I am porting some program from Matlab to C++ for efficiency. It is important for the output of both programs to be exactly the same (\*\*).

I am facing different results for this operation:

```
std::sin(0.497418836818383950)   = 0.477158760259608410 (C++)
sin(0.497418836818383950)        = 0.47715876025960846000 (Matlab)
N[Sin[0.497418836818383950], 20] = 0.477158760259608433 (Mathematica)

```

So, as far as I know both C++ and Matlab are using IEEE754 defined double arithmetic. I think I have read somewhere that IEEE754 allows differents results in the last bit. Using mathematica to decide, seems like C++ is more close to the result. **How can I force Matlab to compute the sin with precision to the last bit included, so that the results are the same?**

In my program this behaviour leads to big errors because the numerical differential equation solver keeps increasing this error in the last bit. However I am not sure that C++ ported version is correct. I am guessing that **even if the IEEE754 allows the last bit to be different, somehow guarantees that this error does not get bigger** when using the result in more IEEE754 defined double operations (because otherwise, two different programs correct according to the IEEE754 standard could produce completely different outputs). So the other question is **Am I right about this?** 

I would like get an answer to both bolded questions. **Edit: The first question is being quite controversial, but is the less important, can someone comment about the second one?**

Note: This is not an error in the printing, just in case you want to check, this is how I obtained these results:

<http://i.imgur.com/cy5ToYy.png>

Note (\*\*): What I mean by this is that the final output, which are the results of some calculations showing some real numbers with 4 decimal places, need to be exactly the same. The error I talk about in the question gets bigger (because of more operations, each of one is different in Matlab and in C++) so the final differences are huge) (If you are curious enough to see how the difference start getting bigger, here is the full output [link soon], but this has nothing to do with the question)