Chapter 6. Advanced Pig Latin

In the previous chapter we worked through the basics of Pig Latin. In this chapter we will plumb its depths, and we will also discuss how Pig handles more complex data flows. Finally, we will look at how to use macros and modules to modularize your scripts.

Advanced Relational Operations

We will now discuss the more advanced Pig Latin operators, as well as additional options for operators that were introduced in the previous chapter.

Advanced Features of foreach

In our introduction to foreach (see “foreach”), we discussed how it could take a list of expressions to output for every record in your data pipeline. Now we will look at ways it can explode the number of records in your pipeline, and also how it can be used to apply a set of operations to each record.

flatten

Sometimes you have data in a bag or a tuple and you want to remove that level of nesting. The baseball data available on GitHub (see “Code Examples in This Book”) can be used as an example. Because a player can play more than one position, position is stored in a bag. This allows us to still have one entry per player in the baseball file.[15] But when you want to switch around your data on the fly and group by a particular position, you need a way to pull those entries out of the bag. To do this, Pig provides the flatten modifier in foreach:

--flatten.pig
players = load 'baseball' as (name:chararray, team:chararray,
            position:bag{t:(p:chararray)}, bat:map[]);
pos     = foreach players generate name, flatten(position) as position;
bypos   = group pos by position;

A foreach with a flatten produces a cross product of every record in the bag with all of the other expressions in the generate statement. Looking at the first record in baseball, we see it is the following (replacing tabs with commas for clarity):

Jorge Posada,New York Yankees,{(Catcher),(Designated_hitter)},...

Once this has passed through the flatten statement, it will be two records:

Jorge Posada,Catcher
Jorge Posada,Designated_hitter

If there is more than one bag and both are flattened, this cross product will be done with members of each bag as well as other expressions in the generate statement. So rather than getting n rows (where n is the number of records in one bag), you will get n * m rows.

One side effect that surprises many users is that if the bag is empty, no records are produced. So if there had been an entry in baseball with no position, either because the bag is null or empty, that record would not be contained in the output of flatten.pig. The record with the empty bag would be swallowed by foreach. There are a couple of reasons for this behavior. One, since Pig may or may not have the schema of the data in the bag, it might have no idea how to fill in nulls for the missing fields. Two, from a mathematical perspective, this is what you would expect. Crossing a set S with the empty set results in the empty set. If you wish to avoid this, use a bincond to replace empty bags with a constant bag:

--flatten_noempty.pig
players = load 'baseball' as (name:chararray, team:chararray,
            position:bag{t:(p:chararray)}, bat:map[]);
noempty = foreach players generate name,
            ((position is null or IsEmpty(position)) ? {('unknown')} : position)
            as position;
pos     = foreach noempty generate name, flatten(position) as position;
bypos   = group pos by position;

flatten can also be applied to a tuple. In this case, it does not produce a cross product; instead, it elevates each field in the tuple to a top-level field. Again, empty tuples will remove the entire record.

If the fields in a bag or tuple that is being flattened have names, Pig will carry those names along. As with join, to avoid ambiguity, the field name will have the bag’s name and :: prepended to it. As long as the field name is not ambiguous, you are not required to use the bagname:: prefix.

If you wish to change the names of the fields, or if the fields initially did not have names, you can attach an as clause to your flatten, as in the preceding example. If there is more than one field in the bag or tuple that you are assigning names to, you must surround the set of field names with parentheses.

Finally, if you flatten a bag or tuple without a schema and do not provide an as clause, the resulting records coming out of your foreach will have a null schema. This is because Pig will not know how many fields the flatten will result in.[16]

Nested foreach

So far, all of the examples of foreach that we have seen immediately generate one or more lines of output. But foreach is more powerful than this. It can also apply a set of relational operations to each record in your pipeline. This is referred to as a nested foreach, or inner foreach. One example of how this can be used is to find the number of unique entries in a group. For example, to find the number of unique stock symbols for each exchange in the NYSE_daily data:

--distinct_symbols.pig
daily    = load 'NYSE_daily' as (exchange, symbol); -- not interested in other fields
grpd     = group daily by exchange;
uniqcnt  = foreach grpd {
           sym      = daily.symbol;
           uniq_sym = distinct sym;
           generate group, COUNT(uniq_sym);
};

There are several new things here to unpack; we will walk through each. In this example, rather than generate immediately following foreach, a { (open brace) signals that we will be nesting operators inside this foreach. In this nested code, each record passed to foreach is handled one at a time.

In the first line we see a syntax that we have not seen outside of foreach. In fact, sym = daily.symbol would not be legal outside of foreach. It is roughly equivalent to the top-level statement sym = foreach grpd generate daily.symbol, but it is not stated that way inside the foreach because it is not really another foreach. There is no relation for it to be associated with (that is, grpd is not defined here). This line takes the bag daily and produces a new relation sym, which is a bag with tuples that have only the field symbol.

The second line applies the distinct operator to the relation sym. Note that even inside foreach, relational operators can be applied only to relations; they cannot be applied to expressions. For example, the statement uniq_sym = distinct daily.symbol will produce a syntax error because daily.symbol is an expression, not a relation. sym is a relation. This distinction may seem arbitrary, but it results in Pig Latin having a coherent definition as a language. Without this, strange statements such as C = distinct 1 + 2 would be legal. One way to think about this is that the assignment operator inside foreach can be used to take an expression and create a relation, as happens in this example.

The last line in a nested foreach must always be generate. This tells Pig how to take the results of the nested operations and produce a record to be put in the outer relation (in this case, uniqcnt). So, generate is the operator that takes the inner relations and turns them back into expressions for inclusion in the outer relation. That is, if the script read generate group, uniq_sym, uniq_sym would be treated as a bag for the purpose of the generate statement.

Theoretically, any Pig Latin relational operator should be legal inside foreach. However, at the moment, only distinct, filter, limit, and order are supported.

Let’s look at a few more examples of how this feature can be useful, such as to sort the contents of a bag before the bag is passed to a UDF. This is convenient for UDFs that require all of their input to come in a certain order. Consider a stock-analysis UDF that wants to track information about a particular stock over time. The UDF will want input sorted by timestamp:

--analyze_stock.pig
register 'acme.jar';
define analyze com.acme.financial.AnalyzeStock();
daily    = load 'NYSE_daily' as (exchange:chararray, symbol:chararray,
               date:chararray, open:float, high:float, low:float,
               close:float, volume:int, adj_close:float);
grpd     = group daily by symbol;
analyzed = foreach grpd {
            sorted = order daily by date;
            generate group, analyze(sorted);
};

Doing the sorting in Pig Latin, rather than in your UDF, is important for a couple of reasons. One, it means Pig can offload the sorting to MapReduce. MapReduce has the ability to sort data by a secondary key while grouping it. So, the order statement in this case does not require a separate sorting operation. Two, it means that your UDF does not need to wait for all data to be available before it starts processing. Instead, it can use the Accumulator interface (see “Accumulator Interface”), which is much more memory efficient.

This feature can be used to find the top k elements in a group. The following example will find the top three dividends payed for each stock:

--hightest_dividend.pig
divs = load 'NYSE_dividends' as (exchange:chararray, symbol:chararray,
            date:chararray, dividends:float);
grpd = group divs by symbol;
top3 = foreach grpd {
            sorted = order divs by dividends desc;
            top    = limit sorted 3;
            generate group, flatten(top);
};

Currently, these nested portions of code are always run serially for each record handed to them. Of course the foreach itself will be running in multiple map or reduce tasks, but each instance of the foreach will not spawn subtasks to do the nested operations in parallel. So if we added a parallel 10 clause to the grpd = group divs by symbol statement in the previous example, this ordering and limiting would take place in 10 reducers. But each group of stocks would be sorted and the top three records taken serially within one of those 10 reducers.

There is, of course, no requirement that the pipeline inside the foreach be a simple linear pipeline. For example, if you wanted to calculate two distinct counts together, you could do the following:

--double_distinct.pig
divs = load 'NYSE_dividends' as (exchange:chararray, symbol:chararray);
grpd = group divs all;
uniq = foreach grpd {
            exchanges      = divs.exchange;
            uniq_exchanges = distinct exchanges;
            symbols        = divs.symbol;
            uniq_symbols   = distinct symbols;
            generate COUNT(uniq_exchanges), COUNT(uniq_symbols);
};

For simplicity, Pig actually runs this pipeline once for each expression in generate. Here this has no side effects because the two data flows are completely disjointed. However, if you constructed a pipeline where there was a split in the flow, and you put a UDF in the shared portion, you would find that it was invoked more often than you expected.

Using Different Join Implementations

When we covered join in the previous chapter (see “Join”), we discussed only the default join behavior. However, Pig offers multiple join implementations, which we will discuss here.

In RDBMS systems, traditionally the SQL optimizer chooses a join implementation for the user. This is nice as long as the optimizer chooses well, which it does in most cases. But Pig has taken a different approach. In the Pig team we like to say that our optimizer is located between the user’s chair and keyboard. We empower the user to make these choices rather than having Pig make them. So for operators such as join where there are multiple implementations, Pig lets the user indicate his choice via a using clause.

This approach fits well with our philosophy that Pigs are domestic animals (i.e., Pig does what you tell it; see “Pig Philosophy”). Also, as a relatively new product, Pig has a lot of functionality to add. It makes more sense to focus on adding implementation choices and letting the user choose which ones to use, rather than focusing on building an optimizer capable of choosing well.

Joining small to large data

A common type of join is doing a lookup in a smaller input. For example, suppose you were processing data where you needed to translate a US ZIP code (postal code) to the state and city it referred to. As there are at most 100,000 zip codes in the US, this translation table should easily fit in memory. Rather than forcing a reduce phase that will sort your big file plus this tiny zip code translation file, it makes sense instead to send the zip code file to every machine, load it into memory, and then do the join by streaming through the large file and looking up each record in the zip code file. This is called a fragment-replicate join (because you fragment one file and replicate the other):

--repljoin.pig
daily = load 'NYSE_daily' as (exchange:chararray, symbol:chararray,
            date:chararray, open:float, high:float, low:float,
            close:float, volume:int, adj_close:float);
divs  = load 'NYSE_dividends' as (exchange:chararray, symbol:chararray,
            date:chararray, dividends:float);
jnd   = join daily by (exchange, symbol), divs by (exchange, symbol)
            using 'replicated';

The using 'replicated' tells Pig to use the fragment-replicate algorithm to execute this join. Because no reduce phase is necessary, all of this can be done in the map task.

The second input listed in the join (in this case, divs) is always the input that is loaded into memory. Pig does not check beforehand that the specified input will fit into memory. If Pig cannot fit the replicated input into memory, it will issue an error and fail.

Due to the way Java stores objects in memory, the size of the data on disk will not be the size of the data in memory. See “Memory Requirements of Pig Data Types” for a discussion of how data expands in memory in Pig. You will need more memory for a replicated join than you need space on disk to store the replicated input.

Fragment-replicate join supports only inner and left outer joins. It cannot do a right outer join, because when a given map task sees a record in the replicated input that does not match any record in the fragmented input, it has no idea whether it would match a record in a different fragment. So, it does not know whether to emit a record. If you want a right or full outer join, you will need to use the default join operation.

Fragment-replicate join can be used with more than two tables. In this case, all but the first (left-most) table are read into memory.

Pig implements the fragment-replicate join by loading the replicated input into Hadoop’s distributed cache. The distributed cache is a tool provided by Hadoop that preloads a file onto the local disk of nodes that will be executing the maps or reduces for that job. This has two important benefits. First, if you have a fragment-replicate join that is going to run on 1,000 maps, opening one file in HDFS from 1,000 different machines all at once puts a serious strain on the NameNode and the three data nodes that contain the block for that file. The distributed cache is built specifically to manage these kinds of issues without straining HDFS. Second, if multiple map tasks are located on the same physical machine, the files in the distributed cache are shared between those instances, thus reducing the number of times the file has to be copied.

Pig runs a map-only MapReduce job to preprocess the file and get it ready for loading into the distributed cache. If there is a filter or foreach between the load and join, these will be done as part of this initial job so that the file to be stored in the distributed cache is as small as possible. The join itself will be done in a second map-only job.

Joining skewed data

As we have seen elsewhere, much of the data you will be processing with Pig has significant skew in the number of records per key. For example, if you were building a map of the Web and joining by the domain of the URL (your key), you would expect to see significant skew for values such as yahoo.com. Pig’s default join algorithm is very sensitive to skew, because it collects all of the records for a given key together on a single reducer. In many data sets, there are a few keys that have three or more orders of magnitude more records than other keys. This results in one or two reducers that will take much longer than the rest. To deal with this, Pig provides skew join.

Skew join works by first sampling one input for the join. In that input it identifies any keys that have so many records that skew join estimates it will not be able to fit them all into memory. Then, in a second MapReduce job, it does the join. For all records except those identified in the sample, it does a standard join, collecting records with the same key onto the same reducer. Those keys identified as too large are treated differently. Based on how many records were seen for a given key, those records are split across the appropriate number of reducers. The number of reducers is chosen based on Pig’s estimate of how wide the data must be split such that each reducer can fit its split into memory. For the input to the join that is not split, those keys that were split are then replicated to each reducer that contains that key.[17]

For example, let’s look at how the following Pig Latin script would work:

users = load 'users' as (name:chararray, city:chararray);
cinfo = load 'cityinfo' as (city:chararray, population:int);
jnd   = join cinfo by city, users by city using 'skewed';

Assume that the cities in users are distributed such that 20 users live in Barcelona, 100,000 in New York, and 350 in Portland. Let’s further assume that Pig determined that it could fit 75,000 records into memory on each reducer. When this data was joined, New York would be identified as a key that needed to be split across reducers. During the join phase, all records with keys other than New York would be treated as in a default join. Records from users with New York as the key would be split between two separate reducers. Records from cityinfo with New York as a key would be duplicated and sent to both of those reducers.

The second input in the join, in this case users, is the one that will be sampled and have its keys with a large number of values split across reducers. The first input will have records with those values replicated across reducers.

This algorithm addresses skew in only one input. If both inputs have skew, this algorithm will still work, but it will be slow. Much of the motivation behind this approach was that it guarantees the join will still finish, given time. Before Pig introduced skew join in version 0.4, data that was skewed on both sides could not be joined in Pig because it was not possible to fit all the records for the high-cardinality key values in memory for either side.

Skew join can be done on inner or outer joins. However, it can take only two join inputs. Multiway joins must be broken into a series of joins if they need to use skew join.

Since data often has skew, why not use skew join all of the time? There is a small performance penalty for using skew join, because one of the inputs must be sampled first to find any key values with a large number of records. This usually adds about 5% to the time it takes to calculate the join. If your data frequently has skew, it might be worth it to always use skew join and pay the 5% tax in order to avoid failing or running very slowly with the default join and then needing to rerun using skewed join.

As stated earlier, Pig estimates how much data it can fit into memory when deciding which key values to split and how wide to split them. For the purposes of this calculation, Pig looks at the record sizes in the sample and assumes it can use 30% of the JVM’s heap to materialize records that will be joined. In your particular case you might find you need to increase or decrease this size. You should decrease the value if your join is still failing with out-of-memory errors even when using skew join. This indicates that Pig is estimating memory usage improperly, so you should tell it to use less. If profiling indicates that Pig is not utilizing all of your heap, you might want to increase the value in order to do the join more efficiently; the less ways the key values are split, the more efficient the join will be. You can do that by setting the property pig.skewedjoin.reduce.memusage to a value between 0 and 1. For example, if you wanted it to use 25% instead of 30%, you could add -Dpig.skewedjoin.reduce.memusage=0.25 to your Pig command line or define the value in your properties file.

Like order, skew join breaks the MapReduce convention that all records with the same key will be processed by the same reducer. This means records with the same key might be placed in separate part files. If you plan to process the data in a way that depends on all records with the same key being in the same part file, you cannot use skew join.

Joining sorted data

A common database join strategy is to first sort both inputs on the join key and then walk through both inputs together, doing the join. This is referred to as a sort-merge join. In MapReduce, because a sort requires a full MapReduce job, as does Pig’s default join, this technique is not more efficient than the default. However, if your inputs are already sorted on the join key, this approach makes sense. The join can be done in the map phase by opening both files and walking through them. Pig refers to this as a merge join because it is a sort-merge join, but the sort has already been done:

--mergejoin.pig
-- use sort_for_mergejoin.pig to build NYSE_daily_sorted and NYSE_dividends_sorted
daily = load 'NYSE_daily_sorted' as (exchange:chararray, symbol:chararray,
            date:chararray, open:float, high:float, low:float,
            close:float, volume:int, adj_close:float);
divs  = load 'NYSE_dividends_sorted' as (exchange:chararray, symbol:chararray,
            date:chararray, dividends:float);
jnd   = join daily by symbol, divs by symbol using 'merge';

To execute this join, Pig will first run a MapReduce job that samples the second input, NYSE_dividends_sorted. This sample builds an index that tells Pig the value of the join keys, symbol in the first record in every input split (usually each HDFS block). Because this sample reads only one record per split, it runs very quickly. Pig will then run a second MapReduce job that takes the first input, NYSE_daily_sorted, as its input. When each map reads the first record in its split of NYSE_daily_sorted, it takes the value of symbol and looks it up in the index built by the previous job. It looks for the last entry that is less than its value of symbol. It then opens NYSE_dividends_sorted at the corresponding block for that entry. For example, if the index contained entries (CA, 1), (CHY, 2), (CP, 3), and the first symbol in a given map’s input split of NYSE_daily_sorted was CJA, that map would open block 2 of NYSE_dividends_sorted. (Even if CP was the first user ID in NYSE_daily_sorted’s split, block 2 of NYSE_dividends_sorted would be opened, as there could be records with a key of CP in that block.) Once NYSE_dividends_sorted is opened, Pig throws away records until it reaches a record with symbol of CJA. Once it finds a match, it collects all the records with that value into memory and then does the join. It then advances the first input, NYSE_daily_sorted. If the key is the same, it again does the join. If not, it advances the second input, NYSE_dividends_sorted, again until it finds a value greater than or equal to the next value in the first input, NYSE_daily_sorted. If the value is greater, it advances the first input and continues. Because both inputs are sorted, it never needs to look in the index after the initial lookup.

All of this can be done without a reduce phase, and so it is more efficient than a default join. This algorithm, which was introduced in version 0.4, currently supports only two-way inner joins.

cogroup

cogroup is a generalization of group. Instead of collecting records of one input based on a key, it collects records of n inputs based on a key. The result is a record with a key and one bag for each input. Each bag contains all records from that input that have the given value for the key:

A = load 'input1' as (id:int, val:float);
B = load 'input2' as (id:int, val2:int);
C = cogroup A by id, B by id;
describe C;

C: {group: int,A: {id: int,val: float},B: {id: int,val2: int}}

Another way to think of cogroup is as the first half of a join. The keys are collected together, but the cross product is not done. In fact, cogroup plus foreach, where each bag is flattened, is equivalent to a join—as long as there are no null values in the keys.

cogroup handles null values in the keys similarly to group and unlike join. That is, all records with a null value in the key will be collected together.

cogroup is useful when you want to do join-like things but not a full join. For example, Pig Latin does not have a semi-join operator, but you can do a semi-join:

--semijoin.pig
daily = load 'NYSE_daily' as (exchange:chararray, symbol:chararray,
            date:chararray, open:float, high:float, low:float,
            close:float, volume:int, adj_close:float);
divs  = load 'NYSE_dividends' as (exchange:chararray, symbol:chararray,
            date:chararray, dividends:float);
grpd  = cogroup daily by (exchange, symbol), divs by (exchange, symbol);
sjnd  = filter grpd by not IsEmpty(divs);
final = foreach sjnd generate flatten(daily);

Because cogroup needs to collect records with like keys together, it requires a reduce phase.

union

Sometimes you want to put two data sets together by concatenating them instead of joining them. Pig Latin provides union for this purpose. If you had two files you wanted to use for input and there was no glob that could describe them, you could do the following:

A = load '/user/me/data/files/input1';
B = load '/user/someoneelse/info/input2';
C = union A, B;

Unlike union in SQL, Pig does not require that both inputs share the same schema. If both do share the same schema, the output of the union will have that schema. If one schema can be produced from another by a set of implicit casts, the union will have that resulting schema. If neither of these conditions hold, the output will have no schema (that is, different records will have different fields). This schema comparison includes names, so even different field names will result in the output having no schema. You can get around this by placing a foreach before the union that renames fields.

A = load 'input1' as (x:int, y:float);
B = load 'input2' as (x:int, y:float);
C = union A, B;
describe C;

C: {x: int,y: float}

A = load 'input1' as (x:int, y:float);
B = load 'input2' as (x:int, y:double);
C = union A, B;
describe C;

C: {x: int,y: double}

A = load 'input1' as (x:int, y:float);
B = load 'input2' as (x:int, y:chararray);
C = union A, B;
describe C;

Schema for C unknown.

union does not perform a mathematical set union. That is, duplicate records are not eliminated. In this manner it is like SQL’s union all. Also, union does not require a separate reduce phase.

Sometimes your data changes over time. If you have data you collect every month, you might add a new column this month. Now you are prevented from using union because your schemas do not match. If you want to union this data and force your data into a common schema, you can add the keyword onschema to your union statement:

A = load 'input1' as (w:chararray, x:int, y:float);
B = load 'input2' as (x:int, y:double, z:chararray);
C = union onschema A, B;
describe C;

C: {w: chararray,x: int,y: double,z: chararray}

union onschema requires that all inputs have schemas. It also requires that a shared schema for all inputs can be produced by adding fields and implicit casts. Matching of fields is done by name, not position. So, in the preceding example, w:chararray is added from input1 and z:chararray is added from input2. Also, a cast from float to double is added for input1 so that field y is a double. If a shared schema cannot be produced by this method, an error is returned. When the data is read, nulls are inserted for fields not present in a given input.

cross

cross matches the mathematical set operation of the same name. In the following Pig Latin, cross takes every record in NYSE_daily and combines it with every record in NYSE_dividends:

--cross.pig
-- you may want to run this in a cluster, it produces about 3G of data
daily     = load 'NYSE_daily' as (exchange:chararray, symbol:chararray,
                date:chararray, open:float, high:float, low:float,
                close:float, volume:int, adj_close:float);
divs      = load 'NYSE_dividends' as (exchange:chararray, symbol:chararray,
                date:chararray, dividends:float);
tonsodata = cross daily, divs parallel 10;

cross tends to produce a lot of data. Given inputs with n and m records respectively, cross will produce output with n x m records.

Pig does implement cross in a parallel fashion. It does this by generating a synthetic join key, replicating rows, and then doing the cross as a join. The previous script is rewritten to:

daily     = load 'NYSE_daily' as (exchange:chararray, symbol:chararray,
                date:chararray, open:float, high:float, low:float,
                close:float, volume:int, adj_close:float);
divs      = load 'NYSE_dividends' as (exchange:chararray, symbol:chararray,
                date:chararray, dividends:float);
A         = foreach daily generate flatten(GFCross(0, 2)), flatten(*);
B         = foreach divs generate flatten(GFCross(1, 2)), flatten(*);
C         = cogroup A by ($0, $1), B by ($0, $1) parallel 10;
tonsodata = foreach C generate flatten(A), flatten(B);

GFCross is an internal UDF. The first argument is the input number, and the second argument is the total number of inputs. In this example, the output is a bag that contains four records.[18] These records have a schema of (int, int). The field that is the same number as the first argument to GFCross contains a random number between zero and three. The other field counts from zero to three. So, if we assume for a given two records, one in each input, that the random number for the first input is 3 and for the second is 2, then the outputs of GFCross would look like:

A {(3, 0), (3, 1), (3, 2), (3, 3)}
B {(0, 2), (1, 2), (2, 2), (3, 2)}

When these records are flattened, four copies of each input record will be created in the map. They then are joined on the artificial keys. For every record in each input, it is guaranteed that there is one and only one instance of the artificial keys that will match and produce a record. Because the random numbers are chosen differently for each record, the resulting joins are done on an even distribution of the reducers.

This algorithm does enable crossing of data in parallel. However, it creates a burden on the shuffle phase by increasing the number of records in each input being shuffled. Also, no matter what you do, cross outputs a lot of data. Writing all of this data to disk is expensive, even when done in parallel.

This is not to say you should not use cross. There are instances when it is indispensable. Pig’s join operator supports only equi-joins, that is, joins on an equality condition. Because general join implementations (ones that do not depend on the data being sorted or small enough to fit in memory) in MapReduce depend on collecting records with the same join key values onto the same reducer, non-equi-joins (also called theta joins) are difficult to do. They can be done in Pig using cross followed by filter:

--thetajoin.pig
--I recommend running this one on a cluster too
daily   = load 'NYSE_daily' as (exchange:chararray, symbol:chararray,
            date:chararray, open:float, high:float, low:float,
            close:float, volume:int, adj_close:float);
divs    = load 'NYSE_dividends' as (exchange:chararray, symbol:chararray,
            date:chararray, dividends:float);
crossed = cross daily, divs;
tjnd    = filter crossed by daily::date < divs::date;

Fuzzy joins could also be done in this manner, where the fuzzy comparison is done after the cross. However, whenever possible, it is better to use a UDF to conform fuzzy values to a standard value and then do a regular join. For example, if you wanted to join two inputs on city but wanted to join any time two cities were in the same metropolitan area (e.g., you wanted Los Angeles and Pasadena to be viewed as equal), you could first run your records through a UDF that generated a single join key for all cities in a metropolitan area and then do the join.

Integrating Pig with Legacy Code and MapReduce

One tenet of Pig’s philosophy is that Pig allows users to integrate their own code with Pig wherever possible (see “Pig Philosophy”). The most obvious way Pig does that is through its UDFs. But it also allows you to directly integrate other executables and MapReduce jobs.

stream

To specify an executable that you want to insert into your data flow, use stream. You may want to do this when you have a legacy program that you do not want to modify or are unable to change. You can also use stream when you have a program you use frequently, or one you have tested on small data sets and now want to apply to a large data set. Let’s look at an example where you have a Perl program highdiv.pl that filters out all stocks with a dividend below $1.00:

-- streamsimple.pig
divs = load 'NYSE_dividends' as (exchange, symbol, date, dividends);
highdivs = stream divs through `highdiv.pl` as (exchange, symbol, date, dividends);

Notice the as clause in the stream command. This is not required. But Pig has no idea what the executable will return, so if you do not provide the as clause, the relation highdivs will have no schema.

The executable highdiv.pl is invoked once on every map or reduce task. It is not invoked once per record. Pig instantiates the executable and keeps feeding data to it via stdin. It also keeps checking stdout, passing any results to the next operator in your data flow. The executable can choose whether to produce an output for every input, only every so many inputs, or only after all inputs have been received.

The preceding example assumes that you already have highdiv.pl installed on your grid, and that it is runnable from the working directory on the task machines. If that is not the case, which it usually will not be, you can ship the executable to the grid. To do this, use a define statement:

--streamship.pig
define hd `highdiv.pl` ship('highdiv.pl');
divs = load 'NYSE_dividends' as (exchange, symbol, date, dividends);
highdivs = stream divs through hd as (exchange, symbol, date, dividends);

This define does two things. First, it defines the executable that will be used. Now in stream we refer to highdiv.pl by the alias we gave it, hp, rather than referring to it directly. Second, it tells Pig to pick up the file ./highdiv.pl and ship it to Hadoop as part of this job. This file will be picked up from the specified location on the machine where you launch the job. It will be placed in the working directory of the task on the task machines. So, the command you pass to stream must refer to it relative to the current working directory, not via an absolute path. If your executable depends on other modules or files, they can be specified as part of the ship clause as well. For example, if highdiv.pl depends on a Perl module called Financial.pm, you can send them both to the task machines:

define hd `highdiv.pl` ship('highdiv.pl', 'Financial.pm');
divs = load 'NYSE_dividends' as (exchange, symbol, date, dividends);
highdivs = stream divs through hd as (exchange, symbol, date, dividends);

Many scripting languages assume certain paths for modules based on their hierarchy. For example, Perl expects to find a module Acme::Financial in Acme/Financial.pm. However, the ship clause always puts files in your current working directory, and it does not take directories, so you could not ship Acme. The workaround for this is to create a TAR file and ship that, and then have a step in your executable that unbundles the TAR file. You then need to set your module include path (for Perl, -I or the PERLLIB environment variables) to contain . (dot).

ship moves files into the grid from the machine where you are launching your job. But sometimes the file you want is already in the grid. If you have a grid file that will be accessed by every map or reduce task in your job, the proper way to access it is via the distributed cache. The distributed cache is a mechanism Hadoop provides to share files. It reduces the load on HDFS by preloading the file to the local disk on the machine that will be executing the task. You can use the distributed cache for your executable by using the cache clause in define:

crawl      = load 'webcrawl' as (url, pageid);
normalized = foreach crawl generate normalize(url);
define blc `blacklistchecker.py` cache('/data/shared/badurls#badurls');
goodurls   = stream normalized through blc as (url, pageid);

The string before the # is the path on HDFS, in this case, /data/shared/badurls. The string after the # is the name of the file as viewed by the executable. So, Hadoop will put a copy of /data/shared/badurls into the task’s working directory and call it badurls.

So far we have assumed that your executable takes data on stdin and writes it to stdout. This might not work, depending on your executable. If your executable needs a file to read from, write to, or both, you can specify that with the input and output clauses in the define command. Continuing with our previous example, let’s say that blacklistchecker.py expects to read its input from a file specified by -i on its command line and write to a file specified by -o:

crawl      = load 'webcrawl' as (url, pageid);
normalized = foreach crawl generate normalize(url);
define blc `blacklistchecker.py -i urls -o good` input('urls') output('good');
goodurls   = stream normalized through blc as (url, pageid);

Again, file locations are specified from the working directory on the task machines. In this example, Pig will write out all the input for a given task for blacklistchecker.py to urls, then invoke the executable, and then read good to get the results. Again, the executable will be invoked only once per map or reduce task, so Pig will first write out all the input to the file.

mapreduce

Beginning in Pig 0.8, you can also include MapReduce jobs directly in your data flow with the mapreduce command. This is convenient if you have processing that is better done in MapReduce than Pig but must be integrated with the rest of your Pig data flow. It can also make it easier to incorporate legacy processing written in MapReduce with newer processing you want to write in Pig Latin.

MapReduce jobs expect to read their input from and write their output to a storage device (usually HDFS). So to integrate them with your data flow, Pig first has to store the data, then invoke the MapReduce job, and then read the data back. This is done via store and load clauses in the mapreduce statement that invoke regular load and store functions. You also provide Pig with the name of the JAR that contains the code for your MapReduce job.

As an example, let’s continue with the blacklisting of URLs that we considered in the previous section. Only now let’s assume that this is done by a MapReduce job instead of a Python script:

crawl      = load 'webcrawl' as (url, pageid);
normalized = foreach crawl generate normalize(url);
goodurls   = mapreduce 'blacklistchecker.jar'
                store normalized into 'input'
                load 'output' as (url, pageid);

mapreduce takes as its first argument the JAR containing the code to run a MapReduce job. It uses load and store phrases to specify how data will be moved from Pig’s data pipeline to the MapReduce job. Notice that the input alias is contained in the store clause. As with stream, the output of mapreduce is opaque to Pig, so if we want the resulting relation goodurls to have a schema, we have to tell Pig what it is. This example also assumes that the Java code in blacklistchecker.jar knows which input and output files to look for and has a default class to run specified in its manifest. Often this will not be the case. Any arguments you wish to pass to the invocation of the Java command that will run the MapReduce task can be put in backquotes after the load clause:

crawl      = load 'webcrawl' as (url, pageid);
normalized = foreach crawl generate normalize(url);
goodurls   = mapreduce 'blacklistchecker.jar'
                 store normalized into 'input'
                 load 'output' as (url, pageid)
                 `com.acmeweb.security.BlackListChecker -i input -o output`;

The string in the backquotes will be passed directly to your MapReduce job as is. So if you wanted to pass Java options, etc., you can do that as well.

The load and store clauses of the mapreduce command have the same syntax as the load and store statements, so you can use different load and store functions, pass constructor arguments, and so on. See “Load” and “Store” for full details.

Nonlinear Data Flows

So far our examples have been linear data flows or trees. In a linear data flow, one input is loaded, processed, and stored. We have looked at operators that combine multiple data flows: join, cogroup, union, and cross. With these you can build tree structures where multiple inputs all flow to a single output. But in complex data-processing situations, you often also want to split your data flow. That is, one input will result in more than one output. You might also have diamonds, places where the data flow is split and eventually joined back together. Pig supports these directed acyclic graph (DAG) data flows.

Splits in your data flow can be either implicit or explicit. In an implicit split, no specific operator or syntax is required in your script. You simply refer to a given relation multiple times. Let’s consider data from our baseball example data. You might, for example, want to analyze players by position and by team at the same time:

--multiquery.pig
players    = load 'baseball' as (name:chararray, team:chararray,
                position:bag{t:(p:chararray)}, bat:map[]);
pwithba    = foreach players generate name, team, position,
                bat#'batting_average' as batavg;
byteam     = group pwithba by team;
avgbyteam  = foreach byteam generate group, AVG(pwithba.batavg);
store avgbyteam into 'by_team';
flattenpos = foreach pwithba generate name, team,
                flatten(position) as position, batavg;
bypos      = group flattenpos by position;
avgbypos   = foreach bypos generate group, AVG(flattenpos.batavg);
store avgbypos into 'by_position';

The pwithba relation is referred to by the group operators for both the byteam and bypos relations. Pig builds a data flow that takes every record from pwithba and ships it to both group operators.

Splitting data flows can also be done explicitly via the split operator, which allows you to split your data flow as many ways as you like. Let’s take an example where you want to split data into different files depending on the date the record was created:

wlogs = load 'weblogs' as (pageid, url, timestamp);
split wlogs into apr03 if timestamp < '20110404',
          apr02 if timestamp < '20110403' and timestamp > '20110401',
          apr01 if timestamp < '20110402' and timestamp > '20110331';
store apr03 into '20110403';
store apr02 into '20110402';
store apr01 into '20110401';

At first glance, split looks like a switch or case statement, but it is not. A single record can go to multiple legs of the split since you use different filters for each if clause. And a record can go to no leg. In the preceding example, if a record were found with a date of 20110331, it would be dropped. And there is no default clause—no way to send any leftover records to a particular alias.

split is semantically identical to an implicit split that users filters. The previous example could be rewritten as:

wlogs = load 'weblogs' as (pageid, url, timestamp);
apr03 = filter wlogs by timestamp < '20110404';
apr02 = filter wlogs by timestamp < '20110403' and timestamp > '20110401';
apr01 = filter wlogs by timestamp < '20110402' and timestamp > '20110331';
store apr03 into '20110403';
store apr02 into '20110402';
store apr01 into '20110401';

In fact, Pig will internally rewrite the original script that has split in exactly this way.

Let’s take a look at how Pig executes these nonlinear data flows. Whenever possible, it combines them into single MapReduce jobs. This is referred to as a multiquery. In cases where all operators will fit into a single map task, this is easy. Pig creates separate pipelines inside the map and sends the appropriate records to each pipeline. The example using split to store data by date will be executed in this way.

Pig can also combine multiple group operators together in many cases. In the example given at the beginning of this section, where the baseball data is grouped by both team and position, this entire Pig Latin script will be executed inside one MapReduce job. Pig accomplishes this by duplicating records on the map side and annotating each record with its pipeline number. When the data is partitioned during the shuffle, the appropriate key is used for each record. That is, records from the pipeline grouping by team will use team as their shuffle key, and records from the pipeline grouping by position will use position as their shuffle key. This is done by declaring the key type to be tuple and placing the correct values in the key tuple for each record. Once the data has been collected to reducers, the pipeline number is used as part of the sort key so that records from each pipeline and group are collected together. In the reduce task, Pig instantiates multiple pipelines, one for each group operator. It sends each record down the appropriate pipeline based on its annotated pipeline number. In this way, input data can be scanned once but grouped many different ways. An example of how one record flows through this pipeline is shown in Figure 6-1. Although this does not provide linear speedup, we find it often approaches it.

Multiquery illustration
Figure 6-1. Multiquery illustration

There are cases where Pig will not combine multiple operators into a single MapReduce job. Pig does not use multiquery for any of the multiple-input operators: join, union, cross, or cogroup. It does not use multiquery for order statements either. Also, if it has multiple group statements and some would use Hadoop’s combiner and some would not, it combines only those statements that use Hadoop’s combiner into a multiquery. This is because we have found that combining the Hadoop combiner and non-Hadoop combiner jobs together does not perform well.

Multiquery scripts tend to perform better than loading the same input multiple times, but this approach does have limits. Because it requires replicating records in the map, it does slow down the shuffle phase. Eventually the increased cost of the shuffle phase outweighs the reduced cost of rescanning the input data. Pig has no way to estimate when this will occur. Currently, the optimizer is optimistic and always combines jobs with multiquery whenever it can. If it combines too many jobs and becomes slower than splitting some of the jobs, you can turn off multiquery or you can rewrite your Pig Latin into separate scripts so Pig does not attempt to combine them all. To turn off multiquery, you can pass either -M or -no_multiquery on the command line or set the property opt.multiquery to false.

We must also consider what happens when one job in a multiquery fails but others succeed. If all jobs succeed, Pig will return 0, meaning success. If all of the jobs fail, Pig will return 2. If some jobs fail and some succeed, Pig will return 3. By default, if one of the jobs fails, Pig will continue processing the other jobs. However, if you want Pig to stop as soon as one of the jobs fails, you can pass -F or -stop_on_failure. In this case, any jobs that have not yet been finished will be terminated, and any that have not started will not be started. Any jobs that are already finished will not be cleaned up.

Controlling Execution

In addition to providing many relational and dataflow operators, Pig Latin provides ways for you to control how your jobs execute on MapReduce. It allows you to set values that control your environment and details of MapReduce, such as how your data is partitioned.

set

The set command is used to set the environment in which Pig runs the MapReduce jobs. Table 6-1 shows Pig-specific parameters that can be controlled via set.

Table 6-1. Pig-specific set parameters
Parameter Value type Description
debug string Sets the logging level to DEBUG. Equivalent to passing -debug DEBUG on the command line.
default_parallel integer Sets a default parallel level for all reduce operations in the script. See “Parallel” for details.
job.name string Assigns a name to the Hadoop job. By default the name is the filename of the script being run, or a randomly generated name for interactive sessions.
job.priority string If your Hadoop cluster is using the Capacity Scheduler with priorities enabled for queues, this allows you to set the priority of your Pig job. Allowed values are very_low, low, normal, high, and very_high.

For example, to set the default parallelism of your Pig Latin script and set the job name to my_job:

set default_parallel 10;
set job.name my_job;
users = load 'users';

In addition to these predefined values, set can be used to pass Java property settings to Pig and Hadoop. Both Pig and Hadoop use a number of Java properties to control their behavior. Consider an example where you want to turn multiquery off for a given script, and you want to tell Hadoop to use a higher value than usual for its map-side sort buffer:

set opt.multiquery false;
set io.sort.mb 2048; --give it 2G

You can also use this mechanism to pass properties to UDFs. All of the properties are passed to the tasks on the Hadoop nodes when they are executed. They are not set as Java properties in that environment; rather, they are placed in a Hadoop object called JobConf. UDFs have access to the JobConf. Thus, anything you set in the script can be seen by your UDFs. This can be a convenient way to control UDF behavior. For information on how to retrieve this information in your UDFs, see “Constructors and Passing Data from Frontend to Backend”.

Values that are set in your script are global for the whole script. If they are reset later in the script, that second value will overwrite the first and be used throughout the whole script.

Setting the Partitioner

Hadoop uses a class called Partitioner to partition records to reducers during the shuffle phase. For details on partitioners, see “Shuffle Phase”. Pig does not override the default partitioner, except for order and skew join. The balancing operations in these require special Partitioners.

Beginning in version 0.8, Pig allows you to set the partitioner, except in the cases where it is already overriding it. To do this, you need to tell Pig which Java class to use to partition your data. This class must extend Hadoop’s org.apache.hadoop.mapreduce.Partitioner<KEY,VALUE>. Note that this is the newer (version 0.20 and later) mapreduce API and not the older mapred:

register acme.jar; --jar containing the partitioner
users = load 'users' as (id, age, zip);
grp   = group users by id partition by com.acme.userpartitioner parallel 100;

Operators that reduce data can take the partition clause. These operators are cogroup, cross, distinct, group, and join (again, not in conjunction with skew join).

Pig Latin Preprocessor

Pig Latin has a preprocessor that runs before your Pig Latin script is parsed. In 0.8 and earlier, this provided parameter substitution, roughly similar to a very simple version of #define in C. Starting with 0.9, it also provides inclusion of other Pig Latin scripts and function-like macro definitions, so that you can write Pig Latin in a modular way.

Parameter Substitution

Pig Latin scripts that are used frequently often have elements that need to change based on when or where they are run. A script that is run every day is likely to have a date component in its input files or filters. Rather than edit and change the script every day, you want to pass in the date as a parameter. Parameter substitution provides this capability with a basic string-replacement functionality. Parameters must start with a letter or an underscore and can then have any amount of letters, numbers, or underscores. Values for the parameters can be passed in on the command line or from a parameter file:

--daily.pig
daily     = load 'NYSE_daily' as (exchange:chararray, symbol:chararray,
                date:chararray, open:float, high:float, low:float, close:float,
                volume:int, adj_close:float);
yesterday = filter daily by date == '$DATE';
grpd      = group yesterday all;
minmax    = foreach grpd generate MAX(yesterday.high), MIN(yesterday.low);

When you run daily.pig, you must provide a definition for the parameter DATE; otherwise, you will get an error telling you that you have undefined parameters:

pig -p DATE=2009-12-17 daily.pig

You can repeat the -p command-line switch as many times as needed. Parameters can also be placed in a file, which is convenient if you have more than a few of them. The format of the file is parameter=value, one per line. Comments in the file should be preceded by a #. You then indicate the file to be used with -m or -param_file:

pig -param_file daily.params daily.pig

Parameters passed on the command line take precedence over parameters provided in files. This way, you can provide all your standard parameters in a file and override a few as needed on the command line.

Parameters can contain other parameters. So, for example, you could have the following parameter file:

#Param file
YEAR=2009-
MONTH=12-
DAY=17
DATE=$YEAR$MONTH$DAY

A parameter must be defined before it is referenced. The parameter file here would produce an error if the DAY line came after the DATE line. The other caveat is that there is no special character to delimit the end of a parameter. Any alphanumeric or underscore character will be interpreted as part of the parameter, and any other character will be interpreted as itself. So, if you had a script that ran at the first of every month, you could not do the following:

wlogs = load 'clicks/$YEAR$MONTH01' as (url, pageid, timestamp);

This would try to resolve a parameter MONTH01 when you meant MONTH.

When using parameter substitution, all parameters in your script must be resolved after the preprocessor is finished. If not, Pig will issue an error message and not continue. You can see the results of your parameter substitution by using the -dryrun flag on the Pig command line. Pig will write out a version of your Pig Latin script with the parameter substitution done, but it will not execute the script.

You can also define parameters inside your Pig Latin script using %declare and %default. %declare allows you to define a parameter in the script itself. %default is useful to provide a common default value that can be overridden when needed. Consider a case where most of the time your script is run on one Hadoop cluster, but occasionally it is run on a different cluster with different hardware:

%default parallel_factor 10;
wlogs = load 'clicks' as (url, pageid, timestamp);
grp   = group wlogs by pageid parallel $parallel_factor;
cntd  = foreach grp generate group, COUNT(wlogs);

When running your script in the usual configuration, there is no need to set the parameter parallel_factor. On the occasions it is run in a different setup, the parallel factor can be changed by passing a value on the command line.

Macros

Starting in 0.9, Pig added the ability to define macros. This makes it possible to make your Pig Latin scripts modular. It also makes it possible to share segments of Pig Latin code among users. This can be particularly useful for defining standard practices and making sure all data producers and consumers use them.

Macros are declared with the define statement. A macro takes a set of input parameters, which are string values that will be substituted for the parameters when the macro is expanded. By convention, input relation names are placed first before other parameters. The output relation name is given in a returns statement. The operators of the macro are enclosed in {} (braces). Anywhere the parameters—including the output relation name—are referenced inside the macro, they must be preceded by a $ (dollar sign). The macro is then invoked in your Pig Latin by assigning it to a relation:

--macro.pig
-- Given daily input and a particular year, analyze how
-- stock prices changed on days dividends were paid out.
define dividend_analysis (daily, year, daily_symbol, daily_open, daily_close)
returns analyzed {
    divs          = load 'NYSE_dividends' as (exchange:chararray,
                        symbol:chararray, date:chararray, dividends:float);
    divsthisyear  = filter divs by date matches '$year-.*';
    dailythisyear = filter $daily by date matches '$year-.*';
    jnd           = join divsthisyear by symbol, dailythisyear by $daily_symbol;
    $analyzed     = foreach jnd generate dailythisyear::$daily_symbol,
                        $daily_close - $daily_open;
};

daily   = load 'NYSE_daily' as (exchange:chararray, symbol:chararray,
            date:chararray, open:float, high:float, low:float, close:float,
            volume:int, adj_close:float);
results = dividend_analysis(daily, '2009', 'symbol', 'open', 'close');

It is also possible to have a macro that does not return a relation. In this case, the returns clause of the define statement is changed to returns void. This can be useful when you want to define a macro that controls how data is partitioned and sorted before being stored to a particular output, such as HBase or a database.

These macros are expanded inline. This is where an important difference between macros and functions becomes apparent. Macros cannot be invoked recursively. Macros can invoke other macros, so a macro A can invoke a macro B, but A cannot invoke itself. And once A has invoked B, B cannot invoke A. Pig will detect these loops and throw an error.

Parameter substitution (see “Parameter Substitution”) cannot be used inside of macros. Parameters should be passed explicitly to macros, and parameter substitution should be used only at the top level.

You can use the -dryrun command-line argument to see how the macros are expanded inline. When the macros are expanded, the alias names are changed to avoid collisions with alias names in the place the macro is being expanded. If we take the previous example and use -dryrun to show us the resulting Pig Latin, we will see the following (reformatted slightly to fit on the page):

daily = load 'NYSE_daily' as (exchange:chararray, symbol:chararray,
            date:chararray, open:float, high:float, low:float, close:float,
            volume:int, adj_close:float);
macro_dividend_analysis_divs_0 = load 'NYSE_dividends' as (exchange:chararray,
            symbol:chararray, date:chararray, dividends:float);
macro_dividend_analysis_divsthisyear_0 =
            filter macro_dividend_analysis_divs_0 BY (date matches '2009-.*');
macro_dividend_analysis_dailythisyear_0 = filter daily BY (date matches '2009-.*');
macro_dividend_analysis_jnd_0 =
            join macro_dividend_analysis_divsthisyear_0 by (symbol),
            macro_dividend_analysis_dailythisyear_0 by (symbol);
results = foreach macro_dividend_analysis_jnd_0 generate
            macro_dividend_analysis_dailythisyear_0::symbol, close - open;

As you can see, the aliases in the macro are expanded with a combination of the macro name and the invocation number. This provides a unique key so that if other macros use the same aliases, or the same macro is used multiple times, there is still no duplication.

Including Other Pig Latin Scripts

For a long time in Pig Latin, the entire script needed to be in one file. This produced some rather unpleasant multithousand-line Pig Latin scripts. Starting in 0.9, the preprocessor can be used to include one Pig Latin script in another. Taken together with the macros (also added in 0.9; see “Macros”), it is now possible to write modular Pig Latin that is easier to debug and reuse.

import is used to include one Pig Latin script in another:

--main.pig
import '../examples/ch6/dividend_analysis.pig';

daily   = load 'NYSE_daily' as (exchange:chararray, symbol:chararray,
            date:chararray, open:float, high:float, low:float, close:float,
            volume:int, adj_close:float);
results = dividend_analysis(daily, '2009', 'symbol', 'open', 'close');

import writes the imported file directly into your Pig Latin script in place of the import statement. In the preceding example, the contents of dividend_analysis.pig will be placed immediately before the load statement. Note that a file cannot be imported twice. If you wish to use the same functionality multiple times, you should write it as a macro and import the file with that macro.

In the example just shown, we used a relative path for the file to be included. Fully qualified paths also can be used. By default, relative paths are taken from the current working directory of Pig when you launch the script. You can set a search path by setting the pig.import.search.path property. This is a comma-separated list of paths that will be searched for your files. The current working directory, . (dot), is always in the search path:

set pig.import.search.path '/usr/local/pig,/grid/pig';
import 'acme/macros.pig';

Imported files are not in separate namespaces. This means that all macros are in the same namespace, even when they have been imported from separate files. Thus, care should be taken to choose unique names for your macros.



[15] Those with database experience will notice that this is a violation of the first normal form as defined by E. F. Codd. This intentional denormalization of data is very common in OLAP systems in general, and in large data-processing systems such as Hadoop in particular. RDBMS systems tend to make joins common and then work to optimize them. In systems such as Hadoop, where storage is cheap and joins are expensive, it is generally better to use nested data structures to avoid the joins.

[16] In versions 0.8 and earlier, there is a bug where this flatten is assigned a schema of one field, which is a bytearray, instead of causing the schema to be null. This bug has been fixed in 0.9.

[17] This algorithm was proposed in the paper “Practical Skew Handling in Parallel Joins,” presented by David J. DeWitt, Jeffrey F. Naughton, Donovan A. Schneider, and S. Seshadri at the 18th International Conference on Very Large Databases.

[18] In 0.8 and earlier, the number of records is always 10. In 0.9, this is changed to be the square root of the parallel factor, rounded up.