mxfp_convert.hh

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#ifndef __ARCH_AMDGPU_COMMON_DTYPE_MXFP_CONVERT_HH__
#define __ARCH_AMDGPU_COMMON_DTYPE_MXFP_CONVERT_HH__
 
#include <cassert>
 
#include "arch/amdgpu/common/dtype/mxfp_type_info.hh"
#include "base/bitfield.hh"
 
namespace gem5
{
 
namespace AMDGPU
{
 
// The various rounding modes for microscaling formats. roundTiesToEven must
// be supported. Other rounding modes may be supported.
enum mxfpRoundingMode
{
    roundTiesToEven,
    roundStochastic
};
 
// Conversion functions - For instructions that convert from one microscaling
// format to another. We only need the conversion functions as there do not
// appear to be any instructions yet which operate directly on the MX formats.
//
// in - An MXFP info struct type
// mode - rounding mode
// seed - input value for stochastic rounding function
template<typename dFMT, typename sFMT>
dFMT convertMXFP(sFMT in, mxfpRoundingMode mode = roundTiesToEven,
                 uint32_t seed = 0)
{
    // We assume that *both* exponent and mantissa bits are both >= or <=
    // the target type. Checkable at compile time.
    //
    // This is not necessarily a limitation, others just are not implemented.
    // Figuring this out would be interesting for converting FP8 <-> BF8 for
    // example. So far all GPU conversion instructions convert explicitly to
    // a larger type from a smaller type or smaller to larger.
    static_assert(((int(sFMT::mbits) >= int(dFMT::mbits)) &&
                   (int(sFMT::ebits) >= int(dFMT::ebits)))
               || ((int(sFMT::mbits) <= int(dFMT::mbits)) &&
                   (int(sFMT::ebits) <= int(dFMT::ebits))));
 
    dFMT out;
    out.storage = 0;
 
    if (int(sFMT::mbits) >= int(dFMT::mbits) &&
        int(sFMT::ebits) >= int(dFMT::ebits)) {
        // Input format is larger, truncate and round mantissa. MX formats
        // are subnormal if exp == 0. Zero out exp in that case.
 
        if (std::isnan(in)) {
            // For types with no NaN return max value.
            if (std::numeric_limits<dFMT>::has_quiet_NaN) {
                out = std::numeric_limits<dFMT>::quiet_NaN();
                // Preserve sign bit
                if (in.storage & 0x80000000) {
                    out.storage |= 0x80000000;
                }
            } else {
                out = std::numeric_limits<dFMT>::max();
                // Preserve sign bit
                if (in.storage & 0x80000000) {
                    out.storage |= 0x80000000;
                }
            }
        } else if (std::isinf(in)) {
            // For types with no Inf return max value.
            if (std::numeric_limits<dFMT>::has_infinity) {
                out = std::numeric_limits<dFMT>::infinity();
                // Preserve sign bit
                if (in.storage & 0x80000000) {
                    out.storage |= 0x80000000;
                }
            } else {
                out = std::numeric_limits<dFMT>::max();
                // Preserve sign bit
                if (in.storage & 0x80000000) {
                    out.storage |= 0x80000000;
                }
            }
        } else if (in.mant == 0 && in.exp == 0) {
            // All MX formats FP32, and FP64 encode 0 as all zeros. Keep sign.
            out.mant = 0;
            out.exp  = 0;
            out.sign = in.sign;
        } else {
            // Extra bits are needed for the mantissa conversion.
            uint32_t mant = in.mant & mask(sFMT::mbits);
            int32_t exp   = in.exp - sFMT::bias + dFMT::bias;
            out.sign = in.sign;
 
            // Input is not subnormal, add the implicit 1 bit.
            if (in.exp) {
                mant |= (1 << sFMT::mbits);
            }
 
            // Save the value for rounding so we don't need to recompute it.
            uint32_t saved_mant = mant;
 
            mant >>= (sFMT::mbits - dFMT::mbits);
 
            // Output became subnormal
            if (exp < 1) {
                int shift = 1 - exp;
                mant >>= shift;
                out.exp = 0;
            } else {
                out.exp = exp;
            }
 
            mant &= mask(dFMT::mbits);
            out.mant = mant;
 
            // roundTiesToEven is the only required rounding mode for MXFP
            // types. Here we take the input mantissa and check the first
            // three bits that were shifted out. These are called guard,
            // round, and sticky bits. The value of these three bits combined
            // are used to determine if we should round up or down. If the
            // value is directly in between, we look at the final bit of the
            // output mantissa with guard, round, sticky shifted out. If the
            // value is one, round to nearest even by rounding down (set it to
            // zero).
            //
            // For denormals, the process is similar, but we shift the input
            // mantissa by 1 - exp more bits before setting the value of guard,
            // round, sticky. Note that for denormals exp < 1 (i.e., shift
            // value is always positive).
            //
            // If the number of destination and source format mantissa bits are
            // the same, the mantissa is unchanged.
            if (int(sFMT::mbits) > int(dFMT::mbits)
                    && mode == roundTiesToEven) {
                bool round_up = false;
 
                // Round using guard, round, sticky bits. We want to make sure
                // there are three bits remaining. This is currently true for
                // all conversion instructions. This would need to be revisited
                // if there are f4 <-> f6 or f6 <-> f8 conversions.
                assert((sFMT::mbits - dFMT::mbits) > 2);
 
                int check_shift = sFMT::mbits - dFMT::mbits - 3;
                uint32_t check_mant = saved_mant;
 
                // Sticky bit is 1 if *any* of the N-2 bits that get shifted
                // off are one. Being zero implies we are directly between two
                // floating point values.
                int sticky = (check_mant & mask(check_shift + 1)) != 0;
 
                check_mant >>= check_shift;
                if (exp < 1) {
                    int shift = 1 - exp;
                    check_mant >>= shift;
                }
 
                // Combine guard, round, sticky into one 3-bit value. If that
                // value is < 0b100 we round down (truncate -- nothing to do),
                // if it is > 0b100 we round up. If it is == 0b100, round to
                // nearest even.
                uint32_t check_test = check_mant & 0x7;
 
                // Add sticky to the 3-bit check value.
                check_test += sticky;
 
                if (check_test > 0x4) {
                    round_up = true;
                } else if (check_test == 0x4) {
                    // We are exactly between two FP values. Round to nearest
                    // even by looking at the last bit of output mantissa.
                    // If the last bit of the output mantissa is 1, round to
                    // nearest even (0 in last bit) which would simply be
                    // rounding down. The bit position of the last bit in this
                    // case is 0x8 since we kept three extra bits for guard,
                    // round, sticky.
                    if (check_mant & 0x8) {
                        out.mant -= 1;
                    }
                }
 
                if (round_up) {
                    if (out.mant == mask(dFMT::mbits)) {
                        // Mantissa at max value, increment exponent if not inf
                        if (out.exp != mask(dFMT::ebits)) {
                            out.exp++;
                        }
                        out.mant = 0;
                    } else {
                        out.mant++;
                    }
                }
            } else if (int(sFMT::mbits) > int(dFMT::mbits)
                    && mode == roundStochastic) {
                // Use the discarded mantissa divided by the max mantissa of
                // the source format to determine the probability of rounding
                // up. An alternate implementation of this would be to get a
                // random number and add that to the input mantissa. Then
                // follow the normal rounding path above.
                uint32_t discarded = in.mant & mask(sFMT::mbits - dFMT::mbits);
                uint32_t max_mant = mask(sFMT::mbits);
 
                float round_prob = float(discarded) / float(max_mant);
 
                // Use a stochastic rounding function with the seed value to
                // determine compare probability. This is implemented as a
                // "Galois LFSR."
                auto srFunc = [](uint32_t in) {
                    uint32_t bit = (in ^ (in >> 1) ^ (in >> 3) ^ (in >> 12));
                    return (in >> 1) | (bit << 15);
                };
 
                // Assume stochastic rounding returns up to max uint32_t.
                // This will return an FP value between 0.0f and 1.0f.
                float draw_prob = float(srFunc(seed))
                    / float(std::numeric_limits<uint32_t>::max());
 
                // Round up if the number we drew is less than the rounding
                // probability. E.g., if round_prob is 90% (0.9) we choose
                // values 0.0f - 0.90f to round up.
                if (round_prob >= draw_prob) {
                    if (out.mant == mask(dFMT::mbits)) {
                        // mantissa at max value, increment exponent if not inf
                        if (out.exp != mask(dFMT::ebits)) {
                            out.exp++;
                        }
                        out.mant = 0;
                    } else {
                        out.mant++;
                    }
                }
            }
        }
    } else if (int(sFMT::mbits) <= int(dFMT::mbits) &&
               int(sFMT::ebits) <= int(dFMT::ebits)) {
        // Input format is smaller. Extend mantissa / exponent and pad with 0.
        // Should be the same for all non-stochastic rounding modes.
 
        if (std::isnan(in)) {
            // For types with no NaN return max value.
            if (std::numeric_limits<dFMT>::has_quiet_NaN) {
                out = std::numeric_limits<dFMT>::quiet_NaN();
                // Preserve sign bit
                if (in.storage & 0x80000000) {
                    out.storage |= 0x80000000;
                }
            } else {
                out = std::numeric_limits<dFMT>::max();
                // Preserve sign bit
                if (in.storage & 0x80000000) {
                    out.storage |= 0x80000000;
                }
            }
        } else if (std::isinf(in)) {
            // For types with no Inf return max value.
            if (std::numeric_limits<dFMT>::has_infinity) {
                out = std::numeric_limits<dFMT>::infinity();
                // Preserve sign bit
                if (in.storage & 0x80000000) {
                    out.storage |= 0x80000000;
                }
            } else {
                out = std::numeric_limits<dFMT>::max();
                // Preserve sign bit
                if (in.storage & 0x80000000) {
                    out.storage |= 0x80000000;
                }
            }
        } else if (in.mant == 0 && in.exp == 0) {
            // All MX formats FP32, and FP64 encode 0 as all zeros. Keep sign.
            out.mant = 0;
            out.exp  = 0;
            out.sign = in.sign;
        } else {
            out.mant = in.mant << (dFMT::mbits - sFMT::mbits);
            out.exp  = in.exp + dFMT::bias - sFMT::bias;
            out.sign = in.sign;
 
            // Normalize input denormals
            if (!in.exp && int(sFMT::ebits) != int(dFMT::ebits)) {
                uint32_t m = out.mant;
                if (m != 0) {
                    out.exp++;
                    while (!(m >> dFMT::mbits)) {
                        m <<= 1;
                        out.exp--;
                    }
                    out.mant = m & mask(dFMT::mbits);
                }
            } else if (!in.exp) {
                // Exponent is the same, but output is not denorm, so add
                // implicit 1. This is specific mainly to bf16 -> f32.
                uint32_t m = out.mant;
                m <<= 1;
                out.mant = m & mask(dFMT::mbits);
            }
        }
    } else {
        assert(false);
    }
 
    return out;
}
 
template<typename FMT>
int min_exp()
{
    return 0;
}
 
template<typename FMT>
int max_exp()
{
    return (1 << FMT::ebits) - 1;
}
 
 
} // namespace AMDGPU
 
} // namespace gem5
 
#endif // __ARCH_AMDGPU_COMMON_DTYPE_MXFP_CONVERT_HH__