The performance gain from the 4870 over the 3870 was ~92% the increase in total ALU count was 2.5 fold (64 to 160). The performance gain from the 5870 over the 4870 was ~68% and the increase in ALU count was two fold (160 to 320). This can give point to measure theoretical performance of the next gen; my personal expectation is a gain of ~40-45% over the 5870 as a result of ALU count increasing from 320 to 480. The new chip's rumored size is 40nm @ ~395mm^2 compared to the 334mm^2 Cypress and the 535mm^2 Fermi.
But the HD 4870 usually proved to be at least twice faster than the HD 3870 and even faster than that in many situations with lots of eye candy due to the AA bug in the HD 3870 and its weak texturing performance. It was more like three times faster, also it's TMU were beefed up, the implementation of Hardware AA resolve and had a more efficient memory controller.
But since the HD 4870 was such a strong performer, that explain why the HD 5870 wasn't twice faster considering that the HD 5870 is about twice of everything compared to the HD 4870 theorically, because the HD 5870 shader processors are less efficient compared to the HD 4870 (Look at the Anandtech's HD 4550 vs 5450 review), means that a nice performance jump can be obtained with the HD 6870 if your information is correct, plus I think that a nice 10%-20% additional performance can be gained if all the optimizations used in the HD 4870 are implemented or improved in the HD 6870. One thing is certain, the chip will be bigger than Cypress if the 40nm process is used, and yet, will be smaller than Thermi.