On Apr 28, 2016, at 8:11 PM, Xiaodi Wu <[email protected]> wrote:
> 
> Sorry, stripped out a little too much, I guess. Let me expand a little:
> 
> In this example, `PortedTransform` has, by virtue of how it works, an upper 
> bound and lower bound for valid input (among other interesting methods and 
> properties). Exceed those bounds for your input and `PortedTransform` 
> regurgitates garbage but does not throw any kind of error. Obviously, linear 
> transform does not care about such silly things because it can transform 
> essentially any FP input value, while the log transform simply traps when it 
> encounters a negative value (which, as a precondition, it should never 
> encounter).
> 
> BLAS is an accelerated linear algebra library; Apple has implemented a very 
> nicely optimized one as part of its Accelerate framework. I use BLAS to sum, 
> for example, two arrays of floating point values--it's very, very highly 
> optimized. In that situation, there's no trapping when a single value is out 
> of bounds (I get NaNs instead), and thus I must determine bounds in order to 
> anticipate when the output will be garbage or NaN. (There are, as part of the 
> Accelerate framework, accelerated functions to clamp entire arrays to given 
> bounds with maximal efficiency).
> 
> For accelerated scaling and unscaling, then, it is essentially always 
> necessary to compute upper and lower bounds even when that's unnecessary for 
> non-accelerated scaling and unscaling, which operates on one value at a time. 
> For that reason, `AcceleratedTransform` requires methods that compute upper 
> and lower bounds, and provides a default implementation of accelerated 
> clamping that calls those bound-computing methods and then uses the results 
> as parameters when calling functions in Accelerate.framework. Methods for the 
> computation of bounds already exist in `PortedTransform` but not in my own 
> transforms. With your proposal, how would I retroactively model this 
> requirement without touching code for `PortedTransform` and without compiling 
> this one class into its own library? I'd like to be able to take advantage of 
> the maximum possible compiler optimization, and optimizing across module 
> boundaries is (as far as I understand) a little dicier. (Moreover, for 
> MyLinTransform, I override the clamping method to return the input without 
> calling out to any framework functions because I know a priori that the 
> bounds are -infinity and infinity. I think that override will still be 
> possible under your proposal, though.)

Without actually trying to understand the details of your math stuff:

* If you add a required member in a declaration or extension that declares 
conformance, it is 'required'. 
* If it is already defaulted, it is `override required`. 
* If it is already defaulted but not required, it is `override`
* If someone else implements the stuff, you still have to pull it in somehow, 
but if you do so by conforming to another protocol with an extension, it's not 
your business, so you don't use any keywords.

You use keywords only for stuff that you specifically write, that clarifies the 
context in which you are writing it. If you do not own a protocol, an 
extension, or an implementation, you do not change or markup the protocol, 
extension, or implementation. You're just offering the compiler hints that your 
otherwise questionable decisions are fully intentional: when overriding an 
existing implementation and when conforming by supplying a required member.

-- E, who still probably missed your point and again apologizes


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