Function to determine if two numbers are nearly equal when rounded to n significant decimal digits

Question

I have been asked to test a library provided by a 3rd party. The library is known to be accurate to n significant figures. Any less-significant errors can safely be

Answer 1

I believe your question is not defined well enough, and the unit-tests you present prove it:

If by 'round to N sig-fig decimal places' you mean 'N decimal places to the right of the decimal point', then the test assert nearlyequal(1e9, 1e9 + 1 , 5) should fail, because even when you round 1000000000 and 1000000001 to 0.00001 accuracy, they are still different.

And if by 'round to N sig-fig decimal places' you mean 'The N most significant digits, regardless of the decimal point', then the test assert nearlyequal(-1e-9, 1e-9, 5) should fail, because 0.000000001 and -0.000000001 are totally different when viewed this way.

If you meant the first definition, then the first answer on this page (by Triptych) is good. If you meant the second definition, please say it, I promise to think about it :-)