This version of reshape (taking a `dimensions` argument, which
effectively fuses in a transpose) seems only to be used in the JVP rule
for lax._reduce_prod (basically np.product), but its transpose rule was
totally busted and untested.
The implementation mechanism is to use a bit of dynamic context to model
the axis name environment at trace time, and for the environment to
track how an axis name maps to an axis size and the corresponding trace
(i.e. the JaxprTrace instance). With that information, we can lift
special primitives that take axis_name parameters into the trace as
needed without having a data dependence on the input.
Call XLA's sqrt instead of defining sqrt to be x**0.5. The two have different behaviors for infinite inputs.
Incorporate improvements to acos, sinh, cosh, asinh, and acosh that have previously been made to the versions in the XLA C++ client libraries.
Here are two desiderata for jax.numpy dtype promotion behavior:
1. follow what NumPy does
2. be invariant to `@jit`
The latter is much more important, so whenever the two are in tension we
prefer the latter. (Also we already can't do a perfect job following
what NumPy does, e.g. around its value-dependent dtype promotion logic.)
Issue #732 showed our code had a special behavior that essentially
handled a case of the former desideratum but also broke the latter. #732
also showed us (again) that our tests really should cover Python
scalars.
In summary, in this commit:
* revise jax.numpy dtype promotion behavior to be invariant to `@jit`
* add Python scalar types to lax_numpy tests
* simplify and update kron implementation to fix dtype issues
Shape.abstract_arrays will only accept dtypes, not scalar type objects.
Add long to the set of types known to abstract_arrays in Python 2.
Make api_test.py accepting of long values in shapes.
This is sufficient to compute first-order derivatives of a product reduction (although not second-order derivatives because there is no JVP for reduce-window-prod).
