Re: [Bug-apl] miscellāneum

[Dr . Jürgen Sauermann]

On 03/05/2019 02:20 AM, Hudson Flavio Meneses Lacerda wrote:

On Sun, 3 Mar 2019 16:21:25 +0100
Dr. Jürgen Sauermann <address@hidden> wrote:
[...]

As far as GNU APL is concerned, first of all apply statement 1. on
page 38 to the interpreter itself rather than to the APL code that is
being interpreted. [...]

Hi.

Do you suggest, when writing GNU APL, to put the emphasis on the
readability and basically ignore optimization? Are there any tips
for better code for GNU APL?

[...]

No. Optimization has always be a concern. However, optimization of design patterns
that look impressive on particular examples that rarely exist in real life (and even if so
only use a small fraction of the CPU time of an application) is a waste of time.

Mr. Bergquist has formulated this for APL programs (which were terribly slow
around 1987) but his statement is true in a much wider context (where it is
known as Amdahl's law).

There are no tips where GNU APL behaves differently than other APLs. But
there have been performance problems reported earlier that could be traced
back  to the use of an (O(N²)) algorithm where an O(N) algorithm exists.

A typical example is this:

Z←⍳0
for 1 millon times: Z←Z,X

this takes time O(N²) (since ⍴Z ist growing, making Z,X slower and slower)
Instead the following:

Z←1 million⍴ 0
for 1 millon times: Z[n]←X

does the same and takes only O(N),

In particular today I would argue that:

[...]

8. I tend to measure time with a (CPU-)clock rather than a ruler. The
remarks on scalars are partly incorrect in the context of scalar
extension (e.g. multiplication of a vector and a scalar).

Those examples seem to involve only scalars and scalar items of vectors.


BTW, are there any significant differences between these expressions
(where f is scalar, and t is a lengthy vector) ?:

a)	cos ← {2○⍵}
	PI ← ○1
	S ← cos 2 × PI × f × t
b)	S ← 2○ ○t×f×2
c)	S ← 2○ (2×○1×f) × t
d)	S ← 2○ (○2×f) × t
e)	S ← 2○ (○f+f) × t
f)	S ← cos(2×PI×f)×t
g)	S ← cos t×(2×PI×f)

I believe that g) is the fastest but the difference is minor, As a general rule, try to move
the longer vectors to the left and the shorter ones to the right. In a) every × and also the
monadic ○  is done ⍴,t times while in g) only the leftmost multiplication is done that often.

Regards,
Hudson