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Notice that in the preceding sample SBB was used on a single operand. This means that SBB will essentially subtract EAX from itself, which of course is a mathematically meaningless operation if you disregard CF. Because CF is added to the second operand, the result will depend solely on the value of CF. If CF == 1, EAX will become 1. If CF == 0, EAX will become zero. It should be obvious that the value of EAX after the first NEG was irrelevant. It is immediately lost in the following SBB because it subtracts EAX from itself. This raises the question of why did the compiler even bother with the NEG instruction The Intel documentation states that beyond reversing the operand s sign, NEG will also set the value of CF based on the value of the operand. If the operand is zero when NEG is executed, CF will be set to zero. If the operand is

These equations can be extended for more than two variables. The marginal distribution is the distribution of a variable for all values of the other variables. For example, for two discrete variables, the marginal pmf of X is pX (x) = P [X = x] =

nonzero, CF will be set to one. It appears that some compilers like to use this additional functionality provided by NEG as a clever way to check whether an operand contains a zero or nonzero value. Let s quickly go over each step in this sequence:

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during the day and cools quickly at night. The sea is slower to heat and cool, and therefore remains a more constant temperature throughout the day. As we move up through the atmosphere, the air cools. We sail in the bottom layer of the weather, but it is important to know what is going on above us. It is very important to get a clear idea of what sort of day it is. This information should come from the forecast. Are things going to stay the same or change If they are going to change, then how quickly Will you need to keep adjusting the rig Or do you just need to get your head out of the boat and see what is going to happen If things are going to alter, then what telltale signs are there that they are going to change And how will you react Getting to a venue early can really help. On a training day try and predict what the weather is going to do. Write this down. Ask someone to get a variety of forecasts (not telling you) and write down what they think is going to happen. You can then compare notes at the end of the day. Some forecasts give you wind arrows, which are easy to follow, but it can be more useful to look at a chart. Here, lines (like contour lines on a map) join places of equal

Use NEG to check whether the source operand is zero or nonzero. The result is stored in CF. Use SBB to transfer the result from CF back to a usable register. Of course, because of the nature of SBB, a nonzero value in CF will become 1 rather than 1. Whether that s a problem or not depends on the nature of the high-level language. Some languages use 1 to denote True, while others use 1. Because the code in the sample came from a C/C++ compiler, which uses 1 to denote True, an additional NEG is required, except that this time NEG is actually employed for reversing the operand s sign. If the operand is 1, it will become 1. If it s zero it will of course remain zero.

pX,Y (x, yi )

The following is a pseudocode that will help clarify the steps described previously:

(A.26)

EAX = EAX & 0x00001000; if (EAX) CF = 1; else CF = 0; EAX = EAX (EAX + CF); EAX = -EAX;

Essentially, what this sequence does is check for a particular bit in EAX (0x00001000), and returns 1 if it is set or zero if it isn t. It is quite elegant in the sense that it is purely arithmetic there are no conditional branch instructions involved. Let s quickly translate this sequence back into a high-level C representation:

and, for two continuous variables, the marginal pdf is fX (x) = The marginal CDF is FX (x) P [X x] =

5

if (LocalVariable & 0x00001000) return TRUE; else return FALSE;

That s much more readable, isn t it Still, as reversers we re often forced to work with such less readable, unattractive code sequences as the one just dissected. Knowing and understanding these types of low-level tricks is very helpful because they are very frequently used in compiler-generated code. Let s take a look at another, slightly more involved, example of how highlevel logical constructs can be implemented using pure arithmetic:

(A.27)

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