This doesn't affect the result dtype at all, AFAICT

**= operates in-place, so should not result in a type promotion (edit: except on scalars, where it does not)

Edit: I'm wrong.

Thanks to #10374, np.reciprocal is unusable in generic code. You can use np.true_divide(1, ord, dtype=...) here instead

I think that there's a deeper problem here with numpy type promotion, and how scalar op= val gives a different promotion to arr op= val

Ah, I see.

x = np.ndarray(1, dtype=np.float32)
x **= 1.0 / 2.0
x.dtype  # => float32

x = np.float32(1)
x **= 1.0 / 2.0
x.dtype  # => float64

Thanks to #10374, np.reciprocal is unusable in generic code.

I think the code in this PR is generic (i.e., works with both scalar and array).
Do you mean such use of np.reciprocal is discouraged (even with dtype=ret.dtype)?

import numpy as np
print('scalar', np.linalg.norm(np.ones((2,), dtype=np.float32), 3, 0, False).dtype)
print('array', np.linalg.norm(np.ones((2,2), dtype=np.float32), 3, 0, False).dtype)

Output from NumPy 1.14.1:

scalar float64
array float32

Output from NumPy 1.14.1 + this PR:

scalar float32
array float32

Fix looks good, but this needs a test.