tag:blogger.com,1999:blog-6264947694886887540.post4155433669180791319..comments2020-08-02T03:51:31.305-07:00Comments on Ken Shirriff's blog: Extracting ROM constants from the 8087 math coprocessor's dieKen Shirriffhttp://www.blogger.com/profile/08097301407311055124noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-6264947694886887540.post-92178406773063056382020-06-13T02:31:31.964-07:002020-06-13T02:31:31.964-07:00It's possible that the exponents are encoded i...It's possible that the exponents are encoded in the chip's microcode instructions, much like multiplication can be encoded in assembly instructions.<br /><br />For example, a compiler can turn:<br />mult a, 18<br /><br />into:<br />shl a, 1<br />mov a, b<br />shl a, 3<br />add a, b<br /><br />which is transforming a * 18 to (a * 16 + a * 2).<br /><br />Another possibility is that they found a way to "store" the values inside existing values. For example, if you have to store the data 0x42ABF170 and also the data 0xABF1, you can just re-use the first piece of data and hardcode in your algorithm to load it, shift left by 8, then shift right by 16.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6264947694886887540.post-53806349902947433622020-06-09T11:32:15.338-07:002020-06-09T11:32:15.338-07:00Hi Ken,
Thank you for such deep analyse – as alway...Hi Ken,<br />Thank you for such deep analyse – as always interesting. I am still amazed what you can do in reverse engineering. I was blown out when I first read about HP35 ROM optical disassembly by Petr Monta (http://www.pmonta.com/calculators/hp-35/).<br />Not to take any credit away it must have been similar reverse engineering techniques to yours used when 8080 chip was cloned by many and it might be interesting to compare the chips. If there is any interest I might try to get hold of MHB8080 produced in former Czechoslovakia (http://www.teslakatalog.cz/MHB8080A.html).<br />I appreciate you keep educating all of us, thank you.<br />KR<br />Pavel<br />Panehttps://www.blogger.com/profile/12120664044006188394noreply@blogger.comtag:blogger.com,1999:blog-6264947694886887540.post-84491072215752034562020-05-24T22:37:08.220-07:002020-05-24T22:37:08.220-07:00And I was proud of myself playing baby Ken S. with...And I was proud of myself playing baby Ken S. with my little power supply reverse engineering. This is just a whole other level. Congrats Master Ken.CuriousMarchttps://www.blogger.com/profile/00156668067084301696noreply@blogger.comtag:blogger.com,1999:blog-6264947694886887540.post-88125511244990940002020-05-19T22:39:53.429-07:002020-05-19T22:39:53.429-07:00Long time reader, first time poster here!
There s...Long time reader, first time poster here!<br /><br />There seem to be inverse pairs present, particularly<br /><br />log2(e) == log(e)/log(2)<br />ln(2) == log(2)/log(e)<br /><br />and<br /><br />ln(2)/3 == log(2)/log(e) * 1/3<br />3*log2(e) == log(e)/log(2) * 3<br /><br />The latter might appear to serve the same purpose as the former, but combining them, if x == 7, e^x = 2^(7*log2(e)) or 2^(3*log2(e)+3*log2(e)+log2(e)).<br /><br />Perhaps this pre-calculation of the log constants multiplied/divided by 3 preserves greater precision and/or reduces cycle time, as one can decompose such calculations into a sequence of additions/subtractions and binary shifts rather than more costly odd-numbered multiplications and divisions?<br /><br />Edit: Actually, to be exact these appear to be "nice numbers" to use the term mentioned in the Quinapalus page you linked to... and that would explain the absence of log2(3/2) as these serve a similar purpose.MartyMacGyverhttps://www.blogger.com/profile/18408169471010499741noreply@blogger.comtag:blogger.com,1999:blog-6264947694886887540.post-73583781832589147792020-05-19T22:28:23.312-07:002020-05-19T22:28:23.312-07:00This comment has been removed by the author.MartyMacGyverhttps://www.blogger.com/profile/18408169471010499741noreply@blogger.comtag:blogger.com,1999:blog-6264947694886887540.post-21256248032548174232020-05-18T17:25:29.144-07:002020-05-18T17:25:29.144-07:00Another interesting job.
It is impressive to know...Another interesting job.<br /><br />It is impressive to know that he is able to open and study all the secrets within the CI and that they are hardly found in books.<br /><br />It is a unique and impressive work that details with excellent clarity and helps with existing doubts.<br /><br />These circuits accompanied my adolescence and I always classified it as magic and I was always trying to understand how it was produced.<br /><br />Thank you one more time.Richardhttps://www.blogger.com/profile/16961829638621596618noreply@blogger.com