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