1a: Basic Arithmetic

++  add
  ~/  %add
  |=  [a=@ b=@]
  ^-  @
  ?:  =(0 a)  b
  $(a (dec a), b +(b))

> (add 2 2)
4

> (add 1 1.000.000)
1.000.001

> (add 1.333 (mul 2 2))
1.337

> (add 'a' 4)
101

> (add 'a' 'b')
195

> (add 0xc 0xf)
27

> `@ux`(add 0xc 0xf)
0x1b

++  dec
  ~/  %dec
  |=  a=@
  ~_  leaf+"decrement-underflow"
  ?<  =(0 a)
  =+  b=0
  |-  ^-  @
  ?:  =(a +(b))  b
  $(b +(b))

> (dec 7)
6

> (dec 0)
! decrement-underflow
! exit

> (dec 'b')
97
> `@t`(dec 'b')
'a'

> (dec 0xc)
11
> `@ux`(dec 0xc)
0xb

++  div
  ~/  %div
  |:  [a=`@`1 b=`@`1]
  ^-  @
  ~_  leaf+"divide-by-zero"
  ?<  =(0 b)
  =+  c=0
  |-
  ?:  (lth a b)  c
  $(a (sub a b), c +(c))

> (div 4 2)
2

> (div 17 8)
2

> (div 20 30)
0

> (div 'ab' 'a')
259
> `@`'ab'
25.185
> `@`a
97

> (div 0x9f 0x29)
6

++  dvr
  ~/  %dvr
  |=  [a=@ b=@]
  ^-  [p=@ q=@]
  [(div a b) (mod a b)]

> (dvr 17 8)
[p=2 q=1]

> (dvr 17 6)
[p=2 q=5]

> (dvr 18 6)
[p=3 q=0]

> (dvr 4 2)
[p=2 q=0]

> (dvr 'ab 'a')
[p=259 q=62]
> `@`'a'
97
> `@`'ab'
25.185

++  gte
  ~/  %gte
  |=  [a=@ b=@]
  ^-  ?
  !(lth a b)

> (gte 100 10)
%.y

> (gte 4 4)
%.y

> (gte 3 4)
%.n

++  gth
  ~/  %gth
  |=  [a=@ b=@]
  ^-  ?
  !(lte a b)

> (gth 'd' 'c')
%.y

> (gth ~h1 ~m61)
%.n

> (gth 'steak' 'brisket')
%.n

++  lte
  ~/  %lte
  |=  [a=@ b=@]
  |(=(a b) (lth a b))

> (lte 4 5)
%.y

> (lte 5 4)
%.n

> (lte 5 5)
%.y

> (lte 0 0)
%.y

> (lte 'a' 'b')
%.y
> `@`'a'
97
> `@`'b'
98

> (lte 'abraham' 'bob')
%.n

> (lte ~m61 ~h1)
%.n

++  lth
  ~/  %lth
  |=  [a=@ b=@]
  ^-  ?
  ?&  !=(a b)
      |-
      ?|  =(0 a)
          ?&  !=(0 b)
              $(a (dec a), b (dec b))
  ==  ==  ==

> (lth 4 5)
%.y

> (lth 5 4)
%.n

> (lth 5 5)
%.n

> (lth 5 0)
%.n

> (lth 'a' 'b')
%.y
> `@`'a'
97
> `@`'b'
98

> (lth 'abraham' 'bob')
%.n

++  max
  ~/  %max
  |=  [a=@ b=@]
  ^-  @
  ?:  (gth a b)  a
  b

> (max 10 100)
100

> (max 10.443 9)
10.443

> (max 1 1)
1

> (max 'abraham' 'bob')
30.787.873.400.840.801

> `@t`(max 'abraham' 'bob')
'abraham'

> `@t`(max 'abraham' 'benjamin')
'benjamin'

> `@dr`(max ~m6 ~h1)
~h1

>`@ux`(max 0xe1 0x1e)
0xe1

++  min
  ~/  %min
  |=  [a=@ b=@]
  ^-  @
  ?:  (lth a b)  a
  b

> (min 10 100)
10

> (min 10.443 9)
9

> (min 1 1)
1

> (min 'abraham' 'bob')
6.451.042

> `@t`(min 'abraham' 'bob')
'bob'

> `@t`(min 'abraham' 'benjamin')
'abraham'

> `@dr`(min ~m6 ~h1)
~m6

++  mod
  ~/  %mod
  |:  [a=`@`1 b=`@`1]
  ^-  @
  ?<  =(0 b)
  (sub a (mul b (div a b)))

> (mod 5 2)
1

> (mod 5 5)
0

> (mod 2 5)
2

> (mod 40 20)
0

> `@`'c'
99
>`@`'a'
97
> (mod 'c' 'a')
2

++  mul
  ~/  %mul
  |:  [a=`@`1 b=`@`1]
  ^-  @
  =+  c=0
  |-
  ?:  =(0 a)  c
  $(a (dec a), c (add b c))

> (mul 3 4)
12

> (mul 0 1)
0

> `@`'a'
97
> `@`'b'
98
> (mul 'a' 'b')
9.506

>`@ux`(mul 0x1f 0xe)
0x1b2

++  sub
  ~/  %sub
  |=  [a=@ b=@]
  ~_  leaf+"subtract-underflow"
  ^-  @
  ?:  =(0 b)  a
  $(a (dec a), b (dec b))

> (sub 10 5)
5

> (sub 243 44)
199

> (sub 5 0)
5

> (sub 0 5)
! subtract-underflow
! exit

> (sub 'c' 'a')
2
> `@`'c'
99
> `@`'a'
97

> (sub 0x1f 0xe)
17
> `@ux`(sub 0x1f 0xe)
0x11