# fixed point taylor sine/cosine approximation model

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Gary on 19 Jun 2022
Commented: Gary on 17 Jul 2022 at 15:38
Can anybody share sine/cosine taylor approx model which is compatible with hdl coder?
##### 2 CommentsShowHide 1 older comment
Gary on 21 Jun 2022
I do not wish to use the inbuilt model of simulink but to build one.

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 =
Gary on 23 Jun 2022
Thank you . It was excellent analysis. I am clear now.

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.
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Gary on 17 Jul 2022 at 15:38
I managed to get 3 digits accuracy sine/cosine using chebhyshev polynomials(order 3). Thank you for sharing all the resources

R2014a

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