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Undefined arctanh evaluating when implementing hyperbolic CORDIC

0

$begingroup$

I am trying to implement an exponential function using the CORDIC method. I am able to get the 'basic' version to work fine, but that only works for a very limited input range (i.e., inputs smaller than 1.11). I found this paper titled 'Expanding the range of convergence of the CORDIC algorithm', which seems to be widely used to expand this range. However, when I try to implement their approach, I am running into an issue. Specifically, with equations 34 and 35. In short, I need to calculate values from a value -M to +N. Based on equation 35, when I calculate the value for i=1, it evaluates arctanh(2^-0). Ofcourse arctanh(1) is undefined and the algorithm cannot proceed.

$i leq 0 : Z_i+1 = Z_i = delta_itanh^-1(1-2^i-2) ... eq(34)$

$i > 0 : Z_i+1 = Z_i = delta_itanh^-1(2^i) ... eq(35)$

It seems this work is widely used as I have seen several other papers implement this. So I feel as though I am doing something wrong. If someone can spot what I am doing wrong, I would greatly appreciate it!

hyperbolic-functions

share|cite|improve this question

edited Mar 19 at 22:07

user3397008

asked Mar 19 at 20:20

user3397008user3397008

11

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  1
  

  
  
  
  
  
  

  
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  Int order to make your question self-contained it would be nice to include equations 34 and 35 as well as a few other needed pieces of context.
  $endgroup$
  – Somos
  Mar 19 at 20:43
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Somos Thank you! I added the equations from the paper as you suggested.
  $endgroup$
  – user3397008
  Mar 19 at 22:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  From you4 eq(35) $i>0$ and so I can't figure out how you got arctanh(2^-0) from that. You need to give us more context for this question.
  $endgroup$
  – Somos
  Mar 19 at 23:02
  
  

  
  
  
  

add a comment | 

0

$begingroup$

I am trying to implement an exponential function using the CORDIC method. I am able to get the 'basic' version to work fine, but that only works for a very limited input range (i.e., inputs smaller than 1.11). I found this paper titled 'Expanding the range of convergence of the CORDIC algorithm', which seems to be widely used to expand this range. However, when I try to implement their approach, I am running into an issue. Specifically, with equations 34 and 35. In short, I need to calculate values from a value -M to +N. Based on equation 35, when I calculate the value for i=1, it evaluates arctanh(2^-0). Ofcourse arctanh(1) is undefined and the algorithm cannot proceed.

$i leq 0 : Z_i+1 = Z_i = delta_itanh^-1(1-2^i-2) ... eq(34)$

$i > 0 : Z_i+1 = Z_i = delta_itanh^-1(2^i) ... eq(35)$

It seems this work is widely used as I have seen several other papers implement this. So I feel as though I am doing something wrong. If someone can spot what I am doing wrong, I would greatly appreciate it!

hyperbolic-functions

share|cite|improve this question

edited Mar 19 at 22:07

user3397008

asked Mar 19 at 20:20

user3397008user3397008

11

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Int order to make your question self-contained it would be nice to include equations 34 and 35 as well as a few other needed pieces of context.
  $endgroup$
  – Somos
  Mar 19 at 20:43
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Somos Thank you! I added the equations from the paper as you suggested.
  $endgroup$
  – user3397008
  Mar 19 at 22:07
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  From you4 eq(35) $i>0$ and so I can't figure out how you got arctanh(2^-0) from that. You need to give us more context for this question.
  $endgroup$
  – Somos
  Mar 19 at 23:02
  
  

  
  
  
  

add a comment | 

$begingroup$

I am trying to implement an exponential function using the CORDIC method. I am able to get the 'basic' version to work fine, but that only works for a very limited input range (i.e., inputs smaller than 1.11). I found this paper titled 'Expanding the range of convergence of the CORDIC algorithm', which seems to be widely used to expand this range. However, when I try to implement their approach, I am running into an issue. Specifically, with equations 34 and 35. In short, I need to calculate values from a value -M to +N. Based on equation 35, when I calculate the value for i=1, it evaluates arctanh(2^-0). Ofcourse arctanh(1) is undefined and the algorithm cannot proceed.

$i leq 0 : Z_i+1 = Z_i = delta_itanh^-1(1-2^i-2) ... eq(34)$

$i > 0 : Z_i+1 = Z_i = delta_itanh^-1(2^i) ... eq(35)$

It seems this work is widely used as I have seen several other papers implement this. So I feel as though I am doing something wrong. If someone can spot what I am doing wrong, I would greatly appreciate it!

hyperbolic-functions

share|cite|improve this question

edited Mar 19 at 22:07

user3397008

asked Mar 19 at 20:20

user3397008user3397008

11

$endgroup$

share|cite|improve this question

edited Mar 19 at 22:07

user3397008

asked Mar 19 at 20:20

user3397008user3397008

11

share|cite|improve this question

edited Mar 19 at 22:07

user3397008

asked Mar 19 at 20:20

user3397008user3397008

11

asked Mar 19 at 20:20

user3397008user3397008

11

asked Mar 19 at 20:20

user3397008user3397008

11