I am gonna laugh really hard if AMD actually beats these specs.
HD5870 is about 0.54 Tflops in DP. GTX580 is 0.79 Tflops in DP. If 6970 is only 40%+ faster, you are looking at 0.8 Tflops in DP already. However, this card has additional DP improvements so getting above 0.8 Tflops is not out of the question. Therefore, HD6990 @ 1.5Tflops is easily doable.
Those stats would be impressive if true. For comparison 6 TFLOPS is roughly 3 times as much as the 6870, or 4 times as much as the 6850.
HD5870's Single Precision performance increased by
2.3x over the HD4870. So I don't really see how 2x Cayman chips will have less than 6 TFlops in single-precision? That's not impressive -- it's more like a
minimum expectation imo! Expect a single HD6970 to
easily break
3 Tflops in SP.
Also comparing HD6870/50 series doesn't make any sense. 68xx series lack DP/FP64 support and is therefore worthless for GPGPU computing market like HD57xx series is (which is expected for a mid-range AMD product). This is another major reason the die sizes for HD68xx series were much smaller as well. They were never meant to be fully-fledged compute cards like the HD5870 is.
HD6900 series will have double precision 1/4 of its Single precision rate. This is already a 25% improvement from 1/5 of SP for HD5800 series without any increases in specs.