diff options
Diffstat (limited to 'tensorflow/core/framework/numeric_types.h')
| -rw-r--r-- | tensorflow/core/framework/numeric_types.h | 251 |
1 files changed, 9 insertions, 242 deletions
diff --git a/tensorflow/core/framework/numeric_types.h b/tensorflow/core/framework/numeric_types.h index d005de2af1..a630bee38d 100644 --- a/tensorflow/core/framework/numeric_types.h +++ b/tensorflow/core/framework/numeric_types.h @@ -44,262 +44,29 @@ typedef Eigen::QUInt16 quint16; // see framework/bfloat16.h for description. struct bfloat16 { EIGEN_DEVICE_FUNC bfloat16() {} - - explicit EIGEN_DEVICE_FUNC bfloat16(float v) { - uint32_t input; - memcpy(&input, &v, sizeof(uint32_t)); - - if ((~input & 0x7f800000) == 0 && (input & 0x007fffff) != 0) { - // If the value is a NaN, squash it to a qNaN with msb of fraction set, - // this makes sure after truncation we don't end up with an inf. - // - // qNaN magic: All exponent bits set + most significant bit of fraction - // set. - value = 0x7fc0; - } else { - // Fast rounding algorithm that rounds a half value to nearest even. This - // reduces expected error when we convert a large number of floats. Here - // is how it works: - // - // Definitions: - // To convert a float 32 to bfloat16, a float 32 can be viewed as 32 bits - // with the following tags: - // - // Sign | Exp (8 bits) | Frac (23 bits) - // S EEEEEEEE FFFFFFLRTTTTTTTTTTTTTTT - // - // S: Sign bit. - // E: Exponent bits. - // F: First 6 bits of fraction. - // L: Least significant bit of resulting bfloat16 if we truncate away the - // rest of the float32. This is also the 7th bit of fraction - // R: Rounding bit, 8th bit of fraction. - // T: Sticky bits, rest of fraction, 15 bits. - // - // To round half to nearest even, there are 3 cases where we want to round - // down (simply truncate the result of the bits away, which consists of - // rounding bit and sticky bits) and two cases where we want to round up - // (truncate then add one to the result). - // - // The fast converting algorithm simply adds lsb (L) to 0x7fff (15 bits of - // 1s) as the rounding bias, adds the rounding bias to the input, then - // truncates the last 16 bits away. - // - // To understand how it works, we can analyze this algorithm case by case: - // - // 1. L = 0, R = 0: - // Expect: round down, this is less than half value. - // - // Algorithm: - // - Rounding bias: 0x7fff + 0 = 0x7fff - // - Adding rounding bias to input may create any carry, depending on - // whether there is any value set to 1 in T bits. - // - R may be set to 1 if there is a carry. - // - L remains 0. - // - Note that this case also handles Inf and -Inf, where all fraction - // bits, including L, R and Ts are all 0. The output remains Inf after - // this algorithm. - // - // 2. L = 1, R = 0: - // Expect: round down, this is less than half value. - // - // Algorithm: - // - Rounding bias: 0x7fff + 1 = 0x8000 - // - Adding rounding bias to input doesn't change sticky bits but - // adds 1 to rounding bit. - // - L remains 1. - // - // 3. L = 0, R = 1, all of T are 0: - // Expect: round down, this is exactly at half, the result is already - // even (L=0). - // - // Algorithm: - // - Rounding bias: 0x7fff + 0 = 0x7fff - // - Adding rounding bias to input sets all sticky bits to 1, but - // doesn't create a carry. - // - R remains 1. - // - L remains 0. - // - // 4. L = 1, R = 1: - // Expect: round up, this is exactly at half, the result needs to be - // round to the next even number. - // - // Algorithm: - // - Rounding bias: 0x7fff + 1 = 0x8000 - // - Adding rounding bias to input doesn't change sticky bits, but - // creates a carry from rounding bit. - // - The carry sets L to 0, creates another carry bit and propagate - // forward to F bits. - // - If all the F bits are 1, a carry then propagates to the exponent - // bits, which then creates the minimum value with the next exponent - // value. Note that we won't have the case where exponents are all 1, - // since that's either a NaN (handled in the other if condition) or inf - // (handled in case 1). - // - // 5. L = 0, R = 1, any of T is 1: - // Expect: round up, this is greater than half. - // - // Algorithm: - // - Rounding bias: 0x7fff + 0 = 0x7fff - // - Adding rounding bias to input creates a carry from sticky bits, - // sets rounding bit to 0, then create another carry. - // - The second carry sets L to 1. - // - // Examples: - // - // Exact half value that is already even: - // Input: - // Sign | Exp (8 bit) | Frac (first 7 bit) | Frac (last 16 bit) - // S E E E E E E E E F F F F F F L RTTTTTTTTTTTTTTT - // 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1000000000000000 - // - // This falls into case 3. We truncate the rest of 16 bits and no - // carry is created into F and L: - // - // Output: - // Sign | Exp (8 bit) | Frac (first 7 bit) - // S E E E E E E E E F F F F F F L - // 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 - // - // Exact half value, round to next even number: - // Input: - // Sign | Exp (8 bit) | Frac (first 7 bit) | Frac (last 16 bit) - // S E E E E E E E E F F F F F F L RTTTTTTTTTTTTTTT - // 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1000000000000000 - // - // This falls into case 4. We create a carry from R and T, - // which then propagates into L and F: - // - // Output: - // Sign | Exp (8 bit) | Frac (first 7 bit) - // S E E E E E E E E F F F F F F L - // 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 - // - // - // Max denormal value round to min normal value: - // Input: - // Sign | Exp (8 bit) | Frac (first 7 bit) | Frac (last 16 bit) - // S E E E E E E E E F F F F F F L RTTTTTTTTTTTTTTT - // 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1111111111111111 - // - // This falls into case 4. We create a carry from R and T, - // propagate into L and F, which then propagates into exponent - // bits: - // - // Output: - // Sign | Exp (8 bit) | Frac (first 7 bit) - // S E E E E E E E E F F F F F F L - // 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 - // - // Max normal value round to Inf: - // Input: - // Sign | Exp (8 bit) | Frac (first 7 bit) | Frac (last 16 bit) - // S E E E E E E E E F F F F F F L RTTTTTTTTTTTTTTT - // 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1111111111111111 - // - // This falls into case 4. We create a carry from R and T, - // propagate into L and F, which then propagates into exponent - // bits: - // - // Sign | Exp (8 bit) | Frac (first 7 bit) - // S E E E E E E E E F F F F F F L - // 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 - // - // - // Least significant bit of resulting bfloat. - uint32_t lsb = (input >> 16) & 1; - uint32_t rounding_bias = 0x7fff + lsb; - input += rounding_bias; - value = static_cast<uint16_t>(input >> 16); - } - } - - template <class T> - explicit EIGEN_DEVICE_FUNC bfloat16(const T& val) - : bfloat16(static_cast<float>(val)) {} - - EIGEN_DEVICE_FUNC EIGEN_EXPLICIT_CAST(float) const { - float result; - - uint16_t* q = reinterpret_cast<uint16_t*>(&result); - + EIGEN_DEVICE_FUNC explicit bfloat16(const float v) { + const uint16_t* p = reinterpret_cast<const uint16_t*>(&v); #if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ - q[0] = value; - q[1] = 0; + value = p[0]; #else - q[0] = 0; - q[1] = value; + value = p[1]; #endif - return result; - } - - EIGEN_DEVICE_FUNC explicit operator bool() const { - return static_cast<bool>(float(*this)); - } - - EIGEN_DEVICE_FUNC explicit operator Eigen::half() const { - return static_cast<Eigen::half>(float(*this)); - } - - EIGEN_DEVICE_FUNC explicit operator short() const { - return static_cast<short>(float(*this)); - } - - EIGEN_DEVICE_FUNC explicit operator int() const { - return static_cast<int>(float(*this)); - } - - EIGEN_DEVICE_FUNC explicit operator char() const { - return static_cast<char>(float(*this)); - } - - EIGEN_DEVICE_FUNC explicit operator signed char() const { - return static_cast<signed char>(float(*this)); - } - - EIGEN_DEVICE_FUNC explicit operator unsigned char() const { - return static_cast<unsigned char>(float(*this)); - } - - EIGEN_DEVICE_FUNC explicit operator unsigned int() const { - return static_cast<unsigned int>(float(*this)); - } - - EIGEN_DEVICE_FUNC explicit operator unsigned long() const { - return static_cast<unsigned long>(float(*this)); - } - - EIGEN_DEVICE_FUNC explicit operator unsigned long long() const { - return static_cast<unsigned long long>(float(*this)); - } - - EIGEN_DEVICE_FUNC explicit operator long long() const { - return static_cast<long long>(float(*this)); - } - - EIGEN_DEVICE_FUNC explicit operator double() const { - return static_cast<double>(float(*this)); } uint16_t value; }; -inline bool operator==(const bfloat16 a, const bfloat16 b) { - return a.value == b.value; -} - -inline bool operator!=(const bfloat16 a, const bfloat16 b) { - return a.value != b.value; -} - } // end namespace tensorflow namespace Eigen { template <> struct NumTraits<tensorflow::bfloat16> : GenericNumTraits<uint16_t> {}; -using ::tensorflow::operator==; -using ::tensorflow::operator!=; +EIGEN_STRONG_INLINE bool operator==(const tensorflow::bfloat16 a, + const tensorflow::bfloat16 b) { + return a.value == b.value; +} + } // namespace Eigen #ifdef COMPILER_MSVC |