Arithmetic Functions¶

`+` Plus¶

Monadic: Conjugate¶

For real numbers, returns the argument unchanged (identity).

Dyadic: Add¶

      3+4
7
      1 2 3+10 20 30
11 22 33
      100+⍳5
101 102 103 104 105

`-` Minus¶

Monadic: Negate¶

Dyadic: Subtract¶

      10-3
7
      10 20 30-1 2 3
9 18 27

`×` Times¶

Monadic: Signum¶

Returns ¯1, 0, or 1 depending on the sign of the argument.

Dyadic: Multiply¶

`÷` Divide¶

Monadic: Reciprocal¶

Returns 1÷⍵. Raises DOMAIN ERROR for zero.

      ÷4
0.25
      ÷2 4 5
0.5 0.25 0.2

Dyadic: Divide¶

Raises DOMAIN ERROR for division by zero.

      10÷4
2.5
      12÷1 2 3 4 6
12 6 4 3 2

`⌈` Upstile¶

Monadic: Ceiling¶

Returns the smallest integer greater than or equal to the argument.

Dyadic: Maximum¶

      3⌈5
5
      1 5 3⌈4 2 6
4 5 6

`⌊` Downstile¶

Monadic: Floor¶

Returns the largest integer less than or equal to the argument.

      ⌊3.7
3
      ⌊¯2.3
¯3

Dyadic: Minimum¶

      3⌊5
3
      1 5 3⌊4 2 6
1 2 3

`*` Star¶

Monadic: Exponential¶

Returns e raised to the power of the argument.

      *1
2.718281828
      *0
1

Dyadic: Power¶

      2*8
256
      2*0 1 2 3 4
1 2 4 8 16

`⍟` Log¶

Monadic: Natural logarithm¶

Dyadic: Logarithm¶

Left argument is the base.

`|` Stile¶

Monadic: Magnitude (absolute value)¶

Dyadic: Residue¶

The remainder when dividing the right argument by the left. Note: APL residue has the left argument as the divisor (opposite to most languages).

      3|7
1
      5|12
2
      2|⍳6
1 0 1 0 1 0

`○` Circle¶

Monadic: Pi times¶

Multiplies the argument by π.

      ○1
3.141592654
      ○0.5
1.570796327

Dyadic: Circular functions¶

The left argument selects a trigonometric or hyperbolic function:

Left	Function	Left	Function
`0`	`√(1-⍵²)`
`1`	sin	`¯1`	arcsin
`2`	cos	`¯2`	arccos
`3`	tan	`¯3`	arctan
`4`	`√(1+⍵²)`	`¯4`	`√(⍵²-1)`
`5`	sinh	`¯5`	arcsinh
`6`	cosh	`¯6`	arccosh
`7`	tanh	`¯7`	arctanh

      1○○0.5           ⍝ sin(π/2) = 1
1
      2○0               ⍝ cos(0) = 1
1
      3○0               ⍝ tan(0) = 0
0