Angle difference between two bearings

From Rosetta Code
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[edit]

Translation of: Rexx
*        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
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[edit]

 
# 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)
}
 
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[edit]

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

 
-----------------------------------------------------------------------
-- 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;
 
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[edit]

Returns an angle in (-180,180]; so two opposite bearings have a difference of 180 degrees, which is more natural than -180 degrees.

[0]   D←B1 DIFF B2
[1] D←180+¯360|180+B2-B1
 
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[edit]

012pv1   2      3        4              5         6           7    8
>&:v >859**%:459**1-`#v_ >12g!:12p#v_\-:459**1-`#v_ >.>
>0`#^_8v >859**-^ >859**-^
^:+**95< > ^
 

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[edit]

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

 
#include<stdlib.h>
#include<stdio.h>
#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;
}
 

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++[edit]

#include <cmath>
#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;
}
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#[edit]

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;
 
//
//
//
}
}
}
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[edit]

(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
 

Common Lisp[edit]

 
(defun angle-difference (b1 b2)
(let ((diff (mod (- b2 b1) 360)))
(if (< diff -180)
(incf diff 360)
(if (> diff 180)
(decf diff 360)
diff))))
 
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[edit]

Translation of: Java
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));
}
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#[edit]

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
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

Fortran[edit]

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.
      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

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

Go[edit]

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.

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
}
}
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.

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

Haskell[edit]

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)
]
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[edit]

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

J[edit]

relativeBearing=: (180 -~ 360 | 180 + -~)/"1
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

Java[edit]

Translation of: C++
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));
}
}
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[edit]

ES5[edit]

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

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";
 
}
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[edit]

(() => {
 
// 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');
})();
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[edit]

Works with: Julia version 0.6
Translation of: Python
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
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[edit]

 
/ 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}
 

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[edit]

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.

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()
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[edit]

Translation of: C++
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)
Output:
25
90
175
-175
170
-170
-118.1184
-80.7109
-139.58328
-72.3340
-161.5030
37.29885


Kotlin[edit]

// 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))
}
}
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[edit]

Translation of: Java
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.

NewLISP[edit]

Taken from Racket solution

 
#!/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))
 
Output:
-25
-90
-175
175
-170
170
118.11839999999995
80.71090000000004
139.58328312338563
72.34391851868713
161.50295230740448
-37.29885558826936

Nim[edit]

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)
 
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[edit]

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.

 
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.
 
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[edit]

Perl's built-in modulo is integer-only, so import a suitable one from the POSIX core module

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);
}
 
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[edit]

Works with: Rakudo version 2016.11
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 }
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[edit]

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)
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[edit]

Translation of: C++
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))
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:

from math import (acos, cos, pi, sin)
 
 
# 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)
 
 
# 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)
)
])
)
 
 
# 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)
])))
 
 
# GENERIC ----------------------------------------------
 
# radians :: Float x => Degrees x -> Radians x
def radians(x):
return (pi * x / 180)
 
 
# degrees :: Float x => Radians x -> Degrees x
def degrees(x):
return (180 * x / pi)
 
 
# justifyRight :: Int -> Char -> String -> String
def justifyRight(n):
return lambda cFiller: lambda s: (
((n * cFiller) + s)[-n:]
)
 
 
# unlines :: [String] -> String
def unlines(xs):
return '\n'.join(xs)
 
 
# unwords :: [String] -> String
def unwords(xs):
return ' '.join(xs)
 
 
main()
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[edit]

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

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

REXX[edit]

Some extra coding was added for a better visual presentation;   the angles were centered,   the answers were aligned.

/*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.*/
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[edit]

 
# 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
 

Output:

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

Ruby[edit]

Translation of: C++
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
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[edit]

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

Sidef[edit]

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))
}
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[edit]

 
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]
 
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


zkl[edit]

Translation of: Perl 6
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;
}
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)) });
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]