I have an Intel i5-4690K based machine with an external AMD Radeon R7 370 card that runs the displays.  It is running Debian unstable with beignet 1.1.1 and kernel 4.4.4.[*]

It seems that beignet will not work unless DISPLAY is either not set or set to a display which is bring run by the Intel GPU.  For example, using clcc to query the devices from my X session running on the AMD GPU

https://github.com/twhitehead/clcc

$ clcc -l
DRM_IOCTL_I915_GEM_APERTURE failed: No such file or directory
Assuming 131072kB available aperture size.
May lead to reduced performance or incorrect rendering.
get chip id failed: -1 [22]
param: 4, val: 0
DRM_IOCTL_I915_GEM_APERTURE failed: No such file or directory
Assuming 131072kB available aperture size.
May lead to reduced performance or incorrect rendering.
get chip id failed: -1 [22]
param: 4, val: 0
beignet-opencl-icd: no supported GPU found, this is probably the wrong opencl-icd package for this hardware
(If you have multiple ICDs installed and OpenCL works, you can ignore this message)
DRM_IOCTL_I915_GEM_APERTURE failed: No such file or directory
Assuming 131072kB available aperture size.
May lead to reduced performance or incorrect rendering.
get chip id failed: -1 [22]
param: 4, val: 0
beignet-opencl-icd: no supported GPU found, this is probably the wrong opencl-icd package for this hardware
(If you have multiple ICDs installed and OpenCL works, you can ignore this message)
Platform 0: Clover
  Device 0: AMD PITCAIRN (DRM 2.43.0, LLVM 3.7.1)
      Type = [ GPU, Accelerator, Custom ]
      Maximum compute units = 20
      Maximum work item dimensions = 3
      Maximum work item sizes = [ 256, 256, 256 ]
      Maximum work group size = 256
      Image support = False
      Global memory size = 1073741824
      Local memory size = 32768
Platform 1: Intel Gen OCL Driver
DRM_IOCTL_I915_GEM_APERTURE failed: No such file or directory
Assuming 131072kB available aperture size.
May lead to reduced performance or incorrect rendering.
get chip id failed: -1 [22]
param: 4, val: 0
beignet-opencl-icd: no supported GPU found, this is probably the wrong opencl-icd package for this hardware
(If you have multiple ICDs installed and OpenCL works, you can ignore this message)
Unable to get number of devices for platform: Device not found

$ DISPLAY= clcc -l
Platform 0: Clover
  Device 0: AMD PITCAIRN (DRM 2.43.0, LLVM 3.7.1)
      Type = [ GPU, Accelerator, Custom ]
      Maximum compute units = 20
      Maximum work item dimensions = 3
      Maximum work item sizes = [ 256, 256, 256 ]
      Maximum work group size = 256
      Image support = False
      Global memory size = 1073741824
      Local memory size = 32768
Platform 1: Intel Gen OCL Driver
  Device 0: Intel(R) HD Graphics Haswell GT2 Desktop
      Type = [ GPU, Accelerator, Custom ]
      Maximum compute units = 20
      Maximum work item dimensions = 3
      Maximum work item sizes = [ 512, 512, 512 ]
      Maximum work group size = 512
      Image support = True
        Image2D maximum width = 8192
        Image2D maximum height = 8192
        Image3D maximum width = 8192
        Image3D maximum height = 8192
        Image3D maximum depth = 2048
      Global memory size = 2147483648
      Local memory size = 65536


Stracing clcc in both cases reveals the issue is that if DISPLAY is set then beignet jumps straight to trying to perform a bunch of DRM_IOCTRL_I915_* operations on the AMD GPU card /dev/dri/card1.  These fail causing it to spit out all the various error messages above.

I'll attach the straces too so you can see the difference.

Thanks!  -Tyson

[*] I believe the kernel version is 4.4.4, but I'm not 100% as uname is reporting 4.4.0.  I thing this is because Debian is eating the last release number.

[    0.000000] Linux version 4.4.0-1-amd64 (debian-kernel@lists.debian.org) (gcc version 5.3.1 20160224 (Debian 5.3.1-10) ) #1 SMP Debian 4.4.4-2 (2016-03-09)