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hc_textsplittextone.html takes the element defined as <strong>Roger Jones</strong> and splits it at position 7. The above is parsed as "Roger Jones" or "Roger\nJones", so splitting at position 7 leaves "ones" as the second item instead of the expected "Jones". I guess the test says 7 because IE stores it with \r\n? I think it should be 6, or maybe the test needs to be changed to split a node whose text doesn't have a newline in it (I'm no parsing expert :).
Ah, hc_textwithnomarkup explained the reason for the off-by-one. The expected value is "Roger\n Jones". However whitespace is usually not kept when parsing HTML, is it? If "Roger Jones" is a valid parsing of that tag, then the tests need to be more flexible about this. Text splitting is properly working in KHTML, it's only that the parsing difference leads to off by ones in the results...
After discussion with other KHTML developers, I have been told that this is really a KHTML bug, we should preserve whitespace in the DOM tree. We'll try to do that shortly, once 3.2 is out. Apologies.