This is an old question, but I still see it discussed on message boards pretty often. Hopefully this post will serve as a resource to answer those message boards debates on the subject.
The answer? We do not actually know the answer, but 176GFLOPS is almost certain.
Why? Well, let's start with some clarification and definitions. "FLOPS" stands for "floating-point operations per second", so a 3GFLOP GPU means it can do in theory do up to 3 billion operations in a single second. How you calculate the theoretical 32-bit FLOPS a system can do is quite simple if you know some basic things about the GPU. All you need to do is take the total number of shaders (also known as stream processors or CUDA cores on Nivida GPUs) found in a GPU, multiply that by 2 (each core can do one one multiply operation and one accumulate operation per cycle), and then multiply that by the clock speed. So, using the stock Tegra X1 as an example with its 256 shader cores and base 1GHz clock speed...
256 * 2 * 1 billion = 512GFLOPS
Or with the Xbox One GPU with its 768 shaders at 853MHz....
768 * 2 * 853 million = 1.31TFLOPS
Simple enough, right? Where did the confusion come in? Well, the problem with the Wii U GPU is that we do not actually know the shader count for certain as Nintendo has never released any specs and the GPU has a number of custom elements. Based off die photos we know do know that it has either 320 or 160 shading units, but beyond that it requires some deductive reasoning. You see most AMD GPUs of the architecture used in the Wii U GPU, like the RV770 which the Wii U GPU was based on, had 20ALUs (shading units) per compute units which with the Wii U's 8CUs would result in 160ALUs, but a few high end GPUs had 40ALUs per CU which would have resulted in 320ALUs. Due to the custom nature of the Wii U's GPU it is not impossible that they could have doubled the shading unit count, but it would not have made much sense for them to and there is not anything to suggest they did, so it is deemed highly unlikely.
