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## Re: [Axiom-developer] 20080130.01.tpd.patch (Ei)

**From**: |
Gregory Vanuxem |

**Subject**: |
Re: [Axiom-developer] 20080130.01.tpd.patch (Ei) |

**Date**: |
Fri, 01 Feb 2008 18:07:08 +0100 |

Hello Tim,
I just wanted to let you know that when you work with DoubleFloat you
can use a trick : if you set $useBFasDefault to false the Spad compiler
will handle floating point numbers as DoubleFloat directly, no need to
coerce them. So you just have to add ')boot $useBFasDefault := false' at
the beginning of the file (and re-set $useBFasDefault to true at the end
of the file). Not a beautiful hack though.
Greg
Le vendredi 01 février 2008 à 08:50 -0600, address@hidden a
écrit :
>* This patch adds the numeric calculation of the principal value of*
>* the Exponential Integral function. This is defined by a 6 segment*
>* piecewise approximation using Chebyshev polynomials. In addition*
>* to the main function Ei, each of the 6 piecewise solutions can be*
>* gotten directly by the EiN functions, which are also exposed. The*
>* EiN functions are normalized to return results in -1 <= x <= 1.*
>* *
>* Ei (-\infty < x < \infty)*
>* *
>* Ei1 (-\infty < x < -10) using xe^xEi(x)*
>* Ei2 (-10 <= x <= -4) using xe^xEi(x)*
>* Ei3 (-4 <= x <= 4) using (Ei(x)-log(abs(x))-\gamma)/x*
>* Ei4 (4 <= x <= 12) using xe^xEi(x)*
>* Ei5 (12 <= x <= 32) using xe^xEi(x)*
>* Ei6 (32 <= x < /infty) using xe^xEi(x)*
>* *
>* The approximation is valid for 10^-30 but the implementation using*
>* DoubleFloat does about 10^-16. The full coefficients are retained*
>* for a future gmp implementation.*
>* *