2c: Bit Arithmetic
+bex
+bexBinary exponent
Computes the result of 2^a, where a is a block size (see $bloq), producing an atom.
Accepts
a is an bloq.
Produces
An atom.
Source
++ bex
~/ %bex
|= a=bloq
^- @
?: =(0 a) 1
(mul 2 $(a (dec a)))Examples
> (bex 4)
16> (bex (add 19 1))
1.048.576> (bex 0)
1+can
+canAssemble
Produces an atom from a list b of length-value pairs p and q, where p is the length in blocks of size a, and q is an atomic value.
Accepts
a is a block size (see $bloq).
b is a list of length-value pairs, p and q:
pis a step.qis a@.
Produces
An atom.
Source
++ can
~/ %can
|= [a=bloq b=(list [p=step q=@])]
^- @
?~ b 0
(add (end [a p.i.b] q.i.b) (lsh [a p.i.b] $(b t.b)))Examples
> `@ub`21 :: @ub is the binary aura
0b1.0101> `@ub`(can 3 ~[[1 21]])
0b1.0101> `@ub`(can 3 ~[[1 1]])
0b1> `@ub`(can 0 ~[[1 255]])
0b1> `@ux`(can 3 [3 0xc1] [1 0xa] ~) :: @ux is the hexadecimal aura
0xa00.00c1> `@ux`(can 3 [3 0xc1] [1 0xa] [1 0x23] ~)
0x23.0a00.00c1> `@ux`(can 4 [3 0xc1] [1 0xa] [1 0x23] ~)
0x23.000a.0000.0000.00c1> `@ux`(can 3 ~[[1 'a'] [2 'bc']])
0x63.6261+cat
+catConcatenate
Concatenates two atoms, b and c, according to block size a, producing an atom.
Accepts
a is a block size (see $bloq).
b is an atom.
c is an atom.
Produces
An atom.
Source
++ cat
~/ %cat
|= [a=bloq b=@ c=@]
(add (lsh [a (met a b)] c) b)Examples
> `@ub`(cat 3 1 0) :: @ub is the binary aura
0b1
> `@ub`(cat 0 1 1)
0b11
> `@ub`(cat 0 2 1)
0b110
> `@ub`(cat 2 1 1)
0b1.0001> `@ub`256
0b1.0000.0000
> `@ub`255
0b1111.1111
> `@ub`(cat 3 256 255)
0b1111.1111.0000.0001.0000.0000
> `@ub`(cat 2 256 255)
0b1111.1111.0001.0000.0000
> (cat 3 256 255)
16.711.936
> (cat 2 256 255)
1.044.736+cut
+cutSlice
Slices c blocks of size a that are positioned b blocks from the end of d. That slice is produced as an atom.
Accepts
a is a block size (see $bloq).
[b c] where:
d is an atom.
Produces
An atom.
Source
++ cut
~/ %cut
|= [a=bloq [b=step c=step] d=@]
(end [a c] (rsh [a b] d))Examples
> (cut 0 [1 1] 2)
1
> (cut 0 [2 1] 4)
1> `@t`(cut 3 [0 3] 'abcdefgh') :: @t is the cord aura
'abc'
> `@t`(cut 3 [1 3] 'abcdefgh')
'bcd'> `@ub`(cut 0 [0 3] 0b1111.0000.1101) :: @ub is the binary aura
0b101
> `@ub`(cut 0 [0 6] 0b1111.0000.1101)
0b1101
> `@ub`(cut 0 [4 6] 0b1111.0000.1101)
0b11.0000
> `@ub`(cut 0 [3 6] 0b1111.0000.1101)
0b10.0001+end
+endTail
Produces an atom by taking the last step blocks of size bloq from b.
Accepts
a is an atom slice specifier (see $bite), which is a block size (see $bloq) with optional block count.
b is an atom.
Produces
An atom.
Source
++ end
~/ %end
|= [a=bite b=@]
=/ [=bloq =step] ?^(a a [a *step])
(mod b (bex (mul (bex bloq) step)))Examples
> (end [2 2] 255)
255
> (end [3 1] 255)
255
> (end 3 255)
255
> (end 3 256)
0> `@ub`12 :: @ub is the binary aura
0b1100
> `@ub`(end [0 3] 12)
0b100
> (end [0 3] 12)
4
> `@ub`(end [1 3] 12)
0b1100
> (end [1 3] 12)
12> `@ux`'abc' :: @ux is the hexademical aura
0x63.6261
> `@ux`(end [3 2] 'abc')
0x6261
> `@t`(end [3 2] 'abc') :: @t is the cord aura
'ab'+fil
+filFill bloqstream
Produces an atom by repeating c for b blocks of size a.
Accepts
a is a block size (see $bloq).
b is a step.
c is an atom.
Produces
An atom.
Source
++ fil
~/ %fil
|= [a=bloq b=step c=@]
=| n=@ud
=. c (end a c)
=/ d c
|- ^- @
?: =(n b)
(rsh a d)
$(d (add c (lsh a d)), n +(n))Examples
> `@t`(fil 3 5 %a) :: @t is the cord (string) aura
'aaaaa'> `@t`(fil 5 10 %ceeb)
'ceebceebceebceebceebceebceebceebceebceeb'> `@t`(fil 4 10 'eced')
'ecececececececececec'> `@tas`(fil 4 10 %bf) :: @tas is the term aura
%bfbfbfbfbfbfbfbfbfbf> `@ub`(fil 2 6 1) :: @ub is the binary aura
0b1.0001.0001.0001.0001.0001+lsh
+lshLeft-shift
Produces an atom by left-shifting b by step blocks of size bloq.
Accepts
a is an atom slice specifier (see $bite), which is a block size (see $bloq) with optional block count.
b is an atom.
Produces
An atom.
Source
++ lsh
~/ %lsh
|= [a=bite b=@]
=/ [=bloq =step] ?^(a a [a *step])
(mul b (bex (mul (bex bloq) step)))Examples
> `@ub`1 :: @ub is the binary aura
0b1
> `@ub`(lsh [0 1] 1)
0b10
> (lsh [0 1] 1)
2
> (lsh 0 1)
2> `@ub`255
0b1111.1111
> `@ub`(lsh [3 1] 255)
0b1111.1111.0000.0000
> (lsh [3 1] 255)
65.280+met
+metMeasure
Computes the number of blocks of size a in b, producing an atom.
Accepts
a is a block size (see $bloq).
b is an atom.
Source
++ met
~/ %met
|= [a=bloq b=@]
^- @
=+ c=0
|-
?: =(0 b) c
$(b (rsh a b), c +(c))Examples
> (met 0 1)
1
> (met 0 2)
2> (met 3 255)
1
> (met 3 256)
2> (met 3 'abcde')
5+rap
+rapAssemble non-zero
Concatenates a list of atoms b using block size a, producing an atom.
Accepts
a is a block size (see +bloq).
b is a list of atoms.
Produces
An atom.
Source
++ rap
~/ %rap
|= [a=bloq b=(list @)]
^- @
?~ b 0
(cat a i.b $(b t.b))Examples
> `@ub`(rap 2 [1 2 3 4 ~]) :: @ub is the binary aura
0b100.0011.0010.0001
> `@ub`(rap 1 [1 2 3 4 ~])
0b1.0011.1001> (rap 0 [0 0 0 ~])
0
> (rap 0 [1 0 1 ~])
3> `@ub`3
0b11
> (rap 0 [0 1 0 0 1 2 ~])
11
> (rap 0 [1 1 2 ~])
11
> `@ub`11
0b1011Discussion
Any element of the value 0 is not included in concatenation.
+rep
+repAssemble single
Produces an atom by assembling a list of atoms b using block size a.
Accepts
a is an atom slice specifier (see $bite), which is a block size (see $bloq) with optional block count.
b is a list of atoms.
Produces
An atom.
Source
++ rep
~/ %rep
|= [a=bite b=(list @)]
=/ [=bloq =step] ?^(a a [a *step])
=| i=@ud
|- ^- @
?~ b 0
%+ add $(i +(i), b t.b)
(lsh [bloq (mul step i)] (end [bloq step] i.b))Examples
> `@ub`(rep 2 [1 2 3 4 ~]) :: @ub is the binary aura
0b100.0011.0010.0001> (rep 0 [0 0 1 ~])
4
> (rep 0 [0 0 0 1 ~])
8> `@ub`(rep 0 [0 0 0 1 ~])
0b1000
> `@ub`8
0b1000> `@ub`(rep 0 [1 0 1 0 ~])
0b101
> `@ub`(rep 0 [1 2 3 4 ~])
0b101> (rep 0 [0 1 0 1 ~])
10
> (rep 0 [1 0 1 0 1 ~])
21
> `@ub`21
0b10.1010> `@ub`(rep 3 [12 166 8 34 ~])
0b10.0010.0000.1000.1010.0110.0000.1100> `*`"abcd"
[97 98 99 100 0]
> `@t`(rep 3 "abcd") :: @t is the text aura
'abcd'+rev
+revReverses block order, accounting for leading zeroes.
Produces an atom from the bits of dat in reverse order according to a block size boz and a size len.
If the total size is less than the length of dat, then only the first bits of dat up to the total size will be taken and reversed. If the total size is longer, trailing zeroes will be added.
Accepts
boz is a block size with optional block count (see $bloq).
len is a @ud of the number of blocks of size boz to be reversed.
dat is an atom.
Produces
An atom.
Source
++ rev
~/ %rev
|= [boz=bloq len=@ud dat=@]
^- @
=. dat (end [boz len] dat)
%+ lsh
[boz (sub len (met boz dat))]
(swp boz dat)Examples
> =a 0b1111.0000.1111.1010.0011
> `@ub`(rev 0 20 a)
0b1100.0101.1111.0000.1111
> `@ub`(rev 0 12 a)
0b1100.0101.1111
> `@ub`(rev 2 5 a)
0b11.1010.1111.0000.1111
> `@ub`(rev 2 4 a)
0b11.1010.1111.0000
> `@ub`(rev 2 6 a)
0b11.1010.1111.0000.1111.0000> (rev 1 10 1.000)
179.200
> (rev 2 5 1.000)
582.400
> (rev 1 5 1.000)
175+rip
+ripDisassemble
Produces a list of atoms from the bits of b using block size a.
Accepts
a is an atom slice specifier (see $bite), which is a block size (see $bloq) with optional block count.
b is an atom.
Produces
A list of atoms.
Source
++ rip
~/ %rip
|= [a=bite b=@]
^- (list @)
?: =(0 b) ~
[(end a b) $(b (rsh a b))]Examples
> `@ub`155 :: @ub is the binary aura
0b1001.1011
> (rip 0 155)
~[1 1 0 1 1 0 0 1]
> (rip 2 155)
~[11 9]> (rip 0 11)
~[1 1 0 1]
> (rip 1 155)
~[3 2 1 2]> `@ub`256
0b1.0000.0000
> (rip 0 256)
~[0 0 0 0 0 0 0 0 1]
> (rip 2 256)
~[0 0 1]
> (rip 3 256)
~[0 1]> `tape`(rip 3 'abcd')
"abcd"+rsh
+rshRight-shift
Right-shifts b by step blocks of size bloq, producing an atom.
Accepts
a is an atom slice specifier (see $bite), which is a block size (see $bloq) with optional block count.
b is an atom.
Produces
An atom.
Source
++ rsh
~/ %rsh
|= [a=bite b=@]
=/ [=bloq =step] ?^(a a [a *step])
(div b (bex (mul (bex bloq) step)))Examples
> `@ub`145 :: @ub is the binary aura
0b1001.0001
> `@ub`(rsh [1 1] 145)
0b10.0100
> (rsh [1 1] 145)
36
> (rsh 1 145)
36
> `@ub`(rsh [2 1] 145)
0b1001
> (rsh [2 1] 145)
9> `@ub`10
0b1010
> `@ub`(rsh [0 1] 10)
0b101
> (rsh [0 1] 10)
5> `@ux`'abc'
0x63.6261
> `@t`(rsh [3 1] 'abc')
'bc'
> `@ux`(rsh [3 1] 'abc')
0x6362+run
+run++turn into atom.
Disassembles atom b into slices specified by a, applies c to each slice, and reassembles the results back into an atom.
Accepts
a is an atom slice specifier (see $bite), which is a block size (see $bloq) with optional block count.
b is an atom.
c is a gate that accepts an atom and produces an atom.
Produces
An atom.
Source
++ run
~/ %run
|= [a=bite b=@ c=$-(@ @)]
(rep a (turn (rip a b) c))Examples
> `@ux`65.535 :: @ux is the hexadecimal aura
0xffff
> `@ux`(run 2 65.535 dec) :: dec is the decrement gate
0xeeee+rut
+rut++turn into list.
Disassembles atom b into slices specified by a, applies c to each slice, and assembles the results back into a.
Accepts
a is an atom slice specifier (see $bite), which is a block size (see $bloq) with optional block count.
b is an atom.
c is a gate that accepts an atom.
Produces
A list.
Source
++ rut
~/ %rut
|* [a=bite b=@ c=$-(@ *)]
(turn (rip a b) c)Examples
> `@ux`65.535 :: @ux is the hexadecimal aura
0xffff
> `(list @ux)`(rut 2 65.535 dec) :: dec is the decrement gate
~[0xe 0xe 0xe 0xe]+sew
+sewStitch one atom into another
Replace c blocks of size a at offset b of atom e with c blocks of size a from atom d.
That is, take (end [a c] d) from d and overwrite the (cut a [b c] e) part of e.
Or in simpler terms, take from the start of d and replace some part of e with it.
Accepts
a is a $bloq (block size).
[b c d] where:
bis a step specifying the number ofbloqs to offset.bis a step specifying the number ofbloqs to replace.dis the donor atom.
e is the recipient atom.
Produces
An atom.
Source
++ sew
~/ %sew
|= [a=bloq [b=step c=step d=@] e=@]
^- @
%+ add
(can a b^e c^d ~)
=/ f [a (add b c)]
(lsh f (rsh f e))Examples
> `@t`(sew 3 [0 0 'XXXX'] 'OOOO')
'OOOO'
> `@t`(sew 3 [0 1 'XXXX'] 'OOOO')
'XOOO'
> `@t`(sew 3 [2 1 'XXXX'] 'OOOO')
'OOXO'
> `@t`(sew 3 [2 2 'XXXX'] 'OOOO')
'OOXX'
> `@t`(sew 3 [0 4 'XXXX'] 'OOOO')
'XXXX'+swp
+swpReverse block order
Switches little-endian to big-endian and vice versa: produces an atom by reversing the block order of b using block size a.
Accepts
a is a block size (see $bloq).
b is an atom.
Produces
An atom
Source
++ swp
~/ %swp
|= [a=bloq b=@]
(rep a (flop (rip a b)))Examples
> `@ub`24 :: @ub is the binary aura
0b1.1000
> (swp 0 24)
3
> `@ub`3
0b11> (swp 0 0)
0
> (swp 0 128)
1+xeb
+xebBinary logarithm
Computes the base-2 logarithm of a, producing an atom.
Accepts
a is an atom.
Produces
An atom.
Source
++ xeb
~/ %xeb
|= a=@
^- @
(met 0 a)Examples
> (xeb 31)
5> (xeb 32)
6> (xeb 49)
6> (xeb 0)
0> (xeb 1)
1> (xeb 2)
2+fe
+feModulo bloq
Core that contains arms for bloq and modular integer operations.
Accepts
a is a bloq.
Source
|_ a=bloq++dif:fe
++dif:feProduces the difference between two atoms in the modular basis representation.
Accepts
a is a bloq (and is the sample of the parent core).
b is an atom.
c is an atom.
Produces
A @s.
Source
++ dif
|=([b=@ c=@] (sit (sub (add out (sit b)) (sit c))))Examples
> (~(dif fe 3) 63 64)
255
> (~(dif fe 3) 5 10)
251
> (~(dif fe 3) 0 1)
255> (~(dif fe 0) 9 10)
1
> (~(dif fe 0) 9 11)
0
> (~(dif fe 0) 9 12)
1> (~(dif fe 2) 9 12)
13
> (~(dif fe 2) 63 64)
15++inv:fe
++inv:feInverse
Inverts the order of the modular field.
Accepts
a is a bloq (and is the sample of the parent core).
b is a bloq. (see $bloq)
Produces
An atom.
Source
++ inv |=(b=@ (sub (dec out) (sit b)))Examples
> (~(inv fe 3) 255)
0
> (~(inv fe 3) 256)
255> (~(inv fe 3) 0)
255
> (~(inv fe 3) 1)
254
> (~(inv fe 3) 2)
253> (~(inv fe 3) 55)
200++net:fe
++net:feFlip endianness
Reverses bytes within a block.
Accepts
a is a bloq (and the sample of the parent core).
b is a bloq. (see $bloq)
Produces
An atom.
Source
++ net |= b=@ ^- @
=> .(b (sit b))
?: (lte a 3)
b
=+ c=(dec a)
%+ con
(lsh c $(a c, b (cut c [0 1] b)))
$(a c, b (cut c [1 1] b))Examples
> (~(net fe 3) 64)
64
> (~(net fe 3) 128)
128
> (~(net fe 3) 255)
255
> (~(net fe 3) 256)
0
> (~(net fe 3) 257)
1> (~(net fe 3) 500)
244
> (~(net fe 3) 511)
255
> (~(net fe 3) 512)
0
> (~(net fe 3) 513)
1> (~(net fe 3) 0)
0
> (~(net fe 3) 1)
1
> (~(net fe 0) 1)
1
> (~(net fe 0) 2)
0
> (~(net fe 0) 3)
1> (~(net fe 6) 1)
72.057.594.037.927.936
> (~(net fe 6) 2)
144.115.188.075.855.872
> (~(net fe 6) 3)
216.172.782.113.783.808
> (~(net fe 6) 4)
288.230.376.151.711.744
> (~(net fe 6) 5)
360.287.970.189.639.680++out:fe
++out:feMax integer value
Produces the maximum integer value that the current block can store; 2^a^a.
Accepts
a is a bloq (and is the sample of the parent core).
Produces
An atom.
Source
++ out (bex (bex a))Examples
> ~(out fe 0)
2
> ~(out fe 1)
4
> ~(out fe 2)
16
> ~(out fe 3)
256
> ~(out fe 4)
65.536> ~(out fe 10)
\/179.769.313.486.231.590.772.930.519.078.902.473.361.797.697.894.230.657.273\/
.430.081.157.732.675.805.500.963.132.708.477.322.407.536.021.120.113.879.87
1.393.357.658.789.768.814.416.622.492.847.430.639.474.124.377.767.893.424.8
65.485.276.302.219.601.246.094.119.453.082.952.085.005.768.838.150.682.342.
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
\/ \/++rol:fe
++rol:feRoll left
Rolls d to the left by c b-sized blocks.
Accepts
a is a bloq (and is the sample of the parent core).
b is a bloq.
c is an atom.
d is an atom.
Produces
An atom.
Source
++ rol |= [b=bloq c=@ d=@] ^- @
=+ e=(sit d)
=+ f=(bex (sub a b))
=+ g=(mod c f)
(sit (con (lsh [b g] e) (rsh [b (sub f g)] e)))Examples
> `@ux`(~(rol fe 6) 4 3 0xabac.dedf.1213)
0x1213.0000.abac.dedf
> `@ux`(~(rol fe 6) 4 2 0xabac.dedf.1213)
0xdedf.1213.0000.abac> `@t`(~(rol fe 5) 3 1 'dfgh')
'hdfg'
> `@t`(~(rol fe 5) 3 2 'dfgh')
'ghdf'
> `@t`(~(rol fe 5) 3 0 'dfgh')
'dfgh'++ror:fe
++ror:feRoll right
Rolls d to the right by c b-sized blocks.
Accepts
a is a bloq (and is the sample of the parent core).
b is a bloq.
c is an atom.
d is an atom.
Produces
An atom.
Source
++ ror |= [b=bloq c=@ d=@] ^- @
=+ e=(sit d)
=+ f=(bex (sub a b))
=+ g=(mod c f)
(sit (con (rsh [b g] e) (lsh [b (sub f g)] e)))Examples
> `@ux`(~(ror fe 6) 4 1 0xabac.dedf.1213)
0x1213.0000.abac.dedf
> `@ux`(~(ror fe 6) 3 5 0xabac.dedf.1213)
0xacde.df12.1300.00ab
> `@ux`(~(ror fe 6) 3 3 0xabac.dedf.1213)
0xdf12.1300.00ab.acde> `@t`(~(rol fe 5) 3 0 'hijk')
'hijk'
> `@t`(~(rol fe 5) 3 1 'hijk')
'khij'
> `@t`(~(rol fe 5) 3 2 'hijk')
'jkhi'++sum:fe
++sum:feSum
Sums two numbers in this modular field.
Accepts
a is a bloq (and is the sample of the parent core).
b is an atom.
c is an atom.
Produces
An atom.
Source
++ sum |=([b=@ c=@] (sit (add b c)))Examples
> (~(sum fe 3) 10 250)
4> (~(sum fe 0) 0 1)
1
> (~(sum fe 0) 0 2)
0> (~(sum fe 2) 14 2)
0
> (~(sum fe 2) 14 3)
1> (~(sum fe 4) 10.000 256)
10.256
> (~(sum fe 4) 10.000 100.000)
44.464++sit:fe
++sit:feEnforce modulo
Produces an atom in the current modular block representation.
Accepts
a is a bloq (and is the sample of the parent core).
b is an atom.
Produces
An atom.
Source
++ sit |=(b=@ (end a b))Examples
> (~(sit fe 3) 255)
255
> (~(sit fe 3) 256)
0
> (~(sit fe 3) 257)
1> (~(sit fe 2) 257)
1
> (~(sit fe 2) 10.000)
0
> (~(sit fe 2) 100)
4
> (~(sit fe 2) 19)
3
> (~(sit fe 2) 17)
1> (~(sit fe 0) 17)
1
> (~(sit fe 0) 0)
0
> (~(sit fe 0) 1)
1Last updated