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.




(defun mapping (a1 a2 b1 b2 s)
   (+ b1 (/ (* (- s a1)
               (- b2 b1))
            (- a2 a1))))
 
(defun map-each (a1 a2 b1 b2 ss)
   (if (endp ss)
       nil
       (cons (mapping a1 a2 b1 b2 (first ss))
             (map-each a1 a2 b1 b2 (rest ss)))))
 
(map-each 0 10 -1 0 '(0 1 2 3 4 5 6 7 8 9 10))
 
;; (-1 -9/10 -4/5 -7/10 -3/5 -1/2 -2/5 -3/10 -1/5 -1/10 0)
 
 