Hi Ho! On Fri, 2009-03-27 at 13:49 +0100, Paolo Bonzini wrote: > Eus wrote: > > Hi Ho! > > > > On Fri, 2009-03-06 at 15:29 +0100, Paolo Bonzini wrote: > >>> So while trapping variants can certainly be introduced it looks like > >>> this task may be more difficult. > >> I don't think you need to introduce trapping tree codes. You can > >> introduce them directly in the front-end as > >> > >> s = x +nv y > >> (((s ^ x) & (s ^ y)) < 0) ? trap () : s > > > > Could you please kindly explain a bit about it? > > > > Suppose s, x, and y are 8-bit signed integer. > > If x and y are -128, s = (-128) + (-128), which will overflow. > > Now if suppose s is 0, ((0 ^ -128) & (0 ^ -128)) == -128, which is less > > than zero and will trap. This is correct. > > But, if s is -128, ((-128 ^ -128) & (-128 ^ -128)) is zero and will not > > trap. This is incorrect, isn't this? > > Don't look at it as an arithmetic test, "< 0" is just a shortcut for > "the most significant bit of the first operand is 1". So the formula's > outcome only depends on the ANDs and XORs of the sign bits; it means, > "trap if the result's sign is different from both addends' signs" or > equivalently "check that the result's sign matches at least one addend's > sign".
Ah, I got it now! :-) Yes, so after I perform the addition, I check for the signs. It was my mistake to think that the check was done without performing the addition first. I mean, `s = x +nv y' == `(((s ^ x) & (s ^ y)) < 0) ? trap () : s'. But, they should be performed one after another: 1) s = x +nv y 2) (((s ^ x) & (s ^ y)) < 0) ? trap () : s > You can also say "((s ^ x) & ~(x ^ y)) < 0", or equivalently "((s ^ y) & > ~(x ^ y)) < 0". These mean "trap if the two addends have the same sign > and the sum has a different sign". It is easy to prove that they are > equivalent: > > s x y s^x s^y ~(x^y) equal? > 0 0 0 0 0 1 yes (0) > 0 0 1 0 1 0 yes (0) > 0 1 0 1 0 0 yes (0) > 0 1 1 1 1 1 yes (1) > 1 0 0 1 1 1 yes (1) > 1 0 1 1 0 0 yes (0) > 1 1 0 0 1 0 yes (0) > 1 1 1 0 0 1 yes (0) Yes, I really understand it now :-) Thank you very much for your kind explanation. I really appreciate it. > Paolo -- Best regards, Eus (FSF member #4445) In this digital era, where computing technology is pervasive, your freedom depends on the software controlling those computing devices. Join free software movement today! It is free as in freedom, not as in free beer! Join: http://www.fsf.org/jf?referrer=4445
