modular

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

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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.