How do calculators calculate trig function?

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Discussion Overview

The discussion centers on how calculators compute trigonometric functions, exploring various methods such as Taylor polynomials and CORDIC. Participants inquire about the efficiency and accuracy of these methods, as well as sources for further learning.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether calculators use Taylor polynomials for trigonometric functions.
  • Another participant asserts that calculators primarily use the CORDIC method, which is faster than Taylor polynomials.
  • A further reply suggests that range reduction algorithms combined with minimax polynomials are even faster than CORDIC for computers, while calculators use CORDIC due to chip size considerations.
  • Some participants express interest in learning more about these methods and seek online resources instead of purchasing books.
  • There is a light-hearted inquiry about the origins of knowledge regarding these methods, questioning whether it stems from formal education or informal sharing among peers.

Areas of Agreement / Disagreement

Participants present multiple competing views regarding the methods used by calculators and computers for trigonometric calculations, with no consensus reached on the superiority of one method over another.

Contextual Notes

Participants mention various methods without detailing their assumptions or the specific contexts in which each method is preferred, leaving some aspects of the discussion unresolved.

Who May Find This Useful

This discussion may be of interest to individuals studying computer science, mathematics, or engineering, particularly those curious about numerical methods and their applications in technology.

Superposed_Cat
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Hi I was wondering how calculators calculate trigonometric functions. Do they use taylor polynomials(if so what order) or what? any help appreciated.
 
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They use a method called CORDIC, which is much faster than evaluating Taylor polynomials:

http://www.qc.cuny.edu/Academics/Degrees/DMNS/Faculty%20Documents/Sultan1.pdf
 
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SteamKing said:
They use a method called CORDIC, which is much faster than evaluating Taylor polynomials.
And range reduction algorithms combined with minimax polynomials are even faster.

A computer is more likely to use range reduction algorithms combined with minimax polynomials, a calculator, CORDIC. Calculators use CORDIC because it reduces chip size. Computers use range reduction and minimpax polynomials because they are fast and accurate. *Nobody* in their right mind uses Taylor series.
 
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could you send me a link DH? I did google it but nothing I could see off a cursory look.
 
Thanks, is there a place that online that i can learn from? i don't want to buy a book on it.
 
you guys are great I always wondered how calculators do calculations, where did you guys learn about these books? was it in school or by word of mouth? do these books reflect your age? 1960's computer scientists? lol
 

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