Math woes

Can anyone else duplicate these results at the command line?:

Command: (setq a 2.015)
2.015

Command: (setq b (- a 2))
0.015

Command: (= 0.015 b)
nil

What am I missing here?

 

I got the same result, so I tried something else:

Command: (= (rtos 0.015) (rtos b))
T

and it worked. Not sure why they didn't equal before.

Tim

 

Try using (equal) and apply a fuzz factor.

 

OK:

Command: (setq a 2.015)
2.015

Command: (setq b (- a 2))
0.015

Command: (= 0.015 b)
nil

Command: (equal 0.015 b 0.0001)
T

Thanks! The fuzz works. But why is this necessary in this situation?

 

Command: (setq a 2.015)
2.015

Command: (setq b (- a 2))
0.015

Command: (rtos b 2 16)
"0.0150000000000001"

 

OK, by converting both sides of the equation to a string and back(and thus controlling the decimal accuracy of all values), I can get the equation to work every time. (BTW, the purpose of the equation is simply to strip away the integer from variable A and compare the remaining value to variable B):

Command: (setq A 2.018)
2.018

Command: (setq B 0.018)
0.018

Command: (= (atof (rtos (- A (atof (rtos A 2 0))) 2 3))(atof (rtos B 2 3)))
T

That still seems like an awful lot of trouble, but at least it works. Thanks to Jason, Bill and Tim for the assistance in sorting this out.

 

How about;

(equal (rem a 1) b 1e-14)

-David

 

You're not seeing the big picture Jason is showing you; use "equal" and a fuzz
factor instead of "=", and you won't have to do the string conversions.

 

This is because of the fundamental incapacity of a computer using base-2
arithmetic to represent exactly every base-10 floating point number.
This is in no way AutoCad -specific, the same problem occurs in just
about every programming language.

For further reading, see any introductory numerical analysis or
computing science text. On a little Googling I found for example
http://www.cs.princeton.edu/introcs/91float/
which has more about this than I ever bothered to learn.

--

 

Thanks for the explanation.

 

The equation I posted was just a test. The equation I'm actually using in my routine involves a "<" comparison for which the equal function doesn't seem to fit in very well.

(< (atof (rtos (- A (atof (rtos A 2 0))) 2 3))(atof (rtos B 2 3)))

 

The equation I posted was a just test of my somewhat convoluted solution. The equation I'm actually using in my routine requires a "<" comparison for which the equal function doesn't seem to fit in very well.

(< (atof (rtos (- A (atof (rtos A 2 0))) 2 3))(atof (rtos B 2 3)))

 

That should have read "just a test". I'd like to think it was "a just test" but I don't feel qualified to judge such matters...

 

= works good on integers.

(or (equal item1 item2 1e-6)
(< item1 item2)
)

Would be what I use if item1 could not be larger than item2.

Bill

 

In my code item1 cannot be less than item2, so with a minor change...

(or (equal item1 item2 1e-6)
(> item1 item2)
)

...this will work. Thank you!

 

You're welcome.





Bill

 

This is because of the fundamental incapacity of a computer using base-2

Hello,

but "=" should compare number with a floating point precision of 10-14
because AutoCAD is sold as this.
It's a very strange to compare number over 14 significant digits of accuracy
while "real numbers are stored in double-precision floating-point format,
providing at least 14 significant digits of precision" as help file says

Effectively, it's not specifique to AutoCAD.

Bruno Toniutti.
(sorry for my english level)