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1 // Copyright 2015, VIXL authors
2 // All rights reserved.
3 //
4 // Redistribution and use in source and binary forms, with or without
5 // modification, are permitted provided that the following conditions are met:
6 //
7 //   * Redistributions of source code must retain the above copyright notice,
8 //     this list of conditions and the following disclaimer.
9 //   * Redistributions in binary form must reproduce the above copyright notice,
10 //     this list of conditions and the following disclaimer in the documentation
11 //     and/or other materials provided with the distribution.
12 //   * Neither the name of ARM Limited nor the names of its contributors may be
13 //     used to endorse or promote products derived from this software without
14 //     specific prior written permission.
15 //
16 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS CONTRIBUTORS "AS IS" AND
17 // ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
18 // WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
19 // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
20 // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21 // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
22 // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
23 // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
24 // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
25 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26 
27 #ifndef VIXL_UTILS_H
28 #define VIXL_UTILS_H
29 
30 #include <cmath>
31 #include <cstring>
32 #include <limits>
33 #include <vector>
34 
35 #include "compiler-intrinsics-vixl.h"
36 #include "globals-vixl.h"
37 
38 namespace vixl {
39 
40 // Macros for compile-time format checking.
41 #if GCC_VERSION_OR_NEWER(4, 4, 0)
42 #define PRINTF_CHECK(format_index, varargs_index) \
43   __attribute__((format(gnu_printf, format_index, varargs_index)))
44 #else
45 #define PRINTF_CHECK(format_index, varargs_index)
46 #endif
47 
48 #ifdef __GNUC__
49 #define VIXL_HAS_DEPRECATED_WITH_MSG
50 #elif defined(__clang__)
51 #ifdef __has_extension(attribute_deprecated_with_message)
52 #define VIXL_HAS_DEPRECATED_WITH_MSG
53 #endif
54 #endif
55 
56 #ifdef VIXL_HAS_DEPRECATED_WITH_MSG
57 #define VIXL_DEPRECATED(replaced_by, declarator) \
58   __attribute__((deprecated("Use \"" replaced_by "\" instead"))) declarator
59 #else
60 #define VIXL_DEPRECATED(replaced_by, declarator) declarator
61 #endif
62 
63 #ifdef VIXL_DEBUG
64 #define VIXL_UNREACHABLE_OR_FALLTHROUGH() VIXL_UNREACHABLE()
65 #else
66 #define VIXL_UNREACHABLE_OR_FALLTHROUGH() VIXL_FALLTHROUGH()
67 #endif
68 
69 template <typename T, size_t n>
ArrayLength(const T (&)[n])70 size_t ArrayLength(const T (&)[n]) {
71   return n;
72 }
73 
74 // Check number width.
75 // TODO: Refactor these using templates.
IsIntN(unsigned n,uint32_t x)76 inline bool IsIntN(unsigned n, uint32_t x) {
77   VIXL_ASSERT((0 < n) && (n < 32));
78   uint32_t limit = UINT32_C(1) << (n - 1);
79   return x < limit;
80 }
IsIntN(unsigned n,int32_t x)81 inline bool IsIntN(unsigned n, int32_t x) {
82   VIXL_ASSERT((0 < n) && (n < 32));
83   int32_t limit = INT32_C(1) << (n - 1);
84   return (-limit <= x) && (x < limit);
85 }
IsIntN(unsigned n,uint64_t x)86 inline bool IsIntN(unsigned n, uint64_t x) {
87   VIXL_ASSERT((0 < n) && (n < 64));
88   uint64_t limit = UINT64_C(1) << (n - 1);
89   return x < limit;
90 }
IsIntN(unsigned n,int64_t x)91 inline bool IsIntN(unsigned n, int64_t x) {
92   VIXL_ASSERT((0 < n) && (n < 64));
93   int64_t limit = INT64_C(1) << (n - 1);
94   return (-limit <= x) && (x < limit);
95 }
is_intn(unsigned n,int64_t x)96 VIXL_DEPRECATED("IsIntN", inline bool is_intn(unsigned n, int64_t x)) {
97   return IsIntN(n, x);
98 }
99 
IsUintN(unsigned n,uint32_t x)100 inline bool IsUintN(unsigned n, uint32_t x) {
101   VIXL_ASSERT((0 < n) && (n < 32));
102   return !(x >> n);
103 }
IsUintN(unsigned n,int32_t x)104 inline bool IsUintN(unsigned n, int32_t x) {
105   VIXL_ASSERT((0 < n) && (n < 32));
106   // Convert to an unsigned integer to avoid implementation-defined behavior.
107   return !(static_cast<uint32_t>(x) >> n);
108 }
IsUintN(unsigned n,uint64_t x)109 inline bool IsUintN(unsigned n, uint64_t x) {
110   VIXL_ASSERT((0 < n) && (n < 64));
111   return !(x >> n);
112 }
IsUintN(unsigned n,int64_t x)113 inline bool IsUintN(unsigned n, int64_t x) {
114   VIXL_ASSERT((0 < n) && (n < 64));
115   // Convert to an unsigned integer to avoid implementation-defined behavior.
116   return !(static_cast<uint64_t>(x) >> n);
117 }
is_uintn(unsigned n,int64_t x)118 VIXL_DEPRECATED("IsUintN", inline bool is_uintn(unsigned n, int64_t x)) {
119   return IsUintN(n, x);
120 }
121 
TruncateToUintN(unsigned n,uint64_t x)122 inline uint64_t TruncateToUintN(unsigned n, uint64_t x) {
123   VIXL_ASSERT((0 < n) && (n < 64));
124   return static_cast<uint64_t>(x) & ((UINT64_C(1) << n) - 1);
125 }
126 VIXL_DEPRECATED("TruncateToUintN",
127                 inline uint64_t truncate_to_intn(unsigned n, int64_t x)) {
128   return TruncateToUintN(n, x);
129 }
130 
131 // clang-format off
132 #define INT_1_TO_32_LIST(V)                                                    \
133 V(1)  V(2)  V(3)  V(4)  V(5)  V(6)  V(7)  V(8)                                 \
134 V(9)  V(10) V(11) V(12) V(13) V(14) V(15) V(16)                                \
135 V(17) V(18) V(19) V(20) V(21) V(22) V(23) V(24)                                \
136 V(25) V(26) V(27) V(28) V(29) V(30) V(31) V(32)
137 
138 #define INT_33_TO_63_LIST(V)                                                   \
139 V(33) V(34) V(35) V(36) V(37) V(38) V(39) V(40)                                \
140 V(41) V(42) V(43) V(44) V(45) V(46) V(47) V(48)                                \
141 V(49) V(50) V(51) V(52) V(53) V(54) V(55) V(56)                                \
142 V(57) V(58) V(59) V(60) V(61) V(62) V(63)
143 
144 #define INT_1_TO_63_LIST(V) INT_1_TO_32_LIST(V) INT_33_TO_63_LIST(V)
145 
146 // clang-format on
147 
148 #define DECLARE_IS_INT_N(N)                                       \
149   inline bool IsInt##N(int64_t x) { return IsIntN(N, x); }        \
150   VIXL_DEPRECATED("IsInt" #N, inline bool is_int##N(int64_t x)) { \
151     return IsIntN(N, x);                                          \
152   }
153 
154 #define DECLARE_IS_UINT_N(N)                                        \
155   inline bool IsUint##N(int64_t x) { return IsUintN(N, x); }        \
156   VIXL_DEPRECATED("IsUint" #N, inline bool is_uint##N(int64_t x)) { \
157     return IsUintN(N, x);                                           \
158   }
159 
160 #define DECLARE_TRUNCATE_TO_UINT_32(N)                             \
161   inline uint32_t TruncateToUint##N(uint64_t x) {                  \
162     return static_cast<uint32_t>(TruncateToUintN(N, x));           \
163   }                                                                \
164   VIXL_DEPRECATED("TruncateToUint" #N,                             \
165                   inline uint32_t truncate_to_int##N(int64_t x)) { \
166     return TruncateToUint##N(x);                                   \
167   }
168 
169 INT_1_TO_63_LIST(DECLARE_IS_INT_N)
INT_1_TO_63_LIST(DECLARE_IS_UINT_N)170 INT_1_TO_63_LIST(DECLARE_IS_UINT_N)
171 INT_1_TO_32_LIST(DECLARE_TRUNCATE_TO_UINT_32)
172 
173 #undef DECLARE_IS_INT_N
174 #undef DECLARE_IS_UINT_N
175 #undef DECLARE_TRUNCATE_TO_INT_N
176 
177 // Bit field extraction.
178 inline uint64_t ExtractUnsignedBitfield64(int msb, int lsb, uint64_t x) {
179   VIXL_ASSERT((static_cast<size_t>(msb) < sizeof(x) * 8) && (lsb >= 0) &&
180               (msb >= lsb));
181   if ((msb == 63) && (lsb == 0)) return x;
182   return (x >> lsb) & ((static_cast<uint64_t>(1) << (1 + msb - lsb)) - 1);
183 }
184 
185 
ExtractUnsignedBitfield32(int msb,int lsb,uint32_t x)186 inline uint32_t ExtractUnsignedBitfield32(int msb, int lsb, uint32_t x) {
187   VIXL_ASSERT((static_cast<size_t>(msb) < sizeof(x) * 8) && (lsb >= 0) &&
188               (msb >= lsb));
189   return TruncateToUint32(ExtractUnsignedBitfield64(msb, lsb, x));
190 }
191 
192 
ExtractSignedBitfield64(int msb,int lsb,int64_t x)193 inline int64_t ExtractSignedBitfield64(int msb, int lsb, int64_t x) {
194   VIXL_ASSERT((static_cast<size_t>(msb) < sizeof(x) * 8) && (lsb >= 0) &&
195               (msb >= lsb));
196   uint64_t temp = ExtractUnsignedBitfield64(msb, lsb, x);
197   // If the highest extracted bit is set, sign extend.
198   if ((temp >> (msb - lsb)) == 1) {
199     temp |= ~UINT64_C(0) << (msb - lsb);
200   }
201   int64_t result;
202   memcpy(&result, &temp, sizeof(result));
203   return result;
204 }
205 
206 
ExtractSignedBitfield32(int msb,int lsb,int32_t x)207 inline int32_t ExtractSignedBitfield32(int msb, int lsb, int32_t x) {
208   VIXL_ASSERT((static_cast<size_t>(msb) < sizeof(x) * 8) && (lsb >= 0) &&
209               (msb >= lsb));
210   uint32_t temp = TruncateToUint32(ExtractSignedBitfield64(msb, lsb, x));
211   int32_t result;
212   memcpy(&result, &temp, sizeof(result));
213   return result;
214 }
215 
216 
RotateRight(uint64_t value,unsigned int rotate,unsigned int width)217 inline uint64_t RotateRight(uint64_t value,
218                             unsigned int rotate,
219                             unsigned int width) {
220   VIXL_ASSERT((width > 0) && (width <= 64));
221   uint64_t width_mask = ~UINT64_C(0) >> (64 - width);
222   rotate &= 63;
223   if (rotate > 0) {
224     value &= width_mask;
225     value = (value << (width - rotate)) | (value >> rotate);
226   }
227   return value & width_mask;
228 }
229 
230 
231 // Wrapper class for passing FP16 values through the assembler.
232 // This is purely to aid with type checking/casting.
233 class Float16 {
234  public:
235   explicit Float16(double dvalue);
Float16()236   Float16() : rawbits_(0x0) {}
237   friend uint16_t Float16ToRawbits(Float16 value);
238   friend Float16 RawbitsToFloat16(uint16_t bits);
239 
240  protected:
241   uint16_t rawbits_;
242 };
243 
244 // Floating point representation.
245 uint16_t Float16ToRawbits(Float16 value);
246 
247 
248 uint32_t FloatToRawbits(float value);
249 VIXL_DEPRECATED("FloatToRawbits",
250                 inline uint32_t float_to_rawbits(float value)) {
251   return FloatToRawbits(value);
252 }
253 
254 uint64_t DoubleToRawbits(double value);
255 VIXL_DEPRECATED("DoubleToRawbits",
256                 inline uint64_t double_to_rawbits(double value)) {
257   return DoubleToRawbits(value);
258 }
259 
260 Float16 RawbitsToFloat16(uint16_t bits);
261 
262 float RawbitsToFloat(uint32_t bits);
263 VIXL_DEPRECATED("RawbitsToFloat",
rawbits_to_float(uint32_t bits)264                 inline float rawbits_to_float(uint32_t bits)) {
265   return RawbitsToFloat(bits);
266 }
267 
268 double RawbitsToDouble(uint64_t bits);
269 VIXL_DEPRECATED("RawbitsToDouble",
rawbits_to_double(uint64_t bits)270                 inline double rawbits_to_double(uint64_t bits)) {
271   return RawbitsToDouble(bits);
272 }
273 
274 namespace internal {
275 
276 // Internal simulation class used solely by the simulator to
277 // provide an abstraction layer for any half-precision arithmetic.
278 class SimFloat16 : public Float16 {
279  public:
280   // TODO: We should investigate making this constructor explicit.
281   // This is currently difficult to do due to a number of templated
282   // functions in the simulator which rely on returning double values.
SimFloat16(double dvalue)283   SimFloat16(double dvalue) : Float16(dvalue) {}  // NOLINT(runtime/explicit)
SimFloat16(Float16 f)284   SimFloat16(Float16 f) {                         // NOLINT(runtime/explicit)
285     this->rawbits_ = Float16ToRawbits(f);
286   }
SimFloat16()287   SimFloat16() : Float16() {}
288   SimFloat16 operator-() const;
289   SimFloat16 operator+(SimFloat16 rhs) const;
290   SimFloat16 operator-(SimFloat16 rhs) const;
291   SimFloat16 operator*(SimFloat16 rhs) const;
292   SimFloat16 operator/(SimFloat16 rhs) const;
293   bool operator<(SimFloat16 rhs) const;
294   bool operator>(SimFloat16 rhs) const;
295   bool operator==(SimFloat16 rhs) const;
296   bool operator!=(SimFloat16 rhs) const;
297   // This is necessary for conversions peformed in (macro asm) Fmov.
298   bool operator==(double rhs) const;
299   operator double() const;
300 };
301 }  // namespace internal
302 
303 uint32_t Float16Sign(internal::SimFloat16 value);
304 
305 uint32_t Float16Exp(internal::SimFloat16 value);
306 
307 uint32_t Float16Mantissa(internal::SimFloat16 value);
308 
309 uint32_t FloatSign(float value);
310 VIXL_DEPRECATED("FloatSign", inline uint32_t float_sign(float value)) {
311   return FloatSign(value);
312 }
313 
314 uint32_t FloatExp(float value);
315 VIXL_DEPRECATED("FloatExp", inline uint32_t float_exp(float value)) {
316   return FloatExp(value);
317 }
318 
319 uint32_t FloatMantissa(float value);
320 VIXL_DEPRECATED("FloatMantissa", inline uint32_t float_mantissa(float value)) {
321   return FloatMantissa(value);
322 }
323 
324 uint32_t DoubleSign(double value);
325 VIXL_DEPRECATED("DoubleSign", inline uint32_t double_sign(double value)) {
326   return DoubleSign(value);
327 }
328 
329 uint32_t DoubleExp(double value);
330 VIXL_DEPRECATED("DoubleExp", inline uint32_t double_exp(double value)) {
331   return DoubleExp(value);
332 }
333 
334 uint64_t DoubleMantissa(double value);
335 VIXL_DEPRECATED("DoubleMantissa",
336                 inline uint64_t double_mantissa(double value)) {
337   return DoubleMantissa(value);
338 }
339 
340 internal::SimFloat16 Float16Pack(uint16_t sign,
341                                  uint16_t exp,
342                                  uint16_t mantissa);
343 
344 float FloatPack(uint32_t sign, uint32_t exp, uint32_t mantissa);
345 VIXL_DEPRECATED("FloatPack",
float_pack(uint32_t sign,uint32_t exp,uint32_t mantissa)346                 inline float float_pack(uint32_t sign,
347                                         uint32_t exp,
348                                         uint32_t mantissa)) {
349   return FloatPack(sign, exp, mantissa);
350 }
351 
352 double DoublePack(uint64_t sign, uint64_t exp, uint64_t mantissa);
353 VIXL_DEPRECATED("DoublePack",
double_pack(uint32_t sign,uint32_t exp,uint64_t mantissa)354                 inline double double_pack(uint32_t sign,
355                                           uint32_t exp,
356                                           uint64_t mantissa)) {
357   return DoublePack(sign, exp, mantissa);
358 }
359 
360 // An fpclassify() function for 16-bit half-precision floats.
361 int Float16Classify(Float16 value);
float16classify(uint16_t value)362 VIXL_DEPRECATED("Float16Classify", inline int float16classify(uint16_t value)) {
363   return Float16Classify(RawbitsToFloat16(value));
364 }
365 
366 bool IsZero(Float16 value);
367 
IsNaN(float value)368 inline bool IsNaN(float value) { return std::isnan(value); }
369 
IsNaN(double value)370 inline bool IsNaN(double value) { return std::isnan(value); }
371 
IsNaN(Float16 value)372 inline bool IsNaN(Float16 value) { return Float16Classify(value) == FP_NAN; }
373 
IsInf(float value)374 inline bool IsInf(float value) { return std::isinf(value); }
375 
IsInf(double value)376 inline bool IsInf(double value) { return std::isinf(value); }
377 
IsInf(Float16 value)378 inline bool IsInf(Float16 value) {
379   return Float16Classify(value) == FP_INFINITE;
380 }
381 
382 
383 // NaN tests.
IsSignallingNaN(double num)384 inline bool IsSignallingNaN(double num) {
385   const uint64_t kFP64QuietNaNMask = UINT64_C(0x0008000000000000);
386   uint64_t raw = DoubleToRawbits(num);
387   if (IsNaN(num) && ((raw & kFP64QuietNaNMask) == 0)) {
388     return true;
389   }
390   return false;
391 }
392 
393 
IsSignallingNaN(float num)394 inline bool IsSignallingNaN(float num) {
395   const uint32_t kFP32QuietNaNMask = 0x00400000;
396   uint32_t raw = FloatToRawbits(num);
397   if (IsNaN(num) && ((raw & kFP32QuietNaNMask) == 0)) {
398     return true;
399   }
400   return false;
401 }
402 
403 
IsSignallingNaN(Float16 num)404 inline bool IsSignallingNaN(Float16 num) {
405   const uint16_t kFP16QuietNaNMask = 0x0200;
406   return IsNaN(num) && ((Float16ToRawbits(num) & kFP16QuietNaNMask) == 0);
407 }
408 
409 
410 template <typename T>
IsQuietNaN(T num)411 inline bool IsQuietNaN(T num) {
412   return IsNaN(num) && !IsSignallingNaN(num);
413 }
414 
415 
416 // Convert the NaN in 'num' to a quiet NaN.
ToQuietNaN(double num)417 inline double ToQuietNaN(double num) {
418   const uint64_t kFP64QuietNaNMask = UINT64_C(0x0008000000000000);
419   VIXL_ASSERT(IsNaN(num));
420   return RawbitsToDouble(DoubleToRawbits(num) | kFP64QuietNaNMask);
421 }
422 
423 
ToQuietNaN(float num)424 inline float ToQuietNaN(float num) {
425   const uint32_t kFP32QuietNaNMask = 0x00400000;
426   VIXL_ASSERT(IsNaN(num));
427   return RawbitsToFloat(FloatToRawbits(num) | kFP32QuietNaNMask);
428 }
429 
430 
ToQuietNaN(internal::SimFloat16 num)431 inline internal::SimFloat16 ToQuietNaN(internal::SimFloat16 num) {
432   const uint16_t kFP16QuietNaNMask = 0x0200;
433   VIXL_ASSERT(IsNaN(num));
434   return internal::SimFloat16(
435       RawbitsToFloat16(Float16ToRawbits(num) | kFP16QuietNaNMask));
436 }
437 
438 
439 // Fused multiply-add.
FusedMultiplyAdd(double op1,double op2,double a)440 inline double FusedMultiplyAdd(double op1, double op2, double a) {
441   return fma(op1, op2, a);
442 }
443 
444 
FusedMultiplyAdd(float op1,float op2,float a)445 inline float FusedMultiplyAdd(float op1, float op2, float a) {
446   return fmaf(op1, op2, a);
447 }
448 
449 
LowestSetBit(uint64_t value)450 inline uint64_t LowestSetBit(uint64_t value) { return value & -value; }
451 
452 
453 template <typename T>
HighestSetBitPosition(T value)454 inline int HighestSetBitPosition(T value) {
455   VIXL_ASSERT(value != 0);
456   return (sizeof(value) * 8 - 1) - CountLeadingZeros(value);
457 }
458 
459 
460 template <typename V>
WhichPowerOf2(V value)461 inline int WhichPowerOf2(V value) {
462   VIXL_ASSERT(IsPowerOf2(value));
463   return CountTrailingZeros(value);
464 }
465 
466 
467 unsigned CountClearHalfWords(uint64_t imm, unsigned reg_size);
468 
469 
470 int BitCount(uint64_t value);
471 
472 
473 template <typename T>
ReverseBits(T value)474 T ReverseBits(T value) {
475   VIXL_ASSERT((sizeof(value) == 1) || (sizeof(value) == 2) ||
476               (sizeof(value) == 4) || (sizeof(value) == 8));
477   T result = 0;
478   for (unsigned i = 0; i < (sizeof(value) * 8); i++) {
479     result = (result << 1) | (value & 1);
480     value >>= 1;
481   }
482   return result;
483 }
484 
485 
486 template <typename T>
SignExtend(T val,int bitSize)487 inline T SignExtend(T val, int bitSize) {
488   VIXL_ASSERT(bitSize > 0);
489   T mask = (T(2) << (bitSize - 1)) - T(1);
490   val &= mask;
491   T sign_bits = -((val >> (bitSize - 1)) << bitSize);
492   val |= sign_bits;
493   return val;
494 }
495 
496 
497 template <typename T>
ReverseBytes(T value,int block_bytes_log2)498 T ReverseBytes(T value, int block_bytes_log2) {
499   VIXL_ASSERT((sizeof(value) == 4) || (sizeof(value) == 8));
500   VIXL_ASSERT((1U << block_bytes_log2) <= sizeof(value));
501   // Split the 64-bit value into an 8-bit array, where b[0] is the least
502   // significant byte, and b[7] is the most significant.
503   uint8_t bytes[8];
504   uint64_t mask = UINT64_C(0xff00000000000000);
505   for (int i = 7; i >= 0; i--) {
506     bytes[i] = (static_cast<uint64_t>(value) & mask) >> (i * 8);
507     mask >>= 8;
508   }
509 
510   // Permutation tables for REV instructions.
511   //  permute_table[0] is used by REV16_x, REV16_w
512   //  permute_table[1] is used by REV32_x, REV_w
513   //  permute_table[2] is used by REV_x
514   VIXL_ASSERT((0 < block_bytes_log2) && (block_bytes_log2 < 4));
515   static const uint8_t permute_table[3][8] = {{6, 7, 4, 5, 2, 3, 0, 1},
516                                               {4, 5, 6, 7, 0, 1, 2, 3},
517                                               {0, 1, 2, 3, 4, 5, 6, 7}};
518   uint64_t temp = 0;
519   for (int i = 0; i < 8; i++) {
520     temp <<= 8;
521     temp |= bytes[permute_table[block_bytes_log2 - 1][i]];
522   }
523 
524   T result;
525   VIXL_STATIC_ASSERT(sizeof(result) <= sizeof(temp));
526   memcpy(&result, &temp, sizeof(result));
527   return result;
528 }
529 
530 template <unsigned MULTIPLE, typename T>
IsMultiple(T value)531 inline bool IsMultiple(T value) {
532   VIXL_ASSERT(IsPowerOf2(MULTIPLE));
533   return (value & (MULTIPLE - 1)) == 0;
534 }
535 
536 template <typename T>
IsMultiple(T value,unsigned multiple)537 inline bool IsMultiple(T value, unsigned multiple) {
538   VIXL_ASSERT(IsPowerOf2(multiple));
539   return (value & (multiple - 1)) == 0;
540 }
541 
542 template <typename T>
IsAligned(T pointer,int alignment)543 inline bool IsAligned(T pointer, int alignment) {
544   VIXL_ASSERT(IsPowerOf2(alignment));
545   return (pointer & (alignment - 1)) == 0;
546 }
547 
548 // Pointer alignment
549 // TODO: rename/refactor to make it specific to instructions.
550 template <unsigned ALIGN, typename T>
IsAligned(T pointer)551 inline bool IsAligned(T pointer) {
552   VIXL_ASSERT(sizeof(pointer) == sizeof(intptr_t));  // NOLINT(runtime/sizeof)
553   // Use C-style casts to get static_cast behaviour for integral types (T), and
554   // reinterpret_cast behaviour for other types.
555   return IsAligned((intptr_t)(pointer), ALIGN);
556 }
557 
558 template <typename T>
IsWordAligned(T pointer)559 bool IsWordAligned(T pointer) {
560   return IsAligned<4>(pointer);
561 }
562 
563 // Increment a pointer until it has the specified alignment. The alignment must
564 // be a power of two.
565 template <class T>
AlignUp(T pointer,typename Unsigned<sizeof (T)* kBitsPerByte>::type alignment)566 T AlignUp(T pointer,
567           typename Unsigned<sizeof(T) * kBitsPerByte>::type alignment) {
568   VIXL_ASSERT(IsPowerOf2(alignment));
569   // Use C-style casts to get static_cast behaviour for integral types (T), and
570   // reinterpret_cast behaviour for other types.
571 
572   typename Unsigned<sizeof(T)* kBitsPerByte>::type pointer_raw =
573       (typename Unsigned<sizeof(T) * kBitsPerByte>::type)pointer;
574   VIXL_STATIC_ASSERT(sizeof(pointer) <= sizeof(pointer_raw));
575 
576   size_t mask = alignment - 1;
577   T result = (T)((pointer_raw + mask) & ~mask);
578   VIXL_ASSERT(result >= pointer);
579 
580   return result;
581 }
582 
583 // Decrement a pointer until it has the specified alignment. The alignment must
584 // be a power of two.
585 template <class T>
AlignDown(T pointer,typename Unsigned<sizeof (T)* kBitsPerByte>::type alignment)586 T AlignDown(T pointer,
587             typename Unsigned<sizeof(T) * kBitsPerByte>::type alignment) {
588   VIXL_ASSERT(IsPowerOf2(alignment));
589   // Use C-style casts to get static_cast behaviour for integral types (T), and
590   // reinterpret_cast behaviour for other types.
591 
592   typename Unsigned<sizeof(T)* kBitsPerByte>::type pointer_raw =
593       (typename Unsigned<sizeof(T) * kBitsPerByte>::type)pointer;
594   VIXL_STATIC_ASSERT(sizeof(pointer) <= sizeof(pointer_raw));
595 
596   size_t mask = alignment - 1;
597   return (T)(pointer_raw & ~mask);
598 }
599 
600 
601 template <typename T>
ExtractBit(T value,unsigned bit)602 inline T ExtractBit(T value, unsigned bit) {
603   return (value >> bit) & T(1);
604 }
605 
606 template <typename Ts, typename Td>
ExtractBits(Ts value,int least_significant_bit,Td mask)607 inline Td ExtractBits(Ts value, int least_significant_bit, Td mask) {
608   return Td((value >> least_significant_bit) & Ts(mask));
609 }
610 
611 template <typename Ts, typename Td>
AssignBit(Td & dst,int bit,Ts value)612 inline void AssignBit(Td& dst,  // NOLINT(runtime/references)
613                       int bit,
614                       Ts value) {
615   VIXL_ASSERT((value == Ts(0)) || (value == Ts(1)));
616   VIXL_ASSERT(bit >= 0);
617   VIXL_ASSERT(bit < static_cast<int>(sizeof(Td) * 8));
618   Td mask(1);
619   dst &= ~(mask << bit);
620   dst |= Td(value) << bit;
621 }
622 
623 template <typename Td, typename Ts>
AssignBits(Td & dst,int least_significant_bit,Ts mask,Ts value)624 inline void AssignBits(Td& dst,  // NOLINT(runtime/references)
625                        int least_significant_bit,
626                        Ts mask,
627                        Ts value) {
628   VIXL_ASSERT(least_significant_bit >= 0);
629   VIXL_ASSERT(least_significant_bit < static_cast<int>(sizeof(Td) * 8));
630   VIXL_ASSERT(((Td(mask) << least_significant_bit) >> least_significant_bit) ==
631               Td(mask));
632   VIXL_ASSERT((value & mask) == value);
633   dst &= ~(Td(mask) << least_significant_bit);
634   dst |= Td(value) << least_significant_bit;
635 }
636 
637 class VFP {
638  public:
FP32ToImm8(float imm)639   static uint32_t FP32ToImm8(float imm) {
640     // bits: aBbb.bbbc.defg.h000.0000.0000.0000.0000
641     uint32_t bits = FloatToRawbits(imm);
642     // bit7: a000.0000
643     uint32_t bit7 = ((bits >> 31) & 0x1) << 7;
644     // bit6: 0b00.0000
645     uint32_t bit6 = ((bits >> 29) & 0x1) << 6;
646     // bit5_to_0: 00cd.efgh
647     uint32_t bit5_to_0 = (bits >> 19) & 0x3f;
648     return static_cast<uint32_t>(bit7 | bit6 | bit5_to_0);
649   }
FP64ToImm8(double imm)650   static uint32_t FP64ToImm8(double imm) {
651     // bits: aBbb.bbbb.bbcd.efgh.0000.0000.0000.0000
652     //       0000.0000.0000.0000.0000.0000.0000.0000
653     uint64_t bits = DoubleToRawbits(imm);
654     // bit7: a000.0000
655     uint64_t bit7 = ((bits >> 63) & 0x1) << 7;
656     // bit6: 0b00.0000
657     uint64_t bit6 = ((bits >> 61) & 0x1) << 6;
658     // bit5_to_0: 00cd.efgh
659     uint64_t bit5_to_0 = (bits >> 48) & 0x3f;
660 
661     return static_cast<uint32_t>(bit7 | bit6 | bit5_to_0);
662   }
Imm8ToFP32(uint32_t imm8)663   static float Imm8ToFP32(uint32_t imm8) {
664     //   Imm8: abcdefgh (8 bits)
665     // Single: aBbb.bbbc.defg.h000.0000.0000.0000.0000 (32 bits)
666     // where B is b ^ 1
667     uint32_t bits = imm8;
668     uint32_t bit7 = (bits >> 7) & 0x1;
669     uint32_t bit6 = (bits >> 6) & 0x1;
670     uint32_t bit5_to_0 = bits & 0x3f;
671     uint32_t result = (bit7 << 31) | ((32 - bit6) << 25) | (bit5_to_0 << 19);
672 
673     return RawbitsToFloat(result);
674   }
Imm8ToFP64(uint32_t imm8)675   static double Imm8ToFP64(uint32_t imm8) {
676     //   Imm8: abcdefgh (8 bits)
677     // Double: aBbb.bbbb.bbcd.efgh.0000.0000.0000.0000
678     //         0000.0000.0000.0000.0000.0000.0000.0000 (64 bits)
679     // where B is b ^ 1
680     uint32_t bits = imm8;
681     uint64_t bit7 = (bits >> 7) & 0x1;
682     uint64_t bit6 = (bits >> 6) & 0x1;
683     uint64_t bit5_to_0 = bits & 0x3f;
684     uint64_t result = (bit7 << 63) | ((256 - bit6) << 54) | (bit5_to_0 << 48);
685     return RawbitsToDouble(result);
686   }
IsImmFP32(float imm)687   static bool IsImmFP32(float imm) {
688     // Valid values will have the form:
689     // aBbb.bbbc.defg.h000.0000.0000.0000.0000
690     uint32_t bits = FloatToRawbits(imm);
691     // bits[19..0] are cleared.
692     if ((bits & 0x7ffff) != 0) {
693       return false;
694     }
695 
696 
697     // bits[29..25] are all set or all cleared.
698     uint32_t b_pattern = (bits >> 16) & 0x3e00;
699     if (b_pattern != 0 && b_pattern != 0x3e00) {
700       return false;
701     }
702     // bit[30] and bit[29] are opposite.
703     if (((bits ^ (bits << 1)) & 0x40000000) == 0) {
704       return false;
705     }
706     return true;
707   }
IsImmFP64(double imm)708   static bool IsImmFP64(double imm) {
709     // Valid values will have the form:
710     // aBbb.bbbb.bbcd.efgh.0000.0000.0000.0000
711     // 0000.0000.0000.0000.0000.0000.0000.0000
712     uint64_t bits = DoubleToRawbits(imm);
713     // bits[47..0] are cleared.
714     if ((bits & 0x0000ffffffffffff) != 0) {
715       return false;
716     }
717     // bits[61..54] are all set or all cleared.
718     uint32_t b_pattern = (bits >> 48) & 0x3fc0;
719     if ((b_pattern != 0) && (b_pattern != 0x3fc0)) {
720       return false;
721     }
722     // bit[62] and bit[61] are opposite.
723     if (((bits ^ (bits << 1)) & (UINT64_C(1) << 62)) == 0) {
724       return false;
725     }
726     return true;
727   }
728 };
729 
730 class BitField {
731   // ForEachBitHelper is a functor that will call
732   // bool ForEachBitHelper::execute(ElementType id) const
733   //   and expects a boolean in return whether to continue (if true)
734   //   or stop (if false)
735   // check_set will check if the bits are on (true) or off(false)
736   template <typename ForEachBitHelper, bool check_set>
ForEachBit(const ForEachBitHelper & helper)737   bool ForEachBit(const ForEachBitHelper& helper) {
738     for (int i = 0; static_cast<size_t>(i) < bitfield_.size(); i++) {
739       if (bitfield_[i] == check_set)
740         if (!helper.execute(i)) return false;
741     }
742     return true;
743   }
744 
745  public:
BitField(unsigned size)746   explicit BitField(unsigned size) : bitfield_(size, 0) {}
747 
Set(int i)748   void Set(int i) {
749     VIXL_ASSERT((i >= 0) && (static_cast<size_t>(i) < bitfield_.size()));
750     bitfield_[i] = true;
751   }
752 
Unset(int i)753   void Unset(int i) {
754     VIXL_ASSERT((i >= 0) && (static_cast<size_t>(i) < bitfield_.size()));
755     bitfield_[i] = true;
756   }
757 
IsSet(int i)758   bool IsSet(int i) const { return bitfield_[i]; }
759 
760   // For each bit not set in the bitfield call the execute functor
761   // execute.
762   // ForEachBitSetHelper::execute returns true if the iteration through
763   // the bits can continue, otherwise it will stop.
764   // struct ForEachBitSetHelper {
765   //   bool execute(int /*id*/) { return false; }
766   // };
767   template <typename ForEachBitNotSetHelper>
ForEachBitNotSet(const ForEachBitNotSetHelper & helper)768   bool ForEachBitNotSet(const ForEachBitNotSetHelper& helper) {
769     return ForEachBit<ForEachBitNotSetHelper, false>(helper);
770   }
771 
772   // For each bit set in the bitfield call the execute functor
773   // execute.
774   template <typename ForEachBitSetHelper>
ForEachBitSet(const ForEachBitSetHelper & helper)775   bool ForEachBitSet(const ForEachBitSetHelper& helper) {
776     return ForEachBit<ForEachBitSetHelper, true>(helper);
777   }
778 
779  private:
780   std::vector<bool> bitfield_;
781 };
782 
783 namespace internal {
784 
785 typedef int64_t Int64;
786 class Uint64;
787 class Uint128;
788 
789 class Uint32 {
790   uint32_t data_;
791 
792  public:
793   // Unlike uint32_t, Uint32 has a default constructor.
Uint32()794   Uint32() { data_ = 0; }
Uint32(uint32_t data)795   explicit Uint32(uint32_t data) : data_(data) {}
796   inline explicit Uint32(Uint64 data);
Get()797   uint32_t Get() const { return data_; }
798   template <int N>
GetSigned()799   int32_t GetSigned() const {
800     return ExtractSignedBitfield32(N - 1, 0, data_);
801   }
GetSigned()802   int32_t GetSigned() const { return data_; }
803   Uint32 operator~() const { return Uint32(~data_); }
804   Uint32 operator-() const { return Uint32(-data_); }
805   bool operator==(Uint32 value) const { return data_ == value.data_; }
806   bool operator!=(Uint32 value) const { return data_ != value.data_; }
807   bool operator>(Uint32 value) const { return data_ > value.data_; }
808   Uint32 operator+(Uint32 value) const { return Uint32(data_ + value.data_); }
809   Uint32 operator-(Uint32 value) const { return Uint32(data_ - value.data_); }
810   Uint32 operator&(Uint32 value) const { return Uint32(data_ & value.data_); }
811   Uint32 operator&=(Uint32 value) {
812     data_ &= value.data_;
813     return *this;
814   }
815   Uint32 operator^(Uint32 value) const { return Uint32(data_ ^ value.data_); }
816   Uint32 operator^=(Uint32 value) {
817     data_ ^= value.data_;
818     return *this;
819   }
820   Uint32 operator|(Uint32 value) const { return Uint32(data_ | value.data_); }
821   Uint32 operator|=(Uint32 value) {
822     data_ |= value.data_;
823     return *this;
824   }
825   // Unlike uint32_t, the shift functions can accept negative shift and
826   // return 0 when the shift is too big.
827   Uint32 operator>>(int shift) const {
828     if (shift == 0) return *this;
829     if (shift < 0) {
830       int tmp = -shift;
831       if (tmp >= 32) return Uint32(0);
832       return Uint32(data_ << tmp);
833     }
834     int tmp = shift;
835     if (tmp >= 32) return Uint32(0);
836     return Uint32(data_ >> tmp);
837   }
838   Uint32 operator<<(int shift) const {
839     if (shift == 0) return *this;
840     if (shift < 0) {
841       int tmp = -shift;
842       if (tmp >= 32) return Uint32(0);
843       return Uint32(data_ >> tmp);
844     }
845     int tmp = shift;
846     if (tmp >= 32) return Uint32(0);
847     return Uint32(data_ << tmp);
848   }
849 };
850 
851 class Uint64 {
852   uint64_t data_;
853 
854  public:
855   // Unlike uint64_t, Uint64 has a default constructor.
Uint64()856   Uint64() { data_ = 0; }
Uint64(uint64_t data)857   explicit Uint64(uint64_t data) : data_(data) {}
Uint64(Uint32 data)858   explicit Uint64(Uint32 data) : data_(data.Get()) {}
859   inline explicit Uint64(Uint128 data);
Get()860   uint64_t Get() const { return data_; }
GetSigned(int N)861   int64_t GetSigned(int N) const {
862     return ExtractSignedBitfield64(N - 1, 0, data_);
863   }
GetSigned()864   int64_t GetSigned() const { return data_; }
ToUint32()865   Uint32 ToUint32() const {
866     VIXL_ASSERT((data_ >> 32) == 0);
867     return Uint32(static_cast<uint32_t>(data_));
868   }
GetHigh32()869   Uint32 GetHigh32() const { return Uint32(data_ >> 32); }
GetLow32()870   Uint32 GetLow32() const { return Uint32(data_ & 0xffffffff); }
871   Uint64 operator~() const { return Uint64(~data_); }
872   Uint64 operator-() const { return Uint64(-data_); }
873   bool operator==(Uint64 value) const { return data_ == value.data_; }
874   bool operator!=(Uint64 value) const { return data_ != value.data_; }
875   Uint64 operator+(Uint64 value) const { return Uint64(data_ + value.data_); }
876   Uint64 operator-(Uint64 value) const { return Uint64(data_ - value.data_); }
877   Uint64 operator&(Uint64 value) const { return Uint64(data_ & value.data_); }
878   Uint64 operator&=(Uint64 value) {
879     data_ &= value.data_;
880     return *this;
881   }
882   Uint64 operator^(Uint64 value) const { return Uint64(data_ ^ value.data_); }
883   Uint64 operator^=(Uint64 value) {
884     data_ ^= value.data_;
885     return *this;
886   }
887   Uint64 operator|(Uint64 value) const { return Uint64(data_ | value.data_); }
888   Uint64 operator|=(Uint64 value) {
889     data_ |= value.data_;
890     return *this;
891   }
892   // Unlike uint64_t, the shift functions can accept negative shift and
893   // return 0 when the shift is too big.
894   Uint64 operator>>(int shift) const {
895     if (shift == 0) return *this;
896     if (shift < 0) {
897       int tmp = -shift;
898       if (tmp >= 64) return Uint64(0);
899       return Uint64(data_ << tmp);
900     }
901     int tmp = shift;
902     if (tmp >= 64) return Uint64(0);
903     return Uint64(data_ >> tmp);
904   }
905   Uint64 operator<<(int shift) const {
906     if (shift == 0) return *this;
907     if (shift < 0) {
908       int tmp = -shift;
909       if (tmp >= 64) return Uint64(0);
910       return Uint64(data_ >> tmp);
911     }
912     int tmp = shift;
913     if (tmp >= 64) return Uint64(0);
914     return Uint64(data_ << tmp);
915   }
916 };
917 
918 class Uint128 {
919   uint64_t data_high_;
920   uint64_t data_low_;
921 
922  public:
Uint128()923   Uint128() : data_high_(0), data_low_(0) {}
Uint128(uint64_t data_low)924   explicit Uint128(uint64_t data_low) : data_high_(0), data_low_(data_low) {}
Uint128(Uint64 data_low)925   explicit Uint128(Uint64 data_low)
926       : data_high_(0), data_low_(data_low.Get()) {}
Uint128(uint64_t data_high,uint64_t data_low)927   Uint128(uint64_t data_high, uint64_t data_low)
928       : data_high_(data_high), data_low_(data_low) {}
ToUint64()929   Uint64 ToUint64() const {
930     VIXL_ASSERT(data_high_ == 0);
931     return Uint64(data_low_);
932   }
GetHigh64()933   Uint64 GetHigh64() const { return Uint64(data_high_); }
GetLow64()934   Uint64 GetLow64() const { return Uint64(data_low_); }
935   Uint128 operator~() const { return Uint128(~data_high_, ~data_low_); }
936   bool operator==(Uint128 value) const {
937     return (data_high_ == value.data_high_) && (data_low_ == value.data_low_);
938   }
939   Uint128 operator&(Uint128 value) const {
940     return Uint128(data_high_ & value.data_high_, data_low_ & value.data_low_);
941   }
942   Uint128 operator&=(Uint128 value) {
943     data_high_ &= value.data_high_;
944     data_low_ &= value.data_low_;
945     return *this;
946   }
947   Uint128 operator|=(Uint128 value) {
948     data_high_ |= value.data_high_;
949     data_low_ |= value.data_low_;
950     return *this;
951   }
952   Uint128 operator>>(int shift) const {
953     VIXL_ASSERT((shift >= 0) && (shift < 128));
954     if (shift == 0) return *this;
955     if (shift >= 64) {
956       return Uint128(0, data_high_ >> (shift - 64));
957     }
958     uint64_t tmp = (data_high_ << (64 - shift)) | (data_low_ >> shift);
959     return Uint128(data_high_ >> shift, tmp);
960   }
961   Uint128 operator<<(int shift) const {
962     VIXL_ASSERT((shift >= 0) && (shift < 128));
963     if (shift == 0) return *this;
964     if (shift >= 64) {
965       return Uint128(data_low_ << (shift - 64), 0);
966     }
967     uint64_t tmp = (data_high_ << shift) | (data_low_ >> (64 - shift));
968     return Uint128(tmp, data_low_ << shift);
969   }
970 };
971 
Uint32(Uint64 data)972 Uint32::Uint32(Uint64 data) : data_(data.ToUint32().Get()) {}
Uint64(Uint128 data)973 Uint64::Uint64(Uint128 data) : data_(data.ToUint64().Get()) {}
974 
975 Int64 BitCount(Uint32 value);
976 
977 }  // namespace internal
978 
979 // The default NaN values (for FPCR.DN=1).
980 extern const double kFP64DefaultNaN;
981 extern const float kFP32DefaultNaN;
982 extern const Float16 kFP16DefaultNaN;
983 
984 // Floating-point infinity values.
985 extern const Float16 kFP16PositiveInfinity;
986 extern const Float16 kFP16NegativeInfinity;
987 extern const float kFP32PositiveInfinity;
988 extern const float kFP32NegativeInfinity;
989 extern const double kFP64PositiveInfinity;
990 extern const double kFP64NegativeInfinity;
991 
992 // Floating-point zero values.
993 extern const Float16 kFP16PositiveZero;
994 extern const Float16 kFP16NegativeZero;
995 
996 // AArch64 floating-point specifics. These match IEEE-754.
997 const unsigned kDoubleMantissaBits = 52;
998 const unsigned kDoubleExponentBits = 11;
999 const unsigned kFloatMantissaBits = 23;
1000 const unsigned kFloatExponentBits = 8;
1001 const unsigned kFloat16MantissaBits = 10;
1002 const unsigned kFloat16ExponentBits = 5;
1003 
1004 enum FPRounding {
1005   // The first four values are encodable directly by FPCR<RMode>.
1006   FPTieEven = 0x0,
1007   FPPositiveInfinity = 0x1,
1008   FPNegativeInfinity = 0x2,
1009   FPZero = 0x3,
1010 
1011   // The final rounding modes are only available when explicitly specified by
1012   // the instruction (such as with fcvta). It cannot be set in FPCR.
1013   FPTieAway,
1014   FPRoundOdd
1015 };
1016 
1017 enum UseDefaultNaN { kUseDefaultNaN, kIgnoreDefaultNaN };
1018 
1019 // Assemble the specified IEEE-754 components into the target type and apply
1020 // appropriate rounding.
1021 //  sign:     0 = positive, 1 = negative
1022 //  exponent: Unbiased IEEE-754 exponent.
1023 //  mantissa: The mantissa of the input. The top bit (which is not encoded for
1024 //            normal IEEE-754 values) must not be omitted. This bit has the
1025 //            value 'pow(2, exponent)'.
1026 //
1027 // The input value is assumed to be a normalized value. That is, the input may
1028 // not be infinity or NaN. If the source value is subnormal, it must be
1029 // normalized before calling this function such that the highest set bit in the
1030 // mantissa has the value 'pow(2, exponent)'.
1031 //
1032 // Callers should use FPRoundToFloat or FPRoundToDouble directly, rather than
1033 // calling a templated FPRound.
1034 template <class T, int ebits, int mbits>
FPRound(int64_t sign,int64_t exponent,uint64_t mantissa,FPRounding round_mode)1035 T FPRound(int64_t sign,
1036           int64_t exponent,
1037           uint64_t mantissa,
1038           FPRounding round_mode) {
1039   VIXL_ASSERT((sign == 0) || (sign == 1));
1040 
1041   // Only FPTieEven and FPRoundOdd rounding modes are implemented.
1042   VIXL_ASSERT((round_mode == FPTieEven) || (round_mode == FPRoundOdd));
1043 
1044   // Rounding can promote subnormals to normals, and normals to infinities. For
1045   // example, a double with exponent 127 (FLT_MAX_EXP) would appear to be
1046   // encodable as a float, but rounding based on the low-order mantissa bits
1047   // could make it overflow. With ties-to-even rounding, this value would become
1048   // an infinity.
1049 
1050   // ---- Rounding Method ----
1051   //
1052   // The exponent is irrelevant in the rounding operation, so we treat the
1053   // lowest-order bit that will fit into the result ('onebit') as having
1054   // the value '1'. Similarly, the highest-order bit that won't fit into
1055   // the result ('halfbit') has the value '0.5'. The 'point' sits between
1056   // 'onebit' and 'halfbit':
1057   //
1058   //            These bits fit into the result.
1059   //               |---------------------|
1060   //  mantissa = 0bxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
1061   //                                     ||
1062   //                                    / |
1063   //                                   /  halfbit
1064   //                               onebit
1065   //
1066   // For subnormal outputs, the range of representable bits is smaller and
1067   // the position of onebit and halfbit depends on the exponent of the
1068   // input, but the method is otherwise similar.
1069   //
1070   //   onebit(frac)
1071   //     |
1072   //     | halfbit(frac)          halfbit(adjusted)
1073   //     | /                      /
1074   //     | |                      |
1075   //  0b00.0 (exact)      -> 0b00.0 (exact)                    -> 0b00
1076   //  0b00.0...           -> 0b00.0...                         -> 0b00
1077   //  0b00.1 (exact)      -> 0b00.0111..111                    -> 0b00
1078   //  0b00.1...           -> 0b00.1...                         -> 0b01
1079   //  0b01.0 (exact)      -> 0b01.0 (exact)                    -> 0b01
1080   //  0b01.0...           -> 0b01.0...                         -> 0b01
1081   //  0b01.1 (exact)      -> 0b01.1 (exact)                    -> 0b10
1082   //  0b01.1...           -> 0b01.1...                         -> 0b10
1083   //  0b10.0 (exact)      -> 0b10.0 (exact)                    -> 0b10
1084   //  0b10.0...           -> 0b10.0...                         -> 0b10
1085   //  0b10.1 (exact)      -> 0b10.0111..111                    -> 0b10
1086   //  0b10.1...           -> 0b10.1...                         -> 0b11
1087   //  0b11.0 (exact)      -> 0b11.0 (exact)                    -> 0b11
1088   //  ...                   /             |                      /   |
1089   //                       /              |                     /    |
1090   //                                                           /     |
1091   // adjusted = frac - (halfbit(mantissa) & ~onebit(frac));   /      |
1092   //
1093   //                   mantissa = (mantissa >> shift) + halfbit(adjusted);
1094 
1095   static const int mantissa_offset = 0;
1096   static const int exponent_offset = mantissa_offset + mbits;
1097   static const int sign_offset = exponent_offset + ebits;
1098   VIXL_ASSERT(sign_offset == (sizeof(T) * 8 - 1));
1099 
1100   // Bail out early for zero inputs.
1101   if (mantissa == 0) {
1102     return static_cast<T>(sign << sign_offset);
1103   }
1104 
1105   // If all bits in the exponent are set, the value is infinite or NaN.
1106   // This is true for all binary IEEE-754 formats.
1107   static const int infinite_exponent = (1 << ebits) - 1;
1108   static const int max_normal_exponent = infinite_exponent - 1;
1109 
1110   // Apply the exponent bias to encode it for the result. Doing this early makes
1111   // it easy to detect values that will be infinite or subnormal.
1112   exponent += max_normal_exponent >> 1;
1113 
1114   if (exponent > max_normal_exponent) {
1115     // Overflow: the input is too large for the result type to represent.
1116     if (round_mode == FPTieEven) {
1117       // FPTieEven rounding mode handles overflows using infinities.
1118       exponent = infinite_exponent;
1119       mantissa = 0;
1120     } else {
1121       VIXL_ASSERT(round_mode == FPRoundOdd);
1122       // FPRoundOdd rounding mode handles overflows using the largest magnitude
1123       // normal number.
1124       exponent = max_normal_exponent;
1125       mantissa = (UINT64_C(1) << exponent_offset) - 1;
1126     }
1127     return static_cast<T>((sign << sign_offset) |
1128                           (exponent << exponent_offset) |
1129                           (mantissa << mantissa_offset));
1130   }
1131 
1132   // Calculate the shift required to move the top mantissa bit to the proper
1133   // place in the destination type.
1134   const int highest_significant_bit = 63 - CountLeadingZeros(mantissa);
1135   int shift = highest_significant_bit - mbits;
1136 
1137   if (exponent <= 0) {
1138     // The output will be subnormal (before rounding).
1139     // For subnormal outputs, the shift must be adjusted by the exponent. The +1
1140     // is necessary because the exponent of a subnormal value (encoded as 0) is
1141     // the same as the exponent of the smallest normal value (encoded as 1).
1142     shift += -exponent + 1;
1143 
1144     // Handle inputs that would produce a zero output.
1145     //
1146     // Shifts higher than highest_significant_bit+1 will always produce a zero
1147     // result. A shift of exactly highest_significant_bit+1 might produce a
1148     // non-zero result after rounding.
1149     if (shift > (highest_significant_bit + 1)) {
1150       if (round_mode == FPTieEven) {
1151         // The result will always be +/-0.0.
1152         return static_cast<T>(sign << sign_offset);
1153       } else {
1154         VIXL_ASSERT(round_mode == FPRoundOdd);
1155         VIXL_ASSERT(mantissa != 0);
1156         // For FPRoundOdd, if the mantissa is too small to represent and
1157         // non-zero return the next "odd" value.
1158         return static_cast<T>((sign << sign_offset) | 1);
1159       }
1160     }
1161 
1162     // Properly encode the exponent for a subnormal output.
1163     exponent = 0;
1164   } else {
1165     // Clear the topmost mantissa bit, since this is not encoded in IEEE-754
1166     // normal values.
1167     mantissa &= ~(UINT64_C(1) << highest_significant_bit);
1168   }
1169 
1170   // The casts below are only well-defined for unsigned integers.
1171   VIXL_STATIC_ASSERT(std::numeric_limits<T>::is_integer);
1172   VIXL_STATIC_ASSERT(!std::numeric_limits<T>::is_signed);
1173 
1174   if (shift > 0) {
1175     if (round_mode == FPTieEven) {
1176       // We have to shift the mantissa to the right. Some precision is lost, so
1177       // we need to apply rounding.
1178       uint64_t onebit_mantissa = (mantissa >> (shift)) & 1;
1179       uint64_t halfbit_mantissa = (mantissa >> (shift - 1)) & 1;
1180       uint64_t adjustment = (halfbit_mantissa & ~onebit_mantissa);
1181       uint64_t adjusted = mantissa - adjustment;
1182       T halfbit_adjusted = (adjusted >> (shift - 1)) & 1;
1183 
1184       T result =
1185           static_cast<T>((sign << sign_offset) | (exponent << exponent_offset) |
1186                          ((mantissa >> shift) << mantissa_offset));
1187 
1188       // A very large mantissa can overflow during rounding. If this happens,
1189       // the exponent should be incremented and the mantissa set to 1.0
1190       // (encoded as 0). Applying halfbit_adjusted after assembling the float
1191       // has the nice side-effect that this case is handled for free.
1192       //
1193       // This also handles cases where a very large finite value overflows to
1194       // infinity, or where a very large subnormal value overflows to become
1195       // normal.
1196       return result + halfbit_adjusted;
1197     } else {
1198       VIXL_ASSERT(round_mode == FPRoundOdd);
1199       // If any bits at position halfbit or below are set, onebit (ie. the
1200       // bottom bit of the resulting mantissa) must be set.
1201       uint64_t fractional_bits = mantissa & ((UINT64_C(1) << shift) - 1);
1202       if (fractional_bits != 0) {
1203         mantissa |= UINT64_C(1) << shift;
1204       }
1205 
1206       return static_cast<T>((sign << sign_offset) |
1207                             (exponent << exponent_offset) |
1208                             ((mantissa >> shift) << mantissa_offset));
1209     }
1210   } else {
1211     // We have to shift the mantissa to the left (or not at all). The input
1212     // mantissa is exactly representable in the output mantissa, so apply no
1213     // rounding correction.
1214     return static_cast<T>((sign << sign_offset) |
1215                           (exponent << exponent_offset) |
1216                           ((mantissa << -shift) << mantissa_offset));
1217   }
1218 }
1219 
1220 
1221 // See FPRound for a description of this function.
FPRoundToDouble(int64_t sign,int64_t exponent,uint64_t mantissa,FPRounding round_mode)1222 inline double FPRoundToDouble(int64_t sign,
1223                               int64_t exponent,
1224                               uint64_t mantissa,
1225                               FPRounding round_mode) {
1226   uint64_t bits =
1227       FPRound<uint64_t, kDoubleExponentBits, kDoubleMantissaBits>(sign,
1228                                                                   exponent,
1229                                                                   mantissa,
1230                                                                   round_mode);
1231   return RawbitsToDouble(bits);
1232 }
1233 
1234 
1235 // See FPRound for a description of this function.
FPRoundToFloat16(int64_t sign,int64_t exponent,uint64_t mantissa,FPRounding round_mode)1236 inline Float16 FPRoundToFloat16(int64_t sign,
1237                                 int64_t exponent,
1238                                 uint64_t mantissa,
1239                                 FPRounding round_mode) {
1240   return RawbitsToFloat16(
1241       FPRound<uint16_t,
1242               kFloat16ExponentBits,
1243               kFloat16MantissaBits>(sign, exponent, mantissa, round_mode));
1244 }
1245 
1246 
1247 // See FPRound for a description of this function.
FPRoundToFloat(int64_t sign,int64_t exponent,uint64_t mantissa,FPRounding round_mode)1248 static inline float FPRoundToFloat(int64_t sign,
1249                                    int64_t exponent,
1250                                    uint64_t mantissa,
1251                                    FPRounding round_mode) {
1252   uint32_t bits =
1253       FPRound<uint32_t, kFloatExponentBits, kFloatMantissaBits>(sign,
1254                                                                 exponent,
1255                                                                 mantissa,
1256                                                                 round_mode);
1257   return RawbitsToFloat(bits);
1258 }
1259 
1260 
1261 float FPToFloat(Float16 value, UseDefaultNaN DN, bool* exception = NULL);
1262 float FPToFloat(double value,
1263                 FPRounding round_mode,
1264                 UseDefaultNaN DN,
1265                 bool* exception = NULL);
1266 
1267 double FPToDouble(Float16 value, UseDefaultNaN DN, bool* exception = NULL);
1268 double FPToDouble(float value, UseDefaultNaN DN, bool* exception = NULL);
1269 
1270 Float16 FPToFloat16(float value,
1271                     FPRounding round_mode,
1272                     UseDefaultNaN DN,
1273                     bool* exception = NULL);
1274 
1275 Float16 FPToFloat16(double value,
1276                     FPRounding round_mode,
1277                     UseDefaultNaN DN,
1278                     bool* exception = NULL);
1279 }  // namespace vixl
1280 
1281 #endif  // VIXL_UTILS_H
1282