A modular arithmetic library with an emphasis on speed
Float64
Float32
Modular tries to leverage pre-computation as much as possible to allow direct computation in Congruent() and Index(), using fastdiv and pre-computed lookup tables. I can't test it on all hardware, but in principle should perform better than traditional modulo functions on all but the strangest of hardware.
For example, on my machine with a modulo of 1e-25;
float64
| Number | Math.Mod | Modulus.Congruent | Indexer.Index |
|---|---|---|---|
| 0 | 14.1 ns/op | 6.07 ns/op | 12.4 ns/op |
| 2.5e-25 | 29.2 ns/op | 14.4 ns/op | 15.7 ns/op |
| 1 | 467 ns/op | 37.5 ns/op | 38.1 ns/op |
| 1e300 | 8063 ns/op | 36.3 ns/op | 39.4 ns/op |
float32
| Number | Math.Mod | Modulus.Congruent | Indexer.Index |
|---|---|---|---|
| 0 | 15.6 ns/op | 5.49 ns/op | 11.3 ns/op |
| 2.5e-25 | 33.5 ns/op | 12.1 ns/op | 11.3 ns/op |
| 1 | 766 ns/op | 12.0 ns/op | 10.9 ns/op |
| 1e25 | 1259 ns/op | 12.0 ns/op | 11.0 ns/op |
I've use the name 'Congruent' as it's a more explicit definition of the function, and helps avoid confusion with other functions. It is the same as a euclidian 'modulo' function; that is, it finds the number satisfying '0 <= n < modulus' that is representative of the given number's congruency class, hence the name Congruent.