iota to array

[Jonathan M Davis]

On Monday, February 26, 2018 16:04:59 H. S. Teoh via Digitalmars-d-learn 
wrote:
> On Mon, Feb 26, 2018 at 11:34:06PM +0000, psychoticRabbit via
> Digitalmars-d-learn wrote: [...]
>
> > and what's going on here btw?
> >
> > assert( 1 == 1.000000000000000001 );  // assertion error in DMD but not
> > in LDC
> > assert( 1 == 1.0000000000000000001 );  // no assertion error??
> >
> > (compiled in 64bit mode)
>
> A 64-bit double can only hold about 14-15 decimal digits of precision.
> Anything past that, and there's a chance your "different" numbers are
> represented by exactly the same bits and the computer can't tell the
> difference.
>
> If you want arbitrary precision you'll have to use an arbitrary
> precision library like GMP.  It will be a lot slower than built-in
> floats or doubles, though.
>
> In general, real numbers have an infinite number of digits, and so would
> require infinite memory and infinite time to perform any computations at
> all.  What we have now is a reasonably practical compromise. :-D  But
> that also means there will be some inherent inexactness because we're
> trying to represent an infinite number of digits in a small, finite
> space.
>
> (There *are* exact representations for certain subsets of irrationals
> that allow fast computation that does not lose precision. But generally,
> they are only useful for specific applications where you know beforehand
> what form(s) your numbers will take. For general arithmetic, you have to
> compromise between speed and accuracy.)

No. No. No. Floating point values are just insane. ;)

http://dconf.org/2016/talks/clugston.html

In all seriousness, floating point values do tend to be highly frustrating
to deal with, and personally, I've gotten to the point that I generally
avoid them unless I need them. And much as that talks is titled "Using
Floating Point Without Losing Your Sanity," I came away from it even more
convinced that avoiding floating point values is pretty much the only sane
solution - though unfortunately, sometimes, you really don't have a choice.

- Jonathan M Davis