International audienceThe Cody and Waite argument reduction technique works perfectly for reasonably large arguments, but as the input grows, there are no bits left to approximate the constant with enough accuracy. Under mild assumptions, we show that the result computed with a fused multiply-add provides a fully accurate result for many possible values of the input with a constant almost accurate to the full working precision. We also present an algorithm for a fully accurate second reduction step to reach full double accuracy (all the significand bits of two numbers are accurate) even in the worst cases of argument reduction. Our work recalls the common algorithms and presents proofs of correctness. All the proofs are formally verified us...
We present techniques for accelerating the floating-point computation of x/y when y is known before ...
International audienceThe verification of floating-point mathematical libraries requires computing n...
International audienceWe analyze several classical basic building blocks of double-word arithmetic (...
International audienceThe Cody and Waite argument reduction technique works perfectly for reasonably...
International audienceA commonly used argument reduction technique in elementary function computatio...
International audienceThe fused multiply accumulate-add (FMA) instruction, specified by the IEEE 754...
International audienceRounding to odd is a non-standard rounding on floating-point numbers. By using...
International audienceFloating-point arithmetic is a very efficient solution to perform computa-tion...
We describe an algorithm for arbitrary-precision computation of the elementary functions (exp, log, ...
Range-reduction is a key point for getting accurate elementary function routines. We introduce a new...
International audienceWe introduce an algorithm for multiplying a floating-point number $x$ by a con...
The fused multiply accumulate instruction (fused-mac) that is available on some current processors s...
International audienceThe standard floating-point fused multiply and add (FMA) computes R=AB+C with ...
International audienceThe accuracy analysis of complex floating-point multiplication done by Brent, ...
International audienceThis paper deals with the accuracy of complex division in radix-two floating-p...
We present techniques for accelerating the floating-point computation of x/y when y is known before ...
International audienceThe verification of floating-point mathematical libraries requires computing n...
International audienceWe analyze several classical basic building blocks of double-word arithmetic (...
International audienceThe Cody and Waite argument reduction technique works perfectly for reasonably...
International audienceA commonly used argument reduction technique in elementary function computatio...
International audienceThe fused multiply accumulate-add (FMA) instruction, specified by the IEEE 754...
International audienceRounding to odd is a non-standard rounding on floating-point numbers. By using...
International audienceFloating-point arithmetic is a very efficient solution to perform computa-tion...
We describe an algorithm for arbitrary-precision computation of the elementary functions (exp, log, ...
Range-reduction is a key point for getting accurate elementary function routines. We introduce a new...
International audienceWe introduce an algorithm for multiplying a floating-point number $x$ by a con...
The fused multiply accumulate instruction (fused-mac) that is available on some current processors s...
International audienceThe standard floating-point fused multiply and add (FMA) computes R=AB+C with ...
International audienceThe accuracy analysis of complex floating-point multiplication done by Brent, ...
International audienceThis paper deals with the accuracy of complex division in radix-two floating-p...
We present techniques for accelerating the floating-point computation of x/y when y is known before ...
International audienceThe verification of floating-point mathematical libraries requires computing n...
International audienceWe analyze several classical basic building blocks of double-word arithmetic (...