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As far as I understand the "branch-on-sign" is the name of some kind of if statement that does something depending on sign. I'm not sure that it's just if (x<0) then ... else ....

However, the name "branch-on-sign" seems to denote something very concrete. So, what is it? Perhaps, it's language-specific, but I don't really know. Probably, it's related to embedded development.

+2  A: 

In assembler, it is an instruction which branches (jumps) if the result of the last arithmetic operation had a specific sign. So,

ADD A, B
JMI FOOBAR

would jump to location FOOBAR if the result of adding A and B was negative, for some hypothetical architecture.

anon