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
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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 "mozilla/FloatingPoint.h"
31 
32 #include <cmath>
33 #include <cstring>
34 #include <limits>
35 #include <vector>
36 
37 #include "jit/arm64/vixl/CompilerIntrinsics-vixl.h"
38 #include "jit/arm64/vixl/Globals-vixl.h"
39 
40 namespace vixl {
41 
42 // Macros for compile-time format checking.
43 #if GCC_VERSION_OR_NEWER(4, 4, 0)
44 #define PRINTF_CHECK(format_index, varargs_index) \
45   __attribute__((format(gnu_printf, format_index, varargs_index)))
46 #else
47 #define PRINTF_CHECK(format_index, varargs_index)
48 #endif
49 
50 #ifdef __GNUC__
51 #define VIXL_HAS_DEPRECATED_WITH_MSG
52 #elif defined(__clang__)
53 #ifdef __has_extension
54 #define VIXL_HAS_DEPRECATED_WITH_MSG
55 #endif
56 #endif
57 
58 #ifdef VIXL_HAS_DEPRECATED_WITH_MSG
59 #define VIXL_DEPRECATED(replaced_by, declarator) \
60   __attribute__((deprecated("Use \"" replaced_by "\" instead"))) declarator
61 #else
62 #define VIXL_DEPRECATED(replaced_by, declarator) declarator
63 #endif
64 
65 #ifdef VIXL_DEBUG
66 #define VIXL_UNREACHABLE_OR_FALLTHROUGH() VIXL_UNREACHABLE()
67 #else
68 #define VIXL_UNREACHABLE_OR_FALLTHROUGH() VIXL_FALLTHROUGH()
69 #endif
70 
71 template <typename T, size_t n>
ArrayLength(const T (&)[n])72 size_t ArrayLength(const T (&)[n]) {
73   return n;
74 }
75 
76 // Check number width.
77 // TODO: Refactor these using templates.
IsIntN(unsigned n,uint32_t x)78 inline bool IsIntN(unsigned n, uint32_t x) {
79   VIXL_ASSERT((0 < n) && (n < 32));
80   uint32_t limit = UINT32_C(1) << (n - 1);
81   return x < limit;
82 }
IsIntN(unsigned n,int32_t x)83 inline bool IsIntN(unsigned n, int32_t x) {
84   VIXL_ASSERT((0 < n) && (n < 32));
85   int32_t limit = INT32_C(1) << (n - 1);
86   return (-limit <= x) && (x < limit);
87 }
IsIntN(unsigned n,uint64_t x)88 inline bool IsIntN(unsigned n, uint64_t x) {
89   VIXL_ASSERT((0 < n) && (n < 64));
90   uint64_t limit = UINT64_C(1) << (n - 1);
91   return x < limit;
92 }
IsIntN(unsigned n,int64_t x)93 inline bool IsIntN(unsigned n, int64_t x) {
94   VIXL_ASSERT((0 < n) && (n < 64));
95   int64_t limit = INT64_C(1) << (n - 1);
96   return (-limit <= x) && (x < limit);
97 }
is_intn(unsigned n,int64_t x)98 VIXL_DEPRECATED("IsIntN", inline bool is_intn(unsigned n, int64_t x)) {
99   return IsIntN(n, x);
100 }
101 
IsUintN(unsigned n,uint32_t x)102 inline bool IsUintN(unsigned n, uint32_t x) {
103   VIXL_ASSERT((0 < n) && (n < 32));
104   return !(x >> n);
105 }
IsUintN(unsigned n,int32_t x)106 inline bool IsUintN(unsigned n, int32_t x) {
107   VIXL_ASSERT((0 < n) && (n < 32));
108   // Convert to an unsigned integer to avoid implementation-defined behavior.
109   return !(static_cast<uint32_t>(x) >> n);
110 }
IsUintN(unsigned n,uint64_t x)111 inline bool IsUintN(unsigned n, uint64_t x) {
112   VIXL_ASSERT((0 < n) && (n < 64));
113   return !(x >> n);
114 }
IsUintN(unsigned n,int64_t x)115 inline bool IsUintN(unsigned n, int64_t x) {
116   VIXL_ASSERT((0 < n) && (n < 64));
117   // Convert to an unsigned integer to avoid implementation-defined behavior.
118   return !(static_cast<uint64_t>(x) >> n);
119 }
is_uintn(unsigned n,int64_t x)120 VIXL_DEPRECATED("IsUintN", inline bool is_uintn(unsigned n, int64_t x)) {
121   return IsUintN(n, x);
122 }
123 
TruncateToUintN(unsigned n,uint64_t x)124 inline uint64_t TruncateToUintN(unsigned n, uint64_t x) {
125   VIXL_ASSERT((0 < n) && (n < 64));
126   return static_cast<uint64_t>(x) & ((UINT64_C(1) << n) - 1);
127 }
128 VIXL_DEPRECATED("TruncateToUintN",
129                 inline uint64_t truncate_to_intn(unsigned n, int64_t x)) {
130   return TruncateToUintN(n, x);
131 }
132 
133 // clang-format off
134 #define INT_1_TO_32_LIST(V)                                                    \
135 V(1)  V(2)  V(3)  V(4)  V(5)  V(6)  V(7)  V(8)                                 \
136 V(9)  V(10) V(11) V(12) V(13) V(14) V(15) V(16)                                \
137 V(17) V(18) V(19) V(20) V(21) V(22) V(23) V(24)                                \
138 V(25) V(26) V(27) V(28) V(29) V(30) V(31) V(32)
139 
140 #define INT_33_TO_63_LIST(V)                                                   \
141 V(33) V(34) V(35) V(36) V(37) V(38) V(39) V(40)                                \
142 V(41) V(42) V(43) V(44) V(45) V(46) V(47) V(48)                                \
143 V(49) V(50) V(51) V(52) V(53) V(54) V(55) V(56)                                \
144 V(57) V(58) V(59) V(60) V(61) V(62) V(63)
145 
146 #define INT_1_TO_63_LIST(V) INT_1_TO_32_LIST(V) INT_33_TO_63_LIST(V)
147 
148 // clang-format on
149 
150 #define DECLARE_IS_INT_N(N)                                       \
151   inline bool IsInt##N(int64_t x) { return IsIntN(N, x); }        \
152   VIXL_DEPRECATED("IsInt" #N, inline bool is_int##N(int64_t x)) { \
153     return IsIntN(N, x);                                          \
154   }
155 
156 #define DECLARE_IS_UINT_N(N)                                        \
157   inline bool IsUint##N(int64_t x) { return IsUintN(N, x); }        \
158   VIXL_DEPRECATED("IsUint" #N, inline bool is_uint##N(int64_t x)) { \
159     return IsUintN(N, x);                                           \
160   }
161 
162 #define DECLARE_TRUNCATE_TO_UINT_32(N)                             \
163   inline uint32_t TruncateToUint##N(uint64_t x) {                  \
164     return static_cast<uint32_t>(TruncateToUintN(N, x));           \
165   }                                                                \
166   VIXL_DEPRECATED("TruncateToUint" #N,                             \
167                   inline uint32_t truncate_to_int##N(int64_t x)) { \
168     return TruncateToUint##N(x);                                   \
169   }
170 
171 INT_1_TO_63_LIST(DECLARE_IS_INT_N)
INT_1_TO_63_LIST(DECLARE_IS_UINT_N)172 INT_1_TO_63_LIST(DECLARE_IS_UINT_N)
173 INT_1_TO_32_LIST(DECLARE_TRUNCATE_TO_UINT_32)
174 
175 #undef DECLARE_IS_INT_N
176 #undef DECLARE_IS_UINT_N
177 #undef DECLARE_TRUNCATE_TO_INT_N
178 
179 // Bit field extraction.
180 inline uint64_t ExtractUnsignedBitfield64(int msb, int lsb, uint64_t x) {
181   VIXL_ASSERT((static_cast<size_t>(msb) < sizeof(x) * 8) && (lsb >= 0) &&
182               (msb >= lsb));
183   if ((msb == 63) && (lsb == 0)) return x;
184   return (x >> lsb) & ((static_cast<uint64_t>(1) << (1 + msb - lsb)) - 1);
185 }
186 
187 
ExtractUnsignedBitfield32(int msb,int lsb,uint32_t x)188 inline uint32_t ExtractUnsignedBitfield32(int msb, int lsb, uint32_t x) {
189   VIXL_ASSERT((static_cast<size_t>(msb) < sizeof(x) * 8) && (lsb >= 0) &&
190               (msb >= lsb));
191   return TruncateToUint32(ExtractUnsignedBitfield64(msb, lsb, x));
192 }
193 
194 
ExtractSignedBitfield64(int msb,int lsb,int64_t x)195 inline int64_t ExtractSignedBitfield64(int msb, int lsb, int64_t x) {
196   VIXL_ASSERT((static_cast<size_t>(msb) < sizeof(x) * 8) && (lsb >= 0) &&
197               (msb >= lsb));
198   uint64_t temp = ExtractUnsignedBitfield64(msb, lsb, x);
199   // If the highest extracted bit is set, sign extend.
200   if ((temp >> (msb - lsb)) == 1) {
201     temp |= ~UINT64_C(0) << (msb - lsb);
202   }
203   int64_t result;
204   memcpy(&result, &temp, sizeof(result));
205   return result;
206 }
207 
208 
ExtractSignedBitfield32(int msb,int lsb,int32_t x)209 inline int32_t ExtractSignedBitfield32(int msb, int lsb, int32_t x) {
210   VIXL_ASSERT((static_cast<size_t>(msb) < sizeof(x) * 8) && (lsb >= 0) &&
211               (msb >= lsb));
212   uint32_t temp = TruncateToUint32(ExtractSignedBitfield64(msb, lsb, x));
213   int32_t result;
214   memcpy(&result, &temp, sizeof(result));
215   return result;
216 }
217 
218 
RotateRight(uint64_t value,unsigned int rotate,unsigned int width)219 inline uint64_t RotateRight(uint64_t value,
220                             unsigned int rotate,
221                             unsigned int width) {
222   VIXL_ASSERT((width > 0) && (width <= 64));
223   uint64_t width_mask = ~UINT64_C(0) >> (64 - width);
224   rotate &= 63;
225   if (rotate > 0) {
226     value &= width_mask;
227     value = (value << (width - rotate)) | (value >> rotate);
228   }
229   return value & width_mask;
230 }
231 
232 
233 // Wrapper class for passing FP16 values through the assembler.
234 // This is purely to aid with type checking/casting.
235 class Float16 {
236  public:
237   explicit Float16(double dvalue);
Float16()238   Float16() : rawbits_(0x0) {}
239   friend uint16_t Float16ToRawbits(Float16 value);
240   friend Float16 RawbitsToFloat16(uint16_t bits);
241 
242  protected:
243   uint16_t rawbits_;
244 };
245 
246 // Floating point representation.
247 uint16_t Float16ToRawbits(Float16 value);
248 
249 
250 uint32_t FloatToRawbits(float value);
251 VIXL_DEPRECATED("FloatToRawbits",
252                 inline uint32_t float_to_rawbits(float value)) {
253   return FloatToRawbits(value);
254 }
255 
256 uint64_t DoubleToRawbits(double value);
257 VIXL_DEPRECATED("DoubleToRawbits",
258                 inline uint64_t double_to_rawbits(double value)) {
259   return DoubleToRawbits(value);
260 }
261 
262 Float16 RawbitsToFloat16(uint16_t bits);
263 
264 float RawbitsToFloat(uint32_t bits);
265 VIXL_DEPRECATED("RawbitsToFloat",
rawbits_to_float(uint32_t bits)266                 inline float rawbits_to_float(uint32_t bits)) {
267   return RawbitsToFloat(bits);
268 }
269 
270 double RawbitsToDouble(uint64_t bits);
271 VIXL_DEPRECATED("RawbitsToDouble",
rawbits_to_double(uint64_t bits)272                 inline double rawbits_to_double(uint64_t bits)) {
273   return RawbitsToDouble(bits);
274 }
275 
276 namespace internal {
277 
278 // Internal simulation class used solely by the simulator to
279 // provide an abstraction layer for any half-precision arithmetic.
280 class SimFloat16 : public Float16 {
281  public:
282   // TODO: We should investigate making this constructor explicit.
283   // This is currently difficult to do due to a number of templated
284   // functions in the simulator which rely on returning double values.
SimFloat16(double dvalue)285   SimFloat16(double dvalue) : Float16(dvalue) {}  // NOLINT(runtime/explicit)
SimFloat16(Float16 f)286   SimFloat16(Float16 f) {                         // NOLINT(runtime/explicit)
287     this->rawbits_ = Float16ToRawbits(f);
288   }
SimFloat16()289   SimFloat16() : Float16() {}
290   SimFloat16 operator-() const;
291   SimFloat16 operator+(SimFloat16 rhs) const;
292   SimFloat16 operator-(SimFloat16 rhs) const;
293   SimFloat16 operator*(SimFloat16 rhs) const;
294   SimFloat16 operator/(SimFloat16 rhs) const;
295   bool operator<(SimFloat16 rhs) const;
296   bool operator>(SimFloat16 rhs) const;
297   bool operator==(SimFloat16 rhs) const;
298   bool operator!=(SimFloat16 rhs) const;
299   // This is necessary for conversions peformed in (macro asm) Fmov.
300   bool operator==(double rhs) const;
301   operator double() const;
302 };
303 }  // namespace internal
304 
305 uint32_t Float16Sign(internal::SimFloat16 value);
306 
307 uint32_t Float16Exp(internal::SimFloat16 value);
308 
309 uint32_t Float16Mantissa(internal::SimFloat16 value);
310 
311 uint32_t FloatSign(float value);
312 VIXL_DEPRECATED("FloatSign", inline uint32_t float_sign(float value)) {
313   return FloatSign(value);
314 }
315 
316 uint32_t FloatExp(float value);
317 VIXL_DEPRECATED("FloatExp", inline uint32_t float_exp(float value)) {
318   return FloatExp(value);
319 }
320 
321 uint32_t FloatMantissa(float value);
322 VIXL_DEPRECATED("FloatMantissa", inline uint32_t float_mantissa(float value)) {
323   return FloatMantissa(value);
324 }
325 
326 uint32_t DoubleSign(double value);
327 VIXL_DEPRECATED("DoubleSign", inline uint32_t double_sign(double value)) {
328   return DoubleSign(value);
329 }
330 
331 uint32_t DoubleExp(double value);
332 VIXL_DEPRECATED("DoubleExp", inline uint32_t double_exp(double value)) {
333   return DoubleExp(value);
334 }
335 
336 uint64_t DoubleMantissa(double value);
337 VIXL_DEPRECATED("DoubleMantissa",
338                 inline uint64_t double_mantissa(double value)) {
339   return DoubleMantissa(value);
340 }
341 
342 internal::SimFloat16 Float16Pack(uint16_t sign,
343                                  uint16_t exp,
344                                  uint16_t mantissa);
345 
346 float FloatPack(uint32_t sign, uint32_t exp, uint32_t mantissa);
347 VIXL_DEPRECATED("FloatPack",
float_pack(uint32_t sign,uint32_t exp,uint32_t mantissa)348                 inline float float_pack(uint32_t sign,
349                                         uint32_t exp,
350                                         uint32_t mantissa)) {
351   return FloatPack(sign, exp, mantissa);
352 }
353 
354 double DoublePack(uint64_t sign, uint64_t exp, uint64_t mantissa);
355 VIXL_DEPRECATED("DoublePack",
double_pack(uint32_t sign,uint32_t exp,uint64_t mantissa)356                 inline double double_pack(uint32_t sign,
357                                           uint32_t exp,
358                                           uint64_t mantissa)) {
359   return DoublePack(sign, exp, mantissa);
360 }
361 
362 // An fpclassify() function for 16-bit half-precision floats.
363 int Float16Classify(Float16 value);
float16classify(uint16_t value)364 VIXL_DEPRECATED("Float16Classify", inline int float16classify(uint16_t value)) {
365   return Float16Classify(RawbitsToFloat16(value));
366 }
367 
368 bool IsZero(Float16 value);
369 
IsNaN(float value)370 inline bool IsNaN(float value) { return std::isnan(value); }
371 
IsNaN(double value)372 inline bool IsNaN(double value) { return std::isnan(value); }
373 
IsNaN(Float16 value)374 inline bool IsNaN(Float16 value) { return Float16Classify(value) == FP_NAN; }
375 
IsInf(float value)376 inline bool IsInf(float value) { return std::isinf(value); }
377 
IsInf(double value)378 inline bool IsInf(double value) { return std::isinf(value); }
379 
IsInf(Float16 value)380 inline bool IsInf(Float16 value) {
381   return Float16Classify(value) == FP_INFINITE;
382 }
383 
384 
385 // NaN tests.
IsSignallingNaN(double num)386 inline bool IsSignallingNaN(double num) {
387   const uint64_t kFP64QuietNaNMask = UINT64_C(0x0008000000000000);
388   uint64_t raw = DoubleToRawbits(num);
389   if (IsNaN(num) && ((raw & kFP64QuietNaNMask) == 0)) {
390     return true;
391   }
392   return false;
393 }
394 
395 
IsSignallingNaN(float num)396 inline bool IsSignallingNaN(float num) {
397   const uint32_t kFP32QuietNaNMask = 0x00400000;
398   uint32_t raw = FloatToRawbits(num);
399   if (IsNaN(num) && ((raw & kFP32QuietNaNMask) == 0)) {
400     return true;
401   }
402   return false;
403 }
404 
405 
IsSignallingNaN(Float16 num)406 inline bool IsSignallingNaN(Float16 num) {
407   const uint16_t kFP16QuietNaNMask = 0x0200;
408   return IsNaN(num) && ((Float16ToRawbits(num) & kFP16QuietNaNMask) == 0);
409 }
410 
411 
412 template <typename T>
IsQuietNaN(T num)413 inline bool IsQuietNaN(T num) {
414   return IsNaN(num) && !IsSignallingNaN(num);
415 }
416 
417 
418 // Convert the NaN in 'num' to a quiet NaN.
ToQuietNaN(double num)419 inline double ToQuietNaN(double num) {
420   const uint64_t kFP64QuietNaNMask = UINT64_C(0x0008000000000000);
421   VIXL_ASSERT(IsNaN(num));
422   return RawbitsToDouble(DoubleToRawbits(num) | kFP64QuietNaNMask);
423 }
424 
425 
ToQuietNaN(float num)426 inline float ToQuietNaN(float num) {
427   const uint32_t kFP32QuietNaNMask = 0x00400000;
428   VIXL_ASSERT(IsNaN(num));
429   return RawbitsToFloat(FloatToRawbits(num) | kFP32QuietNaNMask);
430 }
431 
432 
ToQuietNaN(internal::SimFloat16 num)433 inline internal::SimFloat16 ToQuietNaN(internal::SimFloat16 num) {
434   const uint16_t kFP16QuietNaNMask = 0x0200;
435   VIXL_ASSERT(IsNaN(num));
436   return internal::SimFloat16(
437       RawbitsToFloat16(Float16ToRawbits(num) | kFP16QuietNaNMask));
438 }
439 
440 
441 // Fused multiply-add.
FusedMultiplyAdd(double op1,double op2,double a)442 inline double FusedMultiplyAdd(double op1, double op2, double a) {
443   return fma(op1, op2, a);
444 }
445 
446 
FusedMultiplyAdd(float op1,float op2,float a)447 inline float FusedMultiplyAdd(float op1, float op2, float a) {
448   return fmaf(op1, op2, a);
449 }
450 
451 
LowestSetBit(uint64_t value)452 inline uint64_t LowestSetBit(uint64_t value) { return value & -value; }
453 
454 
455 template <typename T>
HighestSetBitPosition(T value)456 inline int HighestSetBitPosition(T value) {
457   VIXL_ASSERT(value != 0);
458   return (sizeof(value) * 8 - 1) - CountLeadingZeros(value);
459 }
460 
461 
462 template <typename V>
WhichPowerOf2(V value)463 inline int WhichPowerOf2(V value) {
464   VIXL_ASSERT(IsPowerOf2(value));
465   return CountTrailingZeros(value);
466 }
467 
468 
469 unsigned CountClearHalfWords(uint64_t imm, unsigned reg_size);
470 
471 
472 int BitCount(uint64_t value);
473 
474 
475 template <typename T>
ReverseBits(T value)476 T ReverseBits(T value) {
477   VIXL_ASSERT((sizeof(value) == 1) || (sizeof(value) == 2) ||
478               (sizeof(value) == 4) || (sizeof(value) == 8));
479   T result = 0;
480   for (unsigned i = 0; i < (sizeof(value) * 8); i++) {
481     result = (result << 1) | (value & 1);
482     value >>= 1;
483   }
484   return result;
485 }
486 
487 
488 template <typename T>
SignExtend(T val,int bitSize)489 inline T SignExtend(T val, int bitSize) {
490   VIXL_ASSERT(bitSize > 0);
491   T mask = (T(2) << (bitSize - 1)) - T(1);
492   val &= mask;
493   T sign_bits = -((val >> (bitSize - 1)) << bitSize);
494   val |= sign_bits;
495   return val;
496 }
497 
498 
499 template <typename T>
ReverseBytes(T value,int block_bytes_log2)500 T ReverseBytes(T value, int block_bytes_log2) {
501   VIXL_ASSERT((sizeof(value) == 4) || (sizeof(value) == 8));
502   VIXL_ASSERT((1U << block_bytes_log2) <= sizeof(value));
503   // Split the 64-bit value into an 8-bit array, where b[0] is the least
504   // significant byte, and b[7] is the most significant.
505   uint8_t bytes[8];
506   uint64_t mask = UINT64_C(0xff00000000000000);
507   for (int i = 7; i >= 0; i--) {
508     bytes[i] = (static_cast<uint64_t>(value) & mask) >> (i * 8);
509     mask >>= 8;
510   }
511 
512   // Permutation tables for REV instructions.
513   //  permute_table[0] is used by REV16_x, REV16_w
514   //  permute_table[1] is used by REV32_x, REV_w
515   //  permute_table[2] is used by REV_x
516   VIXL_ASSERT((0 < block_bytes_log2) && (block_bytes_log2 < 4));
517   static const uint8_t permute_table[3][8] = {{6, 7, 4, 5, 2, 3, 0, 1},
518                                               {4, 5, 6, 7, 0, 1, 2, 3},
519                                               {0, 1, 2, 3, 4, 5, 6, 7}};
520   uint64_t temp = 0;
521   for (int i = 0; i < 8; i++) {
522     temp <<= 8;
523     temp |= bytes[permute_table[block_bytes_log2 - 1][i]];
524   }
525 
526   T result;
527   VIXL_STATIC_ASSERT(sizeof(result) <= sizeof(temp));
528   memcpy(&result, &temp, sizeof(result));
529   return result;
530 }
531 
532 template <unsigned MULTIPLE, typename T>
IsMultiple(T value)533 inline bool IsMultiple(T value) {
534   VIXL_ASSERT(IsPowerOf2(MULTIPLE));
535   return (value & (MULTIPLE - 1)) == 0;
536 }
537 
538 template <typename T>
IsMultiple(T value,unsigned multiple)539 inline bool IsMultiple(T value, unsigned multiple) {
540   VIXL_ASSERT(IsPowerOf2(multiple));
541   return (value & (multiple - 1)) == 0;
542 }
543 
544 template <typename T>
IsAligned(T pointer,int alignment)545 inline bool IsAligned(T pointer, int alignment) {
546   VIXL_ASSERT(IsPowerOf2(alignment));
547   return (pointer & (alignment - 1)) == 0;
548 }
549 
550 // Pointer alignment
551 // TODO: rename/refactor to make it specific to instructions.
552 template <unsigned ALIGN, typename T>
IsAligned(T pointer)553 inline bool IsAligned(T pointer) {
554   VIXL_ASSERT(sizeof(pointer) == sizeof(intptr_t));  // NOLINT(runtime/sizeof)
555   // Use C-style casts to get static_cast behaviour for integral types (T), and
556   // reinterpret_cast behaviour for other types.
557   return IsAligned((intptr_t)(pointer), ALIGN);
558 }
559 
560 template <typename T>
IsWordAligned(T pointer)561 bool IsWordAligned(T pointer) {
562   return IsAligned<4>(pointer);
563 }
564 
565 // Increment a pointer until it has the specified alignment. The alignment must
566 // be a power of two.
567 template <class T>
AlignUp(T pointer,typename Unsigned<sizeof (T)* kBitsPerByte>::type alignment)568 T AlignUp(T pointer,
569           typename Unsigned<sizeof(T) * kBitsPerByte>::type alignment) {
570   VIXL_ASSERT(IsPowerOf2(alignment));
571   // Use C-style casts to get static_cast behaviour for integral types (T), and
572   // reinterpret_cast behaviour for other types.
573 
574   typename Unsigned<sizeof(T)* kBitsPerByte>::type pointer_raw =
575       (typename Unsigned<sizeof(T) * kBitsPerByte>::type)pointer;
576   VIXL_STATIC_ASSERT(sizeof(pointer) <= sizeof(pointer_raw));
577 
578   size_t mask = alignment - 1;
579   T result = (T)((pointer_raw + mask) & ~mask);
580   VIXL_ASSERT(result >= pointer);
581 
582   return result;
583 }
584 
585 // Decrement a pointer until it has the specified alignment. The alignment must
586 // be a power of two.
587 template <class T>
AlignDown(T pointer,typename Unsigned<sizeof (T)* kBitsPerByte>::type alignment)588 T AlignDown(T pointer,
589             typename Unsigned<sizeof(T) * kBitsPerByte>::type alignment) {
590   VIXL_ASSERT(IsPowerOf2(alignment));
591   // Use C-style casts to get static_cast behaviour for integral types (T), and
592   // reinterpret_cast behaviour for other types.
593 
594   typename Unsigned<sizeof(T)* kBitsPerByte>::type pointer_raw =
595       (typename Unsigned<sizeof(T) * kBitsPerByte>::type)pointer;
596   VIXL_STATIC_ASSERT(sizeof(pointer) <= sizeof(pointer_raw));
597 
598   size_t mask = alignment - 1;
599   return (T)(pointer_raw & ~mask);
600 }
601 
602 
603 template <typename T>
ExtractBit(T value,unsigned bit)604 inline T ExtractBit(T value, unsigned bit) {
605   return (value >> bit) & T(1);
606 }
607 
608 template <typename Ts, typename Td>
ExtractBits(Ts value,int least_significant_bit,Td mask)609 inline Td ExtractBits(Ts value, int least_significant_bit, Td mask) {
610   return Td((value >> least_significant_bit) & Ts(mask));
611 }
612 
613 template <typename Ts, typename Td>
AssignBit(Td & dst,int bit,Ts value)614 inline void AssignBit(Td& dst,  // NOLINT(runtime/references)
615                       int bit,
616                       Ts value) {
617   VIXL_ASSERT((value == Ts(0)) || (value == Ts(1)));
618   VIXL_ASSERT(bit >= 0);
619   VIXL_ASSERT(bit < static_cast<int>(sizeof(Td) * 8));
620   Td mask(1);
621   dst &= ~(mask << bit);
622   dst |= Td(value) << bit;
623 }
624 
625 template <typename Td, typename Ts>
AssignBits(Td & dst,int least_significant_bit,Ts mask,Ts value)626 inline void AssignBits(Td& dst,  // NOLINT(runtime/references)
627                        int least_significant_bit,
628                        Ts mask,
629                        Ts value) {
630   VIXL_ASSERT(least_significant_bit >= 0);
631   VIXL_ASSERT(least_significant_bit < static_cast<int>(sizeof(Td) * 8));
632   VIXL_ASSERT(((Td(mask) << least_significant_bit) >> least_significant_bit) ==
633               Td(mask));
634   VIXL_ASSERT((value & mask) == value);
635   dst &= ~(Td(mask) << least_significant_bit);
636   dst |= Td(value) << least_significant_bit;
637 }
638 
639 class VFP {
640  public:
FP32ToImm8(float imm)641   static uint32_t FP32ToImm8(float imm) {
642     // bits: aBbb.bbbc.defg.h000.0000.0000.0000.0000
643     uint32_t bits = FloatToRawbits(imm);
644     // bit7: a000.0000
645     uint32_t bit7 = ((bits >> 31) & 0x1) << 7;
646     // bit6: 0b00.0000
647     uint32_t bit6 = ((bits >> 29) & 0x1) << 6;
648     // bit5_to_0: 00cd.efgh
649     uint32_t bit5_to_0 = (bits >> 19) & 0x3f;
650     return static_cast<uint32_t>(bit7 | bit6 | bit5_to_0);
651   }
FP64ToImm8(double imm)652   static uint32_t FP64ToImm8(double imm) {
653     // bits: aBbb.bbbb.bbcd.efgh.0000.0000.0000.0000
654     //       0000.0000.0000.0000.0000.0000.0000.0000
655     uint64_t bits = DoubleToRawbits(imm);
656     // bit7: a000.0000
657     uint64_t bit7 = ((bits >> 63) & 0x1) << 7;
658     // bit6: 0b00.0000
659     uint64_t bit6 = ((bits >> 61) & 0x1) << 6;
660     // bit5_to_0: 00cd.efgh
661     uint64_t bit5_to_0 = (bits >> 48) & 0x3f;
662 
663     return static_cast<uint32_t>(bit7 | bit6 | bit5_to_0);
664   }
Imm8ToFP32(uint32_t imm8)665   static float Imm8ToFP32(uint32_t imm8) {
666     //   Imm8: abcdefgh (8 bits)
667     // Single: aBbb.bbbc.defg.h000.0000.0000.0000.0000 (32 bits)
668     // where B is b ^ 1
669     uint32_t bits = imm8;
670     uint32_t bit7 = (bits >> 7) & 0x1;
671     uint32_t bit6 = (bits >> 6) & 0x1;
672     uint32_t bit5_to_0 = bits & 0x3f;
673     uint32_t result = (bit7 << 31) | ((32 - bit6) << 25) | (bit5_to_0 << 19);
674 
675     return RawbitsToFloat(result);
676   }
Imm8ToFP64(uint32_t imm8)677   static double Imm8ToFP64(uint32_t imm8) {
678     //   Imm8: abcdefgh (8 bits)
679     // Double: aBbb.bbbb.bbcd.efgh.0000.0000.0000.0000
680     //         0000.0000.0000.0000.0000.0000.0000.0000 (64 bits)
681     // where B is b ^ 1
682     uint32_t bits = imm8;
683     uint64_t bit7 = (bits >> 7) & 0x1;
684     uint64_t bit6 = (bits >> 6) & 0x1;
685     uint64_t bit5_to_0 = bits & 0x3f;
686     uint64_t result = (bit7 << 63) | ((256 - bit6) << 54) | (bit5_to_0 << 48);
687     return RawbitsToDouble(result);
688   }
IsImmFP32(float imm)689   static bool IsImmFP32(float imm) {
690     // Valid values will have the form:
691     // aBbb.bbbc.defg.h000.0000.0000.0000.0000
692     uint32_t bits = FloatToRawbits(imm);
693     // bits[19..0] are cleared.
694     if ((bits & 0x7ffff) != 0) {
695       return false;
696     }
697 
698 
699     // bits[29..25] are all set or all cleared.
700     uint32_t b_pattern = (bits >> 16) & 0x3e00;
701     if (b_pattern != 0 && b_pattern != 0x3e00) {
702       return false;
703     }
704     // bit[30] and bit[29] are opposite.
705     if (((bits ^ (bits << 1)) & 0x40000000) == 0) {
706       return false;
707     }
708     return true;
709   }
IsImmFP64(double imm)710   static bool IsImmFP64(double imm) {
711     // Valid values will have the form:
712     // aBbb.bbbb.bbcd.efgh.0000.0000.0000.0000
713     // 0000.0000.0000.0000.0000.0000.0000.0000
714     uint64_t bits = DoubleToRawbits(imm);
715     // bits[47..0] are cleared.
716     if ((bits & 0x0000ffffffffffff) != 0) {
717       return false;
718     }
719     // bits[61..54] are all set or all cleared.
720     uint32_t b_pattern = (bits >> 48) & 0x3fc0;
721     if ((b_pattern != 0) && (b_pattern != 0x3fc0)) {
722       return false;
723     }
724     // bit[62] and bit[61] are opposite.
725     if (((bits ^ (bits << 1)) & (UINT64_C(1) << 62)) == 0) {
726       return false;
727     }
728     return true;
729   }
730 };
731 
732 class BitField {
733   // ForEachBitHelper is a functor that will call
734   // bool ForEachBitHelper::execute(ElementType id) const
735   //   and expects a boolean in return whether to continue (if true)
736   //   or stop (if false)
737   // check_set will check if the bits are on (true) or off(false)
738   template <typename ForEachBitHelper, bool check_set>
ForEachBit(const ForEachBitHelper & helper)739   bool ForEachBit(const ForEachBitHelper& helper) {
740     for (int i = 0; static_cast<size_t>(i) < bitfield_.size(); i++) {
741       if (bitfield_[i] == check_set)
742         if (!helper.execute(i)) return false;
743     }
744     return true;
745   }
746 
747  public:
BitField(unsigned size)748   explicit BitField(unsigned size) : bitfield_(size, 0) {}
749 
Set(int i)750   void Set(int i) {
751     VIXL_ASSERT((i >= 0) && (static_cast<size_t>(i) < bitfield_.size()));
752     bitfield_[i] = true;
753   }
754 
Unset(int i)755   void Unset(int i) {
756     VIXL_ASSERT((i >= 0) && (static_cast<size_t>(i) < bitfield_.size()));
757     bitfield_[i] = true;
758   }
759 
IsSet(int i)760   bool IsSet(int i) const { return bitfield_[i]; }
761 
762   // For each bit not set in the bitfield call the execute functor
763   // execute.
764   // ForEachBitSetHelper::execute returns true if the iteration through
765   // the bits can continue, otherwise it will stop.
766   // struct ForEachBitSetHelper {
767   //   bool execute(int /*id*/) { return false; }
768   // };
769   template <typename ForEachBitNotSetHelper>
ForEachBitNotSet(const ForEachBitNotSetHelper & helper)770   bool ForEachBitNotSet(const ForEachBitNotSetHelper& helper) {
771     return ForEachBit<ForEachBitNotSetHelper, false>(helper);
772   }
773 
774   // For each bit set in the bitfield call the execute functor
775   // execute.
776   template <typename ForEachBitSetHelper>
ForEachBitSet(const ForEachBitSetHelper & helper)777   bool ForEachBitSet(const ForEachBitSetHelper& helper) {
778     return ForEachBit<ForEachBitSetHelper, true>(helper);
779   }
780 
781  private:
782   std::vector<bool> bitfield_;
783 };
784 
785 namespace internal {
786 
787 typedef int64_t Int64;
788 class Uint64;
789 class Uint128;
790 
791 class Uint32 {
792   uint32_t data_;
793 
794  public:
795   // Unlike uint32_t, Uint32 has a default constructor.
Uint32()796   Uint32() { data_ = 0; }
Uint32(uint32_t data)797   explicit Uint32(uint32_t data) : data_(data) {}
798   inline explicit Uint32(Uint64 data);
Get()799   uint32_t Get() const { return data_; }
800   template <int N>
GetSigned()801   int32_t GetSigned() const {
802     return ExtractSignedBitfield32(N - 1, 0, data_);
803   }
GetSigned()804   int32_t GetSigned() const { return data_; }
805   Uint32 operator~() const { return Uint32(~data_); }
806   Uint32 operator-() const { return Uint32(-data_); }
807   bool operator==(Uint32 value) const { return data_ == value.data_; }
808   bool operator!=(Uint32 value) const { return data_ != value.data_; }
809   bool operator>(Uint32 value) const { return data_ > value.data_; }
810   Uint32 operator+(Uint32 value) const { return Uint32(data_ + value.data_); }
811   Uint32 operator-(Uint32 value) const { return Uint32(data_ - value.data_); }
812   Uint32 operator&(Uint32 value) const { return Uint32(data_ & value.data_); }
813   Uint32 operator&=(Uint32 value) {
814     data_ &= value.data_;
815     return *this;
816   }
817   Uint32 operator^(Uint32 value) const { return Uint32(data_ ^ value.data_); }
818   Uint32 operator^=(Uint32 value) {
819     data_ ^= value.data_;
820     return *this;
821   }
822   Uint32 operator|(Uint32 value) const { return Uint32(data_ | value.data_); }
823   Uint32 operator|=(Uint32 value) {
824     data_ |= value.data_;
825     return *this;
826   }
827   // Unlike uint32_t, the shift functions can accept negative shift and
828   // return 0 when the shift is too big.
829   Uint32 operator>>(int shift) const {
830     if (shift == 0) return *this;
831     if (shift < 0) {
832       int tmp = -shift;
833       if (tmp >= 32) return Uint32(0);
834       return Uint32(data_ << tmp);
835     }
836     int tmp = shift;
837     if (tmp >= 32) return Uint32(0);
838     return Uint32(data_ >> tmp);
839   }
840   Uint32 operator<<(int shift) const {
841     if (shift == 0) return *this;
842     if (shift < 0) {
843       int tmp = -shift;
844       if (tmp >= 32) return Uint32(0);
845       return Uint32(data_ >> tmp);
846     }
847     int tmp = shift;
848     if (tmp >= 32) return Uint32(0);
849     return Uint32(data_ << tmp);
850   }
851 };
852 
853 class Uint64 {
854   uint64_t data_;
855 
856  public:
857   // Unlike uint64_t, Uint64 has a default constructor.
Uint64()858   Uint64() { data_ = 0; }
Uint64(uint64_t data)859   explicit Uint64(uint64_t data) : data_(data) {}
Uint64(Uint32 data)860   explicit Uint64(Uint32 data) : data_(data.Get()) {}
861   inline explicit Uint64(Uint128 data);
Get()862   uint64_t Get() const { return data_; }
GetSigned(int N)863   int64_t GetSigned(int N) const {
864     return ExtractSignedBitfield64(N - 1, 0, data_);
865   }
GetSigned()866   int64_t GetSigned() const { return data_; }
ToUint32()867   Uint32 ToUint32() const {
868     VIXL_ASSERT((data_ >> 32) == 0);
869     return Uint32(static_cast<uint32_t>(data_));
870   }
GetHigh32()871   Uint32 GetHigh32() const { return Uint32(data_ >> 32); }
GetLow32()872   Uint32 GetLow32() const { return Uint32(data_ & 0xffffffff); }
873   Uint64 operator~() const { return Uint64(~data_); }
874   Uint64 operator-() const { return Uint64(-data_); }
875   bool operator==(Uint64 value) const { return data_ == value.data_; }
876   bool operator!=(Uint64 value) const { return data_ != value.data_; }
877   Uint64 operator+(Uint64 value) const { return Uint64(data_ + value.data_); }
878   Uint64 operator-(Uint64 value) const { return Uint64(data_ - value.data_); }
879   Uint64 operator&(Uint64 value) const { return Uint64(data_ & value.data_); }
880   Uint64 operator&=(Uint64 value) {
881     data_ &= value.data_;
882     return *this;
883   }
884   Uint64 operator^(Uint64 value) const { return Uint64(data_ ^ value.data_); }
885   Uint64 operator^=(Uint64 value) {
886     data_ ^= value.data_;
887     return *this;
888   }
889   Uint64 operator|(Uint64 value) const { return Uint64(data_ | value.data_); }
890   Uint64 operator|=(Uint64 value) {
891     data_ |= value.data_;
892     return *this;
893   }
894   // Unlike uint64_t, the shift functions can accept negative shift and
895   // return 0 when the shift is too big.
896   Uint64 operator>>(int shift) const {
897     if (shift == 0) return *this;
898     if (shift < 0) {
899       int tmp = -shift;
900       if (tmp >= 64) return Uint64(0);
901       return Uint64(data_ << tmp);
902     }
903     int tmp = shift;
904     if (tmp >= 64) return Uint64(0);
905     return Uint64(data_ >> tmp);
906   }
907   Uint64 operator<<(int shift) const {
908     if (shift == 0) return *this;
909     if (shift < 0) {
910       int tmp = -shift;
911       if (tmp >= 64) return Uint64(0);
912       return Uint64(data_ >> tmp);
913     }
914     int tmp = shift;
915     if (tmp >= 64) return Uint64(0);
916     return Uint64(data_ << tmp);
917   }
918 };
919 
920 class Uint128 {
921   uint64_t data_high_;
922   uint64_t data_low_;
923 
924  public:
Uint128()925   Uint128() : data_high_(0), data_low_(0) {}
Uint128(uint64_t data_low)926   explicit Uint128(uint64_t data_low) : data_high_(0), data_low_(data_low) {}
Uint128(Uint64 data_low)927   explicit Uint128(Uint64 data_low)
928       : data_high_(0), data_low_(data_low.Get()) {}
Uint128(uint64_t data_high,uint64_t data_low)929   Uint128(uint64_t data_high, uint64_t data_low)
930       : data_high_(data_high), data_low_(data_low) {}
ToUint64()931   Uint64 ToUint64() const {
932     VIXL_ASSERT(data_high_ == 0);
933     return Uint64(data_low_);
934   }
GetHigh64()935   Uint64 GetHigh64() const { return Uint64(data_high_); }
GetLow64()936   Uint64 GetLow64() const { return Uint64(data_low_); }
937   Uint128 operator~() const { return Uint128(~data_high_, ~data_low_); }
938   bool operator==(Uint128 value) const {
939     return (data_high_ == value.data_high_) && (data_low_ == value.data_low_);
940   }
941   Uint128 operator&(Uint128 value) const {
942     return Uint128(data_high_ & value.data_high_, data_low_ & value.data_low_);
943   }
944   Uint128 operator&=(Uint128 value) {
945     data_high_ &= value.data_high_;
946     data_low_ &= value.data_low_;
947     return *this;
948   }
949   Uint128 operator|=(Uint128 value) {
950     data_high_ |= value.data_high_;
951     data_low_ |= value.data_low_;
952     return *this;
953   }
954   Uint128 operator>>(int shift) const {
955     VIXL_ASSERT((shift >= 0) && (shift < 128));
956     if (shift == 0) return *this;
957     if (shift >= 64) {
958       return Uint128(0, data_high_ >> (shift - 64));
959     }
960     uint64_t tmp = (data_high_ << (64 - shift)) | (data_low_ >> shift);
961     return Uint128(data_high_ >> shift, tmp);
962   }
963   Uint128 operator<<(int shift) const {
964     VIXL_ASSERT((shift >= 0) && (shift < 128));
965     if (shift == 0) return *this;
966     if (shift >= 64) {
967       return Uint128(data_low_ << (shift - 64), 0);
968     }
969     uint64_t tmp = (data_high_ << shift) | (data_low_ >> (64 - shift));
970     return Uint128(tmp, data_low_ << shift);
971   }
972 };
973 
Uint32(Uint64 data)974 Uint32::Uint32(Uint64 data) : data_(data.ToUint32().Get()) {}
Uint64(Uint128 data)975 Uint64::Uint64(Uint128 data) : data_(data.ToUint64().Get()) {}
976 
977 Int64 BitCount(Uint32 value);
978 
979 }  // namespace internal
980 
981 // The default NaN values (for FPCR.DN=1).
982 extern const double kFP64DefaultNaN;
983 extern const float kFP32DefaultNaN;
984 extern const Float16 kFP16DefaultNaN;
985 
986 // Floating-point infinity values.
987 extern const Float16 kFP16PositiveInfinity;
988 extern const Float16 kFP16NegativeInfinity;
989 extern const float kFP32PositiveInfinity;
990 extern const float kFP32NegativeInfinity;
991 extern const double kFP64PositiveInfinity;
992 extern const double kFP64NegativeInfinity;
993 
994 // Floating-point zero values.
995 extern const Float16 kFP16PositiveZero;
996 extern const Float16 kFP16NegativeZero;
997 
998 // AArch64 floating-point specifics. These match IEEE-754.
999 const unsigned kDoubleMantissaBits = 52;
1000 const unsigned kDoubleExponentBits = 11;
1001 const unsigned kFloatMantissaBits = 23;
1002 const unsigned kFloatExponentBits = 8;
1003 const unsigned kFloat16MantissaBits = 10;
1004 const unsigned kFloat16ExponentBits = 5;
1005 
1006 enum FPRounding {
1007   // The first four values are encodable directly by FPCR<RMode>.
1008   FPTieEven = 0x0,
1009   FPPositiveInfinity = 0x1,
1010   FPNegativeInfinity = 0x2,
1011   FPZero = 0x3,
1012 
1013   // The final rounding modes are only available when explicitly specified by
1014   // the instruction (such as with fcvta). It cannot be set in FPCR.
1015   FPTieAway,
1016   FPRoundOdd
1017 };
1018 
1019 enum UseDefaultNaN { kUseDefaultNaN, kIgnoreDefaultNaN };
1020 
1021 // Assemble the specified IEEE-754 components into the target type and apply
1022 // appropriate rounding.
1023 //  sign:     0 = positive, 1 = negative
1024 //  exponent: Unbiased IEEE-754 exponent.
1025 //  mantissa: The mantissa of the input. The top bit (which is not encoded for
1026 //            normal IEEE-754 values) must not be omitted. This bit has the
1027 //            value 'pow(2, exponent)'.
1028 //
1029 // The input value is assumed to be a normalized value. That is, the input may
1030 // not be infinity or NaN. If the source value is subnormal, it must be
1031 // normalized before calling this function such that the highest set bit in the
1032 // mantissa has the value 'pow(2, exponent)'.
1033 //
1034 // Callers should use FPRoundToFloat or FPRoundToDouble directly, rather than
1035 // calling a templated FPRound.
1036 template <class T, int ebits, int mbits>
FPRound(int64_t sign,int64_t exponent,uint64_t mantissa,FPRounding round_mode)1037 T FPRound(int64_t sign,
1038           int64_t exponent,
1039           uint64_t mantissa,
1040           FPRounding round_mode) {
1041   VIXL_ASSERT((sign == 0) || (sign == 1));
1042 
1043   // Only FPTieEven and FPRoundOdd rounding modes are implemented.
1044   VIXL_ASSERT((round_mode == FPTieEven) || (round_mode == FPRoundOdd));
1045 
1046   // Rounding can promote subnormals to normals, and normals to infinities. For
1047   // example, a double with exponent 127 (FLT_MAX_EXP) would appear to be
1048   // encodable as a float, but rounding based on the low-order mantissa bits
1049   // could make it overflow. With ties-to-even rounding, this value would become
1050   // an infinity.
1051 
1052   // ---- Rounding Method ----
1053   //
1054   // The exponent is irrelevant in the rounding operation, so we treat the
1055   // lowest-order bit that will fit into the result ('onebit') as having
1056   // the value '1'. Similarly, the highest-order bit that won't fit into
1057   // the result ('halfbit') has the value '0.5'. The 'point' sits between
1058   // 'onebit' and 'halfbit':
1059   //
1060   //            These bits fit into the result.
1061   //               |---------------------|
1062   //  mantissa = 0bxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
1063   //                                     ||
1064   //                                    / |
1065   //                                   /  halfbit
1066   //                               onebit
1067   //
1068   // For subnormal outputs, the range of representable bits is smaller and
1069   // the position of onebit and halfbit depends on the exponent of the
1070   // input, but the method is otherwise similar.
1071   //
1072   //   onebit(frac)
1073   //     |
1074   //     | halfbit(frac)          halfbit(adjusted)
1075   //     | /                      /
1076   //     | |                      |
1077   //  0b00.0 (exact)      -> 0b00.0 (exact)                    -> 0b00
1078   //  0b00.0...           -> 0b00.0...                         -> 0b00
1079   //  0b00.1 (exact)      -> 0b00.0111..111                    -> 0b00
1080   //  0b00.1...           -> 0b00.1...                         -> 0b01
1081   //  0b01.0 (exact)      -> 0b01.0 (exact)                    -> 0b01
1082   //  0b01.0...           -> 0b01.0...                         -> 0b01
1083   //  0b01.1 (exact)      -> 0b01.1 (exact)                    -> 0b10
1084   //  0b01.1...           -> 0b01.1...                         -> 0b10
1085   //  0b10.0 (exact)      -> 0b10.0 (exact)                    -> 0b10
1086   //  0b10.0...           -> 0b10.0...                         -> 0b10
1087   //  0b10.1 (exact)      -> 0b10.0111..111                    -> 0b10
1088   //  0b10.1...           -> 0b10.1...                         -> 0b11
1089   //  0b11.0 (exact)      -> 0b11.0 (exact)                    -> 0b11
1090   //  ...                   /             |                      /   |
1091   //                       /              |                     /    |
1092   //                                                           /     |
1093   // adjusted = frac - (halfbit(mantissa) & ~onebit(frac));   /      |
1094   //
1095   //                   mantissa = (mantissa >> shift) + halfbit(adjusted);
1096 
1097   static const int mantissa_offset = 0;
1098   static const int exponent_offset = mantissa_offset + mbits;
1099   static const int sign_offset = exponent_offset + ebits;
1100   VIXL_ASSERT(sign_offset == (sizeof(T) * 8 - 1));
1101 
1102   // Bail out early for zero inputs.
1103   if (mantissa == 0) {
1104     return static_cast<T>(sign << sign_offset);
1105   }
1106 
1107   // If all bits in the exponent are set, the value is infinite or NaN.
1108   // This is true for all binary IEEE-754 formats.
1109   static const int infinite_exponent = (1 << ebits) - 1;
1110   static const int max_normal_exponent = infinite_exponent - 1;
1111 
1112   // Apply the exponent bias to encode it for the result. Doing this early makes
1113   // it easy to detect values that will be infinite or subnormal.
1114   exponent += max_normal_exponent >> 1;
1115 
1116   if (exponent > max_normal_exponent) {
1117     // Overflow: the input is too large for the result type to represent.
1118     if (round_mode == FPTieEven) {
1119       // FPTieEven rounding mode handles overflows using infinities.
1120       exponent = infinite_exponent;
1121       mantissa = 0;
1122     } else {
1123       VIXL_ASSERT(round_mode == FPRoundOdd);
1124       // FPRoundOdd rounding mode handles overflows using the largest magnitude
1125       // normal number.
1126       exponent = max_normal_exponent;
1127       mantissa = (UINT64_C(1) << exponent_offset) - 1;
1128     }
1129     return static_cast<T>((sign << sign_offset) |
1130                           (exponent << exponent_offset) |
1131                           (mantissa << mantissa_offset));
1132   }
1133 
1134   // Calculate the shift required to move the top mantissa bit to the proper
1135   // place in the destination type.
1136   const int highest_significant_bit = 63 - CountLeadingZeros(mantissa);
1137   int shift = highest_significant_bit - mbits;
1138 
1139   if (exponent <= 0) {
1140     // The output will be subnormal (before rounding).
1141     // For subnormal outputs, the shift must be adjusted by the exponent. The +1
1142     // is necessary because the exponent of a subnormal value (encoded as 0) is
1143     // the same as the exponent of the smallest normal value (encoded as 1).
1144     shift += -exponent + 1;
1145 
1146     // Handle inputs that would produce a zero output.
1147     //
1148     // Shifts higher than highest_significant_bit+1 will always produce a zero
1149     // result. A shift of exactly highest_significant_bit+1 might produce a
1150     // non-zero result after rounding.
1151     if (shift > (highest_significant_bit + 1)) {
1152       if (round_mode == FPTieEven) {
1153         // The result will always be +/-0.0.
1154         return static_cast<T>(sign << sign_offset);
1155       } else {
1156         VIXL_ASSERT(round_mode == FPRoundOdd);
1157         VIXL_ASSERT(mantissa != 0);
1158         // For FPRoundOdd, if the mantissa is too small to represent and
1159         // non-zero return the next "odd" value.
1160         return static_cast<T>((sign << sign_offset) | 1);
1161       }
1162     }
1163 
1164     // Properly encode the exponent for a subnormal output.
1165     exponent = 0;
1166   } else {
1167     // Clear the topmost mantissa bit, since this is not encoded in IEEE-754
1168     // normal values.
1169     mantissa &= ~(UINT64_C(1) << highest_significant_bit);
1170   }
1171 
1172   // The casts below are only well-defined for unsigned integers.
1173   VIXL_STATIC_ASSERT(std::numeric_limits<T>::is_integer);
1174   VIXL_STATIC_ASSERT(!std::numeric_limits<T>::is_signed);
1175 
1176   if (shift > 0) {
1177     if (round_mode == FPTieEven) {
1178       // We have to shift the mantissa to the right. Some precision is lost, so
1179       // we need to apply rounding.
1180       uint64_t onebit_mantissa = (mantissa >> (shift)) & 1;
1181       uint64_t halfbit_mantissa = (mantissa >> (shift - 1)) & 1;
1182       uint64_t adjustment = (halfbit_mantissa & ~onebit_mantissa);
1183       uint64_t adjusted = mantissa - adjustment;
1184       T halfbit_adjusted = (adjusted >> (shift - 1)) & 1;
1185 
1186       T result =
1187           static_cast<T>((sign << sign_offset) | (exponent << exponent_offset) |
1188                          ((mantissa >> shift) << mantissa_offset));
1189 
1190       // A very large mantissa can overflow during rounding. If this happens,
1191       // the exponent should be incremented and the mantissa set to 1.0
1192       // (encoded as 0). Applying halfbit_adjusted after assembling the float
1193       // has the nice side-effect that this case is handled for free.
1194       //
1195       // This also handles cases where a very large finite value overflows to
1196       // infinity, or where a very large subnormal value overflows to become
1197       // normal.
1198       return result + halfbit_adjusted;
1199     } else {
1200       VIXL_ASSERT(round_mode == FPRoundOdd);
1201       // If any bits at position halfbit or below are set, onebit (ie. the
1202       // bottom bit of the resulting mantissa) must be set.
1203       uint64_t fractional_bits = mantissa & ((UINT64_C(1) << shift) - 1);
1204       if (fractional_bits != 0) {
1205         mantissa |= UINT64_C(1) << shift;
1206       }
1207 
1208       return static_cast<T>((sign << sign_offset) |
1209                             (exponent << exponent_offset) |
1210                             ((mantissa >> shift) << mantissa_offset));
1211     }
1212   } else {
1213     // We have to shift the mantissa to the left (or not at all). The input
1214     // mantissa is exactly representable in the output mantissa, so apply no
1215     // rounding correction.
1216     return static_cast<T>((sign << sign_offset) |
1217                           (exponent << exponent_offset) |
1218                           ((mantissa << -shift) << mantissa_offset));
1219   }
1220 }
1221 
1222 
1223 // See FPRound for a description of this function.
FPRoundToDouble(int64_t sign,int64_t exponent,uint64_t mantissa,FPRounding round_mode)1224 inline double FPRoundToDouble(int64_t sign,
1225                               int64_t exponent,
1226                               uint64_t mantissa,
1227                               FPRounding round_mode) {
1228   uint64_t bits =
1229       FPRound<uint64_t, kDoubleExponentBits, kDoubleMantissaBits>(sign,
1230                                                                   exponent,
1231                                                                   mantissa,
1232                                                                   round_mode);
1233   return RawbitsToDouble(bits);
1234 }
1235 
1236 
1237 // See FPRound for a description of this function.
FPRoundToFloat16(int64_t sign,int64_t exponent,uint64_t mantissa,FPRounding round_mode)1238 inline Float16 FPRoundToFloat16(int64_t sign,
1239                                 int64_t exponent,
1240                                 uint64_t mantissa,
1241                                 FPRounding round_mode) {
1242   return RawbitsToFloat16(
1243       FPRound<uint16_t,
1244               kFloat16ExponentBits,
1245               kFloat16MantissaBits>(sign, exponent, mantissa, round_mode));
1246 }
1247 
1248 
1249 // See FPRound for a description of this function.
FPRoundToFloat(int64_t sign,int64_t exponent,uint64_t mantissa,FPRounding round_mode)1250 static inline float FPRoundToFloat(int64_t sign,
1251                                    int64_t exponent,
1252                                    uint64_t mantissa,
1253                                    FPRounding round_mode) {
1254   uint32_t bits =
1255       FPRound<uint32_t, kFloatExponentBits, kFloatMantissaBits>(sign,
1256                                                                 exponent,
1257                                                                 mantissa,
1258                                                                 round_mode);
1259   return RawbitsToFloat(bits);
1260 }
1261 
1262 
1263 float FPToFloat(Float16 value, UseDefaultNaN DN, bool* exception = NULL);
1264 float FPToFloat(double value,
1265                 FPRounding round_mode,
1266                 UseDefaultNaN DN,
1267                 bool* exception = NULL);
1268 
1269 double FPToDouble(Float16 value, UseDefaultNaN DN, bool* exception = NULL);
1270 double FPToDouble(float value, UseDefaultNaN DN, bool* exception = NULL);
1271 
1272 Float16 FPToFloat16(float value,
1273                     FPRounding round_mode,
1274                     UseDefaultNaN DN,
1275                     bool* exception = NULL);
1276 
1277 Float16 FPToFloat16(double value,
1278                     FPRounding round_mode,
1279                     UseDefaultNaN DN,
1280                     bool* exception = NULL);
1281 }  // namespace vixl
1282 
1283 #endif  // VIXL_UTILS_H
1284