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## 10 Named Functions

This chapter covers the non-symbol named functions. This includes some math (eg. sqrt but not +), wrapper (eg. count for #) and range (eg. within) functions.

```math:    sqrt exp log sin cos div mod bar
wrapper: count first last min max sum avg
range:   in bin within
```

### 10.1 Math Functions ⇒ sqrt exp log sin cos div mod bar

#### 10.1.1 sqrt ⇒ sqrt x

``` sqrt 2
1.414214
```

#### 10.1.2 exp ⇒ exp x

``` exp 1
2.718282
```

#### 10.1.3 log ⇒ log x

Log computes the natural log.

``` log 10
2.302585
```

#### 10.1.4 sin ⇒ sin x

sin computes the sine of x where x is in radians.

``` sin 0
0f
sin 3.1416%2
1.
```

#### 10.1.5 cos ⇒ cos x

cos computes the cosine of x where x is in radians.

``` cos 0
1f
cos 3.1416%4
0.7071055
```

#### 10.1.6 div ⇒ x div y

y divided by x using integer division. x and y must be integers.

``` 2 div 7
3
5 div 22
4
```

#### 10.1.7 mod ⇒ x mod y

The remainder after y divided by x using integer division. x and y must be integers.

``` 12 mod 27
3
5 mod 22
2
```

#### 10.1.8 bar ⇒ x bar y

For each value in y determine the number of integer multiples of x that is less than or equal to each x.

``` 10 bar 9 10 11 19 20 21
0 10 10 10 20 20
```

### 10.2 Wrapper Functions ⇒ count first last min max sum avg

These functions exist as verbs but also can be called with the names above.

``` n:3.2 1.7 5.6
sum n
10.5
+/n
10.5
```

### 10.3 Range Functions ⇒ in bin within

#### 10.3.1 in ⇒ x in y

Determine if x is in list y. Similar to has but arguments reversed.

``` `b in `a`b`d`e
1b
`c in `a`b`d`e
0b
```

#### 10.3.2 bin ⇒ x bin y

Given a sorted (increasing) list x, find the greatest index, i, where y>x[i].

``` n:exp 0.01*!5;n
1 1.01005 1.020201 1.030455 1.040811
1.025 bin n
2
```

#### 10.3.3 within ⇒ x within y

Test if x is equal to or greater than y and less than y.

``` 3 within (0;12)
1b
12 within (0;12)
0b
23 within (0;12)
0b
```

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