I have this question because I cant find official information from Google, Mozilla or Microsoft. I just found 2014 dated entries. I would like that kind of efficiency on the browser.
To the moderator: Please keep this question while as its answer evolve with time.
The latest Version of the spec is (in June 2016) still in "draft"-status: https://www.khronos.org/registry/webcl/specs/latest/1.0/
No browser vendor seems to have implemented it or even having concrete plans to implement it at the moment.
For performance-intensive calculations WebAssembly is currently probably the better horse to place a bet on: http://webassembly.github.io/