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4.2.2

Evaluating minimal symbol offsets

Several primary instructions have an operand that is an offset between the current

value of the instruction pointer and some other part of the code. Generating the

optimal prefix sequence to create the instruction data value for one of these

instructions is more complicated. This is because two, or more, instructions with offset

operands can interlock so that the minimal prefix sequences for each instruction is

dependent on the prefixing sequences used for the others.

For example consider the interlocking jumps below which can be prefixed in two

distinct ways. The instructions

j and cj are respectively jump and conditional jump.

These are explained in more detail later. The sequence:

cj +16; j -257

can be coded as

pfix 1; cj 0; pfix 1; nfix 0; j 15

but this can be optimized to be

cj 15; nfix 15; j 1

which is the encoding for the sequence

cj +15; j -255

This is because when the two offsets are reduced, their prefixing sequences take 1

byte less so that the two interlocking jumps will still transfer control to the same

instructions as before. This compaction of non-optimal prefix sequences is difficult to

perform and a better method is to slowly build up the prefix sequences so that the

optimal solution is achieved. The following algorithm performs this.

Associate with each jump instruction or offset load an ‘estimate’ of the number

of bytes required to code it and initially set them all to 0.

Evaluate all jump and load offsets under the current assumptions of the size of

prefix sequences to the jumps and offset loads

For each jump or load offset set the number of bytes needed to the number in

the shortest sequence that will build up the current offset.†

If any change was made to the number of bytes required then go back to 2 oth-

erwise the code has reached a stable state.

The stable state that is achieved will be the optimal state.

Steps 2 and 3 can be combined so that the number of bytes required by each jump is

updated as the offset is calculated. This does mean that if an estimate is increased

then some previously calculated offsets may have been invalidated, but step 4 forces

another loop to be performed when those offsets can be corrected.

By initially setting the estimated size of offsets to zero, all jumps whose destination is

the next instruction are optimized out.

† Where the code being analyzed has alignment directives, then it is possible that this algorithm will not reach a stable state. One

solution to this, is to allow the algorithm to increase the instruction size but not allow it to reduce the size. This is achieved by

modifying stage 3 to choose the larger of: the currently calculated length, and the previously calculated length. This approach

does not always lead to minimal sized code, but it guarantees termination of the algorithm.

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