[swift-evolution] Epic: Typesafe calculations

[Stephen Canon]

… in exact arithmetic, not in floating-point, which is what people tend to actually use for matrices.  For that matter, the entire notion of “invertible” as a binary attribute is problematic when dealing with approximate arithmetic; a matrix may be formally invertible but so ill-conditioned that the result is effectively meaningless.

Not really trying to shoot you down, just observing that this is an extremely subtle example with lots of hidden sharp edges.

– Steve

> On Jan 13, 2016, at 1:19 PM, Matt Whiteside via swift-evolution <swift-evolution at swift.org> wrote:
> 
> That was my thinking when I wrote it, but I’m not sure exactly what the limits would be.  For example, the product of 2 invertible matrices is an invertible matrix, giving you another way to construct one.
> 
> Matt
> 
> 
>> On Jan 13, 2016, at 09:56, Thorsten Seitz <tseitz42 at icloud.com <mailto:tseitz42 at icloud.com>> wrote:
>> 
>> 
>> Am 12.01.2016 um 23:49 schrieb Matt Whiteside via swift-evolution <swift-evolution at swift.org <mailto:swift-evolution at swift.org>>:
>> 
>>> struct InvertibleMatrix: SquareMatrix where determinant() != 0 
>>> //                       ^~~ 'restriction’ clause, i.e., not inheritance;
>>> //                       determinant() is executed at compile time,
>>> //                       since `entries` is a constexpr
>> 
>> Wouldn't that only work for literal matrices?
>> 
>> -Thorsten 
> 
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