// 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 <cstdio>
#include "utils-vixl.h"
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