urbit/arvo/test.hoon
2016-03-09 14:05:18 -08:00

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Plaintext

!: ::
:::: /hoon/hoon ::
:: ::
=> %151 =>
:: ::
:::: 0: version stub ::
:: ::
|%
++ hoon +
-- =>
:: ::
:::: 1: layer one ::
:: ::
:: 1a: basic arithmetic ::
:: 1b: tree addressing ::
:: 1c: ideal containers ::
::
|%
:: ::
:::: 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 $@($~ {$~ u/a})) :: maybe
-- =>
:: ::
:::: 2: layer two ::
:: ::
:: 2a: unit logic ::
:: 2b: list logic ::
:: 2c: bit arithmetic ::
:: 2d: bit logic ::
:: 2e: insecure hashing ::
:: 2f: noun ordering ::
:: 2g: unsigned powers ::
:: 2h: set logic ::
:: 2i: map logic ::
:: 2j: jar and jug logic ::
:: 2k: queue logic ::
:: 2l: container from container ::
:: 2m: container from noun ::
:: 2n: functional hacks ::
:: 2o: normalizing containers ::
:: 2p: serialization ::
::
|%
:: ::
:::: 2a: unit logic ::
:: ::
:: biff, bind, bond, both, clap, drop, ::
:: fall, flit, lift, mate, need, some ::
::
++ biff :: apply
|* {a/(unit) b/$-(* (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 rem/sqrt
~/ %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)]
++ char @tD
-- =>
:: ::
:::: 3: layer three ::
:: ::
|%
::
:::: 3a: signed and modular ints ::
:: ::
:: fe, si ::
::
++ 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
--
::
++ 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
--
--
.