Gobsmacked by ksh93 floating point arithmetic.


 
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Operating Systems OS X (Apple) Gobsmacked by ksh93 floating point arithmetic.
# 8  
Old 10-18-2018
A version that doesn't need the table:

Code:
        F=1     # N factorial
        for ((N=1; N<=13; ))
        do
                (( SIN += (ANGLE**N)/F ))
                ((F *= ++N))
                ((F *= - ++N))
        done

This User Gave Thanks to Corona688 For This Post:
# 9  
Old 10-18-2018
Quote:
Originally Posted by Corona688
Interesting, a few obvious improvements.
  • You don't need $ on variable names inside (( ))
  • (( )) replaces [ ] for integer mathematics, especially float
  • The && construct will tremendously reduce redundancy here
  • You should use typeset to declare a local variable, otherwise you're unintentionally stomping on each other's ANGLE all the time
  • You should not be using global variables for all communication
  • You can make that giant equation one short loop
  • Not everything needs to be a function, many things are shorter and more readable as the single value they are
  • A bit more sanitization for negative input values
Apologies for any typos...

1: True but we had a discussion about it on this site WRT shellcheck and I decided I was going to keep '$' due to discrepancies of some combinations.

Here:
A $(( expression )) bug?

2: The ksh version is of 2007 vintage and I assumed double parentheses (in the method you have used them) to be unavailable, however...
3: I never even thought about the && construct as I had no idea my incarnation would even remotely give reasonably accurate results.
4: 'typeset' is duly noted and will be used in COSINE soon. Good point about stomping on its own variable. As this was a prototype that point hadn't crossed my mind.
5: I tend to use global variables a great deal, even in Python, my mind tends to work globally. <wink>
6: Using the 'set' statement like you have done is completely new to me and is cool. Logged in the old grey matter for future use.
7: True and AudioScope has the mixture.
8: Negative values; love it, nice-n-simple. I was more interested in my code snippet working and I never expected anyone to strip it and better it so quickly. I will now put your code in the script and take it from there.

Not sure whether to use a modified version of the sin() section of the code as a whole for COS(X) or use the SIN(X) script and call it as SIN(X+90) for the same result.

Will experiment and find out over the next day or so.

------ Post updated at 08:51 PM ------

Quote:
Originally Posted by Corona688
A version that doesn't need the table:

Code:
        F=1     # N factorial
        for ((N=1; N<=13; ))
        do
                (( SIN += (ANGLE**N)/F ))
                ((F *= ++N))
                ((F *= - ++N))
        done

Neat, but...
I don't quite understand how this works.
Surely ((F *= - ++N)) would overwrite ((F *= ++N)), if NOT then I don't understand why?
Please explain...

Last edited by wisecracker; 10-18-2018 at 05:18 PM.. Reason: No idea why a separate post has become an edit on a previuos one!
# 10  
Old 10-18-2018
Quote:
Originally Posted by wisecracker
. . .
I don't quite understand how this works.
Surely ((F *= - ++N)) would overwrite ((F *= ++N)), if NOT then I don't understand why?
Please explain...

May I jump in here: That's one of the "assignment operators"; A += B is to be read like A = A + B, so the "former" value of A is not lost / overwritten. Corona688 is using those abundantly in his above sin(x) script.
# 11  
Old 10-18-2018
Quote:
Originally Posted by wisecracker
Apologies for any typos...

1: True but we had a discussion about it on this site WRT shellcheck and I decided I was going to keep '$' due to discrepancies of some combinations.
That rare ambiguity does not apply to any of these combinations. You are safe.

I can think of plenty of situations where leaving the $ in will cause problems, however!

Quote:
2: The ksh version is of 2007 vintage and I assumed double parentheses (in the method you have used them) to be unavailable, however...
You were already using them. They might even be mandatory.

Quote:
Neat, but...
I don't quite understand how this works.
Surely ((F *= - ++N)) would overwrite ((F *= ++N)), if NOT then I don't understand why?
Please explain...
It's a short form of F = F * N, so it doesn't overwrite it as much as advance it.

Since the factorials jump by two every loop, it needs to multiply twice.

One of them is inverted, to make the sign alternate every loop.
This User Gave Thanks to Corona688 For This Post:
# 12  
Old 10-18-2018
Hi RudiC...
Longhand OSX 10.13.6, default bash terminal running ksh:
Code:
Last login: Thu Oct 18 22:04:50 on ttys000
AMIGA:amiga~> ksh
AMIGA:uw> F=1
AMIGA:uw> N=3
AMIGA:uw> (( F *= ++N ))
AMIGA:uw> echo "$F"
4
AMIGA:uw> (( F *= - ++N ))
AMIGA:uw> echo "$F"
-20
AMIGA:uw> _

You see my point...
'F' has been overwritten the 'echo' command shows it...
Something else is happening that I don't quite understand.
It must be something to do with 'for' statement for ((N=1; N<=13; )) where the increment of "STEP 2" is done inside the loop itself, ..... ++N effectively twice.
I didn't think that was possible in most languages as I have not seen it before.
If this is the case then I understand perfectly what is going on.
# 13  
Old 10-18-2018
It did exactly what it was supposed to: Incremented N by 1, then F = F * N. By doing this repeatedly, you can calculate factorials like 1*2*3*4*5*6, which are the large numbers in the series of your sin equation.
# 14  
Old 10-18-2018
Though with F=1 and N=3, you're calculating something like 5!/3!
This User Gave Thanks to Corona688 For This Post:
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