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EXC/ x<>Rn for stack efficiency
06-17-2017, 12:49 PM
Post: #34
RE: EXC/ x<>Rn for stack efficiency
(06-16-2017 06:32 PM)Matt Agajanian Wrote:  So, Pauli, If I were to use this formula correctly, what are the inputs for the ->P and ->R operations? It seems obvious, but to avoid mistakes, how should I interpret the X and Y registers for both ->P and ->R operations? Thanks.

This is a basic info which you will find in any manual of you RPN calculators. However, in this case the ->R function is not required, instead ->P does both calculations.

The ->P function takes two rectangular coordinates in X and Y and converts them to polar coordinates, i.e. a distance and an angle:

Code:
input        output
----------------------
  y        arctan(y/x)
  x        √(x² + y²)

Now take a look at the nominator of the posted formula. There are two terms that are squared and then the sqrt of the sum is calculated. That's exactly what the ->P function returns in X. Try 3 ENTER 4 and a simple ->P returns 5, which is shorter and faster than 3 x² 4 x² + √.

Then take a look at the whole fraction. The arctangent of a quotient has to be calculated. That's what the ->P function returns in Y. Actually the result may be slightly different from a simple arctan(y/x) as there is a certain sign convention for the angle, but let's neglect this here.

So you may calculate the two terms under the square root in the nominator first (without squaring them), then ->P returns the result of the complete nominator. Then calculate the denominator (with the previous result still in y) and another ->P returns the arctan of the quotient in Y. Since ->P x<>y is not shorter than a division and arctan (two steps in both cases) the only advantage of the ->P method may be that if the denominator is negative the returned angle is positive: arctan(1/–1) returns –45° while 1 ENTER –1 ->P yields +135°.

Dieter
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RE: EXC/ x<>Rn for stack efficiency - Dieter - 06-17-2017 12:49 PM



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