OpenEuphoria

RE: printf() on decimals

• Posted by gertie at visionsix.com Jul 01, 2003
• 613 views

On 1 Jul 2003, at 10:18, Matt Lewis wrote:

>=20
>=20
>=20
> aku saya wrote:
>=20
> > printf(1, "%.16g\n", 8999999999999990)
> > printf(1, "%.16g\n", 9999999999999990)
> >=20
> > Why is the last line printed differently?
>=20
> I think it's because you've gone over what 64-bit precision can handle.=
=20=20
> A double floating point number (what Euphoria uses) has a 53-bit=20
> mantissa (along with a 10-bit exponent and a sign bit).  Therefore, the=
=20
> largest number you can accurately represent is 9,007,199,254,740,990--a=
=20
> number I'd call *just* (what's 7 billion among friends :) over 9=20
> quadrillion (though I suppose it'd be 9 trillion for those who use the=
=20
> British style numbering).
>=20
> Try this
> ? 9999999999999990 - 9999999999999990
> ? 9999999999999991 - 9999999999999990
> ? 9999999999999992 - 9999999999999990
> ? 9999999999999993 - 9999999999999990
> ? 9999999999999994 - 9999999999999990
> ? 9999999999999995 - 9999999999999990
> ? 9999999999999996 - 9999999999999990
> ? 9999999999999997 - 9999999999999990
> ? 9999999999999998 - 9999999999999990
>=20
> On W2K, I get:
> Result  Correct
>      0       0
>      2       1
>      2       2
>      2       3
>      4       4
>      6       5
>      6       6
>      6       7
>      8       8
>=20
> What does Linux report?
>=20
> "15 digits of accuracy" is really an estimate, since 10^15 !=3D 2^53, but=
=20
> the two are 'relatively' close (10^15 is only about a quadrillion more=
=20
> than 2^53, or within about 10% :).  As Rob said, it's probably the=20
> difference between gcc's and Watcom's libraries, though one could say=20
> that Watcom is being more honest about the result.
>=20
> You shouldn't trust the precision of any results larger than 2^53.  It's=
=20
> just like considering that decimal places are rounded off.

This is why i was asking for (and i wrote) a string math lib, and so many=
=20
people poo-poo'd the idea. There are no reasonable limits to precision or d=
igit=20
count in string math. You can have 1000's of digits on both sides of the=
=20
decimal point, in any base you desire. I can't believe people are still gri=
peing=20
about the limits of the built-in math, and not using string math libs.

Kat,
noticing the developer of the C1 puter stopped talking to her when she gave=
=20
away the secrets for a much faster code morphing design. (well, no one irl=
=20
has done anything but laugh about it). S=E7=AE=EBw l=EEf=E8.