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+// 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.
+
+#include "jit/arm64/vixl/Utils-vixl.h"
+
+#include <cstdio>
+
+namespace vixl {
+
+// The default NaN values (for FPCR.DN=1).
+const double kFP64DefaultNaN = RawbitsToDouble(UINT64_C(0x7ff8000000000000));
+const float kFP32DefaultNaN = RawbitsToFloat(0x7fc00000);
+const Float16 kFP16DefaultNaN = RawbitsToFloat16(0x7e00);
+
+// Floating-point zero values.
+const Float16 kFP16PositiveZero = RawbitsToFloat16(0x0);
+const Float16 kFP16NegativeZero = RawbitsToFloat16(0x8000);
+
+// Floating-point infinity values.
+const Float16 kFP16PositiveInfinity = RawbitsToFloat16(0x7c00);
+const Float16 kFP16NegativeInfinity = RawbitsToFloat16(0xfc00);
+const float kFP32PositiveInfinity = RawbitsToFloat(0x7f800000);
+const float kFP32NegativeInfinity = RawbitsToFloat(0xff800000);
+const double kFP64PositiveInfinity =
+ RawbitsToDouble(UINT64_C(0x7ff0000000000000));
+const double kFP64NegativeInfinity =
+ RawbitsToDouble(UINT64_C(0xfff0000000000000));
+
+bool IsZero(Float16 value) {
+ uint16_t bits = Float16ToRawbits(value);
+ return (bits == Float16ToRawbits(kFP16PositiveZero) ||
+ bits == Float16ToRawbits(kFP16NegativeZero));
+}
+
+uint16_t Float16ToRawbits(Float16 value) { return value.rawbits_; }
+
+uint32_t FloatToRawbits(float value) {
+ uint32_t bits = 0;
+ memcpy(&bits, &value, 4);
+ return bits;
+}
+
+
+uint64_t DoubleToRawbits(double value) {
+ uint64_t bits = 0;
+ memcpy(&bits, &value, 8);
+ return bits;
+}
+
+
+Float16 RawbitsToFloat16(uint16_t bits) {
+ Float16 f;
+ f.rawbits_ = bits;
+ return f;
+}
+
+
+float RawbitsToFloat(uint32_t bits) {
+ float value = 0.0;
+ memcpy(&value, &bits, 4);
+ return value;
+}
+
+
+double RawbitsToDouble(uint64_t bits) {
+ double value = 0.0;
+ memcpy(&value, &bits, 8);
+ return value;
+}
+
+
+uint32_t Float16Sign(internal::SimFloat16 val) {
+ uint16_t rawbits = Float16ToRawbits(val);
+ return ExtractUnsignedBitfield32(15, 15, rawbits);
+}
+
+
+uint32_t Float16Exp(internal::SimFloat16 val) {
+ uint16_t rawbits = Float16ToRawbits(val);
+ return ExtractUnsignedBitfield32(14, 10, rawbits);
+}
+
+uint32_t Float16Mantissa(internal::SimFloat16 val) {
+ uint16_t rawbits = Float16ToRawbits(val);
+ return ExtractUnsignedBitfield32(9, 0, rawbits);
+}
+
+
+uint32_t FloatSign(float val) {
+ uint32_t rawbits = FloatToRawbits(val);
+ return ExtractUnsignedBitfield32(31, 31, rawbits);
+}
+
+
+uint32_t FloatExp(float val) {
+ uint32_t rawbits = FloatToRawbits(val);
+ return ExtractUnsignedBitfield32(30, 23, rawbits);
+}
+
+
+uint32_t FloatMantissa(float val) {
+ uint32_t rawbits = FloatToRawbits(val);
+ return ExtractUnsignedBitfield32(22, 0, rawbits);
+}
+
+
+uint32_t DoubleSign(double val) {
+ uint64_t rawbits = DoubleToRawbits(val);
+ return static_cast<uint32_t>(ExtractUnsignedBitfield64(63, 63, rawbits));
+}
+
+
+uint32_t DoubleExp(double val) {
+ uint64_t rawbits = DoubleToRawbits(val);
+ return static_cast<uint32_t>(ExtractUnsignedBitfield64(62, 52, rawbits));
+}
+
+
+uint64_t DoubleMantissa(double val) {
+ uint64_t rawbits = DoubleToRawbits(val);
+ return ExtractUnsignedBitfield64(51, 0, rawbits);
+}
+
+
+internal::SimFloat16 Float16Pack(uint16_t sign,
+ uint16_t exp,
+ uint16_t mantissa) {
+ uint16_t bits = (sign << 15) | (exp << 10) | mantissa;
+ return RawbitsToFloat16(bits);
+}
+
+
+float FloatPack(uint32_t sign, uint32_t exp, uint32_t mantissa) {
+ uint32_t bits = (sign << 31) | (exp << 23) | mantissa;
+ return RawbitsToFloat(bits);
+}
+
+
+double DoublePack(uint64_t sign, uint64_t exp, uint64_t mantissa) {
+ uint64_t bits = (sign << 63) | (exp << 52) | mantissa;
+ return RawbitsToDouble(bits);
+}
+
+
+int Float16Classify(Float16 value) {
+ uint16_t bits = Float16ToRawbits(value);
+ uint16_t exponent_max = (1 << 5) - 1;
+ uint16_t exponent_mask = exponent_max << 10;
+ uint16_t mantissa_mask = (1 << 10) - 1;
+
+ uint16_t exponent = (bits & exponent_mask) >> 10;
+ uint16_t mantissa = bits & mantissa_mask;
+ if (exponent == 0) {
+ if (mantissa == 0) {
+ return FP_ZERO;
+ }
+ return FP_SUBNORMAL;
+ } else if (exponent == exponent_max) {
+ if (mantissa == 0) {
+ return FP_INFINITE;
+ }
+ return FP_NAN;
+ }
+ return FP_NORMAL;
+}
+
+
+unsigned CountClearHalfWords(uint64_t imm, unsigned reg_size) {
+ VIXL_ASSERT((reg_size % 8) == 0);
+ int count = 0;
+ for (unsigned i = 0; i < (reg_size / 16); i++) {
+ if ((imm & 0xffff) == 0) {
+ count++;
+ }
+ imm >>= 16;
+ }
+ return count;
+}
+
+
+int BitCount(uint64_t value) { return CountSetBits(value); }
+
+// Float16 definitions.
+
+Float16::Float16(double dvalue) {
+ rawbits_ =
+ Float16ToRawbits(FPToFloat16(dvalue, FPTieEven, kIgnoreDefaultNaN));
+}
+
+namespace internal {
+
+SimFloat16 SimFloat16::operator-() const {
+ return RawbitsToFloat16(rawbits_ ^ 0x8000);
+}
+
+// SimFloat16 definitions.
+SimFloat16 SimFloat16::operator+(SimFloat16 rhs) const {
+ return static_cast<double>(*this) + static_cast<double>(rhs);
+}
+
+SimFloat16 SimFloat16::operator-(SimFloat16 rhs) const {
+ return static_cast<double>(*this) - static_cast<double>(rhs);
+}
+
+SimFloat16 SimFloat16::operator*(SimFloat16 rhs) const {
+ return static_cast<double>(*this) * static_cast<double>(rhs);
+}
+
+SimFloat16 SimFloat16::operator/(SimFloat16 rhs) const {
+ return static_cast<double>(*this) / static_cast<double>(rhs);
+}
+
+bool SimFloat16::operator<(SimFloat16 rhs) const {
+ return static_cast<double>(*this) < static_cast<double>(rhs);
+}
+
+bool SimFloat16::operator>(SimFloat16 rhs) const {
+ return static_cast<double>(*this) > static_cast<double>(rhs);
+}
+
+bool SimFloat16::operator==(SimFloat16 rhs) const {
+ if (IsNaN(*this) || IsNaN(rhs)) {
+ return false;
+ } else if (IsZero(rhs) && IsZero(*this)) {
+ // +0 and -0 should be treated as equal.
+ return true;
+ }
+ return this->rawbits_ == rhs.rawbits_;
+}
+
+bool SimFloat16::operator!=(SimFloat16 rhs) const { return !(*this == rhs); }
+
+bool SimFloat16::operator==(double rhs) const {
+ return static_cast<double>(*this) == static_cast<double>(rhs);
+}
+
+SimFloat16::operator double() const {
+ return FPToDouble(*this, kIgnoreDefaultNaN);
+}
+
+Int64 BitCount(Uint32 value) { return CountSetBits(value.Get()); }
+
+} // namespace internal
+
+float FPToFloat(Float16 value, UseDefaultNaN DN, bool* exception) {
+ uint16_t bits = Float16ToRawbits(value);
+ uint32_t sign = bits >> 15;
+ uint32_t exponent =
+ ExtractUnsignedBitfield32(kFloat16MantissaBits + kFloat16ExponentBits - 1,
+ kFloat16MantissaBits,
+ bits);
+ uint32_t mantissa =
+ ExtractUnsignedBitfield32(kFloat16MantissaBits - 1, 0, bits);
+
+ switch (Float16Classify(value)) {
+ case FP_ZERO:
+ return (sign == 0) ? 0.0f : -0.0f;
+
+ case FP_INFINITE:
+ return (sign == 0) ? kFP32PositiveInfinity : kFP32NegativeInfinity;
+
+ case FP_SUBNORMAL: {
+ // Calculate shift required to put mantissa into the most-significant bits
+ // of the destination mantissa.
+ int shift = CountLeadingZeros(mantissa << (32 - 10));
+
+ // Shift mantissa and discard implicit '1'.
+ mantissa <<= (kFloatMantissaBits - kFloat16MantissaBits) + shift + 1;
+ mantissa &= (1 << kFloatMantissaBits) - 1;
+
+ // Adjust the exponent for the shift applied, and rebias.
+ exponent = exponent - shift + (-15 + 127);
+ break;
+ }
+
+ case FP_NAN:
+ if (IsSignallingNaN(value)) {
+ if (exception != NULL) {
+ *exception = true;
+ }
+ }
+ if (DN == kUseDefaultNaN) return kFP32DefaultNaN;
+
+ // Convert NaNs as the processor would:
+ // - The sign is propagated.
+ // - The payload (mantissa) is transferred entirely, except that the top
+ // bit is forced to '1', making the result a quiet NaN. The unused
+ // (low-order) payload bits are set to 0.
+ exponent = (1 << kFloatExponentBits) - 1;
+
+ // Increase bits in mantissa, making low-order bits 0.
+ mantissa <<= (kFloatMantissaBits - kFloat16MantissaBits);
+ mantissa |= 1 << 22; // Force a quiet NaN.
+ break;
+
+ case FP_NORMAL:
+ // Increase bits in mantissa, making low-order bits 0.
+ mantissa <<= (kFloatMantissaBits - kFloat16MantissaBits);
+
+ // Change exponent bias.
+ exponent += (-15 + 127);
+ break;
+
+ default:
+ VIXL_UNREACHABLE();
+ }
+ return RawbitsToFloat((sign << 31) | (exponent << kFloatMantissaBits) |
+ mantissa);
+}
+
+
+float FPToFloat(double value,
+ FPRounding round_mode,
+ UseDefaultNaN DN,
+ bool* exception) {
+ // Only the FPTieEven rounding mode is implemented.
+ VIXL_ASSERT((round_mode == FPTieEven) || (round_mode == FPRoundOdd));
+ USE(round_mode);
+
+ switch (std::fpclassify(value)) {
+ case FP_NAN: {
+ if (IsSignallingNaN(value)) {
+ if (exception != NULL) {
+ *exception = true;
+ }
+ }
+ if (DN == kUseDefaultNaN) return kFP32DefaultNaN;
+
+ // Convert NaNs as the processor would:
+ // - The sign is propagated.
+ // - The payload (mantissa) is transferred as much as possible, except
+ // that the top bit is forced to '1', making the result a quiet NaN.
+ uint64_t raw = DoubleToRawbits(value);
+
+ uint32_t sign = raw >> 63;
+ uint32_t exponent = (1 << 8) - 1;
+ uint32_t payload =
+ static_cast<uint32_t>(ExtractUnsignedBitfield64(50, 52 - 23, raw));
+ payload |= (1 << 22); // Force a quiet NaN.
+
+ return RawbitsToFloat((sign << 31) | (exponent << 23) | payload);
+ }
+
+ case FP_ZERO:
+ case FP_INFINITE: {
+ // In a C++ cast, any value representable in the target type will be
+ // unchanged. This is always the case for +/-0.0 and infinities.
+ return static_cast<float>(value);
+ }
+
+ case FP_NORMAL:
+ case FP_SUBNORMAL: {
+ // Convert double-to-float as the processor would, assuming that FPCR.FZ
+ // (flush-to-zero) is not set.
+ uint64_t raw = DoubleToRawbits(value);
+ // Extract the IEEE-754 double components.
+ uint32_t sign = raw >> 63;
+ // Extract the exponent and remove the IEEE-754 encoding bias.
+ int32_t exponent =
+ static_cast<int32_t>(ExtractUnsignedBitfield64(62, 52, raw)) - 1023;
+ // Extract the mantissa and add the implicit '1' bit.
+ uint64_t mantissa = ExtractUnsignedBitfield64(51, 0, raw);
+ if (std::fpclassify(value) == FP_NORMAL) {
+ mantissa |= (UINT64_C(1) << 52);
+ }
+ return FPRoundToFloat(sign, exponent, mantissa, round_mode);
+ }
+ }
+
+ VIXL_UNREACHABLE();
+ return value;
+}
+
+// TODO: We should consider implementing a full FPToDouble(Float16)
+// conversion function (for performance reasons).
+double FPToDouble(Float16 value, UseDefaultNaN DN, bool* exception) {
+ // We can rely on implicit float to double conversion here.
+ return FPToFloat(value, DN, exception);
+}
+
+
+double FPToDouble(float value, UseDefaultNaN DN, bool* exception) {
+ switch (std::fpclassify(value)) {
+ case FP_NAN: {
+ if (IsSignallingNaN(value)) {
+ if (exception != NULL) {
+ *exception = true;
+ }
+ }
+ if (DN == kUseDefaultNaN) return kFP64DefaultNaN;
+
+ // Convert NaNs as the processor would:
+ // - The sign is propagated.
+ // - The payload (mantissa) is transferred entirely, except that the top
+ // bit is forced to '1', making the result a quiet NaN. The unused
+ // (low-order) payload bits are set to 0.
+ uint32_t raw = FloatToRawbits(value);
+
+ uint64_t sign = raw >> 31;
+ uint64_t exponent = (1 << 11) - 1;
+ uint64_t payload = ExtractUnsignedBitfield64(21, 0, raw);
+ payload <<= (52 - 23); // The unused low-order bits should be 0.
+ payload |= (UINT64_C(1) << 51); // Force a quiet NaN.
+
+ return RawbitsToDouble((sign << 63) | (exponent << 52) | payload);
+ }
+
+ case FP_ZERO:
+ case FP_NORMAL:
+ case FP_SUBNORMAL:
+ case FP_INFINITE: {
+ // All other inputs are preserved in a standard cast, because every value
+ // representable using an IEEE-754 float is also representable using an
+ // IEEE-754 double.
+ return static_cast<double>(value);
+ }
+ }
+
+ VIXL_UNREACHABLE();
+ return static_cast<double>(value);
+}
+
+
+Float16 FPToFloat16(float value,
+ FPRounding round_mode,
+ UseDefaultNaN DN,
+ bool* exception) {
+ // Only the FPTieEven rounding mode is implemented.
+ VIXL_ASSERT(round_mode == FPTieEven);
+ USE(round_mode);
+
+ uint32_t raw = FloatToRawbits(value);
+ int32_t sign = raw >> 31;
+ int32_t exponent = ExtractUnsignedBitfield32(30, 23, raw) - 127;
+ uint32_t mantissa = ExtractUnsignedBitfield32(22, 0, raw);
+
+ switch (std::fpclassify(value)) {
+ case FP_NAN: {
+ if (IsSignallingNaN(value)) {
+ if (exception != NULL) {
+ *exception = true;
+ }
+ }
+ if (DN == kUseDefaultNaN) return kFP16DefaultNaN;
+
+ // Convert NaNs as the processor would:
+ // - The sign is propagated.
+ // - The payload (mantissa) is transferred as much as possible, except
+ // that the top bit is forced to '1', making the result a quiet NaN.
+ uint16_t result = (sign == 0) ? Float16ToRawbits(kFP16PositiveInfinity)
+ : Float16ToRawbits(kFP16NegativeInfinity);
+ result |= mantissa >> (kFloatMantissaBits - kFloat16MantissaBits);
+ result |= (1 << 9); // Force a quiet NaN;
+ return RawbitsToFloat16(result);
+ }
+
+ case FP_ZERO:
+ return (sign == 0) ? kFP16PositiveZero : kFP16NegativeZero;
+
+ case FP_INFINITE:
+ return (sign == 0) ? kFP16PositiveInfinity : kFP16NegativeInfinity;
+
+ case FP_NORMAL:
+ case FP_SUBNORMAL: {
+ // Convert float-to-half as the processor would, assuming that FPCR.FZ
+ // (flush-to-zero) is not set.
+
+ // Add the implicit '1' bit to the mantissa.
+ mantissa += (1 << 23);
+ return FPRoundToFloat16(sign, exponent, mantissa, round_mode);
+ }
+ }
+
+ VIXL_UNREACHABLE();
+ return kFP16PositiveZero;
+}
+
+
+Float16 FPToFloat16(double value,
+ FPRounding round_mode,
+ UseDefaultNaN DN,
+ bool* exception) {
+ // Only the FPTieEven rounding mode is implemented.
+ VIXL_ASSERT(round_mode == FPTieEven);
+ USE(round_mode);
+
+ uint64_t raw = DoubleToRawbits(value);
+ int32_t sign = raw >> 63;
+ int64_t exponent = ExtractUnsignedBitfield64(62, 52, raw) - 1023;
+ uint64_t mantissa = ExtractUnsignedBitfield64(51, 0, raw);
+
+ switch (std::fpclassify(value)) {
+ case FP_NAN: {
+ if (IsSignallingNaN(value)) {
+ if (exception != NULL) {
+ *exception = true;
+ }
+ }
+ if (DN == kUseDefaultNaN) return kFP16DefaultNaN;
+
+ // Convert NaNs as the processor would:
+ // - The sign is propagated.
+ // - The payload (mantissa) is transferred as much as possible, except
+ // that the top bit is forced to '1', making the result a quiet NaN.
+ uint16_t result = (sign == 0) ? Float16ToRawbits(kFP16PositiveInfinity)
+ : Float16ToRawbits(kFP16NegativeInfinity);
+ result |= mantissa >> (kDoubleMantissaBits - kFloat16MantissaBits);
+ result |= (1 << 9); // Force a quiet NaN;
+ return RawbitsToFloat16(result);
+ }
+
+ case FP_ZERO:
+ return (sign == 0) ? kFP16PositiveZero : kFP16NegativeZero;
+
+ case FP_INFINITE:
+ return (sign == 0) ? kFP16PositiveInfinity : kFP16NegativeInfinity;
+ case FP_NORMAL:
+ case FP_SUBNORMAL: {
+ // Convert double-to-half as the processor would, assuming that FPCR.FZ
+ // (flush-to-zero) is not set.
+
+ // Add the implicit '1' bit to the mantissa.
+ mantissa += (UINT64_C(1) << 52);
+ return FPRoundToFloat16(sign, exponent, mantissa, round_mode);
+ }
+ }
+
+ VIXL_UNREACHABLE();
+ return kFP16PositiveZero;
+}
+
+} // namespace vixl