# Differences

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 floating-point-equality [2017/11/21 10:26]awf floating-point-equality [2018/09/05 14:53]awf [But my case is more subtle than that] Both sides previous revision Previous revision 2018/09/05 15:14 awf 2018/09/05 14:53 awf [But my case is more subtle than that] 2017/11/21 12:27 awf 2017/11/21 10:28 awf 2017/11/21 10:26 awf 2017/04/19 12:15 awf 2017/04/19 12:15 awf 2015/03/10 02:01 awf 2015/03/10 02:01 awf 2015/03/10 02:00 awf 2015/03/10 01:56 awf 2015/03/10 01:54 awf created Next revision Previous revision 2018/09/05 15:14 awf 2018/09/05 14:53 awf [But my case is more subtle than that] 2017/11/21 12:27 awf 2017/11/21 10:28 awf 2017/11/21 10:26 awf 2017/04/19 12:15 awf 2017/04/19 12:15 awf 2015/03/10 02:01 awf 2015/03/10 02:01 awf 2015/03/10 02:00 awf 2015/03/10 01:56 awf 2015/03/10 01:54 awf created Last revision Both sides next revision Line 34: Line 34: "Ah, but I want the additional error checking".  OK, fine.  I'm with you.  But is this the right place? "Ah, but I want the additional error checking".  OK, fine.  I'm with you.  But is this the right place? - Why did the caller called the routine with nearly equal very small numbers? + Why did the caller call the routine with nearly equal very small numbers? + Is that physically likely in whatever real-world problem you're trying to solve? + If not, one should probably protect at the call site with an assert. Or maybe it's a precondition of the function call that a not be equal to b, and it's a coding bug if not satisfied. Or maybe it's a precondition of the function call that a not be equal to b, and it's a coding bug if not satisfied. double func(double a, double b) { double func(double a, double b) { - assert(a != b); + assert(a - b != 0); return 1/(a-b); return 1/(a-b); } } - Don't forget to [[assert-always|leave your asserts on in all builds]] unless the profiler tells you otherwise.  But hang on, you're on a platform which will give you line number here when you get the divby0 right?   So the assert is superfluous. + Don't forget to [[assert-always|leave your asserts on in all builds]] unless the profiler tells you otherwise. + But hang on, you're on a platform which will give you line number here when you get the divby0 right? + So the assert is superfluous -- just enable exceptions on divide by zero, underflow, and overflow. ==== But my case is more subtle than that ==== ==== But my case is more subtle than that ==== Line 57: Line 61: - Even here, you can think about what a better value to compare to might be.   First note that sin(x)/x works fine for all normalized floats except zero, so you can avoid a dependency on fabs and a definition of epsilon by just comparing to zero. + Even here, you can think about what a better value to compare to might be.   First note that sin(x)/x works fine for all floats except zero, so you can avoid a dependency on fabs and a definition of epsilon by just comparing to zero. But perhaps the profiler has told you that a big chunk of program time is spent in computing sin() and dividing, and furthermore you know that most times it's called with values near zero.  Well then, let's do what we do with any special function that goes slow: chop up the domain and special case.   It's true that sin(x)/x is exactly floating point 1.0 when x is small.  In fact, compute the taylor series, see that But perhaps the profiler has told you that a big chunk of program time is spent in computing sin() and dividing, and furthermore you know that most times it's called with values near zero.  Well then, let's do what we do with any special function that goes slow: chop up the domain and special case.   It's true that sin(x)/x is exactly floating point 1.0 when x is small.  In fact, compute the taylor series, see that Line 73: Line 77: } } + + It's a good idea then to write a blog post about the issue, because Toby Sharp might comment (see below) and point out that there is a much better choice: + + > "... since we need some kind of test for x=0 anyway, I don't see why we shouldn't take the opportunity to improve accuracy in this vicinity. And yes, it only costs 2 multiplies which is less than using the sin in those cases. So we are improving both performance and accuracy in the range (0, threshold). threshold is chosen to be the largest value such that the quadratic approximation is as good as the direct evaluation." + + + float sinc(float x) { + // Toby's threshold, determined through binary search as the best value for minimizing absolute error + if (std::abs(x) < 0.0406015441f) + return 1.0f - (x * x) * (1.0f / 6.0f); + else + return std::sin(x) / x; + } + + === And templates? === === And templates? ===