Half.h

#pragma once

/// Defines the Half type (half-precision floating-point) including conversions
/// to standard C types and basic arithmetic operations. Note that arithmetic
/// operations are implemented by converting to floating point and
/// performing the operation in float32, instead of using CUDA half intrinisics.
/// Most uses of this type within ATen are memory bound, including the
/// element-wise kernels, and the half intrinisics aren't efficient on all GPUs.
/// If you are writing a compute bound kernel, you can use the CUDA half
/// intrinsics directly on the Half type from device code.

#include <c10/core/bitcasts.h>
#include <c10/macros/Macros.h>
#include <c10/util/C++17.h>

#if defined(__cplusplus) && (__cplusplus >= 201103L)
#include <cmath>
#include <cstdint>
#elif !defined(__OPENCL_VERSION__)
#include <math.h>
#include <stdint.h>
#endif

#ifdef _MSC_VER
#include <intrin.h>
#endif

#include <complex>
#include <cstring>
#include <iosfwd>
#include <limits>
#include <sstream>
#include <stdexcept>
#include <string>
#include <utility>

#ifdef __CUDACC__
#include <cuda_fp16.h>
#endif

#ifdef __HIPCC__
#include <hip/hip_fp16.h>
#endif

namespace c10 {

namespace detail {

  /*
   * Convert a 16-bit floating-point number in IEEE half-precision format, in bit representation, to
   * a 32-bit floating-point number in IEEE single-precision format, in bit representation.
   *
   * @note The implementation doesn't use any floating-point operations.
   */
  static inline uint32_t fp16_ieee_to_fp32_bits(uint16_t h) {
  	/*
  	 * Extend the half-precision floating-point number to 32 bits and shift to the upper part of the 32-bit word:
  	 *      +---+-----+------------+-------------------+
  	 *      | S |EEEEE|MM MMMM MMMM|0000 0000 0000 0000|
  	 *      +---+-----+------------+-------------------+
  	 * Bits  31  26-30    16-25            0-15
  	 *
  	 * S - sign bit, E - bits of the biased exponent, M - bits of the mantissa, 0 - zero bits.
  	 */
  	const uint32_t w = (uint32_t) h << 16;
  	/*
  	 * Extract the sign of the input number into the high bit of the 32-bit word:
  	 *
  	 *      +---+----------------------------------+
  	 *      | S |0000000 00000000 00000000 00000000|
  	 *      +---+----------------------------------+
  	 * Bits  31                 0-31
  	 */
  	const uint32_t sign = w & UINT32_C(0x80000000);
  	/*
  	 * Extract mantissa and biased exponent of the input number into the bits 0-30 of the 32-bit word:
  	 *
  	 *      +---+-----+------------+-------------------+
  	 *      | 0 |EEEEE|MM MMMM MMMM|0000 0000 0000 0000|
  	 *      +---+-----+------------+-------------------+
  	 * Bits  30  27-31     17-26            0-16
  	 */
  	const uint32_t nonsign = w & UINT32_C(0x7FFFFFFF);
  	/*
  	 * Renorm shift is the number of bits to shift mantissa left to make the half-precision number normalized.
  	 * If the initial number is normalized, some of its high 6 bits (sign == 0 and 5-bit exponent) equals one.
  	 * In this case renorm_shift == 0. If the number is denormalize, renorm_shift > 0. Note that if we shift
  	 * denormalized nonsign by renorm_shift, the unit bit of mantissa will shift into exponent, turning the
  	 * biased exponent into 1, and making mantissa normalized (i.e. without leading 1).
  	 */
#ifdef _MSC_VER
        unsigned long nonsign_bsr;
        _BitScanReverse(&nonsign_bsr, (unsigned long)nonsign);
        uint32_t renorm_shift = (uint32_t)nonsign_bsr ^ 31;
#else
        uint32_t renorm_shift = __builtin_clz(nonsign);
#endif
        renorm_shift = renorm_shift > 5 ? renorm_shift - 5 : 0;
        /*
         * Iff half-precision number has exponent of 15, the addition overflows
         * it into bit 31, and the subsequent shift turns the high 9 bits
         * into 1. Thus inf_nan_mask == 0x7F800000 if the half-precision number
         * had exponent of 15 (i.e. was NaN or infinity) 0x00000000 otherwise
         */
        const int32_t inf_nan_mask =
            ((int32_t)(nonsign + 0x04000000) >> 8) & INT32_C(0x7F800000);
        /*
         * Iff nonsign is 0, it overflows into 0xFFFFFFFF, turning bit 31
         * into 1. Otherwise, bit 31 remains 0. The signed shift right by 31
         * broadcasts bit 31 into all bits of the zero_mask. Thus zero_mask ==
         * 0xFFFFFFFF if the half-precision number was zero (+0.0h or -0.0h)
         * 0x00000000 otherwise
         */
        const int32_t zero_mask = (int32_t)(nonsign - 1) >> 31;
        /*
         * 1. Shift nonsign left by renorm_shift to normalize it (if the input
         * was denormal)
         * 2. Shift nonsign right by 3 so the exponent (5 bits originally)
         * becomes an 8-bit field and 10-bit mantissa shifts into the 10 high
         * bits of the 23-bit mantissa of IEEE single-precision number.
         * 3. Add 0x70 to the exponent (starting at bit 23) to compensate the
         * different in exponent bias (0x7F for single-precision number less 0xF
         * for half-precision number).
         * 4. Subtract renorm_shift from the exponent (starting at bit 23) to
         * account for renormalization. As renorm_shift is less than 0x70, this
         * can be combined with step 3.
         * 5. Binary OR with inf_nan_mask to turn the exponent into 0xFF if the
         * input was NaN or infinity.
         * 6. Binary ANDNOT with zero_mask to turn the mantissa and exponent
         * into zero if the input was zero.
         * 7. Combine with the sign of the input number.
         */
        return sign |
            ((((nonsign << renorm_shift >> 3) + ((0x70 - renorm_shift) << 23)) |
              inf_nan_mask) &
             ~zero_mask);
  }

  /*
   * Convert a 16-bit floating-point number in IEEE half-precision format, in bit representation, to
   * a 32-bit floating-point number in IEEE single-precision format.
   *
   * @note The implementation relies on IEEE-like (no assumption about rounding mode and no operations on denormals)
   * floating-point operations and bitcasts between integer and floating-point variables.
   */
  static inline float fp16_ieee_to_fp32_value(uint16_t h) {
  	/*
  	 * Extend the half-precision floating-point number to 32 bits and shift to the upper part of the 32-bit word:
  	 *      +---+-----+------------+-------------------+
  	 *      | S |EEEEE|MM MMMM MMMM|0000 0000 0000 0000|
  	 *      +---+-----+------------+-------------------+
  	 * Bits  31  26-30    16-25            0-15
  	 *
  	 * S - sign bit, E - bits of the biased exponent, M - bits of the mantissa, 0 - zero bits.
  	 */
  	const uint32_t w = (uint32_t) h << 16;
  	/*
  	 * Extract the sign of the input number into the high bit of the 32-bit word:
  	 *
  	 *      +---+----------------------------------+
  	 *      | S |0000000 00000000 00000000 00000000|
  	 *      +---+----------------------------------+
  	 * Bits  31                 0-31
  	 */
  	const uint32_t sign = w & UINT32_C(0x80000000);
  	/*
  	 * Extract mantissa and biased exponent of the input number into the high bits of the 32-bit word:
  	 *
  	 *      +-----+------------+---------------------+
  	 *      |EEEEE|MM MMMM MMMM|0 0000 0000 0000 0000|
  	 *      +-----+------------+---------------------+
  	 * Bits  27-31    17-26            0-16
  	 */
  	const uint32_t two_w = w + w;

  	/*
  	 * Shift mantissa and exponent into bits 23-28 and bits 13-22 so they become mantissa and exponent
  	 * of a single-precision floating-point number:
  	 *
  	 *       S|Exponent |          Mantissa
  	 *      +-+---+-----+------------+----------------+
  	 *      |0|000|EEEEE|MM MMMM MMMM|0 0000 0000 0000|
  	 *      +-+---+-----+------------+----------------+
  	 * Bits   | 23-31   |           0-22
  	 *
  	 * Next, there are some adjustments to the exponent:
  	 * - The exponent needs to be corrected by the difference in exponent bias between single-precision and half-precision
  	 *   formats (0x7F - 0xF = 0x70)
  	 * - Inf and NaN values in the inputs should become Inf and NaN values after conversion to the single-precision number.
  	 *   Therefore, if the biased exponent of the half-precision input was 0x1F (max possible value), the biased exponent
  	 *   of the single-precision output must be 0xFF (max possible value). We do this correction in two steps:
  	 *   - First, we adjust the exponent by (0xFF - 0x1F) = 0xE0 (see exp_offset below) rather than by 0x70 suggested
  	 *     by the difference in the exponent bias (see above).
  	 *   - Then we multiply the single-precision result of exponent adjustment by 2**(-112) to reverse the effect of
  	 *     exponent adjustment by 0xE0 less the necessary exponent adjustment by 0x70 due to difference in exponent bias.
  	 *     The floating-point multiplication hardware would ensure than Inf and NaN would retain their value on at least
  	 *     partially IEEE754-compliant implementations.
  	 *
  	 * Note that the above operations do not handle denormal inputs (where biased exponent == 0). However, they also do not
  	 * operate on denormal inputs, and do not produce denormal results.
  	 */
  	const uint32_t exp_offset = UINT32_C(0xE0) << 23;
    // const float exp_scale = 0x1.0p-112f;
    uint32_t scale_bits = (uint32_t) 15 << 23;
    float exp_scale_val;
    std::memcpy(&exp_scale_val, &scale_bits, sizeof(exp_scale_val));
    const float exp_scale = exp_scale_val;
    const float normalized_value = fp32_from_bits((two_w >> 4) + exp_offset) * exp_scale;

  	/*
  	 * Convert denormalized half-precision inputs into single-precision results (always normalized).
  	 * Zero inputs are also handled here.
  	 *
  	 * In a denormalized number the biased exponent is zero, and mantissa has on-zero bits.
  	 * First, we shift mantissa into bits 0-9 of the 32-bit word.
  	 *
  	 *                  zeros           |  mantissa
  	 *      +---------------------------+------------+
  	 *      |0000 0000 0000 0000 0000 00|MM MMMM MMMM|
  	 *      +---------------------------+------------+
  	 * Bits             10-31                0-9
  	 *
  	 * Now, remember that denormalized half-precision numbers are represented as:
  	 *    FP16 = mantissa * 2**(-24).
  	 * The trick is to construct a normalized single-precision number with the same mantissa and thehalf-precision input
  	 * and with an exponent which would scale the corresponding mantissa bits to 2**(-24).
  	 * A normalized single-precision floating-point number is represented as:
  	 *    FP32 = (1 + mantissa * 2**(-23)) * 2**(exponent - 127)
  	 * Therefore, when the biased exponent is 126, a unit change in the mantissa of the input denormalized half-precision
  	 * number causes a change of the constructud single-precision number by 2**(-24), i.e. the same ammount.
  	 *
  	 * The last step is to adjust the bias of the constructed single-precision number. When the input half-precision number
  	 * is zero, the constructed single-precision number has the value of
  	 *    FP32 = 1 * 2**(126 - 127) = 2**(-1) = 0.5
  	 * Therefore, we need to subtract 0.5 from the constructed single-precision number to get the numerical equivalent of
  	 * the input half-precision number.
  	 */
  	const uint32_t magic_mask = UINT32_C(126) << 23;
  	const float magic_bias = 0.5f;
  	const float denormalized_value = fp32_from_bits((two_w >> 17) | magic_mask) - magic_bias;

  	/*
  	 * - Choose either results of conversion of input as a normalized number, or as a denormalized number, depending on the
  	 *   input exponent. The variable two_w contains input exponent in bits 27-31, therefore if its smaller than 2**27, the
  	 *   input is either a denormal number, or zero.
  	 * - Combine the result of conversion of exponent and mantissa with the sign of the input number.
  	 */
  	const uint32_t denormalized_cutoff = UINT32_C(1) << 27;
  	const uint32_t result = sign |
  		(two_w < denormalized_cutoff ? fp32_to_bits(denormalized_value) : fp32_to_bits(normalized_value));
  	return fp32_from_bits(result);
  }

  /*
   * Convert a 32-bit floating-point number in IEEE single-precision format to a 16-bit floating-point number in
   * IEEE half-precision format, in bit representation.
   *
   * @note The implementation relies on IEEE-like (no assumption about rounding mode and no operations on denormals)
   * floating-point operations and bitcasts between integer and floating-point variables.
   */
  static inline uint16_t fp16_ieee_from_fp32_value(float f) {
    // const float scale_to_inf = 0x1.0p+112f;
    // const float scale_to_zero = 0x1.0p-110f;
    uint32_t scale_to_inf_bits = (uint32_t) 239 << 23;
    uint32_t scale_to_zero_bits = (uint32_t) 17 << 23;
    float scale_to_inf_val, scale_to_zero_val;
    std::memcpy(&scale_to_inf_val, &scale_to_inf_bits, sizeof(scale_to_inf_val));
    std::memcpy(&scale_to_zero_val, &scale_to_zero_bits, sizeof(scale_to_zero_val));
    const float scale_to_inf = scale_to_inf_val;
    const float scale_to_zero = scale_to_zero_val;

  	float base = (fabsf(f) * scale_to_inf) * scale_to_zero;

  	const uint32_t w = fp32_to_bits(f);
  	const uint32_t shl1_w = w + w;
  	const uint32_t sign = w & UINT32_C(0x80000000);
  	uint32_t bias = shl1_w & UINT32_C(0xFF000000);
  	if (bias < UINT32_C(0x71000000)) {
  		bias = UINT32_C(0x71000000);
  	}

  	base = fp32_from_bits((bias >> 1) + UINT32_C(0x07800000)) + base;
  	const uint32_t bits = fp32_to_bits(base);
  	const uint32_t exp_bits = (bits >> 13) & UINT32_C(0x00007C00);
  	const uint32_t mantissa_bits = bits & UINT32_C(0x00000FFF);
  	const uint32_t nonsign = exp_bits + mantissa_bits;
  	return (sign >> 16) | (shl1_w > UINT32_C(0xFF000000) ? UINT16_C(0x7E00) : nonsign);
  }

} // namespace detail

struct alignas(2) Half {
  unsigned short x;

  struct from_bits_t {};
  static constexpr from_bits_t from_bits = from_bits_t();

  // HIP wants __host__ __device__ tag, CUDA does not
#ifdef __HIP_PLATFORM_HCC__
  C10_HOST_DEVICE Half() = default;
#else
  Half() = default;
#endif

  constexpr C10_HOST_DEVICE Half(unsigned short bits, from_bits_t) : x(bits){};
  inline C10_HOST_DEVICE Half(float value);
  inline C10_HOST_DEVICE operator float() const;

#if defined(__CUDACC__) || defined(__HIPCC__)
  inline C10_HOST_DEVICE Half(const __half& value);
  inline C10_HOST_DEVICE operator __half() const;
#endif
};

// This is just a placeholder for whatever complex representation we
// end up deciding to use for half-precision complex numbers.
struct alignas(4) ComplexHalf {
  Half real_;
  Half imag_;
  ComplexHalf() = default;
  Half real() const {
    return real_;
  }
  Half imag() const {
    return imag_;
  }
  inline ComplexHalf(std::complex<float> value)
      : real_(value.real()), imag_(value.imag()) {}
  inline operator std::complex<float>() const {
    return {real_, imag_};
  }
};

template <typename T>
struct is_complex_t : public std::false_type {};

template <typename T>
struct is_complex_t<std::complex<T>> : public std::true_type {};

template <>
struct is_complex_t<ComplexHalf> : public std::true_type {};

// Extract double from std::complex<double>; is identity otherwise
// TODO: Write in more idiomatic C++17
template <typename T>
struct scalar_value_type {
  using type = T;
};
template <typename T>
struct scalar_value_type<std::complex<T>> {
  using type = T;
};
template <>
struct scalar_value_type<ComplexHalf> {
  using type = Half;
};

// The old implementation of Converter as a function made nvcc's head explode
// when we added std::complex on top of the specializations for CUDA-only types
// like __half, so I rewrote it as a templated class (so, no more overloads,
// just (partial) specialization).

template <typename To, typename From, typename Enable = void>
struct Converter {
  To operator()(From f) {
    return static_cast<To>(f);
  }
};

template <typename To, typename From>
To convert(From from) {
  return Converter<To, From>()(from);
}

template <typename To, typename FromV>
struct Converter<
    To,
    std::complex<FromV>,
    typename std::enable_if<
        c10::guts::negation<is_complex_t<To>>::value>::type> {
  To operator()(std::complex<FromV> f) {
    return static_cast<To>(f.real());
  }
};

// skip isnan and isinf check for integral types
template <typename To, typename From>
typename std::enable_if<std::is_integral<From>::value, bool>::type overflows(
    From f) {
  using limit = std::numeric_limits<typename scalar_value_type<To>::type>;
  if (!limit::is_signed && std::numeric_limits<From>::is_signed) {
    // allow for negative numbers to wrap using two's complement arithmetic.
    // For example, with uint8, this allows for `a - b` to be treated as
    // `a + 255 * b`.
    return f > limit::max() ||
        (f < 0 && -static_cast<uint64_t>(f) > limit::max());
  } else {
    return f < limit::lowest() || f > limit::max();
  }
}

template <typename To, typename From>
typename std::enable_if<std::is_floating_point<From>::value, bool>::type
overflows(From f) {
  using limit = std::numeric_limits<typename scalar_value_type<To>::type>;
  if (limit::has_infinity && std::isinf(static_cast<double>(f))) {
    return false;
  }
  if (!limit::has_quiet_NaN && (f != f)) {
    return true;
  }
  return f < limit::lowest() || f > limit::max();
}

template <typename To, typename From>
typename std::enable_if<is_complex_t<From>::value, bool>::type overflows(
    From f) {
  // casts from complex to real are considered to overflow if the
  // imaginary component is non-zero
  if (!is_complex_t<To>::value && f.imag() != 0) {
    return true;
  }
  // Check for overflow componentwise
  // (Technically, the imag overflow check is guaranteed to be false
  // when !is_complex_t<To>, but any optimizer worth its salt will be
  // able to figure it out.)
  return overflows<
             typename scalar_value_type<To>::type,
             typename From::value_type>(f.real()) ||
      overflows<
             typename scalar_value_type<To>::type,
             typename From::value_type>(f.imag());
}

template <typename To, typename From>
To checked_convert(From f, const char* name) {
  if (overflows<To, From>(f)) {
    std::ostringstream oss;
    oss << "value cannot be converted to type " << name
        << " without overflow: " << f;
    throw std::domain_error(oss.str());
  }
  return convert<To, From>(f);
}

C10_API std::ostream& operator<<(std::ostream& out, const Half& value);

} // namespace c10

#include "c10/Half-inl.h"