fixed point taylor sine/cosine approximation model

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Gary 2022-6-19

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https://ww2.mathworks.cn/matlabcentral/answers/1743600-fixed-point-taylor-sine-cosine-approximation-model

评论： Gary 2022-7-17

Can anybody share sine/cosine taylor approx model which is compatible with hdl coder?

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Walter Roberson 2022-6-19

is there a reason why you are not using https://www.mathworks.com/help/fixedpoint/ref/cordicsin.html

Gary 2022-6-21

I do not wish to use the inbuilt model of simulink but to build one.

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Sulaymon Eshkabilov 2022-6-19

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https://ww2.mathworks.cn/matlabcentral/answers/1743600-fixed-point-taylor-sine-cosine-approximation-model#answer_988930

在 MATLAB Online 中打开

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 =

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Walter Roberson 2022-6-22

在 MATLAB Online 中打开

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 =

fplot([t, f], [0 2*pi])

fplot(t-f, [0 2*pi])

Gary 2022-6-23

Thank you . It was excellent analysis. I am clear now.

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Kiran Kintali 2022-7-4

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1743600-fixed-point-taylor-sine-cosine-approximation-model#answer_999980

在 MATLAB Online 中打开

Taylor-series approx using HDL Coder.pdf

HDL Coder supports code generation for single precision trigonometric functions.

Getting Started with HDL Coder Native Floating-Point Support

https://www.mathworks.com/help/hdlcoder/ug/native-floating-point-support.html

https://www.mathworks.com/help/hdlcoder/ug/hdl-coder-support-for-native-floating-point-library-mapping.html

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.

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 2022-7-17