08:00 to 09:30 **Registration and Coffee**

09:30 to 09:45 **Welcome and Introduction**

09:45 to 10:45 **SESSION 1: Keynote Talk**

Chair: Sylvie Boldo

**Calculating in Floating Sexagesimal Place Value
Notation, 4000 years ago**
(slides)

*Christine Proust, Laboratoire SPHERE (CNRS & Université Paris
Diderot), France*

Abstract: By the end of the third millennium BCE in Mesopotamia an innovation of major significance for the history of mathematics occurred: the sexagesimal place value notation. A sophisticated mathematical culture was subsequently developed by masters attached to the scribal schools that flourished in Iraq, Iran and Syria during the first centuries of the second millennium BCE. The best known aspect of this mathematical culture is the art of solving quadratic problems. The numerical algorithms exploiting the properties of base 60 and the floating notation are less known. This talk presents some of these algorithms, especially those based on factorization methods.

10:45 to 11:45 **SESSION 2: Arithmetic Units 1**

Chair: Neil Burgess

**Low-Cost Duplicate Multiplication**
(slides)

*Michael Sullivan and Earl Swartzlander*

**Minimizing Energy by Achieving Optimal
Sparseness in Parallel Adders**
(slides)

*Mustafa Aktan, Dursun Baran, and Vojin Oklobdzija*

12:00 to 13:30 **Lunch**

13:30 to 14:30 **SESSION 3: Arithmetic Units 2**

Chair: Vojin Oklobdzija

**An Efficient Softcore Multiplier Architecture
for Xilinx FPGAs**
(slides)

*Martin Kumm, Shahid Abbas, and Peter Zipf*

**Design and Implementation of an Embedded FPGA
Floating Point DSP Block**

*Martin Langhammer and Bogdan Pasca*

14:45 to 15:45 **SESSION 4: Elementary and Special Functions 1**

Chair: Peter Tang

**Hardware implementations of fixed-point
Atan2**
(slides)

*Matei Istoan and Florent de Dinechin*

**A robust general-purpose method for faithfully
rounded floating-point function approximation in FPGAs**
(slides)

*David Thomas*

16:00 to 17:00 **Ceremony**

**Presentation of the Medal of École Normale
Supérieure de Lyon to Milos Ercegovac by the President of ENS Lyon**
(slides)

17:00 to 18:30 **SPECIAL SESSION on the State of
the Art of FP Units**

Chair: Alberto Nannarelli

**Intel(r) AVX-512 Instructions and Their Use in
the Implementation of Math Functions**
(slides)

*Marius Cornea, INTEL, USA*

**Floating-point Arithmetic in AMD Processors**
(slides)

*Michael Schulte, AMD, USA*

**The IBM z13 SIMD Accelerators for Integer,
String, and Floating-Point**
(slides)

*Eric Schwarz, IBM, USA*

**ARM FPUs: Low Latency is Low Energy**
(slides)

*David Lutz, ARM, USA*

08:00 to 09:30 **SESSION 5: Elementary and Special Functions 2**

Chair: Naofumi Takagi

**Precise and fast computation of elliptic
integrals and functions**
(slides)

*Toshio Fukushima*

**Code generators for mathematical functions**
(slides)

*Nicolas Brunie, Florent de Dinechin, Olga Kupriianova, and Christoph Lauter*

**Semi-Automatic Floating-Point Implementation of
Special Functions**
(slides)

*Christoph Lauter and Marc Mezzarobba*

09:30 to 10:00 **Coffee Break**

10:00 to 11:00 **SESSION 6: Keynote Talk**

Chair: David Hough

**The End of Numerical Error**
(slides)

*John Gustafson*

Abstract: It is time to overthrow a century of
methods based on floating point arithmetic. Current technical computing
is based on the acceptance of rounding error using numerical
representations that were invented in 1914, and acceptance of sampling
error using algorithms designed for a time when transistors were very
expensive. By sticking to an antiquated storage format (now codified as
an IEEE standard) well into the exascale area, we are wasting power,
energy, storage, bandwidth, and programmer effort. The pursuit of
exascale floating point is ridiculous, since we do not need to be making
10^{18} sloppy rounding errors per second; we need instead to get
provable, valid results for the first time, by turning the speed of
parallel computers into higher quality answers instead of more junk per
second.

We introduce the 'unum' (universal number), a superset of IEEE Floating Point, that contains extra metadata fields that actually save storage, yet give more accurate answers that do not round, overflow, or underflow. The potential they offer for improved programmer productivity is enormous. They also provide, for the first time, the hope of a numerical standard that guarantees bitwise identical results across different computer architectures. Unum format is the basis for the 'ubox' method, which redefines what is meant by "high performance" by measuring performance in terms of the knowledge obtained about the answer and not the operations performed per second. Examples are given for practical application to structural analysis, radiation transfer, the n-body problem, linear and nonlinear systems of equations, and Laplace's equation. This is a fresh approach to scientific computing that allows proper, rigorous representation of real number sets for the first time.

11:00 to 12:00 **SESSION 7: Medium and Multiple Precision 1**

Chair: Eric Schwarz

**Faster FFTs in medium precision**

*Joris van der Hoeven and Grégoire Lecerf*

**Efficient implementation of elementary
functions in the medium-precision range**

*Fredrik Johansson*
(slides)

12:00 to 13:30 **Lunch**

13:30 to 14:30 **SESSION 8: Medium and Multiple Precision 2**

Chair: Michael Schulte

**Efficient divide-and-conquer multiprecision
integer division**
(slides)

*William Hart*

**Reliable evaluation of the Worst-Case Peak Gain matrix in multiple precision**
(slides)

*Anastasia Volkova, Thibault Hilaire, and Christoph Lauter*

14:30 to 15:00 **Coffee Break**

15:00 to 16:00 **SESSION 9: Keynote Talk**

Chair: Milos Ercegovac

**Numerical challenges in long term integrations
of the Solar system**

*Jacques Laskar, CNRS, Observatoire de Paris, France*

Abstract: Long time integrations of the planetary motion in the Solar System has been a challenging work in the past decades. The progress have followed the improvements of computer technology, but also the improvements in the integration algorithms. This quest has led to the development of high order dedicated symplectic integrators that have a stable behavior over long time scales. As important in the increase of the computing performances is the use of parallel algorithms that have divided the computing times by an order of magnitude. A specific aspect of these long term computation is also a careful monitoring of the accumulation of the roundoff error in the numerical algorithms, where all bias should be avoided. It should also be noted that for these computations, not only compensated summation is required, but also 80 bits extended precision floating point arithmetics.

Integrating the equation of motion is only a part of the work. One needs also to determine precise initial conditions in order to ensure that the long time integration represent actually the motion of the real Solar System.

Once these steps are fulfilled, the main limitation in the obtention of a precise solution of the planetary motion will be given by the chaotic nature of the Solar system that will strictly limit the possibility of precise prediction for the motion of the planets to about 60 Myr.

16:00 to 17:00 **SESSION 10: Residue Number Systems**

Chair: David Matula

**Contributions to the Design of Residue Number
System Architectures**
(slides)

*Benoît Gérard, Jean-Gabriel Kammerer, and Nabil Merkiche*

**RNS Arithmetic Approach in Lattice-based
Cryptography - Accelerating the "Rounding-off" Core Procedure**
(slides)

*Jean-Claude Bajard, Julien Eynard, Nabil Merkiche, and Thomas Plantard*

17:45 to 22:00 **Visit of the "Musée des
Confluences" and Conference banquet**

08:00 to 10:00 **SESSION 11: Modular and Finite-Field Arithmetic**

Chair: Peter Kornerup

**Modulo-(2 ^{n}-2^{q}-1) Parallel
Prefix Addition via Excess-Modulo Encoding of Residues**
(slides)

**New Bit-Level Serial GF(2 ^{m})
Multiplication Using Polynomial Basis**
(slides)

**Modular multiplication and division algorithms based on continued fraction expansion**
(slides)

*Mourad Gouicem*

**Efficient Modular Exponentiation Based on
Multiple Multiplications by a Common Operand**
(slides)

*Christophe Negre, Thomas Plantard, and Jean-Marc Robert*

10:00 to 10:30 **Coffee Break**

10:30 to 12:00 **SESSION 12: Miscellaneous**

Chair: Javier Bruguera

**Reproducible Tall-Skinny QR factorization**
(slides)

*Hong Diep Nguyen and James Demmel*

**An Automatable Formal Semantics for IEEE-754
Floating-Point Arithmetic**
(slides)

*Martin Brain, Cesare Tinelli, Philipp Ruemmer, and Thomas Wahl*

**The exact real arithmetical algorithm in binary
continued fractions**
(slides)

*Petr Kurka*

12:00 to 12:30 **Conference Close and Final Remarks**

12:30 to 14:00 **Lunch**

Afternoon **Visit of the old Lyon**