I'm debugging some old C code and it has a definition #define PI 3.14... where ... is about 50 other digits.
Why is this? I said I could reduce the number to about 16 decimal places but my boss snarled at me saying that the other numbers are there for platform independence and forward compatibility. But will is slow the program down?
No, this will not slow down the program, unless you are running on an incredibly underpowered 1MHz DSP chip that has to do floating point arithmetic in software as opposed to passing it off to a dedicated FPU. This would mean that any mathematical operations that use floating point data are much slower than just using integer arithmetic.
In general, greater precision is only going to introduce a slowdown if the most time-consuming part of your program is doing a lot of calculations in rapid succession, and floating point calculations are especially slow. On a modern CPU, this is generally not the case, with the possible exception of certain chips that cause an 80-cycle stall on things like floating point underflow. That kind of issue likely exceeds the domain of this question.
First, it's better to use a common standard definition of PI, like in the C standard header, <math.h>, where it is defined as #define M_PI 3.14159265358979323846. If you insist, you can go ahead and define it manually.
Also, the best precision currently available in C is the equivalent of about 19 digits.
According to Wikipedia, 80-bit "Intel" IEEE 754 extended-precision long double, which is 80 bits padded to 16 bytes in memory, has 64 bits mantissa, with no implicit bit, which gets you 19.26 decimal digits. This has been the almost universal standard for long double for ages, but recently things have started to change.
The newer 128-bit quad-precision format has 112 mantissa bits plus an implicit bit, which gets you 34 decimal digits. GCC implements this as the __float128 type and there is (if memory serves) a compiler option to set long double to it.
Personally, if I were required to use our own definition of pi, I'd write something like this:
#ifndef M_PI
#define PI 3.14159265358979323846264338327950288419716939937510
#else
#define PI M_PI
#endif
If the latest C standard supports an even wider floating point primitive data type, it's pretty much a guarantee that constants in the math library would be updated to support this.
References
<https://stackoverflow.com/questions/15659668/more-precise-floating-point-data-types-than-double><https://stackoverflow.com/questions/9912151/math-constant-pi-value-in-c>