To make it short, Zeta v097 and v098 make excessive use of the slower Global Memory, therefore the computed nodes per second scale linear with the memory bandwidth and not with the amount of cores or their clock rates.

Here some alternative algorithms to plain MiniMax AlphaBeta search...

• Best-first minimax search by Richard E. Korf and David Maxwell Chickering, http://maxchickering.com/publications/aij96.pdf
• CNS, Conspiracy Number Search
• Monte Carlo Tree Search, with or without UCT extension.
• Nagging, http://www.academia.edu/
• Parallel Game Tree Search on SIMD machines by Holger Hopp and Peter Sanders, http://algo2.iti.kit.edu/sanders/papers/gamet.ps.gz
• Parallel Randomized Best-First Minimax Search by Yaron Shoham and Sivan Toledo, http://www.cs.tau.ac.il/~stoledo/Pubs/rbf-ai.pdf

 

1. SIMT architecture of GPUs
   GPUs consists of tens to hundreds of SIMD or Vector Units that process multiple threads in multiple Warps or Wavefronts in SIMT fashion.
2. Memory architecture of GPUs
   To hide latency of Global Memory (VRAM) GPUs can run multiple Warps or Wavefronts and prefer to do computation by the use of Local or Private Memory. So, the more Work-Items and Work-Groups you run to hide latency, the less Local and Private Memory per thread will be available.
3. Thousands of threads on GPUs
   MiniMax search with Alpha-Beta pruning performs best serial, not parallel.

* edit on 2015-03-30 *

• GPU Chess by Hieronymus
• Parallelis by Philippe Vigier
• GPU Hex by Daniel Shawul
• Chess on GPGPU by Samuel
• perft gpu by Ankan Banerjee
• CudaChess
• NIKOLA Chess
• WeeChess by Ewan Crawford
• Pigeon by Stuart Riffle
• LC0 - Leela Chess Zero
• Tinsmith by Graham Jones
• Eta by Srdja Matovic

 * updated on 2019-03-07 *

Here an overview of what happened before....

Zeta (099m)

• patch for ABDADA parallel search
• disabled RMO parallel search
• removed max device memory limitation
• mods in time control
• cleanups
• Zeta 099m on Nvidia V100, 160 workers, ~ 13.5 Mnps
• Zeta 099m on Nvidia V100, 1 worker, ~ 85 Knps

-- Srdja Matovic 13 Jul 2019

Zeta (099l)

• patch for parallel search scaling
• max device memory increased from 1 GB to 16 GB

-- Srdja Matovic Jun 2019

Zeta (099h to 099k)

• fixes n cleanups
• switch from Lazy SMP to ABDADA parallel search
• added IID - Internal Iterative Deepening
• one cl file for all gpu generations with inlined optimizations
• Zeta 099k on AMD Radeon R9 Fury X, 256 workers, ~ 7.6 Mnps
• Zeta 099k on Nvidia GeForce GTX 750, 16 workers, ~ 800 Knps
• Zeta 099k on AMD Radeon HD 7750, 32 workers, ~ 700 Knps
• Zeta 099k on Nvidia GeForce 8800 GT, 14 workers, ~ 110 Knps

-- Srdja Matovic 2018

Zeta (099b to 099g)

• switch from KoggeStone based move generation to Dumb7Fill
• added atomic features for different gpu generations

-- Srdja Matovic 2017

Zeta (099a)

• switch from best first minimax search to parallel alphabeta (lazy smp)
• ported all (except IID) search techniques from Zeta Dva v0305 to OpenCL
• ported the evaluation function of Zeta Dva v0305 to OpenCL
• vectorized and generalized 64 bit Kogge-Stone move generator
• 64 threads are now coupled to one worker, performing move generation,
  move picking and evaluation, square-wise, in parallel on the same node
• portability over performance, should run on the very first gpus with
  OpenCL 1.x support (>= 2008)

-- Srdja Matovic 2017

Zeta (098d to 098g)

• mostly cleanup and fixes
• restored simple heuristics from Zeta Dva (~2000 Elo on CCRL) engine
• protocol fixes
• fixed autoconfig for AMD gpus
• switched to KoggeStone based move generator
• switched to rotate left based Zobrist hashes
• switched to move picker
• switched to GPL >= 2
• Zeta 098e on Nvidia GeForce GTX 580, ca. 6 Mnps, est. 1800 Elo on CCRL
• Zeta 098e on AMD Radeon HD 7750, ca. 1 Mnps
• Zeta 098e on AMD Phenom X4, ca. 1 Mnps
• Zeta 098e on Nvidia GeForce 8800 GT, ca. 500 Knps

-- Srdja Matovic 2016

Zeta (098a to 098c)

• Improved heuristics, partly ported from the Stockfish chess engine
• AutoConfig for OpenCL devices
• Parameter tuning
• Zeta 098c on Nvidia GeForce GTX 480, ca. 5 Mnps, est. 2000 Elo on CCRL
• Zeta 098c on AMD Radeon R9 290, ca. 3.2 Mnps

-- Srdja Matovic Aug 2013

Zeta (097a to 097z)

• Implementation of an BestFirstMiniMax search algorithm with UCT parameters for parallelization
• Zeta 097x on Nvidia GeForce GTX 480, ca. 5 Mnps, est. 1800 Elo on CCRL
• Zeta 097x on AMD Radeon HD 7750, ca. 800 Knps

-- Srdja Matovic Jan 2013

Zeta (0930 to 0960)

• Tested Monte Carlo Tree Search without UCT across multiple Compute Units of the GPU
• Tested LIFO-Stack based load balancing for AlphaBeta search on one Compute Unit of the GPU
• Tested the 'Nagging' and 'Spam' parallelization approach for AlphaBeta search on one Compute Unit of the GPU
• Tested 'RBFMS', Randomized BestFirstMiniMax Search, a parallelized version of BestFirstMinixMax, across multiple Compute Units of the GPU

-- Srdja Matovic 2012

Zeta (0915 to 0918)

• 64 bit Magic Bitboard Move Generator running
• AlphaBeta search algorithm with 'SPPS'-parallelization running 128 threads on one Compute Unit of the GPU

-- Srdja Matovic 2011

Zeta (0900 to 0910)

• Tested 32 bit 0x88 and 64 bit Magic Bitboard Move Generator
• Ported Heuristics, the Evaluation Function, from CPU engine 'ZetaDva' (~2000 Elo) to OpenCL

-- Srdja Matovic 2010

 

* updated on 2019-07-13 *

Zeta and Zeta Dva support only some basic Xboard protocol commands and some users have reported problems with the configuration and interface of the last Zeta versions.‭ ‬So i will publish the source code again when these parts are more user friendly designed and tested for Windows Chess-GUIs like Winboard or Arena.