The IEEE 32-bit float explorer that I wrote about previously, has now been extended from just float (e8m23) to include floating point support for a number of other representations, including additional CPU floating point types:
- 64-bit IEEE (double: e11m52),
- Intel “80-bit” (long double: e15m64),
- 128-bit IEEE (long double on ARM Linux: e15m122). This is also the GCC quadmath representation,
and GPU floating point types:
- e5m2
- e4m3
- fp16 (e5m10)
- bf16 (e8m7)
The CUDA API is used for floating point conversions of the GPU floating point types (if available), and a manual convertor has been implemented if CUDA is not available.
The Intel long double format is currently only supported when building on x64. This type is different from all the others, where normal values do not use an implicit leading mantissa bit.
I have not implemented mainframe HEXFLOAT support.
Here is some sample output:
type: bf16 value: 3 hex: 4040 bits: 0100000001000000 sign: 0 exponent: 10000000 (127 +1) mantissa: 1000000 number: 1.1000000 x 2^(1) type: fp16 value: 3 hex: 4200 bits: 0100001000000000 sign: 0 exponent: 10000 (15 +1) mantissa: 1000000000 number: 1.1000000000 x 2^(1) type: e4m3 value: 3 hex: 44 bits: 01000100 sign: 0 exponent: 1000 (7 +1) mantissa: 100 number: 1.100 x 2^(1) type: e5m2 value: 3 hex: 42 bits: 01000010 sign: 0 exponent: 10000 (15 +1) mantissa: 10 number: 1.10 x 2^(1) type: float value: 3 hex: 40400000 bits: 01000000010000000000000000000000 sign: 0 exponent: 10000000 (127 +1) mantissa: 10000000000000000000000 number: 1.10000000000000000000000 x 2^(1) type: double value: 3 hex: 4008000000000000 bits: 0100000000001000000000000000000000000000000000000000000000000000 sign: 0 exponent: 10000000000 (1023 +1) mantissa: 1000000000000000000000000000000000000000000000000000 number: 1.1000000000000000000000000000000000000000000000000000 x 2^(1) type: long double value: 3 hex: 4000C000000000000000 bits: 01000000000000001100000000000000000000000000000000000000000000000000000000000000 sign: 0 exponent: 100000000000000 (16383 +1) mantissa: 1100000000000000000000000000000000000000000000000000000000000000 number: 0.1100000000000000000000000000000000000000000000000000000000000000 x 2^(2) type: float128 value: 3.000000 hex: 40008000000000000000000000000000 bits: 01000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 sign: 0 exponent: 100000000000000 (16383 +1) mantissa: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 number: 1.1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 x 2^(1)