Features:
- Support fp32, fp16, bf16, for dimension up to 32768.
- Implicitly pad with zeros if dimension is not a power of 2.
from fast_hadamard_transform import hadamard_transform
def hadamard_transform(x, scale=1.0):
"""
Arguments:
x: (..., dim)
scale: float. Multiply the output by this number.
Returns:
out: (..., dim)
Multiply each row of x by the Hadamard transform matrix.
Equivalent to F.linear(x, torch.tensor(scipy.linalg.hadamard(dim))) * scale.
If dim is not a power of 2, we implicitly pad x with zero so that dim is the next power of 2.
"""
Benchmarked on A100, for not too small batch size, compared to memcpy (torch.clone), which is a lower bound for the time taken as we'd need to read inputs from GPU memory and write output to GPU memory anyway.
| Data type | Dimension | Time taken vs memcpy |
|---|---|---|
| fp16/bf16 | <= 512 | 1.0x |
| 512 - 8192 | <= 1.2x | |
| 16384 | 1.3x | |
| 32768 | 1.8x | |
| fp32 | <= 8192 | 1.0x |
| 16384 | 1.1x | |
| 32768 | 1.2x |