Advances in the Parallelization of Music and Audio Applications

1. Advances in the Parallelization of Music and Audio Applications Eric Battenberg, David Wessel & Juan Colmenares

2. Overview • Parallelism today in the popular interactive music languages • Parallel Partitioned Convolution • Accelerating Non-Negative Matrix Factorization (NMF) for use in audio source separation and music information retrieval and the importance of Selective, Embedded Just In Time Specialization (SEJITS) • Real-time in the Tessellation OS • A plea for more flexible I/0 with GPUs

3. Current Support for Parallelism is Copy-Based • The widely used languages for music and audio applications are fundamentally sequential in character – this includes Max/MSP, PD, SuperCollider, and CHUCK among others. • Limited multithreading • One approach to exploiting multi-core processors is to run copies of the applications on separate cores. • Max/MSP provides a useful multi-threading mechanism called poly~ . • PD provides PD~ each instance of which runs in a separate thread inside a PD patch.

4. Partitioned Convolution • First real-time app in the Par Lab. • Partitioned Convolution – an efficient way to do low-latency filtering with a long (> 1 sec) impulse response. • Important in real-time reverb processing for environment simulation. • Sound examples: …convolved with a sine sweep Acoustic Guitar …in a giant mausoleum Impulse response Impulse response

5. Partitioned Convolution • Convolution: a way to do linear filtering with a finite impulse response (FIR) filter. • Direct convolution: • For length L filter, O(L) ops per output point, zero delay. • L can be greater than 100,000 samples (> 3 sec of audio) • Block FFT Convolution: • Only O(log(L)) ops per output point, but delay of L. • How can we trade off between complexity and latency? x y FFT Complex Mult IFFT H H = FFT(h)

6. Uniform Partitioned Convolution • We would like the latency to be less than 10ms (512 samples) • Cut an impulse response up into equal-sized blocks. • Then we can use a parallellayout of Block FFT convolverswith delays to implement the filter. • The latency is now N, and we still get complexity savings. 1 2 3 4 5 L N Block FFT Convolver x 1 delay(N) 2 delay(N) + y 3 delay(N) 4 delay(N) 5

7. Frequency Delay Line Convolution • We can also exploit linearity of the FFT so that only one FFT/IFFT is required. • So the parallel Block FFT Convolver above becomes a Frequency Delay Line (FDL) Convolver: x 1 delay(N) + y 2 Block FFT Convolver delay(N) 3 IFFT FFT Complex Mult H1 H1 x FFT Complex Mult delay(N) H2 + y IFFT Complex Mult delay(N) H3 Complex Mult Frequency Delay Line Convolver

8. Multiple FDL Convolution • If L is big (e.g. > 100,000) and N is small (e.g. < 1000), our FDL will have 100’s of partitions to handle. • We can connect multiple FDL’s in parallel to get the best of both worlds. x FDL y x FDL 1 delay(Nx6) + FDL 2 y delay(4Nx4) FDL 3

9. Scheduling Multiple FDLs • FDLs are run in separate threads. • Each is allowed to compute for a length of time corresponding to its block size. • Synchronization is performed at the vertical lines.

10. Auto-Tuning for Real-Time • We are not trying to only maximize throughput. • We are trying to improve our ability to make real-time guarantees. • For now, we estimate a Worst-Case Execution Time (WCET) for each size of FDL. • Then we combine the FDLs that are most likely to meet their scheduling deadlines. • In the future, we will use a notion of predictability along with more robust scheduling. • We are finishing development on a Max/MSP object, Audio Unit plugin, and a portable standalone version of this.

11. Accelerating Non-Negative Matrix Factorization (NMF) NMF is widely used in audio source separation. The idea is to factor the time/frequency representation (spectogram) into source coupled spectral (W) and gain (H) matricies.

12. The Importance of SEJITSin Developing an Information Retrieval (MIR) Application • Rather using a domain restricted language developers write in a full blown scripting language such as PYTHON or RUBY. • Functions are selected by annotation as performance critical. • If efficiency layer implementations of these functions are available appropriate code is generated and JIT compiled. • If not the selected function is executed in the scripting language itself. • The scripted implementation remains as the portable reference implementation.

13. A real-time application in Tessellation In cooperation with the OS Group Music Program Additional Cells Input Output Filter Parallel version of a partition-based convolution algorithm F Most of the engine’s functionality Intermediate Deadline End-to-end Deadline F Channel 2nd-level RT scheduler A 2nd-level RT scheduler B Shell Sound card Cell B Cell A Initial Cell Audio Processing & Synthesis Engine With this simple music computer application we expect to initially show that Tessellation can provide acceptable performance and time predictability Audio Input

14. Cell 1.A) Cell and Space Partitioning • A Spatial Partition (or Cell) comprises a group of processors acting within a hardware boundary • Each cell receives a vector of basic resources • Some number of processors, a portion of physical memory, a portion of shared cache memory, and potentially a fraction of memory bandwidth • A cell may also receive • Exclusive access to other resources (e.g., certain hardware devices and raw storage partition) • Guaranteed fractional services (i.e., QoS guarantees) from other partitions (e.g., network service and file service) CPU CPU CPU CPU CPU CPU 2nd-level Scheduling L1 L1 L1 L1 L1 L1 L1 Interconnect Tessellation Kernel (Partition Support) L2 Bank L2 Bank L2 Bank L2 Bank L2 Bank L2 Bank DRAM & I/O Interconnect (+) Fraction of memory bandwidth DRAM DRAM DRAM DRAM DRAM DRAM (*) Bottom part of the diagram was adapted from Liu and Asanovic, “Mitosys: ParLabManycore OS Architecture,” Jan. 2008.

15. Example of Music Application Music program Audio-processing / Synthesis Engine (Pinned/TT partition) Time-sensitive Network Subsystem Input device (Pinned/TT Partition) Output device (Pinned/TT Partition) GUI Subsystem Network Service (Net Partition) Graphical Interface (GUI Partition) Communication with other audio-processing nodes Preliminary

16. A plea for more flexible GPU I/O

17. Thanks for your attention.

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19. Large Compute-Bound Application Large Compute-Bound Application Large Compute-Bound Application Large Compute-Bound Application NetworkQoS NetworkQoS NetworkQoS NetworkQoS Monitor And Adapt Monitor And Adapt Monitor And Adapt Monitor And Adapt Large I/O-Bound Application Large I/O-Bound Application Large I/O-Bound Application Large I/O-Bound Application Other Devices Other Devices Other Devices Other Devices Persistent Storage & Parallel File System Persistent Storage & Parallel File System Persistent Storage & Parallel File System Persistent Storage & Parallel File System Disk I/O Drivers Disk I/O Drivers Disk I/O Drivers Disk I/O Drivers Tessellation in Server Environment QoS Guarantees QoS Guarantees Cloud Storage BW QoS QoS Guarantees QoS Guarantees Tessellation OS