Don't use an out-of-line lowering for integer_pow for small powers.

This yields a smaller stablehlo output.

Add a fast path for y == 1 and y == -1, which turn out to be reasonably common.

Author: hawkinsp

jax/_src/lax/lax.py

@@ -2633,24 +2633,24 @@ def _integer_pow(x, *, y):
 def _integer_pow_lowering(ctx, x, *, y):
   # These cases are subsumed by the general case, but it's faster to emit these
   # common cases directly.
-  if y == 2:
+  if y == 1:
+    out = x
+  elif y == 2:
     out = hlo.multiply(x, x)
   elif y == 3:
     out = hlo.multiply(hlo.multiply(x, x), x)
+  elif y == -1:
+    out = hlo.divide(mlir.full_like_aval(ctx, 1, ctx.avals_in[0]), x)
   else:
     lowering = mlir.lower_fun(_integer_pow, multiple_results=False)
-    # TODO(b/217551391): emitting an out-of-line call leads to a large
-    # expansion when the MLIR is lowered to HLO, because the HLO lowering
-    # clones the callee. Consider unconditionally caching when the MLIR->HLO
-    # lowering doesn't expand the program.
-    lowering = mlir.cache_lowering(lowering)
-    out = lowering(ctx, x, y=y)
+    if builtins.abs(y) >= 3:
+      lowering = mlir.cache_lowering(lowering)
+    out, = lowering(ctx, x, y=y)
   if config.sharding_in_types.value:
     aval_out, = ctx.avals_out
     proto = aval_out.sharding._to_xla_hlo_sharding(aval_out.ndim).to_proto()
-    out = out[0] if isinstance(out, list) else out
     return [mlir.wrap_with_sharding_op(ctx, out, aval_out, proto)]
-  return out if isinstance(out, list) else [out]
+  return [out]
 
 mlir.register_lowering(integer_pow_p, _integer_pow_lowering)