Given two ranges:

   



[

a

1


,

a

2


]


{\displaystyle [a_{1},a_{2}]}

   and 
   



[

b

1


,

b

2


]


{\displaystyle [b_{1},b_{2}]}

; 
   then a value   



s


{\displaystyle s}

   in range   



[

a

1


,

a

2


]


{\displaystyle [a_{1},a_{2}]}


   is linearly mapped to a value   



t


{\displaystyle t}

   in range   



[

b

1


,

b

2


]


{\displaystyle [b_{1},b_{2}]}


   where:



   



t
=

b

1


+



(
s
−

a

1


)
(

b

2


−

b

1


)


(

a

2


−

a

1


)





{\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}}




Task

Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range.

Use this function to map values from the range    [0, 10]    to the range    [-1, 0]. 



Extra credit

Show additional idiomatic ways of performing the mapping, using tools available to the language.




import Foundation
 
func mapRanges(_ r1: ClosedRange<Double>, _ r2: ClosedRange<Double>, to: Double) -> Double {
  let num = (to - r1.lowerBound) * (r2.upperBound - r2.lowerBound)
  let denom = r1.upperBound - r1.lowerBound
 
  return r2.lowerBound + num / denom
}
 
for i in 0...10 {
  print(String(format: "%2d maps to %5.2f", i, mapRanges(0...10, -1...0, to: Double(i))))
}