Default matrix-multiplication precision on TPUs

[shoyer]

Currently, matrix multiplication on TPUs (with float32 dtypes) defaults to bfloat16 multiplication with float32 accumulation. This allows for really fantastic performance for neural nets.

Using higher precision requires explicitly setting it, e.g., jax.numpy.matmul(x, y, precision=jax.lax.Precision.HIGHEST). (We could conceivably shorten this by supporting strings, e.g., jax.numpy.matmul(x, y, precision='highest'))

Is this the right default behavior for functions like jax.numpy.matmul and the @ matmul operator? Or should we switch precision to default to full float32 precision, at the price of extra matrix-multiplication passes? This would probably be a little more annoying for neural network users, but it is arguably less surprising, especially for users who are using matrix-multiplication for other uses.

[shoyer]

Closing this in favor of #2161 (apparently I'm bad at remembering that I already opened an issue on something!)

[patrickvonplaten]

Note that the precision can also be globally set with JAX_DEFAULT_MATMUL_PRECISION as explained here