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592e076125
urbit/arvo/test.hoon
C. Guy Yarvin 592e076125 Various fixes and improvements.
2016-03-09 14:05:18 -08:00

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!: ::
:::: /hoon/hoon ::
:: ::
=> %151 =>
:: ::
:::: 0: version stub ::
:: ::
|%
++ hoon +
-- =>
:: ::
:::: 1: layer one ::
:: ::
:: 1a: basic arithmetic ::
:: 1b: tree addressing ::
:: 1c: molds and mold builders ::
::
|%
:: ::
:::: 1a: unsigned arithmetic and tree addressing ::
:: ::
:: add, dec, div, dvr, gte, gth, lte, ::
:: lth, max, min, mod, mul, sub ::
::
++ add :: unsigned addition
~/ %add
|= {a/@ b/@}
^- @
?: =(0 a) b
$(a (dec a), b +(b))
::
++ dec :: unsigned decrement
~/ %dec
|= a/@
~> %mean.[0 %leaf "decrement-underflow"]
?< =(0 a)
=+ b=0
|- ^- @
?: =(a +(b)) b
$(b +(b))
::
++ div :: unsigned divide
~/ %div
=+ [a=`@`1 b=`@`1]
|.
^- @
~> %mean.[0 %leaf "divide-by-zero"]
?< =(0 b)
=+ c=0
|-
?: (lth a b) c
$(a (sub a b), c +(c))
::
++ dvr :: divide w/remainder
~/ %dvr
|= {a/@ b/@}
^- {p/@ q/@}
[(div a b) (mod a b)]
::
++ gte :: unsigned greater/eq
~/ %gte
|= {a/@ b/@}
^- ?
!(lth a b)
::
++ gth :: unsigned greater
~/ %gth
|= {a/@ b/@}
^- ?
!(lte a b)
::
++ lte :: unsigned less/eq
~/ %lte
|= {a/@ b/@}
|(=(a b) (lth a b))
::
++ lth :: unsigned less
~/ %lth
|= {a/@ b/@}
^- ?
?& !=(a b)
|-
?| =(0 a)
?& !=(0 b)
$(a (dec a), b (dec b))
== == ==
::
++ max :: unsigned maximum
~/ %max
|= {a/@ b/@}
^- @
?: (gth a b) a
b
::
++ min :: unsigned minimum
~/ %min
|= {a/@ b/@}
^- @
?: (lth a b) a
b
::
++ mod :: unsigned modulus
~/ %mod
|: [a=`@`1 b=`@`1]
^- @
?< =(0 b)
(sub a (mul b (div a b)))
::
++ mul :: unsigned multiply
~/ %mul
|: [a=`@`1 b=`@`1]
^- @
=+ c=0
|-
?: =(0 a) c
$(a (dec a), c (add b c))
::
++ sub :: subtract
~/ %sub
|= {a/@ b/@}
~> %mean.[0 %leaf "subtract-underflow"]
^- @
?: =(0 b) a
$(a (dec a), b (dec b))
:: ::
:::: 1b: tree addressing ::
:: ::
:: cap, mas, peg ::
::
++ cap :: fragment head
~/ %cap
|= a/@
^- ?($2 $3)
?- a
$2 %2
$3 %3
?($0 $1) !!
* $(a (div a 2))
==
::
++ mas :: fragment body
~/ %mas
|= a/@
^- @
?- a
$1 !!
$2 1
$3 1
* (add (mod a 2) (mul $(a (div a 2)) 2))
==
::
++ peg :: fragment compose
~/ %peg
|= {a/@ b/@}
^- @
?- b
$1 a
$2 (mul a 2)
$3 +((mul a 2))
* (add (mod b 2) (mul $(b (div b 2)) 2))
==
:: ::
:::: 1c: ideal containers ::
:: ::
:: ache, bloq, each, gate, list, lone, pair, pole ::
:: qual, quid, quip, trap, tree, trel, unit ::
::
++ ache |*({a/gate b/gate} $%({$| p/b} {$& p/a})) :: a or b, b default
++ bloq @ :: bitblock, eg 3=byte
++ each |*({a/gate b/gate} $%({$& p/a} {$| p/b})) :: a or b, a default
++ gate $-(* *) :: generic gate
++ list |*(a/gate $@($~ {i/a t/(list a)})) :: nullterminated list
++ lone |*(a/gate p/a) :: 1-tuple
++ pair |*({a/gate b/gate} {p/a q/b}) :: 2-tuple
++ pole |*(a/gate $@($~ {a (pole a)})) :: faceless list
++ qual |* {a/gate b/gate c/gate d/gate} :: 4-tuple
{p/a q/b r/c s/d} ::
++ quid |*({a/gate b/*} {a _b}) :: mixed for sip
++ quip |*({a/gate b/*} {(list a) _b}) :: list-mixed for sip
++ trap |*(a/gate _|?(*a)) :: producer
++ tree |*(a/gate $@($~ {n/a l/(tree a) r/(tree a)})) :: binary tree
++ trel |*({a/gate b/gate c/gate} {p/a q/b r/c}) :: 3-tuple
++ unit |*(a/gate $@($~ {$~ u/a})) :: maybe
-- =>
:: ::
:::: 2: layer two ::
:: ::
:: 2a: unit logic ::
:: 2b: list logic ::
:: 2c: bit arithmetic ::
:: 2d: bit logic ::
:: 2e: insecure hashing ::
:: 2f: noun ordering ::
:: 2g: unsigned powers ::
:: 2h: set logic ::
:: 2i: map logic ::
:: 2j: jar and jug logic ::
:: 2k: queue logic ::
:: 2l: container from container ::
:: 2m: container from noun ::
:: 2n: functional hacks ::
:: 2o: normalizing containers ::
:: 2p: serialization ::
:: 2q: molds
::
|%
:: ::
:::: 2a: unit logic ::
:: ::
:: biff, bind, bond, both, clap, drop, ::
:: fall, flit, lift, mate, need, some ::
::
++ biff :: apply
|* {a/(unit) b/$-(* (unit))}
?~ a ~
(b u.a)
::
++ bind :: argue
|* {a/(unit) b/gate}
?~ a ~
[~ u=(b u.a)]
::
++ bond :: replace
|* a/(trap)
|* b/(unit)
?~ b $:a
u.b
::
++ both :: all the above
|* {a/(unit) b/(unit)}
?~ a ~
?~ b ~
[~ u=[u.a u.b]]
::
++ clap :: combine
|* {a/(unit) b/(unit) c/_|=(^ +<-)}
?~ a b
?~ b a
[~ u=(c u.a u.b)]
::
++ drop :: enlist
|* a/(unit)
?~ a ~
[i=u.a t=~]
::
++ fall :: default
|* {a/(unit) b/*}
?~(a b u.a)
::
++ flit :: make filter
|* a/$-(* ?)
|* b/*
?.((a b) ~ [~ u=b])
::
++ lift :: lift gate (fmap)
|* a/gate :: flipped
|* b/(unit) :: curried
(bind b a) :: bind
::
++ mate :: choose
|* {a/(unit) b/(unit)}
?~ b a
?~ a b
?.(=(u.a u.b) ~>(%mean.[0 %leaf "mate"] !!) a)
::
++ need :: demand
|* a/(unit)
?~ a ~>(%mean.[0 %leaf "need"] !!)
u.a
::
++ some :: lift (pure)
|* a/*
[~ u=a]
::
:::: 2b: list logic ::
:: ::
:: flop, homo, lent, levy, lien, limo, murn, reap, ::
:: reel, roll, skid, skim, skip, scag, slag, snag, ::
:: sort, swag, turn, weld, welp, zing ::
:: ::
++ flop :: reverse
~/ %flop
|* a/(list)
=> .(a (homo a))
^+ a
=+ b=`_a`~
|-
?~ a b
$(a t.a, b [i.a b])
::
++ gulf :: range inclusive
|= {a/@ b/@}
^- (list @)
?:(=(a +(b)) ~ [a $(a +(a))])
::
++ homo :: homogenize
|* a/(list)
^+ =< $
|% +- $ ?:(*? ~ [i=(snag 0 a) t=$])
--
a
::
++ lent :: length
~/ %lent
|= a/(list)
^- @
=+ b=0
|-
?~ a b
$(a t.a, b +(b))
::
++ levy
~/ %levy :: all of
|* {a/(list) b/$-(* ?)}
|- ^- ?
?~ a &
?. (b i.a) |
$(a t.a)
::
++ lien :: some of
~/ %lien
|* {a/(list) b/$-(* ?)}
|- ^- ?
?~ a |
?: (b i.a) &
$(a t.a)
::
++ limo :: listify
|* a/*
^+ =< $
|% +- $ ?~(a ~ ?:(*? [i=-.a t=$] $(a +.a)))
--
a
::
++ murn :: maybe transform
~/ %murn
|* {a/(list) b/$-(* (unit))}
|-
?~ a ~
=+ c=(b i.a)
?~ c
$(a t.a)
[i=u.c t=$(a t.a)]
::
++ reap :: replicate
~/ %reap
|* {a/@ b/*}
|- ^- (list _b)
?~ a ~
[b $(a (dec a))]
::
++ reel :: right fold
~/ %reel
|* {a/(list) b/_|=({* *} +<+)}
|- ^+ +<+.b
?~ a
+<+.b
(b i.a $(a t.a))
::
++ roll :: left fold
~/ %roll
|* {a/(list) b/_|=({* *} +<+)}
|- ^+ +<+.b
?~ a
+<+.b
$(a t.a, b b(+<+ (b i.a +<+.b)))
::
++ skid :: separate
~/ %skid
|* {a/(list) b/$-(* ?)}
|- ^+ [p=a q=a]
?~ a [~ ~]
=+ c=$(a t.a)
?:((b i.a) [[i.a p.c] q.c] [p.c [i.a q.c]])
::
++ skim :: only
~/ %skim
|* {a/(list) b/$-(* ?)}
|-
^+ a
?~ a ~
?:((b i.a) [i.a $(a t.a)] $(a t.a))
::
++ skip :: except
~/ %skip
|* {a/(list) b/$-(* ?)}
|-
^+ a
?~ a ~
?:((b i.a) $(a t.a) [i.a $(a t.a)])
::
++ scag :: prefix
~/ %scag
|* {a/@ b/(list)}
|- ^+ b
?: |(?=($~ b) =(0 a)) ~
[i.b $(b t.b, a (dec a))]
::
++ slag :: suffix
~/ %slag
|* {a/@ b/(list)}
|- ^+ b
?: =(0 a) b
?~ b ~
$(b t.b, a (dec a))
::
++ snag :: index
~/ %snag
|* {a/@ b/(list)}
|-
?~ b
~> %mean.[0 %leaf "snag-fail"]
!!
?: =(0 a) i.b
$(b t.b, a (dec a))
::
++ sort !. :: quicksort
~/ %sort
|* {a/(list) b/$-([* *] ?)}
=> .(a ^.(homo a))
|- ^+ a
?~ a ~
%+ weld
$(a (skim t.a |=(c/_i.a (b c i.a))))
^+ t.a
[i.a $(a (skim t.a |=(c/_i.a !(b c i.a))))]
::
++ swag :: slice
|* {{a/@ b/@} c/(list)}
(scag +<-> (slag +<-< c))
::
++ turn :: transform
~/ %turn
|* {a/(list) b/$-(* *)}
|-
?~ a ~
[i=(b i.a) t=$(a t.a)]
::
++ weld :: concatenate
~/ %weld
|* {a/(list) b/(list)}
=> .(a ^.(homo a), b ^.(homo b))
|- ^+ b
?~ a b
[i.a $(a t.a)]
::
++ welp :: faceless weld
=| {* *}
|%
+- $
?~ +<-
+<-(. +<+)
+<-(+ $(+<- +<->))
--
::
++ zing :: promote
=| *
|%
+- $
?~ +<
+<
(welp +<- $(+< +<+))
--
:: ::
:::: 2c: bit arithmetic ::
:: ::
:: bex, can, cat, cut, end, fil, lsh, met, ::
:: rap, rep, rip, rsh, swp, xeb ::
::
++ bex :: binary exponent
~/ %bex
|= a/@
^- @
?: =(0 a) 1
(mul 2 $(a (dec a)))
::
++ can :: assemble
~/ %can
|= {a/bloq b/(list {p/@u q/@})}
^- @
?~ b 0
(add (end a p.i.b q.i.b) (lsh a p.i.b $(b t.b)))
::
++ cat :: concatenate
~/ %cat
|= {a/bloq b/@ c/@}
(add (lsh a (met a b) c) b)
::
++ cut :: slice
~/ %cut
|= {a/bloq {b/@u c/@u} d/@}
(end a c (rsh a b d))
::
++ end :: tail
~/ %end
|= {a/bloq b/@u c/@}
(mod c (bex (mul (bex a) b)))
::
++ fil :: fill bloqstream
|= {a/bloq b/@u c/@}
=+ n=0
=+ d=c
|- ^- @
?: =(n b)
(rsh a 1 d)
$(d (add c (lsh a 1 d)), n +(n))
::
++ lsh :: left-shift
~/ %lsh
|= {a/bloq b/@u c/@}
(mul (bex (mul (bex a) b)) c)
::
++ met :: measure
~/ %met
|= {a/bloq b/@}
^- @
=+ c=0
|-
?: =(0 b) c
$(b (rsh a 1 b), c +(c))
::
++ rap :: assemble nonzero
~/ %rap
|= {a/bloq b/(list @)}
^- @
?~ b 0
(cat a i.b $(b t.b))
::
++ rep :: assemble single
~/ %rep
|= {a/bloq b/(list @)}
^- @
=+ c=0
|-
?~ b 0
(add (lsh a c (end a 1 i.b)) $(c +(c), b t.b))
::
++ rip :: disassemble
~/ %rip
|= {a/bloq b/@}
^- (list @)
?: =(0 b) ~
[(end a 1 b) $(b (rsh a 1 b))]
::
++ rsh :: right-shift
~/ %rsh
|= {a/bloq b/@u c/@}
(div c (bex (mul (bex a) b)))
::
++ swp |=({a/bloq b/@} (rep a (flop (rip a b)))) :: reverse bloq order
++ xeb :: binary logarithm
~/ %xeb
|= a/@
^- @
(met 0 a)
:: ::
:::: 2d: bit logic ::
:: ::
:: con, dis, mix, not ::
::
++ con :: binary or
~/ %con
|= {a/@ b/@}
=+ [c=0 d=0]
|- ^- @
?: ?&(=(0 a) =(0 b)) d
%= $
a (rsh 0 1 a)
b (rsh 0 1 b)
c +(c)
d %+ add d
%^ lsh 0 c
?& =(0 (end 0 1 a))
=(0 (end 0 1 b))
==
==
::
++ dis :: binary and
~/ %dis
|= {a/@ b/@}
=| {c/@ d/@}
|- ^- @
?: ?|(=(0 a) =(0 b)) d
%= $
a (rsh 0 1 a)
b (rsh 0 1 b)
c +(c)
d %+ add d
%^ lsh 0 c
?| =(0 (end 0 1 a))
=(0 (end 0 1 b))
==
==
::
++ mix :: binary xor
~/ %mix
|= {a/@ b/@}
^- @
=+ [c=0 d=0]
|-
?: ?&(=(0 a) =(0 b)) d
%= $
a (rsh 0 1 a)
b (rsh 0 1 b)
c +(c)
d (add d (lsh 0 c =((end 0 1 a) (end 0 1 b))))
==
::
++ not |= {a/bloq b/@ c/@} :: binary not (sized)
(mix c (dec (bex (mul b (bex a)))))
:: ::
:::: 2e: insecure hashing ::
:: ::
:: fnv, mum, mug ::
::
++ fnv |=(a/@ (end 5 1 (mul 16.777.619 a))) :: FNV scrambler
++ mum :: mug with murmur3
~/ %mum
|= a/*
|^ (trim ?@(a a (mix $(a -.a) (mix 0x7fff.ffff $(a +.a)))))
++ spec :: standard murmur3
|= {syd/@ key/@}
?> (lte (met 5 syd) 1)
=+ ^= row
|= {a/@ b/@}
(con (end 5 1 (lsh 0 a b)) (rsh 0 (sub 32 a) b))
=+ mow=|=({a/@ b/@} (end 5 1 (mul a b)))
=+ len=(met 5 key)
=- =. goc (mix goc len)
=. goc (mix goc (rsh 4 1 goc))
=. goc (mow goc 0x85eb.ca6b)
=. goc (mix goc (rsh 0 13 goc))
=. goc (mow goc 0xc2b2.ae35)
(mix goc (rsh 4 1 goc))
^= goc
=+ [inx=0 goc=syd]
|- ^- @
?: =(inx len) goc
=+ kop=(cut 5 [inx 1] key)
=. kop (mow kop 0xcc9e.2d51)
=. kop (row 15 kop)
=. kop (mow kop 0x1b87.3593)
=. goc (mix kop goc)
=. goc (row 13 goc)
=. goc (end 5 1 (add 0xe654.6b64 (mul 5 goc)))
$(inx +(inx))
::
++ trim :: 31-bit nonzero
|= key/@
=+ syd=0xcafe.babe
|- ^- @
=+ haz=(spec syd key)
=+ ham=(mix (rsh 0 31 haz) (end 0 31 haz))
?.(=(0 ham) ham $(syd +(syd)))
--
::
++ mug :: 31bit nonzero FNV1a
~/ %mug
|= a/*
?^ a
=+ b=[p=$(a -.a) q=$(a +.a)]
|- ^- @
=+ c=(fnv (mix p.b (fnv q.b)))
=+ d=(mix (rsh 0 31 c) (end 0 31 c))
?. =(0 c) c
$(q.b +(q.b))
=+ b=2.166.136.261
|- ^- @
=+ c=b
=+ [d=0 e=(met 3 a)]
|- ^- @
?: =(d e)
=+ f=(mix (rsh 0 31 c) (end 0 31 c))
?. =(0 f) f
^$(b +(b))
$(c (fnv (mix c (cut 3 [d 1] a))), d +(d))
:: ::
:::: 2f: noun ordering ::
:: ::
:: aor, dor, gor, hor, lor, vor ::
::
++ aor :: a-order
~/ %aor
|= {a/* b/*}
^- ?
?: =(a b) &
?. ?=(@ a)
?: ?=(@ b) |
?: =(-.a -.b)
$(a +.a, b +.b)
$(a -.a, b -.b)
?. ?=(@ b) &
|-
=+ [c=(end 3 1 a) d=(end 3 1 b)]
?: =(c d)
$(a (rsh 3 1 a), b (rsh 3 1 b))
(lth c d)
::
++ dor :: d-order
~/ %dor
|= {a/* b/*}
^- ?
?: =(a b) &
?. ?=(@ a)
?: ?=(@ b) |
?: =(-.a -.b)
$(a +.a, b +.b)
$(a -.a, b -.b)
?. ?=(@ b) &
(lth a b)
::
++ gor :: g-order
~/ %gor
|= {a/* b/*}
^- ?
=+ [c=(mug a) d=(mug b)]
?: =(c d)
(dor a b)
(lth c d)
::
++ hor :: h-order
~/ %hor
|= {a/* b/*}
^- ?
?: ?=(@ a)
?. ?=(@ b) &
(gor a b)
?: ?=(@ b) |
?: =(-.a -.b)
(gor +.a +.b)
(gor -.a -.b)
::
++ lor :: l-order
~/ %lor
|= {a/* b/*}
^- ?
?: =(a b) &
?@ a
?^ b &
(lth a b)
?: =(-.a -.b)
$(a +.a, b +.b)
$(a -.a, b -.b)
::
++ vor :: v-order
~/ %vor
|= {a/* b/*}
^- ?
=+ [c=(mug (mug a)) d=(mug (mug b))]
?: =(c d)
(dor a b)
(lth c d)
:: ::
:::: ::
:: 2g: unsigned powers ::
:: ::
:: pow, sqt ::
::
++ pow :: unsigned exponent
~/ %pow
|= {a/@ b/@}
?: =(b 0) 1
|- ?: =(b 1) a
=+ c=$(b (div b 2))
=+ d=(mul c c)
?~ (dis b 1) d (mul d a)
::
++ sqt :: unsigned sqrt/rem
~/ %sqt
|= a/@ ^- {p/@ q/@}
?~ a [0 0]
=+ [q=(div (dec (xeb a)) 2) r=0]
=- [-.b (sub a +.b)]
^= b |-
=+ s=(add r (bex q))
=+ t=(mul s s)
?: =(q 0)
?:((lte t a) [s t] [r (mul r r)])
?: (lte t a)
$(r s, q (dec q))
$(q (dec q))
:: ::
:::: ::
:: ::
:: 2h: set logic ::
:: ::
:: in ::
::
++ in :: set engine
~/ %in
|_ a/(tree)
+- all :: logical AND
~/ %all
|* b/$-(* ?)
|- ^- ?
?~ a
&
?&((b n.a) $(a l.a) $(a r.a))
::
+- any :: logical OR
~/ %any
|* b/$-(* ?)
|- ^- ?
?~ a
|
?|((b n.a) $(a l.a) $(a r.a))
::
+- apt :: check correctness
|- ^- ?
?~ a
&
?& ?~(l.a & ?&((vor n.a n.l.a) (hor n.l.a n.a) $(a l.a)))
?~(r.a & ?&((vor n.a n.r.a) (hor n.a n.r.a) $(a r.a)))
==
::
+- bif :: splits a by b
~/ %bif
|* b/*
^+ [l=a r=a]
=< [+< +>]
|- ^+ a
?~ a
[b ~ ~]
?: =(b n.a)
a
?: (hor b n.a)
=+ c=$(a l.a)
?> ?=(^ c)
[n.c l.c [n.a r.c r.a]]
=+ c=$(a r.a)
?> ?=(^ c)
[n.c [n.a l.a l.c] r.c]
::
+- del :: b without any a
~/ %del
|* b/*
|- ^+ a
?~ a
~
?. =(b n.a)
?: (hor b n.a)
[n.a $(a l.a) r.a]
[n.a l.a $(a r.a)]
|- ^- {$?($~ _a)}
?~ l.a r.a
?~ r.a l.a
?: (vor n.l.a n.r.a)
[n.l.a l.l.a $(l.a r.l.a)]
[n.r.a $(r.a l.r.a) r.r.a]
::
+- dif :: difference
~/ %dif
|* b/_a
|- ^+ a
?~ b
a
=+ c=(bif n.b)
?> ?=(^ c)
=+ d=$(a l.c, b l.b)
=+ e=$(a r.c, b r.b)
|- ^- {$?($~ _a)}
?~ d e
?~ e d
?: (vor n.d n.e)
[n.d l.d $(d r.d)]
[n.e $(e l.e) r.e]
::
+- dig :: axis of a in b
|= b/*
=+ c=1
|- ^- (unit @)
?~ a ~
?: =(b n.a) [~ u=(peg c 2)]
?: (hor b n.a)
$(a l.a, c (peg c 6))
$(a r.a, c (peg c 7))
::
+- gas :: concatenate
~/ %gas
|= b/(list _?>(?=(^ a) n.a))
|- ^+ a
?~ b
a
$(b t.b, a (put i.b))
::
+- has :: b exists in a check
~/ %has
|* b/*
|- ^- ?
?~ a
|
?: =(b n.a)
&
?: (hor b n.a)
$(a l.a)
$(a r.a)
::
+- int :: intersection
~/ %int
|* b/_a
|- ^+ a
?~ b
~
?~ a
~
?. (vor n.a n.b)
$(a b, b a)
?: =(n.b n.a)
[n.a $(a l.a, b l.b) $(a r.a, b r.b)]
?: (hor n.b n.a)
%- uni(a $(a l.a, b [n.b l.b ~])) $(b r.b)
%- uni(a $(a r.a, b [n.b ~ r.b])) $(b l.b)
::
+- put :: puts b in a, sorted
~/ %put
|* b/*
|- ^+ a
?~ a
[b ~ ~]
?: =(b n.a)
a
?: (hor b n.a)
=+ c=$(a l.a)
?> ?=(^ c)
?: (vor n.a n.c)
[n.a c r.a]
[n.c l.c [n.a r.c r.a]]
=+ c=$(a r.a)
?> ?=(^ c)
?: (vor n.a n.c)
[n.a l.a c]
[n.c [n.a l.a l.c] r.c]
::
+- rep :: replace by product
|* b/_|=({* *} +<+)
|-
?~ a +<+.b
$(a r.a, +<+.b $(a l.a, +<+.b (b n.a +<+.b)))
::
+- run :: apply gate to values
|* {b/$-(* *) c/*}
|-
?~ a c
$(a r.a, c [(b n.a) $(a l.a)])
::
+- tap :: convert to list
~/ %tap
|= b/(list _?>(?=(^ a) n.a))
^+ b
?~ a
b
$(a r.a, b [n.a $(a l.a)])
::
+- uni :: union
~/ %uni
|* b/_a
?: =(a b) a
|- ^+ a
?~ b
a
?~ a
b
?: (vor n.a n.b)
?: =(n.b n.a)
[n.b $(a l.a, b l.b) $(a r.a, b r.b)]
?: (hor n.b n.a)
$(a [n.a $(a l.a, b [n.b l.b ~]) r.a], b r.b)
$(a [n.a l.a $(a r.a, b [n.b ~ r.b])], b l.b)
?: =(n.a n.b)
[n.b $(b l.b, a l.a) $(b r.b, a r.a)]
?: (hor n.a n.b)
$(b [n.b $(b l.b, a [n.a l.a ~]) r.b], a r.a)
$(b [n.b l.b $(b r.b, a [n.a ~ r.a])], a l.a)
::
+- wyt :: size of set
|- ^- @
?~(a 0 +((add $(a l.a) $(a r.a))))
--
:: ::
:::: 2i: map logic ::
:: ::
:: by ::
::
++ by :: map engine
~/ %by
|_ a/(tree (pair))
+- all :: logical AND
~/ %all
|* b/$-(* ?)
|- ^- ?
?~ a
&
?&((b q.n.a) $(a l.a) $(a r.a))
::
+- any :: logical OR
~/ %any
|* b/$-(* ?)
|- ^- ?
?~ a
|
?|((b q.n.a) $(a l.a) $(a r.a))
::
+- apt :: map invariant
|- ^- ?
?~ a
&
?& ?~(l.a & ?&((vor p.n.a p.n.l.a) (gor p.n.l.a p.n.a) $(a l.a)))
?~(r.a & ?&((vor p.n.a p.n.r.a) (gor p.n.a p.n.r.a) $(a l.a)))
==
+- bif :: splits a by b
~/ %bif
|* {b/* c/*}
^+ [l=a r=a]
=< [+< +>]
|- ^+ a
?~ a
[[b c] ~ ~]
?: =(b p.n.a)
?: =(c q.n.a)
a
[[b c] l.a r.a]
?: (gor b p.n.a)
=+ d=$(a l.a)
?> ?=(^ d)
[n.d l.d [n.a r.d r.a]]
=+ d=$(a r.a)
?> ?=(^ d)
[n.d [n.a l.a l.d] r.d]
::
+- del :: delete at key b
~/ %del
|* b/*
|- ^+ a
?~ a
~
?. =(b p.n.a)
?: (gor b p.n.a)
[n.a $(a l.a) r.a]
[n.a l.a $(a r.a)]
|- ^- {$?($~ _a)}
?~ l.a r.a
?~ r.a l.a
?: (vor p.n.l.a p.n.r.a)
[n.l.a l.l.a $(l.a r.l.a)]
[n.r.a $(r.a l.r.a) r.r.a]
::
+- dif :: difference
~/ %dif
|* b/_a
|- ^+ a
?~ b
a
=+ c=(bif n.b)
?> ?=(^ c)
=+ d=$(a l.c, b l.b)
=+ e=$(a r.c, b r.b)
|- ^- {$?($~ _a)}
?~ d e
?~ e d
?: (vor p.n.d p.n.e)
[n.d l.d $(d r.d)]
[n.e $(e l.e) r.e]
::
+- dig :: axis of b key
|= b/*
=+ c=1
|- ^- (unit @)
?~ a ~
?: =(b p.n.a) [~ u=(peg c 2)]
?: (gor b p.n.a)
$(a l.a, c (peg c 6))
$(a r.a, c (peg c 7))
::
+- gas :: concatenate
~/ %gas
|* b/(list {p/* q/*})
=> .(b `(list _?>(?=(^ a) n.a))`b)
|- ^+ a
?~ b
a
$(b t.b, a (put p.i.b q.i.b))
::
+- get :: grab value by key
~/ %get
|= b/*
^- {$@($~ {$~ u/_?>(?=(^ a) q.n.a)})}
?~ a
~
?: =(b p.n.a)
[~ u=q.n.a]
?: (gor b p.n.a)
$(a l.a)
$(a r.a)
::
+- got
|* b/*
(need (get b))
::
+- has :: key existence check
~/ %has
|* b/*
!=(~ (get b))
::
+- int :: intersection
~/ %int
|* b/_a
|- ^+ a
?~ b
~
?~ a
~
?: (vor p.n.a p.n.b)
?: =(p.n.b p.n.a)
[n.b $(a l.a, b l.b) $(a r.a, b r.b)]
?: (gor p.n.b p.n.a)
%- uni(a $(a l.a, b [n.b l.b ~])) $(b r.b)
%- uni(a $(a r.a, b [n.b ~ r.b])) $(b l.b)
?: =(p.n.a p.n.b)
[n.b $(b l.b, a l.a) $(b r.b, a r.a)]
?: (gor p.n.a p.n.b)
%- uni(a $(b l.b, a [n.a l.a ~])) $(a r.a)
%- uni(a $(b r.b, a [n.a ~ r.a])) $(a l.a)
::
+- mar :: add with validation
|* {b/_?>(?=(^ a) p.n.a) c/(unit _?>(?=(^ a) q.n.a))}
?~ c
(del b)
(put b u.c)
::
+- put :: adds key-value pair
~/ %put
|* {b/* c/*}
|- ^+ a
?~ a
[[b c] ~ ~]
?: =(b p.n.a)
?: =(c q.n.a)
a
[[b c] l.a r.a]
?: (gor b p.n.a)
=+ d=$(a l.a)
?> ?=(^ d)
?: (vor p.n.a p.n.d)
[n.a d r.a]
[n.d l.d [n.a r.d r.a]]
=+ d=$(a r.a)
?> ?=(^ d)
?: (vor p.n.a p.n.d)
[n.a l.a d]
[n.d [n.a l.a l.d] r.d]
::
+- rep :: replace by product
|* b/_|=({* *} +<+)
|-
?~ a +<+.b
$(a r.a, +<+.b $(a l.a, +<+.b (b n.a +<+.b)))
::
+- rib :: transform + product
|* {b/* c/$-(* *)}
|- ^+ [b a]
?~ a [b ~]
=+ d=(c n.a b)
=. n.a +.d
=+ e=$(a l.a, b -.d)
=+ f=$(a r.a, b -.e)
[-.f [n.a +.e +.f]]
::
+- run :: apply gate to values
|* b/$-(* *)
|-
?~ a a
[n=[p=p.n.a q=(b q.n.a)] l=$(a l.a) r=$(a r.a)]
::
+- tap :: listify pairs
~/ %tap
|= b/(list _?>(?=(^ a) n.a))
^+ b
?~ a
b
$(a r.a, b [n.a $(a l.a)])
::
+- uni :: union, merge
~/ %uni
|* b/_a
|- ^+ a
?~ b
a
?~ a
b
?: (vor p.n.a p.n.b)
?: =(p.n.b p.n.a)
[n.b $(a l.a, b l.b) $(a r.a, b r.b)]
?: (gor p.n.b p.n.a)
$(a [n.a $(a l.a, b [n.b l.b ~]) r.a], b r.b)
$(a [n.a l.a $(a r.a, b [n.b ~ r.b])], b l.b)
?: =(p.n.a p.n.b)
[n.b $(b l.b, a l.a) $(b r.b, a r.a)]
?: (gor p.n.a p.n.b)
$(b [n.b $(b l.b, a [n.a l.a ~]) r.b], a r.a)
$(b [n.b l.b $(b r.b, a [n.a ~ r.a])], a l.a)
::
+- urn :: apply gate to nodes
|* b/$-({* *} *)
|-
?~ a ~
[n=[p=p.n.a q=(b p.n.a q.n.a)] l=$(a l.a) r=$(a r.a)]
::
+- wyt :: depth of map
|- ^- @
?~(a 0 +((add $(a l.a) $(a r.a))))
--
:: ::
:::: 2j: jar and jug logic ::
:: ::
::
++ ja :: jar engine
|_ a/(tree (pair * (list)))
+- get :: gets list by key
|* b/*
=+ c=(~(get by a) b)
?~(c ~ u.c)
::
+- add :: adds key-list pair
|* {b/* c/*}
=+ d=(get b)
(~(put by a) b [c d])
--
++ ju :: jug engine
|_ a/(tree (pair * (tree)))
+- del :: del key-set pair
|* {b/* c/*}
^+ a
=+ d=(get b)
=+ e=(~(del in d) c)
?~ e
(~(del by a) b)
(~(put by a) b e)
::
+- gas :: concatenate
|* b/(list {p/* q/*})
=> .(b `(list _?>(?=({{* ^} ^} a) [p=p q=n.q]:n.a))`b)
|- ^+ a
?~ b
a
$(b t.b, a (put p.i.b q.i.b))
::
+- get :: gets set by key
|* b/*
=+ c=(~(get by a) b)
?~(c ~ u.c)
::
+- has :: existence check
|* {b/* c/*}
^- ?
(~(has in (get b)) c)
::
+- put :: add key-set pair
|* {b/* c/*}
^+ a
=+ d=(get b)
(~(put by a) b (~(put in d) c))
--
:: ::
:::: 2k: queue logic ::
:: ::
:: to ::
::
++ to :: queue engine
|_ a/(tree)
+- bal
|- ^+ a
?~ a ~
?. |(?=($~ l.a) (vor n.a n.l.a))
$(a [n.l.a l.l.a $(a [n.a r.l.a r.a])])
?. |(?=($~ r.a) (vor n.a n.r.a))
$(a [n.r.a $(a [n.a l.a l.r.a]) r.r.a])
a
::
+- dep :: max depth of queue
|- ^- @
?~ a 0
+((max $(a l.a) $(a r.a)))
::
+- gas :: insert list to que
|= b/(list _?>(?=(^ a) n.a))
|- ^+ a
?~(b a $(b t.b, a (put i.b)))
::
+- get :: head-rest pair
|- ^+ ?>(?=(^ a) [p=n.a q=*(tree _n.a)])
?~ a
!!
?~ r.a
[n.a l.a]
=+ b=$(a r.a)
:- p.b
?: |(?=($~ q.b) (vor n.a n.q.b))
[n.a l.a q.b]
[n.q.b [n.a l.a l.q.b] r.q.b]
::
+- nap :: removes head
?> ?=(^ a)
?: =(~ l.a) r.a
=+ b=get(a l.a)
bal(a ^+(a [p.b q.b r.a]))
::
+- put :: insert new tail
|* b/*
|- ^+ a
?~ a
[b ~ ~]
bal(a a(l $(a l.a)))
::
+- tap :: adds list to end
|= b/(list _?>(?=(^ a) n.a))
=+ 0 :: breaks tap.in match
^+ b
?~ a
b
$(a r.a, b [n.a $(a l.a)])
::
+- top :: produces head
|- ^- (unit _?>(?=(^ a) n.a))
?~ a ~
?~(r.a [~ n.a] $(a r.a))
--
:: ::
:::: 2l: container from container ::
:: ::
:: malt, molt, silt ::
::
++ malt :: map from list
|* a/(list)
(molt `(list {p/_-<.a q/_->.a})`a)
::
++ molt :: map from pair list
|* a/(list (pair))
(~(gas by `(tree {_p.i.-.a _q.i.-.a})`~) a)
::
++ silt :: set from list
|* a/(list)
=+ b=*(tree _?>(?=(^ a) i.a))
(~(gas in b) a)
:: ::
:::: 2m: container from noun ::
:: ::
:: ly, my, sy ::
::
++ ly :: list from raw noun
|* a/*
^+((homo (limo a)) a)
::
++ my :: map from raw noun
|* a/*
(malt ^+((homo (limo a)) a))
::
++ sy :: set from raw noun
|* a/*
(silt ^+((homo (limo a)) a))
:: ::
:::: 2n: functional hacks ::
:: ::
:: aftr, cork, corl, cury, curr, fore, ::
:: hard, head, same, soft, tail, test ::
::
++ aftr |*(a/$-(* *) |*(b/$-(* *) (pair b a))) :: pair after
++ cork |*({a/_|=(* **) b/gate} (corl b a)) :: compose forward
++ corl :: compose backwards
|* {a/gate b/_|=(* **)}
=< +:|.((a (b))) :: span check
=+ c=+<.b
|.((a (b c)))
::
++ cury :: curry left
|* {a/_|=(^ **) b/*}
=+ c=+<+.a
|.((a b c))
::
++ curr :: curry right
|* {a/_|=(^ **) b/*}
=+ c=+<+.a
|.((a c b))
::
++ fore |*(a/$-(* *) |*(b/$-(* *) (pair a b))) :: pair before
++ hard :: force remold
|* han/$-(* *)
|= fud/* ^- han
~> %mean.[0 %leaf "hard"]
=+ gol=(han fud)
?>(=(gol fud) gol)
::
::
++ head |*(^ +<-) :: get head
++ same |*(* +<) :: identity
++ soft :: maybe remold
|* han/$-(* *)
|= fud/* ^- (unit han)
=+ gol=(han fud)
?.(=(gol fud) ~ [~ gol])
::
++ tail |*(^ +<+) :: get tail
++ test |=(^ =(+<- +<+)) :: equality
::
:: ::
:::: 2o: normalizing containers ::
:: ::
:: jar, jug, map, set, qeu ::
::
++ jar |*({a/gate b/gate} (map a (list b))) :: map of lists
++ jug |*({a/gate b/gate} (map a (set b))) :: map of sets
++ map |* {a/gate b/gate} :: table
$@($~ {n/{p/a q/b} l/(map a b) r/(map a b)}) ::
++ qeu |* a/gate :: queue
$@($~ {n/a l/(qeu a) r/(qeu a)}) ::
++ set |* a/gate :: set
$@($~ {n/a l/(set a) r/(set a)}) ::
::
:::: 2p: serialization ::
:: ::
:: cue, jam, mat, rub ::
::
++ cue :: unpack
~/ %cue
|= a/@
^- *
=+ b=0
=+ m=`(map @ *)`~
=< q
|- ^- {p/@ q/* r/(map @ *)}
?: =(0 (cut 0 [b 1] a))
=+ c=(rub +(b) a)
[+(p.c) q.c (~(put by m) b q.c)]
=+ c=(add 2 b)
?: =(0 (cut 0 [+(b) 1] a))
=+ u=$(b c)
=+ v=$(b (add p.u c), m r.u)
=+ w=[q.u q.v]
[(add 2 (add p.u p.v)) w (~(put by r.v) b w)]
=+ d=(rub c a)
[(add 2 p.d) (need (~(get by m) q.d)) m]
::
++ jam :: pack
~/ %jam
|= a/*
^- @
=+ b=0
=+ m=`(map * @)`~
=< q
|- ^- {p/@ q/@ r/(map * @)}
=+ c=(~(get by m) a)
?~ c
=> .(m (~(put by m) a b))
?: ?=(@ a)
=+ d=(mat a)
[(add 1 p.d) (lsh 0 1 q.d) m]
=> .(b (add 2 b))
=+ d=$(a -.a)
=+ e=$(a +.a, b (add b p.d), m r.d)
[(add 2 (add p.d p.e)) (mix 1 (lsh 0 2 (cat 0 q.d q.e))) r.e]
?: ?&(?=(@ a) (lte (met 0 a) (met 0 u.c)))
=+ d=(mat a)
[(add 1 p.d) (lsh 0 1 q.d) m]
=+ d=(mat u.c)
[(add 2 p.d) (mix 3 (lsh 0 2 q.d)) m]
::
++ mat :: length-encode
~/ %mat
|= a/@
^- {p/@ q/@}
?: =(0 a)
[1 1]
=+ b=(met 0 a)
=+ c=(met 0 b)
:- (add (add c c) b)
(cat 0 (bex c) (mix (end 0 (dec c) b) (lsh 0 (dec c) a)))
::
++ rub :: length-decode
~/ %rub
|= {a/@ b/@}
^- {p/@ q/@}
=+ ^= c
=+ [c=0 m=(met 0 b)]
|- ?< (gth c m)
?. =(0 (cut 0 [(add a c) 1] b))
c
$(c +(c))
?: =(0 c)
[1 0]
=+ d=(add a +(c))
=+ e=(add (bex (dec c)) (cut 0 [d (dec c)] b))
[(add (add c c) e) (cut 0 [(add d (dec c)) e] b)]
::
:::: 2q: molds and mold builders ::
:: ::
:: tape ::
::
++ char @t :: UTF8 byte
++ cord @t :: UTF8, LSB first
++ date {{a/? y/@ud} m/@ud t/tarp} :: parsed date
++ knot @ta :: ASCII text
++ tang (list tank) :: bottom-first error
++ tank $% {$leaf p/tape} :: printing formats
$: $palm :: backstep list
p/{p/tape q/tape r/tape s/tape} ::
q/(list tank) ::
== ::
$: $rose :: flat list
p/{p/tape q/tape r/tape} :: mid open close
q/(list tank) ::
== ::
== ::
++ tanq :: tomorrow's tank
$? {$~ p/(list tanq)} :: list of printables
{$~ $~ p/tape} :: simple string
(pair @tas tanq) :: captioned
== ::
++ tape (list @t) :: UTF8 string as list
++ tarp {d/@ud h/@ud m/@ud s/@ud f/(list @ux)} :: parsed time
++ term @tas :: ascii symbol
++ tone $% {$0 p/*} :: success
{$1 p/(list)} :: blocks
{$2 p/(list {@ta *})} :: error report
== ::
++ toon $% {$0 p/*} :: success
{$1 p/(list)} :: blocks
{$2 p/(list tank)} :: stack trace
== ::
-- =>
:: ::
:::: 3: layer three ::
:: ::
|%
::
:::: 3a: signed and modular ints ::
:: ::
:: egcd, fe, fo, si ::
::
++ egcd !: :: schneier's egcd
|= {a/@ b/@}
=+ si
=+ [c=(sun a) d=(sun b)]
=+ [u=[c=(sun 1) d=--0] v=[c=--0 d=(sun 1)]]
|- ^- {d/@ u/@s v/@s}
?: =(--0 c)
[(abs d) d.u d.v]
:: ?> ?& =(c (sum (pro (sun a) c.u) (pro (sun b) c.v)))
:: =(d (sum (pro (sun a) d.u) (pro (sun b) d.v)))
:: ==
=+ q=(fra d c)
%= $
c (dif d (pro q c))
d c
u [(dif d.u (pro q c.u)) c.u]
v [(dif d.v (pro q c.v)) c.v]
==
::
++ fe :: modulo bloq
|_ a/bloq
++ dif |=({b/@ c/@} (sit (sub (add out (sit b)) (sit c)))) :: difference
++ inv |=(b/@ (sub (dec out) (sit b))) :: inverse
++ net |= b/@ ^- @ :: flip byte endianness
=> .(b (sit b))
?: (lte a 3)
b
=+ c=(dec a)
%+ con
(lsh c 1 $(a c, b (cut c [0 1] b)))
$(a c, b (cut c [1 1] b))
++ out (bex (bex a)) :: mod value
++ rol |= {b/bloq c/@ d/@} ^- @ :: roll left
=+ e=(sit d)
=+ f=(bex (sub a b))
=+ g=(mod c f)
(sit (con (lsh b g e) (rsh b (sub f g) e)))
++ ror |= {b/bloq c/@ d/@} ^- @ :: roll right
=+ e=(sit d)
=+ f=(bex (sub a b))
=+ g=(mod c f)
(sit (con (rsh b g e) (lsh b (sub f g) e)))
++ sum |=({b/@ c/@} (sit (add b c))) :: wrapping add
++ sit |=(b/@ (end a 1 b)) :: enforce modulo
--
::
++ fo :: modulo prime
|_ a/@
++ dif
|= {b/@ c/@}
(sit (sub (add a b) (sit c)))
::
++ exp
|= {b/@ c/@}
?: =(0 b)
1
=+ d=$(b (rsh 0 1 b))
=+ e=(pro d d)
?:(=(0 (end 0 1 b)) e (pro c e))
::
++ fra
|= {b/@ c/@}
(pro b (inv c))
::
++ inv
|= b/@
=+ c=(dul:si u:(egcd b a) a)
c
::
++ pro
|= {b/@ c/@}
(sit (mul b c))
::
++ sit
|= b/@
(mod b a)
::
++ sum
|= {b/@ c/@}
(sit (add b c))
--
::
++ si !: :: signed integer
|%
++ abs |=(a/@s (add (end 0 1 a) (rsh 0 1 a))) :: absolute value
++ dif |= {a/@s b/@s} :: subtraction
(sum a (new !(syn b) (abs b)))
++ dul |= {a/@s b/@} :: modulus
=+(c=(old a) ?:(-.c (mod +.c b) (sub b +.c)))
++ fra |= {a/@s b/@s} :: divide
(new =(0 (mix (syn a) (syn b))) (div (abs a) (abs b)))
++ new |= {a/? b/@} :: [sign value] to @s
`@s`?:(a (mul 2 b) ?:(=(0 b) 0 +((mul 2 (dec b)))))
++ old |=(a/@s [(syn a) (abs a)]) :: [sign value]
++ pro |= {a/@s b/@s} :: multiplication
(new =(0 (mix (syn a) (syn b))) (mul (abs a) (abs b)))
++ rem |=({a/@s b/@s} (dif a (pro b (fra a b)))) :: remainder
++ sum |= {a/@s b/@s} :: addition
=+ [c=(old a) d=(old b)]
?: -.c
?: -.d
(new & (add +.c +.d))
?: (gte +.c +.d)
(new & (sub +.c +.d))
(new | (sub +.d +.c))
?: -.d
?: (gte +.c +.d)
(new | (sub +.c +.d))
(new & (sub +.d +.c))
(new | (add +.c +.d))
++ sun |=(a/@u (mul 2 a)) :: @u to @s
++ syn |=(a/@s =(0 (end 0 1 a))) :: sign test
++ cmp |= {a/@s b/@s} :: compare
^- @s
?: =(a b)
--0
?: (syn a)
?: (syn b)
?: (gth a b)
--1
-1
--1
?: (syn b)
-1
?: (gth a b)
-1
--1
--
:: ::
:::: 3b: floating point ::
:: ::
:: rd, rh, rs, rq ::
:: rlyd, rlys, rlyh, rlyq ::
:: ryld, ryls, rylh, rylq ::
::
-- =>
|%
++ fn :: float, infinity, or NaN
:: s=sign, e=exponent, a=arithmetic form
:: (-1)^s * a * 2^e
$% {$f s/? e/@s a/@u}
{$i s/?}
{$n $~}
==
::
++ dn :: decimal float, infinity, or NaN
:: (-1)^s * a * 10^e
$% {$d s/? e/@s a/@u}
{$i s/?}
{$n $~}
==
::
++ rn :: parsed decimal float
::
$% {$d a/? b/{c/@ {d/@ e/@} f/? i/@}}
{$i a/?}
{$n $~}
==
::
++ fl :: arb. precision fp
=+ ^- {{p/@u v/@s w/@u} r/$?($n $u $d $z $a) d/$?($d $f $i)}
[[113 -16.494 32.765] %n %d]
:: p=precision: number of bits in arithmetic form; must be at least 2
:: v=min exponent: minimum value of e
:: w=width: max - min value of e, 0 is fixed point
:: r=rounding mode: nearest (ties to even), up, down, to zero, away from zero
:: d=behavior: return denormals, flush denormals to zero,
:: infinite exponent range
=>
~% %cofl +> ~
:: internal functions; mostly operating on {e/@s a/@u}, in other words
:: positive numbers. many of these have undefined behavior if a=0.
|%
++ rou
|= {a/{e/@s a/@u}} ^- fn (rau a &)
::
++ rau
|= {a/{e/@s a/@u} t/?} ^- fn
?- r
$z (lug %fl a t) $d (lug %fl a t)
$a (lug %ce a t) $u (lug %ce a t)
$n (lug %ne a t)
==
::
++ add :: add; exact if e
|= {a/{e/@s a/@u} b/{e/@s a/@u} e/?} ^- fn
=+ q=(dif:si e.a e.b)
|- ?. (syn:si q) $(b a, a b, q +(q)) :: a has larger exp
?: e
[%f & e.b (^add (lsh 0 (abs:si q) a.a) a.b)]
=+ [ma=(met 0 a.a) mb=(met 0 a.b)]
=+ ^= w %+ dif:si e.a %- sun:si :: expanded exp of a
?: (gth prc ma) (^sub prc ma) 0
=+ ^= x %+ sum:si e.b (sun:si mb) :: highest exp for b
?: =((cmp:si w x) --1) :: don't need to add
?- r
$z (lug %fl a &) $d (lug %fl a &)
$a (lug %lg a &) $u (lug %lg a &)
$n (lug %na a &)
==
(rou [e.b (^add (lsh 0 (abs:si q) a.a) a.b)])
::
++ sub :: subtract; exact if e
|= {a/{e/@s a/@u} b/{e/@s a/@u} e/?} ^- fn
=+ q=(dif:si e.a e.b)
|- ?. (syn:si q)
(fli $(b a, a b, q +(q), r swr))
=+ [ma=(met 0 a.a) mb=(met 0 a.b)]
=+ ^= w %+ dif:si e.a %- sun:si
?: (gth prc ma) (^sub prc ma) 0
=+ ^= x %+ sum:si e.b (sun:si mb)
?: &(!e =((cmp:si w x) --1))
?- r
$z (lug %sm a &) $d (lug %sm a &)
$a (lug %ce a &) $u (lug %ce a &)
$n (lug %nt a &)
==
=+ j=(lsh 0 (abs:si q) a.a)
|- ?. (gte j a.b)
(fli $(a.b j, j a.b, r swr))
=+ i=(^sub j a.b)
?~ i [%f & zer]
?: e [%f & e.b i] (rou [e.b i])
::
++ mul :: multiply
|= {a/{e/@s a/@u} b/{e/@s a/@u}} ^- fn
(rou (sum:si e.a e.b) (^mul a.a a.b))
::
++ div :: divide
|= {a/{e/@s a/@u} b/{e/@s a/@u}} ^- fn
=+ [ma=(met 0 a.a) mb=(met 0 a.b)]
=+ v=(dif:si (sun:si ma) (sun:si +((^add mb prc))))
=. a ?: (syn:si v) a
a(e (sum:si v e.a), a (lsh 0 (abs:si v) a.a))
=+ [j=(dif:si e.a e.b) q=(dvr a.a a.b)]
(rau [j p.q] =(q.q 0))
::
++ sqt :: square root
|= {a/{e/@s a/@u}} ^- fn
=. a
=+ [w=(met 0 a.a) x=(^mul +(prc) 2)]
=+ ?:((^lth w x) (^sub x w) 0)
=+ ?: =((dis - 1) (dis (abs:si e.a) 1)) -
(^add - 1)
a(e (dif:si e.a (sun:si -)), a (lsh 0 - a.a))
=+ [y=(^sqt a.a) z=(fra:si e.a --2)]
(rau [z p.y] =(q.y 0))
::
++ lth :: less-than
|= {a/{e/@s a/@u} b/{e/@s a/@u}} ^- ?
?: =(e.a e.b) (^lth a.a a.b)
=+ c=(cmp:si (ibl a) (ibl b))
?: =(c -1) & ?: =(c --1) |
?: =((cmp:si e.a e.b) -1)
(^lth (rsh 0 (abs:si (dif:si e.a e.b)) a.a) a.b)
(^lth (lsh 0 (abs:si (dif:si e.a e.b)) a.a) a.b)
::
++ lte :: less-equals
|= {a/{e/@s a/@u} b/{e/@s a/@u}} ^- ?
?: =(e.a e.b) (^lte a.a a.b)
=+ c=(cmp:si (ibl a) (ibl b))
?: =(c -1) & ?: =(c --1) |
?: =((cmp:si e.a e.b) -1)
(^lte a.a (lsh 0 (abs:si (dif:si e.a e.b)) a.b))
(^lte (lsh 0 (abs:si (dif:si e.a e.b)) a.a) a.b)
::
++ equ :: equals
|= {a/{e/@s a/@u} b/{e/@s a/@u}} ^- ?
?. =((ibl a) (ibl b)) |
?: =((cmp:si e.a e.b) -1)
=((lsh 0 (abs:si (dif:si e.a e.b)) a.b) a.a)
=((lsh 0 (abs:si (dif:si e.a e.b)) a.a) a.b)
::
:: integer binary logarithm: 2^ibl(a) <= |a| < 2^(ibl(a)+1)
++ ibl
|= {a/{e/@s a/@u}} ^- @s
(sum:si (sun:si (dec (met 0 a.a))) e.a)
::
:: change to a representation where a.a is odd
:: every fn has a unique representation of this kind
++ uni
|= {a/{e/@s a/@u}}
|- ?: =((end 0 1 a.a) 1) a
$(a.a (rsh 0 1 a.a), e.a (sum:si e.a --1))
::
:: expands to either full precision or to denormalized
++ xpd
|= {a/{e/@s a/@u}}
=+ ma=(met 0 a.a)
?: (gte ma prc) a
=+ ?: =(den %i) (^sub prc ma)
=+ ^= q
=+ w=(dif:si e.a emn)
?: (syn:si w) (abs:si w) 0
(min q (^sub prc ma))
a(e (dif:si e.a (sun:si -)), a (lsh 0 - a.a))
::
:: central rounding mechanism
:: can perform: floor, ceiling, smaller, larger,
:: nearest (round ties to: even, away from 0, toward 0)
:: s is sticky bit: represents a value less than ulp(a) = 2^(e.a)
::
++ lug
~/ %lug
|= {t/$?($fl $ce $sm $lg $ne $na $nt) a/{e/@s a/@u} s/?} ^- fn
?< =(a.a 0)
=-
?. =(den %f) - :: flush denormals
?. ?=({$f *} -) -
?: =((met 0 ->+>) prc) - [%f & zer]
::
=+ m=(met 0 a.a)
?> |(s (gth m prc)) :: require precision
=+ ^= q
=+ ^= f :: reduce precision
?: (gth m prc) (^sub m prc) 0
=+ ^= g %- abs:si :: enforce min. exp
?: =(den %i) --0
?: =((cmp:si e.a emn) -1) (dif:si emn e.a) --0
(max f g)
=^ b a :- (end 0 q a.a)
a(e (sum:si e.a (sun:si q)), a (rsh 0 q a.a))
::
?~ a.a
?< =(den %i)
?- t
$fl [%f & zer]
$sm [%f & zer]
$ce [%f & spd]
$lg [%f & spd]
$ne ?: s [%f & ?:((^lte b (bex (dec q))) zer spd)]
[%f & ?:((^lth b (bex (dec q))) zer spd)]
$nt ?: s [%f & ?:((^lte b (bex (dec q))) zer spd)]
[%f & ?:((^lth b (bex (dec q))) zer spd)]
$na [%f & ?:((^lth b (bex (dec q))) zer spd)]
==
::
=. a (xpd a)
::
=. a
?- t
$fl a
$lg a(a +(a.a))
$sm ?. &(=(b 0) s) a
?: &(=(e.a emn) !=(den %i)) a(a (dec a.a))
=+ y=(dec (^mul a.a 2))
?. (^lte (met 0 y) prc) a(a (dec a.a))
[(dif:si e.a --1) y]
$ce ?: &(=(b 0) s) a a(a +(a.a))
$ne ?~ b a
=+ y=(bex (dec q))
?: &(=(b y) s) :: round halfs to even
?~ (dis a.a 1) a a(a +(a.a))
?: (^lth b y) a a(a +(a.a))
$na ?~ b a
=+ y=(bex (dec q))
?: (^lth b y) a a(a +(a.a))
$nt ?~ b a
=+ y=(bex (dec q))
?: =(b y) ?: s a a(a +(a.a))
?: (^lth b y) a a(a +(a.a))
==
::
=. a ?. =((met 0 a.a) +(prc)) a
a(a (rsh 0 1 a.a), e (sum:si e.a --1))
?~ a.a [%f & zer]
::
?: =(den %i) [%f & a]
?: =((cmp:si emx e.a) -1) [%i &] [%f & a] :: enforce max. exp
::
++ drg :: dragon4;
~/ %drg :: convert to decimal
|= {a/{e/@s a/@u}} ^- {@s @u}
?< =(a.a 0)
=. a (xpd a)
=+ r=(lsh 0 ?:((syn:si e.a) (abs:si e.a) 0) a.a)
=+ s=(lsh 0 ?.((syn:si e.a) (abs:si e.a) 0) 1)
=+ m=(lsh 0 ?:((syn:si e.a) (abs:si e.a) 0) 1)
=+ [k=--0 q=(^div (^add s 9) 10)]
|- ?: (^lth r q)
%= $
k (dif:si k --1)
r (^mul r 10)
m (^mul m 10)
==
|- ?: (gte (^add (^mul r 2) m) (^mul s 2))
$(s (^mul s 10), k (sum:si k --1))
=+ [u=0 o=0]
|-
=+ v=(dvr (^mul r 10) s)
=> %= .
k (dif:si k --1)
u p.v
r q.v
m (^mul m 10)
==
=+ l=(^lth (^mul r 2) m)
=+ ^= h
?| (^lth (^mul s 2) m)
(gth (^mul r 2) (^sub (^mul s 2) m))
==
?: &(!l !h)
$(o (^add (^mul o 10) u))
=+ q=&(h |(!l (gte (^mul r 2) s)))
=. o (^add (^mul o 10) ?:(q +(u) u))
[k o]
::
++ toj :: round to integer
|= {a/{e/@s a/@u}} ^- fn
?. =((cmp:si e.a --0) -1) [%f & a]
=+ x=(abs:si e.a)
=+ y=(rsh 0 x a.a)
?: |(=(r %d) =(r %z)) [%f & --0 y]
=+ z=(end 0 x a.a)
?: |(=(r %u) =(r %a)) [%f & --0 ?~(z y +(y))]
=+ i=(bex (dec x))
?: &(=(z i) =((dis y 1) 0)) [%f & --0 y]
?: (^lth z i) [%f & --0 y] [%f & --0 +(y)]
::
++ ned :: require ?=({$f *} a)
|= {a/fn} ^- {$f s/? e/@s a/@u}
?: ?=({$f *} a) a
~> %mean.[0 leaf+"need-float"]
!!
::
++ shf :: a * 2^b; no rounding
|= {a/fn b/@s}
?: |(?=({$n *} a) ?=({$i *} a)) a
a(e (sum:si e.a b))
::
++ fli :: flip sign
|= {a/fn} ^- fn
?-(-.a $f a(s !s.a), $i a(s !s.a), $n a)
::
++ swr ?+(r r $d %u, $u %d) :: flipped rounding
++ prc ?>((gth p 1) p) :: force >= 2 precision
++ den d :: denorm+flush+inf exp
++ emn v :: minimum exponent
++ emx (sum:si emn (sun:si w)) :: maximum exponent
++ spd [e=emn a=1] :: smallest denormal
++ spn [e=emn a=(bex (dec prc))] :: smallest normal
++ lfn [e=emx a=(fil 0 prc 1)] :: largest
++ lfe (sum:si emx (sun:si prc)) :: 2^lfe is > than all
++ zer [e=--0 a=0]
--
|%
++ rou :: round
|= {a/fn} ^- fn
?. ?=({$f *} a) a
?~ a.a [%f s.a zer]
?: s.a (^rou +>.a)
=.(r swr (fli (^rou +>.a)))
::
++ syn :: get sign
|= {a/fn} ^- ?
?-(-.a $f s.a, $i s.a, $n &)
::
++ abs :: absolute value
|= {a/fn} ^- fn
?: ?=({$f *} a) [%f & e.a a.a]
?: ?=({$i *} a) [%i &] [%n ~]
::
++ add :: add
|= {a/fn b/fn} ^- fn
?: |(?=({$n *} a) ?=({$n *} b)) [%n ~]
?: |(?=({$i *} a) ?=({$i *} b))
?: &(?=({$i *} a) ?=({$i *} b))
?: =(a b) a [%n ~]
?: ?=({$i *} a) a b
?: |(=(a.a 0) =(a.b 0))
?. &(=(a.a 0) =(a.b 0)) %- rou ?~(a.a b a)
[%f ?:(=(r %d) &(s.a s.b) |(s.a s.b)) zer]
%- |= {a/fn}
?. ?=({$f *} a) a
?. =(a.a 0) a
[%f !=(r %d) zer]
?: =(s.a s.b)
?: s.a (^add +>.a +>.b |)
=.(r swr (fli (^add +>.a +>.b |)))
?: s.a (^sub +>.a +>.b |)
(^sub +>.b +>.a |)
::
++ ead :: exact add
|= {a/fn b/fn} ^- fn
?: |(?=({$n *} a) ?=({$n *} b)) [%n ~]
?: |(?=({$i *} a) ?=({$i *} b))
?: &(?=({$i *} a) ?=({$i *} b))
?: =(a b) a [%n ~]
?: ?=({$i *} a) a b
?: |(=(a.a 0) =(a.b 0))
?. &(=(a.a 0) =(a.b 0)) ?~(a.a b a)
[%f ?:(=(r %d) &(s.a s.b) |(s.a s.b)) zer]
%- |= {a/fn}
?. ?=({$f *} a) a
?. =(a.a 0) a
[%f !=(r %d) zer]
?: =(s.a s.b)
?: s.a (^add +>.a +>.b &)
(fli (^add +>.a +>.b &))
?: s.a (^sub +>.a +>.b &)
(^sub +>.b +>.a &)
::
++ sub :: subtract
|= {a/fn b/fn} ^- fn (add a (fli b))
::
++ mul :: multiply
|= {a/fn b/fn} ^- fn
?: |(?=({$n *} a) ?=({$n *} b)) [%n ~]
?: ?=({$i *} a)
?: ?=({$i *} b)
[%i =(s.a s.b)]
?: =(a.b 0) [%n ~] [%i =(s.a s.b)]
?: ?=({$i *} b)
?: =(a.a 0) [%n ~] [%i =(s.a s.b)]
?: |(=(a.a 0) =(a.b 0)) [%f =(s.a s.b) zer]
?: =(s.a s.b) (^mul +>.a +>.b)
=.(r swr (fli (^mul +>.a +>.b)))
::
++ emu :: exact multiply
|= {a/fn b/fn} ^- fn
?: |(?=({$n *} a) ?=({$n *} b)) [%n ~]
?: ?=({$i *} a)
?: ?=({$i *} b)
[%i =(s.a s.b)]
?: =(a.b 0) [%n ~] [%i =(s.a s.b)]
?: ?=({$i *} b)
?: =(a.a 0) [%n ~] [%i =(s.a s.b)]
?: |(=(a.a 0) =(a.b 0)) [%f =(s.a s.b) zer]
[%f =(s.a s.b) (sum:si e.a e.b) (^^mul a.a a.b)]
::
++ div :: divide
|= {a/fn b/fn} ^- fn
?: |(?=({$n *} a) ?=({$n *} b)) [%n ~]
?: ?=({$i *} a)
?: ?=({$i *} b) [%n ~] [%i =(s.a s.b)]
?: ?=({$i *} b) [%f =(s.a s.b) zer]
?: =(a.a 0) ?: =(a.b 0) [%n ~] [%f =(s.a s.b) zer]
?: =(a.b 0) [%i =(s.a s.b)]
?: =(s.a s.b) (^div +>.a +>.b)
=.(r swr (fli (^div +>.a +>.b)))
::
++ fma :: fused multiply-add
|= {a/fn b/fn c/fn} ^- fn :: (a * b) + c
(add (emu a b) c)
::
++ sqt :: square root
|= {a/fn} ^- fn
?: ?=({$n *} a) [%n ~]
?: ?=({$i *} a) ?:(s.a a [%n ~])
?~ a.a [%f s.a zer]
?: s.a (^sqt +>.a) [%n ~]
::
++ inv :: inverse
|= {a/fn} ^- fn
(div [%f & --0 1] a)
::
++ sun :: uns integer to float
|= {a/@u} ^- fn
(rou [%f & --0 a])
::
++ san :: sgn integer to float
|= {a/@s} ^- fn
=+ b=(old:si a)
(rou [%f -.b --0 +.b])
::
:: comparisons return ~ in the event of a NaN
++ lth :: less-than
|= {a/fn b/fn} ^- (unit ?)
?: |(?=({$n *} a) ?=({$n *} b)) ~ :- ~
?: =(a b) |
?: ?=({$i *} a) !s.a ?: ?=({$i *} b) s.b
?: |(=(a.a 0) =(a.b 0))
?: &(=(a.a 0) =(a.b 0)) |
?: =(a.a 0) s.b !s.a
?: !=(s.a s.b) s.b
?: s.a (^lth +>.a +>.b) (^lth +>.b +>.a)
::
++ lte :: less-equal
|= {a/fn b/fn} ^- (unit ?)
?: |(?=({$n *} a) ?=({$n *} b)) ~ :- ~
?: =(a b) &
?: ?=({$i *} a) !s.a ?: ?=({$i *} b) s.b
?: |(=(a.a 0) =(a.b 0))
?: &(=(a.a 0) =(a.b 0)) &
?: =(a.a 0) s.b !s.a
?: !=(s.a s.b) s.b
?: s.a (^lte +>.a +>.b) (^lte +>.b +>.a)
::
++ equ :: equal
|= {a/fn b/fn} ^- (unit ?)
?: |(?=({$n *} a) ?=({$n *} b)) ~ :- ~
?: =(a b) &
?: |(?=({$i *} a) ?=({$i *} b)) |
?: |(=(a.a 0) =(a.b 0))
?: &(=(a.a 0) =(a.b 0)) & |
?: |(=(e.a e.b) !=(s.a s.b)) |
(^equ +>.a +>.b)
::
++ gte :: greater-equal
|= {a/fn b/fn} ^- (unit ?) (lte b a)
::
++ gth :: greater-than
|= {a/fn b/fn} ^- (unit ?) (lth b a)
::
++ drg :: float to decimal
|= {a/fn} ^- dn
?: ?=({$n *} a) [%n ~]
?: ?=({$i *} a) [%i s.a]
?~ a.a [%d s.a --0 0]
[%d s.a (^drg +>.a)]
::
++ grd :: decimal to float
|= {a/dn} ^- fn
?: ?=({$n *} a) [%n ~]
?: ?=({$i *} a) [%i s.a]
=> .(r %n)
=+ q=(abs:si e.a)
?: (syn:si e.a)
(mul [%f s.a --0 a.a] [%f & e.a (pow 5 q)])
(div [%f s.a --0 a.a] [%f & (sun:si q) (pow 5 q)])
::
++ toi :: round to integer @s
|= {a/fn} ^- (unit @s)
=+ b=(toj a)
?. ?=({$f *} b) ~ :- ~
=+ c=(^^mul (bex (abs:si e.b)) a.b)
(new:si s.b c)
::
++ toj :: round to integer fn
|= {a/fn} ^- fn
?. ?=({$f *} a) a
?~ a.a [%f s.a zer]
?: s.a (^toj +>.a)
=.(r swr (fli (^toj +>.a)))
--
::
++ ff :: ieee 754 format fp
|_ {{w/@u p/@u b/@s} r/$?($n $u $d $z $a)}
:: this core has no use outside of the functionality
:: provided to ++rd, ++rs, ++rq, and ++rh
::
:: w=width: bits in exponent field
:: p=precision: bits in fraction field
:: w=bias: added to exponent when storing
:: r=rounding mode: same as in ++fl
::
++ sb (bex (^add w p)) :: sign bit
++ me (dif:si (dif:si --1 b) (sun:si p)) :: minimum exponent
::
++ pa
%*(. fl p +(p), v me, w (^sub (bex w) 3), d %d, r r)
::
++ sea :: @r to fn
|= {a/@r} ^- fn
=+ [f=(cut 0 [0 p] a) e=(cut 0 [p w] a)]
=+ s=(sig a)
?: =(e 0)
?: =(f 0) [%f s --0 0] [%f s me f]
?: =(e (fil 0 w 1))
?: =(f 0) [%i s] [%n ~]
=+ q=:(sum:si (sun:si e) me -1)
=+ r=(^add f (bex p))
[%f s q r]
::
++ bit |= {a/fn} (bif (rou:pa a)) :: fn to @r w+ rounding
::
++ bif :: fn to @r no rounding
|= {a/fn} ^- @r
?: ?=({$i *} a)
=+ q=(lsh 0 p (fil 0 w 1))
?: s.a q (^add q sb)
?: ?=({$n *} a) (lsh 0 (dec p) (fil 0 +(w) 1))
?~ a.a ?: s.a `@r`0 sb
=+ ma=(met 0 a.a)
?. =(ma +(p))
?> =(e.a me)
?> (^lth ma +(p))
?: s.a `@r`a.a (^add a.a sb)
=+ q=(sum:si (dif:si e.a me) --1)
=+ r=(^add (lsh 0 p (abs:si q)) (end 0 p a.a))
?: s.a r (^add r sb)
::
++ sig :: get sign
|= {a/@r} ^- ?
=(0 (cut 0 [(^add p w) 1] a))
::
++ exp :: get exponent
|= {a/@r} ^- @s
(dif:si (sun:si (cut 0 [p w] a)) b)
::
++ add :: add
|= {a/@r b/@r}
(bif (add:pa (sea a) (sea b)))
::
++ sub :: subtract
|= {a/@r b/@r}
(bif (sub:pa (sea a) (sea b)))
::
++ mul :: multiply
|= {a/@r b/@r}
(bif (mul:pa (sea a) (sea b)))
::
++ div :: divide
|= {a/@r b/@r}
(bif (div:pa (sea a) (sea b)))
::
++ fma :: fused multiply-add
|= {a/@r b/@r c/@r}
(bif (fma:pa (sea a) (sea b) (sea c)))
::
++ sqt :: square root
|= {a/@r}
(bif (sqt:pa (sea a)))
::
++ lth :: less-than
|= {a/@r b/@r} (fall (lth:pa (sea a) (sea b)) |)
++ lte :: less-equals
|= {a/@r b/@r} (fall (lte:pa (sea a) (sea b)) |)
++ equ :: equals
|= {a/@r b/@r} (fall (equ:pa (sea a) (sea b)) |)
++ gte :: greater-equals
|= {a/@r b/@r} (fall (gte:pa (sea a) (sea b)) |)
++ gth :: greater-than
|= {a/@r b/@r} (fall (gth:pa (sea a) (sea b)) |)
++ sun :: uns integer to @r
|= {a/@u} (bit [%f & --0 a])
++ san :: signed integer to @r
|= {a/@s} (bit [%f (syn:si a) --0 (abs:si a)])
++ toi :: round to integer
|= {a/@r} (toi:pa (sea a))
++ drg :: @r to decimal float
|= {a/@r} (drg:pa (sea a))
++ grd :: decimal float to @r
|= {a/dn} (bif (grd:pa a))
--
::
++ rlyd |= a/@rd ^- dn (drg:rd a) :: prep @rd for print
++ rlys |= a/@rs ^- dn (drg:rs a) :: prep @rs for print
++ rlyh |= a/@rh ^- dn (drg:rh a) :: prep @rh for print
++ rlyq |= a/@rq ^- dn (drg:rq a) :: prep @rq for print
++ ryld |= a/dn ^- @rd (grd:rd a) :: finish parsing @rd
++ ryls |= a/dn ^- @rs (grd:rs a) :: finish parsing @rs
++ rylh |= a/dn ^- @rh (grd:rh a) :: finish parsing @rh
++ rylq |= a/dn ^- @rq (grd:rq a) :: finish parsing @rq
::
++ rd :: double precision fp
~% %rd +> ~
|_ r/$?($n $u $d $z)
:: round to nearest, round up, round down, round to zero
::
++ ma
%*(. ff w 11, p 52, b --1.023, r r)
::
++ sea :: @rd to fn
|= {a/@rd} (sea:ma a)
::
++ bit :: fn to @rd
|= {a/fn} ^- @rd (bit:ma a)
::
++ add ~/ %add :: add
|= {a/@rd b/@rd} ^- @rd
~> %mean.[0 leaf+"rd-fail"]
(add:ma a b)
::
++ sub ~/ %sub :: subtract
|= {a/@rd b/@rd} ^- @rd
~> %mean.[0 leaf+"rd-fail"]
(sub:ma a b)
::
++ mul ~/ %mul :: multiply
|= {a/@rd b/@rd} ^- @rd
~> %mean.[0 leaf+"rd-fail"]
(mul:ma a b)
::
++ div ~/ %div :: divide
|= {a/@rd b/@rd} ^- @rd
~> %mean.[0 leaf+"rd-fail"]
(div:ma a b)
::
++ fma ~/ %fma :: fused multiply-add
|= {a/@rd b/@rd c/@rd} ^- @rd
~> %mean.[0 leaf+"rd-fail"]
(fma:ma a b c)
::
++ sqt ~/ %sqt :: square root
|= {a/@rd} ^- @rd ~> %mean.[0 leaf+"rd-fail"]
(sqt:ma a)
::
++ lth ~/ %lth :: less-than
|= {a/@rd b/@rd}
~> %mean.[0 leaf+"rd-fail"]
(lth:ma a b)
::
++ lte ~/ %lte :: less-equals
|= {a/@rd b/@rd} ~> %mean.[0 leaf+"rd-fail"] (lte:ma a b)
++ equ ~/ %equ :: equals
|= {a/@rd b/@rd} ~> %mean.[0 leaf+"rd-fail"] (equ:ma a b)
++ gte ~/ %gte :: greater-equals
|= {a/@rd b/@rd} ~> %mean.[0 leaf+"rd-fail"] (gte:ma a b)
++ gth ~/ %gth :: greater-than
|= {a/@rd b/@rd} ~> %mean.[0 leaf+"rd-fail"] (gth:ma a b)
::
++ sun |= {a/@u} ^- @rd (sun:ma a) :: uns integer to @rd
++ san |= {a/@s} ^- @rd (san:ma a) :: sgn integer to @rd
++ sig |= {a/@rd} ^- ? (sig:ma a) :: get sign
++ exp |= {a/@rd} ^- @s (exp:ma a) :: get exponent
++ toi |= {a/@rd} ^- (unit @s) (toi:ma a) :: round to integer
++ drg |= {a/@rd} ^- dn (drg:ma a) :: @rd to decimal float
++ grd |= {a/dn} ^- @rd (grd:ma a) :: decimal float to @rd
--
::
++ rs :: single precision fp
~% %rs +> ~
|_ r/$?($n $u $d $z)
:: round to nearest, round up, round down, round to zero
::
++ ma
%*(. ff w 8, p 23, b --127, r r)
::
++ sea :: @rs to fn
|= {a/@rs} (sea:ma a)
::
++ bit :: fn to @rs
|= {a/fn} ^- @rs (bit:ma a)
::
++ add ~/ %add :: add
|= {a/@rs b/@rs} ^- @rs
~> %mean.[0 leaf+"rs-fail"]
(add:ma a b)
::
++ sub ~/ %sub :: subtract
|= {a/@rs b/@rs} ^- @rs
~> %mean.[0 leaf+"rs-fail"]
(sub:ma a b)
::
++ mul ~/ %mul :: multiply
|= {a/@rs b/@rs} ^- @rs
~> %mean.[0 leaf+"rs-fail"]
(mul:ma a b)
::
++ div ~/ %div :: divide
|= {a/@rs b/@rs} ^- @rs
~> %mean.[0 leaf+"rs-fail"]
(div:ma a b)
::
++ fma ~/ %fma :: fused multiply-add
|= {a/@rs b/@rs c/@rs} ^- @rs
~> %mean.[0 leaf+"rs-fail"]
(fma:ma a b c)
::
++ sqt ~/ %sqt :: square root
|= {a/@rs} ^- @rs
~> %mean.[0 leaf+"rs-fail"]
(sqt:ma a)
::
++ lth ~/ %lth :: less-than
|= {a/@rs b/@rs}
~> %mean.[0 leaf+"rs-fail"]
(lth:ma a b)
::
++ lte ~/ %lte :: less-equals
|= {a/@rs b/@rs}
~> %mean.[0 leaf+"rs-fail"]
(lte:ma a b)
::
++ equ ~/ %equ :: equals
|= {a/@rs b/@rs}
~> %mean.[0 leaf+"rs-fail"]
(equ:ma a b)
::
++ gte ~/ %gte :: greater-equals
|= {a/@rs b/@rs}
~> %mean.[0 leaf+"rs-fail"]
(gte:ma a b)
::
++ gth ~/ %gth :: greater-than
|= {a/@rs b/@rs}
~> %mean.[0 leaf+"rs-fail"]
(gth:ma a b)
::
++ sun |= {a/@u} ^- @rs (sun:ma a) :: uns integer to @rs
++ san |= {a/@s} ^- @rs (san:ma a) :: sgn integer to @rs
++ sig |= {a/@rs} ^- ? (sig:ma a) :: get sign
++ exp |= {a/@rs} ^- @s (exp:ma a) :: get exponent
++ toi |= {a/@rs} ^- (unit @s) (toi:ma a) :: round to integer
++ drg |= {a/@rs} ^- dn (drg:ma a) :: @rs to decimal float
++ grd |= {a/dn} ^- @rs (grd:ma a) :: decimal float to @rs
--
::
++ rq :: quad precision fp
~% %rq +> ~
|_ r/$?($n $u $d $z)
:: round to nearest, round up, round down, round to zero
::
++ ma
%*(. ff w 15, p 112, b --16.383, r r)
::
++ sea :: @rq to fn
|= {a/@rq} (sea:ma a)
::
++ bit :: fn to @rq
|= {a/fn} ^- @rq (bit:ma a)
::
++ add ~/ %add :: add
|= {a/@rq b/@rq} ^- @rq
~> %mean.[0 leaf+"rq-fail"]
(add:ma a b)
::
++ sub ~/ %sub :: subtract
|= {a/@rq b/@rq} ^- @rq
~> %mean.[0 leaf+"rq-fail"]
(sub:ma a b)
::
++ mul ~/ %mul :: multiply
|= {a/@rq b/@rq} ^- @rq
~> %mean.[0 leaf+"rq-fail"]
(mul:ma a b)
::
++ div ~/ %div :: divide
|= {a/@rq b/@rq} ^- @rq
~> %mean.[0 leaf+"rq-fail"]
(div:ma a b)
::
++ fma ~/ %fma :: fused multiply-add
|= {a/@rq b/@rq c/@rq} ^- @rq
~> %mean.[0 leaf+"rq-fail"]
(fma:ma a b c)
::
++ sqt ~/ %sqt :: square root
|= {a/@rq} ^- @rq
~> %mean.[0 leaf+"rq-fail"]
(sqt:ma a)
::
++ lth ~/ %lth :: less-than
|= {a/@rq b/@rq}
~> %mean.[0 leaf+"rq-fail"]
(lth:ma a b)
::
++ lte ~/ %lte :: less-equals
|= {a/@rq b/@rq}
~> %mean.[0 leaf+"rq-fail"]
(lte:ma a b)
::
++ equ ~/ %equ :: equals
|= {a/@rq b/@rq}
~> %mean.[0 leaf+"rq-fail"]
(equ:ma a b)
::
++ gte ~/ %gte :: greater-equals
|= {a/@rq b/@rq}
~> %mean.[0 leaf+"rq-fail"]
(gte:ma a b)
::
++ gth ~/ %gth :: greater-than
|= {a/@rq b/@rq}
~> %mean.[0 leaf+"rq-fail"]
(gth:ma a b)
::
++ sun |= {a/@u} ^- @rq (sun:ma a) :: uns integer to @rq
++ san |= {a/@s} ^- @rq (san:ma a) :: sgn integer to @rq
++ sig |= {a/@rq} ^- ? (sig:ma a) :: get sign
++ exp |= {a/@rq} ^- @s (exp:ma a) :: get exponent
++ toi |= {a/@rq} ^- (unit @s) (toi:ma a) :: round to integer
++ drg |= {a/@rq} ^- dn (drg:ma a) :: @rq to decimal float
++ grd |= {a/dn} ^- @rq (grd:ma a) :: decimal float to @rq
--
::
++ rh :: half precision fp
|_ r/$?($n $u $d $z)
:: round to nearest, round up, round down, round to zero
::
++ ma
%*(. ff w 5, p 10, b --15, r r)
::
++ sea :: @rh to fn
|= {a/@rh} (sea:ma a)
::
++ bit :: fn to @rh
|= {a/fn} ^- @rh (bit:ma a)
::
++ tos :: @rh to @rs
|= {a/@rh} (bit:rs (sea a))
::
++ fos :: @rs to @rh
|= {a/@rs} (bit (sea:rs a))
::
++ lth ~/ %lth :: less-than
|= {a/@rh b/@rh}
~> %mean.[0 leaf+"rh-fail"]
(lth:ma a b)
::
++ lte ~/ %lte :: less-equals
|= {a/@rh b/@rh}
~> %mean.[0 leaf+"rh-fail"]
(lte:ma a b)
::
++ equ ~/ %equ :: equals
|= {a/@rh b/@rh}
~> %mean.[0 leaf+"rh-fail"]
(equ:ma a b)
::
++ gte ~/ %gte :: greater-equals
|= {a/@rh b/@rh}
~> %mean.[0 leaf+"rh-fail"]
(gte:ma a b)
::
++ gth ~/ %gth :: greater-than
|= {a/@rh b/@rh}
~> %mean.[0 leaf+"rh-fail"]
(gth:ma a b)
::
++ sun |= {a/@u} ^- @rh (sun:ma a) :: uns integer to @rh
++ san |= {a/@s} ^- @rh (san:ma a) :: sgn integer to @rh
++ sig |= {a/@rh} ^- ? (sig:ma a) :: get sign
++ exp |= {a/@rh} ^- @s (exp:ma a) :: get exponent
++ toi |= {a/@rh} ^- (unit @s) (toi:ma a) :: round to integer
++ drg |= {a/@rh} ^- dn (drg:ma a) :: @rh to decimal float
++ grd |= {a/dn} ^- @rh (grd:ma a) :: decimal float to @rh
--
:: 3c: urbit time ::
:::: ::
:: year, yore, yell, yule, yall, yawn, yelp, yo ::
::
-- =>
|%
++ year :: date to @d
|= det/date
^- @da
=+ ^= yer
?: a.det
(add 292.277.024.400 y.det)
(sub 292.277.024.400 (dec y.det))
=+ day=(yawn yer m.det d.t.det)
(yule day h.t.det m.t.det s.t.det f.t.det)
::
++ yore :: @d to date
|= now/@da
^- date
=+ rip=(yell now)
=+ ger=(yall d.rip)
:- ?: (gth y.ger 292.277.024.400)
[a=& y=(sub y.ger 292.277.024.400)]
[a=| y=+((sub 292.277.024.400 y.ger))]
[m.ger d.ger h.rip m.rip s.rip f.rip]
::
++ yell :: tarp from @d
|= now/@d
^- tarp
=+ sec=(rsh 6 1 now)
=+ ^= fan
=+ [muc=4 raw=(end 6 1 now)]
|- ^- (list @ux)
?: |(=(0 raw) =(0 muc))
~
=> .(muc (dec muc))
[(cut 4 [muc 1] raw) $(raw (end 4 muc raw))]
=+ day=(div sec day:yo)
=> .(sec (mod sec day:yo))
=+ hor=(div sec hor:yo)
=> .(sec (mod sec hor:yo))
=+ mit=(div sec mit:yo)
=> .(sec (mod sec mit:yo))
[day hor mit sec fan]
::
++ yule :: time atom
|= rip/tarp
^- @d
=+ ^= sec ;: add
(mul d.rip day:yo)
(mul h.rip hor:yo)
(mul m.rip mit:yo)
s.rip
==
=+ ^= fac =+ muc=4
|- ^- @
?~ f.rip
0
=> .(muc (dec muc))
(add (lsh 4 muc i.f.rip) $(f.rip t.f.rip))
(con (lsh 6 1 sec) fac)
::
++ yall :: day / to day of year
|= day/@ud
^- {y/@ud m/@ud d/@ud}
=+ [era=0 cet=0 lep=*?]
=> .(era (div day era:yo), day (mod day era:yo))
=> ^+ .
?: (lth day +(cet:yo))
.(lep &, cet 0)
=> .(lep |, cet 1, day (sub day +(cet:yo)))
.(cet (add cet (div day cet:yo)), day (mod day cet:yo))
=+ yer=(add (mul 400 era) (mul 100 cet))
|- ^- {y/@ud m/@ud d/@ud}
=+ dis=?:(lep 366 365)
?. (lth day dis)
=+ ner=+(yer)
$(yer ner, day (sub day dis), lep =(0 (end 0 2 ner)))
|- ^- {y/@ud m/@ud d/@ud}
=+ [mot=0 cah=?:(lep moy:yo moh:yo)]
|- ^- {y/@ud m/@ud d/@ud}
=+ zis=(snag mot cah)
?: (lth day zis)
[yer +(mot) +(day)]
$(mot +(mot), day (sub day zis))
::
++ yawn :: days since Jesus
|= {yer/@ud mot/@ud day/@ud}
^- @ud
=> .(mot (dec mot), day (dec day))
=> ^+ .
%= .
day
=+ cah=?:((yelp yer) moy:yo moh:yo)
|- ^- @ud
?: =(0 mot)
day
$(mot (dec mot), cah (slag 1 cah), day (add day (snag 0 cah)))
==
|- ^- @ud
?. =(0 (mod yer 4))
=+ ney=(dec yer)
$(yer ney, day (add day ?:((yelp ney) 366 365)))
?. =(0 (mod yer 100))
=+ nef=(sub yer 4)
$(yer nef, day (add day ?:((yelp nef) 1.461 1.460)))
?. =(0 (mod yer 400))
=+ nec=(sub yer 100)
$(yer nec, day (add day ?:((yelp nec) 36.525 36.524)))
(add day (mul (div yer 400) (add 1 (mul 4 36.524))))
::
++ yelp :: leap year
|= yer/@ud ^- ?
&(=(0 (mod yer 4)) |(!=(0 (mod yer 100)) =(0 (mod yer 400))))
::
++ yo :: time constants
|% ++ cet 36.524 :: (add 24 (mul 100 365))
++ day 86.400 :: (mul 24 hor)
++ era 146.097 :: (add 1 (mul 4 cet))
++ hor 3.600 :: (mul 60 mit)
++ jes 106.751.991.084.417 :: (mul 730.692.561 era)
++ mit 60
++ moh `(list @ud)`[31 28 31 30 31 30 31 31 30 31 30 31 ~]
++ moy `(list @ud)`[31 29 31 30 31 30 31 31 30 31 30 31 ~]
++ qad 126.144.001 :: (add 1 (mul 4 yer))
++ yer 31.536.000 :: (mul 365 day)
--
:: ::
:::: 3d: SHA family ::
:: ::
:: shad, shaf, sham, shas, shax, shay, shaw, ::
:: shal, shaz, shan, og ::
::
++ shad |=(ruz/@ (shax (shax ruz))) :: double sha-256
++ shaf :: half sha-256
|= {sal/@ ruz/@}
=+ haz=(shas sal ruz)
(mix (end 7 1 haz) (rsh 7 1 haz))
::
++ sham :: 128bit noun hash
|= yux/* ^- @uvH ^- @
?@ yux
(shaf %mash yux)
(shaf %sham (jam yux))
::
++ shas :: salted hash
|= {sal/@ ruz/@}
(shax (mix sal (shax ruz)))
::
++ shax :: sha-256
~/ %shax
|= ruz/@ ^- @
(shay [(met 3 ruz) ruz])
::
++ shay :: sha-256 with length
~/ %shay
|= {len/@u ruz/@} ^- @
=> .(ruz (cut 3 [0 len] ruz))
=+ [few==>(fe .(a 5)) wac=|=({a/@ b/@} (cut 5 [a 1] b))]
=+ [sum=sum.few ror=ror.few net=net.few inv=inv.few]
=+ ral=(lsh 0 3 len)
=+ ^= ful
%+ can 0
:~ [ral ruz]
[8 128]
[(mod (sub 960 (mod (add 8 ral) 512)) 512) 0]
[64 (~(net fe 6) ral)]
==
=+ lex=(met 9 ful)
=+ ^= kbx 0xc671.78f2.bef9.a3f7.a450.6ceb.90be.fffa.
8cc7.0208.84c8.7814.78a5.636f.748f.82ee.
682e.6ff3.5b9c.ca4f.4ed8.aa4a.391c.0cb3.
34b0.bcb5.2748.774c.1e37.6c08.19a4.c116.
106a.a070.f40e.3585.d699.0624.d192.e819.
c76c.51a3.c24b.8b70.a81a.664b.a2bf.e8a1.
9272.2c85.81c2.c92e.766a.0abb.650a.7354.
5338.0d13.4d2c.6dfc.2e1b.2138.27b7.0a85.
1429.2967.06ca.6351.d5a7.9147.c6e0.0bf3.
bf59.7fc7.b003.27c8.a831.c66d.983e.5152.
76f9.88da.5cb0.a9dc.4a74.84aa.2de9.2c6f.
240c.a1cc.0fc1.9dc6.efbe.4786.e49b.69c1.
c19b.f174.9bdc.06a7.80de.b1fe.72be.5d74.
550c.7dc3.2431.85be.1283.5b01.d807.aa98.
ab1c.5ed5.923f.82a4.59f1.11f1.3956.c25b.
e9b5.dba5.b5c0.fbcf.7137.4491.428a.2f98
=+ ^= hax 0x5be0.cd19.1f83.d9ab.9b05.688c.510e.527f.
a54f.f53a.3c6e.f372.bb67.ae85.6a09.e667
=+ i=0
|- ^- @
?: =(i lex)
(rep 5 (turn (rip 5 hax) net))
=+ ^= wox
=+ dux=(cut 9 [i 1] ful)
=+ wox=(rep 5 (turn (rip 5 dux) net))
=+ j=16
|- ^- @
?: =(64 j)
wox
=+ :* l=(wac (sub j 15) wox)
m=(wac (sub j 2) wox)
n=(wac (sub j 16) wox)
o=(wac (sub j 7) wox)
==
=+ x=:(mix (ror 0 7 l) (ror 0 18 l) (rsh 0 3 l))
=+ y=:(mix (ror 0 17 m) (ror 0 19 m) (rsh 0 10 m))
=+ z=:(sum n x o y)
$(wox (con (lsh 5 j z) wox), j +(j))
=+ j=0
=+ :* a=(wac 0 hax)
b=(wac 1 hax)
c=(wac 2 hax)
d=(wac 3 hax)
e=(wac 4 hax)
f=(wac 5 hax)
g=(wac 6 hax)
h=(wac 7 hax)
==
|- ^- @
?: =(64 j)
%= ^$
i +(i)
hax %+ rep 5
:~ (sum a (wac 0 hax))
(sum b (wac 1 hax))
(sum c (wac 2 hax))
(sum d (wac 3 hax))
(sum e (wac 4 hax))
(sum f (wac 5 hax))
(sum g (wac 6 hax))
(sum h (wac 7 hax))
==
==
=+ l=:(mix (ror 0 2 a) (ror 0 13 a) (ror 0 22 a)) :: s0
=+ m=:(mix (dis a b) (dis a c) (dis b c)) :: maj
=+ n=(sum l m) :: t2
=+ o=:(mix (ror 0 6 e) (ror 0 11 e) (ror 0 25 e)) :: s1
=+ p=(mix (dis e f) (dis (inv e) g)) :: ch
=+ q=:(sum h o p (wac j kbx) (wac j wox)) :: t1
$(j +(j), a (sum q n), b a, c b, d c, e (sum d q), f e, g f, h g)
::
++ shaw :: hash to nbits
|= {sal/@ len/@ ruz/@}
(~(raw og (shas sal (mix len ruz))) len)
::
++ shaz :: sha-512
|= ruz/@ ^- @
(shal [(met 3 ruz) ruz])
::
++ shal :: sha-512 with length
~/ %shal
|= {len/@ ruz/@} ^- @
=> .(ruz (cut 3 [0 len] ruz))
=+ [few==>(fe .(a 6)) wac=|=({a/@ b/@} (cut 6 [a 1] b))]
=+ [sum=sum.few ror=ror.few net=net.few inv=inv.few]
=+ ral=(lsh 0 3 len)
=+ ^= ful
%+ can 0
:~ [ral ruz]
[8 128]
[(mod (sub 1.920 (mod (add 8 ral) 1.024)) 1.024) 0]
[128 (~(net fe 7) ral)]
==
=+ lex=(met 10 ful)
=+ ^= kbx 0x6c44.198c.4a47.5817.5fcb.6fab.3ad6.faec.
597f.299c.fc65.7e2a.4cc5.d4be.cb3e.42b6.
431d.67c4.9c10.0d4c.3c9e.be0a.15c9.bebc.
32ca.ab7b.40c7.2493.28db.77f5.2304.7d84.
1b71.0b35.131c.471b.113f.9804.bef9.0dae.
0a63.7dc5.a2c8.98a6.06f0.67aa.7217.6fba.
f57d.4f7f.ee6e.d178.eada.7dd6.cde0.eb1e.
d186.b8c7.21c0.c207.ca27.3ece.ea26.619c.
c671.78f2.e372.532b.bef9.a3f7.b2c6.7915.
a450.6ceb.de82.bde9.90be.fffa.2363.1e28.
8cc7.0208.1a64.39ec.84c8.7814.a1f0.ab72.
78a5.636f.4317.2f60.748f.82ee.5def.b2fc.
682e.6ff3.d6b2.b8a3.5b9c.ca4f.7763.e373.
4ed8.aa4a.e341.8acb.391c.0cb3.c5c9.5a63.
34b0.bcb5.e19b.48a8.2748.774c.df8e.eb99.
1e37.6c08.5141.ab53.19a4.c116.b8d2.d0c8.
106a.a070.32bb.d1b8.f40e.3585.5771.202a.
d699.0624.5565.a910.d192.e819.d6ef.5218.
c76c.51a3.0654.be30.c24b.8b70.d0f8.9791.
a81a.664b.bc42.3001.a2bf.e8a1.4cf1.0364.
9272.2c85.1482.353b.81c2.c92e.47ed.aee6.
766a.0abb.3c77.b2a8.650a.7354.8baf.63de.
5338.0d13.9d95.b3df.4d2c.6dfc.5ac4.2aed.
2e1b.2138.5c26.c926.27b7.0a85.46d2.2ffc.
1429.2967.0a0e.6e70.06ca.6351.e003.826f.
d5a7.9147.930a.a725.c6e0.0bf3.3da8.8fc2.
bf59.7fc7.beef.0ee4.b003.27c8.98fb.213f.
a831.c66d.2db4.3210.983e.5152.ee66.dfab.
76f9.88da.8311.53b5.5cb0.a9dc.bd41.fbd4.
4a74.84aa.6ea6.e483.2de9.2c6f.592b.0275.
240c.a1cc.77ac.9c65.0fc1.9dc6.8b8c.d5b5.
efbe.4786.384f.25e3.e49b.69c1.9ef1.4ad2.
c19b.f174.cf69.2694.9bdc.06a7.25c7.1235.
80de.b1fe.3b16.96b1.72be.5d74.f27b.896f.
550c.7dc3.d5ff.b4e2.2431.85be.4ee4.b28c.
1283.5b01.4570.6fbe.d807.aa98.a303.0242.
ab1c.5ed5.da6d.8118.923f.82a4.af19.4f9b.
59f1.11f1.b605.d019.3956.c25b.f348.b538.
e9b5.dba5.8189.dbbc.b5c0.fbcf.ec4d.3b2f.
7137.4491.23ef.65cd.428a.2f98.d728.ae22
=+ ^= hax 0x5be0.cd19.137e.2179.1f83.d9ab.fb41.bd6b.
9b05.688c.2b3e.6c1f.510e.527f.ade6.82d1.
a54f.f53a.5f1d.36f1.3c6e.f372.fe94.f82b.
bb67.ae85.84ca.a73b.6a09.e667.f3bc.c908
=+ i=0
|- ^- @
?: =(i lex)
(rep 6 (turn (rip 6 hax) net))
=+ ^= wox
=+ dux=(cut 10 [i 1] ful)
=+ wox=(rep 6 (turn (rip 6 dux) net))
=+ j=16
|- ^- @
?: =(80 j)
wox
=+ :* l=(wac (sub j 15) wox)
m=(wac (sub j 2) wox)
n=(wac (sub j 16) wox)
o=(wac (sub j 7) wox)
==
=+ x=:(mix (ror 0 1 l) (ror 0 8 l) (rsh 0 7 l))
=+ y=:(mix (ror 0 19 m) (ror 0 61 m) (rsh 0 6 m))
=+ z=:(sum n x o y)
$(wox (con (lsh 6 j z) wox), j +(j))
=+ j=0
=+ :* a=(wac 0 hax)
b=(wac 1 hax)
c=(wac 2 hax)
d=(wac 3 hax)
e=(wac 4 hax)
f=(wac 5 hax)
g=(wac 6 hax)
h=(wac 7 hax)
==
|- ^- @
?: =(80 j)
%= ^$
i +(i)
hax %+ rep 6
:~ (sum a (wac 0 hax))
(sum b (wac 1 hax))
(sum c (wac 2 hax))
(sum d (wac 3 hax))
(sum e (wac 4 hax))
(sum f (wac 5 hax))
(sum g (wac 6 hax))
(sum h (wac 7 hax))
==
==
=+ l=:(mix (ror 0 28 a) (ror 0 34 a) (ror 0 39 a)) :: S0
=+ m=:(mix (dis a b) (dis a c) (dis b c)) :: maj
=+ n=(sum l m) :: t2
=+ o=:(mix (ror 0 14 e) (ror 0 18 e) (ror 0 41 e)) :: S1
=+ p=(mix (dis e f) (dis (inv e) g)) :: ch
=+ q=:(sum h o p (wac j kbx) (wac j wox)) :: t1
$(j +(j), a (sum q n), b a, c b, d c, e (sum d q), f e, g f, h g)
::
++ shan :: sha-1 (deprecated)
|= ruz/@
=+ [few==>(fe .(a 5)) wac=|=({a/@ b/@} (cut 5 [a 1] b))]
=+ [sum=sum.few ror=ror.few rol=rol.few net=net.few inv=inv.few]
=+ ral=(lsh 0 3 (met 3 ruz))
=+ ^= ful
%+ can 0
:~ [ral ruz]
[8 128]
[(mod (sub 960 (mod (add 8 ral) 512)) 512) 0]
[64 (~(net fe 6) ral)]
==
=+ lex=(met 9 ful)
=+ kbx=0xca62.c1d6.8f1b.bcdc.6ed9.eba1.5a82.7999
=+ hax=0xc3d2.e1f0.1032.5476.98ba.dcfe.efcd.ab89.6745.2301
=+ i=0
|-
?: =(i lex)
(rep 5 (flop (rip 5 hax)))
=+ ^= wox
=+ dux=(cut 9 [i 1] ful)
=+ wox=(rep 5 (turn (rip 5 dux) net))
=+ j=16
|- ^- @
?: =(80 j)
wox
=+ :* l=(wac (sub j 3) wox)
m=(wac (sub j 8) wox)
n=(wac (sub j 14) wox)
o=(wac (sub j 16) wox)
==
=+ z=(rol 0 1 :(mix l m n o))
$(wox (con (lsh 5 j z) wox), j +(j))
=+ j=0
=+ :* a=(wac 0 hax)
b=(wac 1 hax)
c=(wac 2 hax)
d=(wac 3 hax)
e=(wac 4 hax)
==
|- ^- @
?: =(80 j)
%= ^$
i +(i)
hax %+ rep 5
:~
(sum a (wac 0 hax))
(sum b (wac 1 hax))
(sum c (wac 2 hax))
(sum d (wac 3 hax))
(sum e (wac 4 hax))
==
==
=+ fx=(con (dis b c) (dis (not 5 1 b) d))
=+ fy=:(mix b c d)
=+ fz=:(con (dis b c) (dis b d) (dis c d))
=+ ^= tem
?: &((gte j 0) (lte j 19))
:(sum (rol 0 5 a) fx e (wac 0 kbx) (wac j wox))
?: &((gte j 20) (lte j 39))
:(sum (rol 0 5 a) fy e (wac 1 kbx) (wac j wox))
?: &((gte j 40) (lte j 59))
:(sum (rol 0 5 a) fz e (wac 2 kbx) (wac j wox))
:(sum (rol 0 5 a) fy e (wac 3 kbx) (wac j wox))
$(j +(j), a tem, b a, c (rol 0 30 b), d c, e d)
::
++ og :: shax-powered rng
~/ %og
|_ a/@
++ rad :: random in range
|= b/@ ^- @
=+ c=(raw (met 0 b))
?:((lth c b) c $(a +(a)))
::
++ rads :: random continuation
|= b/@
=+ r=(rad b)
[r +>.$(a (shas %og-s r))]
::
++ raw :: random bits
~/ %raw
|= b/@ ^- @
%+ can
0
=+ c=(shas %og-a (mix b a))
|- ^- (list {@ @})
?: =(0 b)
~
=+ d=(shas %og-b (mix b (mix a c)))
?: (lth b 256)
[[b (end 0 b d)] ~]
[[256 d] $(c d, b (sub b 256))]
::
++ raws :: random bits
|= b/@ :: continuation
=+ r=(raw b)
[r +>.$(a (shas %og-s r))]
--
:: ::
:::: 3e: AES and friends ::
:: ::
:: aesc, ga ::
::
-- =>
|%
++ aesc :: AES-256
~% %aesc + ~
|%
++ en :: ECB enc
~/ %en
|= {a/@I b/@H} ^- @uxH
=+ ahem
(be & (ex a) b)
++ de :: ECB dec
~/ %de
|= {a/@I b/@H} ^- @uxH
=+ ahem
(be | (ix (ex a)) b)
--
++ ahem :: AES helpers
:: XX should be in aesc, isn't for performance reasons
=>
=+ =+ [gr=(ga 8 0x11b 3) few==>(fe .(a 5))]
=+ [pro=pro.gr dif=dif.gr pow=pow.gr ror=ror.few]
[pro=pro dif=dif pow=pow ror=ror nnk=8 nnb=4 nnr=14]
=> |%
++ cipa :: AES params
$_ ^? |%
++ co *{p/@ q/@ r/@ s/@} :: col coefs
++ ix |~(a/@ *@) :: key index
++ ro *{p/@ q/@ r/@ s/@} :: row shifts
++ su *@ :: s-box
--
--
|%
++ pen :: encrypt
^- cipa
|%
++ co [0x2 0x3 1 1]
++ ix |~(a/@ a)
++ ro [0 1 2 3]
++ su 0x16bb.54b0.0f2d.9941.6842.e6bf.0d89.a18c.
df28.55ce.e987.1e9b.948e.d969.1198.f8e1.
9e1d.c186.b957.3561.0ef6.0348.66b5.3e70.
8a8b.bd4b.1f74.dde8.c6b4.a61c.2e25.78ba.
08ae.7a65.eaf4.566c.a94e.d58d.6d37.c8e7.
79e4.9591.62ac.d3c2.5c24.0649.0a3a.32e0.
db0b.5ede.14b8.ee46.8890.2a22.dc4f.8160.
7319.5d64.3d7e.a7c4.1744.975f.ec13.0ccd.
d2f3.ff10.21da.b6bc.f538.9d92.8f40.a351.
a89f.3c50.7f02.f945.8533.4d43.fbaa.efd0.
cf58.4c4a.39be.cb6a.5bb1.fc20.ed00.d153.
842f.e329.b3d6.3b52.a05a.6e1b.1a2c.8309.
75b2.27eb.e280.1207.9a05.9618.c323.c704.
1531.d871.f1e5.a534.ccf7.3f36.2693.fdb7.
c072.a49c.afa2.d4ad.f047.59fa.7dc9.82ca.
76ab.d7fe.2b67.0130.c56f.6bf2.7b77.7c63
--
::
++ pin :: decrypt
^- cipa
|%
++ co [0xe 0xb 0xd 0x9]
++ ix |~(a/@ (sub nnr a))
++ ro [0 3 2 1]
++ su 0x7d0c.2155.6314.69e1.26d6.77ba.7e04.2b17.
6199.5383.3cbb.ebc8.b0f5.2aae.4d3b.e0a0.
ef9c.c993.9f7a.e52d.0d4a.b519.a97f.5160.
5fec.8027.5910.12b1.31c7.0788.33a8.dd1f.
f45a.cd78.fec0.db9a.2079.d2c6.4b3e.56fc.
1bbe.18aa.0e62.b76f.89c5.291d.711a.f147.
6edf.751c.e837.f9e2.8535.ade7.2274.ac96.
73e6.b4f0.cecf.f297.eadc.674f.4111.913a.
6b8a.1301.03bd.afc1.020f.3fca.8f1e.2cd0.
0645.b3b8.0558.e4f7.0ad3.bc8c.00ab.d890.
849d.8da7.5746.155e.dab9.edfd.5048.706c.
92b6.655d.cc5c.a4d4.1698.6886.64f6.f872.
25d1.8b6d.49a2.5b76.b224.d928.66a1.2e08.
4ec3.fa42.0b95.4cee.3d23.c2a6.3294.7b54.
cbe9.dec4.4443.8e34.87ff.2f9b.8239.e37c.
fbd7.f381.9ea3.40bf.38a5.3630.d56a.0952
--
::
++ mcol
|= {a/(list @) b/{p/@ q/@ r/@ s/@}} ^- (list @)
=+ c=[p=*@ q=*@ r=*@ s=*@]
|- ^- (list @)
?~ a ~
=> .(p.c (cut 3 [0 1] i.a))
=> .(q.c (cut 3 [1 1] i.a))
=> .(r.c (cut 3 [2 1] i.a))
=> .(s.c (cut 3 [3 1] i.a))
:_ $(a t.a)
%+ rep 3
%+ turn
%- limo
:~ [[p.c p.b] [q.c q.b] [r.c r.b] [s.c s.b]]
[[p.c s.b] [q.c p.b] [r.c q.b] [s.c r.b]]
[[p.c r.b] [q.c s.b] [r.c p.b] [s.c q.b]]
[[p.c q.b] [q.c r.b] [r.c s.b] [s.c p.b]]
==
|= {a/{@ @} b/{@ @} c/{@ @} d/{@ @}}
:(dif (pro a) (pro b) (pro c) (pro d))
::
++ pode :: explode to block
|= {a/bloq b/@ c/@} ^- (list @)
=+ d=(rip a c)
=+ m=(met a c)
|-
?: =(m b)
d
$(m +(m), d (weld d (limo [0 ~])))
++ sube :: s-box word
|= {a/@ b/@} ^- @
(rep 3 (turn (pode 3 4 a) |=(c/@ (cut 3 [c 1] b))))
--
|%
++ be :: block cipher
|= {a/? b/@ c/@H} ^- @uxH
=> %= .
+
=> +
|%
++ ankh
|= {a/cipa b/@ c/@}
(pode 5 nnb (cut 5 [(mul (ix.a b) nnb) nnb] c))
++ sark
|= {c/(list @) d/(list @)} ^- (list @)
?~ c ~
?~ d !!
[(mix i.c i.d) $(c t.c, d t.d)]
++ srow
|= {a/cipa b/(list @)} ^- (list @)
=+ [c=0 d=~ e=ro.a]
|-
?: =(c nnb)
d
:_ $(c +(c))
%+ rep 3
%+ turn
(limo [0 p.e] [1 q.e] [2 r.e] [3 s.e] ~)
|= {f/@ g/@}
(cut 3 [f 1] (snag (mod (add g c) nnb) b))
++ subs
|= {a/cipa b/(list @)} ^- (list @)
?~ b ~
[(sube i.b su.a) $(b t.b)]
--
==
=+ [d=?:(a pen pin) e=(pode 5 nnb c) f=1]
=> .(e (sark e (ankh d 0 b)))
|-
?. =(nnr f)
=> .(e (subs d e))
=> .(e (srow d e))
=> .(e (mcol e co.d))
=> .(e (sark e (ankh d f b)))
$(f +(f))
=> .(e (subs d e))
=> .(e (srow d e))
=> .(e (sark e (ankh d nnr b)))
(rep 5 e)
::
++ ex :: key expand
|= a/@I ^- @
=+ [b=a c=0 d=su:pen i=nnk]
|-
?: =(i (mul nnb +(nnr)))
b
=> .(c (cut 5 [(dec i) 1] b))
=> ?: =(0 (mod i nnk))
=> .(c (ror 3 1 c))
=> .(c (sube c d))
.(c (mix c (pow (dec (div i nnk)) 2)))
?: &((gth nnk 6) =(4 (mod i nnk)))
.(c (sube c d))
.
=> .(c (mix c (cut 5 [(sub i nnk) 1] b)))
=> .(b (can 5 [i b] [1 c] ~))
$(i +(i))
::
++ ix :: key expand, inv
|= a/@ ^- @
=+ [i=1 j=*@ b=*@ c=co:pin]
|-
?: =(nnr i)
a
=> .(b (cut 7 [i 1] a))
=> .(b (rep 5 (mcol (pode 5 4 b) c)))
=> .(j (sub nnr i))
%= $
i +(i)
a
%+ can 7
:~ [i (cut 7 [0 i] a)]
[1 b]
[j (cut 7 [+(i) j] a)]
==
==
--
++ ga :: GF (bex p.a)
|= a/{p/@ q/@ r/@} :: dim poly gen
=+ si=(bex p.a)
=+ ma=(dec si)
=> |%
++ dif :: add and sub
|= {b/@ c/@}
?> &((lth b si) (lth c si))
(mix b c)
::
++ dub :: mul by x
|= b/@
?> (lth b si)
?: =(1 (cut 0 [(dec p.a) 1] b))
(dif (sit q.a) (sit (lsh 0 1 b)))
(lsh 0 1 b)
::
++ pro :: slow multiply
|= {b/@ c/@}
?: =(0 b)
0
?: =(1 (dis 1 b))
(dif c $(b (rsh 0 1 b), c (dub c)))
$(b (rsh 0 1 b), c (dub c))
::
++ toe :: exp+log tables
=+ ^= nu
|= {b/@ c/@}
^- (map @ @)
=+ d=*(map @ @)
|-
?: =(0 c)
d
%= $
c (dec c)
d (~(put by d) c b)
==
=+ [p=(nu 0 (bex p.a)) q=(nu ma ma)]
=+ [b=1 c=0]
|- ^- {p/(map @ @) q/(map @ @)}
?: =(ma c)
[(~(put by p) c b) q]
%= $
b (pro r.a b)
c +(c)
p (~(put by p) c b)
q (~(put by q) b c)
==
::
++ sit :: reduce
|= b/@
(mod b (bex p.a))
--
=+ toe
|%
++ fra :: divide
|= {b/@ c/@}
(pro b (inv c))
::
++ inv :: invert
|= b/@
=+ c=(~(get by q) b)
?~ c !!
=+ d=(~(get by p) (sub ma u.c))
(need d)
::
++ pow :: exponent
|= {b/@ c/@}
=+ [d=1 e=c f=0]
|-
?: =(p.a f)
d
?: =(1 (cut 0 [f 1] b))
$(d (pro d e), e (pro e e), f +(f))
$(e (pro e e), f +(f))
::
++ pro :: multiply
|= {b/@ c/@}
=+ d=(~(get by q) b)
?~ d 0
=+ e=(~(get by q) c)
?~ e 0
=+ f=(~(get by p) (mod (add u.d u.e) ma))
(need f)
--
:: ::
:::: 3f: scrambling ::
:: ::
:: un (XX), ga ::
::
-- =>
|%
++ un :: =(x (wred (wren x)))
|%
++ wren :: conceal structure
|= pyn/@ ^- @
=+ len=(met 3 pyn)
?: =(0 len)
0
=> .(len (dec len))
=+ mig=(zaft (xafo len (cut 3 [len 1] pyn)))
%+ can 3
%- flop ^- (list {@ @})
:- [1 mig]
|- ^- (list {@ @})
?: =(0 len)
~
=> .(len (dec len))
=+ mog=(zyft :(mix mig (end 3 1 len) (cut 3 [len 1] pyn)))
[[1 mog] $(mig mog)]
::
++ wred :: restore structure
|= cry/@ ^- @
=+ len=(met 3 cry)
?: =(0 len)
0
=> .(len (dec len))
=+ mig=(cut 3 [len 1] cry)
%+ can 3
%- flop ^- (list {@ @})
:- [1 (xaro len (zart mig))]
|- ^- (list {@ @})
?: =(0 len)
~
=> .(len (dec len))
=+ mog=(cut 3 [len 1] cry)
[[1 :(mix mig (end 3 1 len) (zyrt mog))] $(mig mog)]
::
++ xafo |=({a/@ b/@} +((mod (add (dec b) a) 255)))
++ xaro |=({a/@ b/@} +((mod (add (dec b) (sub 255 (mod a 255))) 255)))
::
++ zaft :: forward 255-sbox
|= a/@D
=+ ^= b
0xcc.75bc.86c8.2fb1.9a42.f0b3.79a0.92ca.21f6.1e41.cde5.fcc0.
7e85.51ae.1005.c72d.1246.07e8.7c64.a914.8d69.d9f4.59c2.8038.
1f4a.dca2.6fdf.66f9.f561.a12e.5a16.f7b0.a39f.364e.cb70.7318.
1de1.ad31.63d1.abd4.db68.6a33.134d.a760.edee.5434.493a.e323.
930d.8f3d.3562.bb81.0b24.43cf.bea5.a6eb.52b4.0229.06b2.6704.
78c9.45ec.d75e.58af.c577.b7b9.c40e.017d.90c3.87f8.96fa.1153.
0372.7f30.1c32.ac83.ff17.c6e4.d36d.6b55.e2ce.8c71.8a5b.b6f3.
9d4b.eab5.8b3c.e7f2.a8fe.9574.5de0.bf20.3f15.9784.9939.5f9c.
e609.564f.d8a4.b825.9819.94aa.2c08.8e4c.9b22.477a.2840.3ed6.
3750.6ef1.44dd.89ef.6576.d00a.fbda.9ed2.3b6c.7b0c.bde9.2ade.
5c88.c182.481a.1b0f.2bfd.d591.2726.57ba
(cut 3 [(dec a) 1] b)
::
++ zart :: reverse 255-sbox
|= a/@D
=+ ^= b
0x68.4f07.ea1c.73c9.75c2.efc8.d559.5125.f621.a7a8.8591.5613.
dd52.40eb.65a2.60b7.4bcb.1123.ceb0.1bd6.3c84.2906.b164.19b3.
1e95.5fec.ffbc.f187.fbe2.6680.7c77.d30e.e94a.9414.fd9a.017d.
3a7e.5a55.8ff5.8bf9.c181.e5b6.6ab2.35da.50aa.9293.3bc0.cdc6.
f3bf.1a58.4130.f844.3846.744e.36a0.f205.789e.32d8.5e54.5c22.
0f76.fce7.4569.0d99.d26e.e879.dc16.2df4.887f.1ffe.4dba.6f5d.
bbcc.2663.1762.aed7.af8a.ca20.dbb4.9bc7.a942.834c.105b.c4d4.
8202.3e61.a671.90e6.273d.bdab.3157.cfa4.0c2e.df86.2496.f7ed.
2b48.2a9d.5318.a343.d128.be9c.a5ad.6bb5.6dfa.c5e1.3408.128d.
2c04.0339.97a1.2ff0.49d0.eeb8.6c0a.0b37.b967.c347.d9ac.e072.
e409.7b9f.1598.1d3f.33de.8ce3.8970.8e7a
(cut 3 [(dec a) 1] b)
::
++ zyft :: forward 256-sbox
|= a/@D
=+ ^= b
0xbb49.b71f.b881.b402.17e4.6b86.69b5.1647.115f.dddb.7ca5.
8371.4bd5.19a9.b092.605d.0d9b.e030.a0cc.78ba.5706.4d2d.
986a.768c.f8e8.c4c7.2f1c.effe.3cae.01c0.253e.65d3.3872.
ce0e.7a74.8ac6.daac.7e5c.6479.44ec.4143.3d20.4af0.ee6c.
c828.deca.0377.249f.ffcd.7b4f.eb7d.66f2.8951.042e.595a.
8e13.f9c3.a79a.f788.6199.9391.7fab.6200.4ce5.0758.e2f1.
7594.c945.d218.4248.afa1.e61a.54fb.1482.bea4.96a2.3473.
63c2.e7cb.155b.120a.4ed7.bfd8.b31b.4008.f329.fca3.5380.
9556.0cb2.8722.2bea.e96e.3ac5.d1bc.10e3.2c52.a62a.b1d6.
35aa.d05e.f6a8.0f3b.31ed.559d.09ad.f585.6d21.fd1d.8d67.
370b.26f4.70c1.b923.4684.6fbd.cf8b.5036.0539.9cdc.d93f.
9068.1edf.8f33.b632.d427.97fa.9ee1
(cut 3 [a 1] b)
::
++ zyrt :: reverse 256-sbox
|= a/@D
=+ ^= b
0x9fc8.2753.6e02.8fcf.8b35.2b20.5598.7caa.c9a9.30b0.9b48.
47ce.6371.80f6.407d.00dd.0aa5.ed10.ecb7.0f5a.5c3a.e605.
c077.4337.17bd.9eda.62a4.79a7.ccb8.44cd.8e64.1ec4.5b6b.
1842.ffd8.1dfb.fd07.f2f9.594c.3be3.73c6.2cb6.8438.e434.
8d3d.ea6a.5268.72db.a001.2e11.de8c.88d3.0369.4f7a.87e2.
860d.0991.25d0.16b9.978a.4bf4.2a1a.e96c.fa50.85b5.9aeb.
9dbb.b2d9.a2d1.7bba.66be.e81f.1946.29a8.f5d2.f30c.2499.
c1b3.6583.89e1.ee36.e0b4.6092.937e.d74e.2f6f.513e.9615.
9c5d.d581.e7ab.fe74.f01b.78b1.ae75.af57.0ec2.adc7.3245.
12bf.2314.3967.0806.31dc.cb94.d43f.493c.54a6.0421.c3a1.
1c4a.28ac.fc0b.26ca.5870.e576.f7f1.616d.905f.ef41.33bc.
df4d.225e.2d56.7fd6.1395.a3f8.c582
(cut 3 [a 1] b)
--
::
++ ob
|%
++ feen :: conceal structure v2
|= pyn/@ ^- @
?: &((gte pyn 0x1.0000) (lte pyn 0xffff.ffff))
(add 0x1.0000 (fice (sub pyn 0x1.0000)))
?: &((gte pyn 0x1.0000.0000) (lte pyn 0xffff.ffff.ffff.ffff))
=+ lo=(dis pyn 0xffff.ffff)
=+ hi=(dis pyn 0xffff.ffff.0000.0000)
%+ con hi
(add 0x1.0000 (fice (sub lo 0x1.0000)))
pyn
::
++ fend :: restore structure v2
|= cry/@ ^- @
?: &((gte cry 0x1.0000) (lte cry 0xffff.ffff))
(add 0x1.0000 (teil (sub cry 0x1.0000)))
?: &((gte cry 0x1.0000.0000) (lte cry 0xffff.ffff.ffff.ffff))
=+ lo=(dis cry 0xffff.ffff)
=+ hi=(dis cry 0xffff.ffff.0000.0000)
%+ con hi
(add 0x1.0000 (teil (sub lo 0x1.0000)))
cry
::
++ fice :: adapted from
|= nor/@ :: black and rogaway
^- @ :: "ciphers with
=+ ^= sel :: arbitrary finite
%+ rynd 2 :: domains", 2002
%+ rynd 1
%+ rynd 0
[(mod nor 65.535) (div nor 65.535)]
(add (mul 65.535 -.sel) +.sel)
::
++ teil :: reverse ++fice
|= vip/@
^- @
=+ ^= sel
%+ rund 0
%+ rund 1
%+ rund 2
[(mod vip 65.535) (div vip 65.535)]
(add (mul 65.535 -.sel) +.sel)
::
++ rynd :: feistel round
|= {n/@ l/@ r/@}
^- {@ @}
:- r
?~ (mod n 2)
(~(sum fo 65.535) l (en:aesc (snag n raku) r))
(~(sum fo 65.536) l (en:aesc (snag n raku) r))
::
++ rund :: reverse round
|= {n/@ l/@ r/@}
^- {@ @}
:- r
?~ (mod n 2)
(~(dif fo 65.535) l (en:aesc (snag n raku) r))
(~(dif fo 65.536) l (en:aesc (snag n raku) r))
::
++ raku
^- (list @ux)
:~ 0x15f6.25e3.083a.eb3e.7a55.d4db.fb99.32a3.
43af.2750.219e.8a24.e5f8.fac3.6c36.f968
0xf2ff.24fe.54d0.1abd.4b2a.d8aa.4402.8e88.
e82f.19ec.948d.b1bb.ed2e.f791.83a3.8133
0xa3d8.6a7b.400e.9e91.187d.91a7.6942.f34a.
6f5f.ab8e.88b9.c089.b2dc.95a6.aed5.e3a4
==
--
--
.
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