Incorrect calculations: csc(x) near x=k*π

This content originally appeared on DEV Community and was authored by Caleb Zhao

In this blog post, we explore incorrect calculations of the cosecant function csc(x) in MATLAB near numbers around $k\pi .$

Example 1. Given that x1=0.942477796123e1≈3 π x_1=0.942477796123\textup{e}1 \approx 3\,\pix1​=0.942477796123e1≈3π and
x2=0.7853981633974e2≈25 π ,x_2=0.7853981633974\textup{e}2 \approx 25\,\pi\,, x2​=0.7853981633974e2≈25π, calculate csc⁡(x1) \csc(x_1) csc(x1​) and csc⁡(x2) \csc(x_2) csc(x2​) in MATLAB.

Using MATLAB, we computed the values of csc⁡(x1) \csc(x_1) csc(x1​) and csc⁡(x2). \csc(x_2). csc(x2​). The result is shown in the following screenshot.

From the above screenshot, it can be seen that the outputs from MATLAB are
$-2.170988725424315\text{e}+09$ and $2.069879330499836\text{e}+11$ , respectively.

However, the correct values with 16 significant digits are -0.217098558923038e10 and 0.2069981278717736e12, respectively (as provided by ISRealsoft).

Thus, the output of MATLAB contains only 6 and 4 correct digits, with error rates of (16-6)/16 = 62.5% and (16-4)/16 = 75% respectively for the significant figures.

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This content originally appeared on DEV Community and was authored by Caleb Zhao

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