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[PDF] Top 20 Arithmetic algorithms for extended precision using floating-point expansions

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Arithmetic algorithms for extended precision using floating-point expansions

Arithmetic algorithms for extended precision using floating-point expansions

... standard floating-point (FP) ...of using directly available and highly optimized hardware implemented FP ...multiple-term algorithms straightforwardly portable to highly parallel ... Voir le document complet

18

A new multiplication algorithm for extended precision using floating-point expansions

A new multiplication algorithm for extended precision using floating-point expansions

... libraries for high-precision FP ...corresponding arithmetic algorithms. Recent work showed that algorithms for FP expansions, that is, a representation based on ... Voir le document complet

9

Parallel floating-point expansions for extended-precision GPU computations

Parallel floating-point expansions for extended-precision GPU computations

... more precision that the one offered by current ...by floating-point (FP) expansions, ...different arithmetic algorithms for manipulating them have been ...these ... Voir le document complet

9

Implementation and performance evaluation of an extended precision floating-point arithmetic library for high-accuracy semidefinite programming

Implementation and performance evaluation of an extended precision floating-point arithmetic library for high-accuracy semidefinite programming

... double floating-point arithmetic, which is very efficient as it is implemented in ...in precision, for example to quad-precision (binary128) or more, comes with a significant ... Voir le document complet

9

MPFR: A Multiple-Precision Binary Floating-Point Library With Correct Rounding

MPFR: A Multiple-Precision Binary Floating-Point Library With Correct Rounding

... library for multiple-precision floating-point arithmetic with such clear semantics, which extends IEEE ...(GMP for short) [11], and freely distributed under the GNU Lesser ... Voir le document complet

19

Formal correctness of comparison algorithms between binary64 and decimal64 floating-point numbers

Formal correctness of comparison algorithms between binary64 and decimal64 floating-point numbers

... are using in this formalisation is the interval tactic ...proximation using standard techniques of interval arithmetic. For example, the following error bound of an approximation of the ... Voir le document complet

15

Variable Precision Floating-Point RISC-V Coprocessor Evaluation using Lightweight Software and Compiler Support

Variable Precision Floating-Point RISC-V Coprocessor Evaluation using Lightweight Software and Compiler Support

... representation for exponent and ...accesses. For this, our proposed ISA [4] offers load and store instructions which return the address of the first chunk after the accessed element ...memory for a ... Voir le document complet

7

Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic

Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic

... available. For instance, to guarantee – in some cases – correctly rounded integer powers in double precision arithmetic using our algorithms based on iterated products, we will have to ... Voir le document complet

24

A Study on Convolution Operator Using Half Precision Floating Point Numbers on GPU for Radioastronomy Deconvolution

A Study on Convolution Operator Using Half Precision Floating Point Numbers on GPU for Radioastronomy Deconvolution

... of precision. Stability of algorithms using FP16 format is an open problem ...observed for tomography reconstruction ...use for another inverse problem, the deconvolution for ... Voir le document complet

7

A Formally-Verified C Compiler Supporting Floating-Point Arithmetic

A Formally-Verified C Compiler Supporting Floating-Point Arithmetic

... Terms—floating-point arithmetic; verified compilation; formal proof; floating-point semantic preservation; ...of floating-point (FP) arithmetic have in- tensified ... Voir le document complet

10

Emulating round-to-nearest ties-to-zero "augmented" floating-point operations using round-to-nearest ties-to-even arithmetic

Emulating round-to-nearest ties-to-zero "augmented" floating-point operations using round-to-nearest ties-to-even arithmetic

... traces for overflow, underflow and inexact a global IEEE754 flag setting is computed and applied to IEEE754 flag registers by executing a dummy FP operation that make the appropriate flags be ...our ... Voir le document complet

13

Numerical validation in quadruple precision using stochastic arithmetic

Numerical validation in quadruple precision using stochastic arithmetic

... Stochastic Arithmetic (DSA) enables one to estimate rounding errors and to detect numerical instabilities in simulation ...programs using quadruple precision floating-point variables, ... Voir le document complet

16

Midpoints and exact points of some algebraic functions in floating-point arithmetic

Midpoints and exact points of some algebraic functions in floating-point arithmetic

... When using the implementation of a mathematical function in floating-point arithmetic, in most practical cases, the input and output precisions are the ...may, for example, wish to ... Voir le document complet

15

Meta-implementation of vectorized logarithm function in binary floating-point arithmetic

Meta-implementation of vectorized logarithm function in binary floating-point arithmetic

... that using our approach, we achieve a binary32 implementation with a reciprocal throughput of ≈ ...CPE for vector size = 4 and ≈ 10.5 CPE for vector size = ...CPE for vector size = 2 and ≈ ... Voir le document complet

9

On using floating-point computations to help an exact linear arithmetic decision procedure

On using floating-point computations to help an exact linear arithmetic decision procedure

... procedure for conjunctions of atoms in T . If T is linear real arithmetic (LRA), then this decision procedure must decide whether a set of linear inequalities with rational or integer coefficients has ... Voir le document complet

15

Single Precision Natural Logarithm Architecture for Hard Floating-Point and DSP-Enabled FPGAs

Single Precision Natural Logarithm Architecture for Hard Floating-Point and DSP-Enabled FPGAs

... architecture for the single-precision natural logarithm targeted at FPGA architec- tures with hardware support for floating-point addition and multiplication, such as the Arria10 ... Voir le document complet

8

On formal methods for certifying floating-point C programs

On formal methods for certifying floating-point C programs

... the floating-point numbers are supposed to be reals and the floating-point operations are done with infinite ...a floating-point operation is not greater than the maximal float ... Voir le document complet

35

A type-safe arbitrary precision arithmetic portability layer for HLS tools

A type-safe arbitrary precision arithmetic portability layer for HLS tools

... operators using HLS is that the operators can be both platform-independent and efficient, pro- viding open-source and debuggable operators with similar perfor- mance to vendor IP ...libraries for ... Voir le document complet

7

Faster Gaussian Lattice Sampling Using Lazy Floating-Point Arithmetic

Faster Gaussian Lattice Sampling Using Lazy Floating-Point Arithmetic

... reduction algorithms in a rigorous way, our work might be its first application to provable ...The precision used for floating-point arithmetic has non-negligible practical ... Voir le document complet

19

Fast and Correct SIMD Algorithms for Interval Arithmetic

Fast and Correct SIMD Algorithms for Interval Arithmetic

... his algorithms suffer from the same unreliability as brute-force algorithms, even if to a lesser ...interval Arithmetic As in JAIL, we propose to use the rounding direction towards +∞ ...double ... Voir le document complet

11

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