Publications related to Arbitrary-precision arithmetic

Generalized programmable counter arrays

Philip Brisk, Alessandro Cevrero, Hadi Parandeh Afshar

A Generalized Programmable Counter Array (GPCA) is a reconfigurable multi-operand adder, which can be reprogrammed to sum a plurality of operands of arbitrary size. The GPCA is configured to compress the input words down to two operands using parallel coun ...

2014

A New Basic Logic Structure for Data-Path Computation

Giovanni De Micheli, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù

Nowadays, Field Programmable Gate Arrays (FPGA) implement arithmetic functions using specific circuits at the logic block level, such as the carry paths, or at the structure level adopting Digital Signal Processing (DSP) blocks. Nevertheless, all these app ...

2014

Fast and accurate CMB computations in non-flat FLRW universes

Julien Lesgourgues

We present a new method for calculating CMB anisotropies in a non-flat Friedmann universe, relying on a very stable algorithm for the calculation of hyperspherical Bessel functions, that can be pushed to arbitrary precision levels. We also introduce a new ...

Iop Publishing Ltd2014

Generalized Bombieri-Lagarias' Theorem And Generalized Li'S Criterion With Its Arithmetic Interpretation

We show that Li's criterion equivalent to the Riemann hypothesis, i.e., the statement that the sums k(n) = Sigma(rho)(1-(1-1/rho)(n)) over zeros of the Riemann xi-function and the derivatives lambda(n) equivalent to 1/(n-1)! d(n)/dz(n)(z(n-1) ln (xi(z)))ve ...

Springer Verlag2014

Almost Polynomial Factor Hardness for Closest Vector Problem with Preprocessing

Nisheeth Vishnoi

We prove that for an arbitrarily small constant < 0, the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor 2log1-en, under the assumption that NP ⊈ SIZE(2logO(1/e)n). © 2014 Soc ...

Society for Industrial and Applied Mathematics2014

On the Generation of Precise Fixed-Point Expressions

Viktor Kuncak, Eva Darulova, Indranil Saha

Several problems in the implementations of control systems, signal-processing systems, and scientific computing systems reduce to compiling a polynomial expression over the reals into an imperative program using fixed-point arithmetic. Fixed-point arithmet ...

2013

On Sound Compilation of Reals

Viktor Kuncak, Eva Darulova

Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued implementation and sp ...

2013

Synthesis of Fixed-Point Programs

Viktor Kuncak, Eva Darulova, Indranil Saha

Several problems in the implementations of control systems, signal-processing systems, and scientific computing systems reduce to compiling a polynomial expression over the reals into an imperative program using fixed-point arithmetic. Fixed-point arithmet ...

2013

From Discrete Measurements to Bounded Gradient Estimates: A Look at Some Regularizing Structures

Dominique Bonvin, Grégory François, Gene Bunin

Obtaining a reliable gradient estimate for an unknown function when given only its discrete measurements is a common problem in many engineering disciplines. While there are many approaches to obtaining an estimate of a gradient, obtaining lower and upper ...

American Chemical Society2013

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Robert Granger, Jens Markus Zumbrägel

In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as

L_{q^n}(1/3,(4/9)1/3)

for computing arbitrary logarithms, but also in an heuristic polynomial time alg ...

Springer Berlin Heidelberg2013

Arbitrary-precision arithmetic

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Generalized programmable counter arrays

A New Basic Logic Structure for Data-Path Computation

Fast and accurate CMB computations in non-flat FLRW universes

Generalized Bombieri-Lagarias' Theorem And Generalized Li'S Criterion With Its Arithmetic Interpretation

Almost Polynomial Factor Hardness for Closest Vector Problem with Preprocessing

On the Generation of Precise Fixed-Point Expressions

On Sound Compilation of Reals

Synthesis of Fixed-Point Programs

From Discrete Measurements to Bounded Gradient Estimates: A Look at Some Regularizing Structures

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Fast and accurate CMB computations in non-flat FLRW universes

A New Basic Logic Structure for Data-Path Computation

Generalized Bombieri-Lagarias' Theorem And Generalized Li'S Criterion With Its Arithmetic Interpretation

Almost Polynomial Factor Hardness for Closest Vector Problem with Preprocessing

On Sound Compilation of Reals

Synthesis of Fixed-Point Programs

From Discrete Measurements to Bounded Gradient Estimates: A Look at Some Regularizing Structures

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Generalized programmable counter arrays

On the Generation of Precise Fixed-Point Expressions