Finding the angle between two bearings is often confusing.[1]



Task

Find the angle which is the result of the subtraction b2 - b1, where b1 and b2 are the bearings.


Input bearings are expressed in the range   -180   to   +180   degrees.

The  result  is also expressed in the range   -180   to   +180   degrees.



Compute the angle for the following pairs:

 20 degrees (b1) and 45 degrees (b2)
 -45 and 45
 -85 and 90
 -95 and 90
 -45 and 125
 -45 and 145
 29.4803 and -88.6381
 -78.3251 and -159.036


Optional extra
 
Allow the input bearings to be any (finite) value.



Test cases

 -70099.74233810938 and 29840.67437876723
 -165313.6666297357 and 33693.9894517456
 1174.8380510598456 and -154146.66490124757
 60175.77306795546 and 42213.07192354373


#!r6rs
 
(import (rnrs base (6))
        (rnrs io simple (6)))
 
(define (bearing-difference bearing-2 bearing-1)
  (- (mod (+ (mod (- bearing-2 bearing-1)
                  360)
             540)
          360)
     180))
 
(define (bearing-difference-test)
  (define test-cases
    '((20 45)
      (-45 45)
      (-85 90)
      (-95 90)
      (-45 125)
      (-45 145)
      (29.4803 -88.6381)
      (-78.3251 -159.036)
      (-70099.74233810938 29840.67437876723)
      (-165313.6666297357 33693.9894517456)
      (1174.8380510598456 -154146.66490124757)
      (60175.77306795546 42213.07192354373)))
  (for-each
   (lambda (argument-list)
     (display (apply bearing-difference argument-list))
     (newline))
   test-cases))