Hello,
while the official driver doesn't support old HD7900 series card under linux, I'm doing some test with one HD7990 and I found that the latest amdgpu-pro 17.50 driver can provide a working X11 driver and boinc-compatible OpenCL libraries.
Sadly, milkyway application refuse to crunch and exits with this log:

<core_client_version>7.8.4</core_client_version>
<![CDATA[
<message>
process got signal 11</message>
<stderr_txt>
<search_application> milkyway_separation 1.46 Linux x86_64 double OpenCL </search_application>
Reading preferences ended prematurely
BOINC GPU type suggests using OpenCL vendor 'Advanced Micro Devices, Inc.'
Error loading Lua script 'astronomy_parameters.txt': [string "number_parameters: 4..."]:1: '<name>' expected near '4'
Switching to Parameter File 'astronomy_parameters.txt'
<number_WUs> 5 </number_WUs>
<number_params_per_WU> 20 </number_params_per_WU>
Using AVX path
Error! Fail to load fglrx kernel module! Maybe you can switch to root user to load kernel module directly
Error! Fail to load fglrx kernel module! Maybe you can switch to root user to load kernel module directly
Error! Fail to load fglrx kernel module! Maybe you can switch to root user to load kernel module directly
Found 3 platforms
Platform 0 information:
Name: AMD Accelerated Parallel Processing
Version: OpenCL 2.1 AMD-APP (2527.3)
Vendor: Advanced Micro Devices, Inc.
Extensions: cl_khr_icd cl_amd_event_callback cl_amd_offline_devices
Profile: FULL_PROFILE
Platform 1 information:
Name: AMD Accelerated Parallel Processing
Version: OpenCL 2.0 AMD-APP (1800.11)
Vendor: Advanced Micro Devices, Inc.
Extensions: cl_khr_icd cl_amd_event_callback cl_amd_offline_devices
Profile: FULL_PROFILE
Platform 2 information:
Name: AMD Accelerated Parallel Processing
Version: OpenCL 2.0 AMD-APP (1800.11)
Vendor: Advanced Micro Devices, Inc.
Extensions: cl_khr_icd cl_amd_event_callback cl_amd_offline_devices
Profile: FULL_PROFILE
Using device 0 on platform 0
Found 2 CL devices
Device 'Hainan' (Advanced Micro Devices, Inc.:0x1002) (CL_DEVICE_TYPE_GPU)
Board: AMD Radeon HD 7900 Series
Driver version: 2527.3
Version: OpenCL 1.2 AMD-APP (2527.3)
Compute capability: 0.0
Max compute units: 5
Clock frequency: 950 Mhz
Global mem size: 3170762752
Local mem size: 32768
Max const buf size: 65536
Double extension: cl_khr_fp64
Error creating command queue (-6): CL_OUT_OF_HOST_MEMORY
Error getting device and context (-6): CL_OUT_OF_HOST_MEMORY
Failed to calculate likelihood
Using AVX path
Found 3 platforms
Platform 0 information:
Name: AMD Accelerated Parallel Processing
Version: OpenCL 2.1 AMD-APP (2527.3)
Vendor: Advanced Micro Devices, Inc.
Extensions: cl_khr_icd cl_amd_event_callback cl_amd_offline_devices
Profile: FULL_PROFILE
Platform 1 information:
Name: AMD Accelerated Parallel Processing
Version: OpenCL 2.0 AMD-APP (1800.11)
Vendor: Advanced Micro Devices, Inc.
Extensions: cl_khr_icd cl_amd_event_callback cl_amd_offline_devices
Profile: FULL_PROFILE
Platform 2 information:
Name: AMD Accelerated Parallel Processing
Version: OpenCL 2.0 AMD-APP (1800.11)
Vendor: Advanced Micro Devices, Inc.
Extensions: cl_khr_icd cl_amd_event_callback cl_amd_offline_devices
Profile: FULL_PROFILE
Using device 0 on platform 0
Found 2 CL devices
Device 'Hainan' (Advanced Micro Devices, Inc.:0x1002) (CL_DEVICE_TYPE_GPU)
Board: AMD Radeon HD 7900 Series
Driver version: 2527.3
Version: OpenCL 1.2 AMD-APP (2527.3)
Compute capability: 0.0
Max compute units: 5
Clock frequency: 950 Mhz
Global mem size: 3170762752
Local mem size: 32768
Max const buf size: 65536
Double extension: cl_khr_fp64

</stderr_txt>
]]>

Seems that milkyway application search for fglrx driver, but for newer card the future driver will be amdgpu or amdgpu-pro.

Thanks.

Update:
I've switched to 2nd generation of GCN cards, and it seems to work correctly even with some warnings:

<core_client_version>7.8.4</core_client_version>
<![CDATA[
<stderr_txt>
<search_application> milkyway_separation 1.46 Linux x86_64 double OpenCL </search_application>
Reading preferences ended prematurely
BOINC GPU type suggests using OpenCL vendor 'Advanced Micro Devices, Inc.'
Error loading Lua script 'astronomy_parameters.txt': [string "number_parameters: 4..."]:1: '<name>' expected near '4'
Switching to Parameter File 'astronomy_parameters.txt'
<number_WUs> 5 </number_WUs>
<number_params_per_WU> 20 </number_params_per_WU>
Using AVX path
Found 2 platforms
Platform 0 information:
Name: AMD Accelerated Parallel Processing
Version: OpenCL 2.1 AMD-APP (2527.3)
Vendor: Advanced Micro Devices, Inc.
Extensions: cl_khr_icd cl_amd_event_callback cl_amd_offline_devices
Profile: FULL_PROFILE
Platform 1 information:
Name: AMD Accelerated Parallel Processing
Version: OpenCL 2.1 AMD-APP (2527.3)
Vendor: Advanced Micro Devices, Inc.
Extensions: cl_khr_icd cl_amd_event_callback cl_amd_offline_devices
Profile: FULL_PROFILE
Using device 0 on platform 0
Found 1 CL device
Device 'Bonaire' (Advanced Micro Devices, Inc.:0x1002) (CL_DEVICE_TYPE_GPU)
Board: AMD Radeon R7 200 Series
Driver version: 2527.3
Version: OpenCL 1.2 AMD-APP (2527.3)
Compute capability: 0.0
Max compute units: 14
Clock frequency: 1000 Mhz
Global mem size: 2119696384
Local mem size: 32768
Max const buf size: 1591759667
Double extension: cl_khr_fp64
Build log:
--------------------------------------------------------------------------------
/tmp/OCL5752T3.cl:183:72: warning: unknown attribute 'max_constant_size' ignored
__constant real* _ap_consts __attribute__((max_constant_size(18 * sizeof(real)))),
^
/tmp/OCL5752T3.cl:185:62: warning: unknown attribute 'max_constant_size' ignored
__constant SC* sc __attribute__((max_constant_size(NSTREAM * sizeof(SC)))),
^
/tmp/OCL5752T3.cl:186:67: warning: unknown attribute 'max_constant_size' ignored
__constant real* sg_dx __attribute__((max_constant_size(256 * sizeof(real)))),
^
3 warnings generated.

--------------------------------------------------------------------------------
Estimated AMD GPU GFLOP/s: 140 SP GFLOP/s, 28 DP FLOP/s
Warning: Bizarrely low flops (28). Defaulting to 100
Using a target frequency of 60.0
Using a block size of 3584 with 14 blocks/chunk
Using clWaitForEvents() for polling (mode -1)
Range: { nu_steps = 320, mu_steps = 800, r_steps = 700 }
Iteration area: 560000
Chunk estimate: 11
Num chunks: 12
Chunk size: 50176
Added area: 42112
Effective area: 602112
Initial wait: 13 ms
Integration time: 85.490338 s. Average time per iteration = 267.157307 ms
Integral 0 time = 85.602002 s
Running likelihood with 84044 stars
Likelihood time = 0.867170 s
<background_integral> 0.000113895186054 </background_integral>
<stream_integral> 4.649345951854182 266.270544038968524 64.288018047107187 </stream_integral>
<background_likelihood> -3.391531412791383 </background_likelihood>
<stream_only_likelihood> -123.587044118632946 -3.936056474621145 -3.757556745837058 </stream_only_likelihood>
<search_likelihood> -2.973183683358055 </search_likelihood>

I'm using amdgpu-pro 17.50 driver with amd opencl libraries.