The above pattern detection scheme can be applied in two ways:

• If we look at a single branch instruction, we talk about local history.
• We can also look at the sequence of all taken/not taken events, regardless of which branch instruction caused them. This is called global history.

Implementing local history

To keep local history for different branches, we need a two-stage lookup: For some number of address bits a, keep a table of 2^a shift registers with b bits each. Each of these indexes a separate table of 2^b n-bit counters, bringing the total number of bits needed to 2^a × b  +  2^a+b × n.

This two-stage scheme and variations of it have been implemented in many designs, but not in MMIX. [Patt, Yeh]