Cost of GNU basic (multi-precision) operations

Paul Zimmermann Paul.Zimmermann at
Fri Sep 7 08:46:12 CEST 2007

> From: "Miodrag Petkovic" <msp at>
> Date: Thu, 6 Sep 2007 23:52:17 +0200
> Dear Sir,
> My fields of interest are problems of numerical analysis, in particular, solving nonlinear equations.
> More than 10 years I have implemented my fast iterative root-solvers
> using the programming package MAPLE and MATHEMATICA in multiple precision
> arithmetic (they, actually, use GNU). For the purpose of a scientific paper in preparation, 
> I need some date about 
> the cost of basic arithmetic operations; namely, if the (CPU) cost of ADDITION
> and SUBTRACTION are normalized to 1, what is the cost of MULTIPLICATION and DIVISION?
> Or, which is the same, what is the numbers of these four operations executed  in 1 second
> I have these data for some digital computers including super-computers, but
> not for the mentioned packages. Of course, I know that this cost depends on the used processor and
> the number of the employed decimal digits, but some estimates probably exist.
> I would like to learn these data and I ask you to help me.
> My scientific contribution can be found on my Web site
> Thank you very much in advance.
> Kindest regards
> Professor Miodrag Petkovic
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You will find some data in Section 5.7 of
For other mathematical operations, you can also look at the reference
[FoHaLePeZi07] below. Of course the mul/add ratio depends on the precision!

  author = 	 {Laurent Fousse and Guillaume Hanrot and Vincent Lef{\`e}vre
                  and Patrick P{\'e}lissier and Paul Zimmermann},
  title = 	 {{MPFR}: A Multiple-Precision Binary Floating-Point Library
                  With Correct Rounding},
  journal = 	 "ACM Transactions on Mathematical Software",
  volume =       33,
  number =       2,
  month =        jun,
  year =         2007,
  annote = {}

Paul Zimmermann

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