Function Cudd_PrintInfo can be called to print out the values of parameters and statistics for a manager. The output of Cudd_PrintInfo is divided in two sections. The first reports the values of parameters that are under the application control. The second reports the values of statistical counters and other non-modifiable parameters. A quick guide to the interpretation of all these quantities follows. For ease of exposition, we reverse the order and describe the non-modifiable parameters first. We'll use a sample run as example. There is nothing special about this run.
The list of non-modifiable parameters starts with:
**** CUDD non-modifiable parameters **** Memory in use: 36282948This is the memory used by CUDD for three things mainly: Unique table (including all DD nodes in use), node free list, and computed table. This number almost never decreases in the lifetime of a CUDD manager, because CUDD does not release memory when it frees nodes. Rather, it puts the nodes on its own free list. This number is in bytes. It does not represent the peak memory occupation, because it does not include the size of data structures created temporarily by some functions (e.g., local look-up tables).
Peak number of nodes: 837018This number is the number of nodes that the manager has allocated. This is not the largest size of the BDDs, because the manager will normally have some dead nodes and some nodes on the free list.
Number of BDD variables: 198 Number of ZDD variables: 0These numbers tell us this run was not using ZDDs.
Number of cache entries: 1048576Current number of slots of the computed table. If one has a performance problem, this is one of the numbers to look at. The cache size is always a power of 2.
Number of cache look-ups: 5357600 Number of cache hits: 3761921These numbers give an indication of the hit rate in the computed table. It is not unlikely for model checking runs to get very high hit rates like this one (69.95%).
Number of cache insertions: 1595768 Number of cache collisions: 859151 Number of cache deletions: 0A collision occurs when a cache entry is overwritten. A deletion occurs when a cache entry is invalidated (e.g., during garbage collection). If the number of deletions is high compared to the number of collisions, it means that garbage collection occurs too often. In this case there were no garbage collections; hence, no deletions.
Cache used slots = 70.25%Percentage of cache slots that do not contain a valid entry. If this number is small, it may signal one of three conditions:
Soft limit for cache size: 956416This number says how large the cache can grow. This limit is based on the size of the unique table and is to be interpreted as the largest size for which a resizing is still possible. Hence, as in our case, the cache can exceed this limit, but by less than a factor of 2. CUDD uses a reward-based policy for growing the cache. (See Section 4.4.1.) The default hit rate for resizing is 30% and the value in effect is reported among the modifiable parameters.
Number of buckets in unique table: 478208This number is exactly half the one above. This is indeed how the soft limit is determined currently, unless the computed table hits the specified hard limit. (See below.)
Used buckets in unique table: 77.86%Percentage of unique table buckets that contain at least one node. Remarks analogous to those made about the used cache slots apply.
Number of BDD and ADD nodes: 836894 Number of ZDD nodes: 0How many nodes are currently in the unique table, either alive or dead.
Number of dead BDD and ADD nodes: 836496 Number of dead ZDD nodes: 0Subtract these numbers from those above to get the number of live nodes.
Total number of nodes allocated: 836894This is the total number of nodes that were requested and obtained from the free list. It never decreases, and is not an indication of memory occupation after the first garbage collection. Rather, it is a measure of the package activity.
Total number of nodes reclaimed: 18499505These are the nodes that were resuscitated from the dead. If they are many more than the allocated nodes, and the total number of slots is low relative to the number of nodes, then one may want to increase the limit for fast unique table growth.
Garbage collections so far: 0 Time for garbage collections: 0.00 sec Reorderings so far: 0 Time for reordering: 0.00 secThere is a GC for each reordering. Hence the first count will always be at least as large as the second.
Next reordering threshold: 4004When the number of nodes crosses this threshold, reordering will be triggered. (If enabled; in this case it is not.)
Let us now consider the modifiable parameters, that is, those settings on which the application or the user has control.
**** CUDD modifiable parameters **** Hard limit for cache size: 13421772This number counts entries. Each entry is 20 bytes if CUDD is compiled to use 32-bit pointers. Two important observations are in order:
Cache hit threshold for resizing: 15%This number can be changed if one suspects performance is hindered by the small size of the cache, and the cache is not growing towards the soft limit sufficiently fast. In such a case one can change the default 30% to 15% (as in this case) or even 1%.
Garbage collection enabled: yesOne can disable it, but there are few good reasons for doing so. It is normally preferable to raise the limit for fast unique table growth. (See below.)
Limit for fast unique table growth: 8388608See Section 4.5 and the comments above about reclaimed nodes and hard limit for the cache size. This value was chosen automatically by CUDD for a datasize limit of 1 GB.
Maximum number of variables sifted per reordering: 1000 Maximum number of variable swaps per reordering: 2000000 Maximum growth while sifting a variable: 1.2Lowering these numbers will cause reordering to be less accurate and faster. Results are somewhat unpredictable, because larger BDDs after one reordering do not necessarily mean the process will go faster or slower.
Dynamic reordering of BDDs enabled: yes Default BDD reordering method: 4 Dynamic reordering of ZDDs enabled: no Default ZDD reordering method: 4These lines tell whether automatic reordering can take place and what method would be used. The mapping from numbers to methods is in cudd.h. One may want to try different BDD reordering methods. If variable groups are used, however, one should not expect to see big differences, because CUDD uses the reported method only to reorder each leaf variable group (typically corresponding present and next state variables). For the relative order of the groups, it always uses the same algorithm, which is effectively sifting.
As for enabling dynamic reordering or not, a sensible recommendation is the following: Unless the circuit is rather small or one has a pretty good idea of what the order should be, reordering should be enabled.
Realignment of ZDDs to BDDs enabled: no Realignment of BDDs to ZDDs enabled: no Dead nodes counted in triggering reordering: no Group checking criterion: 7 Recombination threshold: 0 Symmetry violation threshold: 0 Arc violation threshold: 0 GA population size: 0 Number of crossovers for GA: 0Parameters for reordering. See the documentation of the functions used to control these parameters for the details.
The following symbols can be defined during compilation to increase the amount of statistics gathered and the number of messages produced by the package: