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fixed point taylor sine/cosine approximation model

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Can anybody share sine/cosine taylor approx model which is compatible with hdl coder?
  2 Comments
Walter Roberson
Walter Roberson on 19 Jun 2022
is there a reason why you are not using https://www.mathworks.com/help/fixedpoint/ref/cordicsin.html
Gary
Gary on 21 Jun 2022
I do not wish to use the inbuilt model of simulink but to build one.

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Answers (2)

Sulaymon Eshkabilov
Sulaymon Eshkabilov on 19 Jun 2022
WHy not to use matlab's built-in taylor() expansion fcn: https://www.mathworks.com/help/symbolic/sym.taylor.html?s_tid=doc_ta
E.g.:
syms x
taylor(sin(x), x, pi)
ans = 
taylor(cos(x), x, pi/2)
ans = 
  20 Comments
Walter Roberson
Walter Roberson on 22 Jun 2022
You need order 22 (x^21) to have an error of less than 1/1000
syms x
f = sin(x);
target = 1/1000;
for order = 2:50
t = taylor(f, x, 0, 'order', order);
val_at_end = subs(t, x, 2*pi);
if abs(val_at_end) < target; break; end
end
order
order = 22
t
t = 
fplot([t, f], [0 2*pi])
fplot(t-f, [0 2*pi])
Gary
Gary on 23 Jun 2022
Thank you . It was excellent analysis. I am clear now.

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Kiran Kintali
Kiran Kintali on 4 Jul 2022
HDL Coder supports code generation for single precision trigonometric functions.
Getting Started with HDL Coder Native Floating-Point Support
Taylor series approximation using HDL Coder
If you want to build Taylor series approximation by youself you could build using basic Math operations and sufficient amount of fixed-point conversion.
syms x
f = sin(x);
T2sin = taylor(f, x, 'Order', 2); % T2sin = x
T4sin = taylor(f, x, 'Order', 4); % T4sin = -x^3/6 + x
T6sin = taylor(f, x, 'Order', 6); % T6sin = x^5/120 - x^3/6 + x
On you build such a model you can further use optimizations such as multiplier partitioning, resource sharing and pipelining options to optimize the model for area/performance/latency/power.
  2 Comments
Walter Roberson
Walter Roberson on 4 Jul 2022
They were already using a model with basic math blocks to calculate Taylor series of sine and cosine. I showed, however, that in their target range 0 to 2π that the error for their model was unacceptable, and that to bring the error to 1/1000 you need taylor order 21.
Gary
Gary on 17 Jul 2022
I managed to get 3 digits accuracy sine/cosine using chebhyshev polynomials(order 3). Thank you for sharing all the resources

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