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Modern GPUs do have a full set of integer instructions, they just don't run as fast as floating point instructions.

Depending on how well a problem maps to the massively parallel architecture of a GPU, this may not matter.

This is wrong. The rate of integer and logical instructions that can be run per clock is equal to or higher than floating point instructions. For example, AMD GPUs 5-way VLIW units can execute, per clock: 5 integer/logical op, or 5 single precision flop, or 1 double precision flop. Nvidia GT200 GPU streaming processors can execute, per (shader) clock: 1 integer/logical op, or 1 single precision flop, or 0.5 double precision flop.

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