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.




using System;
using System.Console;
 
module Maprange
{
    Maprange(a : double * double, b : double * double, s : double) : double
    {
        def (a1, a2) = a; def (b1, b2) = b;
 
        b1 + (((s - a1) * (b2 - b1))/(a2 - a1))
    }
 
    Main() : void
    {
        foreach (i in [0 .. 10]) 
            WriteLine("{0, 2:f0} maps to {1:f1}", i, Maprange((0.0, 10.0), (-1.0, 0.0), i));
    }
}