Numerical Algorithms

, Volume 70, Issue 3, pp 653–667 | Cite as

On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic

  • Stef Graillat
  • Vincent Lefèvre
  • Jean-Michel Muller
Original Paper


We improve the usual relative error bound for the computation of x n through iterated multiplications by x in binary floating-point arithmetic. The obtained error bound is only slightly better than the usual one, but it is simpler. We also discuss the more general problem of computing the product of n terms.


Floating-point arithmetic Rounding error Accurate error bound Exponentiation 

Mathematics Subject Classification (2010)

15-04 65G99 65-04 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Stef Graillat
    • 1
    • 2
  • Vincent Lefèvre
    • 3
  • Jean-Michel Muller
    • 4
  1. 1.Sorbonne Universités, UPMC Univ Paris 06, UMR 7606, LIP6ParisFrance
  2. 2.CNRS, UMR 7606, LIP6ParisFrance
  3. 3.Inria, Laboratoire LIPUniversité de LyonLyonFrance
  4. 4.CNRS, Laboratoire LIPUniversité de LyonLyonFrance

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