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### Re: [Raku] Arcane treatment of doubles and rationals

by holli (Abbot)
 on Apr 03, 2021 at 22:41 UTC Need Help??

display the fact that the (double precision) values held by \$d_1 and \$d_2 are exactly equivalent to the rational value 3602879701896397/36028797018963968
I think your assumption is wrong.
```\$ say 3602879701896397/36028797018963968 == 0.100000000000000006;
True
\$ say 10000000000000001/100000000000000000 == 0.10000000000000001 == 0
+.10000000000000001e0 == 0.1 + 1e-18;
True

== and the other operators don't care about the type of the number they work with, they will coerce every operand to Num anyway. However
```\$ say 3602879701896397/36028797018963968 =~= 0.10000000000000001;
True
There is also a unicode variant of the approximately-equal operator but it won't display correctly here.

holli

You can lead your users to water, but alas, you cannot drown them.

Replies are listed 'Best First'.
Re^2: [Raku] Arcane treatment of doubles and rationals
by syphilis (Bishop) on Apr 04, 2021 at 00:24 UTC
\$ say 3602879701896397/36028797018963968 == 0.100000000000000006;
True

Have they changed the spec ?
```> say 3602879701896397/36028797018963968 == 0.100000000000000006;
False
I have:
```\$ raku -v
Welcome to Rakudo(tm) v2021.03.
Implementing the Raku(tm) programming language v6.d.
Built on MoarVM version 2021.03.
If the RHS is a rational, then it's fairly easy to show that 3602879701896397/36028797018963968 != 100000000000000006/1000000000000000000.
(A/B == C/D if and only if A*D == B*C. In this case, A*D ends in zero and B*C ends in 8 so the equivalence cannot possibly hold.)

If the RHS is a double, then it's correct that 3602879701896397/36028797018963968 == 0.100000000000000006.
However, the 3 doubles assigned (respectively) the 3 values 0.100000000000000006, 0.10000000000000001 and 0.1 are all exactly the same. So we find, as expected:
```> say 3602879701896397/36028797018963968 == 0.100000000000000006e0;
True
> say 3602879701896397/36028797018963968 == 0.10000000000000001e0;
True
> say 3602879701896397/36028797018963968 == 0.1e0;
True
I've long been curious about the mindset that has created the rational/double arithmetic on raku, and I had thought (hoped) it might be a simple task to see how it all fits together.
Alas no, and I'm starting to see that I'm going to have to locate and work through the relevant documentation if I ever want to understand it.

Cheers,
Rob
There is a loss of precision happening when using the exponential form.
```\$ raku -e "dd 0.10000000000000006e0"
0.10000000000000006e0
\$ raku -e "dd 0.100000000000000006e0"
0.1e0
The exponential form creates a Num which needs to be between -1.7976931348623157e308 to 1.7976931348623158e308. See what Raku considers Infinity.

holli

You can lead your users to water, but alas, you cannot drown them.
I'd consider this a bug

Yes, I think there's something that's definitely not right.
For a start, there's never any need to assign an 18-significant-digit (decimal) value to a double.
Whatever value is assigned to a double by the 18-siginificant-digit 0.100000000000000006 will also be assigned by the 17-significant-digit 0.10000000000000001.

As I said (in the reply to myself that I posted shortly after your post), I will raise the issues with them.

Cheers,
Rob

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