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ML Floating-Point Formats in HDF5

Floating-point Flavors

IEEE FP16

#define FP16_BYTES  2
#define FP16_ORDER  H5T_ORDER_LE
#define FP16_PREC   16
#define FP16_OFFSET 0
#define FP16_SPOS   15
#define FP16_EPOS   10
#define FP16_ESIZE  5
#define FP16_EBIAS  15
#define FP16_MPOS   0
#define FP16_MSIZE  10
#define FP16_NORM   H5T_NORM_MSBSET
#define FP16_INPAD  H5T_PAD_ZERO
#define FP16_LSB    H5T_PAD_ZERO
#define FP16_MSB    H5T_PAD_ZERO

Google BFloat16

#define BFLOAT16_BYTES  2
#define BFLOAT16_ORDER  H5T_ORDER_LE
#define BFLOAT16_PREC   16
#define BFLOAT16_OFFSET 0
#define BFLOAT16_SPOS   15
#define BFLOAT16_EPOS   7
#define BFLOAT16_ESIZE  8
#define BFLOAT16_EBIAS  127
#define BFLOAT16_MPOS   0
#define BFLOAT16_MSIZE  7
#define BFLOAT16_NORM   H5T_NORM_MSBSET
#define BFLOAT16_INPAD  H5T_PAD_ZERO
#define BFLOAT16_LSB    H5T_PAD_ZERO
#define BFLOAT16_MSB    H5T_PAD_ZERO

NVIDIA TensorFloat

#define TF32_BYTES  3
#define TF32_ORDER  H5T_ORDER_LE
#define TF32_PREC   19
#define TF32_OFFSET 0
#define TF32_SPOS   18
#define TF32_EPOS   10
#define TF32_ESIZE  8
#define TF32_EBIAS  127
#define TF32_MPOS   0
#define TF32_MSIZE  10
#define TF32_NORM   H5T_NORM_MSBSET
#define TF32_INPAD  H5T_PAD_ZERO
#define TF32_LSB    H5T_PAD_ZERO
#define TF32_MSB    H5T_PAD_ZERO

Can we pack these closer together?

AMD FP24

#define FP24_BYTES  3
#define FP24_ORDER  H5T_ORDER_LE
#define FP24_PREC   24
#define FP24_OFFSET 0
#define FP24_SPOS   23
#define FP24_EPOS   16
#define FP24_ESIZE  7
#define FP24_EBIAS  63
#define FP24_MPOS   0
#define FP24_MSIZE  16
#define FP24_NORM   H5T_NORM_MSBSET
#define FP24_INPAD  H5T_PAD_ZERO
#define FP24_LSB    H5T_PAD_ZERO
#define FP24_MSB    H5T_PAD_ZERO

Consider n-bit filter?

HDF5 Datatype Definition

Custom HDF5 floating-point datatype

hid_t make_fp_datatype
(
 size_t      bytes,
 H5T_order_t byte_order,
 size_t      precision,
 size_t      offset,
 size_t      spos,
 size_t      epos,
 size_t      esize,
 size_t      ebias,
 size_t      mpos,
 size_t      msize,
 H5T_norm_t  norm,
 H5T_pad_t   inpad,
 H5T_pad_t   lsb,
 H5T_pad_t   msb
 )
{
  hid_t result = (byte_order == H5T_ORDER_LE) ?
    H5Tcopy(H5T_IEEE_F64LE) : H5Tcopy(H5T_IEEE_F64BE);
  assert(result >= 0);
  assert(H5Tset_size(result, bytes) >= 0);
  assert(H5Tset_precision(result, precision) >= 0);
  assert(H5Tset_offset(result, offset) >= 0);
  assert(H5Tset_fields(result, spos, epos, esize, mpos, msize) >= 0);
  assert(H5Tset_ebias(result, ebias) >= 0);
  assert(H5Tset_norm(result, norm) >= 0);
  assert(H5Tset_inpad(result, inpad) >= 0);
  assert(H5Tset_pad(result, lsb, msb) >= 0);

  return result;
}

hid_t make_fp16()
{
  return make_fp_datatype(FP16_BYTES, FP16_ORDER, FP16_PREC,
                          FP16_ORDER, FP16_SPOS, FP16_EPOS,
                          FP16_ESIZE, FP16_EBIAS, FP16_MPOS,
                          FP16_MSIZE, FP16_NORM, FP16_INPAD,
                          FP16_LSB, FP16_MSB);
}

hid_t make_bfloat16()
{
  return make_fp_datatype(BFLOAT16_BYTES, BFLOAT16_ORDER, BFLOAT16_PREC,
                          BFLOAT16_ORDER, BFLOAT16_SPOS, BFLOAT16_EPOS,
                          BFLOAT16_ESIZE, BFLOAT16_EBIAS, BFLOAT16_MPOS,
                          BFLOAT16_MSIZE, BFLOAT16_NORM, BFLOAT16_INPAD,
                          BFLOAT16_LSB, BFLOAT16_MSB);
}

hid_t make_tf32()
{
  return make_fp_datatype(TF32_BYTES, TF32_ORDER, TF32_PREC,
                          TF32_ORDER, TF32_SPOS, TF32_EPOS,
                          TF32_ESIZE, TF32_EBIAS, TF32_MPOS,
                          TF32_MSIZE, TF32_NORM, TF32_INPAD,
                          TF32_LSB, TF32_MSB);
}

hid_t make_fp24()
{
  return make_fp_datatype(FP24_BYTES, FP24_ORDER, FP24_PREC,
                          FP24_ORDER, FP24_SPOS, FP24_EPOS,
                          FP24_ESIZE, FP24_EBIAS, FP24_MPOS,
                          FP24_MSIZE, FP24_NORM, FP24_INPAD,
                          FP24_LSB, FP24_MSB);
}

Add more sanity checks

Library

#include "hdf5.h"

<<fp16>>
<<bfloat16>>
<<tf32>>
<<fp24>>

extern hid_t make_fp_datatype
(
 size_t      bytes,
 H5T_order_t byte_order,
 size_t      precision,
 size_t      offset,
 size_t      spos,
 size_t      epos,
 size_t      esize,
 size_t      ebias,
 size_t      mpos,
 size_t      msize,
 H5T_norm_t  norm,
 H5T_pad_t   inpad,
 H5T_pad_t   lsb,
 H5T_pad_t   msb
 );

extern hid_t make_fp16();
extern hid_t make_bfloat16();
extern hid_t make_tf32();
extern hid_t make_fp24();
#include "fmb.h"

<<fp-maker>>

Unit Testing

How we test all this?

Create a sample HDF5 file with datasets for each type

  • Create a 1024 element dataset with [FP_MIN, -511.0, …, 0.0, …, 510.0, FP_MAX]
  • Create a dataset where we check the mantissa range
  • Create a dataset where we check the exponent range
  • Create a dataset where we check the NaN behavior
  • Create a dataset where we check the rounding properties
  • …

Include the corresponding MIN and MAX values

Conversion

Find conversion libraries

Check the availability of conversions on devices

Other

  • NVIDIA GPU Direct storage access to PCIe attached devices
  • How do we do that w/ HDF5?
    • Pass the dataset/chunk addresses to the GPU
      • Make sure that the chunks have been allocated!

References