T.F = Float;
354 	return T.I;
355 }
356 
357 /// MinAlign - A and B are either alignments or offsets.  Return the minimum
358 /// alignment that may be assumed after adding the two together.
MinAlign(uint64_t A,uint64_t B)359 static inline uint64_t MinAlign(uint64_t A, uint64_t B) {
360 	// The largest power of 2 that divides both A and B.
361 	//
362 	// Replace "-Value" by "1+~Value" in the following commented code to avoid
363 	// MSVC warning C4146
364 	//    return (A | B) & -(A | B);
365 	return (A | B) & (1 + ~(A | B));
366 }
367 
368 /// NextPowerOf2 - Returns the next power of two (in 64-bits)
369 /// that is strictly greater than A.  Returns zero on overflow.
NextPowerOf2(uint64_t A)370 static inline uint64_t NextPowerOf2(uint64_t A) {
371 	A |= (A >> 1);
372 	A |= (A >> 2);
373 	A |= (A >> 4);
374 	A |= (A >> 8);
375 	A |= (A >> 16);
376 	A |= (A >> 32);
377 	return A + 1;
378 }
379 
380 /// Returns the next integer (mod 2**64) that is greater than or equal to
381 /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
382 ///
383 /// Examples:
384 /// \code
385 ///   RoundUpToAlignment(5, 8) = 8
386 ///   RoundUpToAlignment(17, 8) = 24
387 ///   RoundUpToAlignment(~0LL, 8) = 0
388 /// \endcode
RoundUpToAlignment(uint64_t Value,uint64_t Align)389 static inline uint64_t RoundUpToAlignment(uint64_t Value, uint64_t Align) {
390 	return ((Value + Align - 1) / Align) * Align;
391 }
392 
393 /// Returns the offset to the next integer (mod 2**64) that is greater than
394 /// or equal to \p Value and is a multiple of \p Align. \p Align must be
395 /// non-zero.
OffsetToAlignment(uint64_t Value,uint64_t Align)396 static inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
397 	return RoundUpToAlignment(Value, Align) - Value;
398 }
399 
400 /// abs64 - absolute value of a 64-bit int.  Not all environments support
401 /// "abs" on whatever their name for the 64-bit int type is.  The absolute
402 /// value of the largest negative number is undefined, as with "abs".
abs64(int64_t x)403 static inline int64_t abs64(int64_t x) {
404 	return (x < 0) ? -x : x;
405 }
406 
407 /// \brief Sign extend number in the bottom B bits of X to a 32-bit int.
408 /// Requires 0 < B <= 32.
SignExtend32(uint32_t X,unsigned B)409 static inline int32_t SignExtend32(uint32_t X, unsigned B) {
410 	return (int32_t)(X << (32 - B)) >> (32 - B);
411 }
412 
413 /// \brief Sign extend number in the bottom B bits of X to a 64-bit int.
414 /// Requires 0 < B <= 64.
SignExtend64(uint64_t X,unsigned B)415 static inline int64_t SignExtend64(uint64_t X, unsigned B) {
416 	return (int64_t)(X << (64 - B)) >> (64 - B);
417 }
418 
419 /// \brief Count number of 0's from the most significant bit to the least
420 ///   stopping at the first 1.
421 ///
422 /// Only unsigned integral types are allowed.
423 ///
424 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
425 ///   valid arguments.
countLeadingZeros(int x)426 static inline unsigned int countLeadingZeros(int x)
427 {
428 	unsigned count = 0;
429 	int i;
430 	const unsigned bits = sizeof(x) * 8;
431 
432 	for (i = bits; --i; ) {
433 		if (x < 0) break;
434 		count++;
435 		x <<= 1;
436 	}
437 
438 	return count;
439 }
440 
441 #endif
442