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Fast Computation of Database Operations using Graphics Processors Naga K. Govindaraju Univ. of North Carolina Modified By, Mahendra Chavan for CS632 Goal • Utilize graphics processors for fast computation of common database operations Motivation: Fast operations • Increasing database sizes • Faster processor speeds but low improvement in query execution time – Memory stalls – Branch mispredictions – Resource stalls Eg. Instruction dependency • Utilize the available architectural features and exploit parallel execution possibilities Graphics Processors • Present in almost every PC • Have multiple vertex and pixel processing engines running parallel • Can process tens of millions of geometric primitives per second • Peak Perf. Of GPU is increasing at the rate of 2.5-3 times a year! • Programmable- fragment programs – executed on pixel processing engines Main Contributions • Algorithms for predicates, boolean combinations and aggregations • Utilize SIMD capabilities of pixel processing engines • They have used these algorithms for selection queries on one or more attributes and aggregate queries Related Work • Hardware Acceleration for DB operations – Vector processors for relational DB operations [Meki and Kambayashi 2000] – SIMD instructions for relational DB operations [ Zhou and Ross 2002] – GPUs for spatial selections and joins [Sun et al. 2003] Graphics Processors: Design Issues • Programming model is limited due to lack of random access writes – Design algorithms avoiding data rearrangements • Programmable pipeline has poor branching – Design algorithms without branching in programmable pipeline - evaluate branches using fixed function tests Frame Buffer • Pixels stored on graphics card in a frame buffer. • Frame buffer conceptually divided into: • Color Buffer – Stores color component of each pixel in the frame buffer • Depth Buffer – Stores depth value associated with each pixel. The depth is used to determine surface visibility • Stencil Buffer – Stores stencil value for each pixel . Called Stencil because, it is typically used for enabling/disabling writes to frame buffer Graphics Pipeline Vertices Vertex Processing Engine Setup Engine Pixel processing Engine Alpha Test Stencil Test Depth Test Graphics Pipeline • Vertex Processing Engine – Transforms vertices to points on screen • Setup Engine – Generates Info. For color, depth etc. associated with primitive vertices • Pixel processing Engines – Fragment processors, performs a series of tests before writing the fragments to frame buffer Pixel processing Engines • Alpha Test – Compares fragments alpha value to user-specified reference value • Stencil Test – Compares fragments’ pixel’s stencil value to user-specified reference value • Depth Test – Compares depth value of the fragment to the reference depth value. Operators • = • < • > • <= • >= • Never • Always Fragment Programs • Users can supply custom fragment programs on each fragment Occlusion Query •Gives no. of fragments that pass different no. of tests Radeon R770 GPU by AMD Graphics Product Group Data Representation on GPUs • Textures – 2 D arrays- may have multiple channels • We store data in textures in floating point formats • To perform computations on the values, render the quadrilateral, generate fragments, run fragment programs and perform tests! Stencil Tests • Fragments failing Stencil test are rejected from the rasterization pipeline • Stencil Operations – – – – – – KEEP: keep the stencil value in the stencil buffer INCR: stencil value ++ DECR: stencil value – ZERO: stencil value = 0 REPLACE: stencil value = reference value INVERT: bitwise invert (stencil value) Stencil and Depth Tests • We can setup the stencilOP routine as below • For each fragment , three possible outcomes, based on the outcome, corresponding stencil op. is executed • Op1: when a fragment fails stencil test • Op2: when a fragment passes stencil test but fails depth test • Op3: when a fragment passes stencil and depth test Outline • Database Operations on GPUs • Implementation & Results • Analysis • Conclusions Outline • Database Operations on GPUs • Implementation & Results • Analysis • Conclusions Overview • Database operations require comparisons • Utilize depth test functionality of GPUs for performing comparisons – Implements all possible comparisons <, <=, >=, >, ==, !=, ALWAYS, NEVER • Utilize stencil test for data validation and storing results of comparison operations Basic Operations Basic SQL query Select A From T Where C A= attributes or aggregations (SUM, COUNT, MAX etc) T=relational table C= Boolean Combination of Predicates (using operators AND, OR, NOT) Outline: Database Operations • Predicate Evaluation – (a op constant) – depth test and stencil test – (a op b) = (a-b op 0 ) – can be executed on GPUs • Boolean Combinations of Predicates – Express as CNF and repetitively use stencil tests • Aggregations – Occlusion queries Outline: Database Operations • Predicate Evaluation • Boolean Combinations of Predicates • Aggregations Basic Operations • Predicates – ai op constant or ai op aj – Op is one of <,>,<=,>=,!=, =, TRUE, FALSE • Boolean combinations – Conjunctive Normal Form (CNF) expression evaluation • Aggregations – COUNT, SUM, MAX, MEDIAN, AVG Predicate Evaluation • ai op constant (d) – Copy the attribute values ai into depth buffer – Define the comparison operation using depth test – Draw a screen filling quad at depth d ai op d If ( ai op d ) pass fragment P Else reject fragment Screen d Predicate Evaluation • ai op aj – Treat as (ai – aj) op 0 • Semi-linear queries – Defined as linear combination of attribute values compared against a constant – Linear combination is computed as a dot product of two vectors – Utilize the vector processing capabilities of GPUs Data Validation • Performed using stencil test • Valid stencil values are set to a given value “s” • Data values that fail predicate evaluation are set to “zero” Outline: Database Operations • Predicate Evaluation • Boolean Combinations of Predicates • Aggregations Boolean Combinations • Expression provided as a CNF • CNF is of form (A1 AND A2 AND … AND Ak) where Ai = (Bi1 OR Bi2 OR … OR Bimi ) • CNF does not have NOT operator – If CNF has a NOT operator, invert comparison operation to eliminate NOT Eg. NOT (ai < d) => (ai >= d) Boolean Combination • We will focus on (A1 AND A2) • All cases are considered – A1 = (TRUE AND A1) – If Ei = (A1 AND A2 AND … AND Ai-1 AND Ai), Ei = (Ei-1 AND Ai) • Clear stencil value to 1 • For each Ai , i=1,….,k • do – if (mod(I,2)) /* Valid stencil value is 1 */ • Stencil test to pass if stencil value is equal to 1 • StencilOp (KEEP,KEPP, INCR) – Else • Stencil test to pass if stencil value is equal to 2 • StencilOp (KEEP,KEPP, DECR) – Endif – For each Bij, j=1,…..,mi – Do • Perform Bij using COMPARE /* depth test */ – End for – If (mod(I,2)) /* valid stencil value is 2 */ • If stencil value on screen is 1 , REPLACE with 0 – Else /* valid stencil value is 1 */ • If stencil value on screen is 2, REPLACE with 0 – Endif • End For A1 AND A2 B23 A1 B22 B21 A1 AND A2 Stencil value = 1 A1 AND A2 Stencil value = 1 A1 A1 AND A2 Stencil value = 0 Stencil value = 2 A1 A1 AND A2 St = 0 St=2 St=0 St=1 B22 A1 St=1 B23 St=1 B21 A1 AND A2 Stencil = 0 St = 0 St=1 B22 A1 St=1 B23 St=1 B21 A1 AND A2 St = 0 St = 1 A1 AND B22 St=1 A1 AND B23 St=1 A1 AND B21 Range Query • Compute ai within [low, high] – Evaluated as ( ai >= low ) AND ( ai <= high ) Outline: Database Operations • Predicate Evaluation • Boolean Combinations of Predicates • Aggregations Aggregations • COUNT, MAX, MIN, SUM, AVG • No data rearrangements COUNT • Use occlusion queries to get pixel pass count • Syntax: – – – – Begin occlusion query Perform database operation End occlusion query Get count of number of attributes that passed database operation • Involves no additional overhead! MAX, MIN, MEDIAN • We compute Kth-largest number • Traditional algorithms require data rearrangements • We perform no data rearrangements, no frame buffer readbacks K-th Largest Number • Say vk is the k-th largest number • How do we generate a number m equal to vk? – Without knowing vk’s bit-representation and using comparisons Our algorithm • b_max = max. no. of bits in the values in tex • x=0 • For i= b_max-1 down to 0 – Count = Compare (text >= x + 2^i) – If Count > k-1 • x=x+2^i • Return x K-th Largest Number • Lemma: Let vk be the k-th largest number. Let count be the number of values >= m – If count > (k-1): m<= vk – If count <= (k-1): m>vk • Apply the earlier algorithm ensuring that count >(k1) Example • Vk = 11101001 • M = 00000000 Example • Vk = 11101001 • M = 10000000 • M <= Vk Example • Vk = 11101001 • M = 11000000 • M <= Vk Example • Vk = 11101001 • M = 11100000 • M <= Vk Example • Vk = 11101001 • M = 11110000 • M > Vk Make the bit 0 M = 11100000 Example • Vk = 11101001 • M = 11101000 • M <= Vk Example • Vk = 11101001 • M = 11101100 • M > Vk • Make this bit 0 • M = 11101000 Example • Vk = 11101001 • M = 11101010 • M > Vk • M = 11101000 Example • Vk = 11101001 • M = 11101001 • M <= Vk Example • Integers ranging from 0 to 255 • Represent them in depth buffer – Idea – Use depth functions to perform comparisons – Use NV_occlusion_query to determine maximum Example: Parallel Max • S={10,24,37,99,192,200,200,232} • Step 1: Draw Quad at 128 – S = {10,24,37,99,192,200,200,232} • Step 2: Draw Quad at 192 – S = {10,24,37,192,200,200,232} • Step 3: Draw Quad at 224 – S = {10,24,37,192,200,200,232} • Step 4: Draw Quad at 240 – No values pass • Step 5: Draw Quad at 232 – S = {10,24,37,192,200,200,232} • Step 6,7,8: Draw Quads at 236,234,233 – No values pass • Max is 232 SUM and AVG • Mipmaps – multi resolution textures consisting of multiple levels • Highest level contains average of all values at lowest level • SUM = AVG * COUNT • Problems with mipmaps – If we want sum of a subset of values then we have to introduce conditions in the fragment programs – Floating point representations may have problems Accumulator • Data representation is of form • ak 2k + ak-1 2k-1 + … + a0 Sum = sum(ak) 2k+ sum(ak-1) 2k-1+…+sum(a0) Current GPUs support no bit-masking operations AVG = SUM/COUNT TestBit • Read the data value from texture, say ai • F= frac(ai/2k+1) • If F>=0.5, then k-th bit of ai is 1 • Set F to alpha value. Alpha test passes a fragment if alpha value>=0.5 Outline • Database Operations on GPUs • Implementation & Results • Analysis • Conclusions Implementation • Dell Precision Workstation with Dual 2.8GHz Xeon Processor • NVIDIA GeForce FX 5900 Ultra GPU • 2GB RAM Implementation • CPU – Intel compiler 7.1 with hyperthreading, multithreading, SIMD optimizations • GPU – NVIDIA Cg Compiler Benchmarks • TCP/IP database with 1 million records and four attributes • Census database with 360K records Copy Time Predicate Evaluation (3 times faster) Range Query(5.5 times faster) Multi-Attribute Query (2 times) Semi-linear Query (9 times faster) COUNT • Same timings for GPU implementation Kth-Largest for median(2.5 times) Kth-Largest Kth-Largest conditional Accumulator(20 times slower!) Outline • Database Operations on GPUs • Implementation & Results • Analysis • Conclusions Analysis: Issues • Precision – Currently depth buffer has only 24 bit precision , inadequate • Copy time – Copy from texture to depth buffer – no mechanism in GPU • Integer arithmetic – Not enough arithmetic inst. In pixel processing engines • Depth compare masking – Useful to have comparison mask for depth function Analysis: Issues • Memory management – Current GPUS have 512 MB video memory, we may use the out-of–core techniques and swap • No random writes – No data re-arrangements possible Analysis: Performance • Relative Performance Gain – High Performance – Predicate evaluation, multi-attribute queries, semi-linear queries, count – Medium Performance – Kth-largest number – Low Performance - Accumulator High Performance • Parallel pixel processing engines • Pipelining – Multi-attribute queries get advantage • Early Depth culling – Before passing through the pixel processing engine • Eliminate branch mispredictions Medium Performance • Parallelism • FX 5900 has clock speed 450MHz, 8 pixel processing engines • Rendering single 1000x1000 quad takes 0.278ms • Rendering 19 such quads take 5.28ms. Observed time is 6.6ms • 80% efficiency in parallelism!! Low Performance • No gain over SIMD based CPU implementation • Two main reasons: – Lack of integer-arithmetic – Clock rate Outline • Database Operations on GPUs • Implementation & Results • Analysis • Conclusions Conclusions • Novel algorithms to perform database operations on GPUs – • Evaluation of predicates, boolean combinations of predicates, aggregations Algorithms take into account GPU limitations – – No data rearrangements No frame buffer readbacks Conclusions • Preliminary comparisons with optimized CPU implementations is promising • Discussed possible improvements on GPUs • GPU as a useful co-processor Relational Joins • Modern GPUs have thread groups • Each thread group have several threads • Data Parallel primitives – Map – Scatter – scatters the Data of a relation with respect to an array L – Gather – reverse of scatter – Split – Divides the relation into a number of disjoint partitions with a given partitioning function NINLJ R Thread Group 1 S Thread Group j Thread Group i Thread Group Bp INLJ • Used Cache Optimized Search Trees (CSS trees) for index structure • Inner relation as the CSS tree • Multiple keys are searched in parallel on the tree Sort Merge join • Merge step is done in parallel • 3 steps – Divide relation S into Q chunks Q= ||S|| / M – Find the corresponding matching chunks from R by using the start and end of each chunk of S – Merge each pair of S and R chunk in parallel. 1 thread group per pair. Hash join • Partitioning – Use the Split primitive to partition both the relations • Matching – Read the inner relation in memory relation – Each tuple from the outer relation uses sequential/binary search on the inner relation – For binary search, the inner relation will be sorted using bitonic sort.