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We can compute the intersection of two bitmaps easily by using a for loop: the ith iteration of the loop computes the and of the ith bits of the two bitmaps We can speed up computation of the intersection greatly by using bit-wise and instructions supported by most computer instruction sets A word usually consists of 32 or 64 bits, depending on the architecture of the computer A bit-wise and instruction takes two words as input and outputs a word where each bit is the logical and of the bits in corresponding positions of the input words What is important to note is that a single bit-wise and instruction can compute the intersection of 32 or 64 bits at once If a relation had 1 million records, each bitmap would contain 1 million bits, or equivalently 128 Kbytes Only 31,250 instructions are needed to compute the intersection of two bitmaps for our relation, assuming a 32-bit word length Thus, computing bitmap intersections is an extremely fast operation Just like bitmap intersection is useful for computing the and of two conditions, bitmap union is useful for computing the or of two conditions The procedure for bitmap union is exactly the same as for intersection, except we use bit-wise or instructions instead of bit-wise and instructions The complement operation can be used to compute a predicate involving the negation of a condition, such as not (income-level = L1) The complement of a bitmap is generated by complementing every bit of the bitmap (the complement of 1 is 0 and the complement of 0 is 1) It may appear that not (income-level = L1) can be implemented by just computing the complement of the bitmap for income level L1 If some records have been deleted, however, just computing the complement of a bitmap is not suf cient Bits corresponding to such records would be 0 in the original bitmap, but would become 1 in the complement, although the records don t exist A similar problem also arises when the value of an attribute is null For instance, if the value of income-level is null, the bit would be 0 in the original bitmap for value L1, and 1 in the complement bitmap To make sure that the bits corresponding to deleted records are set to 0 in the result, the complement bitmap must be intersected with the existence bitmap to turn off the bits for deleted records Similarly, to handle null values, the complement bitmap must also be intersected with the complement of the bitmap for the value null1 Counting the number of bits that are 1 in a bitmap can be done fast by a clever technique We can maintain an array with 256 entries, where the ith entry stores the.

Layer 3/4 policy maps associate one or more policies to traffic that matches a match command in a layer 3/4 class map When more than one policy is associated with the class map, the policies are enforced in the order listed next: 1 Connection limits, connection timeouts, and TCP sequence number randomization 2 CSC card 3 Stateful and application inspection 4 IPS card 5 Input policing 6 Output policing 7 Priority queuing The following sections will discuss how to create layer 3/4 policy maps and how to associate policies with layer 3/4 class maps

1 Handling predicates such as is unknown would cause further complications, which would in general require use of an extra bitmap to to track which operation results are unknown

Creating a layer 3/4 policy map is done with the policy-map command:

The McGraw Hill Companies, 2001

ciscoasa(config)# policy-map policy_map_name ciscoasa(config-pmap)# class class_map_name ciscoasa(config-pmap-c)#

Summary

The policy-map command takes you into a subcommand mode where you reference your layer-3/4 class map name or names with the class command When referencing a class map, you are taken into a second subcommand mode In this second mode, you reference the actual policies for the class of traffic Note that you can specify more than one policy for a class of traffic The following sections will discuss how to set up the specific policies

number of bits that are 1 in the binary representation of i Set the total count initially to 0 We take each byte of the bitmap, use it to index into this array, and add the stored count to the total count The number of addition operations would be 1 of the 8 number of tuples, and thus the counting process is very ef cient A large array (using 216 = 65536 entries), indexed by pairs of bytes, would give even higher speedup, but at a higher storage cost

Observations As Figure 5-29 illustrates, the payout impact is both positive (did exceed goal on the second measure) and negative (did not exceed goal on the second measure) Some organizations prefer to have only a positive multiplier with no take-away of a negative deduction