The IEEE 754 floating-point standard RECOMMENDS that languages implement sin to have correct rounding.
Correct rounding means that if the ideal infinite precision result was between two representable values in the floating-point type being used, then correct rounding would output one of those two representable values. The specific direction up or down of the value output should depend on the rounding mode floor, ceiling, nearests-ties-to-even, etc. currently in effect. Round nearests-ties-to-even is the mode most commonly in effect for floating-point units.
Implementations wouldn't normally compute the exact value, but instead compute something close enough to make a "good" rounding decision on what to output. It may not always be "perfect".
These good but not perfect implementations could vary by implementor. Thus it would not be shocking for find cases where one implementation had rounded up while another had rounded down.
For example, suppose the input to sin was
single(0.499999791)
the output sin ideally should be
0.479425355526204...
the two nearest representable values in single are
single(0.479425341)
single(0.479425371)
The nearest answer is the latter which is what MATLAB outputs.
Now other implementations
visual studio on windows 64 bit intel
gcc on windows 64 bit intel
gcc on linux 64 bit intel
gcc on ARM Cortex-M4 with FPU hardware
gcc on ARM Cortex-M4 without software emulation of floating-point
might be slightly different and round to the former value instead.
If it is just a matter of differences in rounding, then difference should just be the distance between representable values.
In MATLAB, eps(value) give the distance from one representable value to the next representable value away from zero in that type.
So you could check this by doing
absErr = abs( output1 - output2 );
epsVec1 = eps(output1); % critical that output1 is type of interest, i.e. single
epsVec2 = eps(output2); % critical that output2 is type of interest, i.e. single
epsVec = max( epsVec1, epsVec2 ); % small chance two eps are different so use bigger of two
errEpsRatio = absErr ./ epsVec;
plot(errEpsRatio,'r.'), shg
If any of the plotted dots are higher than 1, then it's not just a minor rounding choice.
If all the red dots in the plot are value 0 or 1, then it's just a rounding difference in the implementations.
In my testing of MATLAB vs Visual Studio sinf on Windows Intel 64 bit, I saw ratios of 1 but nothing higher.
A rounding difference in the implementation of these floating-point C library functions is something you may have to live with.
Keep in mind that the implementation on ARM may match MATLAB, Visual Studio, or neither.
