128-bit (64.64) signed fixed-point arithmetic.
R128 provides a data structure and routines for manipulating 128-bit (64.64) fixed-point quantities. Including:
- Basic arithmetic (add, subtract, multiply, divide)
- Bitwise operations (and, or, xor, not, shift)
- Comparison (min, max, floor, ceiling)
- Conversion (to and from floating point and ASCII/UTF-8 string)
- Square root and reciprocal square root
Sometimes you need more, or more consistent, precision over a given range than is possible with double-precision floating-point, but don't need fully arbitrary-precision arithmetic. In these cases, fixed-point gives you adequate precision without sacrificing a fixed memory footprint and bounded run-time.
128 bits has sufficient range and precision to cover the diameter of the observable universe accurate to within the width of one hydrogen atom, or to track the lifetime of the universe accurate to the time it takes a photon to travel the width of that same hydrogen atom. This is probably sufficient for most applications to obviate the need for an arbitrary-precision library.
Place r128.h somewhere in your project and include it wherever it is needed. There is no separate .c file for this library. To get the code, in one file in your project, put:
#define R128_IMPLEMENTATION
before you include r128.h. You don't need to clone the repository unless you want to run the tests.
This library requires a C99 compliant compiler, however it could be made to compile with a pre-C99 compiler that supports 64-bit integers. The only two changes needed are providing suitable typedefs for int64_t and uint64_t and replacing the ull integer suffix with the appropriate one for your compiler.
On x86 and x64 targets, Intel intrinsics are used for speed. If your compiler does not support these intrinsics, you can add #define R128_STDC_ONLY in your implementation file before including r128.h.
The only C runtime library functionality used by this library is <assert.h>. This can be avoided by defining an R128_ASSERT macro in your implementation file. Since this library uses 64-bit arithmetic, this may implicitly add a runtime library dependency on 32-bit platforms.
C++ constructors and operator overloads are provided for C++ files that include r128.h. All C++-isms are guarded by conditional compilation blocks, and all C++ functions are marked static inline, so r128.h can be included in both C and C++ source files. The source file that defines R128_IMPLEMENTATION can be either C or C++.
Visualizing R128 values in a debugger can be difficult. To help with this, in the R128_IMPLEMENTATION file, you can define R128_DEBUG_VIS to enable a global variable called R128_last, which will contain the results of the last r128 function call as a string. You can watch this variable in the debugger as you step through code.
Fixed-point uses integer machine instructions, which on most modern processors are no faster, and often slower, than their floating-point equivalents. Therefore, if performance is a concern, it may be better to use fixed-point for storage of values, and to do computation on the differences between values as floating point, if the precision loss of conversion is acceptable.
Attempts have been made to provide optimized code paths for 32-bit x86, but performance on any 32-bit system--especially of multiplication and division-- will be much worse than on a 64-bit system.
R128 is released into the public domain. See LICENSE for details.
Special thanks go to Sean Barrett for developing the single-file library idea.