# Floating-point Approximation in Kotlin

## The challenge

Given

- a semi-inclusive interval
`I = [l, u)`

(l is in interval I but u is not)`l`

and`u`

being floating numbers`(0 <= l < u)`

, - an integer
`n (n > 0)`

- a function
`f: x (float number) -> f(x) (float number)`

we want to return as a list the `n`

values:

`f(l), f(l + d), ..., f(u -d)`

where `d = (u - l) / n`

or as a string (Bash, Nim):

`"f(l), f(l + d), ..., f(u -d)"`

where `d = (u - l) / n`

Call this function `interp`

:

`interp(f, l, u, n) -> [f(l), f(l + d), ..., f(u -d)]`

The `n`

resulting values `f(l), f(l + d), ..., f(u -d)`

will be `**floored**`

to two decimals (except Shell and Nim: see below).

For that you can use: `floor(y * 100.0) / 100.0`

.

### Examples

```
interp(x -> x, 0.0, 0.9, 3) -> [0.; 0.3; 0.6]
interp(x -> x, 0.0, 0.9, 4) -> [0.; 0.22; 0.45; 0.67]
interp(x -> x, 0.0, 1.0, 4) -> [0.; 0.25; 0.5; 0.75]
interp(x -> sin x, 0.0, 0.9, 3) -> [0.; 0.29; 0.56]
```

## The solution in Kotlin

Option 1:

```
package approxfloat
fun interp(f: (Double) -> Double, l:Double, u:Double, n:Int):List<Double> {
val d = (u - l) / n
return (0 until n).map { Math.floor(f(it * d) * 100.0) / 100.0 }.toList()
}
```

Option 2:

```
package approxfloat
fun interp(f: (Double) -> Double, l: Double, u: Double, n: Int): List<Double> =
MutableList<Double>(n){ l + it * (u - l) / n }
.map{ f(it) }
.map{ Math.floor(it * 100) / 100 }
```

Option 3:

```
package approxfloat
import kotlin.math.floor
fun interp(f: (Double) -> Double, l:Double, u:Double, n:Int):List<Double> {
val d = (u - l) / n
val sequence = generateSequence(l) { it + d }
return sequence
.map { floor(f(it) * 100) / 100}
.take(n).toList()
}
```

## Test cases to validate our solution

```
package approxfloat
import kotlin.test.assertEquals
import org.junit.Test
import java.util.Random
import org.junit.Assert.*
import java.util.ArrayList
class ApproxFloatTest {
fun testing(actual:String, expected:String) {
assertEquals(expected, actual)
}
@Test
fun test1() {
println("{ x-> x }")
testing(interp({ x -> x }, 0.0, 9.0, 4).toString(),
"[0.0, 2.25, 4.5, 6.75]")
}
@Test
fun test2() {
println("{ x-> sin(x) }")
testing(interp({ x -> Math.sin(x.toDouble()) }, 0.0, 18.0, 12).toString(),
"[0.0, 0.99, 0.14, -0.98, -0.28, 0.93, 0.41, -0.88, -0.54, 0.8, 0.65, -0.72]")
}
@Test
fun test3() {
println("{ x-> cos(x) }")
testing(interp({ x -> Math.cos(x.toDouble()) }, 0.0, 21.0, 7).toString(),
"[1.0, -0.99, 0.96, -0.92, 0.84, -0.76, 0.66]")
}
}
```