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Modular SIMD arithmetic in Mathemagix

Joris Van Der Hoeven, Grégoire Lecerf, Guillaume Quintin
2016 ACM Transactions on Mathematical Software  
Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes.  ...  In this article, we survey existing algorithms for modular integer arithmetic, and present detailed vectorized counterparts.  ...  Mathemagix 0.0060 0.022 0.095 0.44 2.3 13 Modular SIMD arithmetic in Mathemagix Joris van der Hoeven, Grégoire Lecerf, Guillaume Quintin Modular SIMD arithmetic in Mathemagix  ... 
doi:10.1145/2876503 fatcat:jfnjpisdanh5plurfmsoiz6tfi

Modular SIMD arithmetic in Mathemagix [article]

Joris van der Hoeven, Grégoire Lecerf, Guillaume Quintin
2014 arXiv   pre-print
Modular integer arithmetic occurs in many algorithms for computer algebra, cryptography, and error correcting codes.  ...  In this article, we survey existing algorithms for modular integer arithmetic, and present detailed vectorized counterparts.  ...  Mathemagix 0.0060 0.022 0.095 0.44 2.3 13 Modular SIMD arithmetic in Mathemagix Joris van der Hoeven, Grégoire Lecerf, Guillaume Quintin  ... 
arXiv:1407.3383v1 fatcat:5hmk2abyzndfzbz3wndajxekb4

Faster FFTs in Medium Precision

Joris van der Hoeven, Gregoire Lecerf
2015 2015 IEEE 22nd Symposium on Computer Arithmetic  
The main idea behind our algorithms is to develop efficient vectorial multiple precision fixed point arithmetic, capable of exploiting SIMD instructions in modern processors.  ...  On the other hand, asymptotically fast algorithms for multiple precision arithmetic do not pay off yet.  ...  Redundant representations have also found some use in modular arithmetic. For instance, they recently allowed to speed up modular FFTs [13] .  ... 
doi:10.1109/arith.2015.10 dblp:conf/arith/HoevenL15 fatcat:zhxjeow6gnhz7p5di5ql4e5mqu

Interfacing mathemagix with C++

Joris van der Hoeven, Grégoire Lecerf
2013 Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation - ISSAC '13  
In this paper, we give a detailed description of the interface between the Mathemagix language and C++.  ...  In particular, we describe the mechanism which allows us to import a C++ template library (which only permits static instantiation) as a fully generic Mathemagix template library.  ...  Acknowledgments We would like to thank Jean-Charles Faugère for helping us in the interface with FGb, and also Karim Belabas and Bill Allombert for their precious advices in the design of our interface  ... 
doi:10.1145/2465506.2465511 dblp:conf/issac/HoevenL13 fatcat:or72t4ckqjfyviddrspbxmggr4

Simultaneous Conversions with the Residue Number System Using Linear Algebra

Javad Doliskani, Pascal Giorgi, Romain Lebreton, Eric Schost
2018 ACM Transactions on Mathematical Software  
CCS Concepts: •Mathematics of computing → Mathematical software performance; Computations in finite fields; Computations on matrices; •Theory of computation → Design and analysis of algorithms;  ...  In this paper, we are interested in the latter kind of computation, specifically in the context of multi-precision arithmetic.  ...  FLINT (classic) with some hand-tuned inline integer arithmetic, and multi-modular algorithm FLINT (multi-modular) using divide-and-conquer techniques for conversions to and from the RNS.  ... 
doi:10.1145/3145573 fatcat:fuoxsgt4w5aqloywzp4xld36cm

Intel HEXL: Accelerating Homomorphic Encryption with Intel AVX512-IFMA52 [article]

Fabian Boemer, Sejun Kim, Gelila Seifu, Fillipe D. M. de Souza, Vinodh Gopal
2021 arXiv   pre-print
Two of the biggest performance bottlenecks in HE primitives and applications are polynomial modular multiplication and the forward and inverse number-theoretic transform (NTT).  ...  Intel HEXL also provides up to 6.0x speedup on the element-wise vector-vector modular multiplication, and 1.7x speedup on the element-wise vector-scalar modular multiplication.  ...  The Mathemagix library [17] provides Intel AVX-accelerated implementations of modular integer arithmetic using a SIMD programming model.  ... 
arXiv:2103.16400v3 fatcat:sfnjonx7orhgrgvo7gbrn2h6za

Fast Polynomial Multiplication over F260

David Harvey, Joris van der Hoeven, Grégoire Lecerf
2016 Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16  
Our Mathemagix implementation is based on the automatic generation of assembly codelets.  ...  Can post-SchönhageStrassen multiplication algorithms be competitive in practice for large input sizes?  ...  On the current platform this is not yet a problem: fully vectorized arithmetic in F 2 60[z ; y] / (P k (z); Q (z; y)) would also require SIMD versions of carry-less multiplication which are not available  ... 
doi:10.1145/2930889.2930920 dblp:conf/issac/HarveyHL16 fatcat:3uwa3q4i3rgljmwplbfl43plji

Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic

Fredrik Johansson
2017 IEEE transactions on computers  
Arb is a C library for arbitrary-precision interval arithmetic using the midpoint-radius representation, also known as ball arithmetic.  ...  The core number types are designed for versatility and speed in a range of scenarios, allowing performance that is competitive with non-interval arbitrary-precision types such as MPFR and MPC floating-point  ...  Special thanks go to the people who have made contributions to Arb: Bill Hart, Alex Griffing, Pascal Molin, and many others who are credited in the documentation.  ... 
doi:10.1109/tc.2017.2690633 fatcat:u7nre2c7vzb3racekrrav4slfi