Searching for authors named "Nicolas Brisebarre" – sorted by Relevance.
11 documents found, showing 1 through 10.
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Correctly Rounded Multiplication by Arbitrary Precision Constants
- …We introduce an algorithm for multiplying a floating-point number x by a constant C that is not exactly representable in floating-point arithmetic. Our algorithm uses a multiplication and a fused multiply accumulate instruction. We give methods for checking whether, for a given value of C and a give…
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DOI: 10.1051/ita:2007002 CORRECT ROUNDING OF ALGEBRAIC FUNCTIONS
- …Abstract. We explicit the link between the computer arithmetic problem of providing correctly rounded algebraic functions and some diophantine approximation issues. This allows to get bounds on the accuracy with which intermediate calculations must be performed to correctly round these functions. Ma…
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Effective lower and upper bounds for the Fourier coefficients of powers of the modular invariant j
- …Using an elementary approach based on careful handlings of Cauchy integrals, we give precise effective lower and upper bounds for the Fourier coefficients of powers of the modular invariant j. Moreover, we adapt an old result of Rademacher to get a convergent series expansion of these Fourier coecie…
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A coprocessor for the final exponentiation of the ηT pairing in characteristic three. Cryptology ePrint Archive, Report 2007/045
- …Abstract. Since the introduction of pairings over (hyper)elliptic curves in constructive cryptographic applications, an ever increasing number of protocols based on pairings have appeared in the literature. Software implementations being rather slow, the study of hardware architectures became an act…
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Correctly Rounded Multiplication By Arbitrary Precision Constants
- …We introduce an algorithm for multiplying a floating-point number x by a constant C that is not exactly representable in floating-point arithmetic. Our algorithm uses a multiplication and a fused multiply accumulate instruction. We give methods for checking whether, for a given value of C and a giv…
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Supplementary Material to ’Accelerating Correctly Rounded Floating-Point Division when the Divisor Is Known in Advance’,” http://computer.org/tc/archives.htm or http:// perso.ens-lyon.fr/jean-michel.muller/fpdiv.html
- …Appendix: tables, proofs and intermediate lemmas We will frequently use the two following well-known properties, whose proofs are straightforward: Property 5 • Let y ∈ Mn. There exists q ∈ N such that 1/y belongs to Mq if and only if y is a power of 2. • If m>n, the exact quotient of two n-bit numbe…
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A New Range-Reduction Algorithm
- …Range-reduction is a key point for getting accurate elementary function routines. We introduce a new algorithm that is fast for input arguments belonging to the most common domains, yet accurate over the full double-precision range.…
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Accelerating Correctly Rounded Floating-Point Division when the Divisor Is Known in Advance
- …We present techniques for accelerating the floating-point computation of x=y when y is known before x. The proposed algorithms are oriented toward architectures with available fused-mac operations. The goal is to get exactly the same result as with usual division with rounding to nearest. It is kn…
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An Algorithm For Finding Entire Solutions Of Systems Of Difference Equations
- …We present an algorithm that computes the entire solutions of systems of two dierence equations and of systems of one dierential equation and one dierence equation, all with complex polynomials coecients.…
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Finding the "truncated" Polynomial That is Closest to a Function
- …When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given interval) a function has coefficients that are not exactly …
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