sinpi - Compute sin(X*pi) accurately - MATLAB (original) (raw)

Main Content

Compute sin(X*pi) accurately

Syntax

Description

Y = sinpi([X](#mw%5Faaf95f81-d1af-457b-8e56-51714dc8cc99)) computessin(X*pi) without explicitly computing X*pi. This calculation is more accurate than sin(X*pi) because the floating-point value of pi is an approximation of π. In particular:

For integers, sinpi(n) is exactly zero.
For odd integers, sinpi(n/2) is +1 or -1.

example

Examples

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Compare the accuracy of sinpi(X) vs. sin(X*pi).

Create a vector of values.

Calculate the sine of X*pi using the normal sin function.

Y = 1×5

     0    1.0000    0.0000   -1.0000   -0.0000

The results contain small numerical errors due to the fact that pi is a floating-point approximation of the true value of π. For instance, Y(3) is not exactly zero even though sin(π)=0.

Use sinpi to calculate the same values. In this case, the results are exact.

Input Arguments

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Input array, specified as a scalar, vector, matrix, multidimensional array, table, or timetable.

Data Types: single | double | table | timetable
Complex Number Support: Yes

Extended Capabilities

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Thesinpi function fully supports tall arrays. For more information, see Tall Arrays.

The sinpi function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2018b

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The sinpi function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.