glsl: Query GL Device for FP16 extension support

src/video_core/renderer_opengl/gl_device.cpp

@@ -158,6 +158,8 @@ Device::Device() {
     has_vertex_buffer_unified_memory = GLAD_GL_NV_vertex_buffer_unified_memory;
     has_debugging_tool_attached = IsDebugToolAttached(extensions);
     has_depth_buffer_float = HasExtension(extensions, "GL_NV_depth_buffer_float");
+    has_nv_gpu_shader_5 = GLAD_GL_NV_gpu_shader5;
+    has_amd_shader_half_float = GLAD_GL_AMD_gpu_shader_half_float;
 
     // At the moment of writing this, only Nvidia's driver optimizes BufferSubData on exclusive
     // uniform buffers as "push constants"

src/video_core/renderer_opengl/gl_device.h

@@ -120,6 +120,14 @@ public:
         return has_depth_buffer_float;
     }
 
+    bool HasNvGpuShader5() const {
+        return has_nv_gpu_shader_5;
+    }
+
+    bool HasAmdShaderHalfFloat() const {
+        return has_amd_shader_half_float;
+    }
+
 private:
     static bool TestVariableAoffi();
     static bool TestPreciseBug();
@@ -151,6 +159,8 @@ private:
     bool use_asynchronous_shaders{};
     bool use_driver_cache{};
     bool has_depth_buffer_float{};
+    bool has_nv_gpu_shader_5{};
+    bool has_amd_shader_half_float{};
 };
 
 } // namespace OpenGL

src/video_core/renderer_opengl/gl_shader_cache.cpp

@@ -217,6 +217,8 @@ ShaderCache::ShaderCache(RasterizerOpenGL& rasterizer_, Core::Frontend::EmuWindo
           .support_demote_to_helper_invocation = false,
           .support_int64_atomics = false,
           .support_derivative_control = device.HasDerivativeControl(),
+          .support_gl_nv_gpu_shader_5 = device.HasNvGpuShader5(),
+          .support_gl_amd_gpu_shader_half_float = device.HasAmdShaderHalfFloat(),
 
           .warp_size_potentially_larger_than_guest = true,