Internals of Hash-Join-v4 and Hash-Build-Probe-v4

This document describes the structure and execution of Hash-Join-V4 and Hash-Build-Probe-V4, implemented as hashJoinV4 and hashBuildProbeV4 function.

The Hash-Join-v4 and Hash-Build-Probe-v4 are general primitives to accelerate Hash-Join algorithm utilizing the advantage of high memory bandwidth in Xilinx FPGA. Compared with hashJoinV3 and hashBuildProbeV3, v4 primitive provides Bloom-Filter to avoid redundant access to HBMs which can further reduce the efficiency of Hash-Join algorithm. Hash-Join-v4 performs Hash-Join in single-call mode which means the small table and the big table should be scanned one after another. Hash-Build-Probe-v4 provides a separative solution for build and probe in Hash-Join. In Hash-Build-Probe, incremental build is supported, and the work flow can be scheduled as build0 -> build1 -> probe0 -> build2 -> probe2…

Workload is distributed based on MSBs of hash value of join key to Processing Unit (PU), so that each PU can work independently. Current design uses maximum number of 8 PUs, served by 4 input channels through each of which a pair of key and payload can be passed in each cycle. By the way, overflow processing is provided in this design.

The number of PU is set to 8, as each PU requires two dedicated bank to temporarily store rows in small table (one for base rows and another for overflow rows). Due to DDR/HBM memory access delay, 4 channels can serve enough data to these PUs. Each PU performs HASH-JOIN in 3 phases.

1. Build: with small table as input, the number of keys falls into each hash values are counted. The value of hash counters are stored in bit vector in URAM. Every hash value has a fixed depth of storage in HBM to store rows of small table. If the counter of hash value is larger than the fixed depth, it means that overflow happens. Another bit vector is used for counting overflow rows. In v4 primitive, the overflow hash counter is stored in HBM to save URAM storage for bloom filter bit vector. Also, the overflow of small table will be stored in another area of the HBM.

2. Merge: accumulating the overflow hash counter to get the offsets of each hash value. Then, the overflow rows will be read in from one HBM and write out to another HBM. The output address of overflow rows is according to the offset of its hash value. By operation of Merge, we can put the overflow rows into its right position and waiting for Probe. In order to provide high throughput in this operation, two dedicated HBM ports is required for each PU, which provides read and write accessibilities at the same time.

3. Probe: the big table is read in and filtered by bit vector of bloom filter. It will reduce the size of big table stream. We can get the number of hash collision in hash counter and then the possible matched key and payload pairs can be retrieved from DDR/HBM to join with the big table’s payload after key comparison.

Important

Make sure the size of small table is smaller than the size of HBM buffers. Small table and big table should be fed only ONCE.

Caution

Currently, this primitive expects unique key in small table.

The primitive has only one port for key input and one port for payload input. If your tables are joined by multiple key columns or has multiple columns as payload, please use combineCol to merge the column streams, and use splitCol to split the output to columns.

There is a deep relation in the template parameters of the primitive. In general, the maximum capacity of rows and depth of hash entry is limited by the size of HTB. Each PU has one HTB in this design, and the size of one HTB is equal to the size of one pseudo-channel in HBM. Here is an example of row capacity when PU=8:

HTB Size	Key Size	Payload Size	Row Capacity	Hash Entry	Max Depth for Hash Entry	Overflow Capacity
8x256MB	32 bit	32 bit	64M	1M	63 (base rows take 63M)	1M
8x256MB	128 bit	128 bit	16M	1M	15 (base rows take 15M)	1M

The Number of hash entry is limited by the number of URAM in a single SLR. For example, there are 320 URAMs in a SLR of U280, and 1M hash entry will take 64 URAMs. Because the number of hash entry must be the power of 2, we have to control the size of hash entry in bloom filter and hash counter to avoid crossing SLR logic. This table shows an example for URAM utilization in different size of hash entries:

Bloom Filter Number	Bloom Filter Hash Entry	URAM for Bloom Filter	Hash Entry	URAM for Hash Entry	Total URAM
1	16M(16Mx1bit)	1x64(3x64x64bitx4K)	2M(2Mx16bit)	128(64x64bitx4K)	192
3	16M(16Mx1bit)	3x64(3x64x64bitx4K)	1M(1Mx16bit)	64(64x64bitx4K)	256