Angle difference between two bearings: Difference between revisions

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37.29885559</pre>
37.29885559</pre>

=={{header|Factor}}==
{{trans|F#}}
{{works with|Factor|development release 2019-03-17+}}
<lang factor>USING: combinators generalizations kernel math prettyprint ;
IN: rosetta-code.bearings

: delta-bearing ( x y -- z )
swap - 360 mod {
{ [ dup 180 > ] [ 360 - ] }
{ [ dup -180 < ] [ 360 + ] }
[ ]
} cond ;

: bearings-demo ( -- )
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
[ delta-bearing . ] 2 12 mnapply ;

MAIN: bearings-demo</lang>
{{out}}
<pre>
25
90
175
-175
170
-170
-118.1184
-80.7109
-139.5832831233856
-72.34391851868713
-161.5029523074045
37.29885558826936
</pre>


=={{header|Fortran}}==
=={{header|Fortran}}==

Revision as of 17:53, 20 March 2019

Task
Angle difference between two bearings
You are encouraged to solve this task according to the task description, using any language you may know.

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



360 Assembly

Translation of: Rexx

<lang 360asm>* Angle difference between two bearings - 06/06/2018 ANGLEDBB CSECT 

        USING  ANGLEDBB,R13       base register
        B      72(R15)            skip savearea
        DC     17F'0'             savearea
        SAVE   (14,12)            save previous context
        ST     R13,4(R15)         link backward
        ST     R15,8(R13)         link forward
        LR     R13,R15            set addressability
        LA     R10,T-4            @t
        LA     R6,1               i=1
      DO WHILE=(C,R6,LE,N)        do i=1 to n
        LA     R10,4(R10)           next @t
        L      R7,0(R10)            a=t(i,1)
        LA     R10,4(R10)           next @t
        L      R8,0(R10)            b=t(i,2)
        LR     R4,R8                b
        SR     R4,R7                b-a
        SRDA   R4,32                ~
        D      R4,=F'3600000'       /360
        A      R4,=F'5400000'       +540
        SRDA   R4,32                ~
        D      R4,=F'3600000'       /360
        S      R4,=F'1800000'       x=((((b-a)//360)+540)//360)-180         
        XDECO  R7,XDEC              edit a
        MVC    PG(8),XDEC           output a
        MVC    PG+9(4),XDEC+8       output a decimals
        XDECO  R8,XDEC              edit b
        MVC    PG+14(8),XDEC        output b
        MVC    PG+23(4),XDEC+8      output b decimals
        XDECO  R4,XDEC              edit x
        MVC    PG+28(8),XDEC        output x
        MVC    PG+37(4),XDEC+8      output x decimals
        XPRNT  PG,L'PG              print
        LA     R6,1(R6)             i++
      ENDDO    ,                  enddo i
        L      R13,4(0,R13)       restore previous savearea pointer
        RETURN (14,12),RC=0       restore registers from calling sav

N DC F'8' number of pairs T DC F'200000',F'450000',F'-450000',F'450000' 

        DC     F'-850000',F'900000',F'-950000',F'900000'
        DC     F'-450000',F'1250000',F'450000',F'1450000'
        DC     F'294803',F'-886361',F'-783251',F'-1590360'

PG DC CL80'12345678.1234 12345678.1234 12345678.1234' XDEC DS CL12 temp 

        YREGS
        END    ANGLEDBB</lang>
Output:
      20.0000       45.0000       25.0000
     -45.0000       45.0000       90.0000
     -85.0000       90.0000      175.0000
     -95.0000       90.0000     -175.0000
     -45.0000      125.0000      170.0000
      45.0000      145.0000      100.0000
      29.4803      -88.6361     -118.1164
     -78.3251     -159.0360      -80.7109


AWK

<lang AWK>

  1. syntax: GAWK -f ANGLE_DIFFERENCE_BETWEEN_TWO_BEARINGS.AWK

BEGIN { 

   fmt = "%11s %11s %11s\n"
   while (++i <= 11) { u = u "-" }
   printf(fmt,"B1","B2","DIFFERENCE")
   printf(fmt,u,u,u)
   main(20,45)
   main(-45,45)
   main(-85,90)
   main(-95,90)
   main(-45,125)
   main(-45,145)
   main(29.4803,-88.6381)
   main(-78.3251,-159.036)
   main(-70099.74233810938,29840.67437876723)
   main(-165313.6666297357,33693.9894517456)
   main(1174.8380510598456,-154146.66490124757)
   main(60175.77306795546,42213.07192354373)
   exit(0)

} function main(b1,b2) { 

   printf("%11.2f %11.2f %11.2f\n",b1,b2,angle_difference(b1,b2))

} function angle_difference(b1,b2, r) { 

   r = (b2 - b1) % 360
   if (r < -180) {
     r += 360
   }
   if (r >= 180) {
     r -= 360
   }
   return(r)

} </lang>

Output:
         B1          B2  DIFFERENCE
----------- ----------- -----------
      20.00       45.00       25.00
     -45.00       45.00       90.00
     -85.00       90.00      175.00
     -95.00       90.00     -175.00
     -45.00      125.00      170.00
     -45.00      145.00     -170.00
      29.48      -88.64     -118.12
     -78.33     -159.04      -80.71
  -70099.74    29840.67     -139.58
 -165313.67    33693.99      -72.34
    1174.84  -154146.66     -161.50
   60175.77    42213.07       37.30

Ada

Ada does not provide a built-in mod function for floating point types. This program supplies one. <lang Ada>

-- Angle difference between two bearings

with Ada.Text_IO; use Ada.Text_IO;

procedure Bearing_Angles is 

  type Real is digits 8;
  Package Real_Io is new Ada.Text_IO.Float_IO(Real);
  use Real_IO;
  type Angles is record
     B1 : Real;
     B2 : Real;
  end record;
  type Angle_Arr is array(Positive range <>) of Angles;
  
  function fmod(Left, Right : Real) return Real is
     Result : Real;
  begin
     Result := Left - Right*Real'Truncation(Left / Right);
     return Result;
  end fmod;
  
  The_Angles : Angle_Arr := ((20.0,45.0),(-45.0, 45.0), (-85.0, 90.0),
                             (-95.0, 90.0), (-14.0, 125.0), (29.4803, -88.6381),
                             (-78.3251, -159.036),
                             (-70099.74233810938, 29840.67437876723),
                             (-165313.6666297357, 33693.9894517456),
                             (1174.8380510598456, -154146.66490124757),
                             (60175.77306795546, 42213.07192354373));
  Diff : Real;

begin 

  for A of The_Angles loop
     Diff := fmod(A.b2 - A.b1, 360.0);
     If Diff < -180.0 then
        Diff := Diff + 360.0;
     elsif Diff > 180.0 then
        Diff := Diff - 360.0;
     end if;
     
     Put("Difference between ");
     Put(Item => A.B2, Fore => 7, Aft => 4, Exp => 0);
     Put(" and ");
     Put(Item => A.B1, Fore => 7, Aft => 4, Exp => 0);
     Put(" is ");
     Put(Item => Diff, Fore => 4, Aft => 4, Exp => 0);
     New_Line;
  end loop;

end Bearing_Angles; </lang>

Output:
Difference between      45.0000 and      20.0000 is   25.0000
Difference between      45.0000 and     -45.0000 is   90.0000
Difference between      90.0000 and     -85.0000 is  175.0000
Difference between      90.0000 and     -95.0000 is -175.0000
Difference between     125.0000 and     -14.0000 is  139.0000
Difference between     -88.6381 and      29.4803 is -118.1184
Difference between    -159.0360 and     -78.3251 is  -80.7109
Difference between   29840.6744 and  -70099.7423 is -139.5833
Difference between   33693.9895 and -165313.6666 is  -72.3439
Difference between -154146.6649 and    1174.8381 is -161.5030
Difference between   42213.0719 and   60175.7731 is   37.2989

APL

Returns an angle in (-180,180]; so two opposite bearings have a difference of 180 degrees, which is more natural than -180 degrees. <lang APL>[0] D←B1 DIFF B2 [1] D←180+¯360|180+B2-B1 </lang>

Output:
      'B1' 'B2' 'DIFFERENCE'⍪(⊂'¯¯¯¯¯¯¯¯¯¯')⍪(⊃B),DIFF/¨B
         B1          B2  DIFFERENCE 
 ¯¯¯¯¯¯¯¯¯¯  ¯¯¯¯¯¯¯¯¯¯  ¯¯¯¯¯¯¯¯¯¯ 
      20          45          25    
     ¯45          45          90    
     ¯85          90         175    
     ¯95          90        ¯175    
     ¯45         125         170    
     ¯45         145        ¯170    
      29.48      ¯88.64     ¯118.12 
     ¯78.33     ¯159.04      ¯80.71 
  ¯70099.74    29840.67     ¯139.59 
 ¯165313.67     3369.99     ¯156.34 
    1174.84  ¯154146.66     ¯161.5  
   60175.77    42213.07       37.3  

      270 DIFF 90.01
¯179.99
      270 DIFF 90
180

Befunge

<lang befunge>012pv1 2 3 4 5 6 7 8 

   >&:v   >859**%:459**1-`#v_     >12g!:12p#v_\-:459**1-`#v_     >.>
      >0`#^_8v             >859**-^                       >859**-^
      ^:+**95<                              >                      ^

</lang> The labelled points are: 1. Initialise write/not write and read input, 2. Put in the range 0-360 if negative, 3. Likewise if positive, 4. Put in range -180 - 180, 5. Check if write/not write step, 6. If write find difference, 7. Scale to -180 - 180, 8. Write out and onto next pair.

Unfortunately, due to the lack of floating-point arithmetic in befunge, it is impossible to do the full challenge, however, given the integer truncations of these values it works.

Input: 

20 45
-45 45
-85 90
-95 90
-45 125
-45 145
29 -88
-78 -159
-70099 29840
-165313 33693
1174 -154146
60175 42213
Output:
25 90 175 -175 170 -170 -117 -81 -141 -74 -160 38

C

This implementation either reads two bearings from the console or a file containing a list of bearings. Usage printed on incorrect invocation. <lang C>

  1. include<stdlib.h>
  2. include<stdio.h>
  3. include<math.h>

void processFile(char* name){

int i,records; double diff,b1,b2; FILE* fp = fopen(name,"r");

fscanf(fp,"%d\n",&records);

for(i=0;i<records;i++){ fscanf(fp,"%lf%lf",&b1,&b2);

diff = fmod(b2-b1,360.0); printf("\nDifference between b2(%lf) and b1(%lf) is %lf",b2,b1,(diff<-180)?diff+360:((diff>=180)?diff-360:diff)); }

fclose(fp); }

int main(int argC,char* argV[]) { double diff;

if(argC < 2) printf("Usage : %s <bearings separated by a space OR full file name which contains the bearing list>",argV[0]); else if(argC == 2) processFile(argV[1]); else{ diff = fmod(atof(argV[2])-atof(argV[1]),360.0); printf("Difference between b2(%s) and b1(%s) is %lf",argV[2],argV[1],(diff<-180)?diff+360:((diff>=180)?diff-360:diff)); }

return 0; } </lang> Invocation and output for two bearings : 

C:\rosettaCode>bearingDiff.exe 29.4803 -88.6381
Difference between b2(-88.6381) and b1(29.4803) is -118.118400

File format for bearing list : 

<Number of records>
<Each record consisting of two bearings separated by a space>

Input file : 

12
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

Invocation and output for above bearing list file : 

C:\rosettaCode>bearingDiff.exe bearingList.txt

Difference between b2(45.000000) and b1(20.000000) is 25.000000
Difference between b2(45.000000) and b1(-45.000000) is 90.000000
Difference between b2(90.000000) and b1(-85.000000) is 175.000000
Difference between b2(90.000000) and b1(-95.000000) is -175.000000
Difference between b2(125.000000) and b1(-45.000000) is 170.000000
Difference between b2(145.000000) and b1(-45.000000) is -170.000000
Difference between b2(-88.638100) and b1(29.480300) is -118.118400
Difference between b2(-159.036000) and b1(-78.325100) is -80.710900
Difference between b2(29840.674379) and b1(-70099.742338) is -139.583283
Difference between b2(33693.989452) and b1(-165313.666630) is -72.343919
Difference between b2(-154146.664901) and b1(1174.838051) is -161.502952
Difference between b2(42213.071924) and b1(60175.773068) is 37.298856

C++

<lang cpp>#include <cmath>

  1. include <iostream>

using namespace std;

double getDifference(double b1, double b2) { double r = fmod(b2 - b1, 360.0); if (r < -180.0) r += 360.0; if (r >= 180.0) r -= 360.0; return r; }

int main() { cout << "Input in -180 to +180 range" << endl; cout << getDifference(20.0, 45.0) << endl; cout << getDifference(-45.0, 45.0) << endl; cout << getDifference(-85.0, 90.0) << endl; cout << getDifference(-95.0, 90.0) << endl; cout << getDifference(-45.0, 125.0) << endl; cout << getDifference(-45.0, 145.0) << endl; cout << getDifference(-45.0, 125.0) << endl; cout << getDifference(-45.0, 145.0) << endl; cout << getDifference(29.4803, -88.6381) << endl; cout << getDifference(-78.3251, -159.036) << endl;

cout << "Input in wider range" << endl; cout << getDifference(-70099.74233810938, 29840.67437876723) << endl; cout << getDifference(-165313.6666297357, 33693.9894517456) << endl; cout << getDifference(1174.8380510598456, -154146.66490124757) << endl; cout << getDifference(60175.77306795546, 42213.07192354373) << endl;

return 0; }</lang>

Output:
Input in -180 to +180 range
25
90
175
-175
170
-170
170
-170
-118.118
-80.7109
Input in wider range
-139.583
-72.3439
-161.503
37.2989

C#

<lang csharp>using System;

namespace Angle_difference_between_two_bearings { class Program { public static void Main(string[] args) { Console.WriteLine(); Console.WriteLine("Hello World!"); Console.WriteLine();

// Calculate standard test cases Console.WriteLine(Delta_Bearing( 20M,45)); Console.WriteLine(Delta_Bearing(-45M,45M)); Console.WriteLine(Delta_Bearing(-85M,90M)); Console.WriteLine(Delta_Bearing(-95M,90M)); Console.WriteLine(Delta_Bearing(-45M,125M)); Console.WriteLine(Delta_Bearing(-45M,145M)); Console.WriteLine(Delta_Bearing( 29.4803M,-88.6381M)); Console.WriteLine(Delta_Bearing(-78.3251M, -159.036M));

// Calculate optional test cases Console.WriteLine(Delta_Bearing(-70099.74233810938M, 29840.67437876723M)); Console.WriteLine(Delta_Bearing(-165313.6666297357M, 33693.9894517456M)); Console.WriteLine(Delta_Bearing( 1174.8380510598456M, -154146.66490124757M)); Console.WriteLine(Delta_Bearing( 60175.77306795546M, 42213.07192354373M));

Console.WriteLine(); Console.Write("Press any key to continue . . . "); Console.ReadKey(true); }

static decimal Delta_Bearing(decimal b1, decimal b2) { /* * Optimal solution * decimal d = 0;

d = (b2-b1)%360;

if(d>180) d -= 360; else if(d<-180) d += 360;

return d; * * */


// // // decimal d = 0;

// Convert bearing to W.C.B if(b1<0) b1 += 360; if(b2<0) b2 += 360;

///Calculate delta bearing //and //Convert result value to Q.B. d = (b2 - b1)%360;

if(d>180) d -= 360; else if(d<-180) d += 360;

return d;

// // // } } }</lang>

Output:
Hello World!

25
90
175
-175
170
-170
-118,1184
-80,7109
-139,58328312339
-72,3439185187
-161,5029523074156
37,29885558827

Press any key to continue . . .

Clojure

<lang clojure>(defn angle-difference [a b] 

 (let [r (mod (- b a) 360)]
   (if (>= r 180)
     (- r 360)
     r)))

(angle-difference 20 45)  ; 25 (angle-difference -45 45) ; 90 (angle-difference -85 90) ; 175 (angle-difference -95 90) ; -175 (angle-difference -70099.74 29840.67) ; -139.59 </lang>

Common Lisp

<lang common lisp> (defun angle-difference (b1 b2) (let ((diff (mod (- b2 b1) 360))) (if (< diff -180) (incf diff 360) (if (> diff 180) (decf diff 360) diff)))) </lang>

Output:

CL-USER> (angle-difference 20 45)
25
CL-USER> (angle-difference -45 45)
90
CL-USER> (angle-difference -85 90)
175
CL-USER> (angle-difference -95 90)
-175
CL-USER> (angle-difference -70099.74 29840.67)
-139.58594

D

Translation of: Java

<lang D>import std.stdio;

double getDifference(double b1, double b2) { 

   double r = (b2 - b1) % 360.0;
   if (r < -180.0) {
       r += 360.0;
   }
   if (r >= 180.0) {
       r -= 360.0;
   }
   return r;

}

void main() { 

   writeln("Input in -180 to +180 range");
   writeln(getDifference(20.0, 45.0));
   writeln(getDifference(-45.0, 45.0));
   writeln(getDifference(-85.0, 90.0));
   writeln(getDifference(-95.0, 90.0));
   writeln(getDifference(-45.0, 125.0));
   writeln(getDifference(-45.0, 145.0));
   writeln(getDifference(-45.0, 125.0));
   writeln(getDifference(-45.0, 145.0));
   writeln(getDifference(29.4803, -88.6381));
   writeln(getDifference(-78.3251, -159.036));

   writeln("Input in wider range");
   writeln(getDifference(-70099.74233810938, 29840.67437876723));
   writeln(getDifference(-165313.6666297357, 33693.9894517456));
   writeln(getDifference(1174.8380510598456, -154146.66490124757));
   writeln(getDifference(60175.77306795546, 42213.07192354373));

}</lang>

Output:
Input in -180 to +180 range
25
90
175
-175
170
-170
170
-170
-118.118
-80.7109
Input in wider range
-139.583
-72.3439
-161.503
37.2989

F#

<lang fsharp>let deltaBearing (b1:double) (b2:double) = 

   let r = (b2 - b1) % 360.0;
   if r > 180.0 then
       r - 360.0
   elif r < -180.0 then
       r + 360.0
   else
       r

[<EntryPoint>] let main _ = 

   printfn "%A" (deltaBearing      20.0                  45.0)
   printfn "%A" (deltaBearing     -45.0                  45.0)
   printfn "%A" (deltaBearing     -85.0                  90.0)
   printfn "%A" (deltaBearing     -95.0                  90.0)
   printfn "%A" (deltaBearing     -45.0                 125.0)
   printfn "%A" (deltaBearing     -45.0                 145.0)
   printfn "%A" (deltaBearing      29.4803              -88.6381)
   printfn "%A" (deltaBearing     -78.3251             -159.036)
   printfn "%A" (deltaBearing  -70099.74233810938     29840.67437876723)
   printfn "%A" (deltaBearing -165313.6666297357      33693.9894517456)
   printfn "%A" (deltaBearing    1174.8380510598456 -154146.66490124757)
   printfn "%A" (deltaBearing   60175.77306795546     42213.07192354373)
   0 // return an integer exit code</lang>
Output:
25.0
90.0
175.0
-175.0
170.0
-170.0
-118.1184
-80.7109
-139.5832831
-72.34391852
-161.5029523
37.29885559

Factor

Translation of: F#
Works with: Factor version development release 2019-03-17+

<lang factor>USING: combinators generalizations kernel math prettyprint ; IN: rosetta-code.bearings

delta-bearing ( x y -- z )
   swap - 360 mod {
       { [ dup 180 > ] [ 360 - ] }
       { [ dup -180 < ] [ 360 + ] }
       [ ]
   } cond ;
bearings-demo ( -- )
   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
   [ delta-bearing . ] 2 12 mnapply ;

MAIN: bearings-demo</lang>

Output:
25
90
175
-175
170
-170
-118.1184
-80.7109
-139.5832831233856
-72.34391851868713
-161.5029523074045
37.29885558826936

Fortran

Rather than calculate angle differences and mess about with folding the results into ±180 and getting the sign right, why not use some mathematics? These days, trigonometrical functions are calculated swiftly by specialised hardware (well, microcode), and with the availability of functions working in degrees, matters are eased further nor is precision lost in converting from degrees to radians. So, the first step is to convert a bearing into an (x,y) unit vector via function CIS(t) = cos(t) + i.sin(t), which will handle all the annoyance of bearings specified in values above 360. Then, using the dot product of the two vectors allows the cosine of the angle to be known, and the cross product determines the sign.

However, this relies on the unit vectors being accurately so, and their subsequent dot product not exceeding one in size: given the rounding of results with the limited precision actual floating-point arithmetic, there may be problems. Proving that a calculation will not suffer these on a specific computer is difficult, especially as the desire for such a result may mean that any apparent pretext leading to that belief will be seized upon. Because calculations on the IBM pc and similar computers are conducted with 80-bit floating-point arithmetic, rounding errors for 64-bit results are likely to be small, but past experience leads to a "fog of fear" about the precise behaviour of floating-point arithmetic.

As it happens, the test data did not provoke any objections from the ACOSD function, but even so, a conversion to using arctan instead of arccos to recover angles would be safer. By using the four-quadrant arctan(x,y) function, the sign of the angle difference is also delivered and although that result could be in 0°-360° it turns out to be in ±180° as desired. On the other hand, the library of available functions did not include an arctan for complex parameters, so the complex number Z had to be split into its real and imaginary parts, thus requiring two appearances and to avoid repeated calculation, a temporary variable Z is needed. Otherwise, the statement could have been just T = ATAN2D(Z1*CONJG(Z2)) and the whole calculation could be effected in one statement, T = ATAN2D(CIS(90 - B1)*CONJG(CIS(90 - B2))) And, since cis(t) = exp(i.t), T = ATAN2D(EXP(CMPLX(0,90 - B1))*CONJG(EXP(CMPLX(0,90 - B2)))) - although using the arithmetic statement function does seem less intimidating.

The source style is F77 (even using the old-style arithmetic statement function) except for the convenience of generic functions taking the type of their parameters to save on the bother of DCMPLX instead of just CMPLX, etc. Floating-point constants in the test data are specified with ~D0, the exponential form that signifies double precision otherwise they would be taken as single precision values. Some compilers offer an option stating that all floating-point constants are to be taken as double precision. REAL*8 precision amounts to about sixteen decimal digits, so some of the supplied values will not be accurately represented, unless something beyond REAL*8 is available. <lang Fortran> SUBROUTINE BDIFF (B1,B2) !Difference B2 - B1, as bearings. All in degrees, not radians. 

      REAL*8 B1,B2	!Maximum precision, for large-angle folding.
      COMPLEX*16 CIS,Z1,Z2,Z	!Scratchpads.
      CIS(T) = CMPLX(COSD(T),SIND(T))	!Convert an angle into a unit vector.
       Z1 = CIS(90 - B1)	!Bearings run clockwise from north (y) around to east (x).
       Z2 = CIS(90 - B2)	!Mathematics runs counterclockwise from x (east).
       Z = Z1*CONJG(Z2)	!(Z1x,Z1y)(Z2x,-Z2y) = (Z1x.Z2x + Z1y.Z2y, Z1y.Z2x - Z1x.Z2y)
       T = ATAN2D(AIMAG(Z),REAL(Z))	!Madly, arctan(x,y) is ATAN(Y,X)!
       WRITE (6,10) B1,Z1,B2,Z2,T	!Two sets of numbers, and a result.
  10   FORMAT (2(F14.4,"(",F9.6,",",F9.6,")"),F9.3)	!Two lots, and a tail.
     END SUBROUTINE BDIFF	!Having functions in degrees saves some bother.

     PROGRAM ORIENTED
     REAL*8 B(24)	!Just prepare a wad of values.
     DATA B/20D0,45D0, -45D0,45D0, -85D0,90D0, -95D0,90D0,	!As specified.
    1      -45D0,125D0, -45D0,145D0, 29.4803D0,-88.6381D0,
    2      -78.3251D0,              -159.036D0,
    3   -70099.74233810938D0,      29840.67437876723D0,
    4  -165313.6666297357D0,       33693.9894517456D0,
    5     1174.8380510598456D0,  -154146.66490124757D0,
    6    60175.77306795546D0,      42213.07192354373D0/

     WRITE (6,1) ("B",I,"x","y", I = 1,2)	!Or, one could just list them twice.
   1 FORMAT (28X,"Bearing calculations, in degrees"//
    * 2(A13,I1,"(",A9,",",A9,")"),A9)	!Compare format 10, above.

     DO I = 1,23,2	!Step through the pairs.
       CALL BDIFF(B(I),B(I + 1))
     END DO

     END</lang>

The output shows the stages: 

                            Bearing calculations, in degrees

            B1(        x,        y)            B2(        x,        y)
       20.0000( 0.342020, 0.939693)       45.0000( 0.707107, 0.707107)   25.000
      -45.0000(-0.707107, 0.707107)       45.0000( 0.707107, 0.707107)   90.000
      -85.0000(-0.996195, 0.087156)       90.0000( 1.000000, 0.000000)  175.000
      -95.0000(-0.996195,-0.087156)       90.0000( 1.000000, 0.000000) -175.000
      -45.0000(-0.707107, 0.707107)      125.0000( 0.819152,-0.573576)  170.000
      -45.0000(-0.707107, 0.707107)      145.0000( 0.573576,-0.819152) -170.000
       29.4803( 0.492124, 0.870525)      -88.6381(-0.999718, 0.023767) -118.118
      -78.3251(-0.979312, 0.202358)     -159.0360(-0.357781,-0.933805)  -80.711
   -70099.7423( 0.984016,-0.178078)    29840.6744(-0.633734, 0.773551) -139.584
  -165313.6666(-0.959667, 0.281138)    33693.9895(-0.559023,-0.829152)  -72.340
     1174.8381( 0.996437,-0.084339)  -154146.6649(-0.918252, 0.395996) -161.510
    60175.7731( 0.826820, 0.562467)    42213.0719( 0.998565,-0.053561)   37.297

FreeBASIC

<lang freebasic>' version 28-01-2019 ' compile with: fbc -s console

  1. Include "string.bi"

Function frmt(num As Double) As String 

   Dim As String temp = Format(num, "#######.#############")
   Dim As Integer i = Len(temp) -1

   If temp[i] = Asc(".") Then temp[i] = 32
   If InStr(temp, ".") = 0 Then
       Return Right(Space(10) + temp, 9) + Space(13)
   End If
   temp = Space(10) + temp + Space(13)
   Return Mid(temp, InStr(temp, ".") -8, 22)

End Function

' ------=< MAIN >=------

Dim As Double b1, b2, bb1, bb2, diff

Print Print " b1 b2 difference" Print " -----------------------------------------------------------"

Do 

   Read b1, b2
   If b1 = 0 And b2 = 0 Then Exit Do
   diff = b2 - b1
   diff = diff - Int(diff / 360) * 360
   If diff > 180 Then diff -= 360
   Print frmt(b1); frmt(b2); frmt(diff)

Loop

Data 20,45, -45,45, -85,90 Data -95,90, -45,125, -45,145 Data 29.4803,-88.6381, -78.3251,-159.036 Data -70099.74233810938, 29840.67437876723 Data -165313.6666297357, 33693.9894517456 Data 1174.8380510598456, -154146.66490124757 Data 60175.77306795546, 42213.07192354373

' empty keyboard buffer While InKey <> "" : Wend Print : Print "hit any key to end program" Sleep End</lang>

Output:
      b1                    b2                    difference
 -----------------------------------------------------------
      20                    45                    25
     -45                    45                    90
     -85                    90                   175
     -95                    90                  -175
     -45                   125                   170
     -45                   145                  -170
      29.4803              -88.6381             -118.1184
     -78.3251             -159.036               -80.7109
  -70099.7423381093831   29840.6743787672312    -139.5832831233856
 -165313.6666297357006   33693.9894517455978     -72.3439185186871
    1174.8380510598461 -154146.6649012475973    -161.5029523074336
   60175.7730679554588   42213.0719235437282      37.2988555882694

Go

Basic task solution:

One feature of this solution is that if you can rely on the input bearings being in the range -180 to 180, you don't have to use math.Mod. Another feature is the bearing type and method syntax. <lang go>package main

import "fmt"

type bearing float64

var testCases = []struct{ b1, b2 bearing }{ 

   {20, 45},
   {-45, 45},
   {-85, 90},
   {-95, 90},
   {-45, 125},
   {-45, 145},
   {29.4803, -88.6381},
   {-78.3251, -159.036},

}

func main() { 

   for _, tc := range testCases {
       fmt.Println(tc.b2.Sub(tc.b1))
   }

}

func (b2 bearing) Sub(b1 bearing) bearing { 

   switch d := b2 - b1; {
   case d < -180:
       return d + 360
   case d > 180:
       return d - 360
   default:
       return d
   }

}</lang>

Output:
25
90
175
-175
170
-170
-118.1184
-80.7109

Optional extra solution:

A feature here is that the function body is a one-liner sufficient for the task test cases. <lang go>package main

import ( 

   "fmt"
   "math"

)

var testCases = []struct{ b1, b2 float64 }{ 

   {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},

}

func main() { 

   for _, tc := range testCases {
       fmt.Println(angleDifference(tc.b2, tc.b1))
   }

}

func angleDifference(b2, b1 float64) float64 { 

   return math.Mod(math.Mod(b2-b1, 360)+360+180, 360) - 180

}</lang>

Output:
25
90
175
-175
170
-170
-118.11840000000001
-80.71089999999998
-139.58328312338563
-72.34391851868713
-161.50295230740448
37.29885558826936

Haskell

<lang Haskell>import Text.Printf (printf)

type Radians = Float

type Degrees = Float

angleBetweenDegrees :: Degrees -> Degrees -> Degrees angleBetweenDegrees a b = degrees $ bearingDelta (radians a) (radians b)

bearingDelta :: Radians -> Radians -> Radians bearingDelta a b -- sign * dot-product 

= sign * acos ((ax * bx) + (ay * by))
 where
   (ax, ay) = (sin a, cos a)
   (bx, by) = (sin b, cos b)
   sign
     | ((ay * bx) - (by * ax)) > 0 = 1
     | otherwise = -1

degrees :: Radians -> Degrees degrees = (/ pi) . (180 *)

radians :: Degrees -> Radians radians = (/ 180) . (pi *)

-- TEST ----------------------------------------------------------------------- main :: IO () main = 

 putStrLn . unlines $
 uncurry
   (((<*>) . printf "%6.2f° + %6.2f°  ->  %7.2f°") <*> angleBetweenDegrees) <$>
 [ (20.0, 45.0)
 , (-45.0, 45.0)
 , (-85.0, 90.0)
 , (-95.0, 90.0)
 , (-45.0, 125.0)
 , (-45.0, 145.0)
 ]</lang>
Output:
 20.00° +  45.00°  ->    25.00°
-45.00° +  45.00°  ->    90.00°
-85.00° +  90.00°  ->   175.00°
-95.00° +  90.00°  ->  -175.00°
-45.00° + 125.00°  ->   170.00°
-45.00° + 145.00°  ->  -170.00°

IS-BASIC

<lang IS-BASIC>100 INPUT PROMPT "1. angle: ":A1 110 INPUT PROMPT "2. angle: ":A2 120 LET B=MOD(A2-A1,360) 130 IF B>180 THEN LET B=B-360 140 IF B<-180 THEN LET B=B+360 150 PRINT "Difference: ";B</lang>

J

<lang j>relativeBearing=: (180 -~ 360 | 180 + -~)/"1</lang> <lang j>tests=: _99&".;._2 noun define 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 ) 

  tests ,. relativeBearing tests
     20       45       25
    _45       45       90
    _85       90      175
    _95       90     _175
    _45      125      170
    _45      145     _170
29.4803 _88.6381 _118.118

_78.3251 _159.036 _80.7109 _70099.7 29840.7 _139.583 

_165314    33694 _72.3439
1174.84  _154147 _161.503
60175.8  42213.1  37.2989</lang>

Java

Translation of: C++

<lang java>public class AngleDifference { 

   public static double getDifference(double b1, double b2) {
       double r = (b2 - b1) % 360.0;
       if (r < -180.0)
           r += 360.0;
       if (r >= 180.0)
           r -= 360.0;
       return r;
   }

   public static void main(String[] args) {
       System.out.println("Input in -180 to +180 range");
       System.out.println(getDifference(20.0, 45.0));
       System.out.println(getDifference(-45.0, 45.0));
       System.out.println(getDifference(-85.0, 90.0));
       System.out.println(getDifference(-95.0, 90.0));
       System.out.println(getDifference(-45.0, 125.0));
       System.out.println(getDifference(-45.0, 145.0));
       System.out.println(getDifference(-45.0, 125.0));
       System.out.println(getDifference(-45.0, 145.0));
       System.out.println(getDifference(29.4803, -88.6381));
       System.out.println(getDifference(-78.3251, -159.036));

       System.out.println("Input in wider range");
       System.out.println(getDifference(-70099.74233810938, 29840.67437876723));
       System.out.println(getDifference(-165313.6666297357, 33693.9894517456));
       System.out.println(getDifference(1174.8380510598456, -154146.66490124757));
       System.out.println(getDifference(60175.77306795546, 42213.07192354373));
   }

}</lang>

Output:
Input in -180 to +180 range
25.0
90.0
175.0
-175.0
170.0
-170.0
170.0
-170.0
-118.1184
-80.7109
Input in wider range
-139.58328312338563
-72.34391851868713
-161.50295230740448
37.29885558826936

JavaScript

ES5

This approach should be reliable but it is also very inefficient.

<lang javascript>function relativeBearing(b1Rad, b2Rad) { b1y = Math.cos(b1Rad); b1x = Math.sin(b1Rad); b2y = Math.cos(b2Rad); b2x = Math.sin(b2Rad); crossp = b1y * b2x - b2y * b1x; dotp = b1x * b2x + b1y * b2y; if(crossp > 0.) return Math.acos(dotp); return -Math.acos(dotp); }

function test() { var deg2rad = 3.14159265/180.0; var rad2deg = 180.0/3.14159265; return "Input in -180 to +180 range\n" +relativeBearing(20.0*deg2rad, 45.0*deg2rad)*rad2deg+"\n" +relativeBearing(-45.0*deg2rad, 45.0*deg2rad)*rad2deg+"\n" +relativeBearing(-85.0*deg2rad, 90.0*deg2rad)*rad2deg+"\n" +relativeBearing(-95.0*deg2rad, 90.0*deg2rad)*rad2deg+"\n" +relativeBearing(-45.0*deg2rad, 125.0*deg2rad)*rad2deg+"\n" +relativeBearing(-45.0*deg2rad, 145.0*deg2rad)*rad2deg+"\n"

+relativeBearing(29.4803*deg2rad, -88.6381*deg2rad)*rad2deg+"\n" +relativeBearing(-78.3251*deg2rad, -159.036*deg2rad)*rad2deg+"\n"

+ "Input in wider range\n" +relativeBearing(-70099.74233810938*deg2rad, 29840.67437876723*deg2rad)*rad2deg+"\n" +relativeBearing(-165313.6666297357*deg2rad, 33693.9894517456*deg2rad)*rad2deg+"\n" +relativeBearing(1174.8380510598456*deg2rad, -154146.66490124757*deg2rad)*rad2deg+"\n" +relativeBearing(60175.77306795546*deg2rad, 42213.07192354373*deg2rad)*rad2deg+"\n";

}</lang>

Output:
Input in -180 to +180 range
25.000000000000004
90
174.99999999999997
-175.00000041135993
170.00000000000003
-170.00000041135996
-118.1184
-80.71089999999998
Input in wider range
-139.5833974814558
-72.34414600076728
-161.50277501127033
37.2988761562732

ES6

<lang JavaScript>(() => { 

   // bearingDelta :: Radians -> Radians -> Radians
   const bearingDelta = (ar, br) => {
       const [ax, ay] = [sin(ar), cos(ar)], [bx, by] = [sin(br), cos(br)],

       // Cross-product > 0 ?
       sign = ((ay * bx) - (by * ax)) > 0 ? +1 : -1;

       // Sign * dot-product
       return sign * acos((ax * bx) + (ay * by));
   };

   // Pi, sin, cos, acos :: Function
   const [Pi, sin, cos, acos] = ['PI', 'sin', 'cos', 'acos']
   .map(k => Math[k]),
       degRad = x => Pi * x / 180.0,
       radDeg = x => 180.0 * x / Pi;



   // TEST ------------------------------------------------------------------

   // justifyRight :: Int -> Char -> Text -> Text
   const justifyRight = (n, cFiller, strText) =>
       n > strText.length ? (
           (cFiller.repeat(n) + strText)
           .slice(-n)
       ) : strText;

   // showMap :: Degrees -> Degrees -> String
   const showMap = (da, db) =>
       justifyRight(6, ' ', `${da}° +`) +
       justifyRight(11, ' ', ` ${db}°  ->  `) +
       justifyRight(7, ' ', `${(radDeg(bearingDelta(degRad(da), degRad(db))))
           .toPrecision(4)}°`);

   return [
           [20, 45],
           [-45, 45],
           [-85, 90],
           [-95, 90],
           [-45, 125],
           [-45, 145]
       ].map(xy => showMap(...xy))
       .join('\n');

})();</lang>

Output:
 20° +  45°  ->   25.00°
-45° +  45°  ->   90.00°
-85° +  90°  ->   175.0°
-95° +  90°  ->  -175.0°
-45° + 125°  ->   170.0°
-45° + 145°  ->  -170.0°

Julia

Works with: Julia version 0.6
Translation of: Python

<lang julia>function angdiff(a, b) 

   r = (b - a) % 360.0
   if r ≥ 180.0
       r -= 360.0
   end

   return r

end

println("Input in -180 to +180 range:") for (a, b) in [(20.0, 45.0), (-45.0, 45.0), (-85.0, 90.0), (-95.0, 90.0), (-45.0, 125.0), (-45.0, 145.0), 

   (-45.0, 125.0), (-45.0, 145.0), (29.4803, -88.6381), (-78.3251, -159.036)]
   @printf("% 6.1f - % 6.1f = % 6.1f\n", a, b, angdiff(a, b))

end

println("\nInput in wider range:") for (a, b) in [(-70099.74233810938, 29840.67437876723), (-165313.6666297357, 33693.9894517456), 

   (1174.8380510598456, -154146.66490124757), (60175.77306795546, 42213.07192354373)]
   @printf("% 9.1f - % 9.1f = % 6.1f\n", a, b, angdiff(a, b))

end</lang>

Output:
Input in -180 to +180 range:
  20.0 -   45.0 =   25.0
 -45.0 -   45.0 =   90.0
 -85.0 -   90.0 =  175.0
 -95.0 -   90.0 = -175.0
 -45.0 -  125.0 =  170.0
 -45.0 -  145.0 = -170.0
 -45.0 -  125.0 =  170.0
 -45.0 -  145.0 = -170.0
  29.5 -  -88.6 = -118.1
 -78.3 - -159.0 =  -80.7

Input in wider range:
 -70099.7 -   29840.7 = -139.6
-165313.7 -   33694.0 =  -72.3
   1174.8 - -154146.7 = -161.5
  60175.8 -   42213.1 = -322.7

K

<lang K> / Angle difference between two angles / angledif.k

angdif: {[b1;b2]; :[(r:(b2-b1)!360.0)<-180.0;r+:360.0;r>180.0;r-:360.0];:r} </lang>

The output of a session is given below:

Output:
K Console - Enter \ for help

  \l angledif

  angdif[20;45]
25.0
  angdif[-45;45]
90.0
  angdif[-85;90]
175.0
  angdif[-95;90]
-175.0
  angdif[-45;125]
170.0
  angdif[29.4803;-88.6381]
-118.1184
  angdif[-78.3251;-159.036]
-80.7109
  angdif[-70099.74233810938;29840.67437876723]
-139.5833

Lua

Each bearing will be stored in an object that inherits methods to accomplish all parts of the task: accept a new number of degrees, automatically adjusting to the range [-180, 180]; construct new bearing objects; subtract another bearing from itself and return the difference; construct a list of new bearing objects given a list of arbitrary degree sizes; and format the number of degrees into a modest human-readable format. Bearings will be zero-initialized by default if no degree size is provided.

<lang lua>bearing = {degrees = 0} -- prototype object

function bearing:assign(angle) angle = tonumber(angle) or 0 while angle > 180 do angle = angle - 360 end while angle < -180 do angle = angle + 360 end self.degrees = angle end

function bearing:new(size) local child_object = {} setmetatable(child_object, {__index = self}) child_object:assign(size) return child_object end

function bearing:subtract(other) local difference = self.degrees - other.degrees return self:new(difference) end

function bearing:list(sizes) local bearings = {} for index, size in ipairs(sizes) do table.insert(bearings, self:new(size)) end return bearings end

function bearing:text() return string.format("%.4f deg", self.degrees) end

function main() local subtrahends = bearing:list{ 20, -45, -85, -95, -45, -45, 29.4803, -78.3251, -70099.74233810938, -165313.6666297357, 1174.8380510598456, 60175.77306795546 } local minuends = bearing:list{ 45, 45, 90, 90, 125, 145, -88.6381, -159.036, 29840.67437876723, 33693.9894517456, -154146.66490124757, 42213.07192354373 } for index = 1, #minuends do local b2, b1 = minuends[index], subtrahends[index] local b3 = b2:subtract(b1) local statement = string.format( "%s - %s = %s\n", b2:text(), b1:text(), b3:text() ) io.write(statement) end end

main()</lang>

Output:
45.0000 deg - 20.0000 deg = 25.0000 deg
45.0000 deg - -45.0000 deg = 90.0000 deg
90.0000 deg - -85.0000 deg = 175.0000 deg
90.0000 deg - -95.0000 deg = -175.0000 deg
125.0000 deg - -45.0000 deg = 170.0000 deg
145.0000 deg - -45.0000 deg = -170.0000 deg
-88.6381 deg - 29.4803 deg = -118.1184 deg
-159.0360 deg - -78.3251 deg = -80.7109 deg
-39.3256 deg - 100.2577 deg = -139.5833 deg
-146.0105 deg - -73.6666 deg = -72.3439 deg
-66.6649 deg - 94.8381 deg = -161.5030 deg
93.0719 deg - 55.7731 deg = 37.2989 deg

Maple

Translation of: C++

<lang Maple>getDiff := proc(b1,b2) local r: r := frem(b2 - b1, 360): if r >= 180 then r := r - 360: fi: return r: end proc: getDiff(20,45); getDiff(-45,45); getDiff(-85,90); getDiff(-95,90); getDiff(-45,125); getDiff(-45,145); getDiff(29.4803, -88.6381); getDiff(-78.3251,-159.036); getDiff(-70099.74233810938,29840.67437876723); getDiff(-165313.6666297357,33693.9894517456); getDiff(1174.8380510598456,-154146.66490124757); getDiff(60175.77306795546,42213.07192354373)</lang>

Output:
25
90
175
-175
170
-170
-118.1184
-80.7109
-139.58328
-72.3340
-161.5030
37.29885


Kotlin

<lang scala>// version 1.1.2

class Angle(d: Double) { 

   val value = when {
      d in -180.0 .. 180.0 -> d
      d > 180.0            -> (d - 180.0) % 360.0 - 180.0
      else                 -> (d + 180.0) % 360.0 + 180.0
   }

   operator fun minus(other: Angle) = Angle(this.value - other.value)

}

fun main(args: Array<String>) { 

   val anglePairs = arrayOf(
        20.0 to 45.0,
       -45.0 to 45.0,
       -85.0 to 90.0,
       -95.0 to 90.0,
       -45.0 to 125.0,
       -45.0 to 145.0,
        29.4803 to -88.6381,
       -78.3251 to -159.036,
       -70099.74233810938 to 29840.67437876723,
       -165313.6666297357 to 33693.9894517456,
        1174.8380510598456 to -154146.66490124757,
        60175.77306795546 to 42213.07192354373
   )
   println("       b1            b2           diff")
   val f = "% 12.4f  % 12.4f  % 12.4f"
   for (ap in anglePairs) {
       val diff = Angle(ap.second) - Angle(ap.first)
       println(f.format(ap.first, ap.second, diff.value))
   }

}</lang>

Output:
       b1            b2           diff
     20.0000       45.0000       25.0000
    -45.0000       45.0000       90.0000
    -85.0000       90.0000      175.0000
    -95.0000       90.0000     -175.0000
    -45.0000      125.0000      170.0000
    -45.0000      145.0000     -170.0000
     29.4803      -88.6381     -118.1184
    -78.3251     -159.0360      -80.7109
 -70099.7423    29840.6744     -139.5833
-165313.6666    33693.9895      -72.3439
   1174.8381  -154146.6649     -161.5030
  60175.7731    42213.0719       37.2989

Modula-2

Translation of: Java

<lang modula2>FROM Terminal IMPORT *;

PROCEDURE WriteRealLn(value : REAL); VAR str : ARRAY[0..16] OF CHAR; BEGIN 

   RealToStr(value, str);
   WriteString(str);
   WriteLn;

END WriteRealLn;

PROCEDURE AngleDifference(b1, b2 : REAL) : REAL; VAR r : REAL; BEGIN 

   r := (b2 - b1);
   WHILE r < -180.0 DO
       r := r + 360.0;
   END;
   WHILE r >= 180.0 DO
       r := r - 360.0;
   END;
   RETURN r;

END AngleDifference;

BEGIN 

   WriteString('Input in -180 to +180 range');
   WriteLn;
   WriteRealLn(AngleDifference(20.0, 45.0));
   WriteRealLn(AngleDifference(-45.0, 45.0));
   WriteRealLn(AngleDifference(-85.0, 90.0));
   WriteRealLn(AngleDifference(-95.0, 90.0));
   WriteRealLn(AngleDifference(-45.0, 125.0));
   WriteRealLn(AngleDifference(-45.0, 145.0));
   WriteRealLn(AngleDifference(29.4803, -88.6381));
   WriteRealLn(AngleDifference(-78.3251, -159.036));

   WriteString('Input in wider range');
   WriteLn;
   WriteRealLn(AngleDifference(-70099.74233810938, 29840.67437876723));
   WriteRealLn(AngleDifference(-165313.6666297357, 33693.9894517456));
   WriteRealLn(AngleDifference(1174.8380510598456, -154146.66490124757));
   WriteRealLn(AngleDifference(60175.77306795546, 42213.07192354373));

   ReadChar;

END Bearings.</lang>

NewLISP

Taken from Racket solution

<lang lisp>

  1. !/usr/bin/env newlisp

(define (bearing- bearing heading) (sub (mod (add (mod (sub bearing heading) 360.0) 540.0) 360.0) 180.0))

(bearing- 20 45) (bearing- -45 45) (bearing- -85 90) (bearing- -95 90) (bearing- -45 125) (bearing- -45 145) (bearing- 29.4803 -88.6381) (bearing- -78.3251 -159.036) (bearing- -70099.74233810938 29840.67437876723) (bearing- -165313.6666297357 33693.9894517456) (bearing- 1174.8380510598456 -154146.66490124757) (bearing- 60175.77306795546 42213.07192354373)) </lang>

Output:
-25
-90
-175
175
-170
170
118.11839999999995
80.71090000000004
139.58328312338563
72.34391851868713
161.50295230740448
-37.29885558826936

Nim

<lang nim>import math import strutils


proc delta(b1, b2: float) : float = 

 result = (b2 - b1) mod 360.0

 if result < -180.0:
   result += 360.0
 elif result >= 180.0:
   result -= 360.0


let testVectors : seq[tuple[b1, b2: float]] = @[ 

     (20.00,       45.00 ),
    (-45.00,       45.00 ),
    (-85.00,       90.00 ),
    (-95.00,       90.00 ),
    (-45.00,      125.00 ),
    (-45.00,      145.00 ),
    ( 29.48,      -88.64 ),
    (-78.33,     -159.04 ),
 (-70099.74,    29840.67 ),
(-165313.67,    33693.99 ),
   (1174.84,  -154146.66 ),
  (60175.77,    42213.07 ) ]

for vector in testVectors: 

 echo vector.b1.formatFloat(ffDecimal, 2).align(13) &
      vector.b2.formatFloat(ffDecimal, 2).align(13) &
      delta(vector.b1, vector.b2).formatFloat(ffDecimal, 2).align(13)

</lang>

Output:
        
        20.00        45.00        25.00
       -45.00        45.00        90.00
       -85.00        90.00       175.00
       -95.00        90.00      -175.00
       -45.00       125.00       170.00
       -45.00       145.00      -170.00
        29.48       -88.64      -118.12
       -78.33      -159.04       -80.71
    -70099.74     29840.67      -139.59
   -165313.67     33693.99       -72.34
      1174.84   -154146.66      -161.50
     60175.77     42213.07        37.30

Pascal

This program is meant to be saved in the same folder as a file angles.txt containing the input. Each pair of angles to subtract appears on its own line in the input file.

<lang Pascal> Program Bearings; { Reads pairs of angles from a file and subtracts them }

Const 

 fileName = 'angles.txt';

Type 

 degrees = real;

Var 

 subtrahend, minuend: degrees;
 angleFile: text;

function Simplify(angle: degrees): degrees; { Returns an number in the range [-180.0, 180.0] } 

 begin
   while angle > 180.0 do
     angle := angle - 360.0;
   while angle < -180.0 do
     angle := angle + 360.0;
   Simplify := angle
 end;

function Difference(b1, b2: degrees): degrees; { Subtracts b1 from b2 and returns a simplified result } 

 begin
   Difference := Simplify(b2 - b1)
 end;

procedure Subtract(b1, b2: degrees); { Subtracts b1 from b2 and shows the whole equation onscreen } 

 var
   b3: degrees;
 begin
   b3 := Difference(b1, b2);
   writeln(b2:20:11, '   - ', b1:20:11, '   = ', b3:20:11)
 end;

Begin 

 assign(angleFile, fileName);
 reset(angleFile);
 while not eof(angleFile) do
   begin
     readln(angleFile, subtrahend, minuend);
     Subtract(subtrahend, minuend)
   end;
 close(angleFile)

End. </lang>

Input:
                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
Output:
     45.00000000000   -       20.00000000000   =       25.00000000000
     45.00000000000   -      -45.00000000000   =       90.00000000000
     90.00000000000   -      -85.00000000000   =      175.00000000000
     90.00000000000   -      -95.00000000000   =     -175.00000000000
    125.00000000000   -      -45.00000000000   =      170.00000000000
    145.00000000000   -      -45.00000000000   =     -170.00000000000
    -88.63810000000   -       29.48030000000   =     -118.11840000000
   -159.03600000000   -      -78.32510000000   =      -80.71090000000
  29840.67437876723   -   -70099.74233810938   =     -139.58328312339
  33693.98945174560   -  -165313.66662973570   =      -72.34391851869
-154146.66490124760   -     1174.83805105985   =     -161.50295230740
  42213.07192354373   -    60175.77306795546   =       37.29885558827

Perl

Perl's built-in modulo is integer-only, so import a suitable one from the POSIX core module <lang perl>use POSIX 'fmod';

sub angle { my($b1,$b2) = @_; 

  my $b = fmod( ($b2 - $b1 + 720) , 360);
  $b -= 360 if $b >  180;
  $b += 360 if $b < -180;
  return $b;

}

@bearings = ( 

   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

);

while(my ($b1,$b2) = splice(@bearings,0,2)) { 

   printf "%10.2f %10.2f = %8.2f\n", $b1, $b2, angle($b1,$b2);

} </lang>

Output:
     20.00      45.00 =    25.00
    -45.00      45.00 =    90.00
    -85.00      90.00 =   175.00
    -95.00      90.00 =  -175.00
    -45.00     125.00 =   170.00
    -45.00     145.00 =  -170.00
     29.48     -88.64 =  -118.12
    -78.33    -159.04 =   -80.71
 -70099.74   29840.67 =  -139.58
-165313.67   33693.99 =   -72.34
   1174.84 -154146.66 =  -161.50
  60175.77   42213.07 =    37.30

Perl 6

Works with: Rakudo version 2016.11

<lang perl6>sub infix:<∠> (Real $b1, Real $b2) { 

  (my $b = ($b2 - $b1 + 720) % 360) > 180 ?? $b - 360 !! $b;

}

for 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

 -> $b1, $b2 { printf "%10.2f %10.2f = %8.2f\n", $b1, $b2, $b1 ∠ $b2 }</lang>
Output:
     20.00      45.00 =    25.00
    -45.00      45.00 =    90.00
    -85.00      90.00 =   175.00
    -95.00      90.00 =  -175.00
    -45.00     125.00 =   170.00
    -45.00     145.00 =  -170.00
     29.48     -88.64 =  -118.12
    -78.33    -159.04 =   -80.71
 -70099.74   29840.67 =  -139.58
-165313.67   33693.99 =   -72.34
   1174.84 -154146.66 =  -161.50
  60175.77   42213.07 =    37.30

Phix

<lang Phix>function tz(atom a) -- trim trailing zeroes and decimal point 

   string res = sprintf("%16f",a)
   for i=length(res) to 1 by -1 do
       integer ch = res[i]
       if ch='0' or ch='.' then
           res[i] = ' '
       end if
       if ch!='0' then exit end if
   end for
   return res

end function

procedure test(atom b1, b2) 

   atom diff = mod(b2-b1,360)
   diff -= iff(diff>180?360:0)
   printf(1,"%s %s %s\n",{tz(b1),tz(b2),tz(diff)})

end procedure

puts(1," b1 b2 diff\n") puts(1,"---------------- ---------------- ----------------\n") test(20,45) test(-45,45) test(-85,90) test(-95,90) test(-45,125) test(-45,145) test(29.4803,-88.6381) test(-78.3251,-159.036) test(-70099.74233810938,29840.67437876723) test(-165313.6666297357,33693.9894517456) test(1174.8380510598456,-154146.66490124757) test(60175.77306795546,42213.07192354373)</lang>

Output:
       b1               b2             diff
---------------- ---------------- ----------------
       20               45               25
      -45               45               90
      -85               90              175
      -95               90             -175
      -45              125              170
      -45              145             -170
       29.4803         -88.6381        -118.1184
      -78.3251        -159.036          -80.7109
   -70099.742338     29840.674379      -139.583283
  -165313.66663      33693.989452       -72.343919
     1174.838051   -154146.664901      -161.502952
    60175.773068     42213.071924        37.298856

Python

Translation of: C++

<lang python>from __future__ import print_function

def getDifference(b1, b2): r = (b2 - b1) % 360.0 # Python modulus has same sign as divisor, which is positive here, # so no need to consider negative case if r >= 180.0: r -= 360.0 return r

if __name__ == "__main__": print ("Input in -180 to +180 range") print (getDifference(20.0, 45.0)) print (getDifference(-45.0, 45.0)) print (getDifference(-85.0, 90.0)) print (getDifference(-95.0, 90.0)) print (getDifference(-45.0, 125.0)) print (getDifference(-45.0, 145.0)) print (getDifference(-45.0, 125.0)) print (getDifference(-45.0, 145.0)) print (getDifference(29.4803, -88.6381)) print (getDifference(-78.3251, -159.036))

print ("Input in wider range") print (getDifference(-70099.74233810938, 29840.67437876723)) print (getDifference(-165313.6666297357, 33693.9894517456)) print (getDifference(1174.8380510598456, -154146.66490124757)) print (getDifference(60175.77306795546, 42213.07192354373))</lang>

Output:
Input in -180 to +180 range
25.0
90.0
175.0
-175.0
170.0
-170.0
170.0
-170.0
-118.11840000000001
-80.71089999999998
Input in wider range
-139.58328312338563
-72.34391851868713
-161.50295230740448
37.29885558826936


Or, generalising a little by deriving the degrees from a (Radians -> Radians) function, and formatting the output in columns: <lang python>from math import (acos, cos, pi, sin)


  1. bearingDelta :: Radians -> Radians -> Radians

def bearingDelta(ar): 

   def go(br):
       [(ax, ay), (bx, by)] = map(
           lambda x: (sin(x), cos(x)),
           [ar, br]
       )
       # cross-product > 0 ?
       sign = +1 if 0 < ((ay * bx) - (by * ax)) else -1
       # sign * dot-product
       return sign * acos((ax * bx) + (ay * by))
   return lambda br: go(br)


  1. showMap :: Degrees -> Degrees -> String

def showMap(da, db): 

   return unwords(
       map(lambda x: justifyRight(x[0])(' ')(str(x[1])), [
           (22, str(da) + ' +'),
           (23, str(db) + '  -> '),
           (6, round(
               degrees(
                   bearingDelta
                   (radians(da))
                   (radians(db))
               ), 2)
            )
       ])
   )


  1. main :: IO ()

def main(): 

   print (
       unlines(map(lambda ab: showMap(*ab), [
           (20, 45),
           (-45, 45),
           (-85, 90),
           (-95, 90),
           (-45, 125),
           (-45, 145),
           (-70099.74233810938, 29840.67437876723),
           (-165313.6666297357, 33693.9894517456),
           (1174.8380510598456, -154146.66490124757),
           (60175.77306795546, 42213.07192354373)
       ])))


  1. GENERIC ----------------------------------------------
  1. radians :: Float x => Degrees x -> Radians x

def radians(x): 

   return (pi * x / 180)


  1. degrees :: Float x => Radians x -> Degrees x

def degrees(x): 

   return (180 * x / pi)


  1. justifyRight :: Int -> Char -> String -> String

def justifyRight(n): 

   return lambda cFiller: lambda s: (
       ((n * cFiller) + s)[-n:]
   )


  1. unlines :: [String] -> String

def unlines(xs): 

   return '\n'.join(xs)


  1. unwords :: [String] -> String

def unwords(xs): 

   return ' '.join(xs)


main()</lang>

Output:
                  20 +                 45  ->    25.0
                 -45 +                 45  ->    90.0
                 -85 +                 90  ->   175.0
                 -95 +                 90  ->  -175.0
                 -45 +                125  ->   170.0
                 -45 +                145  ->  -170.0
  -70099.74233810938 +  29840.67437876723  ->  139.58
  -165313.6666297357 +   33693.9894517456  ->  -72.34
  1174.8380510598456 + 154146.66490124757  ->  -161.5
   60175.77306795546 +  42213.07192354373  ->    37.3

Racket

see my comments in discussion regards bearing-heading or vice versa

<lang racket>#lang racket (define (% a b) (- a (* b (truncate (/ a b)))))

(define (bearing- bearing heading) 

 (- (% (+ (% (- bearing heading) 360) 540) 360) 180))

(module+ main 

 (bearing- 20 45)
 (bearing- -45 45)
 (bearing- -85 90)
 (bearing- -95 90)
 (bearing- -45 125)
 (bearing- -45 145)
 (bearing- 29.4803 -88.6381)
 (bearing- -78.3251 -159.036)

 (bearing- -70099.74233810938 29840.67437876723)
 (bearing- -165313.6666297357 33693.9894517456)
 (bearing- 1174.8380510598456 -154146.66490124757)
 (bearing- 60175.77306795546 42213.07192354373))

(module+ test 

 (require rackunit)

 (check-equal? (% 7.5 10) 7.5)
 (check-equal? (% 17.5 10) 7.5)
 (check-equal? (% -7.5 10) -7.5)
 (check-equal? (% -17.5 10) -7.5))</lang>
Output:
-25
-90
-175
175
-170
170
118.11839999999995
80.71090000000004
139.58328312338563
72.34391851868713
161.50295230740448
-37.29885558826936

REXX

Some extra coding was added for a better visual presentation;   the angles were centered,   the answers were aligned. <lang rexx>/*REXX pgm calculates difference between two angles (in degrees), normalizes the result.*/ numeric digits 25 /*use enough dec. digits for angles*/ call show 20, 45 /*display angular difference (deg).*/ call show -45, 45 /* " " " " */ call show -85, 90 /* " " " " */ call show -95, 90 /* " " " " */ call show -45, 125 /* " " " " */ call show 45, 145 /* " " " " */ call show 29.4803, -88.6361 /* " " " " */ call show -78.3251, -159.036 /* " " " " */ call show -70099.74233810938, 29840.67437876723 /* " " " " */ call show -165313.6666297357, 33693.9894517456 /* " " " " */ call show 1174.8380510598456, -154146.66490124757 /* " " " " */ call show 60175.773067955546, 42213.07192354373 /* " " " " */ exit /*stick a fork in it, we're done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ show: parse arg a,b; d=digits(); $='º' /*obtain the 2 angles (are in degrees).*/ 

     x=format( ( ( ((b-a) // 360) + 540) // 360) - 180, 4, d)   /*compute and format.  */
     if pos(., x)\==0  then x=strip( strip(x, 'T', 0), "T", .)  /*strip trailing chaff.*/
     say center(a || $, d)      '─'      center(b || $, d)       " ────► "      x || $
     return                                     /* [↑]  display the angular difference.*/</lang>
output:
           20º            ─            45º             ────►    25º
          -45º            ─            45º             ────►    90º
          -85º            ─            90º             ────►   175º
          -95º            ─            90º             ────►  -175º
          -45º            ─           125º             ────►   170º
           45º            ─           145º             ────►   100º
        29.4803º          ─         -88.6361º          ────►  -118.1164º
        -78.3251º         ─         -159.036º          ────►   -80.7109º
   -70099.74233810938º    ─    29840.67437876723º      ────►  -139.58328312339º
   -165313.6666297357º    ─     33693.9894517456º      ────►   -72.3439185187º
   1174.8380510598456º    ─   -154146.66490124757º     ────►  -161.5029523074156º
   60175.773067955546º    ─    42213.07192354373º      ────►    37.298855588184º

Ring

<lang ring>

  1. Project : Angle difference between two bearings

decimals(4) see "Input in -180 to +180 range:" + nl see getDifference(20.0, 45.0) + nl see getDifference(-45.0, 45.0) + nl see getDifference(-85.0, 90.0) + nl see getDifference(-95.0, 90.0) + nl see getDifference(-45.0, 125.0) + nl see getDifference(-45.0, 145.0) + nl see getDifference(-45.0, 125.0) + nl see getDifference(-45.0, 145.0) + nl see getDifference(29.4803, -88.6381) + nl see getDifference(-78.3251, -159.036) + nl

func getDifference(b1, b2) 

    r = (b2 - b1) % 360.0
    if r >= 180.0
       r = r - 360.0
    end
    return r

</lang> Output: 

Input in -180 to +180 range:
25
90
175
-175
170
-170
170
-170
-118.1184
-80.7109

Ruby

Translation of: C++

<lang ruby>def getDifference(b1, b2) r = (b2 - b1) % 360.0 # Ruby modulus has same sign as divisor, which is positive here, # so no need to consider negative case if r >= 180.0 r -= 360.0 end return r end

if __FILE__ == $PROGRAM_NAME puts "Input in -180 to +180 range" puts getDifference(20.0, 45.0) puts getDifference(-45.0, 45.0) puts getDifference(-85.0, 90.0) puts getDifference(-95.0, 90.0) puts getDifference(-45.0, 125.0) puts getDifference(-45.0, 145.0) puts getDifference(-45.0, 125.0) puts getDifference(-45.0, 145.0) puts getDifference(29.4803, -88.6381) puts getDifference(-78.3251, -159.036)

puts "Input in wider range" puts getDifference(-70099.74233810938, 29840.67437876723) puts getDifference(-165313.6666297357, 33693.9894517456) puts getDifference(1174.8380510598456, -154146.66490124757) puts getDifference(60175.77306795546, 42213.07192354373) end</lang>

Output:
Input in -180 to +180 range
25.0
90.0
175.0
-175.0
170.0
-170.0
170.0
-170.0
-118.11840000000001
-80.71089999999998
Input in wider range
-139.58328312338563
-72.34391851868713
-161.50295230740448
37.29885558826936

Scala

Output:

Best seen running in your browser either by ScalaFiddle (ES aka JavaScript, non JVM) or Scastie (remote JVM).

<lang Scala>object AngleDifference extends App { 

 private def getDifference(b1: Double, b2: Double) = {
   val r = (b2 - b1) % 360.0
   if (r < -180.0) r + 360.0 else if (r >= 180.0) r - 360.0 else r
 }

 println("Input in -180 to +180 range")
 println(getDifference(20.0, 45.0))
 println(getDifference(-45.0, 45.0))
 println(getDifference(-85.0, 90.0))
 println(getDifference(-95.0, 90.0))
 println(getDifference(-45.0, 125.0))
 println(getDifference(-45.0, 145.0))
 println(getDifference(-45.0, 125.0))
 println(getDifference(-45.0, 145.0))
 println(getDifference(29.4803, -88.6381))
 println(getDifference(-78.3251, -159.036))

 println("Input in wider range")
 println(getDifference(-70099.74233810938, 29840.67437876723))
 println(getDifference(-165313.6666297357, 33693.9894517456))
 println(getDifference(1174.8380510598456, -154146.66490124757))
 println(getDifference(60175.77306795546, 42213.07192354373))

}</lang>

Sidef

<lang ruby>func bearingAngleDiff(b1, b2) { 

   (var b = ((b2 - b1 + 720) % 360)) > 180 ? (b - 360) : b

}

printf("%25s %25s %25s\n", "B1", "B2", "Difference") printf("%25s %25s %25s\n", "-"*20, "-"*20, "-"*20)


for b1,b2 in ([ 

                      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
   ].slices(2)

) { 

   printf("%25s %25s %25s\n", b1, b2, bearingAngleDiff(b1, b2))

}</lang>

Output:
                       B1                        B2                Difference
     --------------------      --------------------      --------------------
                       20                        45                        25
                      -45                        45                        90
                      -85                        90                       175
                      -95                        90                      -175
                      -45                       125                       170
                      -45                       145                      -170
                  29.4803                  -88.6381                 -118.1184
                 -78.3251                  -159.036                  -80.7109
       -70099.74233810938         29840.67437876723          -139.58328312339
       -165313.6666297357          33693.9894517456            -72.3439185187
       1174.8380510598456       -154146.66490124757        -161.5029523074156
        60175.77306795546         42213.07192354373            37.29885558827

Tcl

<lang tcl> proc angleDiff {b1 b2} { 

 set angle [::tcl::mathfunc::fmod [expr ($b2 - $b1)] 360]
 if {$angle < -180.0} {
   set angle [expr $angle + 360.0]
 }
 if {$angle >= 180.0} {
   set angle [expr $angle - 360.0]
 }
 return $angle

}

puts "Input in -180 to +180 range" puts [angleDiff 20.0 45.0] puts [angleDiff -45.0 45.0] puts [angleDiff -85.0 90.0] puts [angleDiff -95.0 90.0] puts [angleDiff -45.0 125.0] puts [angleDiff -45.0 145.0] puts [angleDiff -45.0 125.0] puts [angleDiff -45.0 145.0] puts [angleDiff 29.4803 -88.6381] puts [angleDiff -78.3251 -159.036]

puts "Input in wider range" puts [angleDiff -70099.74233810938 29840.67437876723] puts [angleDiff -165313.6666297357 33693.9894517456] puts [angleDiff 1174.8380510598456 -154146.66490124757] puts [angleDiff 60175.77306795546 42213.07192354373] </lang>

Output:
Input in -180 to +180 range
25.0
90.0
175.0
-175.0
170.0
-170.0
170.0
-170.0
-118.1184
-80.7109
Input in wider range
-139.58328312338563
-72.34391851868713
-161.50295230740448
37.29885558826936


VBA

Translation of: Phix

<lang vb>Private Function tx(a As Variant) As String 

   Dim s As String
   s = CStr(Format(a, "0.######"))
   If Right(s, 1) = "," Then
       s = Mid(s, 1, Len(s) - 1) & "       "
   Else
       i = InStr(1, s, ",")
       s = s & String$(6 - Len(s) + i, " ")
   End If
   tx = s

End Function Private Sub test(b1 As Variant, b2 As Variant) 

   Dim diff As Variant
   diff = (b2 - b1) - ((b2 - b1) \ 360) * 360
   diff = diff - IIf(diff > 180, 360, 0)
   diff = diff + IIf(diff < -180, 360, 0)
   Debug.Print Format(tx(b1), "@@@@@@@@@@@@@@@@"); Format(tx(b2), "@@@@@@@@@@@@@@@@@"); Format(tx(diff), "@@@@@@@@@@@@@@@@@")

End Sub Public Sub angle_difference() 

   Debug.Print "       b1               b2             diff"
   Debug.Print "---------------- ---------------- ----------------"
   test 20, 45
   test -45, 45
   test -85, 90
   test -95, 90
   test -45, 125
   test -45, 145
   test 29.4803, -88.6381
   test -78.3251, -159.036
   test -70099.7423381094, 29840.6743787672
   test -165313.666629736, 33693.9894517456
   test 1174.83805105985, -154146.664901248
   test 60175.7730679555, 42213.0719235437

End Sub</lang>

Output:
       b1               b2             diff
---------------- ---------------- ----------------
       20               45               25       
      -45               45               90       
      -85               90              175       
      -95               90             -175       
      -45              125              170       
      -45              145             -170       
       29,4803         -88,6381        -118,1184  
      -78,3251        -159,036          -80,7109  
   -70099,742338     29840,674379      -139,583283
  -165313,66663      33693,989452       -72,343919
     1174,838051   -154146,664901      -161,502952
    60175,773068     42213,071924        37,298856

zkl

Translation of: Perl 6

<lang zkl>fcn bearingAngleDiff(b1,b2){ // -->Float, b1,b2 can be int or float 

 ( (b:=(0.0 + b2 - b1 + 720)%360) > 180 ) and b - 360 or b;

}</lang> <lang zkl>T( 20,45, -45,45, -85,90, -95,90, -45,125, -45,145 ) .pump(Console.println,Void.Read, 

     fcn(b1,b2){ "%.1f\UB0; + %.1f\UB0; = %.1f\UB0;"
                 .fmt(b1,b2,bearingAngleDiff(b1,b2)) });</lang>
Output:
20.0° + 45.0° = 25.0°
-45.0° + 45.0° = 90.0°
-85.0° + 90.0° = 175.0°
-95.0° + 90.0° = -175.0°
-45.0° + 125.0° = 170.0°
-45.0° + 145.0° = -170.0°

References

  1. ↑ [1]
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