Hi Samuel,

thank you for the interesting sources!

Best regards,
Simon

On 2020-04-08, Samuel Lelievre <samuel.lelie...@gmail.com> wrote:
> About Sage and floating-point numbers, if I remember correctly,
>
> - IEEE 754 is not a complete specification, some details are left
>   up to the implementation and therefore IEEE 754 compliant
>   computations can vary from machine to machine (depending
>   on processor or OS)
> - in Sage, `RDF` and `float` use machine floats and so follow IEEE 754
> - by contrast RR and RealField are specified more tightly so as to
>   give the same computations on any machine
> - the range of exponents in RR is a lot wider than in RDF
> - RDF is a lot faster than RR
>
> Two excellent sources on real and floating-point numbers in Sage
>
> - The many ways of computing with real numbers
>   Talk by Vincent Delecroix at Sage Days 88 in IMA, U Minnesota, 2017
>   https://www.ima.umn.edu/2017-2018.2/W8.21-25.17/26308
>
> - What are the different real numbers in Sage
>   https://ask.sagemath.org/question/9950
>
> Related Sage Trac tickets
>
> - Deprecate is_RealField / is_RealNumber
>   https://trac.sagemath.org/ticket/24525
>
> - rename RealField/RealNumber
>   https://trac.sagemath.org/ticket/24524
>
> - Modernize sage.rings.real_mpfr
>   https://trac.sagemath.org/ticket/24457
>
> - Thematic tutorial about real and complex numbers in Sage
>   https://trac.sagemath.org/ticket/15944
>
> - Deprecate global RealNumber() and ComplexNumber()
>   https://trac.sagemath.org/ticket/13110
>

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