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.




 
map: procedure options (main); /* 24/11/2011 */
   declare (a1, a2, b1, b2) float;
   declare d fixed decimal (3,1);
 
   do d = 0 to 10 by 0.9, 10;
      put skip edit ( d, ' maps to ', map(0, 10, -1, 0, d) ) (f(5,1), a, f(10,6));
   end;
 
map: procedure (a1, a2, b1, b2, s) returns (float);
   declare (a1, a2, b1, b2, s) float;
   return (b1 + (s - a1)*(b2 - b1) / (a2 - a1) );
end map;
end map;
 