bfloat16 support is still immature, but this PR adds some initial support.
Fixes#76, at least enough that we can declare it fixed and open specific issues for specific bfloat16 problems.
The main awkwardness that this change deals with is that classic NumPy doesn't understand bfloat16 promotion rules, so we must:
implement our own type promotion operators that understand bfloat16 types
wrap a number of the reference implementations in tests to temporarily cast to float32 for computation.
* Change scalar promotion rules to prefer array types over scalar types.
Currently JAX does not treat Python scalars specially during type promotion. This means that, for example:
`1. + np.array([...], np.float32)`
ends up as an array of type np.float64. The `1.` is promoted to a default type (here np.float64), and the type promotion of a np.float64 and an np.float32 is an np.float64. This is unlike classic NumPy, which treats scalars specially during type promotion, in particular, preferring the type of an array over the type of a scalar.
This change adds a notion of weak_type to JAX avals. During type promotion, we prefer non-weak types, i.e., the type of the array in the example above, ignoring the type of the scalar.
In contexts where a Python scalar is to be promoted to a NumPy value, a default type is used (e.g., `np.float_`). This change also makes it possible to use 32-bit default types that differ from NumPy's default types. The JAX test suite passes with 32-bit default types. However, we do not yet enable this change or expose it in the API.
* Move internal type-related functions into a new (internal) jax.types module.
Avoid calling onp type functions in lieu of the wrappers in jax.types. Currently these do the same thing, but future changes will make the behavior of the jax type functions diverge from the classic NumPy versions in some cases.
Move xla_bridge.canonicalize_dtype into jax.types, since it fits there more naturally.
* Rename jax.types to jax.dtypes.
* s/types/dtypes/ in tests.
* Add tests for float16 support in lax_test.py.
Make test tolerances per-type, rather than a single tolerance based on the x64 mode.
Don't test float16 on TPU because it doesn't support float16.
Rework a number of the gradient tests. For linear primitives, increase eps and use a per-type tol.
* Perform float16 sinh and cosh in float32 precision.
More tweaks to test tolerances to get tests to pass.
* Add float16 testing to lax_numpy_test.py as well.
* Fix tolerance computation for testReducer test.
Relax tolerance for polyval.
* Relax some test tolerances further.
* Further relax test tolerances.
* Another tolerance relaxation.
* Use decorator for the upcast to fp32 for computation pattern.
Relax test tolerance for float_power.
Fixes a bug where constants associated with relu gradients were being hoisted out of loops and materialized, causing a fairly large performance penalty (~20%) for a Resnet-50 model in a loop using infeed.
This change adds the following APIs:
* jax.devices(). This returns a list of available Device subclass instances.
* jax.host_id(). Currently always 0, but will be useful on multi-host platforms.
* jax.local_device_count(). Currently always equal to jax.device_count(), but
will be useful on multi-host platforms.
* Optional `devices` argument to pmap. This can be used to specify which devices
should be used in the replicated computation.
