编译时与运行时常量

Question

I'm currently developing my own math lib to improve my c++ skills. I stumbled over boost's constants header file and I'm asking myself what is the point of using compile-time constants over runtime declared constants?

const float root_two = 1.414213562373095048801688724209698078e+00;
const float root_two = std::sqrt( 2.0f );

Isn't there an error introduced when using the fixed compile-time constant but calculations while running the application with functions? Wouldn't then the error be negleted if you use runtime constants?

Answer 1

1. As HansPassant said, it may save you a micro-Watt. However, note that the compiler will sometimes optimize that away by evaluating the expression during compilation and substituting in the literal value. See this answer to my earlier question about this.

2. Isn't there an error introduced when using the fixed compile-time constant? If you are using arbitrary-precision data types, perhaps. But it is more efficient to use plain data types like double and these are limited to about 16 decimal digits of precision anyways.

3. Based on (2), your second initialization would not be more precise than your first one. In fact, if you precomputed the value of the square root with an arbitrary precision calculator, the literal may even be more precise.

Answer 2

A library such as Boost must work in tons of environments. The application that uses the library could have set FPU could be in flush-to-zero mode, giving you 0.0 for denormalized (tiny) results.

Or the application could have been compiled with the -fast-math flag, giving inaccurate results.

Furthermore, a runtime computation of (a + b + c) depends on how the compiler generated code will store intermediate results. It might chose to pop (a + b) from the FPU as a 64-bit double, or it could leave it on the FPU stack as 80 bits. It depends on tons of things, also algebraic rewrites of associativity.

All in all, if you mix different processors, operating systems, compilers and the different applications the library is used inside, you will get a different result for each permutation of the above.

In some (rare) siturations this is not wanted; you can be in need for an exact constant value.