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.




let mapRange r1 r2 s =>
    +
        (at r2 0)
        (/
            (*
                (-
                    s
                    (at r1 0)
                )
                (-
                    (at r2 1)
                    (at r2 0)
                )
            )
            (-
                (at r1 1)
                (at r1 0)
            )
        )
    ;
 
let s => import 'stream';
let str => import 'strings';
 
s.range 10
-> s.map (@ enum v => [v; mapRange [0; 10] [-1; 0] v])
-> s.map (@ print v => str.format '{} -> {}' (at v 0) (at v 1) -- io.writeln io.stdout)
-> s.drain
;