ch-ch-update: series, closed-form series, and strides

[Ary Borenszweig]

Ary Borenszweig escribió:
> Andrei Alexandrescu escribió:
>> Ary Borenszweig wrote:
>>> Andrei Alexandrescu escribió:
>>>> I've updated my code and documentation to include series (as in 
>>>> math) in the form of infinite ranges. Also series in closed form 
>>>> (given n can compute the nth value without iterating) are supported 
>>>> as random-access ranges.
>>>>
>>>> Also Stride is provided. The Matrix container (speaking of 
>>>> scientific computing with D!) will support various representational 
>>>> choices, most importantly the ones endorsed by high-performance 
>>>> libraries. For Matrix, Stride is an important component as I'm sure 
>>>> anyone who's ever written a matrix knows.
>>>>
>>>> http://ssli.ee.washington.edu/~aalexand/d/web/phobos/std_range.html
>>>> http://ssli.ee.washington.edu/~aalexand/d/web/phobos/std_algorithm.html
>>>>
>>>> Back to series. Finally my dream has come true: I can define a 
>>>> decent Fibonacci series clearly and efficiently in one line of code. 
>>>> No more idiotic recursive function that takes exponential time to 
>>>> finish!
>>>>
>>>> auto fib = series!("a[n-1] + a[n]")(1, 1);
>>>> // write 10 Fibonacci numbers
>>>> foreach (e; take(10, fib)) writeln(e);
>>>
>>> That is *SO* awesome!!
>>
>> Thanks! Constant-space factorial is just a line away:
>>
>> auto fact = series!("a[n] * (n + 1)")(1);
>> foreach (e; take(10, fact)) writeln(e);
>>
>> writes:
>>
>> 1
>> 1
>> 2
>> 6
>> 24
>> 120
>> 720
>> 5040
>> 40320
>> 362880
>>
>> And this lousy series approximating pi:
>>
>> auto piapprox = series!("a[n] + (n & 1 ? 4. : -4.) / (2 * n + 3)")(4.);
>> foreach (e; take(200, piapprox)) writeln(e);
>>
>> Very slowly convergent. :o)
> 
> Nice! :-)
> 
> I showed the Fibonacci example to a friend of mine and he said "that 
> string stuff scares me a little". The same happens to me.
> 
> What kind of error do you get if you mistype something in that string 
> expression?
> 
> Can you pass a delegate instead of a string? Something like:
> 
> auto fib = series!((Range a, int n) { return a[n-1] + a[n]; })(1, 1);
> 
> That seems much safe and will probably give a reasonable error if you 
> mistype something. I know, it's longer than the previous one. But it 
> would be nice if D had the following rule (or something similar to it): 
> "if a delegate doesn't return, the last statement is converted to a 
> return" (and you can ommit the semicolon). So now you can write:
> 
> auto fib = series!((Range a, int n) { a[n-1] + a[n] })(1, 1);
> 
> And if you could just ommit the types in the delegate...
> 
> auto fib = series!((a, n) { a[n-1] + a[n] })(1, 1);
> 
> Still a little longer than the original, but you get all the benefits of 
> not using a string.

Ah... But I can see the problem with delegates. I guess with strings you 
just mix them in a bigger expression and it's like inlining the call. 
With delegates you can't do that. So there's also a performance tradeoff...