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Stable air refers to the amount of mixing. How shifty a breeze is will also be determined by the amount of high landmass it has passed over. Big thick, cumulus clouds are a sure sign of air instability. Big white clouds suck up wind. Avoid them at all costs; try and stay under the patches of blue sky! Head for dark clouds which are dropping wind and rain, but do not sail directly under them as you get lifted around the outside of the cloud. The clouds drop wind and rain when their height is greater than the height they are above the land/sea. In the northern hemisphere we get several types of breezes. North-easterly breezes are wet and cold and (no surprise) they tend to come in the winter (Brrrrrrr!). In the summer we get a south-westerly wind that changes as different fronts move across. On the south coast, especially in the south west of England, the north east wind will have come over lots of land so will be especially shifty, whereas the south west wind has not passed over much land and is therefore not as shifty. Remember, no one can get the weather forecast right all the time, and even with accurate observation the weather can be very unpredictable and may change very quickly!

With fixed-point arithmetic, the exponent component (which is the position of the decimal dot in floating-point data types) is not used, and the position of the decimal dot remains fixed This is in contrast to hardware floating-point mechanisms in which the hardware is responsible for allocating the available bits between the integral value and the fractional value Because of this mechanism floatingpoint data types can represent a huge range of values, from extremely small (between 0 and 1) to extremely large (with dozens of zeros before the decimal point) To represent an approximation of a real number in an integer, you define an imaginary dot within our integer that defines which portion of it represents the number s integral value and which portion represents the fractional value The integral value is represented as a regular integer, using the number of bits available to it based on our division.

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Many applications of functions of random variables involve integrating the probability density functions. The most common examples are calculations of the moments of a joint probability distribution. From calculus we know that, if there is a set of variables xi that can be expressed in terms of another set yi and we want to integrate some function g(xi ), it may be more convenient to express the integral in terms of the yi variables. However, it is then necessary to transform the dxi into the dyi , and this requires using the Jacobian determinant. The equation for two variables in each set is g(xi , x2 ) dx1 dx2 = The Jacobian determinant is x1 (x1 , x2 ) y1 = x2 (y1 , y2 ) y1 x1 y2 x2 y2 g[x1 (y1 , y2 ), x2 (y1 , y2 )] (x1 , x2 ) dy1 dy2 (y1 , y2 ) (A.50)

The fractional value represents an approximation of the number s distance from the current integral value (for example, 1) to the next one up (to follow this example, 2), as accurately as possible with the available number of bits Needless to say, this is always an approximation many real numbers can never be accurately represented For example, in order to represent 5, the fractional value would contain 0x80000000 (assuming a 32-bit fractional value) To represent 1, the fractional value would contain 0x20000000 To go back to the original problem, in order to multiply a 32-bit dividend by an integer reciprocal the compiler multiplies the dividend by a 32-bit reciprocal This produces a 64-bit result The lower 32 bits contain the remainder (also represented as a fractional value) and the upper 32 bits actually contain the desired result Table B1 presents several examples of 32-bit reciprocals used by compilers.

Every reciprocal is used together with a divisor which is always a powers of two (essentially a right shift, we re trying to avoid actual division here) Compilers combine right shifts with the reciprocals in order to achieve greater accuracy because reciprocals are not accurate enough when working with large dividends..

(A.51)

In order to avoid having to access the RAM for every single instruction, microprocessors use internal memory that can be accessed with little or no performance penalty There are several different elements of internal memory inside the average microprocessor, but the one of interest at the moment is the register Registers are small chunks of internal memory that reside within the processor and can be accessed very easily, typically with no performance penalty whatsoever The downside with registers is that there are usually very few of them For instance, current implementations of IA-32 processors only have eight 32-bit registers that are truly generic There are quite a few others, but they re mostly there for specific purposes and can t always be used Assembly language code revolves around registers because they are the easiest way for the processor to manage and access immediate data.

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