in the case of the sin function, the sum from -N to N should be zero, so the closer to zero the more accurate
What does represent the sum of xsin, what should it be ?
If both should be 0 then sum of sin is better in C but xsin is better in FPC 3.2.2 and above.
In FPC, if you use Linux 64 bit, you get the floating point unit x87 FPU Extended precision (80 bit extended) calculation but if using Win 64, you get Double floating ) point (64 bit double) calculation. So what is it you want ?