0x05

0x05

[dec] [home] [inc]

[See this riddle on the book]

sub      rax,5
cmp      rax,4

See explanation

5 <= x <= 9

I had some trouble understanding this, so I cheated, and looked at Raptor's solution . I can't remember if I solved this back then, but probably not.

So, since I cheated, I'll try at least to provide some more information to beg your forgiveness.

This snippet allows checking if a number is in the range [5-9] using only one jump instruction. The jump instruction is not shown, but it can be either jbe or jna - they are equivalent and translate to the same opcode (76cb).

Geometry to the rescue

It is easier to understand this snippet if you figure out a geometrical axis x, and mark the two spots 5 and 9:

-----0----5---9------->

In order to check if x is between 5 and 9 you can either:

1. check if it is smaller or equal than 5, and jump out if so
2. check if it is greater or equal than 9, and jump out if so
3. at this point you know that it is in range, and continue

Or "shift left" our reference frame so that what was 5 is now the center (the 0) of the reference frame Graphically, we have shifted the x axis to the left by 5:

-----0----4----->
^    ^    ^
|    |    |
|    |    this was 9 before shifting
|    this was 5 before shifting
this was 0 before shifting

The shifting is done with sub. this instruction also sets RFLAGS accordingly.

Remember that sub and cmp are essentially the same instruction, except that cmp does not modify the destination operand. This also means that the rules to set RFLAGS are the same in both instructions. It is essential to understand how RFLAGS is affected in order to understand this riddle. To make it easier, let's write down what happens with two dummy operands a and b:

• if a < b, CF=1, SF=1, ZF=0 (other flags may change too, but they are not relevant to this discussion)
• if a == b, CF=0, SF=0, ZF=1
• if a > b, CF=0, SF=0, ZF=0

After executing the two instructions of this riddle, RFLAGS will be manipulated twice, and will look like the the following:

• if x < 5, CF=1, ZF=0, SF=1
• if 5 <= x < 8, CF=1, ZF=0, SF=1
• if x == 9, CF=0, ZF=1, SF=0
• if x > 9, CF=0, ZF=0, SF=0

As said initially, only jbe and jna can be used with this snippet. With jbe we check if The Jcc instructions can jump accordingly to these values. The documentation should be sufficient to know what to choose in each case. To jump when x is within the [5, 9] range you can use either jbe or jna, which as already seen, are in fact the same instruction.

[dec] [home] [inc]