Consideration of multipass algorithms brings up the issue of how what is drawn in the framebuffer is or is not affected by changing parameter values. If, for instance, changing the viewpoint affected the way in which colors were assigned to primitives, the accumulation buffer algorithm would not work. For a more plausible example, if some OpenGL feature is not available in hardware, then an OpenGL implementation must switch from hardware to software when that feature is switched on. Such a switch may significantly affect what eventually reaches the framebuffer because of slight differences in the hardware and software implementations.
The OpenGL specification is not pixel exact; it does not indicate the exact values to which certain pixels must be set given a certain input. The reason is that such specification, besides being difficult, would be too restrictive. Different implementations of OpenGL run on different hardware with different floating-point formats, rasterization algorithms, and framebuffer configurations. It should be possible, nonetheless, to implement a variety of multipass algorithms and expect to get reasonable results.
For this reason, the OpenGL specification gives certain invariance rules that dictate under what circumstances one may expect identical results from one particular implementation given certain inputs (implementations on different systems are never required to produce identical results given identical inputs). These rules typically indicate that changing parameters that control an operation cannot affect the results due to any other operation, but that such invariance is not required when an operation is turned on or off. This makes it possible for an implementation to switch from hardware to software when a mode is invoked without breaking invariance. On the other hand, a programmer may still want invariance even when toggling some mode. To accommodate this case, any operation covered by the invariance rules admits a setting of its controlling parameters that cause the operation to act as if it were turned off even when it is on. A comparison, for instance, may be turned on or off, but when on, the comparison that is performed can be set to always (or never) pass.