Valid exponents and mantissas

exp_mant.md

Valid Data Types

Weight Bits: 2

Exponent Bits	Mantissa Bits
1	0

Weight Bits: 3

Exponent Bits	Mantissa Bits
1	1
2	0

Weight Bits: 4

Exponent Bits	Mantissa Bits
1	2
2	1
3	0

Weight Bits: 5

Exponent Bits	Mantissa Bits
1	3
2	2
3	1
4	0

Weight Bits: 6

Exponent Bits	Mantissa Bits
1	4
2	3
3	2
4	1
5	0

Weight Bits: 7

Exponent Bits	Mantissa Bits
1	5
2	4
3	3
4	2
5	1

Weight Bits: 8

Exponent Bits	Mantissa Bits
1	6
2	5
3	4
4	3
5	2

Weight Bits: 9

Exponent Bits	Mantissa Bits
1	7
2	6
3	5
4	4
5	3

Weight Bits: 10

Exponent Bits	Mantissa Bits
1	8
2	7
3	6
4	5
5	4

Weight Bits: 11

Exponent Bits	Mantissa Bits
1	9
2	8
3	7
4	6
5	5

Weight Bits: 12

Exponent Bits	Mantissa Bits
1	10
2	9
3	8
4	7
5	6

Weight Bits: 13

Exponent Bits	Mantissa Bits
1	11
2	10
3	9
4	8
5	7

Weight Bits: 14

Exponent Bits	Mantissa Bits
1	12
2	11
3	10
4	9
5	8

Weight Bits: 15

Exponent Bits	Mantissa Bits
1	13
2	12
3	11
4	10
5	9

Invalid Combinations

Exponent bits above 5 are invalid, because they result in negative bit shift, see this:

template <int EXPONENT, int MANTISSA>
__device__ __forceinline__ uint32_t MultScale(uint32_t PackedFP16Pair,
                                              half Scale) {
  constexpr int BIAS_OFFSET = (int(1) << (5 - 1)) - (int(1) << (EXPONENT - 1));
  constexpr int BIAS = int(1) << BIAS_OFFSET;
  //
  half* FP16_1 = reinterpret_cast<half*>(&PackedFP16Pair);
  half* FP16_2 = FP16_1 + 1;
  uint32_t output;
  half* output_half_ptr = reinterpret_cast<half*>(&output);
  output_half_ptr[0] =
      __hmul(__hmul(*FP16_1, __float2half(1.0f * BIAS)), Scale);
  output_half_ptr[1] =
      __hmul(__hmul(*FP16_2, __float2half(1.0f * BIAS)), Scale);
  return output;
}

Exponent Bits	Mantissa Bits
6	0
6	1
6	2
6	3
6	4
6	5
6	6
6	7
6	8
7	0
7	1
7	2
7	3
7	4
7	5
7	6
7	7
8	0
8	1
8	2
8	3
8	4
8	5
8	6
9	0
9	1
9	2
9	3
9	4
9	5
10	0
10	1
10	2
10	3
10	4
11	0
11	1
11	2
11	3
12	0
12	1
12	2
13	0
13	1
14	0