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urbit/base/pub/doc/hoon/library/3ba.md
Anton Dyudin 6cbb6b060d Revert "remove docs for demo", "remove odds and ends", "demo network", "DEMO ONLY: root beak as %demo.", "DEMO ONLY: don't show doznec flapping.", "Prinrtf." 
This reverts commit 8e1e40d75b3ab15c194b6bf9570f3edc46e2de58.
This reverts commit f073c490f9fd7c5abc033af4857df92229877de7.
This reverts commit f187d2d7e01a54823f3e979af9bbd148b398e7e9.
This reverts commit bc272862a73cfce1b118586ca39d3a377d841f1b.
This reverts commit 30a397513f8890a3406dc7ab91c6e067e3bbfbbb.
This reverts commit 4fc6856fb50d88c20a0f533392ca606641c5f38f.

Conflicts:
	urb/urbit.pill
	urb/zod/base/lib/drum.hoon
2015-06-15 18:10:02 -07:00

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section 3bA, lite number theory

++fu

++  fu                                                  ::  modulo (mul p q)
  |=  a=[p=@ q=@]
  =+  b=?:(=([0 0] a) 0 (~(inv fo p.a) (~(sit fo p.a) q.a)))
  |%

XX document

++dif

  ++  dif
    |=  [c=[@ @] d=[@ @]]
    [(~(dif fo p.a) -.c -.d) (~(dif fo q.a) +.c +.d)]
  ::

XX document

++exp

  ++  exp
    |=  [c=@ d=[@ @]]
    :-  (~(exp fo p.a) (mod c (dec p.a)) -.d)
    (~(exp fo q.a) (mod c (dec q.a)) +.d)
  ::

XX document

++out

  ++  out                                               ::  garner's formula
    |=  c=[@ @]
    %+  add
      +.c
    (mul q.a (~(pro fo p.a) b (~(dif fo p.a) -.c (~(sit fo p.a) +.c))))
  ::

XX document

++pro

  ++  pro
    |=  [c=[@ @] d=[@ @]]
    [(~(pro fo p.a) -.c -.d) (~(pro fo q.a) +.c +.d)]
  ::

XX document

++sum

  ++  sum
    |=  [c=[@ @] d=[@ @]]
    [(~(sum fo p.a) -.c -.d) (~(sum fo q.a) +.c +.d)]
  ::

XX document

++sit

  ++  sit
    |=  c=@
    [(mod c p.a) (mod c q.a)]

XX document