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Sometimes software developers don t fully understand the semantics of the programming language they are using. These semantics can be critical because they define (among other things) how data is going to be handled at a low level. Type conversion errors take place when developers mishandle incoming data types and perform incorrect conversions on them. For example, consider the following variant on my famous allocate_object function:

allocate_object: 00401021 push 00401022 movsx 00401027 push 00401028 lea 0040102b push 0040102c call 00401031 pop 00401032 xor 00401034 cmp 00401036 jnz 00401038 xor 0040103a jmp 0040103c mov 0040103f mov esi esi,word ptr [esp+0xc] edi edi,[esi+0x18] edi 7!malloc (004010d9) ecx ecx,ecx eax,ecx 7!allocate_object+0x1b (0040103c) eax,eax 7!allocate_object+0x43 (00401064) [eax+0x4],ecx [eax+0x8],ecx

Table 17.3 Results from Monte Carlo simulation of vertical cut Results n 100 1,000 10,000 exact M 47.90 kPa 49.71 kPa 49.95 kPa 50.00 kPa M 30.05 kPa 28.03 kPa 27.66 kPa 27.84 kPa 1.594 1.773 1.806 1.796 pf 5.55 10 2 3.81 10 2 3.55 10 2 3.62 10 2

00401042 00401045 00401048 0040104b 0040104d 00401051 00401053 00401055 00401058 0040105b 0040105d 0040105f 00401062 00401064 00401065 00401066 mov mov mov mov mov mov mov shr lea rep mov and rep pop pop ret [eax+0xc],ecx [eax+0x10],ecx [eax+0x14],ecx ecx,esi esi,[esp+0xc] edx,ecx [eax],edi ecx,0x2 edi,[eax+0x18] movsd ecx,edx ecx,0x3 movsb edi esi

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The important thing about this version of allocate_object is the supplied buffer length s data type. When reading assembly language code, you must always be aware of every little detail that s exactly where all the valuable information is hidden. See if you can find the difference between this function and the earlier version. It turns out that this function is treating the buffer length as a signed short. This creates a potential problem because in C and C++ the compiler doesn t really care what you re doing with an integer as long as it s defined as signed and it s converted into a longer data type, it will be sign extended, no matter what the target data type is. In this particular example, malloc takes a size_t, which is of course unsigned. This means that the buffer length would be sign extended before it is passed into malloc and to the code that adds 0x18 to it. Here is what you should be looking for:

The previous section shows what might be called the brute-force Monte Carlo method A set of randomly distributed points is generated; they are used to compute a sample of values of the desired function or integral; and the statistical properties of the result are calculated from the sample As the examples show, obtaining satisfactory accuracy requires that a large number of random points be used Is there any way to reduce the computational burden or, equivalently, to increase the accuracy for the same number of points It turns out that this is indeed possible, and the techniques as usually described as variance reduction methods Variance reduction is something of a misnomer The techniques are actually methods of obtaining the same level of accuracy with fewer simulations.

Often regattas are sailed with several races over several days, which can be really hard, and it is not unusual to feel completely mentally drained. Try experimenting with the best way to relax and get this energy back: reading, watching TV, chatting to friends, going to the cinema. However if you cannot maintain concentration you need to refocus as soon as possible (see below).

00401022 movsx esi,word ptr [esp+0xc]

Rubinstein (1981) summarizes the goals and conditions as well as anybody: Variance reduction can be viewed as a means to use known information about the problem In fact, if nothing is known about the problem, variance reduction cannot be achieved At the other extreme, that is, complete knowledge, the variance is equal to zero and there is no need for simulation Variance reduction cannot be obtained from nothing; it is merely a way of not wasting information One way to gain this information is through a direct crude simulation process Results from this simulation can then be used to de ne variance reduction techniques that will re ne and improve the ef ciency of a second simulation Therefore the more that is known about the problem, the more effective the variance reduction techniques that can be employed.

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