// Copyright 2015, VIXL authors // All rights reserved. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are met: // // * Redistributions of source code must retain the above copyright notice, // this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above copyright notice, // this list of conditions and the following disclaimer in the documentation // and/or other materials provided with the distribution. // * Neither the name of ARM Limited nor the names of its contributors may be // used to endorse or promote products derived from this software without // specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS CONTRIBUTORS "AS IS" AND // ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED // WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. #ifndef VIXL_UTILS_H #define VIXL_UTILS_H #include "mozilla/FloatingPoint.h" #include #include #include #include #include "jit/arm64/vixl/CompilerIntrinsics-vixl.h" #include "jit/arm64/vixl/Globals-vixl.h" namespace vixl { // Macros for compile-time format checking. #if GCC_VERSION_OR_NEWER(4, 4, 0) #define PRINTF_CHECK(format_index, varargs_index) \ __attribute__((format(gnu_printf, format_index, varargs_index))) #else #define PRINTF_CHECK(format_index, varargs_index) #endif #ifdef __GNUC__ #define VIXL_HAS_DEPRECATED_WITH_MSG #elif defined(__clang__) #ifdef __has_extension #define VIXL_HAS_DEPRECATED_WITH_MSG #endif #endif #ifdef VIXL_HAS_DEPRECATED_WITH_MSG #define VIXL_DEPRECATED(replaced_by, declarator) \ __attribute__((deprecated("Use \"" replaced_by "\" instead"))) declarator #else #define VIXL_DEPRECATED(replaced_by, declarator) declarator #endif #ifdef VIXL_DEBUG #define VIXL_UNREACHABLE_OR_FALLTHROUGH() VIXL_UNREACHABLE() #else #define VIXL_UNREACHABLE_OR_FALLTHROUGH() VIXL_FALLTHROUGH() #endif template size_t ArrayLength(const T (&)[n]) { return n; } // Check number width. // TODO: Refactor these using templates. inline bool IsIntN(unsigned n, uint32_t x) { VIXL_ASSERT((0 < n) && (n < 32)); uint32_t limit = UINT32_C(1) << (n - 1); return x < limit; } inline bool IsIntN(unsigned n, int32_t x) { VIXL_ASSERT((0 < n) && (n < 32)); int32_t limit = INT32_C(1) << (n - 1); return (-limit <= x) && (x < limit); } inline bool IsIntN(unsigned n, uint64_t x) { VIXL_ASSERT((0 < n) && (n < 64)); uint64_t limit = UINT64_C(1) << (n - 1); return x < limit; } inline bool IsIntN(unsigned n, int64_t x) { VIXL_ASSERT((0 < n) && (n < 64)); int64_t limit = INT64_C(1) << (n - 1); return (-limit <= x) && (x < limit); } VIXL_DEPRECATED("IsIntN", inline bool is_intn(unsigned n, int64_t x)) { return IsIntN(n, x); } inline bool IsUintN(unsigned n, uint32_t x) { VIXL_ASSERT((0 < n) && (n < 32)); return !(x >> n); } inline bool IsUintN(unsigned n, int32_t x) { VIXL_ASSERT((0 < n) && (n < 32)); // Convert to an unsigned integer to avoid implementation-defined behavior. return !(static_cast(x) >> n); } inline bool IsUintN(unsigned n, uint64_t x) { VIXL_ASSERT((0 < n) && (n < 64)); return !(x >> n); } inline bool IsUintN(unsigned n, int64_t x) { VIXL_ASSERT((0 < n) && (n < 64)); // Convert to an unsigned integer to avoid implementation-defined behavior. return !(static_cast(x) >> n); } VIXL_DEPRECATED("IsUintN", inline bool is_uintn(unsigned n, int64_t x)) { return IsUintN(n, x); } inline uint64_t TruncateToUintN(unsigned n, uint64_t x) { VIXL_ASSERT((0 < n) && (n < 64)); return static_cast(x) & ((UINT64_C(1) << n) - 1); } VIXL_DEPRECATED("TruncateToUintN", inline uint64_t truncate_to_intn(unsigned n, int64_t x)) { return TruncateToUintN(n, x); } // clang-format off #define INT_1_TO_32_LIST(V) \ V(1) V(2) V(3) V(4) V(5) V(6) V(7) V(8) \ V(9) V(10) V(11) V(12) V(13) V(14) V(15) V(16) \ V(17) V(18) V(19) V(20) V(21) V(22) V(23) V(24) \ V(25) V(26) V(27) V(28) V(29) V(30) V(31) V(32) #define INT_33_TO_63_LIST(V) \ V(33) V(34) V(35) V(36) V(37) V(38) V(39) V(40) \ V(41) V(42) V(43) V(44) V(45) V(46) V(47) V(48) \ V(49) V(50) V(51) V(52) V(53) V(54) V(55) V(56) \ V(57) V(58) V(59) V(60) V(61) V(62) V(63) #define INT_1_TO_63_LIST(V) INT_1_TO_32_LIST(V) INT_33_TO_63_LIST(V) // clang-format on #define DECLARE_IS_INT_N(N) \ inline bool IsInt##N(int64_t x) { return IsIntN(N, x); } \ VIXL_DEPRECATED("IsInt" #N, inline bool is_int##N(int64_t x)) { \ return IsIntN(N, x); \ } #define DECLARE_IS_UINT_N(N) \ inline bool IsUint##N(int64_t x) { return IsUintN(N, x); } \ VIXL_DEPRECATED("IsUint" #N, inline bool is_uint##N(int64_t x)) { \ return IsUintN(N, x); \ } #define DECLARE_TRUNCATE_TO_UINT_32(N) \ inline uint32_t TruncateToUint##N(uint64_t x) { \ return static_cast(TruncateToUintN(N, x)); \ } \ VIXL_DEPRECATED("TruncateToUint" #N, \ inline uint32_t truncate_to_int##N(int64_t x)) { \ return TruncateToUint##N(x); \ } INT_1_TO_63_LIST(DECLARE_IS_INT_N) INT_1_TO_63_LIST(DECLARE_IS_UINT_N) INT_1_TO_32_LIST(DECLARE_TRUNCATE_TO_UINT_32) #undef DECLARE_IS_INT_N #undef DECLARE_IS_UINT_N #undef DECLARE_TRUNCATE_TO_INT_N // Bit field extraction. inline uint64_t ExtractUnsignedBitfield64(int msb, int lsb, uint64_t x) { VIXL_ASSERT((static_cast(msb) < sizeof(x) * 8) && (lsb >= 0) && (msb >= lsb)); if ((msb == 63) && (lsb == 0)) return x; return (x >> lsb) & ((static_cast(1) << (1 + msb - lsb)) - 1); } inline uint32_t ExtractUnsignedBitfield32(int msb, int lsb, uint32_t x) { VIXL_ASSERT((static_cast(msb) < sizeof(x) * 8) && (lsb >= 0) && (msb >= lsb)); return TruncateToUint32(ExtractUnsignedBitfield64(msb, lsb, x)); } inline int64_t ExtractSignedBitfield64(int msb, int lsb, int64_t x) { VIXL_ASSERT((static_cast(msb) < sizeof(x) * 8) && (lsb >= 0) && (msb >= lsb)); uint64_t temp = ExtractUnsignedBitfield64(msb, lsb, x); // If the highest extracted bit is set, sign extend. if ((temp >> (msb - lsb)) == 1) { temp |= ~UINT64_C(0) << (msb - lsb); } int64_t result; memcpy(&result, &temp, sizeof(result)); return result; } inline int32_t ExtractSignedBitfield32(int msb, int lsb, int32_t x) { VIXL_ASSERT((static_cast(msb) < sizeof(x) * 8) && (lsb >= 0) && (msb >= lsb)); uint32_t temp = TruncateToUint32(ExtractSignedBitfield64(msb, lsb, x)); int32_t result; memcpy(&result, &temp, sizeof(result)); return result; } inline uint64_t RotateRight(uint64_t value, unsigned int rotate, unsigned int width) { VIXL_ASSERT((width > 0) && (width <= 64)); uint64_t width_mask = ~UINT64_C(0) >> (64 - width); rotate &= 63; if (rotate > 0) { value &= width_mask; value = (value << (width - rotate)) | (value >> rotate); } return value & width_mask; } // Wrapper class for passing FP16 values through the assembler. // This is purely to aid with type checking/casting. class Float16 { public: explicit Float16(double dvalue); Float16() : rawbits_(0x0) {} friend uint16_t Float16ToRawbits(Float16 value); friend Float16 RawbitsToFloat16(uint16_t bits); protected: uint16_t rawbits_; }; // Floating point representation. uint16_t Float16ToRawbits(Float16 value); uint32_t FloatToRawbits(float value); VIXL_DEPRECATED("FloatToRawbits", inline uint32_t float_to_rawbits(float value)) { return FloatToRawbits(value); } uint64_t DoubleToRawbits(double value); VIXL_DEPRECATED("DoubleToRawbits", inline uint64_t double_to_rawbits(double value)) { return DoubleToRawbits(value); } Float16 RawbitsToFloat16(uint16_t bits); float RawbitsToFloat(uint32_t bits); VIXL_DEPRECATED("RawbitsToFloat", inline float rawbits_to_float(uint32_t bits)) { return RawbitsToFloat(bits); } double RawbitsToDouble(uint64_t bits); VIXL_DEPRECATED("RawbitsToDouble", inline double rawbits_to_double(uint64_t bits)) { return RawbitsToDouble(bits); } namespace internal { // Internal simulation class used solely by the simulator to // provide an abstraction layer for any half-precision arithmetic. class SimFloat16 : public Float16 { public: // TODO: We should investigate making this constructor explicit. // This is currently difficult to do due to a number of templated // functions in the simulator which rely on returning double values. SimFloat16(double dvalue) : Float16(dvalue) {} // NOLINT(runtime/explicit) SimFloat16(Float16 f) { // NOLINT(runtime/explicit) this->rawbits_ = Float16ToRawbits(f); } SimFloat16() : Float16() {} SimFloat16 operator-() const; SimFloat16 operator+(SimFloat16 rhs) const; SimFloat16 operator-(SimFloat16 rhs) const; SimFloat16 operator*(SimFloat16 rhs) const; SimFloat16 operator/(SimFloat16 rhs) const; bool operator<(SimFloat16 rhs) const; bool operator>(SimFloat16 rhs) const; bool operator==(SimFloat16 rhs) const; bool operator!=(SimFloat16 rhs) const; // This is necessary for conversions peformed in (macro asm) Fmov. bool operator==(double rhs) const; operator double() const; }; } // namespace internal uint32_t Float16Sign(internal::SimFloat16 value); uint32_t Float16Exp(internal::SimFloat16 value); uint32_t Float16Mantissa(internal::SimFloat16 value); uint32_t FloatSign(float value); VIXL_DEPRECATED("FloatSign", inline uint32_t float_sign(float value)) { return FloatSign(value); } uint32_t FloatExp(float value); VIXL_DEPRECATED("FloatExp", inline uint32_t float_exp(float value)) { return FloatExp(value); } uint32_t FloatMantissa(float value); VIXL_DEPRECATED("FloatMantissa", inline uint32_t float_mantissa(float value)) { return FloatMantissa(value); } uint32_t DoubleSign(double value); VIXL_DEPRECATED("DoubleSign", inline uint32_t double_sign(double value)) { return DoubleSign(value); } uint32_t DoubleExp(double value); VIXL_DEPRECATED("DoubleExp", inline uint32_t double_exp(double value)) { return DoubleExp(value); } uint64_t DoubleMantissa(double value); VIXL_DEPRECATED("DoubleMantissa", inline uint64_t double_mantissa(double value)) { return DoubleMantissa(value); } internal::SimFloat16 Float16Pack(uint16_t sign, uint16_t exp, uint16_t mantissa); float FloatPack(uint32_t sign, uint32_t exp, uint32_t mantissa); VIXL_DEPRECATED("FloatPack", inline float float_pack(uint32_t sign, uint32_t exp, uint32_t mantissa)) { return FloatPack(sign, exp, mantissa); } double DoublePack(uint64_t sign, uint64_t exp, uint64_t mantissa); VIXL_DEPRECATED("DoublePack", inline double double_pack(uint32_t sign, uint32_t exp, uint64_t mantissa)) { return DoublePack(sign, exp, mantissa); } // An fpclassify() function for 16-bit half-precision floats. int Float16Classify(Float16 value); VIXL_DEPRECATED("Float16Classify", inline int float16classify(uint16_t value)) { return Float16Classify(RawbitsToFloat16(value)); } bool IsZero(Float16 value); inline bool IsNaN(float value) { return std::isnan(value); } inline bool IsNaN(double value) { return std::isnan(value); } inline bool IsNaN(Float16 value) { return Float16Classify(value) == FP_NAN; } inline bool IsInf(float value) { return std::isinf(value); } inline bool IsInf(double value) { return std::isinf(value); } inline bool IsInf(Float16 value) { return Float16Classify(value) == FP_INFINITE; } // NaN tests. inline bool IsSignallingNaN(double num) { const uint64_t kFP64QuietNaNMask = UINT64_C(0x0008000000000000); uint64_t raw = DoubleToRawbits(num); if (IsNaN(num) && ((raw & kFP64QuietNaNMask) == 0)) { return true; } return false; } inline bool IsSignallingNaN(float num) { const uint32_t kFP32QuietNaNMask = 0x00400000; uint32_t raw = FloatToRawbits(num); if (IsNaN(num) && ((raw & kFP32QuietNaNMask) == 0)) { return true; } return false; } inline bool IsSignallingNaN(Float16 num) { const uint16_t kFP16QuietNaNMask = 0x0200; return IsNaN(num) && ((Float16ToRawbits(num) & kFP16QuietNaNMask) == 0); } template inline bool IsQuietNaN(T num) { return IsNaN(num) && !IsSignallingNaN(num); } // Convert the NaN in 'num' to a quiet NaN. inline double ToQuietNaN(double num) { const uint64_t kFP64QuietNaNMask = UINT64_C(0x0008000000000000); VIXL_ASSERT(IsNaN(num)); return RawbitsToDouble(DoubleToRawbits(num) | kFP64QuietNaNMask); } inline float ToQuietNaN(float num) { const uint32_t kFP32QuietNaNMask = 0x00400000; VIXL_ASSERT(IsNaN(num)); return RawbitsToFloat(FloatToRawbits(num) | kFP32QuietNaNMask); } inline internal::SimFloat16 ToQuietNaN(internal::SimFloat16 num) { const uint16_t kFP16QuietNaNMask = 0x0200; VIXL_ASSERT(IsNaN(num)); return internal::SimFloat16( RawbitsToFloat16(Float16ToRawbits(num) | kFP16QuietNaNMask)); } // Fused multiply-add. inline double FusedMultiplyAdd(double op1, double op2, double a) { return fma(op1, op2, a); } inline float FusedMultiplyAdd(float op1, float op2, float a) { return fmaf(op1, op2, a); } inline uint64_t LowestSetBit(uint64_t value) { return value & -value; } template inline int HighestSetBitPosition(T value) { VIXL_ASSERT(value != 0); return (sizeof(value) * 8 - 1) - CountLeadingZeros(value); } template inline int WhichPowerOf2(V value) { VIXL_ASSERT(IsPowerOf2(value)); return CountTrailingZeros(value); } unsigned CountClearHalfWords(uint64_t imm, unsigned reg_size); int BitCount(uint64_t value); template T ReverseBits(T value) { VIXL_ASSERT((sizeof(value) == 1) || (sizeof(value) == 2) || (sizeof(value) == 4) || (sizeof(value) == 8)); T result = 0; for (unsigned i = 0; i < (sizeof(value) * 8); i++) { result = (result << 1) | (value & 1); value >>= 1; } return result; } template inline T SignExtend(T val, int bitSize) { VIXL_ASSERT(bitSize > 0); T mask = (T(2) << (bitSize - 1)) - T(1); val &= mask; T sign_bits = -((val >> (bitSize - 1)) << bitSize); val |= sign_bits; return val; } template T ReverseBytes(T value, int block_bytes_log2) { VIXL_ASSERT((sizeof(value) == 4) || (sizeof(value) == 8)); VIXL_ASSERT((1U << block_bytes_log2) <= sizeof(value)); // Split the 64-bit value into an 8-bit array, where b[0] is the least // significant byte, and b[7] is the most significant. uint8_t bytes[8]; uint64_t mask = UINT64_C(0xff00000000000000); for (int i = 7; i >= 0; i--) { bytes[i] = (static_cast(value) & mask) >> (i * 8); mask >>= 8; } // Permutation tables for REV instructions. // permute_table[0] is used by REV16_x, REV16_w // permute_table[1] is used by REV32_x, REV_w // permute_table[2] is used by REV_x VIXL_ASSERT((0 < block_bytes_log2) && (block_bytes_log2 < 4)); static const uint8_t permute_table[3][8] = {{6, 7, 4, 5, 2, 3, 0, 1}, {4, 5, 6, 7, 0, 1, 2, 3}, {0, 1, 2, 3, 4, 5, 6, 7}}; uint64_t temp = 0; for (int i = 0; i < 8; i++) { temp <<= 8; temp |= bytes[permute_table[block_bytes_log2 - 1][i]]; } T result; VIXL_STATIC_ASSERT(sizeof(result) <= sizeof(temp)); memcpy(&result, &temp, sizeof(result)); return result; } template inline bool IsMultiple(T value) { VIXL_ASSERT(IsPowerOf2(MULTIPLE)); return (value & (MULTIPLE - 1)) == 0; } template inline bool IsMultiple(T value, unsigned multiple) { VIXL_ASSERT(IsPowerOf2(multiple)); return (value & (multiple - 1)) == 0; } template inline bool IsAligned(T pointer, int alignment) { VIXL_ASSERT(IsPowerOf2(alignment)); return (pointer & (alignment - 1)) == 0; } // Pointer alignment // TODO: rename/refactor to make it specific to instructions. template inline bool IsAligned(T pointer) { VIXL_ASSERT(sizeof(pointer) == sizeof(intptr_t)); // NOLINT(runtime/sizeof) // Use C-style casts to get static_cast behaviour for integral types (T), and // reinterpret_cast behaviour for other types. return IsAligned((intptr_t)(pointer), ALIGN); } template bool IsWordAligned(T pointer) { return IsAligned<4>(pointer); } // Increment a pointer until it has the specified alignment. The alignment must // be a power of two. template T AlignUp(T pointer, typename Unsigned::type alignment) { VIXL_ASSERT(IsPowerOf2(alignment)); // Use C-style casts to get static_cast behaviour for integral types (T), and // reinterpret_cast behaviour for other types. typename Unsigned::type pointer_raw = (typename Unsigned::type)pointer; VIXL_STATIC_ASSERT(sizeof(pointer) <= sizeof(pointer_raw)); size_t mask = alignment - 1; T result = (T)((pointer_raw + mask) & ~mask); VIXL_ASSERT(result >= pointer); return result; } // Decrement a pointer until it has the specified alignment. The alignment must // be a power of two. template T AlignDown(T pointer, typename Unsigned::type alignment) { VIXL_ASSERT(IsPowerOf2(alignment)); // Use C-style casts to get static_cast behaviour for integral types (T), and // reinterpret_cast behaviour for other types. typename Unsigned::type pointer_raw = (typename Unsigned::type)pointer; VIXL_STATIC_ASSERT(sizeof(pointer) <= sizeof(pointer_raw)); size_t mask = alignment - 1; return (T)(pointer_raw & ~mask); } template inline T ExtractBit(T value, unsigned bit) { return (value >> bit) & T(1); } template inline Td ExtractBits(Ts value, int least_significant_bit, Td mask) { return Td((value >> least_significant_bit) & Ts(mask)); } template inline void AssignBit(Td& dst, // NOLINT(runtime/references) int bit, Ts value) { VIXL_ASSERT((value == Ts(0)) || (value == Ts(1))); VIXL_ASSERT(bit >= 0); VIXL_ASSERT(bit < static_cast(sizeof(Td) * 8)); Td mask(1); dst &= ~(mask << bit); dst |= Td(value) << bit; } template inline void AssignBits(Td& dst, // NOLINT(runtime/references) int least_significant_bit, Ts mask, Ts value) { VIXL_ASSERT(least_significant_bit >= 0); VIXL_ASSERT(least_significant_bit < static_cast(sizeof(Td) * 8)); VIXL_ASSERT(((Td(mask) << least_significant_bit) >> least_significant_bit) == Td(mask)); VIXL_ASSERT((value & mask) == value); dst &= ~(Td(mask) << least_significant_bit); dst |= Td(value) << least_significant_bit; } class VFP { public: static uint32_t FP32ToImm8(float imm) { // bits: aBbb.bbbc.defg.h000.0000.0000.0000.0000 uint32_t bits = FloatToRawbits(imm); // bit7: a000.0000 uint32_t bit7 = ((bits >> 31) & 0x1) << 7; // bit6: 0b00.0000 uint32_t bit6 = ((bits >> 29) & 0x1) << 6; // bit5_to_0: 00cd.efgh uint32_t bit5_to_0 = (bits >> 19) & 0x3f; return static_cast(bit7 | bit6 | bit5_to_0); } static uint32_t FP64ToImm8(double imm) { // bits: aBbb.bbbb.bbcd.efgh.0000.0000.0000.0000 // 0000.0000.0000.0000.0000.0000.0000.0000 uint64_t bits = DoubleToRawbits(imm); // bit7: a000.0000 uint64_t bit7 = ((bits >> 63) & 0x1) << 7; // bit6: 0b00.0000 uint64_t bit6 = ((bits >> 61) & 0x1) << 6; // bit5_to_0: 00cd.efgh uint64_t bit5_to_0 = (bits >> 48) & 0x3f; return static_cast(bit7 | bit6 | bit5_to_0); } static float Imm8ToFP32(uint32_t imm8) { // Imm8: abcdefgh (8 bits) // Single: aBbb.bbbc.defg.h000.0000.0000.0000.0000 (32 bits) // where B is b ^ 1 uint32_t bits = imm8; uint32_t bit7 = (bits >> 7) & 0x1; uint32_t bit6 = (bits >> 6) & 0x1; uint32_t bit5_to_0 = bits & 0x3f; uint32_t result = (bit7 << 31) | ((32 - bit6) << 25) | (bit5_to_0 << 19); return RawbitsToFloat(result); } static double Imm8ToFP64(uint32_t imm8) { // Imm8: abcdefgh (8 bits) // Double: aBbb.bbbb.bbcd.efgh.0000.0000.0000.0000 // 0000.0000.0000.0000.0000.0000.0000.0000 (64 bits) // where B is b ^ 1 uint32_t bits = imm8; uint64_t bit7 = (bits >> 7) & 0x1; uint64_t bit6 = (bits >> 6) & 0x1; uint64_t bit5_to_0 = bits & 0x3f; uint64_t result = (bit7 << 63) | ((256 - bit6) << 54) | (bit5_to_0 << 48); return RawbitsToDouble(result); } static bool IsImmFP32(float imm) { // Valid values will have the form: // aBbb.bbbc.defg.h000.0000.0000.0000.0000 uint32_t bits = FloatToRawbits(imm); // bits[19..0] are cleared. if ((bits & 0x7ffff) != 0) { return false; } // bits[29..25] are all set or all cleared. uint32_t b_pattern = (bits >> 16) & 0x3e00; if (b_pattern != 0 && b_pattern != 0x3e00) { return false; } // bit[30] and bit[29] are opposite. if (((bits ^ (bits << 1)) & 0x40000000) == 0) { return false; } return true; } static bool IsImmFP64(double imm) { // Valid values will have the form: // aBbb.bbbb.bbcd.efgh.0000.0000.0000.0000 // 0000.0000.0000.0000.0000.0000.0000.0000 uint64_t bits = DoubleToRawbits(imm); // bits[47..0] are cleared. if ((bits & 0x0000ffffffffffff) != 0) { return false; } // bits[61..54] are all set or all cleared. uint32_t b_pattern = (bits >> 48) & 0x3fc0; if ((b_pattern != 0) && (b_pattern != 0x3fc0)) { return false; } // bit[62] and bit[61] are opposite. if (((bits ^ (bits << 1)) & (UINT64_C(1) << 62)) == 0) { return false; } return true; } }; class BitField { // ForEachBitHelper is a functor that will call // bool ForEachBitHelper::execute(ElementType id) const // and expects a boolean in return whether to continue (if true) // or stop (if false) // check_set will check if the bits are on (true) or off(false) template bool ForEachBit(const ForEachBitHelper& helper) { for (int i = 0; static_cast(i) < bitfield_.size(); i++) { if (bitfield_[i] == check_set) if (!helper.execute(i)) return false; } return true; } public: explicit BitField(unsigned size) : bitfield_(size, 0) {} void Set(int i) { VIXL_ASSERT((i >= 0) && (static_cast(i) < bitfield_.size())); bitfield_[i] = true; } void Unset(int i) { VIXL_ASSERT((i >= 0) && (static_cast(i) < bitfield_.size())); bitfield_[i] = true; } bool IsSet(int i) const { return bitfield_[i]; } // For each bit not set in the bitfield call the execute functor // execute. // ForEachBitSetHelper::execute returns true if the iteration through // the bits can continue, otherwise it will stop. // struct ForEachBitSetHelper { // bool execute(int /*id*/) { return false; } // }; template bool ForEachBitNotSet(const ForEachBitNotSetHelper& helper) { return ForEachBit(helper); } // For each bit set in the bitfield call the execute functor // execute. template bool ForEachBitSet(const ForEachBitSetHelper& helper) { return ForEachBit(helper); } private: std::vector bitfield_; }; namespace internal { typedef int64_t Int64; class Uint64; class Uint128; class Uint32 { uint32_t data_; public: // Unlike uint32_t, Uint32 has a default constructor. Uint32() { data_ = 0; } explicit Uint32(uint32_t data) : data_(data) {} inline explicit Uint32(Uint64 data); uint32_t Get() const { return data_; } template int32_t GetSigned() const { return ExtractSignedBitfield32(N - 1, 0, data_); } int32_t GetSigned() const { return data_; } Uint32 operator~() const { return Uint32(~data_); } Uint32 operator-() const { return Uint32(-data_); } bool operator==(Uint32 value) const { return data_ == value.data_; } bool operator!=(Uint32 value) const { return data_ != value.data_; } bool operator>(Uint32 value) const { return data_ > value.data_; } Uint32 operator+(Uint32 value) const { return Uint32(data_ + value.data_); } Uint32 operator-(Uint32 value) const { return Uint32(data_ - value.data_); } Uint32 operator&(Uint32 value) const { return Uint32(data_ & value.data_); } Uint32 operator&=(Uint32 value) { data_ &= value.data_; return *this; } Uint32 operator^(Uint32 value) const { return Uint32(data_ ^ value.data_); } Uint32 operator^=(Uint32 value) { data_ ^= value.data_; return *this; } Uint32 operator|(Uint32 value) const { return Uint32(data_ | value.data_); } Uint32 operator|=(Uint32 value) { data_ |= value.data_; return *this; } // Unlike uint32_t, the shift functions can accept negative shift and // return 0 when the shift is too big. Uint32 operator>>(int shift) const { if (shift == 0) return *this; if (shift < 0) { int tmp = -shift; if (tmp >= 32) return Uint32(0); return Uint32(data_ << tmp); } int tmp = shift; if (tmp >= 32) return Uint32(0); return Uint32(data_ >> tmp); } Uint32 operator<<(int shift) const { if (shift == 0) return *this; if (shift < 0) { int tmp = -shift; if (tmp >= 32) return Uint32(0); return Uint32(data_ >> tmp); } int tmp = shift; if (tmp >= 32) return Uint32(0); return Uint32(data_ << tmp); } }; class Uint64 { uint64_t data_; public: // Unlike uint64_t, Uint64 has a default constructor. Uint64() { data_ = 0; } explicit Uint64(uint64_t data) : data_(data) {} explicit Uint64(Uint32 data) : data_(data.Get()) {} inline explicit Uint64(Uint128 data); uint64_t Get() const { return data_; } int64_t GetSigned(int N) const { return ExtractSignedBitfield64(N - 1, 0, data_); } int64_t GetSigned() const { return data_; } Uint32 ToUint32() const { VIXL_ASSERT((data_ >> 32) == 0); return Uint32(static_cast(data_)); } Uint32 GetHigh32() const { return Uint32(data_ >> 32); } Uint32 GetLow32() const { return Uint32(data_ & 0xffffffff); } Uint64 operator~() const { return Uint64(~data_); } Uint64 operator-() const { return Uint64(-data_); } bool operator==(Uint64 value) const { return data_ == value.data_; } bool operator!=(Uint64 value) const { return data_ != value.data_; } Uint64 operator+(Uint64 value) const { return Uint64(data_ + value.data_); } Uint64 operator-(Uint64 value) const { return Uint64(data_ - value.data_); } Uint64 operator&(Uint64 value) const { return Uint64(data_ & value.data_); } Uint64 operator&=(Uint64 value) { data_ &= value.data_; return *this; } Uint64 operator^(Uint64 value) const { return Uint64(data_ ^ value.data_); } Uint64 operator^=(Uint64 value) { data_ ^= value.data_; return *this; } Uint64 operator|(Uint64 value) const { return Uint64(data_ | value.data_); } Uint64 operator|=(Uint64 value) { data_ |= value.data_; return *this; } // Unlike uint64_t, the shift functions can accept negative shift and // return 0 when the shift is too big. Uint64 operator>>(int shift) const { if (shift == 0) return *this; if (shift < 0) { int tmp = -shift; if (tmp >= 64) return Uint64(0); return Uint64(data_ << tmp); } int tmp = shift; if (tmp >= 64) return Uint64(0); return Uint64(data_ >> tmp); } Uint64 operator<<(int shift) const { if (shift == 0) return *this; if (shift < 0) { int tmp = -shift; if (tmp >= 64) return Uint64(0); return Uint64(data_ >> tmp); } int tmp = shift; if (tmp >= 64) return Uint64(0); return Uint64(data_ << tmp); } }; class Uint128 { uint64_t data_high_; uint64_t data_low_; public: Uint128() : data_high_(0), data_low_(0) {} explicit Uint128(uint64_t data_low) : data_high_(0), data_low_(data_low) {} explicit Uint128(Uint64 data_low) : data_high_(0), data_low_(data_low.Get()) {} Uint128(uint64_t data_high, uint64_t data_low) : data_high_(data_high), data_low_(data_low) {} Uint64 ToUint64() const { VIXL_ASSERT(data_high_ == 0); return Uint64(data_low_); } Uint64 GetHigh64() const { return Uint64(data_high_); } Uint64 GetLow64() const { return Uint64(data_low_); } Uint128 operator~() const { return Uint128(~data_high_, ~data_low_); } bool operator==(Uint128 value) const { return (data_high_ == value.data_high_) && (data_low_ == value.data_low_); } Uint128 operator&(Uint128 value) const { return Uint128(data_high_ & value.data_high_, data_low_ & value.data_low_); } Uint128 operator&=(Uint128 value) { data_high_ &= value.data_high_; data_low_ &= value.data_low_; return *this; } Uint128 operator|=(Uint128 value) { data_high_ |= value.data_high_; data_low_ |= value.data_low_; return *this; } Uint128 operator>>(int shift) const { VIXL_ASSERT((shift >= 0) && (shift < 128)); if (shift == 0) return *this; if (shift >= 64) { return Uint128(0, data_high_ >> (shift - 64)); } uint64_t tmp = (data_high_ << (64 - shift)) | (data_low_ >> shift); return Uint128(data_high_ >> shift, tmp); } Uint128 operator<<(int shift) const { VIXL_ASSERT((shift >= 0) && (shift < 128)); if (shift == 0) return *this; if (shift >= 64) { return Uint128(data_low_ << (shift - 64), 0); } uint64_t tmp = (data_high_ << shift) | (data_low_ >> (64 - shift)); return Uint128(tmp, data_low_ << shift); } }; Uint32::Uint32(Uint64 data) : data_(data.ToUint32().Get()) {} Uint64::Uint64(Uint128 data) : data_(data.ToUint64().Get()) {} Int64 BitCount(Uint32 value); } // namespace internal // The default NaN values (for FPCR.DN=1). extern const double kFP64DefaultNaN; extern const float kFP32DefaultNaN; extern const Float16 kFP16DefaultNaN; // Floating-point infinity values. extern const Float16 kFP16PositiveInfinity; extern const Float16 kFP16NegativeInfinity; extern const float kFP32PositiveInfinity; extern const float kFP32NegativeInfinity; extern const double kFP64PositiveInfinity; extern const double kFP64NegativeInfinity; // Floating-point zero values. extern const Float16 kFP16PositiveZero; extern const Float16 kFP16NegativeZero; // AArch64 floating-point specifics. These match IEEE-754. const unsigned kDoubleMantissaBits = 52; const unsigned kDoubleExponentBits = 11; const unsigned kFloatMantissaBits = 23; const unsigned kFloatExponentBits = 8; const unsigned kFloat16MantissaBits = 10; const unsigned kFloat16ExponentBits = 5; enum FPRounding { // The first four values are encodable directly by FPCR. FPTieEven = 0x0, FPPositiveInfinity = 0x1, FPNegativeInfinity = 0x2, FPZero = 0x3, // The final rounding modes are only available when explicitly specified by // the instruction (such as with fcvta). It cannot be set in FPCR. FPTieAway, FPRoundOdd }; enum UseDefaultNaN { kUseDefaultNaN, kIgnoreDefaultNaN }; // Assemble the specified IEEE-754 components into the target type and apply // appropriate rounding. // sign: 0 = positive, 1 = negative // exponent: Unbiased IEEE-754 exponent. // mantissa: The mantissa of the input. The top bit (which is not encoded for // normal IEEE-754 values) must not be omitted. This bit has the // value 'pow(2, exponent)'. // // The input value is assumed to be a normalized value. That is, the input may // not be infinity or NaN. If the source value is subnormal, it must be // normalized before calling this function such that the highest set bit in the // mantissa has the value 'pow(2, exponent)'. // // Callers should use FPRoundToFloat or FPRoundToDouble directly, rather than // calling a templated FPRound. template T FPRound(int64_t sign, int64_t exponent, uint64_t mantissa, FPRounding round_mode) { VIXL_ASSERT((sign == 0) || (sign == 1)); // Only FPTieEven and FPRoundOdd rounding modes are implemented. VIXL_ASSERT((round_mode == FPTieEven) || (round_mode == FPRoundOdd)); // Rounding can promote subnormals to normals, and normals to infinities. For // example, a double with exponent 127 (FLT_MAX_EXP) would appear to be // encodable as a float, but rounding based on the low-order mantissa bits // could make it overflow. With ties-to-even rounding, this value would become // an infinity. // ---- Rounding Method ---- // // The exponent is irrelevant in the rounding operation, so we treat the // lowest-order bit that will fit into the result ('onebit') as having // the value '1'. Similarly, the highest-order bit that won't fit into // the result ('halfbit') has the value '0.5'. The 'point' sits between // 'onebit' and 'halfbit': // // These bits fit into the result. // |---------------------| // mantissa = 0bxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx // || // / | // / halfbit // onebit // // For subnormal outputs, the range of representable bits is smaller and // the position of onebit and halfbit depends on the exponent of the // input, but the method is otherwise similar. // // onebit(frac) // | // | halfbit(frac) halfbit(adjusted) // | / / // | | | // 0b00.0 (exact) -> 0b00.0 (exact) -> 0b00 // 0b00.0... -> 0b00.0... -> 0b00 // 0b00.1 (exact) -> 0b00.0111..111 -> 0b00 // 0b00.1... -> 0b00.1... -> 0b01 // 0b01.0 (exact) -> 0b01.0 (exact) -> 0b01 // 0b01.0... -> 0b01.0... -> 0b01 // 0b01.1 (exact) -> 0b01.1 (exact) -> 0b10 // 0b01.1... -> 0b01.1... -> 0b10 // 0b10.0 (exact) -> 0b10.0 (exact) -> 0b10 // 0b10.0... -> 0b10.0... -> 0b10 // 0b10.1 (exact) -> 0b10.0111..111 -> 0b10 // 0b10.1... -> 0b10.1... -> 0b11 // 0b11.0 (exact) -> 0b11.0 (exact) -> 0b11 // ... / | / | // / | / | // / | // adjusted = frac - (halfbit(mantissa) & ~onebit(frac)); / | // // mantissa = (mantissa >> shift) + halfbit(adjusted); static const int mantissa_offset = 0; static const int exponent_offset = mantissa_offset + mbits; static const int sign_offset = exponent_offset + ebits; VIXL_ASSERT(sign_offset == (sizeof(T) * 8 - 1)); // Bail out early for zero inputs. if (mantissa == 0) { return static_cast(sign << sign_offset); } // If all bits in the exponent are set, the value is infinite or NaN. // This is true for all binary IEEE-754 formats. static const int infinite_exponent = (1 << ebits) - 1; static const int max_normal_exponent = infinite_exponent - 1; // Apply the exponent bias to encode it for the result. Doing this early makes // it easy to detect values that will be infinite or subnormal. exponent += max_normal_exponent >> 1; if (exponent > max_normal_exponent) { // Overflow: the input is too large for the result type to represent. if (round_mode == FPTieEven) { // FPTieEven rounding mode handles overflows using infinities. exponent = infinite_exponent; mantissa = 0; } else { VIXL_ASSERT(round_mode == FPRoundOdd); // FPRoundOdd rounding mode handles overflows using the largest magnitude // normal number. exponent = max_normal_exponent; mantissa = (UINT64_C(1) << exponent_offset) - 1; } return static_cast((sign << sign_offset) | (exponent << exponent_offset) | (mantissa << mantissa_offset)); } // Calculate the shift required to move the top mantissa bit to the proper // place in the destination type. const int highest_significant_bit = 63 - CountLeadingZeros(mantissa); int shift = highest_significant_bit - mbits; if (exponent <= 0) { // The output will be subnormal (before rounding). // For subnormal outputs, the shift must be adjusted by the exponent. The +1 // is necessary because the exponent of a subnormal value (encoded as 0) is // the same as the exponent of the smallest normal value (encoded as 1). shift += -exponent + 1; // Handle inputs that would produce a zero output. // // Shifts higher than highest_significant_bit+1 will always produce a zero // result. A shift of exactly highest_significant_bit+1 might produce a // non-zero result after rounding. if (shift > (highest_significant_bit + 1)) { if (round_mode == FPTieEven) { // The result will always be +/-0.0. return static_cast(sign << sign_offset); } else { VIXL_ASSERT(round_mode == FPRoundOdd); VIXL_ASSERT(mantissa != 0); // For FPRoundOdd, if the mantissa is too small to represent and // non-zero return the next "odd" value. return static_cast((sign << sign_offset) | 1); } } // Properly encode the exponent for a subnormal output. exponent = 0; } else { // Clear the topmost mantissa bit, since this is not encoded in IEEE-754 // normal values. mantissa &= ~(UINT64_C(1) << highest_significant_bit); } // The casts below are only well-defined for unsigned integers. VIXL_STATIC_ASSERT(std::numeric_limits::is_integer); VIXL_STATIC_ASSERT(!std::numeric_limits::is_signed); if (shift > 0) { if (round_mode == FPTieEven) { // We have to shift the mantissa to the right. Some precision is lost, so // we need to apply rounding. uint64_t onebit_mantissa = (mantissa >> (shift)) & 1; uint64_t halfbit_mantissa = (mantissa >> (shift - 1)) & 1; uint64_t adjustment = (halfbit_mantissa & ~onebit_mantissa); uint64_t adjusted = mantissa - adjustment; T halfbit_adjusted = (adjusted >> (shift - 1)) & 1; T result = static_cast((sign << sign_offset) | (exponent << exponent_offset) | ((mantissa >> shift) << mantissa_offset)); // A very large mantissa can overflow during rounding. If this happens, // the exponent should be incremented and the mantissa set to 1.0 // (encoded as 0). Applying halfbit_adjusted after assembling the float // has the nice side-effect that this case is handled for free. // // This also handles cases where a very large finite value overflows to // infinity, or where a very large subnormal value overflows to become // normal. return result + halfbit_adjusted; } else { VIXL_ASSERT(round_mode == FPRoundOdd); // If any bits at position halfbit or below are set, onebit (ie. the // bottom bit of the resulting mantissa) must be set. uint64_t fractional_bits = mantissa & ((UINT64_C(1) << shift) - 1); if (fractional_bits != 0) { mantissa |= UINT64_C(1) << shift; } return static_cast((sign << sign_offset) | (exponent << exponent_offset) | ((mantissa >> shift) << mantissa_offset)); } } else { // We have to shift the mantissa to the left (or not at all). The input // mantissa is exactly representable in the output mantissa, so apply no // rounding correction. return static_cast((sign << sign_offset) | (exponent << exponent_offset) | ((mantissa << -shift) << mantissa_offset)); } } // See FPRound for a description of this function. inline double FPRoundToDouble(int64_t sign, int64_t exponent, uint64_t mantissa, FPRounding round_mode) { uint64_t bits = FPRound(sign, exponent, mantissa, round_mode); return RawbitsToDouble(bits); } // See FPRound for a description of this function. inline Float16 FPRoundToFloat16(int64_t sign, int64_t exponent, uint64_t mantissa, FPRounding round_mode) { return RawbitsToFloat16( FPRound(sign, exponent, mantissa, round_mode)); } // See FPRound for a description of this function. static inline float FPRoundToFloat(int64_t sign, int64_t exponent, uint64_t mantissa, FPRounding round_mode) { uint32_t bits = FPRound(sign, exponent, mantissa, round_mode); return RawbitsToFloat(bits); } float FPToFloat(Float16 value, UseDefaultNaN DN, bool* exception = NULL); float FPToFloat(double value, FPRounding round_mode, UseDefaultNaN DN, bool* exception = NULL); double FPToDouble(Float16 value, UseDefaultNaN DN, bool* exception = NULL); double FPToDouble(float value, UseDefaultNaN DN, bool* exception = NULL); Float16 FPToFloat16(float value, FPRounding round_mode, UseDefaultNaN DN, bool* exception = NULL); Float16 FPToFloat16(double value, FPRounding round_mode, UseDefaultNaN DN, bool* exception = NULL); } // namespace vixl #endif // VIXL_UTILS_H