Re: [Axiom-developer] [Richard Fateman <address@hidden>] Re: [Maxima] strange behaviour with simple decimals / Axiom

[Bill Page]

Quoting Gabriel Dos Reis <address@hidden>:

> ... 
> Bill Page wrote:
> | (%i2) 1.96 - 1.4^2;
> | (%o2)                       2.2204460492503131E-16
> | (%i3)
>
> I believe that can explained by the fact that Axiom uses the host
> "long double" C datatype for DoubleFloat whereas Maxima must be
> using the more conventional and reliable "double" C datatype. 

No. By default Axiom uses it's own adjustable precision floating
point. See domain Float and the 'precision()' function. 

If you want DoubleFloat you would write:

(1) -> A:=1.4::DoubleFloat

   (1)  1.3999999999999999
                                      Type: DoubleFloat

(2) -> A^2

   (2)  1.9599999999999997
                                      Type: DoubleFloat

(3) -> B:=1.9599999999999997::DoubleFloat

   (3)  1.9599999999999997
                                      Type: DoubleFloat

(4) -> B-A^2

   (4)  0.0
                                      Type: DoubleFloat

Of the "machine" float:

(5) -> A:=1.4::MachineFloat

   (5)  1.4
                                      Type: MachineFloat

(6) -> A^2

   (6)  1.96
                                      Type: MachineFloat

(7) -> B:=1.96::MachineFloat

   (7)  1.96
                                      Type: MachineFloat

(8) -> B-A^2

   (8)  0.2220446049 250313 E -15
                                      Type: MachineFloat

> ... 
> | In Axiom version of  1/17/2005
> |
> | 1.4^2  comes out as 1.96
> |
> | 1.96 - 1.4^2  comes out as  0.7 E -20
> |