urbit/pub/doc/hoon/library/2c.md

chapter 2c, simple noun surgery
===============================

section 2cA, bit surgery
------------------------

<h3 id="++bex"><code>++bex</code></h3>

Binary exponent

    ++  bex                                                 ::  binary exponent
      ~/  %bex
      |=  a=@
      ^-  @
      ?:  =(0 a)  1
      (mul 2 $(a (dec a)))

Computes the result of `2^a`, producing an atom.

`a` is an [atom](atom).

    ~zod/try=> (bex 4)
    16
    ~zod/try=> (bex (add 19 1))
    1.048.576
    ~zod/try=> (bex 0)
    1

------------------------------------------------------------------------

<h3 id="++xeb"><code>++xeb</code></h3>

Binary logarithm

    ++  xeb                                                 ::  binary logarithm
      ::  ~/  %xeb
      |=  a=@
      ^-  @
      (met 0 a)

Computes the base-2 logarithm of `a`, producing an atom.

`a` is an [atom](atom).

    ~zod/try=> (xeb 31)
    5
    ~zod/try=> (xeb 32)
    6
    ~zod/try=> (xeb 49)
    6
    ~zod/try=> (xeb 0)
    0
    ~zod/try=> (xeb 1)
    1
    ~zod/try=> (xeb 2)
    2

------------------------------------------------------------------------

<h3 id="++can"><code>++can</code></h3>

Assemble

    ++  can                                                 ::  assemble
      ~/  %can
      |=  [a=bloq b=(list ,[p=@ q=@])]
      ^-  @
      ?~  b  0
      (mix (end a p.i.b q.i.b) (lsh a p.i.b $(b t.b)))

Produces an atom from a list `b` of length-value pairs `p` and `q`,
where `p` is the length in bloqs of size `a`, and `q` is an atomic
value.

`a` is a block size (see [++bloq]()).

`b` is a [list](list) of length value pairs, `p` and `q`.

    ~zod/try=> `@ub`(can 3 ~[[1 1]])
    0b1 
    ~zod/try=> `@ub`(can 0 ~[[1 255]])
    0b1
    ~zod/try=> `@ux`(can 3 [3 0xc1] [1 0xa] ~)
    0xa00.00c1
    ~zod/try=> `@ux`(can 3 [3 0xc1] [1 0xa] [1 0x23] ~)
    0x23.0a00.00c1
    ~zod/try=> `@ux`(can 4 [3 0xc1] [1 0xa] [1 0x23] ~)
    0x23.000a.0000.0000.00c1
    ~zod/try=> `@ux`(can 3 ~[[1 'a'] [2 'bc']])
    0x63.6261

------------------------------------------------------------------------

<h3 id="++cat"><code>++cat</code></h3>

Concatenate

    ++  cat                                                 ::  concatenate
      ~/  %cat
      |=  [a=bloq b=@ c=@]
      (add (lsh a (met a b) c) b)

Concatenates two atoms, `b` and `c`, using bloq size `a`, producing an
atom.

`a` is a block size (see [++bloq]()).

`b` is an [atom]().

`c` is an [atom]().

    ~zod/try=> `@ub`(cat 3 1 0)
    0b1
    ~zod/try=> `@ub`(cat 0 1 1)
    0b11
    ~zod/try=> `@ub`(cat 0 2 1)
    0b110
    ~zod/try=> `@ub`(cat 2 1 1)
    0b1.0001
    ~zod/try=> `@ub`256
    0b1.0000.0000
    ~zod/try=> `@ub`255
    0b1111.1111
    ~zod/try=> `@ub`(cat 3 256 255)
    0b1111.1111.0000.0001.0000.0000
    ~zod/try=> `@ub`(cat 2 256 255)
    0b1111.1111.0001.0000.0000
    ~zod/try=> (cat 3 256 255)
    16.711.936

------------------------------------------------------------------------

<h3 id="++cut"><code>++cut</code></h3>

Slice

    ++  cut                                                 ::  slice
      ~/  %cut
      |=  [a=bloq [b=@ c=@] d=@]
      (end a c (rsh a b d))

Slices `c` blocks of size `a` that are `b` blocks from the end of `d`.
Produces an atom.

`a` is a block size (see [++bloq]()).

`b` is an [atom]().

`c` is an [atom]().

    ~zod/try=> (cut 0 [1 1] 2)
    1
    ~zod/try=> (cut 0 [2 1] 4)
    1
    ~zod/try=> `@t`(cut 3 [0 3] 'abcdefgh')
    'abc'
    ~zod/try=> `@t`(cut 3 [1 3] 'abcdefgh')
    'bcd'
    ~zod/try=> `@ub`(cut 0 [0 3] 0b1111.0000.1101)
    0b101
    ~zod/try=> `@ub`(cut 0 [0 6] 0b1111.0000.1101)
    0b1101
    ~zod/try=> `@ub`(cut 0 [4 6] 0b1111.0000.1101)
    0b11.0000
    ~zod/try=> `@ub`(cut 0 [3 6] 0b1111.0000.1101)
    0b10.0001

------------------------------------------------------------------------

<h3 id="++end"><code>++end</code></h3>

Tail

    ++  end                                                 ::  tail
      ~/  %end
      |=  [a=bloq b=@ c=@]
      (mod c (bex (mul (bex a) b)))

Produces an atom by taking the last `b` blocks of size `a` from `c`.

`a` is a block size (see [++bloq]()).

`b` is an [atom]().

`c` is an [atom]().

    ~zod/try=> `@ub`12
    0b1100
    ~zod/try=> `@ub`(end 0 3 12)
    0b100
    ~zod/try=> (end 0 3 12)
    4
    ~zod/try=> `@ub`(end 1 3 12)
    0b1100
    ~zod/try=> (end 1 3 12)
    12
    ~zod/try=> `@ux`'abc'
    0x63.6261
    ~zod/try=> `@ux`(end 3 2 'abc')
    0x6261
    ~zod/try=> `@t`(end 3 2 'abc')
    'ab'

------------------------------------------------------------------------

<h3 id="++fil"><code>++fil</code></h3>

Fill bloqstream

    ++  fil                                                 ::  fill bloqstream
      |=  [a=bloq b=@ c=@]
      =+  n=0
      =+  d=c
      |-  ^-  @
      ?:  =(n b)
        (rsh a 1 d)
      $(d (add c (lsh a 1 d)), n +(n))

Produces an atom by repeating `c` for `b` blocks of size `a`.

`a` is a block size (see [++bloq]()).

`b` is an [atom]().

`c` is an [atom]().

    ~zod/try=> `@t`(fil 3 5 %a)
    'aaaaa'
    ~zod/try=> `@t`(fil 5 10 %ceeb)
    'ceebceebceebceebceebceebceebceebceebceeb'
    ~zod/try=> `@t`(fil 4 10 %eced)
    'ʇʇʇʇʇʇʇʇʇʇed'
    ~zod/try=> `@tas`(fil 4 10 %bf)
    %bfbfbfbfbfbfbfbfbfbf

------------------------------------------------------------------------

<h3 id="++lsh"><code>++lsh</code></h3>

Left-shift

    ++  lsh                                                 ::  left-shift
      ~/  %lsh
      |=  [a=bloq b=@ c=@]
      (mul (bex (mul (bex a) b)) c)

Produces an atom by left-shifting `c` by `b` blocks of size `a`.

`a` is a block size (see [++bloq]()).

`b` is an [atom]().

`c` is an [atom]().

    ~zod/try=> `@ub`1
    0b1
    ~zod/try=> `@ub`(lsh 0 1 1)
    0b10
    ~zod/try=> (lsh 0 1 1)
    2
    ~zod/try=> `@ub`255
    0b1111.1111
    ~zod/try=> `@ub`(lsh 3 1 255)
    0b1111.1111.0000.0000
    ~zod/try=> (lsh 3 1 255)
    65.280

------------------------------------------------------------------------

<h3 id="++met"><code>++met</code></h3>

Measure

    ++  met                                                 ::  measure
      ~/  %met
      |=  [a=bloq b=@]
      ^-  @
      =+  c=0
      |-
      ?:  =(0 b)  c
      $(b (rsh a 1 b), c +(c))

Computes the number of blocks of size `a` in `b`, producing an atom.

`a` is a block size (see [++bloq]()).

`b` is an [atom]().

    ~zod/try=> (met 0 1)
    1
    ~zod/try=> (met 0 2)
    2
    ~zod/try=> (met 3 255)
    1
    ~zod/try=> (met 3 256)
    2
    ~zod/try=> (met 3 'abcde')
    5

------------------------------------------------------------------------

<h3 id="++rap"><code>++rap</code></h3>

Assemble non-zero

    ++  rap                                                 ::  assemble nonzero
      ~/  %rap
      |=  [a=bloq b=(list ,@)]
      ^-  @
      ?~  b  0
      (cat a i.b $(b t.b))

Concatenate a list of atoms `b` using blocksize `a`, producing an atom.

`a` is a block size (see [++bloq]()).

`b` is a [list]() of [atoms]().

    ~zod/try=> `@ub`(rap 2 (limo [1 2 3 4 ~]))
    0b100.0011.0010.0001
    ~zod/try=> `@ub`(rap 1 (limo [1 2 3 4 ~]))
    0b1.0011.1001
    ~zod/try=> (rap 0 (limo [0 0 0 ~]))
    0
    ~zod/try=> (rap 0 (limo [1 0 1 ~]))
    3

------------------------------------------------------------------------

<h3 id="++rep"><code>++rep</code></h3>

Assemble single

    ++  rep                                                 ::  assemble single
      ~/  %rep
      |=  [a=bloq b=(list ,@)]
      ^-  @
      =+  c=0
      |-
      ?~  b  0
      (con (lsh a c (end a 1 i.b)) $(c +(c), b t.b))

Produces an atom by assembling a list of atoms `b` using block size `a`.

`a` is a block size (see [++bloq]()).

`b` is a list of [atoms]().

    ~zod/try=> `@ub`(rep 2 (limo [1 2 3 4 ~]))
    0b100.0011.0010.0001
    ~zod/try=> (rep 0 (limo [0 0 1 ~]))
    4
    ~zod/try=> (rep 0 (limo [0 0 0 1 ~]))
    8
    ~zod/try=> (rep 0 (limo [0 1 0 0 ~]))
    2
    ~zod/try=> (rep 0 (limo [0 1 0 1 ~]))
    10
    ~zod/try=> (rep 0 (limo [0 1 0 1 0 1 ~]))
    42
    ~zod/try=> `@ub`42
    0b10.1010

------------------------------------------------------------------------

<h3 id="++rip"><code>++rip</code></h3>

Disassemble

    ++  rip                                                 ::  disassemble
      ~/  %rip
      |=  [a=bloq b=@]
      ^-  (list ,@)
      ?:  =(0 b)  ~
      [(end a 1 b) $(b (rsh a 1 b))]

Produces a list of atoms from the bits of `b` using block size `a`.

`a` is a block size (see [++bloq]()).

`b` is an [atom]().

    ~zod/try=> `@ub`155
    0b1001.1011
    ~zod/try=> (rip 0 155)
    ~[1 1 0 1 1 0 0 1]
    ~zod/try=> (rip 2 155)
    ~[11 9]
    ~zod/try=> (rip 1 155)
    ~[3 2 1 2]
    ~zod/try=> `@ub`256
    0b1.0000.0000
    ~zod/try=> (rip 0 256)
    ~[0 0 0 0 0 0 0 0 1]
    ~zod/try=> (rip 2 256)
    ~[0 0 1]
    ~zod/try=> (rip 3 256)
    ~[0 1]

------------------------------------------------------------------------

<h3 id="++rsh"><code>++rsh</code></h3>

Right-shift

    ++  rsh                                                 ::  right-shift
      ~/  %rsh
      |=  [a=bloq b=@ c=@]
      (div c (bex (mul (bex a) b)))

Right-shifts `c` by `b` blocks of size `a`, producing an atom.

`a` is a block size (see [++bloq]()).

`b` is an [atom]().

`c` is an [atom]().

    ~zod/try=> `@ub`145
    0b1001.0001
    ~zod/try=> `@ub`(rsh 1 1 145)
    0b10.0100
    ~zod/try=> (rsh 1 1 145)
    36
    ~zod/try=> `@ub`(rsh 2 1 145)
    0b1001
    ~zod/try=> (rsh 2 1 145)
    9
    ~zod/try=> `@ub`10
    0b1010
    ~zod/try=> `@ub`(rsh 0 1 10)
    0b101
    ~zod/try=> (rsh 0 1 10)
    5
    ~zod/try=> `@ux`'abc'
    0x63.6261
    ~zod/try=> `@t`(rsh 3 1 'abc')
    'bc'
    ~zod/try=> `@ux`(rsh 3 1 'abc')
    0x6362

------------------------------------------------------------------------

<h3 id="++swap"><code>++swap</code></h3>

Reverse block order

    ++  swap  |=([a=bloq b=@] (rep a (flop (rip a b))))     ::  reverse bloq order

Switches little ending to big and vice versa: produces an atom by
reversing the block order of `b` using block size `a`.

`a` is a block size (see [++bloq]()).

`b` is an [atom]()

    ~zod/try=> `@ub`24
    0b1.1000
    ~zod/try=> (swap 0 24)
    3
    ~zod/try=> `@ub`3
    0b11
    ~zod/try=> (swap 0 0)
    0
    ~zod/try=> (swap 0 128)
    1

------------------------------------------------------------------------

section 2cB, bit logic
----------------------

<h3 id="++con"><code>++con</code></h3>

Binary OR

    ++  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))
              ==
      ==

Computes the bit-wise logical OR of two atoms, `a` and `b`, producing an
atom.

`a` is an [atom]()

`b` is an [atom]()

    ~zod/try=> (con 0b0 0b1)
    1
    ~zod/try=> (con 0 1)
    1
    ~zod/try=> (con 0 0)
    0
    ~zod/try=> `@ub`(con 0b1111.0000 0b1.0011)
    0b1111.0011    
    ~zod/try=> (con 4 4)
    4
    ~zod/try=> (con 10.000 234)
    10.234

------------------------------------------------------------------------

<h3 id="++dis"><code>++dis</code></h3>

Binary AND

    ++  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))
              ==
      ==

Computes the bit-wise logical AND of two atoms `a` and `b`, producing an
atom.

`a` is an [atom]()

`b` is an [atom]()

    ~zod/try=> `@ub`9
    0b1001
    ~zod/try=> `@ub`5
    0b101
    ~zod/try=> `@ub`(dis 9 5)
    0b1
    ~zod/try=> (dis 9 5)
    1
    ~zod/try=> `@ub`534
    0b10.0001.0110
    ~zod/try=> `@ub`987
    0b11.1101.1011
    ~zod/try=> `@ub`(dis 534 987)
    0b10.0001.0010
    ~zod/try=> (dis 534 987)
    530

------------------------------------------------------------------------

<h3 id="++mix"><code>++mix</code></h3>

Binary XOR

    ++  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))))
      ==

Produces the bit-wise logical XOR of `a` and `b`, producing an atom.

`a` is an [atom]()

`b` is an [atom]()

    ~zod/try=> `@ub`2
    0b10
    ~zod/try=> `@ub`3
    0b11
    ~zod/try=> `@ub`(mix 2 3)
    0b1
    ~zod/try=> (mix 2 3)
    1
    ~zod/try=> `@ub`(mix 2 2)
    0b0
    ~zod/try=> (mix 2 2)
    0

------------------------------------------------------------------------

<h3 id="++not"><code>++not</code></h3>

Binary NOT

    ++  not  |=  [a=bloq b=@ c=@]                           ::  binary not (sized)
      (mix c (dec (bex (mul b (bex a)))))

Computes the bit-wise logical NOT of the bottom `b` blocks of size `a`
of `c`.

`a` is a block size (see [++bloq]()).

`b` is an [atom]().

`c` is an [atom]().

    ~zod/try=> `@ub`24
    0b1.1000
    ~zod/try=> (not 0 5 24)
    7
    ~zod/try=> `@ub`7
    0b111
    ~zod/try=> (not 2 5 24)
    1.048.551
    ~zod/try=> (not 2 5 1.048.551)
    24
    ~zod/try=> (not 1 1 (not 1 1 10))
    10

------------------------------------------------------------------------

section 2cC, noun orders
------------------------

<h3 id="++aor"><code>++aor</code></h3>

Alphabetic order

    ++  aor                                                 ::  alphabetic-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)

Computes whether `a` and `b` are in alphabetical order, producing a
loobean.

`a` is a [noun]().

`b` is a [noun]().

    ~zod/try=> (aor 'a' 'b')
    %.y
    ~zod/try=> (aor 'b' 'a')
    %.n
    ~zod/try=> (aor "foo" "bar")
    %.n
    ~zod/try=> (aor "bar" "foo")
    %.y
    ~zod/try=> (aor "abcdefz" "abcdefa")
    %.n
    ~zod/try=> (aor "abcdefa" "abcdefz")
    %.y
    ~zod/try=> (aor 10.000 17.000)
    %.y
    ~zod/try=> (aor 10 9)
    %.n

------------------------------------------------------------------------

<h3 id="++dor"><code>++dor</code></h3>

Numeric order

    ++  dor                                                 ::  d-order
      ~/  %dor
      |=  [a=* b=*]
      ^-  ?
      ?:  =(a b)  &
      ?.  ?=(@ a)
        ?:  ?=(@ b)  |
        ?:  =(-.a -.b)
          $(a +.a, b +.b)
        $(a -.a, b -.b)
      ?.  ?=(@ b)  &
      (lth a b)

Computes whether `a` and `b` are in ascending numeric order, producing a
loobean.

`a` is a [noun]().

`b` is a [noun]().

    ~zod/try=> (dor 1 2)
    %.y
    ~zod/try=> (dor 2 1)
    %.n
    ~zod/try=> (dor ~[1 2 3] ~[1 2 4])
    %.y
    ~zod/try=> (dor ~[1 2 4] ~[1 2 3])
    %.n
    ~zod/try=> (dor (limo ~[99 100 10.000]) ~[99 101 10.000])
    %.y
    ~zod/try=> (dor ~[99 101 10.999] (limo ~[99 100 10.000]))
    %.n

------------------------------------------------------------------------

<h3 id="++gor"><code>++gor</code></h3>

Hash order

    ++  gor                                                 ::  g-order
      ~/  %gor
      |=  [a=* b=*]
      ^-  ?
      =+  [c=(mug a) d=(mug b)]
      ?:  =(c d)
        (dor a b)
      (lth c d)

XX revisit

    ~zod/try=> (gor 'd' 'c')
    %.y
    ~zod/try=> 'd'
    'd'
    ~zod/try=> 'c'
    ~zod/try=> `@ud`'d'
    100
    ~zod/try=> `@ud`'c'
    99
    ~zod/try=> (mug 'd')
    1.628.185.714
    ~zod/try=> (mug 'c')
    1.712.073.811
    ~zod/try=> (gor 'd' 'c')
    %.y
    ~zod/try=> (gor 'c' 'd')
    %.n
    ~zod/try=> (gor "foo" "bar")
    %.n
    ~zod/try=> (gor (some 10) (limo [1 2 3 ~]))
    %.n

------------------------------------------------------------------------

<h3 id="++hor"><code>++hor</code></h3>

Hash order

    ++  hor                                                 ::  h-order
      ~/  %hor
      |=  [a=* b=*]
      ^-  ?
      ?:  ?=(@ a)
        ?.  ?=(@ b)  &
        (gor a b)
      ?:  ?=(@ b)  |
      ?:  =(-.a -.b)
        (gor +.a +.b)
      (gor -.a -.b)

XX revisit

Recursive hash comparator gate.

    ~zod/try=> (hor . 1)
    %.n
    ~zod/try=> (hor 1 2)
    %.y
    ~zod/try=> (hor "abc" "cba")
    %.y
    ~zod/try=> (hor 'c' 'd')
    %.n

------------------------------------------------------------------------

<h3 id="++vor"><code>++vor</code></h3>

    ++  vor                                                 ::  v-order
      ~/  %vor
      |=  [a=* b=*]
      ^-  ?
      =+  [c=(mug (mug a)) d=(mug (mug b))]
      ?:  =(c d)
        (dor a b)
      (lth c d)

XX revisit

Double hash comparator gate.

    ~zod/try=> (vor 'f' 'g')
    %.y
    ~zod/try=> (vor 'a' 'z')
    %.n
    ~zod/try=> (vor 43.326 41.106)
    %.n

section 2cD, insecure hashing
-----------------------------

<h3 id="++fnv"><code>++fnv</code></h3>

    ++  fnv  |=(a=@ (end 5 1 (mul 16.777.619 a)))           ::  FNV scrambler

Hashes an atom with the 32-bit FNV non-cryptographic hash algorithm.
Multiplies `a` by the prime number 16,777,619 and then takes the block
of size 5 off the product's end, producing atom.

`a` is an [atom]().

    ~zod/try=> (fnv 10.000)
    272.465.456
    ~zod/try=> (fnv 10.001)
    289.243.075
    ~zod/try=> (fnv 1)
    16.777.619

------------------------------------------------------------------------

<h3 id="++mum"><code>++mum</code></h3>

    ++  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)))
      --
    ::

XX document

    ~zod/try=> (mum 10.000)
    1.232.632.901
    ~zod/try=> (mum 10.001)
    658.093.079
    ~zod/try=> (mum 1)
    818.387.364
    ~zod/try=> (mum (some 10))
    1.177.215.703
    ~zod/try=> (mum ~[1 2 3 4 5])
    1.517.902.092

<h3 id="++mug"><code>++mug</code></h3>

    ++  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))

Hashes `a` with the 31-bit nonzero FNV-1a non-cryptographic hash
algorithm, producing an atom.

    ~zod/try=> (mug 10.000)
    178.152.889
    ~zod/try=> (mug 10.001)
    714.838.017
    ~zod/try=> (mug 1)
    67.918.732
    ~zod/try=> (mug (some 10))
    1.872.403.737
    ~zod/try=> (mug (limo [1 2 3 4 5 ~]))
    1.067.931.605

section 2cE, phonetic base
--------------------------

<h3 id="++po"><code>++po</code></h3>

    ++  po
      ~/  %po
      =+  :-  ^=  sis                                       ::  prefix syllables
          'dozmarbinwansamlitsighidfidlissogdirwacsabwissib\
          /rigsoldopmodfoglidhopdardorlorhodfolrintogsilmir\
          /holpaslacrovlivdalsatlibtabhanticpidtorbolfosdot\
          /losdilforpilramtirwintadbicdifrocwidbisdasmidlop\
          /rilnardapmolsanlocnovsitnidtipsicropwitnatpanmin\
          /ritpodmottamtolsavposnapnopsomfinfonbanporworsip\
          /ronnorbotwicsocwatdolmagpicdavbidbaltimtasmallig\
          /sivtagpadsaldivdactansidfabtarmonranniswolmispal\
          /lasdismaprabtobrollatlonnodnavfignomnibpagsopral\
          /bilhaddocridmocpacravripfaltodtiltinhapmicfanpat\
          /taclabmogsimsonpinlomrictapfirhasbosbatpochactid\
          /havsaplindibhosdabbitbarracparloddosbortochilmac\
          /tomdigfilfasmithobharmighinradmashalraglagfadtop\
          /mophabnilnosmilfopfamdatnoldinhatnacrisfotribhoc\
          /nimlarfitwalrapsarnalmoslandondanladdovrivbacpol\
          /laptalpitnambonrostonfodponsovnocsorlavmatmipfap'
          ^=  dex                                           ::  suffix syllables
          'zodnecbudwessevpersutletfulpensytdurwepserwylsun\
          /rypsyxdyrnuphebpeglupdepdysputlughecryttyvsydnex\
          /lunmeplutseppesdelsulpedtemledtulmetwenbynhexfeb\
          /pyldulhetmevruttylwydtepbesdexsefwycburderneppur\
          /rysrebdennutsubpetrulsynregtydsupsemwynrecmegnet\
          /secmulnymtevwebsummutnyxrextebfushepbenmuswyxsym\
          /selrucdecwexsyrwetdylmynmesdetbetbeltuxtugmyrpel\
          /syptermebsetdutdegtexsurfeltudnuxruxrenwytnubmed\
          /lytdusnebrumtynseglyxpunresredfunrevrefmectedrus\
          /bexlebduxrynnumpyxrygryxfeptyrtustyclegnemfermer\
          /tenlusnussyltecmexpubrymtucfyllepdebbermughuttun\
          /bylsudpemdevlurdefbusbeprunmelpexdytbyttyplevmyl\
          /wedducfurfexnulluclennerlexrupnedlecrydlydfenwel\
          /nydhusrelrudneshesfetdesretdunlernyrsebhulryllud\
          /remlysfynwerrycsugnysnyllyndyndemluxfedsedbecmun\
          /lyrtesmudnytbyrsenwegfyrmurtelreptegpecnelnevfes'
      |%

Provides the phonetic syllables and name generators for the Urbit naming
system. The two faces, `sis` and `dex` are available to the arms
contained in this section.

------------------------------------------------------------------------

<h3 id="++ind"><code>++ind</code></h3>

Parse prefix

      ++  ind  ~/  %ind                                     ::  parse prefix
               |=  a=@
               =+  b=0
               |-  ^-  (unit ,@)
               ?:(=(256 b) ~ ?:(=(a (tod b)) [~ b] $(b +(b))))

Produces the byte of the right-hand syllable `a`.

`a` is an [atom]().

    ~zod/try=> (ind:po 'zod')
    [~ 0]
    ~zod/try=> (ind:po 'zam')
    ~
    ~zod/try=> (ind:po 'del')
    [~ 37]

------------------------------------------------------------------------

<h3 id="++ins"><code>++ins</code></h3>

Parse suffix

      ++  ins  ~/  %ins                                     ::  parse suffix
               |=  a=@
               =+  b=0
               |-  ^-  (unit ,@)
               ?:(=(256 b) ~ ?:(=(a (tos b)) [~ b] $(b +(b))))

Produces the byte of the left-hand phonetic syllable `b`.

`a` is an [atom]().

    ~zod/try=> (ins:po 'mar')
    [~ 1]
    ~zod/try=> (ins:po 'son')
    [~ 164]
    ~zod/try=> (ins:po 'pit')
    [~ 242]
    ~zod/try=> (ins:po 'pok')
    ~

------------------------------------------------------------------------

<h3 id="++tod"><code>++tod</code></h3>

Fetch prefix

      ++  tod  ~/  %tod                                     ::  fetch prefix
               |=(a=@ ?>((lth a 256) (cut 3 [(mul 3 a) 3] dex)))

Produces the phonetic prefix syllable from index `a` within `dex` as an
atom.

`a` is an [atom]()

    ~zod/try=> `@t`(tod:po 1)
    'nec'
    ~zod/try=> `@t`(tod:po 98)
    'dec'
    ~zod/try=> `@t`(tod:po 0)
    'zod'
    ~zod/try=> `@t`(tod:po 150)
    'ryg'
    ~zod/try=> `@t`(tod:po 255)
    'fes'
    ~zod/try=> `@t`(tod:po 256)
    ! exit

------------------------------------------------------------------------

<h3 id="++tos"><code>++tos</code></h3>

Fetch suffix

      ++  tos  ~/  %tos                                     ::  fetch suffix
               |=(a=@ ?>((lth a 256) (cut 3 [(mul 3 a) 3] sis)))

Produces the phonetic prefix syllable from index `a` within `sis` as an
atom.

    ~zod/try=> `@t`(tos:po 0)
    'doz'
    ~zod/try=> `@t`(tos:po 120)
    'fab'
    ~zod/try=> `@t`(tos:po 43)
    'pid'
    ~zod/try=> `@t`(tos:po 253)
    'mat'

------------------------------------------------------------------------

section 2cF, signed and modular ints
------------------------------------

<h3 id="++si"><code>++si</code></h3>

    ++  si  !:                                              ::  signed integer
      |%

Container for the signed integer functions.

------------------------------------------------------------------------

<h3 id="++abs"><code>++abs</code></h3>

    ++  abs  |=(a=@s (add (end 0 1 a) (rsh 0 1 a)))       ::  absolute value

Produces the absolute value of a signed integer.

`a` is a signed integer, `@s`.

    ~zod/try=> (abs:si -2)
    2
    ~zod/try=> (abs:si -10.000)
    10.000
    ~zod/try=> (abs:si --2)
    2

------------------------------------------------------------------------

<h3 id="++dif"><code>++dif</code></h3>

      ++  dif  |=  [a=@s b=@s]                              ::  subtraction
               (sum a (new !(syn b) (abs b)))

Produces the difference between two signed integers `b` and `c`.

`a` is a signed integer, `@s`.

`b` is a signed integer, `@s`.

    ~zod/try=> (dif:si --10 -7)
    --17
    ~zod/try=> (dif:si --10 --7)
    --3
    ~zod/try=> (dif:si `@s`0 --7)
    -7
    ~zod/try=> (dif:si `@s`0 `@s`7)
    --4

------------------------------------------------------------------------

<h3 id="++dul"><code>++dul</code></h3>

      ++  dul  |=  [a=@s b=@]                               ::  modulus
               =+(c=(old a) ?:(-.c (mod +.c b) (sub b +.c)))

Produces the modulus of two signed integers.

`a` is a signed integer, `@s`.

`b` is an [atom]().

    ~zod/try=> (dul:si --9 3)
    0
    ~zod/try=> (dul:si --9 4)
    1
    ~zod/try=> (dul:si --9 5)
    4
    ~zod/try=> (dul:si --9 6)
    3
    ~zod/try=> (dul:si --90 --10)
    10

------------------------------------------------------------------------

<h3 id="++fra"><code>++fra</code></h3>

      ++  fra  |=  [a=@s b=@s]                              ::  divide
               (new =(0 (mix (syn a) (syn b))) (div (abs a) (abs b)))

Produces the quotient of two signed integers.

`a` is a signed integer, `@s`.

`b` is a signed integer, `@s`.

    ~zod/try=> (fra:si --10 -2)
    -5
    ~zod/try=> (fra:si -20 -5)
    --4

------------------------------------------------------------------------

<h3 id="++new"><code>++new</code></h3>

      ++  new  |=  [a=? b=@]                                ::  [sign value] to @s
               `@s`?:(a (mul 2 b) ?:(=(0 b) 0 +((mul 2 (dec b)))))

Produces a signed integer from a loobean sign value `a` and an atom `b`.

`a` is a loobean.

`b` is an [atom]().

    ~zod/try=> (new:si [& 10])
    --10
    ~zod/try=> (new:si [| 10])
    -10
    ~zod/try=> (new:si [%.y 7])
    --7

------------------------------------------------------------------------

<h3 id="++old"><code>++old</code></h3>

      ++  old  |=(a=@s [(syn a) (abs a)])                   ::  [sign value]

Produces the cell `[sign value]` representations of a signed integer.

`a` is a signed integer, `@s`.

    ~zod/try=> (old:si 7)
    ! type-fail
    ! exit
    ~zod/try=> (old:si -7)
    [%.n 7]
    ~zod/try=> (old:si --7)
    [%.y 7]
    ~zod/try=> (old:si `@s`7)
    [%.n 4]
    ~zod/try=> (old:si -0)
    [%.y 0]

------------------------------------------------------------------------

<h3 id="++pro"><code>++pro</code></h3>

      ++  pro  |=  [a=@s b=@s]                              ::  multiplication
               (new =(0 (mix (syn a) (syn b))) (mul (abs a) (abs b)))

Produces the product of two signed integers.

`a` is a signed integer, `@s`.

`b` is a signed integer, `@s`.

    ~zod/try=> (pro:si -4 --2)
    -8
    ~zod/try=> (pro:si -4 -2)
    --8
    ~zod/try=> (pro:si --10.000.000 -10)
    -100.000.000
    ~zod/try=> (pro:si -1.337 --0)
    --0

------------------------------------------------------------------------

<h3 id="++rem"><code>++rem</code></h3>

      ++  rem  |=([a=@s b=@s] (dif a (pro b (fra a b))))    ::  remainder

Produces the remainder from a division of two signed integers.

`a` is a signed integer, `@s`.

`b` is a signed integer, `@s`.

    ~zod/try=> (rem:si -10 -4)
    -2
    ~zod/try=> (rem:si --10 --4)
    --2
    ~zod/try=> (rem:si --10 -4)
    --2
    ~zod/try=> (rem:si --7 --3)
    --1
    ~zod/try=> (rem:si --0 --10.000)
    --0

------------------------------------------------------------------------

<h3 id="++sum"><code>++sum</code></h3>

      ++  sum  |=  [a=@s b=@s]                              ::  addition
               ~|  %si-sum
               =+  [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))

Sum two signed integers.

`b` is a signed integer, `@s`.

`c` is a signed integer, `@s`.

    ~zod/try=> (sum:si --10 --10)
    --20
    ~zod/try=> (sum:si --10 -0)
    --10
    ~zod/try=> (sum:si -10 -7)
    -17
    ~zod/try=> (sum:si -10 --7)
    -3

------------------------------------------------------------------------

<h3 id="++sun"><code>++sun</code></h3>

      ++  sun  |=(a=@u (mul 2 a))                           ::  @u to @s

Produces a signed integer from an unsigned integer.

Note that the result must be manually cast to some @s odor to be
inferred as an unsigned integer in the type system.

`a` is an unsigned integer, `@u`.

    ~zod/try=> `@s`10
    --5
    ~zod/try=> (sun:si 10)
    20
    ~zod/try=> `@s`(sun:si 10)
    --10
    ~zod/try=> `@sd`(sun:si 10)
    --10
    ~zod/try=> `@sd`(sun:si 12.345)
    --12.345

------------------------------------------------------------------------

<h3 id="++syn"><code>++syn</code></h3>

      ++  syn  |=(a=@s =(0 (end 0 1 a)))                    ::  sign test

Produce the sign of a signed integer, `&` being posiitve, `|` negative.

`a` is a signed integer, `@s`.

    ~zod/try=> (syn:si -2)
    %.n
    ~zod/try=> (syn:si --2)
    %.y
    ~zod/try=> (syn:si -0)
    %.y

------------------------------------------------------------------------

<h3 id="++cmp"><code>++cmp</code></h3>

      ++  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

Compare two signed integers.

`b` is a signed integer, `@s`.

`c` is a signed integer, `@s`.

    ~zod/try=> (cmp:si --10 --10)
    --0
    ~zod/try=> (cmp:si --10 -0)
    --1
    ~zod/try=> (cmp:si -10 -7)
    -1
    ~zod/try=> (cmp:si -10 --7)
    -1

<h3 id="++dif"><code>++dif</code></h3>

      ++  dif  |=([b=@ c=@] (sit (sub (add out (sit b)) (sit c))))

Produces the difference between two atoms in the modular basis
representation.

`b` is an [atom]().

`c` is an [atom]().

    ~zod/try=> (~(dif fe 3) 63 64)
    255
    ~zod/try=> (~(dif fe 3) 5 10)
    251
    ~zod/try=> (~(dif fe 3) 0 1)
    255
    ~zod/try=> (~(dif fe 0) 9 10)
    1
    ~zod/try=> (~(dif fe 0) 9 11)
    0
    ~zod/try=> (~(dif fe 0) 9 12)
    1
    ~zod/try=> (~(dif fe 2) 9 12)
    13
    ~zod/try=> (~(dif fe 2) 63 64)
    15

------------------------------------------------------------------------

<h3 id="++inv"><code>++inv</code></h3>

      ++  inv  |=(b=@ (sub (dec out) (sit b)))

Inverts the order of the modular field.

`b` is an [atom]().

    ~zod/try=> (~(inv fe 3) 255)
    0
    ~zod/try=> (~(inv fe 3) 256)
    255
    ~zod/try=> (~(inv fe 3) 0)
    255
    ~zod/try=> (~(inv fe 3) 1)
    254
    ~zod/try=> (~(inv fe 3) 2)
    253
    ~zod/try=> (~(inv fe 3) 55)
    200

------------------------------------------------------------------------

<h3 id="++net"><code>++net</code></h3>

      ++  net  |=  b=@  ^-  @
               =>  .(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))

Reverse bytes within block.

`b` is an [atom]().

    ~zod/try=> (~(net fe 3) 64)
    64
    ~zod/try=> (~(net fe 3) 128)
    128
    ~zod/try=> (~(net fe 3) 255)
    255
    ~zod/try=> (~(net fe 3) 256)
    0
    ~zod/try=> (~(net fe 3) 257)
    1
    ~zod/try=> (~(net fe 3) 500)
    244
    ~zod/try=> (~(net fe 3) 511)
    255
    ~zod/try=> (~(net fe 3) 512)
    0
    ~zod/try=> (~(net fe 3) 513)
    1
    ~zod/try=> (~(net fe 3) 0)
    0
    ~zod/try=> (~(net fe 3) 1)
    1
    ~zod/try=> (~(net fe 0) 1)
    1
    ~zod/try=> (~(net fe 0) 2)
    0
    ~zod/try=> (~(net fe 0) 3)
    1
    ~zod/try=> (~(net fe 6) 1)
    72.057.594.037.927.936
    ~zod/try=> (~(net fe 6) 2)
    144.115.188.075.855.872
    ~zod/try=> (~(net fe 6) 3)
    216.172.782.113.783.808
    ~zod/try=> (~(net fe 6) 4)
    288.230.376.151.711.744
    ~zod/try=> (~(net fe 6) 5)
    360.287.970.189.639.680
    ~zod/try=> (~(net fe 6) 6)
    432.345.564.227.567.616
    ~zod/try=> (~(net fe 6) 7)
    504.403.158.265.495.552
    ~zod/try=> (~(net fe 6) 512)
    562.949.953.421.312
    ~zod/try=> (~(net fe 6) 513)
    72.620.543.991.349.248

------------------------------------------------------------------------

<h3 id="++out"><code>++out</code></h3>

      ++  out  (bex (bex a))

The maximum integer value that the current block can store.

    ~zod/try=> ~(out fe 0)
    2
    ~zod/try=> ~(out fe 1)
    4
    ~zod/try=> ~(out fe 2)
    16
    ~zod/try=> ~(out fe 3)
    256
    ~zod/try=> ~(out fe 4)
    65.536
    ~zod/try=> ~(out fe 10)
    \/179.769.313.486.231.590.772.930.519.078.902.473.361.797.697.894.230.657.\/
      273.430.081.157.732.675.805.500.963.132.708.477.322.407.536.021.120.113.
      879.871.393.357.658.789.768.814.416.622.492.847.430.639.474.124.377.767.
      893.424.865.485.276.302.219.601.246.094.119.453.082.952.085.005.768.838.
      150.682.342.462.881.473.913.110.540.827.237.163.350.510.684.586.298.239.
      947.245.938.479.716.304.835.356.329.624.224.137.216
    \/                                                                        \/

------------------------------------------------------------------------

<h3 id="++rol"><code>++rol</code></h3>

      ++  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)))

Roll `d` to the left by `c` `b`-sized blocks.

`b` is a block size (see [++bloq]()).

`c` is an [atom]().

`d` is an [atom]().

    ~zod/try=> `@ux`(~(rol fe 6) 4 3 0xabac.dedf.1213)
    0x1213.0000.abac.dedf
    ~zod/try=> `@ux`(~(rol fe 6) 4 2 0xabac.dedf.1213)
    0xdedf.1213.0000.abac
    ~zod/try=> `@t`(~(rol fe 5) 3 1 'dfgh')
    'hdfg'
    ~zod/try=> `@t`(~(rol fe 5) 3 2 'dfgh')
    'ghdf'
    ~zod/try=> `@t`(~(rol fe 5) 3 0 'dfgh')
    'dfgh'

------------------------------------------------------------------------

<h3 id="++ror"><code>++ror</code></h3>

      ++  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)))

Roll `d` to the right by `c` `b`-sized blocks.

`b` is a block size (see [++bloq]()).

`c` is an [atom]().

`d` is an [atom]().

    ~zod/try=> `@ux`(~(ror fe 6) 4 1 0xabac.dedf.1213)
    0x1213.0000.abac.dedf
    ~zod/try=> `@ux`(~(ror fe 6) 3 5 0xabac.dedf.1213)
    0xacde.df12.1300.00ab
    ~zod/try=> `@ux`(~(ror fe 6) 3 3 0xabac.dedf.1213)
    0xdf12.1300.00ab.acde
    ~zod/try=> `@t`(~(rol fe 5) 3 0 'hijk')
    'hijk'
    ~zod/try=> `@t`(~(rol fe 5) 3 1 'hijk')
    'khij'
    ~zod/try=> `@t`(~(rol fe 5) 3 2 'hijk')
    'jkhi'

------------------------------------------------------------------------

<h3 id="++sum"><code>++sum</code></h3>

      ++  sum  |=([b=@ c=@] (sit (add b c)))                ::  wrapping add

Sum two numbers in this modular field.

`b` is an [atom]().

`c` is an [atom]().

    ~zod/try=> (~(sum fe 3) 10 250)
    4
    ~zod/try=> (~(sum fe 0) 0 1)
    1
    ~zod/try=> (~(sum fe 0) 0 2)
    0
    ~zod/try=> (~(sum fe 2) 14 2)
    0
    ~zod/try=> (~(sum fe 2) 14 3)
    1
    ~zod/try=> (~(sum fe 4) 10.000 256)
    10.256
    ~zod/try=> (~(sum fe 4) 10.000 100.000)
    44.464

<h3 id="++sit"><code>++sit</code></h3>

      ++  sit  |=(b=@ (end a 1 b))                          ::  enforce modulo

Produce an atom in the current modular block representation.

`b` is an [atom]().

    ~zod/try=> (~(sit fe 3) 255)
    255
    ~zod/try=> (~(sit fe 3) 256)
    0
    ~zod/try=> (~(sit fe 3) 257)
    1
    ~zod/try=> (~(sit fe 2) 257)
    1
    ~zod/try=> (~(sit fe 2) 10.000)
    0
    ~zod/try=> (~(sit fe 2) 100)
    4
    ~zod/try=> (~(sit fe 2) 19)
    3
    ~zod/try=> (~(sit fe 2) 17)
    1
    ~zod/try=> (~(sit fe 0) 17)
    1
    ~zod/try=> (~(sit fe 0) 0)
    0
    ~zod/try=> (~(sit fe 0) 1)
    1

------------------------------------------------------------------------

section 2cG, floating point
---------------------------

XX awaiting interface rewrite

section 2cH, urbit time
-----------------------

Note that entering '-\<-' in the shell produces the current time in @da
format. We use this for many of our examples.

    ~zod/try=> -<-
    ~2014.8.4..19.39.59..9288

<h3 id="++year"><code>++year</code></h3>

    ++  year                                                ::  date to @d
      |=  det=date
      ^-  @d
      =+  ^=  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)

Accept a parsed date of form `[[a=? y=@ud] m=@ud t=tarp]` and produce
its `@d`representation.

`det` is a [`++date`]()

    ~zod/try=> (year [[a=%.y y=2.014] m=8 t=[d=4 h=20 m=4 s=57 f=~[0xd940]]])
    0x8000000d227df4e9d940000000000000

------------------------------------------------------------------------

<h3 id="++yore"><code>++yore</code></h3>

    ++  yore                                                ::  @d to date
      |=  now=@d
      ^-  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]

Produces a `++date` from a `@d`

`now` is a `@d`.

    ~zod/try=> (yore -<-)
    [[a=%.y y=2.014] m=8 t=[d=4 h=20 m=17 s=1 f=~[0x700d]]]
    ~zod/try=> (yore -<-)
    [[a=%.y y=2.014] m=8 t=[d=4 h=20 m=28 s=53 f=~[0x7b82]]]

<h3 id="++yell"><code>++yell</code></h3>

    ++  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]

Produce a parsed daily time format from an atomic date.

`now` is a `@d`.

    ~zod/try=> (yell ~2014.3.20..05.42.53..7456)
    [d=106.751.991.820.094 h=5 m=42 s=53 f=~[0x7456]]
    ~zod/try=> (yell ~2014.6.9..19.09.40..8b66)
    [d=106.751.991.820.175 h=19 m=9 s=40 f=~[0x8b66]]
    ~zod/try=> (yell ~1776.7.4)
    [d=106.751.991.733.273 h=0 m=0 s=0 f=~]

------------------------------------------------------------------------

<h3 id="++yule"><code>++yule</code></h3>

    ++  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)

Accept a [`++tarp`](/doc/hoon/library/1#++tarp), a parsed daily time, and produces a time atom,
`@d`.

`rip` is a [`++tarp`](/doc/hoon/library/1#++tarp).

    ~zod/try=> =murica (yell ~1776.7.4)
    ~zod/try=> murica
    [d=106.751.991.733.273 h=0 m=0 s=0 f=~]
    ~zod/try=> (yule murica)
    0x8000000b62aaf5800000000000000000
    ~zod/try=> `@da`(yule murica)
    ~1776.7.4
    ~zod/try=> `@da`(yule (yell ~2014.3.20..05.42.53..7456))
    ~2014.3.20..05.42.53..7456
    ~zod/try=> `tarp`[31 12 30 0 ~]
    [d=31 h=12 m=30 s=0 f=~]
    ~zod/try=> `@dr`(yule `tarp`[31 12 30 0 ~])
    ~d31.h12.m30

------------------------------------------------------------------------

<h3 id="++yall"><code>++yall</code></h3>

    ++  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))

Produce the date tuple of `[y=@ud m=@ud d=@ud]` of the year, month, and
day from a number of days from the beginning of time.

`day` is an unsigned decimal, `@ud`.

    ~zod/try=> (yall 198)
    [y=0 m=7 d=17]
    ~zod/try=> (yall 90.398)
    [y=247 m=7 d=3]
    ~zod/try=> (yall 0)
    [y=0 m=1 d=1]

------------------------------------------------------------------------

<h3 id="++yawn"><code>++yawn</code></h3>

    ++  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))))

Inverse of `yall`, computes number of days A.D. from y/m/d date as the
tuple `[yer=@ud mot=@ud day=@ud]`.

`yer` is an unsigned decimal, `@ud`.

`mon` is an unsigned decimal, `@ud`.

`day` is an unsigned decimal, `@ud`.

    ~zod/try=> (yawn 2.014 8 4)
    735.814
    ~zod/try=> (yawn 1.776 7 4)
    648.856
    ~zod/try=> (yawn 1.990 10 11)
    727.116

------------------------------------------------------------------------

<h3 id="++yelp"><code>++yelp</code></h3>

    ++  yelp                                                ::  leap year
      |=  yer=@ud  ^-  ?
      &(=(0 (mod yer 4)) |(!=(0 (mod yer 100)) =(0 (mod yer 400))))

Determines whether a year contains an ISO 8601 leap week. Produces a
loobean.

`yer` is an unsigned decimal, `@ud`.

    ~zod/try=> (yelp 2.014)
    %.n
    ~zod/try=> (yelp 2.008)
    %.y
    ~zod/try=> (yelp 0)
    %.y
    ~zod/try=> (yelp 14.011)
    %.n

------------------------------------------------------------------------

<h3 id="++yo"><code>++yo</code></h3>

    ++  yo                                                  ::  time constants
      

Useful constants for interacting with earth time.

<h3 id="++cet"><code>++cet</code></h3>

      |%  ++  cet  36.524                 ::  (add 24 (mul 100 365))

Days in a century. Derived by multiplying the number of days in a year
(365) by the number of years in a century (100), then adding the number
days from leap years in a century (24).

    ~zod/try=> cet:yo
    36.524
    ~zod/try=> (add 365 cet:yo)
    36.889
    ~zod/try=> (sub (add 24 (mul 100 365)) cet:yo)
    0

------------------------------------------------------------------------

<h3 id="++day"><code>++day</code></h3>

          ++  day  86.400                 ::  (mul 24 hor)

Number of seconds in a day.

    ~zod/try=> day:yo
    86.400
    ~zod/try=> (add 60 day:yo)
    86.460

------------------------------------------------------------------------

<h3 id="++era"><code>++era</code></h3>

          ++  era  146.097                ::  (add 1 (mul 4 cet))

XX Revisit

------------------------------------------------------------------------

<h3 id="++hor"><code>++hor</code></h3>

          ++  hor  3.600                  ::  (mul 60 mit)

The number of seconds in an hour. Derived by multiplying the number of
seconds in a minute by the minutes in an hour.

    ~zod/try=> hor:yo
    3.600
    ~zod/try=> (div hor:yo 60)
    60

------------------------------------------------------------------------

<h3 id="++jes"><code>++jes</code></h3>

          ++  jes  106.751.991.084.417    ::  (mul 730.692.561 era)

XX Revisit

    ~zod/try=> jes:yo
    106.751.991.084.417

------------------------------------------------------------------------

<h3 id="++mit"><code>++mit</code></h3>

          ++  mit  60

The number of seconds in a minute.

    ~zod/try=> mit:yo
    60

------------------------------------------------------------------------

<h3 id="++moh"><code>++moh</code></h3>

          ++  moh  `(list ,@ud)`[31 28 31 30 31 30 31 31 30 31 30 31 ~]

The days in each month of the Gregorian common year. A list of unsigned
decimal atoms (Either 28, 30, or 31) denoting the number of days in the
month at the year at that index.

    ~zod/try=> moh:yo
    ~[31 28 31 30 31 30 31 31 30 31 30 31]
    ~zod/try=> (snag 4 moh:yo)
    31

------------------------------------------------------------------------

<h3 id="++moy"><code>++moy</code></h3>

          ++  moy  `(list ,@ud)`[31 29 31 30 31 30 31 31 30 31 30 31 ~]

The days in each month of the Gregorian leap-year. A list of unsigned
decimal atoms (Either 29,30, or 31) denoting the number of days in the
month at the leap-year at that index.

    ~zod/try=> moy:yo
    ~[31 29 31 30 31 30 31 31 30 31 30 31]
    ~zod/try=> (snag 1 moy:yo)
    29

------------------------------------------------------------------------

<h3 id="++qad"><code>++qad</code></h3>

          ++  qad  126.144.001            ::  (add 1 (mul 4 yer))

The number of seconds in four years. Derived by adding one second to the
number of seconds in four years.

    ~zod/try=> qad:yo
    126.144.001

------------------------------------------------------------------------

<h3 id="++yer"><code>++yer</code></h3>

          ++  yer  31.536.000             ::  (mul 365 day)

The number of seconds in a year. Derived by multiplying the number of
seconds in a day by 365.

    ~zod/try=> yer:yo
    31.536.000

------------------------------------------------------------------------

section 2cI, almost macros
--------------------------

<h3 id="++cury"><code>++cury</code></h3>

    ++  cury
      |*  [a=_|=(^ _*) b=*]
      |*  c=_+<+.a
      (a b c)

Curry a gate, binding the head of its sample

`a` is a [gate]().

`b` is a noun.

    ~zod/try=> =mol (cury add 2)
    ~zod/try=> (mol 4)
    6
    ~zod/try=> (mol 7)
    9

------------------------------------------------------------------------

<h3 id="++curr"><code>++curr</code></h3>

    ++  curr
      |*  [a=_|=(^ _*) c=*]
      |*  b=_+<+.a
      (a b c)

Right curry a gate, binding the tail of its sample

`a` is a gate.

`c` is a noun.

    ~zod/try=> =tep (curr scan sym)
    ~zod/try=> `@t`(tep "asd")
    'asd'
    ~zod/try=> `@t`(tep "lek-om")
    'lek-om'

------------------------------------------------------------------------

<h3 id="++cork"><code>++cork</code></h3>

    ++  cork  |*([a=_,* b=gate] (corl b a))                 ::  compose forward

Build `f` such that `(f x) .= (b (a x))`.

`a` is a noun.

`b` is a gate.

    ~zod/try=> (:(cork dec dec dec) 20)
    17
    ~zod/try=> =mal (mo (limo a/15 b/23 ~))
    ~zod/try=> ((cork ~(got by mal) dec) %a)
    14
    ~zod/try=> ((cork ~(got by mal) dec) %b)
    22

------------------------------------------------------------------------

<h3 id="++corl"><code>++corl</code></h3>

    ++  corl                                                ::  compose backwards
      |*  [a=gate b=_,*]
      |=  c=_+<.b
      (a (b c))

Gate compose

XX Revisit

`a` is a gate.

`b` is a noun.

    ~zod/try=> ((corl (lift bex) (slat %ud)) '2')
    [~ 4]

------------------------------------------------------------------------

<h3 id="++hard"><code>++hard</code></h3>

    ++  hard
      |*  han=$+(* *)
      |=  fud=*  ^-  han
      ~|  %hard
      =+  gol=(han fud)
      ?>(=(gol fud) gol)

Demands that a specific type be produced, crashing the program is it is
not.

    ~zod/try=> ((hard (list)) (limo [1 2 3 ~]))
    ~[1 2 3]
    ~zod/try=> ((hard ,@) (add 2 2))
    4
    ~zod/try=> ((hard ,@t) (crip "Tape to cord, bro!"))
    'Tape to cord, bro'
    ~zod/try=> ((hard tape) (crip "...Tape to cord, bro?..."))
    ! hard
    ! exit

------------------------------------------------------------------------

<h3 id="++soft"><code>++soft</code></h3>

    ++  soft
      |*  han=$+(* *)
      |=  fud=*  ^-  (unit han)
      =+  gol=(han fud)
      ?.(=(gol fud) ~ [~ gol])

Politely requests a specific type to be produced, producing null if it
is not.

    ~zod/try=> ((soft ,%4) (add 2 2))
    [~ %4]
    ~zod/try=> ((soft ,@) (add 2 2))
    [~ 4]
    ~zod/try=> ((soft ,%5) (add 2 2))
    ~
    ~zod/try=> ((soft ,@t) (crip "Tape to cord, Woohoo!"))
    [~ 'Tape to cord, Woohoo!']
    ~zod/try=> ((soft ,@t) (trip 'Cmon man... Tape to cord? Please?!'))
    ~

------------------------------------------------------------------------