OpenEuphoria

Re: New proposal for math.e

• Posted by Juergen Luethje <j.lue at g?x.d?> Aug 04, 2007
• 536 views

Me wrote:

> Pete Lomax wrote:
> 
> > Juergen Luethje wrote:
> > > 
> > > > >    E          = machine_func(47, {105,87,20,139,10,191,5,64}),    --
> 2.7182818284590452e0</font></i>
> > > > >    PI         = machine_func(47, {24,45,68,84,251,33,9,64}),      --
> 3.1415926535897932e0</font></i>
> > Oh, I wasn't paying attention. There is an old thread which maybe should be
> > revisited:
> > <a
> > href="http://www.openeuphoria.org/cgi-bin/esearch.exu?thread=1&fromMonth=4&fromYear=B&toMonth=6&toYear=B&keywords=%22Number+Stability+With+Decimals%22">http://www.openeuphoria.org/cgi-bin/esearch.exu?thread=1&fromMonth=4&fromYear=B&toMonth=6&toYear=B&keywords=%22Number+Stability+With+Decimals%22</a>
> > 
> > In summary, a tweak to the way value(), and eu.ex, load numbers might mean
> > that
> > this is not necessary.
> 
> I would appreciate it, if no such special tricks were necessary in order to
> enter floating point constants in the source code with a precision as high
> as possible.
> 
> > FWIW, if this "trick" is needed,
> 
> Currently it seems to be needed for maximum prcision, isn't it?
> 
> > I'd prefer to see:
> > }}}
<eucode>
> > constant 
> > E  = float64_to_atom({#69,#57,#14,#8B,#0A,#BF,#05,#40}), --(ie 2.7182...)
> > PI = float64_to_atom({#18,#2D,#44,#54,#FB,#21,#09,#40}), --(ie 3.1415...)
> > </eucode>
{{{

> > (I am a bit allergic to machine_func(47 etc, but it is not life-threatening)
> 
> I also think it's better readable. float64_to_atom() would require
>    include machine.e
> I think that was the reason for not using it. But that include statement
> should not cause any problem, should it?
> 
> > If after that, PI/2 is not as accurate as it sh/could be, then something is
> > seriously wrong.
> 
> I created a short test, and division doesn't seem to cause any problem
> (here). The two differences that occur are between assigning a hard-coded
> value vs. assingnimg the corresponding function result. I don't know what
> that means.
> }}}
<eucode>
> global constant
>    E          = machine_func(47, {105,87,20,139,10,191,5,64}),     --
>    2.7182818284590452e0
>    PI         = machine_func(47, {24,45,68,84,251,33,9,64}),       --
>    3.1415926535897932e0
> 
>    LN2        = machine_func(47, {239,57,250,254,66,46,230,63}),   --
>    0.6931471805599453e0
>    LN10       = machine_func(47, {21,85,181,187,177,107,2,64}),    --
>    2.3025850929940456e0
>    SQRT2      = machine_func(47, {204,59,127,102,158,160,246,63}), --
>    1.4142135623730950e0
>    HALF_SQRT2 = machine_func(47, {204,59,127,102,158,160,230,63}), --
>    0.7071067811865475e0
>    HALF_PI    = machine_func(47, {24,45,68,84,251,33,249,63}),     --
>    1.5707963267948966e0
>    QUARTER_PI = machine_func(47, {24,45,68,84,251,33,233,63}),     --
>    0.7853981633974483e0
>    TWO_PI     = machine_func(47, {24,45,68,84,251,33,25,64}),      --
>    6.2831853071795864e0
> 
>    LN2_test        = log(2),
>    LN10_test       = log(10),
>    SQRT2_test      = sqrt(2),
>    HALF_SQRT2_test = SQRT2/2,
>    HALF_PI_test    = PI/2, 
>    QUARTER_PI_test = PI/4, 
>    TWO_PI_test     = PI*2 
> 
> 
> ? compare( LN2       , LN2_test )
> ? compare( LN10      , LN10_test )          -- LN10_test  is bigger!
> ? compare( SQRT2     , SQRT2_test )         -- SQRT2_test is bigger!
> ? compare( HALF_SQRT2, HALF_SQRT2_test )
> ? compare( HALF_PI   , HALF_PI_test ) 
> ? compare( QUARTER_PI, QUARTER_PI_test ) 
> ? compare( TWO_PI    , TWO_PI_test ) 
> </eucode>
{{{

> Tested with EXW.EXE 3.0.2.

I changed the first byte of both constants, and now the values
are equal.

global constant
-- LN10       = machine_func(47, {21,85,181,187,177,107,2,64}),    -- old
LN10       = machine_func(47, {22,85,181,187,177,107,2,64}),    --
   2.3025850929940456e0
-- SQRT2      = machine_func(47, {204,59,127,102,158,160,246,63}), -- old
SQRT2      = machine_func(47, {205,59,127,102,158,160,246,63}), --
   1.4142135623730950e0

   LN10_test  = log(10),
   SQRT2_test = sqrt(2)


? compare( LN10 , LN10_test )
? compare( SQRT2, SQRT2_test )

Regards,
   Juergen