> For the complete documentation index, see [llms.txt](https://docs.urbit.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.urbit.org/hoon/stdlib/1a.md).
# 1a: Basic Arithmetic
Reference for basic arithmetic functions in Hoon including addition, subtraction, multiplication, division, and comparison operations for unsigned integers.
## `+add`
Add.
Produces the sum of `.a` and `.b`.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
An `$atom`.
#### Source
```hoon
++ add
~/ %add
|= [a=@ b=@]
^- @
?: =(0 a) b
$(a (dec a), b +(b))
```
#### Examples
```
> (add 2 2)
4
```
```
> (add 1 1.000.000)
1.000.001
```
```
> (add 1.333 (mul 2 2))
1.337
```
```
> (add 'a' 4)
101
```
```
> (add 'a' 'b')
195
```
```
> (add 0xc 0xf)
27
```
```
> `@ux`(add 0xc 0xf)
0x1b
```
***
## `+dec`
Decrement.
Decrements `.a` by `1`.
#### Accepts
`.a` is an `$atom`.
#### Produces
An `$atom`.
#### Source
```hoon
++ dec
~/ %dec
|= a=@
~_ leaf+"decrement-underflow"
?< =(0 a)
=+ b=0
|- ^- @
?: =(a +(b)) b
$(b +(b))
```
#### Examples
```
> (dec 7)
6
```
```
> (dec 0)
! decrement-underflow
! exit
```
```
> (dec 'b')
97
> `@t`(dec 'b')
'a'
```
```
> (dec 0xc)
11
> `@ux`(dec 0xc)
0xb
```
***
## `+div`
Divide.
Computes `.a` divided by `.b` without remainder.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
An `$atom`.
#### Source
```hoon
++ div
~/ %div
|: [a=`@`1 b=`@`1]
^- @
-:(dvr a b)
```
#### Examples
```
> (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`
Divide with remainder.
Computes `.a` divided by `.b`, producing the quotient and the remainder.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
A cell of `$atom`s.
#### Source
```hoon
++ dvr
~/ %dvr
|: [a=`@`1 b=`@`1]
^- [p=@ q=@]
~_ leaf+"divide-by-zero"
?< =(0 b)
=+ c=0
|-
?: (lth a b) [c a]
$(a (sub a b), c +(c))
```
#### Examples
```
> (dvr 17 8)
[p=2 q=1]
```
```
> (dvr 17 6)
[p=2 q=5]
```
```
> (dvr 18 6)
[p=3 q=0]
```
```
> (dvr 4 2)
[p=2 q=0]
```
```
> (dvr 'ab 'a')
[p=259 q=62]
> `@`'a'
97
> `@`'ab'
25.185
```
***
## `+gte`
Greater-than/equal.
Tests whether `.a` is greater than or equal to `.b`.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
A `$flag`.
#### Source
```hoon
++ gte
~/ %gte
|= [a=@ b=@]
^- ?
!(lth a b)
```
#### Examples
```
> (gte 100 10)
%.y
```
```
> (gte 4 4)
%.y
```
```
> (gte 3 4)
%.n
```
***
## `+gth`
Greater-than.
Tests whether `.a` is greater than `.b`.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
A `$flag`.
#### Source
```hoon
++ gth
~/ %gth
|= [a=@ b=@]
^- ?
!(lte a b)
```
#### Examples
```
> (gth 'd' 'c')
%.y
```
```
> (gth ~h1 ~m61)
%.n
```
```
> (gth 'steak' 'brisket')
%.n
```
***
## `+lte`
Less-than/equal.
Tests whether `.a` is less than or equal to `.b`.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
A `$flag`.
#### Source
```hoon
++ lte
~/ %lte
|= [a=@ b=@]
|(=(a b) (lth a b))
```
#### Examples
```
> (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`
Less-than.
Tests whether `.a` is less than `.b`.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
A `$flag`.
#### Source
```hoon
++ lth
~/ %lth
|= [a=@ b=@]
^- ?
?& !=(a b)
|-
?| =(0 a)
?& !=(0 b)
$(a (dec a), b (dec b))
== == ==
```
#### Examples
```
> (lth 4 5)
%.y
```
```
> (lth 5 4)
%.n
```
```
> (lth 5 5)
%.n
```
```
> (lth 5 0)
%.n
```
```
> (lth 'a' 'b')
%.y
> `@`'a'
97
> `@`'b'
98
```
```
> (lth 'abraham' 'bob')
%.n
```
***
## `+max`
Maximum.
Computes the greater of `.a` and `.b`.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
An `$atom`.
#### Source
```hoon
++ max
~/ %max
|= [a=@ b=@]
^- @
?: (gth a b) a
b
```
#### Examples
```
> (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`
Minimum.
Computes the lesser of `.a` and `.b`.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
An `$atom`.
#### Source
```hoon
++ min
~/ %min
|= [a=@ b=@]
^- @
?: (lth a b) a
b
```
#### Examples
```
> (min 10 100)
10
```
```
> (min 10.443 9)
9
```
```
> (min 1 1)
1
```
```
> (min 'abraham' 'bob')
6.451.042
```
```
> `@t`(min 'abraham' 'bob')
'bob'
```
```
> `@t`(min 'abraham' 'benjamin')
'abraham'
```
```
> `@dr`(min ~m6 ~h1)
~m6
```
***
## `+mod`
Modulus.
Computes the remainder of dividing `.a` by `.b`.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
An `$atom`.
#### Source
```hoon
++ mod
~/ %mod
|: [a=`@`1 b=`@`1]
^- @
+:(dvr a b)
```
#### Examples
```
> (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`
Multiply.
Multiplies `.a` by `.b`.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
An `$atom`.
#### Source
```hoon
++ mul
~/ %mul
|: [a=`@`1 b=`@`1]
^- @
=+ c=0
|-
?: =(0 a) c
$(a (dec a), c (add b c))
```
#### Examples
```
> (mul 3 4)
12
```
```
> (mul 0 1)
0
```
```
> `@`'a'
97
> `@`'b'
98
> (mul 'a' 'b')
9.506
```
```
>`@ux`(mul 0x1f 0xe)
0x1b2
```
***
## `+sub`
Subtract.
Subtracts `.b` from `.a`.
#### Accepts
`.a` is an `$atom`.
`.b` is an `$atom`.
#### Produces
An `$atom`.
#### Source
```hoon
++ sub
~/ %sub
|= [a=@ b=@]
~_ leaf+"subtract-underflow"
^- @
?: =(0 b) a
$(a (dec a), b (dec b))
```
#### Examples
```
> (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
```
---
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