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urbit.org/docs/programming/reference/zuse/core/fu.md
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13bA lite number theory
2======================
4### `++fu`
6 ++ fu :: modulo (mul p q)
7 |= a=[p=@ q=@]
8 =+ b=?:(=([0 0] a) 0 (~(inv fo p.a) (~(sit fo p.a) q.a)))
9 |%
11XX document
13### `++dif`
15 ++ dif
16 |= [c=[@ @] d=[@ @]]
17 [(~(dif fo p.a) -.c -.d) (~(dif fo q.a) +.c +.d)]
18 ::
20XX document
22### `++exp`
24 ++ exp
25 |= [c=@ d=[@ @]]
26 :- (~(exp fo p.a) (mod c (dec p.a)) -.d)
27 (~(exp fo q.a) (mod c (dec q.a)) +.d)
28 ::
30XX document
32### `++out`
34 ++ out :: garner's formula
35 |= c=[@ @]
36 %+ add
37 +.c
38 (mul q.a (~(pro fo p.a) b (~(dif fo p.a) -.c (~(sit fo p.a) +.c))))
39 ::
41XX document
43### `++pro`
45 ++ pro
46 |= [c=[@ @] d=[@ @]]
47 [(~(pro fo p.a) -.c -.d) (~(pro fo q.a) +.c +.d)]
48 ::
50XX document
52### `++sum`
54 ++ sum
55 |= [c=[@ @] d=[@ @]]
56 [(~(sum fo p.a) -.c -.d) (~(sum fo q.a) +.c +.d)]
57 ::
59XX document
61### `++sit`
63 ++ sit
64 |= c=@
65 [(mod c p.a) (mod c q.a)]
67XX document