# Angles (geometric), normalization and conversion

Angles (geometric), normalization and conversion
You are encouraged to solve this task according to the task description, using any language you may know.

This task is about the normalization and/or conversion of (geometric) angles using some common scales.

The angular scales that will be used in this task are:

•   degree
•   mil

Definitions

The angular scales used or referenced here:

•   turn   is a full turn or 360 degrees, also shown as 360º
•   degree   is   1/360   of a turn
•   gradian   is   1/400   of a turn
•   mil   is   1/6400   of a turn
•   radian   is   1/2${\displaystyle \pi }$   of a turn   (or   0.5/${\displaystyle \pi }$   of a turn)

Or, to put it another way,   for a full circle:

•   there are   360   degrees
•   there are   400   gradians
•   there are   6,400   mils
•   there are   2${\displaystyle \pi }$   radians   (roughly equal to 6.283+)

A   mil   is approximately equal to a   milliradian   (which is   1/1000   of a radian).

There is another definition of a   mil   which is   1/1000   of a radian   ─── this definition won't be used in this Rosetta Code task.

Turns   are sometimes known or shown as:

•   turn(s)
•   360 degrees
•   unit circle
•   a (full) circle

Degrees   are sometimes known or shown as:

•   degree(s)
•   deg
•   º       (a symbol)
•   °       (another symbol)

Gradians   are sometimes known or shown as:

•   gon(s)
•   metric degree(s)
•   (Note that   centigrade   was used for 1/100th of a grade, see the note below.)

Mils   are sometimes known or shown as:

•   mil(s)
•   NATO mil(s)

Radians   are sometimes known or shown as:

Notes

In continental Europe, the French term   centigrade   was used for   1/100   of a grad (grade);   this was one reason for the adoption of the term   Celsius   to replace   centigrade   as the name of a temperature scale.

Gradians were commonly used in civil engineering.

Mils were normally used for artillery   (elevations of the gun barrel for ranging).

Positive and negative angles

Although the definition of the measurement of an angle doesn't support the concept of a negative angle,   it's frequently useful to impose a convention that allows positive and negative angular values to represent orientations and/or rotations in opposite directions relative to some reference.   It is this reason that negative angles will keep their sign and not be normalized to positive angles.

Normalization

Normalization   (for this Rosetta Code task)   will keep the same sign,   but it will reduce the magnitude to less than a full circle;   in other words, less than 360º.

Normalization   shouldn't   change   -45º   to   315º,

An angle of   ,   +0º,   0.000000,   or   -0º   should be shown as   .

•   write a function (or equivalent) to do the normalization for each scale
• Suggested names:
• d2d,   g2g,   m2m,   and  r2r
•   write a function (or equivalent) to convert one scale to another
• Suggested names for comparison of different computer language function names:
• d2g,   d2m,   and   d2r   for degrees
• g2d,   g2m,   and   g2r   for gradians
• m2d,   m2g,   and   m2r   for mils
• r2d,   r2g,   and   r2m   for radians
•   normalize all angles used   (except for the "original" or "base" angle)
•   show the angles in every scale and convert them to all other scales
•   show all output here on this page

For the (above) conversions,   use these dozen numbers   (in the order shown):

•   -2   -1   0   1   2   6.2831853   16   57.2957795   359   399   6399   1000000

## 11l

Translation of: Nim
V values = [Float(-2), -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000]

F normd(x) {R fmod(x, 360)}
F normg(x) {R fmod(x, 400)}
F normm(x) {R fmod(x, 6400)}
F normr(x) {R fmod(x, (2 * math:pi))}

F d2g(x) {R normd(x) * 10 / 9}
F d2m(x) {R normd(x) * 160 / 9}
F d2r(x) {R normd(x) * math:pi / 180}

F g2d(x) {R normg(x) * 9 / 10}
F g2m(x) {R normg(x) * 16}
F g2r(x) {R normg(x) * math:pi / 200}

F m2d(x) {R normm(x) * 9 / 160}
F m2g(x) {R normm(x) / 16}
F m2r(x) {R normm(x) * math:pi / 3200}

F r2d(x) {R normr(x) * 180 / math:pi}
F r2g(x) {R normr(x) * 200 / math:pi}
F r2m(x) {R normr(x) * 3200 / math:pi}

print(‘───────────────────────────────────────────────────────────────────────────────────’)
L(val) values
print(‘#7.7  #7.7  #7.7  #7.7  #7.7’.format(val, normd(val), d2g(val), d2m(val), d2r(val)))

print()
print(‘───────────────────────────────────────────────────────────────────────────────────’)
L(val) values
print(‘#7.7  #7.7  #7.7  #7.7  #7.7’.format(val, normg(val), g2d(val), g2m(val), g2r(val)))

print()
print(‘───────────────────────────────────────────────────────────────────────────────────’)
L(val) values
print(‘#7.7  #7.7  #7.7  #7.7  #7.7’.format(val, normm(val), m2d(val), m2g(val), m2r(val)))

print()
print(‘───────────────────────────────────────────────────────────────────────────────────’)
L(val) values
print(‘#7.7  #7.7  #7.7  #7.7  #7.7’.format(val, normr(val), r2d(val), r2g(val), r2m(val)))
Output:
       Degrees        Normalized         Gradians          Mils            Radians
───────────────────────────────────────────────────────────────────────────────────
-2.0000000       -2.0000000       -2.2222222      -35.5555556       -0.0349066
-1.0000000       -1.0000000       -1.1111111      -17.7777778       -0.0174533
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000        1.1111111       17.7777778        0.0174533
2.0000000        2.0000000        2.2222222       35.5555556        0.0349066
6.2831853        6.2831853        6.9813170      111.7010720        0.1096623
16.0000000       16.0000000       17.7777778      284.4444444        0.2792527
57.2957795       57.2957795       63.6619772     1018.5916356        1.0000000
359.0000000      359.0000000      398.8888889     6382.2222222        6.2657320
399.0000000       39.0000000       43.3333333      693.3333333        0.6806784
6399.0000000      279.0000000      310.0000000     4960.0000000        4.8694686
1000000.0000000      280.0000000      311.1111111     4977.7777778        4.8869219

───────────────────────────────────────────────────────────────────────────────────
-2.0000000       -2.0000000       -1.8000000      -32.0000000       -0.0314159
-1.0000000       -1.0000000       -0.9000000      -16.0000000       -0.0157080
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000        0.9000000       16.0000000        0.0157080
2.0000000        2.0000000        1.8000000       32.0000000        0.0314159
6.2831853        6.2831853        5.6548668      100.5309648        0.0986960
16.0000000       16.0000000       14.4000000      256.0000000        0.2513274
57.2957795       57.2957795       51.5662015      916.7324720        0.9000000
359.0000000      359.0000000      323.1000000     5744.0000000        5.6391588
399.0000000      399.0000000      359.1000000     6384.0000000        6.2674773
6399.0000000      399.0000000      359.1000000     6384.0000000        6.2674773
1000000.0000000        0.0000000        0.0000000        0.0000000        0.0000000

───────────────────────────────────────────────────────────────────────────────────
-2.0000000       -2.0000000       -0.1125000       -0.1250000       -0.0019635
-1.0000000       -1.0000000       -0.0562500       -0.0625000       -0.0009817
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000        0.0562500        0.0625000        0.0009817
2.0000000        2.0000000        0.1125000        0.1250000        0.0019635
6.2831853        6.2831853        0.3534292        0.3926991        0.0061685
16.0000000       16.0000000        0.9000000        1.0000000        0.0157080
57.2957795       57.2957795        3.2228876        3.5809862        0.0562500
359.0000000      359.0000000       20.1937500       22.4375000        0.3524474
399.0000000      399.0000000       22.4437500       24.9375000        0.3917173
6399.0000000     6399.0000000      359.9437500      399.9375000        6.2822036
1000000.0000000     1600.0000000       90.0000000      100.0000000        1.5707963

───────────────────────────────────────────────────────────────────────────────────
-2.0000000       -2.0000000     -114.5915590     -127.3239545    -2037.1832716
-1.0000000       -1.0000000      -57.2957795      -63.6619772    -1018.5916358
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000       57.2957795       63.6619772     1018.5916358
2.0000000        2.0000000      114.5915590      127.3239545     2037.1832716
6.2831853        6.2831853      359.9999996      399.9999995     6399.9999927
16.0000000        3.4336294      196.7324722      218.5916358     3497.4661726
57.2957795        0.7471117       42.8063493       47.5626103      761.0017647
359.0000000        0.8584375       49.1848452       54.6498280      874.3972479
399.0000000        3.1593256      181.0160257      201.1289175     3218.0626795
6399.0000000        2.7173573      155.6931042      172.9923380     2767.8774082
1000000.0000000        5.9256211      339.5130823      377.2367581     6035.7881302


## ALGOL 68

Translation of: 11l – using an array of procedures to simplify the output
BEGIN # Angles (geometric), normalization and conversion - translated from the 11l sample #

[]REAL values = ( -2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000 );

PROC norm = ( REAL x, y )REAL:
BEGIN
INT  n  = ENTIER ( ABS x / ABS y );
REAL r := x - ( n * y );
r
END # norm # ;

PROC normd = ( REAL x )REAL: norm( x,  360 );
PROC normg = ( REAL x )REAL: norm( x,  400 );
PROC normm = ( REAL x )REAL: norm( x, 6400 );
PROC normr = ( REAL x )REAL: norm( x, 2 * pi );

PROC d2g = ( REAL x )REAL: normd( x ) * 10 / 9;
PROC d2m = ( REAL x )REAL: normd( x ) * 160 / 9;
PROC d2r = ( REAL x )REAL: normd( x ) * pi / 180;

PROC g2d = ( REAL x )REAL: normg( x ) * 9 / 10;
PROC g2m = ( REAL x )REAL: normg( x ) * 16;
PROC g2r = ( REAL x )REAL: normg( x ) * pi / 200;

PROC m2d = ( REAL x )REAL: normm( x ) * 9 / 160;
PROC m2g = ( REAL x )REAL: normm( x ) / 16;
PROC m2r = ( REAL x )REAL: normm( x ) * pi / 3200;

PROC r2d = ( REAL x )REAL: normr( x ) *  180 / pi;
PROC r2g = ( REAL x )REAL: normr( x ) *  200 / pi;
PROC r2m = ( REAL x )REAL: normr( x ) * 3200 / pi;

STRING underline = "----------------------------------------------------------------------------------";
PROC f7d7 = ( REAL v )STRING: fixed( v, -15, 7 );

PROC print values = ( STRING heading, []PROC(REAL)REAL f )VOID:
BEGIN
print( ( heading, newline ) );
print( ( underline, newline ) );
FOR i FROM LWB values TO UPB values DO
REAL v = values[ i ];
print( ( f7d7( v ) ) );
FOR p FROM LWB f TO UPB f DO
print( ( "  ", f7d7( f[ p ]( v ) ) ) )
OD;
print( ( newline ) )
OD;
print( ( newline ) )
END # print values # ;

print values( "       Degrees        Normalized         Gradians          Mils            Radians"
, ( normd, d2g, d2m, d2r )
);
print values( "      Gradians        Normalized         Degrees           Mils            Radians"
, ( normg, g2d, g2m, g2r )
);
print values( "        Mils          Normalized         Degrees         Gradians          Radians"
, ( normm, m2d, m2g, m2r )
);
print values( "       Radians        Normalized         Degrees         Gradians          Mils"
, ( normr, r2d, r2g, r2m )
)

END
Output:
       Degrees        Normalized         Gradians          Mils            Radians
----------------------------------------------------------------------------------
-2.0000000       -2.0000000       -2.2222222      -35.5555556       -0.0349066
-1.0000000       -1.0000000       -1.1111111      -17.7777778       -0.0174533
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000        1.1111111       17.7777778        0.0174533
2.0000000        2.0000000        2.2222222       35.5555556        0.0349066
6.2831853        6.2831853        6.9813170      111.7010720        0.1096623
16.0000000       16.0000000       17.7777778      284.4444444        0.2792527
57.2957795       57.2957795       63.6619772     1018.5916356        1.0000000
359.0000000      359.0000000      398.8888889     6382.2222222        6.2657320
399.0000000       39.0000000       43.3333333      693.3333333        0.6806784
6399.0000000      279.0000000      310.0000000     4960.0000000        4.8694686
1000000.0000000      280.0000000      311.1111111     4977.7777778        4.8869219

----------------------------------------------------------------------------------
-2.0000000       -2.0000000       -1.8000000      -32.0000000       -0.0314159
-1.0000000       -1.0000000       -0.9000000      -16.0000000       -0.0157080
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000        0.9000000       16.0000000        0.0157080
2.0000000        2.0000000        1.8000000       32.0000000        0.0314159
6.2831853        6.2831853        5.6548668      100.5309648        0.0986960
16.0000000       16.0000000       14.4000000      256.0000000        0.2513274
57.2957795       57.2957795       51.5662015      916.7324720        0.9000000
359.0000000      359.0000000      323.1000000     5744.0000000        5.6391588
399.0000000      399.0000000      359.1000000     6384.0000000        6.2674773
6399.0000000      399.0000000      359.1000000     6384.0000000        6.2674773
1000000.0000000        0.0000000        0.0000000        0.0000000        0.0000000

----------------------------------------------------------------------------------
-2.0000000       -2.0000000       -0.1125000       -0.1250000       -0.0019635
-1.0000000       -1.0000000       -0.0562500       -0.0625000       -0.0009817
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000        0.0562500        0.0625000        0.0009817
2.0000000        2.0000000        0.1125000        0.1250000        0.0019635
6.2831853        6.2831853        0.3534292        0.3926991        0.0061685
16.0000000       16.0000000        0.9000000        1.0000000        0.0157080
57.2957795       57.2957795        3.2228876        3.5809862        0.0562500
359.0000000      359.0000000       20.1937500       22.4375000        0.3524474
399.0000000      399.0000000       22.4437500       24.9375000        0.3917173
6399.0000000     6399.0000000      359.9437500      399.9375000        6.2822036
1000000.0000000     1600.0000000       90.0000000      100.0000000        1.5707963

----------------------------------------------------------------------------------
-2.0000000       -2.0000000     -114.5915590     -127.3239545    -2037.1832716
-1.0000000       -1.0000000      -57.2957795      -63.6619772    -1018.5916358
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000       57.2957795       63.6619772     1018.5916358
2.0000000        2.0000000      114.5915590      127.3239545     2037.1832716
6.2831853        6.2831853      359.9999996      399.9999995     6399.9999927
16.0000000        3.4336294      196.7324722      218.5916358     3497.4661726
57.2957795        0.7471117       42.8063493       47.5626103      761.0017647
359.0000000        0.8584375       49.1848452       54.6498280      874.3972479
399.0000000        3.1593256      181.0160257      201.1289175     3218.0626795
6399.0000000        2.7173573      155.6931042      172.9923380     2767.8774082
1000000.0000000        5.9256211      339.5130823      377.2367581     6035.7881302


## ALGOL W

Translation of: ALGOL 68 – which was a translation of 11l

Algol W doesn't have arrays of procedures so separate parameters for the four functions are used.

begin % Angles (geometric), normalization and conversion                      %
%      - translation of the Algol 68 translation of the 11l sample      %

real procedure norm ( real value x, y ) ;
begin
integer n;
n := entier( abs x / abs y );
x - ( n * y )
end norm ;

real procedure normd ( real value x ) ; norm( x,  360 );
real procedure normg ( real value x ) ; norm( x,  400 );
real procedure normm ( real value x ) ; norm( x, 6400 );
real procedure normr ( real value x ) ; norm( x, 2 * pi );

real procedure d2g ( real value x ) ; normd( x ) * 10 / 9;
real procedure d2m ( real value x ) ; normd( x ) * 160 / 9;
real procedure d2r ( real value x ) ; normd( x ) * pi / 180;

real procedure g2d ( real value x ) ; normg( x ) * 9 / 10;
real procedure g2m ( real value x ) ; normg( x ) * 16;
real procedure g2r ( real value x ) ; normg( x ) * pi / 200;

real procedure m2d ( real value x ) ; normm( x ) * 9 / 160;
real procedure m2g ( real value x ) ; normm( x ) / 16;
real procedure m2r ( real value x ) ; normm( x ) * pi / 3200;

real procedure r2d ( real value x ) ; normr( x ) *  180 / pi;
real procedure r2g ( real value x ) ; normr( x ) *  200 / pi;
real procedure r2m ( real value x ) ; normr( x ) * 3200 / pi;

procedure writeonF7d7 ( real value v ) ; writeon( r_format := "A", r_w := 15, r_d := 7, s_w := 0, v );

procedure printValues ( string(82) value heading
; real procedure f1, f2, f3, f4
; real array values( * )
; integer value numberOfValues
) ;
begin
write( "----------------------------------------------------------------------------------" );
for i := 1 until numberOfValues do begin
real v;
v := values( i );
write();
writeonF7d7( v );
writeon( "  " ); writeonF7d7( f1( v ) ); writeon( "  " ); writeonF7d7( f2( v ) );
writeon( "  " ); writeonF7d7( f3( v ) ); writeon( "  " ); writeonF7d7( f4( v ) );
end for_i ;
write()
end printValues ;

real array values ( 1 :: 12 );
values(  1 ) := -2; values( 2 ) := -1; values( 3 ) := 0; values( 4 ) := 1; values( 5 ) := 2;
values(  6 ) := 6.2831853; values( 7 ) := 16; values( 8 ) := 57.2957795; values( 9 ) := 359;
values( 10 ) := 399; values( 11 ) := 6399; values( 12 ) := 1000000;

printValues( "       Degrees        Normalized         Gradians          Mils            Radians"
, normd, d2g, d2m, d2r, values, 12
);
printValues( "      Gradians        Normalized         Degrees           Mils            Radians"
, normg, g2d, g2m, g2r, values, 12
);
printValues( "        Mils          Normalized         Degrees         Gradians          Radians"
, normm, m2d, m2g, m2r, values, 12
);
printValues( "       Radians        Normalized         Degrees         Gradians          Mils"
, normr, r2d, r2g, r2m, values, 12
)

end.
Output:
       Degrees        Normalized         Gradians          Mils            Radians
----------------------------------------------------------------------------------
-2.0000000       -2.0000000       -2.2222222      -35.5555556       -0.0349066
-1.0000000       -1.0000000       -1.1111111      -17.7777778       -0.0174533
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000        1.1111111       17.7777778        0.0174533
2.0000000        2.0000000        2.2222222       35.5555556        0.0349066
6.2831853        6.2831853        6.9813170      111.7010720        0.1096623
16.0000000       16.0000000       17.7777778      284.4444444        0.2792527
57.2957795       57.2957795       63.6619772     1018.5916356        1.0000000
359.0000000      359.0000000      398.8888889     6382.2222222        6.2657320
399.0000000       39.0000000       43.3333333      693.3333333        0.6806784
6399.0000000      279.0000000      310.0000000     4960.0000000        4.8694686
1000000.0000000      280.0000000      311.1111111     4977.7777778        4.8869219

----------------------------------------------------------------------------------
-2.0000000       -2.0000000       -1.8000000      -32.0000000       -0.0314159
-1.0000000       -1.0000000       -0.9000000      -16.0000000       -0.0157080
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000        0.9000000       16.0000000        0.0157080
2.0000000        2.0000000        1.8000000       32.0000000        0.0314159
6.2831853        6.2831853        5.6548668      100.5309648        0.0986960
16.0000000       16.0000000       14.4000000      256.0000000        0.2513274
57.2957795       57.2957795       51.5662016      916.7324720        0.9000000
359.0000000      359.0000000      323.1000000     5744.0000000        5.6391588
399.0000000      399.0000000      359.1000000     6384.0000000        6.2674773
6399.0000000      399.0000000      359.1000000     6384.0000000        6.2674773
1000000.0000000        0.0000000        0.0000000        0.0000000        0.0000000

----------------------------------------------------------------------------------
-2.0000000       -2.0000000       -0.1125000       -0.1250000       -0.0019635
-1.0000000       -1.0000000       -0.0562500       -0.0625000       -0.0009817
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000        0.0562500        0.0625000        0.0009817
2.0000000        2.0000000        0.1125000        0.1250000        0.0019635
6.2831853        6.2831853        0.3534292        0.3926991        0.0061685
16.0000000       16.0000000        0.9000000        1.0000000        0.0157080
57.2957795       57.2957795        3.2228876        3.5809862        0.0562500
359.0000000      359.0000000       20.1937500       22.4375000        0.3524474
399.0000000      399.0000000       22.4437500       24.9375000        0.3917173
6399.0000000     6399.0000000      359.9437500      399.9375000        6.2822036
1000000.0000000     1600.0000000       90.0000000      100.0000000        1.5707963

----------------------------------------------------------------------------------
-2.0000000       -2.0000000     -114.5915590     -127.3239545    -2037.1832716
-1.0000000       -1.0000000      -57.2957795      -63.6619772    -1018.5916358
0.0000000        0.0000000        0.0000000        0.0000000        0.0000000
1.0000000        1.0000000       57.2957795       63.6619772     1018.5916358
2.0000000        2.0000000      114.5915590      127.3239545     2037.1832716
6.2831853        6.2831853      359.9999996      399.9999995     6399.9999927
16.0000000        3.4336294      196.7324722      218.5916358     3497.4661726
57.2957795        0.7471117       42.8063493       47.5626103      761.0017647
359.0000000        0.8584375       49.1848452       54.6498280      874.3972479
399.0000000        3.1593256      181.0160257      201.1289175     3218.0626795
6399.0000000        2.7173573      155.6931042      172.9923380     2767.8774082
1000000.0000000        5.9256211      339.5130823      377.2367581     6035.7881302


## AutoHotkey

testAngles := [-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000]

result .= "Degrees    Degrees    Gradians    Mils    Radiansn"
for i, a in testAngles
result .= a "t" Deg2Deg(a) "t" Deg2Grad(a) "t" Deg2Mil(a) "t" Deg2Rad(a) "n"
result .= "nGradians    Degrees    Gradians    Mils    Radiansn"
for i, a in testAngles
result .= a "t" Grad2Deg(a) "t" Grad2Grad(a) "t" Grad2Mil(a) "t" Grad2Rad(a) "n"
result .= "nMills    Degrees    Gradians    Mils    Radiansn"
for i, a in testAngles
result .= a "t" Mil2Deg(a) "t" Mil2Grad(a) "t" Mil2Mil(a) "t" Mil2Rad(a) "n"
result .= "nRadians    Degrees    Gradians    Mils    Radiansn"
for i, a in testAngles
result .= a "t" Rad2Deg(a) "t" Rad2Grad(a) "t" Rad2Mil(a) "t" Rad2Rad(a) "n"

MsgBox, 262144, , % result
return
;-------------------------------------------------------
Deg2Deg(Deg){
return Mod(Deg, 360)
}
return Deg2Deg(Deg) * 400 / 360
}
Deg2Mil(Deg){
return Deg2Deg(Deg) * 6400 / 360
}
return Deg2Deg(Deg) * (π:=3.141592653589793) / 180
}
;-------------------------------------------------------
}
}
}
}
;-------------------------------------------------------
Mil2Mil(Mil){
return Mod(Mil, 6400)
}
Mil2Deg(Mil){
return Mil2Mil(Mil) * 360 / 6400
}
return Mil2Mil(Mil) * 400 / 6400
}
return Mil2Mil(Mil) * (π:=3.141592653589793) / 3200
}
;-------------------------------------------------------
}
}
}
}
;-------------------------------------------------------

Output:
Degrees		Degrees		Gradians	Mils		Radians
-2		-2		-2.222222	-35.555556	-0.034907
-1		-1		-1.111111	-17.777778	-0.017453
0		0		0.000000	0.000000	0.000000
1		1		1.111111	17.777778	0.017453
2		2		2.222222	35.555556	0.034907
6.2831853	6.283185	6.981317	111.701072	0.109662
16		16		17.777778	284.444444	0.279253
57.2957795	57.295780	63.661977	1018.591636	1.000000
359		359		398.888889	6382.222222	6.265732
399		39		43.333333	693.333333	0.680678
6399		279		310.000000	4960.000000	4.869469
1000000		280		311.111111	4977.777778	4.886922

-2		-1.800000	-2		-32.000000	-0.031416
-1		-0.900000	-1		-16.000000	-0.015708
0		0.000000	0		0.000000	0.000000
1		0.900000	1		16.000000	0.015708
2		1.800000	2		32.000000	0.031416
6.2831853	5.654867	6.283185	100.530965	0.098696
16		14.400000	16		256.000000	0.251327
57.2957795	51.566202	57.295780	916.732472	0.900000
359		323.100000	359		5744.000000	5.639159
399		359.100000	399		6384.000000	6.267477
6399		359.100000	399		6384.000000	6.267477
1000000		0.000000	0		0.000000	0.000000

-2		-0.112500	-0.125000	-2		-0.001963
-1		-0.056250	-0.062500	-1		-0.000982
0		0.000000	0.000000	0		0.000000
1		0.056250	0.062500	1		0.000982
2		0.112500	0.125000	2		0.001963
6.2831853	0.353429	0.392699	6.283185	0.006169
16		0.900000	1.000000	16		0.015708
57.2957795	3.222888	3.580986	57.295780	0.056250
359		20.193750	22.437500	359		0.352447
399		22.443750	24.937500	399		0.391717
6399		359.943750	399.937500	6399		6.282204
1000000		90.000000	100.000000	1600		1.570796

-2		-114.591559	-127.323954	-2037.183272	-2.000000
-1		-57.295780	-63.661977	-1018.591636	-1.000000
0		0.000000	0.000000	0.000000	0.000000
1		57.295780	63.661977	1018.591636	1.000000
2		114.591559	127.323954	2037.183272	2.000000
6.2831853	360.000000	400.000000	6399.999993	6.283185
16		196.732472	218.591636	3497.466173	3.433629
57.2957795	42.806349	47.562610	761.001765	0.747112
359		49.184845	54.649828	874.397248	0.858437
399		181.016026	201.128917	3218.062679	3.159326
6399		155.693104	172.992338	2767.877408	2.717357
1000000		339.513082	377.236758	6035.788130	5.925621

## AWK

# syntax: GAWK -f ANGLES_(GEOMETRIC)_NORMALIZATION_AND_CONVERSION.AWK
# gawk starts showing discrepancies at test case number 7 when compared with C#
BEGIN {
pi = atan2(0,-1)
data_leng = split("-2,-1,0,1,2,6.2831853,16,57.2957795,359,399,6399,1000000",data_arr,",")
printf("%-10s %-10s %-8s %-12s %-12s %-12s %-12s test#\n","angle","normalized","unit","degrees","gradians","mils","radians")
for (a=1; a<=data_leng; a++) {
angle = data_arr[a]
arr["degree"]  = normalize(angle,360)
arr["mil"]     = normalize(angle,6400)
print("") # optional blank line between groupings
for (b=1; b<=unit_leng; b++) {
key1 = unit_arr[b]
printf("%-10s %-10s %-8s",angle,arr[key1],unit_arr[b])
for (c=1; c<=unit_leng; c++) {
key2 = unit_arr[c]
func_name = sprintf("%s2%s",key1,key2)
printf(" %-12s",(key1 == key2) ? arr[key2] : @func_name(arr[key2]))
}
printf(" %d\n",a)
}
}
#   normalize_usage_stats()
exit(0)
}
function normalize(angle,n,  a) {
a = angle
profile_arr[a][n]["+"] = 0
profile_arr[a][n]["-"] = 0
while (angle <= -n) { angle += n ; profile_arr[a][n]["+"]++ }
while (angle >= n)  { angle -= n ; profile_arr[a][n]["-"]++ }
return(angle)
}
function normalize_usage_stats(  a,b,c,n,total) {
print("")
PROCINFO["sorted_in"] = "@ind_num_asc"
for (a in profile_arr) {
for (b in profile_arr[a]) {
for (c in profile_arr[a][b]) {
n = profile_arr[a][b][c]
if (n == 0) { continue }
printf("%10s %10s %1s %7d\n",a,b,c,n)
total += n
}
}
}
printf("%31d total\n",total)
}
function degree2gradian(angle) { return(angle * 10 / 9) }
function degree2mil(angle) { return(angle * 160 / 9) }
function degree2radian(angle) { return(angle * pi / 180) }
function gradian2degree(angle) { return(angle * 9 / 10) }
function gradian2mil(angle) { return(angle * 16) }
function gradian2radian(angle) { return(angle * pi / 200) }
function mil2degree(angle) { return(angle * 9 / 160) }
function mil2gradian(angle) { return(angle / 16) }
function mil2radian(angle) { return(angle * pi / 3200) }
function radian2degree(angle) { return(angle * 180 / pi) }
function radian2gradian(angle) { return(angle * 200 / pi) }
function radian2mil(angle) { return(angle * 3200 / pi) }

Output:
angle      normalized unit     degrees      gradians     mils         radians      test#

-2         -2         degree   -2           -2.22222     -35.5556     -0.0349066   1
-2         -2         gradian  -1.8         -2           -32          -0.0314159   1
-2         -2         mil      -0.1125      -0.125       -2           -0.0019635   1
-2         -2         radian   -114.592     -127.324     -2037.18     -2           1

-1         -1         degree   -1           -1.11111     -17.7778     -0.0174533   2
-1         -1         gradian  -0.9         -1           -16          -0.015708    2
-1         -1         mil      -0.05625     -0.0625      -1           -0.000981748 2
-1         -1         radian   -57.2958     -63.662      -1018.59     -1           2

0          0          degree   0            0            0            0            3
0          0          gradian  0            0            0            0            3
0          0          mil      0            0            0            0            3
0          0          radian   0            0            0            0            3

1          1          degree   1            1.11111      17.7778      0.0174533    4
1          1          gradian  0.9          1            16           0.015708     4
1          1          mil      0.05625      0.0625       1            0.000981748  4
1          1          radian   57.2958      63.662       1018.59      1            4

2          2          degree   2            2.22222      35.5556      0.0349066    5
2          2          gradian  1.8          2            32           0.0314159    5
2          2          mil      0.1125       0.125        2            0.0019635    5
2          2          radian   114.592      127.324      2037.18      2            5

6.2831853  6.2831853  degree   6.2831853    6.98132      111.701      0.109662     6
6.2831853  6.2831853  gradian  5.65487      6.2831853    100.531      0.098696     6
6.2831853  6.2831853  mil      0.353429     0.392699     6.2831853    0.0061685    6
6.2831853  6.2831853  radian   360          400          6400         6.2831853    6

16         16         degree   16           17.7778      284.444      0.0599281    7
16         16         gradian  14.4         16           256          0.0539353    7
16         16         mil      0.9          1            16           0.00337096   7
16         3.43363    radian   916.732      1018.59      16297.5      3.43363      7

57.2957795 57.2957795 degree   57.2957795   63.662       1018.59      0.0130396    8
57.2957795 57.2957795 gradian  51.5662      57.2957795   916.732      0.0117356    8
57.2957795 57.2957795 mil      3.22289      3.58099      57.2957795   0.000733475  8
57.2957795 0.747112   radian   3282.81      3647.56      58361        0.747112     8

359        359        degree   359          398.889      6382.22      0.0149826    9
359        359        gradian  323.1        359          5744         0.0134843    9
359        359        mil      20.1938      22.4375      359          0.000842769  9
359        0.858437   radian   20569.2      22854.6      365674       0.858437     9

399        39         degree   39           443.333      7093.33      0.0551406    10
399        399        gradian  35.1         399          6384         0.0496266    10
399        399        mil      2.19375      24.9375      399          0.00310166   10
399        3.15933    radian   2234.54      25401.1      406418       3.15933      10

6399       279        degree   279          443.333      113760       0.0474268    11
6399       399        gradian  251.1        399          102384       0.0426841    11
6399       6399       mil      15.6937      24.9375      6399         0.00266776   11
6399       2.71736    radian   15985.5      25401.1      6.51797e+006 2.71736      11

1000000    280        degree   280          0            28444.4      0.103422     12
1000000    0          gradian  252          0            25600        0.0930795    12
1000000    1600       mil      15.75        0            1600         0.00581747   12
1000000    5.92562    radian   16042.8      0            1.62975e+006 5.92562      12


## BBC BASIC

      MODE 15 REM Suitable sized output window so that all output fits neatly
DEF FNMod(a, b) WHILE a >= b a-=b ENDWHILE =a REM Floating point mod

DEF FNd2d(a) = FNMod(a, 360)
DEF FNg2g(a) = FNMod(a, 400)
DEF FNm2m(a) = FNMod(a, 6400)
DEF FNr2r(a) = FNMod(a, 2 * PI)

DEF FNd2g(a) = FNd2d(a) * 10 / 9
DEF FNd2m(a) = FNd2d(a) * 160 / 9
DEF FNd2r(a) = RAD(FNd2d(a))

DEF FNg2d(a) = FNg2g(a) * 9 / 10
DEF FNg2m(a) = FNg2g(a) * 16
DEF FNg2r(a) = FNg2g(a) * PI / 200

DEF FNm2d(a) = FNm2m(a) * 9 / 160
DEF FNm2g(a) = FNm2m(a) / 16
DEF FNm2r(a) = FNm2m(a) * PI / 3200

DEF FNr2d(a) = DEG(FNr2r(a))
DEF FNr2g(a) = FNr2r(a) * 200 / PI
DEF FNr2m(a) = FNr2r(a) * 3200 / PI

@%=&02070F
Dash75$=STRING$(75, "-")

PRINT TAB(0,  0) "       Degrees      Normalized      Gradians         Mils          Radians"'Dash75$PRINT TAB(0, 15) " Gradians Normalized Degrees Mils Radians"'Dash75$
PRINT TAB(0, 30) "        Mils        Normalized       Degrees       Gradians        Radians"'Dash75$PRINT TAB(0, 45) " Radians Normalized Degrees Gradians Mils "'Dash75$

FOR I%=1 TO 12
PRINT TAB(0,  1+I%) Angle, FNd2d(Angle), FNd2g(Angle), FNd2m(Angle), FNd2r(Angle)
PRINT TAB(0, 16+I%) Angle, FNg2g(Angle), FNg2d(Angle), FNg2m(Angle), FNg2r(Angle)
PRINT TAB(0, 31+I%) Angle, FNm2m(Angle), FNm2d(Angle), FNm2g(Angle), FNm2r(Angle)
PRINT TAB(0, 46+I%) Angle, FNr2r(Angle), FNr2d(Angle), FNr2g(Angle), FNr2m(Angle)
NEXT

DATA -2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000

Output:
       Degrees      Normalized      Gradians         Mils          Radians
---------------------------------------------------------------------------
-2.0000000     -2.0000000     -2.2222222    -35.5555556     -0.0349066
-1.0000000     -1.0000000     -1.1111111    -17.7777778     -0.0174533
0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
1.0000000      1.0000000      1.1111111     17.7777778      0.0174533
2.0000000      2.0000000      2.2222222     35.5555556      0.0349066
6.2831853      6.2831853      6.9813170    111.7010720      0.1096623
16.0000000     16.0000000     17.7777778    284.4444444      0.2792527
57.2957795     57.2957795     63.6619772   1018.5916356      1.0000000
359.0000000    359.0000000    398.8888889   6382.2222222      6.2657320
399.0000000     39.0000000     43.3333333    693.3333333      0.6806784
6399.0000000    279.0000000    310.0000000   4960.0000000      4.8694686
1000000.0000000    280.0000000    311.1111111   4977.7777778      4.8869219

---------------------------------------------------------------------------
-2.0000000     -2.0000000     -1.8000000    -32.0000000     -0.0314159
-1.0000000     -1.0000000     -0.9000000    -16.0000000     -0.0157080
0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
1.0000000      1.0000000      0.9000000     16.0000000      0.0157080
2.0000000      2.0000000      1.8000000     32.0000000      0.0314159
6.2831853      6.2831853      5.6548668    100.5309648      0.0986960
16.0000000     16.0000000     14.4000000    256.0000000      0.2513274
57.2957795     57.2957795     51.5662016    916.7324720      0.9000000
359.0000000    359.0000000    323.1000000   5744.0000000      5.6391588
399.0000000    399.0000000    359.1000000   6384.0000000      6.2674773
6399.0000000    399.0000000    359.1000000   6384.0000000      6.2674773
1000000.0000000      0.0000000      0.0000000      0.0000000      0.0000000

---------------------------------------------------------------------------
-2.0000000     -2.0000000     -0.1125000     -0.1250000     -0.0019635
-1.0000000     -1.0000000     -0.0562500     -0.0625000     -0.0009817
0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
1.0000000      1.0000000      0.0562500      0.0625000      0.0009817
2.0000000      2.0000000      0.1125000      0.1250000      0.0019635
6.2831853      6.2831853      0.3534292      0.3926991      0.0061685
16.0000000     16.0000000      0.9000000      1.0000000      0.0157080
57.2957795     57.2957795      3.2228876      3.5809862      0.0562500
359.0000000    359.0000000     20.1937500     22.4375000      0.3524474
399.0000000    399.0000000     22.4437500     24.9375000      0.3917173
6399.0000000   6399.0000000    359.9437500    399.9375000      6.2822036
1000000.0000000   1600.0000000     90.0000000    100.0000000      1.5707963

---------------------------------------------------------------------------
-2.0000000     -2.0000000   -114.5915590   -127.3239545  -2037.1832716
-1.0000000     -1.0000000    -57.2957795    -63.6619772  -1018.5916358
0.0000000      0.0000000      0.0000000      0.0000000      0.0000000
1.0000000      1.0000000     57.2957795     63.6619772   1018.5916358
2.0000000      2.0000000    114.5915590    127.3239545   2037.1832716
6.2831853      6.2831853    359.9999996    399.9999995   6399.9999927
16.0000000      3.4336294    196.7324722    218.5916358   3497.4661726
57.2957795      0.7471117     42.8063493     47.5626103    761.0017647
359.0000000      0.8584375     49.1848452     54.6498280    874.3972479
399.0000000      3.1593256    181.0160257    201.1289175   3218.0626795
6399.0000000      2.7173573    155.6931042    172.9923380   2767.8774082
1000000.0000000      5.9256211    339.5130824    377.2367582   6035.7881314

## C

#define PI 3.141592653589793
#define TWO_PI 6.283185307179586

double normalize2deg(double a) {
while (a < 0) a += 360;
while (a >= 360) a -= 360;
return a;
}
double normalize2grad(double a) {
while (a < 0) a += 400;
while (a >= 400) a -= 400;
return a;
}
double normalize2mil(double a) {
while (a < 0) a += 6400;
while (a >= 6400) a -= 6400;
return a;
}
double normalize2rad(double a) {
while (a < 0) a += TWO_PI;
while (a >= TWO_PI) a -= TWO_PI;
return a;
}

double deg2grad(double a) {return a * 10 / 9;}
double deg2mil(double a) {return a * 160 / 9;}
double deg2rad(double a) {return a * PI / 180;}

double grad2deg(double a) {return a * 9 / 10;}
double grad2mil(double a) {return a * 16;}
double grad2rad(double a) {return a * PI / 200;}

double mil2deg(double a) {return a * 9 / 160;}
double mil2grad(double a) {return a / 16;}
double mil2rad(double a) {return a * PI / 3200;}

double rad2deg(double a) {return a * 180 / PI;}
double rad2grad(double a) {return a * 200 / PI;}
double rad2mil(double a) {return a * 3200 / PI;}


## C#

using System;

public static class Angles
{
public static void Main() => Print(-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 6399, 1_000_000);

public static void Print(params double[] angles) {
string[] names = { "Degrees", "Gradians", "Mils", "Radians" };
Func<double, double> rnd = a => Math.Round(a, 4);
Func<double, double>[] normal = { NormalizeDeg, NormalizeGrad, NormalizeMil, NormalizeRad };

Func<double, double>[,] convert = {
{ a => a, DegToGrad, DegToMil, DegToRad },
{ MilToDeg, MilToGrad, a => a, MilToRad },
};

Console.WriteLine($@"{"Angle",-12}{"Normalized",-12}{"Unit",-12}{ "Degrees",-12}{"Gradians",-12}{"Mils",-12}{"Radians",-12}"); foreach (double angle in angles) { for (int i = 0; i < 4; i++) { double nAngle = normal[i](angle); Console.WriteLine($@"{
rnd(angle),-12}{
rnd(nAngle),-12}{
names[i],-12}{
rnd(convert[i, 0](nAngle)),-12}{
rnd(convert[i, 1](nAngle)),-12}{
rnd(convert[i, 2](nAngle)),-12}{
rnd(convert[i, 3](nAngle)),-12}");
}
}
}

public static double NormalizeDeg(double angle) => Normalize(angle, 360);
public static double NormalizeGrad(double angle) => Normalize(angle, 400);
public static double NormalizeMil(double angle) => Normalize(angle, 6400);
public static double NormalizeRad(double angle) => Normalize(angle, 2 * Math.PI);

private static double Normalize(double angle, double N) {
while (angle <= -N) angle += N;
while (angle >= N) angle -= N;
return angle;
}

public static double DegToGrad(double angle) => angle * 10 / 9;
public static double DegToMil(double angle) => angle * 160 / 9;
public static double DegToRad(double angle) => angle * Math.PI / 180;

public static double GradToDeg(double angle) => angle * 9 / 10;
public static double GradToMil(double angle) => angle * 16;
public static double GradToRad(double angle) => angle * Math.PI / 200;

public static double MilToDeg(double angle) => angle * 9 / 160;
public static double MilToGrad(double angle) => angle / 16;
public static double MilToRad(double angle) => angle * Math.PI / 3200;

public static double RadToDeg(double angle) => angle * 180 / Math.PI;
public static double RadToGrad(double angle) => angle * 200 / Math.PI;
public static double RadToMil(double angle) => angle * 3200 / Math.PI;
}

Output:
Angle       Normalized  Unit        Degrees     Gradians    Mils        Radians
-2          -2          Degrees     -2          -2.2222     -35.5556    -0.0349
-2          -2          Gradiens    -1.8        -2          -32         -0.0314
-2          -2          Mils        -0.1125     -0.125      -2          -0.002
-2          -2          Radians     -114.5916   -127.324    -2037.1833  -2
-1          -1          Degrees     -1          -1.1111     -17.7778    -0.0175
-1          -1          Gradiens    -0.9        -1          -16         -0.0157
-1          -1          Mils        -0.0562     -0.0625     -1          -0.001
-1          -1          Radians     -57.2958    -63.662     -1018.5916  -1
0           0           Degrees     0           0           0           0
0           0           Gradiens    0           0           0           0
0           0           Mils        0           0           0           0
0           0           Radians     0           0           0           0
1           1           Degrees     1           1.1111      17.7778     0.0175
1           1           Gradiens    0.9         1           16          0.0157
1           1           Mils        0.0562      0.0625      1           0.001
1           1           Radians     57.2958     63.662      1018.5916   1
2           2           Degrees     2           2.2222      35.5556     0.0349
2           2           Gradiens    1.8         2           32          0.0314
2           2           Mils        0.1125      0.125       2           0.002
2           2           Radians     114.5916    127.324     2037.1833   2
6.2832      6.2832      Degrees     6.2832      6.9813      111.7011    0.1097
6.2832      6.2832      Gradiens    5.6549      6.2832      100.531     0.0987
6.2832      6.2832      Mils        0.3534      0.3927      6.2832      0.0062
6.2832      6.2832      Radians     360         400         6400        6.2832
16          16          Degrees     16          17.7778     284.4444    0.2793
16          16          Gradiens    14.4        16          256         0.2513
16          16          Mils        0.9         1           16          0.0157
16          3.4336      Radians     196.7325    218.5916    3497.4662   3.4336
57.2958     57.2958     Degrees     57.2958     63.662      1018.5916   1
57.2958     57.2958     Gradiens    51.5662     57.2958     916.7325    0.9
57.2958     57.2958     Mils        3.2229      3.581       57.2958     0.0562
57.2958     0.7471      Radians     42.8063     47.5626     761.0018    0.7471
359         359         Degrees     359         398.8889    6382.2222   6.2657
359         359         Gradiens    323.1       359         5744        5.6392
359         359         Mils        20.1938     22.4375     359         0.3524
359         0.8584      Radians     49.1848     54.6498     874.3972    0.8584
6399        279         Degrees     279         310         4960        4.8695
6399        399         Gradiens    359.1       399         6384        6.2675
6399        6399        Mils        359.9438    399.9375    6399        6.2822
6399        2.7174      Radians     155.6931    172.9923    2767.8774   2.7174
1000000     280         Degrees     280         311.1111    4977.7778   4.8869
1000000     0           Gradiens    0           0           0           0
1000000     1600        Mils        90          100         1600        1.5708
1000000     5.9256      Radians     339.5132    377.2368    6035.7895   5.9256

## C++

Library: Boost
#include <functional>
#include <iostream>
#include <iomanip>
#include <math.h>
#include <sstream>
#include <vector>
#include <boost/algorithm/string.hpp>

template<typename T>
T normalize(T a, double b) { return std::fmod(a, b); }

inline double d2d(double a) { return normalize<double>(a, 360); }
inline double g2g(double a) { return normalize<double>(a, 400); }
inline double m2m(double a) { return normalize<double>(a, 6400); }
inline double r2r(double a) { return normalize<double>(a, 2*M_PI); }

double d2g(double a) { return g2g(a * 10 / 9); }
double d2m(double a) { return m2m(a * 160 / 9); }
double d2r(double a) { return r2r(a * M_PI / 180); }
double g2d(double a) { return d2d(a * 9 / 10); }
double g2m(double a) { return m2m(a * 16); }
double g2r(double a) { return r2r(a * M_PI / 200); }
double m2d(double a) { return d2d(a * 9 / 160); }
double m2g(double a) { return g2g(a / 16); }
double m2r(double a) { return r2r(a * M_PI / 3200); }
double r2d(double a) { return d2d(a * 180 / M_PI); }
double r2g(double a) { return g2g(a * 200 / M_PI); }
double r2m(double a) { return m2m(a * 3200 / M_PI); }

void print(const std::vector<double> &values, const char *s, std::function<double(double)> f) {
using namespace std;
ostringstream out;
out << "                  ┌───────────────────┐\n";
out << "                  │ " << setw(17) << s << " │\n";
out << "┌─────────────────┼───────────────────┤\n";
for (double i : values)
out << "│ " << setw(15) << fixed << i << defaultfloat << " │ " << setw(17) << fixed << f(i) << defaultfloat << " │\n";
out << "└─────────────────┴───────────────────┘\n";
auto str = out.str();
boost::algorithm::replace_all(str, ".000000", "       ");
cout << str;
}

int main() {
std::vector<double> values = { -2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000 };
print(values, "normalized (deg)", d2d);
print(values, "normalized (grad)", g2g);
print(values, "normalized (mil)", m2m);
print(values, "normalized (rad)", r2r);

print(values, "deg -> grad ", d2g);
print(values, "deg -> mil ", d2m);
print(values, "deg -> rad ", d2r);

print(values, "grad -> deg ", g2d);
print(values, "grad -> mil ", g2m);

print(values, "mil -> deg ", m2d);
print(values, "mil -> grad ", m2g);
print(values, "mil -> rad ", m2r);

print(values, "rad -> deg ", r2d);
print(values, "rad -> mil ", r2m);

return 0;
}

Output:
                  ┌───────────────────┐
│  normalized (deg) │
┌─────────────────┼───────────────────┤
│       -2        │         -2        │
│       -1        │         -1        │
│        0        │          0        │
│        1        │          1        │
│        2        │          2        │
│        6.283185 │          6.283185 │
│       16        │         16        │
│       57.295780 │         57.295780 │
│      359        │        359        │
│      399        │         39        │
│     6399        │        279        │
│  1000000        │        280        │
└─────────────────┴───────────────────┘
...
┌───────────────────┐
│       rad -> mil  │
┌─────────────────┼───────────────────┤
│       -2        │      -2037.183272 │
│       -1        │      -1018.591636 │
│        0        │          0        │
│        1        │       1018.591636 │
│        2        │       2037.183272 │
│        6.283185 │       6399.999993 │
│       16        │       3497.466173 │
│       57.295780 │        761.001765 │
│      359        │        874.397248 │
│      399        │       3218.062679 │
│     6399        │       2767.877408 │
│  1000000        │       6035.788130 │
└─────────────────┴───────────────────┘

## Common Lisp

Usage: (angles angle(s)) or (angles) for auto-test. VAL* is unnormalized.

(defun DegToDeg (a) (rem a 360))
(defun MilToMil (a) (rem a 6400))
(defun RadToRad (a) (rem a (* 2 pi)))

(defun DegToRad (a) (RadToRad (* (/ a 360) (* 2 pi))))
(defun DegToMil (a) (MilToMil (* (/ a 360) 6400)))

(defun GradToDeg (a) (DegToDeg (* (/ a 400) 360)))
(defun GradToMil (a) (MilToMil (* (/ a 400) 6400)))

(defun MilToDeg (a) (DegToDeg (* (/ a 6400) 360)))
(defun MilToRad (a) (RadToRad (* (/ a 6400) (* 2 pi))))

(defun RadToDeg (a) (DegToDeg (* (/ a (* 2 pi)) 360)))
(defun RadToMil (a) (MilToMil (* (/ a (* 2 pi)) 6400)))

(defun angles (&rest angles)
(if (not angles) (setf angles '(-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000)))
(dolist (a angles)
(format t "UNIT   ~15@a   ~15@a   ~15@a   ~15@a   ~15@a~%" "VAL*" "DEG" "GRAD" "MIL" "RAD")
(format t "Deg  | ~15f | ~15f | ~15f | ~15f | ~15f~%" a (DegToDeg a) (DegToGrad a) (DegToMil a) (DegToRad a))
(format t "Mil  | ~15f | ~15f | ~15f | ~15f | ~15f~%" a (MilToDeg a) (MilToGrad a) (MilToMil a) (MilToRad a))

Output:
[CLISP]> (angles)
Deg  |            -2.0 |            -2.0 |      -2.2222223 |      -35.555557 | -.0349065850399
Grad |            -2.0 |            -1.8 |            -2.0 |           -32.0 | -.0314159265359
Mil  |            -2.0 |         -0.1125 |          -0.125 |            -2.0 | -.0019634954085
Rad  |            -2.0 | -114.5915590262 | -127.3239544735 | -2037.183271576 |            -2.0

Deg  |            -1.0 |            -1.0 |      -1.1111112 |      -17.777779 | -.0174532925199
Grad |            -1.0 |            -0.9 |            -1.0 |           -16.0 | -.0157079632679
Mil  |            -1.0 |        -0.05625 |         -0.0625 |            -1.0 | -.0009817477042
Rad  |            -1.0 | -57.29577951308 | -63.66197723676 | -1018.591635788 |            -1.0

Deg  |             0.0 |             0.0 |             0.0 |             0.0 |             0.0
Grad |             0.0 |             0.0 |             0.0 |             0.0 |             0.0
Mil  |             0.0 |             0.0 |             0.0 |             0.0 |             0.0
Rad  |             0.0 |             0.0 |             0.0 |             0.0 |             0.0

Deg  |             1.0 |             1.0 |       1.1111112 |       17.777779 | .01745329251994
Grad |             1.0 |             0.9 |             1.0 |            16.0 | .01570796326795
Mil  |             1.0 |         0.05625 |          0.0625 |             1.0 | .00098174770425
Rad  |             1.0 | 57.295779513082 | 63.661977236758 | 1018.5916357881 |             1.0

Deg  |             2.0 |             2.0 |       2.2222223 |       35.555557 | .03490658503989
Grad |             2.0 |             1.8 |             2.0 |            32.0 | 0.0314159265359
Mil  |             2.0 |          0.1125 |           0.125 |             2.0 | .00196349540849
Rad  |             2.0 | 114.59155902616 | 127.32395447352 | 2037.1832715763 |             2.0

Deg  |       6.2831855 |       6.2831855 |        6.981317 |       111.70107 |      0.10966227
Grad |       6.2831855 |        5.654867 |       6.2831855 |       100.53097 |     0.098696046
Mil  |       6.2831855 |       0.3534292 |       0.3926991 |       6.2831855 |     0.006168503
Rad  |       6.2831855 |             0.0 |             0.0 |             0.0 |             0.0

Deg  |            16.0 |            16.0 |       17.777779 |       284.44446 | .27925268031909
Grad |            16.0 |            14.4 |            16.0 |           256.0 | .25132741228718
Mil  |            16.0 |             0.9 |             1.0 |            16.0 | .01570796326795
Rad  |            16.0 | 196.73247220932 | 218.59163578813 | 3497.4661726101 | 3.4336293856408

Deg  |        57.29578 |       57.295784 |        63.66198 |       1018.5917 |      0.99999994
Grad |        57.29578 |       51.566204 |        57.29578 |        916.7325 |      0.90000004
Mil  |        57.29578 |       3.2228878 |       3.5809863 |        57.29578 |     0.056250002
Rad  |        57.29578 |        42.80651 |        47.56279 |       761.00464 |      0.74711454

Deg  |           359.0 |           359.0 |        398.8889 |        6382.222 | 6.2657320146596
Grad |           359.0 |           323.1 |           359.0 |          5744.0 | 5.6391588131937
Mil  |           359.0 |        20.19375 |         22.4375 |           359.0 | 0.3524474258246
Rad  |           359.0 | 49.184845196553 |  54.64982799617 | 874.39724793872 | .85843749076357

Deg  |           399.0 |            39.0 |       43.333332 |        693.3333 | .68067840827779
Grad |           399.0 |           359.1 |           399.0 |          6384.0 | 6.2674773439116
Mil  |           399.0 |        22.44375 |         24.9375 |           399.0 | .39171733399448
Rad  |           399.0 | 181.01602571985 |  201.1289174665 | 3218.0626794639 | 3.1593256476861

Deg  |          6399.0 |           279.0 |           310.0 |          4960.0 | 4.8694686130642
Grad |          6399.0 |           359.1 |           399.0 |          6384.0 | 6.2674773439116
Mil  |          6399.0 |       359.94376 |        399.9375 |          6399.0 | 6.2822035594753
Rad  |          6399.0 | 155.69310421377 |  172.9923380153 | 2767.8774082448 |  2.717357291181

Deg  |       1000000.0 |           280.0 |        311.1111 |        4977.778 | 4.8869219055841
Grad |       1000000.0 |             0.0 |             0.0 |             0.0 |             0.0
Mil  |       1000000.0 |            90.0 |           100.0 |          1600.0 | 1.5707963267949
Rad  |       1000000.0 | 339.51308232088 | 377.23675813431 | 6035.7881301489 | 5.9256211400939

## Delphi

Library: System.Math
Translation of: Go
program normalization_and_conversion;

{$APPTYPE CONSOLE} uses System.SysUtils, System.Math; function d2d(d: double): double; begin result := FMod(d, 360); end; function g2g(g: double): double; begin result := FMod(g, 400); end; function m2m(m: double): double; begin result := FMod(m, 6400); end; function r2r(r: double): double; begin result := FMod(r, 2 * Pi); end; function d2g(d: double): double; begin result := d2d(d) * 400 / 360; end; function d2m(d: double): double; begin result := d2d(d) * 6400 / 360; end; function d2r(d: double): double; begin result := d2d(d) * Pi / 180; end; function g2d(g: double): double; begin result := g2g(g) * 360 / 400; end; function g2m(g: double): double; begin result := g2g(g) * 6400 / 400; end; function g2r(g: double): double; begin result := g2g(g) * Pi / 200; end; function m2d(m: double): double; begin result := m2m(m) * 360 / 6400; end; function m2g(m: double): double; begin result := m2m(m) * 400 / 6400; end; function m2r(m: double): double; begin result := m2m(m) * Pi / 3200; end; function r2d(r: double): double; begin result := r2r(r) * 180 / Pi; end; function r2g(r: double): double; begin result := r2r(r) * 200 / Pi; end; function r2m(r: double): double; begin result := r2r(r) * 3200 / Pi; end; function s(f: double): string; begin var wf := FloatToStrF(f, ffGeneral, 16, 64).Split([FormatSettings.DecimalSeparator], TStringSplitOptions.ExcludeEmpty); if Length(wf) = 1 then exit(format('%7s ', [wf[0]])); var le := length(wf[1]); if le > 7 then le := 7; Result := format('%7s.%-7s', [wf[0], copy(wf[1], 0, le)]); end; begin var angles: TArray<Double> := [-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000]; var ft := '%s %s %s %s %s'; writeln(format(ft, [' degrees ', 'normalized degs', ' gradians ', ' mils ', ' radians'])); for var a in angles do writeln(format(ft, [s(a), s(d2d(a)), s(d2g(a)), s(d2m(a)), s(d2r(a))])); writeln(format(ft, [#10' gradians ', 'normalized grds', ' degrees ', ' mils ', ' radians'])); for var a in angles do writeln(format(ft, [s(a), s(g2g(a)), s(g2d(a)), s(g2m(a)), s(g2r(a))])); writeln(format(ft, [#10' mils ', 'normalized mils', ' degrees ', ' gradians ', ' radians'])); for var a in angles do writeln(format(ft, [s(a), s(m2m(a)), s(m2d(a)), s(m2g(a)), s(m2r(a))])); writeln(format(ft, [#10' radians ', 'normalized rads', ' degrees ', ' gradians ', ' mils '])); for var a in angles do writeln(format(ft, [s(a), s(r2r(a)), s(r2d(a)), s(r2g(a)), s(r2m(a))])); readln; end.  ## EasyLang func angconv ang f$ t$. sgn = sign ang ang = abs ang if f$ = "degree"
turn = ang / 360 mod 1
elif f$= "gradian" turn = ang / 400 mod 1 elif f$ = "mil"
turn = ang / 6400 mod 1
elif f$= "radian" turn = ang / (2 * pi) mod 1 . if t$ = "degree"
ang = turn * 360
elif t$= "gradian" ang = turn * 400 elif t$ = "mil"
ang = turn * 6400
elif t$= "radian" ang = turn * 2 * pi . return ang * sgn . func$ fmt s$. return substr " " 1 (9 - len s$) & s$& " " . # scales$[] = [ "degree" "gradian" "mil" "radian" ]
values[] = [ -2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000 ]
numfmt 3 10
for f$in scales$[]
write fmt f$for t$ in scales$[] write fmt t$
.
print ""
print "  ------------------------------------------------"
for v in values[]
write v
for t$in scales$[]
write angconv v f$t$
.
print ""
.
print ""
.
Output:
   degree    degree   gradian       mil    radian
------------------------------------------------
-2        -2    -2.222   -35.556    -0.035
-1        -1    -1.111   -17.778    -0.017
0         0         0         0         0
1         1     1.111    17.778     0.017
2         2     2.222    35.556     0.035
6.283     6.283     6.981   111.701     0.110
16        16    17.778   284.444     0.279
57.296    57.296    63.662  1018.592     1.000
359       359   398.889  6382.222     6.266
399    39.000    43.333   693.333     0.681
6399   279.000   310.000  4960.000     4.869
1000000   280.000   311.111  4977.778     4.887

------------------------------------------------
-2    -1.800        -2       -32    -0.031
-1    -0.900        -1       -16    -0.016
0         0         0         0         0
1     0.900         1        16     0.016
2     1.800         2        32     0.031
6.283     5.655     6.283   100.531     0.099
16    14.400        16       256     0.251
57.296    51.566    57.296   916.732     0.900
359   323.100       359      5744     5.639
399   359.100       399      6384     6.267
6399   359.100   399.000  6384.000     6.267
1000000         0         0         0         0

------------------------------------------------
-2    -0.113    -0.125        -2    -0.002
-1    -0.056    -0.062        -1    -0.001
0         0         0         0         0
1     0.056     0.062         1     0.001
2     0.113     0.125         2     0.002
6.283     0.353     0.393     6.283     0.006
16     0.900         1        16     0.016
57.296     3.223     3.581    57.296     0.056
359    20.194    22.438       359     0.352
399    22.444    24.938       399     0.392
6399   359.944   399.938      6399     6.282
1000000        90       100      1600     1.571

------------------------------------------------
-2  -114.592  -127.324 -2037.183        -2
-1   -57.296   -63.662 -1018.592        -1
0         0         0         0         0
1    57.296    63.662  1018.592         1
2   114.592   127.324  2037.183         2
6.283   360.000   400.000  6400.000     6.283
16   196.732   218.592  3497.466     3.434
57.296    42.806    47.563   761.002     0.747
359    49.185    54.650   874.397     0.858
399   181.016   201.129  3218.063     3.159
6399   155.693   172.992  2767.877     2.717
1000000   339.513   377.237  6035.788     5.926


## Factor

Radians and degrees are already defined in the units.si vocabulary. Gradiens and mils are defined in terms of degrees. Conversions from unit to unit are handled by inverse functions; [undo] knows how to deconstruct units in terms of other units. (Assuming, of course, new units are defined entirely with words that have inverses.)

USING: accessors combinators formatting inverse kernel math
math.constants quotations qw sequences units.si ;
IN: rosetta-code.angles

ALIAS: degrees arc-deg
: gradiens ( n -- d ) 9/10 * degrees ;
: mils ( n -- d ) 9/160 * degrees ;
: normalize ( d -- d' ) [ 2 pi * mod ] change-value ;
CONSTANT: units { degrees gradiens mils radians }

: .row ( angle unit -- )
2dup "%-12u%-12s" printf ( x -- x ) execute-effect
normalize units [ 1quotation [undo] call( x -- x ) ] with
map "%-12.4f%-12.4f%-12.4f%-12.4f\n" vprintf ;

: .header ( -- )
qw{ angle unit } units append
"%-12s%-12s%-12s%-12s%-12s%-12s\n" vprintf ;

: angles ( -- )
{ -2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000 }
units [ .row ] cartesian-each ;

MAIN: angles

Output:
angle       unit        degrees     gradiens    mils        radians
-2          degrees     -2.0000     -2.2222     -35.5556    -0.0349
-2          gradiens    -1.8000     -2.0000     -32.0000    -0.0314
-2          mils        -0.1125     -0.1250     -2.0000     -0.0020
-2          radians     -114.5916   -127.3240   -2037.1833  -2.0000
-1          degrees     -1.0000     -1.1111     -17.7778    -0.0175
-1          gradiens    -0.9000     -1.0000     -16.0000    -0.0157
-1          mils        -0.0563     -0.0625     -1.0000     -0.0010
-1          radians     -57.2958    -63.6620    -1018.5916  -1.0000
0           degrees     0.0000      0.0000      0.0000      0.0000
0           gradiens    0.0000      0.0000      0.0000      0.0000
0           mils        0.0000      0.0000      0.0000      0.0000
0           radians     0.0000      0.0000      0.0000      0.0000
1           degrees     1.0000      1.1111      17.7778     0.0175
1           gradiens    0.9000      1.0000      16.0000     0.0157
1           mils        0.0563      0.0625      1.0000      0.0010
1           radians     57.2958     63.6620     1018.5916   1.0000
2           degrees     2.0000      2.2222      35.5556     0.0349
2           gradiens    1.8000      2.0000      32.0000     0.0314
2           mils        0.1125      0.1250      2.0000      0.0020
2           radians     114.5916    127.3240    2037.1833   2.0000
6.2831853   degrees     6.2832      6.9813      111.7011    0.1097
6.2831853   gradiens    5.6549      6.2832      100.5310    0.0987
6.2831853   mils        0.3534      0.3927      6.2832      0.0062
6.2831853   radians     360.0000    400.0000    6400.0000   6.2832
16          degrees     16.0000     17.7778     284.4444    0.2793
16          gradiens    14.4000     16.0000     256.0000    0.2513
16          mils        0.9000      1.0000      16.0000     0.0157
16          radians     196.7325    218.5916    3497.4662   3.4336
57.2957795  degrees     57.2958     63.6620     1018.5916   1.0000
57.2957795  gradiens    51.5662     57.2958     916.7325    0.9000
57.2957795  mils        3.2229      3.5810      57.2958     0.0562
57.2957795  radians     42.8063     47.5626     761.0018    0.7471
359         degrees     359.0000    398.8889    6382.2222   6.2657
359         gradiens    323.1000    359.0000    5744.0000   5.6392
359         mils        20.1938     22.4375     359.0000    0.3524
359         radians     49.1848     54.6498     874.3972    0.8584
399         degrees     39.0000     43.3333     693.3333    0.6807
399         gradiens    359.1000    399.0000    6384.0000   6.2675
399         mils        22.4438     24.9375     399.0000    0.3917
399         radians     181.0160    201.1289    3218.0627   3.1593
6399        degrees     279.0000    310.0000    4960.0000   4.8695
6399        gradiens    359.1000    399.0000    6384.0000   6.2675
6399        mils        359.9438    399.9375    6399.0000   6.2822
6399        radians     155.6931    172.9923    2767.8774   2.7174
1000000     degrees     280.0000    311.1111    4977.7778   4.8869
1000000     gradiens    0.0000      0.0000      0.0000      0.0000
1000000     mils        90.0000     100.0000    1600.0000   1.5708
1000000     radians     339.5131    377.2368    6035.7881   5.9256


## FreeBASIC

Provides a single function that does the normalising and converting. Supports D, G, M, R, T for degrees, gradians, mils, radians, and turns respectively.

#define PI 3.1415926535897932384626433832795028842
#define INVALID -99999

function clamp( byval n as double, lo as double, hi as double ) as double
while n <= lo
n += (hi - lo)/2
wend
while n >= hi
n += (lo - hi)/2
wend
return n
end function

function anglenc( byval angle as double, byval source as string, byval targ as string ) as double
source = ucase(source)
targ = ucase(targ)
select case source
case "D":
angle = clamp(angle, -360, 360)
select case targ
case "D":
return angle
case "G":
return angle*10/9
case "M":
return angle*160/9
case "R":
return angle*PI/180
case "T":
return angle/360
case else
return INVALID
end select
case "G":
angle = clamp(angle, -400, 400)
select case targ
case "D":
return angle*9/10
case "G":
return angle
case "M":
return angle*16
case "R":
return angle*PI/200
case "T":
return angle/400
case else
return INVALID
end select
case "M":
angle = clamp(angle, -6400, 6400)
select case targ
case "D":
return angle*9/160
case "G":
return angle/16
case "M":
return angle
case "R":
return angle*PI/3200
case "T":
return angle/6400
case else
return INVALID
end select
case "R":
angle = clamp(angle, -2*PI, 2*PI)
select case targ
case "D":
return angle*180/PI
case "G":
return angle*200/PI
case "M":
return angle*3200/PI
case "R":
return angle
case "T":
return angle/(2*PI)
case else
return INVALID
end select
case "T":
angle = clamp(angle, -1, 1)
select case targ
case "D":
return angle*360
case "G":
return angle*400
case "M":
return angle*6400
case "R":
return angle*2*PI
case "T":
return angle
case else
return INVALID
end select
case else:
return INVALID
end select
end function

function clip( st as string, num as uinteger ) as string
if len(st)<num then return st
return left(st, num)
end function

dim as string scales = "DGMRT", source, targ
dim as double angles(12) = {-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000}
print "Angle       Normalised    Unit            |              D             G             M             R              T"
for k as ubyte = 0 to 11
for i as ubyte = 1 to 5
source = mid(scales,i,1)
print angles(k), clip(str(anglenc(angles(k), source, source )), 10), source, "|",
for j as ubyte = 1 to 5
targ = mid(scales, j, 1)
print clip(str(anglenc(angles(k), source, targ )), 10),
next j
print
next i
next k
Output:
Angle       Normalised    Unit            |              D             G             M             R              T
-2            -2            D             |             -2            -2.2222222    -35.555555    -0.0349065    -0.0055555
-2            -2            G             |             -1.8          -2            -32           -0.0314159    -0.005
-2            -2            M             |             -0.1125       -0.125        -2            -0.0019634    -0.0003125
-2            -2            R             |             -114.59155    -127.32395    -2037.1832    -2            -0.3183098
-2            0             T             |             0             0             0             0             0
-1            -1            D             |             -1            -1.1111111    -17.777777    -0.0174532    -0.0027777
-1            -1            G             |             -0.9          -1            -16           -0.0157079    -0.0025
-1            -1            M             |             -0.05625      -0.0625       -1            -0.0009817    -0.0001562
-1            -1            R             |             -57.295779    -63.661977    -1018.5916    -1            -0.1591549
-1            0             T             |             0             0             0             0             0
0            0             D             |             0             0             0             0             0
0            0             G             |             0             0             0             0             0
0            0             M             |             0             0             0             0             0
0            0             R             |             0             0             0             0             0
0            0             T             |             0             0             0             0             0
1            1             D             |             1             1.11111111    17.7777777    0.01745329    0.00277777
1            1             G             |             0.9           1             16            0.01570796    0.0025
1            1             M             |             0.05625       0.0625        1             0.00098174    0.00015625
1            1             R             |             57.2957795    63.6619772    1018.59163    1             0.15915494
1            0             T             |             0             0             0             0             0
2            2             D             |             2             2.22222222    35.5555555    0.03490658    0.00555555
2            2             G             |             1.8           2             32            0.03141592    0.005
2            2             M             |             0.1125        0.125         2             0.00196349    0.0003125
2            2             R             |             114.591559    127.323954    2037.18327    2             0.31830988
2            0             T             |             0             0             0             0             0
6.2831853    6.2831853     D             |             6.2831853     6.98131700    111.701072    0.10966227    0.01745329
6.2831853    6.2831853     G             |             5.65486677    6.2831853     100.530964    0.09869604    0.01570796
6.2831853    6.2831853     M             |             0.35342917    0.39269908    6.2831853     0.00616850    0.00098174
6.2831853    6.2831853     R             |             359.999999    399.999999    6399.99999    6.2831853     0.99999999
6.2831853    0.28318530    T             |             101.946708    113.274120    1812.38592    1.77930571    0.28318530
16           16            D             |             16            17.7777777    284.444444    0.27925268    0.04444444
16           16            G             |             14.4          16            256           0.25132741    0.04
16           16            M             |             0.9           1             16            0.01570796    0.0025
16           3.43362938    R             |             196.732472    218.591635    3497.46617    3.43362938    0.54647908
16           0             T             |             0             0             0             0             0
57.2957795   57.2957795    D             |             57.2957795    63.6619772    1018.59163    0.99999999    0.15915494
57.2957795   57.2957795    G             |             51.5662015    57.2957795    916.732472    0.89999999    0.14323944
57.2957795   57.2957795    M             |             3.22288759    3.58098621    57.2957795    0.05624999    0.00895246
57.2957795   0.74711173    R             |             42.8063492    47.5626102    761.001764    0.74711173    0.11890652
57.2957795   0.29577950    T             |             106.480620    118.311800    1892.98880    1.85843740    0.29577950
359          359           D             |             359           398.888888    6382.22222    6.26573201    0.99722222
359          359           G             |             323.1         359           5744          5.63915881    0.8975
359          359           M             |             20.19375      22.4375       359           0.35244742    0.05609375
359          0.85843749    R             |             49.1848451    54.6498279    874.397247    0.85843749    0.13662456
359          0             T             |             0             0             0             0             0
399          39            D             |             39            43.3333333    693.333333    0.68067840    0.10833333
399          399           G             |             359.1         399           6384          6.26747734    0.99750000
399          399           M             |             22.44375      24.9375       399           0.39171733    0.06234375
399          3.15932564    R             |             181.016025    201.128917    3218.06267    3.15932564    0.50282229
399          0             T             |             0             0             0             0             0
6399         279           D             |             279           310           4960          4.86946861    0.775
6399         399           G             |             359.1         399           6384          6.26747734    0.99750000
6399         6399          M             |             359.94375     399.9375      6399          6.28220355    0.99984375
6399         2.71735729    R             |             155.693104    172.992338    2767.87740    2.71735729    0.43248084
6399         0             T             |             0             0             0             0             0
1000000      280           D             |             280           311.111111    4977.77777    4.88692190    0.77777777
1000000      0             G             |             0             0             0             0             0
1000000      1600          M             |             90            100           1600          1.57079632    0.25
1000000      5.92562252    R             |             339.513161    377.236846    6035.78954    5.92562252    0.94309211
1000000      0             T             |             0             0             0             0             0

## Go

package main

import (
"fmt"
"math"
"strconv"
"strings"
)

func d2d(d float64) float64 { return math.Mod(d, 360) }

func g2g(g float64) float64 { return math.Mod(g, 400) }

func m2m(m float64) float64 { return math.Mod(m, 6400) }

func r2r(r float64) float64 { return math.Mod(r, 2*math.Pi) }

func d2g(d float64) float64 { return d2d(d) * 400 / 360 }

func d2m(d float64) float64 { return d2d(d) * 6400 / 360 }

func d2r(d float64) float64 { return d2d(d) * math.Pi / 180 }

func g2d(g float64) float64 { return g2g(g) * 360 / 400 }

func g2m(g float64) float64 { return g2g(g) * 6400 / 400 }

func g2r(g float64) float64 { return g2g(g) * math.Pi / 200 }

func m2d(m float64) float64 { return m2m(m) * 360 / 6400 }

func m2g(m float64) float64 { return m2m(m) * 400 / 6400 }

func m2r(m float64) float64 { return m2m(m) * math.Pi / 3200 }

func r2d(r float64) float64 { return r2r(r) * 180 / math.Pi }

func r2g(r float64) float64 { return r2r(r) * 200 / math.Pi }

func r2m(r float64) float64 { return r2r(r) * 3200 / math.Pi }

// Aligns number to decimal point assuming 7 characters before and after.
func s(f float64) string {
wf := strings.Split(strconv.FormatFloat(f, 'g', 15, 64), ".")
if len(wf) == 1 {
return fmt.Sprintf("%7s        ", wf[0])
}
le := len(wf[1])
if le > 7 {
le = 7
}
return fmt.Sprintf("%7s.%-7s", wf[0], wf[1][:le])
}

func main() {
angles := []float64{-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795,
359, 399, 6399, 1000000}
ft := "%s %s %s %s %s\n"
fmt.Printf(ft, "    degrees    ", "normalized degs", "    gradians   ", "     mils      ", "     radians")
for _, a := range angles {
fmt.Printf(ft, s(a), s(d2d(a)), s(d2g(a)), s(d2m(a)), s(d2r(a)))
}
fmt.Printf(ft, "\n   gradians    ", "normalized grds", "    degrees    ", "     mils      ", "     radians")
for _, a := range angles {
fmt.Printf(ft, s(a), s(g2g(a)), s(g2d(a)), s(g2m(a)), s(g2r(a)))
}
fmt.Printf(ft, "\n     mils      ", "normalized mils", "    degrees    ", "   gradians    ", "     radians")
for _, a := range angles {
fmt.Printf(ft, s(a), s(m2m(a)), s(m2d(a)), s(m2g(a)), s(m2r(a)))
}
fmt.Printf(ft, "\n    radians    ", "normalized rads", "    degrees    ", "   gradians    ", "      mils  ")
for _, a := range angles {
fmt.Printf(ft, s(a), s(r2r(a)), s(r2d(a)), s(r2g(a)), s(r2m(a)))
}
}

Output:
    degrees     normalized degs     gradians         mils            radians
-2              -2              -2.2222222     -35.5555555      -0.0349065
-1              -1              -1.1111111     -17.7777777      -0.0174532
0               0               0               0               0
1               1               1.1111111      17.7777777       0.0174532
2               2               2.2222222      35.5555555       0.0349065
6.2831853       6.2831853       6.981317      111.701072        0.1096622
16              16              17.7777777     284.4444444       0.2792526
57.2957795      57.2957795      63.6619772    1018.5916355       0.9999999
359             359             398.8888888    6382.2222222       6.2657320
399              39              43.3333333     693.3333333       0.6806784
6399             279             310            4960               4.8694686
1000000             280             311.1111111    4977.7777777       4.8869219

-2              -2              -1.8           -32              -0.0314159
-1              -1              -0.9           -16              -0.0157079
0               0               0               0               0
1               1               0.9            16               0.0157079
2               2               1.8            32               0.0314159
6.2831853       6.2831853       5.6548667     100.5309648       0.0986960
16              16              14.4           256               0.2513274
57.2957795      57.2957795      51.5662015     916.732472        0.8999999
359             359             323.1          5744               5.6391588
399             399             359.1          6384               6.2674773
6399             399             359.1          6384               6.2674773
1000000               0               0               0               0

-2              -2              -0.1125         -0.125          -0.0019634
-1              -1              -0.05625        -0.0625         -0.0009817
0               0               0               0               0
1               1               0.05625         0.0625          0.0009817
2               2               0.1125          0.125           0.0019634
6.2831853       6.2831853       0.3534291       0.3926990       0.0061685
16              16               0.9             1               0.0157079
57.2957795      57.2957795       3.2228875       3.5809862       0.0562499
359             359              20.19375        22.4375          0.3524474
399             399              22.44375        24.9375          0.3917173
6399            6399             359.94375       399.9375          6.2822035
1000000            1600              90             100               1.5707963

-2              -2            -114.5915590    -127.3239544   -2037.1832715
-1              -1             -57.2957795     -63.6619772   -1018.5916357
0               0               0               0               0
1               1              57.2957795      63.6619772    1018.5916357
2               2             114.5915590     127.3239544    2037.1832715
6.2831853       6.2831853     359.9999995     399.9999995    6399.9999926
16               3.4336293     196.7324722     218.5916357    3497.4661726
57.2957795       0.7471117      42.8063492      47.5626102     761.0017646
359               0.8584374      49.1848451      54.6498279     874.3972479
399               3.1593256     181.0160257     201.1289174    3218.0626794
6399               2.7173572     155.6931042     172.9923380    2767.8774082
1000000               5.9256211     339.5130823     377.2367581    6035.7881301


## Groovy

This solution creates the concept of an angular quantity with subclasses for different units of measure. Rather than creating individual functions (d2d, r2m, etc.) this solution uses inheritance, polymorphism, and operator overloading to implement the conversions and comparisons in a relatively natural way for idiomatic Groovy.

import java.lang.reflect.Constructor

abstract class Angle implements Comparable<? extends Angle> {
double value

Angle(double value = 0) { this.value = normalize(value) }

abstract Number unitCircle()
abstract String unitName()

Number normalize(double n) { n % this.unitCircle() }

def <B extends Angle> B asType(Class<B> bClass){
if (bClass == this.class) return this
bClass.getConstructor(Number.class).newInstance(0).tap {
value = this.value * unitCircle() / this.unitCircle()
}
}

String toString() {
"${String.format('%14.8f',value)}${this.unitName()}"
}

int hashCode() {
value.hashCode() + 17 * unit().hashCode()
}

int compareTo(Angle that) {
this.value * that.unitCircle() <=> that.value * this.unitCircle()
}

boolean equals(that) {
this.is(that)            ? true
: that instanceof Angle  ? (this <=> that) == 0
: that instanceof Number ? this.value == this.normalize(that)
: super.equals(that)
}
}

class Degrees extends Angle {
static final int UNIT_CIRCLE = 360
Number unitCircle() { UNIT_CIRCLE }
static final String UNIT = "º    "
String unitName() { UNIT }
Degrees(Number value = 0) { super(value) }
}

class Gradians extends Angle {
static final int UNIT_CIRCLE = 400
Number unitCircle() { UNIT_CIRCLE }
static final String UNIT = " grad"
String unitName() { UNIT }
Gradians(Number value = 0) { super(value) }
}

class Mils extends Angle {
static final int UNIT_CIRCLE = 6400
Number unitCircle() { UNIT_CIRCLE }
static final String UNIT = " mil "
String unitName() { UNIT }
Mils(Number value = 0) { super(value) }
}

class Radians extends Angle {
static final double UNIT_CIRCLE = Math.PI*2
Number unitCircle() { UNIT_CIRCLE }
static final String UNIT = " rad "
String unitName() { UNIT }
Radians(Number value = 0) { super(value) }
}


This category class allows Angles to interoperate more easily with Numbers:

class AngleCategory {
static Degrees getDeg(Number n) { new Degrees(n) }
static Mils getMil(Number n) { new Mils(n) }
}


Test:

Number.metaClass.mixin AngleCategory

[ -2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000 ].each { rawAngle ->
println "\n raw angle      normalized       ------------------------------   conversions   ------------------------------"
[rawAngle.deg, rawAngle.grad, rawAngle.mil, rawAngle.rad].each { angle ->
printf("%10s %20s %s %s %s %s\n", rawAngle.toString(), angle,
angle as Degrees, angle as Gradians,
angle as Mils, angle as Radians
)
}
}

// some additional checks implied in the task statement
// but not requested for solution demonstration
assert 360.deg == 0.deg
assert 90.deg == 100.grad
assert Math.PI.rad == 3200.mil

Output:
 raw angle      normalized       ------------------------------   conversions   ------------------------------
-2     -2.00000000º        -2.00000000º        -2.22222222 grad   -35.55555556 mil     -0.03490659 rad
-2     -2.00000000 grad    -1.80000000º        -2.00000000 grad   -32.00000000 mil     -0.03141593 rad
-2     -2.00000000 mil     -0.11250000º        -0.12500000 grad    -2.00000000 mil     -0.00196350 rad
-2     -2.00000000 rad   -114.59155903º      -127.32395447 grad -2037.18327158 mil     -2.00000000 rad

raw angle      normalized       ------------------------------   conversions   ------------------------------
-1     -1.00000000º        -1.00000000º        -1.11111111 grad   -17.77777778 mil     -0.01745329 rad
-1     -1.00000000 grad    -0.90000000º        -1.00000000 grad   -16.00000000 mil     -0.01570796 rad
-1     -1.00000000 mil     -0.05625000º        -0.06250000 grad    -1.00000000 mil     -0.00098175 rad
-1     -1.00000000 rad    -57.29577951º       -63.66197724 grad -1018.59163579 mil     -1.00000000 rad

raw angle      normalized       ------------------------------   conversions   ------------------------------
0      0.00000000º         0.00000000º         0.00000000 grad     0.00000000 mil      0.00000000 rad
0      0.00000000 grad     0.00000000º         0.00000000 grad     0.00000000 mil      0.00000000 rad
0      0.00000000 mil      0.00000000º         0.00000000 grad     0.00000000 mil      0.00000000 rad
0      0.00000000 rad      0.00000000º         0.00000000 grad     0.00000000 mil      0.00000000 rad

raw angle      normalized       ------------------------------   conversions   ------------------------------
1      1.00000000º         1.00000000º         1.11111111 grad    17.77777778 mil      0.01745329 rad
1      1.00000000 grad     0.90000000º         1.00000000 grad    16.00000000 mil      0.01570796 rad
1      1.00000000 mil      0.05625000º         0.06250000 grad     1.00000000 mil      0.00098175 rad
1      1.00000000 rad     57.29577951º        63.66197724 grad  1018.59163579 mil      1.00000000 rad

raw angle      normalized       ------------------------------   conversions   ------------------------------
2      2.00000000º         2.00000000º         2.22222222 grad    35.55555556 mil      0.03490659 rad
2      2.00000000 grad     1.80000000º         2.00000000 grad    32.00000000 mil      0.03141593 rad
2      2.00000000 mil      0.11250000º         0.12500000 grad     2.00000000 mil      0.00196350 rad
2      2.00000000 rad    114.59155903º       127.32395447 grad  2037.18327158 mil      2.00000000 rad

raw angle      normalized       ------------------------------   conversions   ------------------------------
6.2831853      6.28318530º         6.28318530º         6.98131700 grad   111.70107200 mil      0.10966227 rad
6.2831853      6.28318530 grad     5.65486677º         6.28318530 grad   100.53096480 mil      0.09869604 rad
6.2831853      6.28318530 mil      0.35342917º         0.39269908 grad     6.28318530 mil      0.00616850 rad
6.2831853      6.28318530 rad    359.99999959º       399.99999954 grad  6399.99999269 mil      6.28318530 rad

raw angle      normalized       ------------------------------   conversions   ------------------------------
16     16.00000000º        16.00000000º        17.77777778 grad   284.44444444 mil      0.27925268 rad
16     16.00000000 grad    14.40000000º        16.00000000 grad   256.00000000 mil      0.25132741 rad
16     16.00000000 mil      0.90000000º         1.00000000 grad    16.00000000 mil      0.01570796 rad
16      3.43362939 rad    196.73247221º       218.59163579 grad  3497.46617261 mil      3.43362939 rad

raw angle      normalized       ------------------------------   conversions   ------------------------------
57.2957795     57.29577950º        57.29577950º        63.66197722 grad  1018.59163556 mil      1.00000000 rad
57.2957795     57.29577950 grad    51.56620155º        57.29577950 grad   916.73247200 mil      0.90000000 rad
57.2957795     57.29577950 mil      3.22288760º         3.58098622 grad    57.29577950 mil      0.05625000 rad
57.2957795      0.74711174 rad     42.80634926º        47.56261029 grad   761.00176466 mil      0.74711174 rad

raw angle      normalized       ------------------------------   conversions   ------------------------------
359    359.00000000º       359.00000000º       398.88888889 grad  6382.22222222 mil      6.26573201 rad
359    359.00000000 grad   323.10000000º       359.00000000 grad  5744.00000000 mil      5.63915881 rad
359    359.00000000 mil     20.19375000º        22.43750000 grad   359.00000000 mil      0.35244743 rad
359      0.85843749 rad     49.18484520º        54.64982800 grad   874.39724794 mil      0.85843749 rad

raw angle      normalized       ------------------------------   conversions   ------------------------------
399     39.00000000º        39.00000000º        43.33333333 grad   693.33333333 mil      0.68067841 rad
399    399.00000000 grad   359.10000000º       399.00000000 grad  6384.00000000 mil      6.26747734 rad
399    399.00000000 mil     22.44375000º        24.93750000 grad   399.00000000 mil      0.39171733 rad
399      3.15932565 rad    181.01602572º       201.12891747 grad  3218.06267946 mil      3.15932565 rad

raw angle      normalized       ------------------------------   conversions   ------------------------------
6399    279.00000000º       279.00000000º       310.00000000 grad  4960.00000000 mil      4.86946861 rad
6399    399.00000000 grad   359.10000000º       399.00000000 grad  6384.00000000 mil      6.26747734 rad
6399   6399.00000000 mil    359.94375000º       399.93750000 grad  6399.00000000 mil      6.28220356 rad
6399      2.71735729 rad    155.69310421º       172.99233802 grad  2767.87740825 mil      2.71735729 rad

raw angle      normalized       ------------------------------   conversions   ------------------------------
1000000    280.00000000º       280.00000000º       311.11111111 grad  4977.77777778 mil      4.88692191 rad
1000000      0.00000000 grad     0.00000000º         0.00000000 grad     0.00000000 mil      0.00000000 rad
1000000   1600.00000000 mil     90.00000000º       100.00000000 grad  1600.00000000 mil      1.57079633 rad
1000000      5.92562114 rad    339.51308232º       377.23675814 grad  6035.78813019 mil      5.92562114 rad

The solution of this seemingly trivial task could be elegantly done by type classes. Each angle unit is represented as a distinct type, preventing from implicit combination of different units. Moreover, adding new units doesn't imply writing new transformers or normalizers.

Isomorphims between all angular types are defined via representation as turns, according to the fact that they all form the same topological space, isomorphic to open interval (-1, 1).

{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}

import Text.Printf

class (Num a, Fractional a, RealFrac a) => Angle a where
fullTurn :: a -- value of the whole turn
mkAngle :: Double -> a
value :: a -> Double
fromTurn :: Double -> a
toTurn :: a -> Double
normalize :: a -> a

-- conversion of angles to rotations in linear case
fromTurn t = angle t * fullTurn
toTurn a = value $a / fullTurn -- normalizer for linear angular unit normalize a = a modulo fullTurn where modulo x r | x == r = r | x < 0 = signum x * abs x modulo r | x >= 0 = x - fromInteger (floor (x / r)) * r -- smart constructor angle :: Angle a => Double -> a angle = normalize . mkAngle -- Two transformers differ only in the order of type application. from :: forall a b. (Angle a, Angle b) => a -> b from = fromTurn . toTurn to :: forall b a. (Angle a, Angle b) => a -> b to = fromTurn . toTurn  Instances of different angular units. -- radians newtype Rad = Rad Double deriving (Eq, Ord, Num, Real, Fractional, RealFrac, Floating) instance Show Rad where show (Rad 0) = printf "∠0" show (Rad r) = printf "∠%.3f" r instance Angle Rad where fullTurn = Rad 2*pi mkAngle = Rad value (Rad r) = r -- degrees newtype Deg = Deg Double deriving (Eq, Ord, Num, Real, Fractional, RealFrac, Floating) instance Show Deg where show (Deg 0) = printf "0°" show (Deg d) = printf "%.3g°" d instance Angle Deg where fullTurn = Deg 360 mkAngle = Deg value (Deg d) = d -- grads newtype Grad = Grad Double deriving (Eq, Ord, Num, Real, Fractional, RealFrac, Floating) instance Show Grad where show (Grad 0) = printf "0g" show (Grad g) = printf "%.3gg" g instance Angle Grad where fullTurn = Grad 400 mkAngle = Grad value (Grad g) = g -- mils newtype Mil = Mil Double deriving (Eq, Ord, Num, Real, Fractional, RealFrac, Floating) instance Show Mil where show (Mil 0) = printf "0m" show (Mil m) = printf "%.3gm" m instance Angle Mil where fullTurn = Mil 6400 mkAngle = Mil value (Mil m) = m -- example of non-linear angular unit newtype Slope = Slope Double deriving (Eq, Ord, Num, Real, Fractional, RealFrac, Floating) instance Show Slope where show (Slope 0) = printf "0%" show (Slope m) = printf "%.g" (m * 100) ++ "%" instance Angle Slope where fullTurn = undefined mkAngle = Slope value (Slope t) = t toTurn = toTurn @Rad . angle . atan . value fromTurn = angle . tan . value . fromTurn @Rad normalize = id  Examples λ> angle 45 :: Deg 45.000° λ> angle pi :: Rad ∠3.141 λ> angle 1000 :: Gon 200.000g λ> normalize 450 :: Deg 90.000° λ> normalize 450 :: Gon 50.000g λ> (from :: Gon -> Rad) 100 ∠1.571 λ> (from :: Rad -> Gon)$ (pi/2)
100.000g

λ> (from :: Deg -> Slope) 45
100%

λ> (from :: Slope -> Mil) 0.5
472.267m

λ> :set -XTypeApplications

λ> from @Gon @Deg (angle 100)
90.000°

λ> to @Gon (angle @Deg 45)
50.000g

The task assignment shows different possible type annotations.

main = do
let xs = [-2, -1, 0, 1, 2, 6.2831853,
16, 57.2957795, 359, 399, 6399, 1000000]

-- using to and angle with type application
putStrLn "converting to radians"
print $to @Rad . angle @Rad <$> xs
print $to @Rad . angle @Deg <$> xs
print $to @Rad . angle @Grad <$> xs
print $to @Rad . angle @Mil <$> xs
print $to @Rad . angle @Slope <$> xs

-- using from with type application
putStrLn "\nconverting to degrees"
print $from @Rad @Deg . angle <$> xs
print $from @Deg @Deg . angle <$> xs
print $from @Grad @Deg . angle <$> xs
print $from @Mil @Deg . angle <$> xs
print $from @Slope @Deg . angle <$> xs

-- using normalization for each unit
putStrLn "\nconverting to grads"
print $to @Grad . normalize . Rad <$> xs
print $to @Grad . normalize . Deg <$> xs
print $to @Grad . normalize . Grad <$> xs
print $to @Grad . normalize . Mil <$> xs
print $to @Grad . normalize . Slope <$> xs

-- using implicit type annotation
putStrLn "\nconverting to mils"
print $(from :: Rad -> Mil) . angle <$> xs
print $(from :: Deg -> Mil) . angle <$> xs
print $(from :: Grad -> Mil) . angle <$> xs
print $(from :: Mil -> Mil) . angle <$> xs
print $(from :: Slope -> Mil) . angle <$> xs

λ> main
[∠-2.000,∠-1.000,∠0,∠1.000,∠2.000,∠6.283,∠3.434,∠0.747,∠0.858,∠3.159,∠2.717,∠5.926]
[∠-0.035,∠-0.017,∠0,∠0.017,∠0.035,∠0.110,∠0.279,∠1.000,∠6.266,∠0.681,∠4.869,∠4.887]
[∠-0.031,∠-0.016,∠0,∠0.016,∠0.031,∠0.099,∠0.251,∠0.900,∠5.639,∠6.267,∠6.267,∠0]
[∠-0.002,∠-0.001,∠0,∠0.001,∠0.002,∠0.006,∠0.016,∠0.056,∠0.352,∠0.392,∠6.282,∠1.571]
[∠-1.107,∠-0.785,∠0,∠0.785,∠1.107,∠1.413,∠1.508,∠1.553,∠1.568,∠1.568,∠1.571,∠1.571]

converting to degrees
[-114.592°,-57.296°,0°,57.296°,114.592°,360.000°,196.732°,42.806°,49.185°,181.016°,155.693°,339.513°]
[-2.000°,-1.000°,0°,1.000°,2.000°,6.283°,16.000°,57.296°,359.000°,39.000°,279.000°,280.000°]
[-1.800°,-0.900°,0°,0.900°,1.800°,5.655°,14.400°,51.566°,323.100°,359.100°,359.100°,0°]
[-0.112°,-5.625e-2°,0°,5.625e-2°,0.112°,0.353°,0.900°,3.223°,20.194°,22.444°,359.944°,90.000°]
[-63.435°,-45.000°,0°,45.000°,63.435°,80.957°,86.424°,89.000°,89.840°,89.856°,89.991°,90.000°]

[-127.324g,-63.662g,0g,63.662g,127.324g,400.000g,218.592g,47.563g,54.650g,201.129g,172.992g,377.237g]
[-2.222g,-1.111g,0g,1.111g,2.222g,6.981g,17.778g,63.662g,398.889g,43.333g,310.000g,311.111g]
[-2.000g,-1.000g,0g,1.000g,2.000g,6.283g,16.000g,57.296g,359.000g,399.000g,399.000g,0g]
[-0.125g,-6.250e-2g,0g,6.250e-2g,0.125g,0.393g,1.000g,3.581g,22.438g,24.938g,399.938g,100.000g]
[-70.483g,-50.000g,0g,50.000g,70.483g,89.952g,96.026g,98.889g,99.823g,99.840g,99.990g,100.000g]

converting to mils
[-2037.183m,-1018.592m,0m,1018.592m,2037.183m,6400.000m,3497.466m,761.002m,874.397m,3218.063m,2767.877m,6035.788m]
[-35.556m,-17.778m,0m,17.778m,35.556m,111.701m,284.444m,1018.592m,6382.222m,693.333m,4960.000m,4977.778m]
[-32.000m,-16.000m,0m,16.000m,32.000m,100.531m,256.000m,916.732m,5744.000m,6384.000m,6384.000m,0m]
[-2.000m,-1.000m,0m,1.000m,2.000m,6.283m,16.000m,57.296m,359.000m,399.000m,6399.000m,1600.000m]
[-1127.732m,-800.000m,0m,800.000m,1127.732m,1439.234m,1536.421m,1582.224m,1597.163m,1597.447m,1599.841m,1599.999m]

## J

given definitions which convert to and from the unit circle, using verbial power (^:) inverse (^: _1), and adverbs to make the sentences read better? or at least differently from other computer languages:

   TAU =: 2p1 NB. tauday.com

normalize =: * * 1 | | NB. signum times the fractional part of absolute value

TurnTo=: &*

as_turn    =:    1 TurnTo
as_degree  =:  360 TurnTo
as_gradian =:  400 TurnTo
as_mil     =: 6400 TurnTo
as_radian  =:  TAU TurnTo

Turn    =: adverb def 'normalize as_turn inv m'
Degree  =: adverb def 'normalize as_degree inv m'
Mil     =: adverb def 'normalize as_mil inv m'


we can compose conversion sentences like

   as_degree   100 Gradian
90


Presuming the following additional definitions:

   NAMES =: > turndegreegradianmilradian
ALL =: as_turnas_degreeas_gradianas_milas_radian
to_all=: NAMES ; ALL:0

VALUES =: _&".'-2   -1   0   1   2   6.2831853   16   57.2957795   359   399   6399   1000000'

to_all   VALUES Turn
+-------+------------------------------------+
|turn   |0 0 0 0 0 0.283185 0 0.29578 0 0 0 0|
|degree |0 0 0 0 0  101.947 0 106.481 0 0 0 0|
|gradian|0 0 0 0 0  113.274 0 118.312 0 0 0 0|
|mil    |0 0 0 0 0  1812.39 0 1892.99 0 0 0 0|
|radian |0 0 0 0 0  1.77931 0 1.85844 0 0 0 0|
+-------+------------------------------------+

to_all   VALUES Degree
+-------+---------------------------------------------------------------------------------------------------------------+
|turn   |_0.00555556 _0.00277778 0 0.00277778 0.00555556 0.0174533 0.0444444 0.159155 0.997222 0.108333   0.775 0.777778|
|degree |         _2          _1 0          1          2   6.28319        16  57.2958      359       39     279      280|
|gradian|   _2.22222    _1.11111 0    1.11111    2.22222   6.98132   17.7778   63.662  398.889  43.3333     310  311.111|
|mil    |   _35.5556    _17.7778 0    17.7778    35.5556   111.701   284.444  1018.59  6382.22  693.333    4960  4977.78|
|radian | _0.0349066  _0.0174533 0  0.0174533  0.0349066  0.109662  0.279253        1  6.26573 0.680678 4.86947  4.88692|
+-------+---------------------------------------------------------------------------------------------------------------+

+-------+----------------------------------------------------------------------------------------------+
|turn   |    _0.005   _0.0025 0   0.0025     0.005 0.015708     0.04 0.143239  0.8975  0.9975  0.9975 0|
|degree |      _1.8      _0.9 0      0.9       1.8  5.65487     14.4  51.5662   323.1   359.1   359.1 0|
|gradian|        _2        _1 0        1         2  6.28319       16  57.2958     359     399     399 0|
|mil    |       _32       _16 0       16        32  100.531      256  916.732    5744    6384    6384 0|
|radian |_0.0314159 _0.015708 0 0.015708 0.0314159 0.098696 0.251327      0.9 5.63916 6.26748 6.26748 0|
+-------+----------------------------------------------------------------------------------------------+

to_all   VALUES Mil
+-------+-------------------------------------------------------------------------------------------------------------------+
|turn   |_0.0003125  _0.00015625 0  0.00015625 0.0003125 0.000981748   0.0025 0.00895247 0.0560937 0.0623438 0.999844   0.25|
|degree |   _0.1125     _0.05625 0     0.05625    0.1125    0.353429      0.9    3.22289   20.1937   22.4438  359.944     90|
|gradian|    _0.125      _0.0625 0      0.0625     0.125    0.392699        1    3.58099   22.4375   24.9375  399.938    100|
|mil    |        _2           _1 0           1         2     6.28319       16    57.2958       359       399     6399   1600|
|radian |_0.0019635 _0.000981748 0 0.000981748 0.0019635   0.0061685 0.015708    0.05625  0.352447  0.391717   6.2822 1.5708|
+-------+-------------------------------------------------------------------------------------------------------------------+

+-------+---------------------------------------------------------------------------------------------------+
|turn   |_0.31831 _0.159155 0 0.159155 0.31831       1 0.546479 0.118907 0.136625 0.502822 0.432481 0.943092|
|degree |_114.592  _57.2958 0  57.2958 114.592     360  196.732  42.8063  49.1848  181.016  155.693  339.513|
|gradian|_127.324   _63.662 0   63.662 127.324     400  218.592  47.5626  54.6498  201.129  172.992  377.237|
|mil    |_2037.18  _1018.59 0  1018.59 2037.18    6400  3497.47  761.002  874.397  3218.06  2767.88  6035.79|
|radian |      _2        _1 0        1       2 6.28319  3.43363 0.747112 0.858437  3.15933  2.71736  5.92562|
+-------+---------------------------------------------------------------------------------------------------+


## Java

import java.text.DecimalFormat;

//  Title:  Angles (geometric), normalization and conversion

public class AnglesNormalizationAndConversion {

public static void main(String[] args) {
DecimalFormat formatAngle = new DecimalFormat("######0.000000");
DecimalFormat formatConv = new DecimalFormat("###0.0000");
for ( double angle : new double[] {-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000} ) {
for ( String units : new String[] {"degrees", "gradiens", "mils", "radians"}) {
double d = 0, g = 0, m = 0, r = 0;
switch (units) {
case "degrees":
d = d2d(angle);
g = d2g(d);
m = d2m(d);
r = d2r(d);
break;
g = g2g(angle);
d = g2d(g);
m = g2m(g);
r = g2r(g);
break;
case "mils":
m = m2m(angle);
d = m2d(m);
g = m2g(m);
r = m2r(m);
break;
r = r2r(angle);
d = r2d(r);
g = r2g(r);
m = r2m(r);
break;
}
System.out.printf("%15s  %8s = %10s  %10s  %10s  %10s%n", formatAngle.format(angle), units, formatConv.format(d), formatConv.format(g), formatConv.format(m), formatConv.format(r));
}
}
}

private static final double DEGREE = 360D;
private static final double GRADIAN = 400D;
private static final double MIL = 6400D;
private static final double RADIAN = (2 * Math.PI);

private static double d2d(double a) {
return a % DEGREE;
}
private static double d2g(double a) {
return a * (GRADIAN / DEGREE);
}
private static double d2m(double a) {
return a * (MIL / DEGREE);
}
private static double d2r(double a) {
return a * (RADIAN / 360);
}

private static double g2d(double a) {
return a * (DEGREE / GRADIAN);
}
private static double g2g(double a) {
return a % GRADIAN;
}
private static double g2m(double a) {
return a * (MIL / GRADIAN);
}
private static double g2r(double a) {
}

private static double m2d(double a) {
return a * (DEGREE / MIL);
}
private static double m2g(double a) {
return a * (GRADIAN / MIL);
}
private static double m2m(double a) {
return a % MIL;
}
private static double m2r(double a) {
return a * (RADIAN / MIL);
}

private static double r2d(double a) {
return a * (DEGREE / RADIAN);
}
private static double r2g(double a) {
}
private static double r2m(double a) {
return a * (MIL / RADIAN);
}
private static double r2r(double a) {
return a % RADIAN;
}

}

Output:
                               degrees    gradiens        mils     radians
-2.000000   degrees =    -2.0000     -2.2222    -35.5556     -0.0349
-2.000000  gradiens =    -1.8000     -2.0000    -32.0000     -0.0314
-2.000000      mils =    -0.1125     -0.1250     -2.0000     -0.0020
-2.000000   radians =  -114.5916   -127.3240  -2037.1833     -2.0000
-1.000000   degrees =    -1.0000     -1.1111    -17.7778     -0.0175
-1.000000  gradiens =    -0.9000     -1.0000    -16.0000     -0.0157
-1.000000      mils =    -0.0563     -0.0625     -1.0000     -0.0010
-1.000000   radians =   -57.2958    -63.6620  -1018.5916     -1.0000
0.000000   degrees =     0.0000      0.0000      0.0000      0.0000
0.000000  gradiens =     0.0000      0.0000      0.0000      0.0000
0.000000      mils =     0.0000      0.0000      0.0000      0.0000
0.000000   radians =     0.0000      0.0000      0.0000      0.0000
1.000000   degrees =     1.0000      1.1111     17.7778      0.0175
1.000000  gradiens =     0.9000      1.0000     16.0000      0.0157
1.000000      mils =     0.0563      0.0625      1.0000      0.0010
1.000000   radians =    57.2958     63.6620   1018.5916      1.0000
2.000000   degrees =     2.0000      2.2222     35.5556      0.0349
2.000000  gradiens =     1.8000      2.0000     32.0000      0.0314
2.000000      mils =     0.1125      0.1250      2.0000      0.0020
2.000000   radians =   114.5916    127.3240   2037.1833      2.0000
6.283185   degrees =     6.2832      6.9813    111.7011      0.1097
6.283185  gradiens =     5.6549      6.2832    100.5310      0.0987
6.283185      mils =     0.3534      0.3927      6.2832      0.0062
6.283185   radians =   360.0000    400.0000   6400.0000      6.2832
16.000000   degrees =    16.0000     17.7778    284.4444      0.2793
16.000000  gradiens =    14.4000     16.0000    256.0000      0.2513
16.000000      mils =     0.9000      1.0000     16.0000      0.0157
16.000000   radians =   196.7325    218.5916   3497.4662      3.4336
57.295780   degrees =    57.2958     63.6620   1018.5916      1.0000
57.295780  gradiens =    51.5662     57.2958    916.7325      0.9000
57.295780      mils =     3.2229      3.5810     57.2958      0.0562
57.295780   radians =    42.8063     47.5626    761.0018      0.7471
359.000000   degrees =   359.0000    398.8889   6382.2222      6.2657
359.000000  gradiens =   323.1000    359.0000   5744.0000      5.6392
359.000000      mils =    20.1938     22.4375    359.0000      0.3524
359.000000   radians =    49.1848     54.6498    874.3972      0.8584
399.000000   degrees =    39.0000     43.3333    693.3333      0.6807
399.000000  gradiens =   359.1000    399.0000   6384.0000      6.2675
399.000000      mils =    22.4438     24.9375    399.0000      0.3917
399.000000   radians =   181.0160    201.1289   3218.0627      3.1593
6399.000000   degrees =   279.0000    310.0000   4960.0000      4.8695
6399.000000  gradiens =   359.1000    399.0000   6384.0000      6.2675
6399.000000      mils =   359.9438    399.9375   6399.0000      6.2822
6399.000000   radians =   155.6931    172.9923   2767.8774      2.7174
1000000.000000   degrees =   280.0000    311.1111   4977.7778      4.8869
1000000.000000  gradiens =     0.0000      0.0000      0.0000      0.0000
1000000.000000      mils =    90.0000    100.0000   1600.0000      1.5708
1000000.000000   radians =   339.5131    377.2368   6035.7881      5.9256


## JavaScript

/*****************************************************************\
| Expects an angle, an origin unit and a unit to convert to,      |
| where in/out units are:                                         |
| --------------------------------------------------------------- |
| 'D'/'d' ..... degrees             'M'/'d' ..... mils            |                                          |
| 'G'/'g' ..... gradians            'R'/'r' ..... radians         |
| --------------------------------------------------------------- |
| example: convert 150 degrees to radians:                        |
| angleConv(150, 'd', 'r')                                        |
\*****************************************************************/
function angleConv(deg, inp, out) {
inp = inp.toLowerCase();
out = out.toLowerCase();
const D = 360,
G = 400,
M = 6400,
R = 2 * Math.PI;
// normalazation
let minus = (deg < 0);  // boolean
deg = Math.abs(deg);
switch (inp) {
case 'd': deg %= D; break;
case 'g': deg %= G; break;
case 'm': deg %= M; break;
case 'r': deg %= R;
}
// we use an internal conversion to Turns (full circle) here
let t;
switch (inp) {
case 'd': t = deg / D; break;
case 'g': t = deg / G; break;
case 'm': t = deg / M; break;
case 'r': t = deg / R;
}
// converting
switch (out) {
case 'd': t *= D; break;
case 'g': t *= G; break;
case 'm': t *= M; break;
case 'r': t *= R;
}
if (minus) return 0 - t;
return t;
}

// mass testing
let nums  = [-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1e6],
units = 'dgmr'.split(''),
x, y, z;
for (x = 0; x < nums.length; x++) {
for (y = 0; y < units.length; y++) {
document.write(
<p>
<b>${nums[x]}<sub>${units[y]}</sub></b><br>
);
for (z = 0; z < units.length; z++)
document.write(
= ${angleConv(nums[x], units[y], units[z])}<sub>${units[z]}</sub>
);
}
}


Output (without bolds and subs):

Output:

-2d
= -2d = -2.2222222222222223g = -35.55555555555556m = -0.03490658503988659r
-2g
= -1.8d = -2g = -32m = -0.031415926535897934r
-2m
= -0.1125d = -0.125g = -2m = -0.001963495408493621r
-2r
= -114.59155902616465d = -127.32395447351628g = -2037.1832715762605m = -2r
-1d
= -1d = -1.1111111111111112g = -17.77777777777778m = -0.017453292519943295r
-1g
= -0.9d = -1g = -16m = -0.015707963267948967r
-1m
= -0.05625d = -0.0625g = -1m = -0.0009817477042468104r
-1r
= -57.29577951308232d = -63.66197723675814g = -1018.5916357881302m = -1r
0d
= 0d = 0g = 0m = 0r
0g
= 0d = 0g = 0m = 0r
0m
= 0d = 0g = 0m = 0r
0r
= 0d = 0g = 0m = 0r
1d
= 1d = 1.1111111111111112g = 17.77777777777778m = 0.017453292519943295r
1g
= 0.9d = 1g = 16m = 0.015707963267948967r
1m
= 0.05625d = 0.0625g = 1m = 0.0009817477042468104r
1r
= 57.29577951308232d = 63.66197723675814g = 1018.5916357881302m = 1r
2d
= 2d = 2.2222222222222223g = 35.55555555555556m = 0.03490658503988659r
2g
= 1.8d = 2g = 32m = 0.031415926535897934r
2m
= 0.1125d = 0.125g = 2m = 0.001963495408493621r
2r
= 114.59155902616465d = 127.32395447351628g = 2037.1832715762605m = 2r
6.2831853d
= 6.2831853d = 6.981317000000001g = 111.70107200000001m = 0.10966227099790768r
6.2831853g
= 5.654866770000001d = 6.2831853g = 100.5309648m = 0.09869604389811691r
6.2831853m
= 0.35342917312500005d = 0.39269908125g = 6.2831853m = 0.006168502743632307r
6.2831853r
= 359.99999958864004d = 399.9999995429334g = 6399.999992686934m = 6.2831853r
16d
= 16d = 17.77777777777778g = 284.44444444444446m = 0.2792526803190927r
16g
= 14.4d = 16g = 256m = 0.25132741228718347r
16m
= 0.9d = 1g = 16m = 0.015707963267948967r
16r
= 196.73247220931714d = 218.59163578813016g = 3497.4661726100826m = 3.433629385640827r
57.2957795d
= 57.2957795d = 63.66197722222222g = 1018.5916355555555m = 0.9999999997716704r
57.2957795g
= 51.56620155d = 57.2957795g = 916.732472m = 0.8999999997945033r
57.2957795m
= 3.222887596875d = 3.58098621875g = 57.2957795m = 0.056249999987156456r
57.2957795r
= 42.80634926218226d = 47.56261029131362g = 761.0017646610179m = 0.7471117353837258r
359d
= 359d = 398.8888888888889g = 6382.222222222223m = 6.265732014659643r
359g
= 323.09999999999997d = 359g = 5744m = 5.639158813193679r
359m
= 20.193749999999998d = 22.4375g = 359m = 0.3524474258246049r
359r
= 49.184845196553994d = 54.649827996171105g = 874.3972479387377m = 0.8584374907635848r
399d
= 39d = 43.333333333333336g = 693.3333333333334m = 0.6806784082777886r
399g
= 359.1d = 399g = 6384m = 6.267477343911637r
399m
= 22.44375d = 24.9375g = 399m = 0.39171733399447733r
399r
= 181.0160257198469d = 201.12891746649657g = 3218.062679463945m = 3.1593256476860674r
6399d
= 279d = 310g = 4960m = 4.869468613064179r
6399g
= 359.1d = 399g = 6384m = 6.267477343911637r
6399m
= 359.94375d = 399.9375g = 6399m = 6.28220355947534r
6399r
= 155.69310421378557d = 172.9923380153173g = 2767.877408245077m = 2.717357291181216r
1000000d
= 280d = 311.11111111111114g = 4977.777777777778m = 4.886921905584122r
1000000g
= 0d = 0g = 0m = 0r
1000000m
= 90d = 100g = 1600m = 1.5707963267948966r
1000000r
= 339.51308232311027d = 377.2367581367892g = 6035.788130188627m = 5.925621140132833r



## jq

Works with: jq

Works with gojq, the Go implementation of jq

Preliminaries

### Formatting

# Right-justify but do not truncate
def rjustify(n):
tostring | length as $length | if n <=$length then . else " " * (n-length) + . end; # Attempt to align decimals so integer part is in a field of width n def align(n):
tostring
| index(".") as $ix | if$ix
then if $n <$ix then .
elif $ix then (.[0:$ix]|rjustify($n)) +.[$ix:]
else rjustify(n) end else . + ".0" | align(n)
end ;

# number of decimal places ($n>=0) def fround($n):
pow(10;$n) as$p
| (. * $p | round ) /$p
| tostring
| index(".") as $ix | ("0" *$n) as $zeros | if$ix then . + $zeros | .[0 :$ix + $n + 1] else . + "." +$zeros
end;

def hide_trailing_zeros:
tostring
| (capture("(?<x>[^.]*[.].)(?<y>00*$)") // null) as$capture
| if $capture then$capture | (.x + (.y|gsub("0"; " ")))
else .
end;

def lpad($len): tostring | ($len - length) as $l | (" " *$l)[:$l] + .; The Task # Normalization as per the task requirements def mod($y):
(if . < 0 then -$y else 0 end) as$adjust
| $adjust + . - ($y * ((. / y)|floor)); def pi: (1|atan) * 4; def d2d: mod(360); def g2g: mod(400); def m2m: mod(6400); def r2r: mod(2*pi); def d2g: d2d * 400 / 360; def d2m: d2d * 6400 / 360; def d2r: d2d * pi / 180; def g2d: g2g * 360 / 400; def g2m: g2g * 6400 / 400; def g2r: g2g * pi / 200; def m2d: m2m * 360 / 6400; def m2g: m2m * 400 / 6400; def m2r: m2m * pi / 3200; def r2d: r2r * 180 / pi; def r2g: r2r * 200 / pi; def r2m: r2r * 3200 / pi; def f1(a;b;c;d;e): "\(a|lpad(15)) \(b|lpad(15)) \(c|lpad(15)) \(d|lpad(15)) \(e|lpad(15))"; def f2(a;b;c;d;e): def al: fround(7) | align(10)| hide_trailing_zeros; "\(a|al) \(b|al) \(c|al) \(d|al) \(e|al)"; def angles: [-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000]; def task1: f1( "degrees"; "normalized degs"; "gradians"; "mils"; "radians"), (angles[] | f2(.; d2d; d2g; d2m; d2r)) ; def task2: f1("gradians"; "normalized grds"; "degrees"; "mils"; "radians"), (angles[] | f2(.; g2g; g2d; g2m; g2r)); def task3: f1("mils"; "normalized mils"; "degrees"; "gradians"; "radians"), (angles[] | f2(.; m2m; m2d; m2g; m2r)); def task4: f1( "radians"; "normalized rads"; "degrees"; "gradians"; "mils"), ( angles[] | f2(.; r2r; r2d; r2g; r2m) ); task1, "", task2, "", task3, "", task4 Output: As for [[#Wren]]  ## Julia using Formatting d2d(d) = d % 360 g2g(g) = g % 400 m2m(m) = m % 6400 r2r(r) = r % 2π d2g(d) = d2d(d) * 10 / 9 d2m(d) = d2d(d) * 160 / 9 d2r(d) = d2d(d) * π / 180 g2d(g) = g2g(g) * 9 / 10 g2m(g) = g2g(g) * 16 g2r(g) = g2g(g) * π / 200 m2d(m) = m2m(m) * 9 / 160 m2g(m) = m2m(m) / 16 m2r(m) = m2m(m) * π / 3200 r2d(r) = r2r(r) * 180 / π r2g(r) = r2r(r) * 200 / π r2m(r) = r2r(r) * 3200 / π fmt(x::Real, width=16) = Int(round(x)) == x ? rpad(Int(x), width) : rpad(format(x, precision=7), width) fmt(x::String, width=16) = rpad(x, width) const t2u = Dict("degrees" => [d2d, d2g, d2m, d2r], "gradians" => [g2d, g2g, g2m, g2r], "mils" => [m2d, m2g, m2m, m2r], "radians" => [r2d, r2g, r2m, r2r]) function testconversions(arr) println("Number Units Degrees Gradians Mils Radians") for num in arr, units in ["degrees", "gradians", "mils", "radians"] print(fmt(num), fmt(units)) for f in t2u[units] print(fmt(f(num))) end println() end end testconversions([-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000])  Output: Number Units Degrees Gradians Mils Radians -2 degrees -2 -2.2222222 -35.5555556 -0.0349066 -2 gradians -1.8000000 -2 -32 -0.0314159 -2 mils -0.1125000 -0.1250000 -2 -0.0019635 -2 radians -114.5915590 -127.3239545 -2037.1832716 -2 -1 degrees -1 -1.1111111 -17.7777778 -0.0174533 -1 gradians -0.9000000 -1 -16 -0.0157080 -1 mils -0.0562500 -0.0625000 -1 -0.0009817 -1 radians -57.2957795 -63.6619772 -1018.5916358 -1 0 degrees 0 0 0 0 0 gradians 0 0 0 0 0 mils 0 0 0 0 0 radians 0 0 0 0 1 degrees 1 1.1111111 17.7777778 0.0174533 1 gradians 0.9000000 1 16 0.0157080 1 mils 0.0562500 0.0625000 1 0.0009817 1 radians 57.2957795 63.6619772 1018.5916358 1 2 degrees 2 2.2222222 35.5555556 0.0349066 2 gradians 1.8000000 2 32 0.0314159 2 mils 0.1125000 0.1250000 2 0.0019635 2 radians 114.5915590 127.3239545 2037.1832716 2 6.2831853 degrees 6.2831853 6.9813170 111.7010720 0.1096623 6.2831853 gradians 5.6548668 6.2831853 100.5309648 0.0986960 6.2831853 mils 0.3534292 0.3926991 6.2831853 0.0061685 6.2831853 radians 359.9999996 399.9999995 6399.9999927 6.2831853 16 degrees 16 17.7777778 284.4444444 0.2792527 16 gradians 14.4000000 16 256 0.2513274 16 mils 0.9000000 1 16 0.0157080 16 radians 196.7324722 218.5916358 3497.4661726 3.4336294 57.2957795 degrees 57.2957795 63.6619772 1018.5916356 1.0000000 57.2957795 gradians 51.5662016 57.2957795 916.7324720 0.9000000 57.2957795 mils 3.2228876 3.5809862 57.2957795 0.0562500 57.2957795 radians 42.8063493 47.5626103 761.0017647 0.7471117 359 degrees 359 398.8888889 6382.2222222 6.2657320 359 gradians 323.1000000 359 5744 5.6391588 359 mils 20.1937500 22.4375000 359 0.3524474 359 radians 49.1848452 54.6498280 874.3972479 0.8584375 399 degrees 39 43.3333333 693.3333333 0.6806784 399 gradians 359.1000000 399 6384 6.2674773 399 mils 22.4437500 24.9375000 399 0.3917173 399 radians 181.0160257 201.1289175 3218.0626795 3.1593256 6399 degrees 279 310 4960 4.8694686 6399 gradians 359.1000000 399 6384 6.2674773 6399 mils 359.9437500 399.9375000 6399 6.2822036 6399 radians 155.6931042 172.9923380 2767.8774082 2.7173573 1000000 degrees 280 311.1111111 4977.7777778 4.8869219 1000000 gradians 0 0 0 0 1000000 mils 90 100 1600 1.5707963 1000000 radians 339.5130823 377.2367581 6035.7881302 5.9256211  ## Kotlin Translation of: Java import java.text.DecimalFormat as DF const val DEGREE = 360.0 const val GRADIAN = 400.0 const val MIL = 6400.0 const val RADIAN = 2 * Math.PI fun d2d(a: Double) = a % DEGREE fun d2g(a: Double) = a * (GRADIAN / DEGREE) fun d2m(a: Double) = a * (MIL / DEGREE) fun d2r(a: Double) = a * (RADIAN / 360) fun g2d(a: Double) = a * (DEGREE / GRADIAN) fun g2g(a: Double) = a % GRADIAN fun g2m(a: Double) = a * (MIL / GRADIAN) fun g2r(a: Double) = a * (RADIAN / GRADIAN) fun m2d(a: Double) = a * (DEGREE / MIL) fun m2g(a: Double) = a * (GRADIAN / MIL) fun m2m(a: Double) = a % MIL fun m2r(a: Double) = a * (RADIAN / MIL) fun r2d(a: Double) = a * (DEGREE / RADIAN) fun r2g(a: Double) = a * (GRADIAN / RADIAN) fun r2m(a: Double) = a * (MIL / RADIAN) fun r2r(a: Double) = a % RADIAN fun main() { val fa = DF("######0.000000") val fc = DF("###0.0000") println(" degrees gradiens mils radians") for (a in listOf(-2.0, -1.0, 0.0, 1.0, 2.0, 6.2831853, 16.0, 57.2957795, 359.0, 399.0, 6399.0, 1000000.0)) for (units in listOf("degrees", "gradiens", "mils", "radians")) { val (d,g,m,r) = when (units) { "degrees" -> { val d = d2d(a) listOf(d, d2g(d), d2m(d), d2r(d)) } "gradiens" -> { val g = g2g(a) listOf(g2d(g), g, g2m(g), g2r(g)) } "mils" -> { val m = m2m(a) listOf(m2d(m), m2g(m), m, m2r(m)) } "radians" -> { val r = r2r(a) listOf(r2d(r), r2g(r), r2m(r), r) } else -> emptyList() } println("%15s %8s = %10s %10s %10s %10s".format(fa.format(a), units, fc.format(d), fc.format(g), fc.format(m), fc.format(r))) } }  Output: See Java output ## Lua range = { degrees=360, gradians=400, mils=6400, radians=2.0*math.pi } function convert(value, fromunit, tounit) return math.fmod(value * range[tounit] / range[fromunit], range[tounit]) end testvalues = { -2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000 } testunits = { "degrees", "gradians", "mils", "radians" } print(string.format("%15s %8s = %15s %15s %15s %15s", "VALUE", "UNIT", "DEGREES", "GRADIANS", "MILS", "RADIANS")) for _, value in ipairs(testvalues) do for _, fromunit in ipairs(testunits) do local d = convert(value, fromunit, "degrees") local g = convert(value, fromunit, "gradians") local m = convert(value, fromunit, "mils") local r = convert(value, fromunit, "radians") print(string.format("%15.7f %8s = %15.7f %15.7f %15.7f %15.7f", value, fromunit, d, g, m, r)) end end  Optionally: -- if you care.. assert(convert(-360,"degrees","degrees") == 0.0) assert(convert(360,"degrees","degrees") == 0.0) assert(convert(-400,"gradians","gradians") == 0.0) assert(convert(400,"gradians","gradians") == 0.0) assert(convert(-6400,"mils","mils") == 0.0) assert(convert(6400,"mils","mils") == 0.0) assert(convert(-2.0*math.pi,"radians","radians") == 0.0) assert(convert(2.0*math.pi,"radians","radians") == 0.0) -- if you must.. function d2d(n) return convert(n,"degrees","degrees") end function d2g(n) return convert(n,"degrees","gradians") end function d2m(n) return convert(n,"degrees","mils") end function d2r(n) return convert(n,"degrees","radians") end function g2d(n) return convert(n,"gradians","degrees") end function g2g(n) return convert(n,"gradians","gradians") end function g2m(n) return convert(n,"gradians","mils") end function g2r(n) return convert(n,"gradians","radians") end function m2d(n) return convert(n,"mils","degrees") end function m2g(n) return convert(n,"mils","gradians") end function m2m(n) return convert(n,"mils","mils") end function m2r(n) return convert(n,"mils","radians") end function r2d(n) return convert(n,"radians","degrees") end function r2g(n) return convert(n,"radians","gradians") end function r2m(n) return convert(n,"radians","mils") end function r2r(n) return convert(n,"radians","radians") end  Output:  VALUE UNIT = DEGREES GRADIANS MILS RADIANS -2.0000000 degrees = -2.0000000 -2.2222222 -35.5555556 -0.0349066 -2.0000000 gradians = -1.8000000 -2.0000000 -32.0000000 -0.0314159 -2.0000000 mils = -0.1125000 -0.1250000 -2.0000000 -0.0019635 -2.0000000 radians = -114.5915590 -127.3239545 -2037.1832716 -2.0000000 -1.0000000 degrees = -1.0000000 -1.1111111 -17.7777778 -0.0174533 -1.0000000 gradians = -0.9000000 -1.0000000 -16.0000000 -0.0157080 -1.0000000 mils = -0.0562500 -0.0625000 -1.0000000 -0.0009817 -1.0000000 radians = -57.2957795 -63.6619772 -1018.5916358 -1.0000000 0.0000000 degrees = 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 gradians = 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 mils = 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 radians = 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 degrees = 1.0000000 1.1111111 17.7777778 0.0174533 1.0000000 gradians = 0.9000000 1.0000000 16.0000000 0.0157080 1.0000000 mils = 0.0562500 0.0625000 1.0000000 0.0009817 1.0000000 radians = 57.2957795 63.6619772 1018.5916358 1.0000000 2.0000000 degrees = 2.0000000 2.2222222 35.5555556 0.0349066 2.0000000 gradians = 1.8000000 2.0000000 32.0000000 0.0314159 2.0000000 mils = 0.1125000 0.1250000 2.0000000 0.0019635 2.0000000 radians = 114.5915590 127.3239545 2037.1832716 2.0000000 6.2831853 degrees = 6.2831853 6.9813170 111.7010720 0.1096623 6.2831853 gradians = 5.6548668 6.2831853 100.5309648 0.0986960 6.2831853 mils = 0.3534292 0.3926991 6.2831853 0.0061685 6.2831853 radians = 359.9999996 399.9999995 6399.9999927 6.2831853 16.0000000 degrees = 16.0000000 17.7777778 284.4444444 0.2792527 16.0000000 gradians = 14.4000000 16.0000000 256.0000000 0.2513274 16.0000000 mils = 0.9000000 1.0000000 16.0000000 0.0157080 16.0000000 radians = 196.7324722 218.5916358 3497.4661726 3.4336294 57.2957795 degrees = 57.2957795 63.6619772 1018.5916356 1.0000000 57.2957795 gradians = 51.5662016 57.2957795 916.7324720 0.9000000 57.2957795 mils = 3.2228876 3.5809862 57.2957795 0.0562500 57.2957795 radians = 42.8063493 47.5626103 761.0017647 0.7471117 359.0000000 degrees = 359.0000000 398.8888889 6382.2222222 6.2657320 359.0000000 gradians = 323.1000000 359.0000000 5744.0000000 5.6391588 359.0000000 mils = 20.1937500 22.4375000 359.0000000 0.3524474 359.0000000 radians = 49.1848452 54.6498280 874.3972479 0.8584375 399.0000000 degrees = 39.0000000 43.3333333 693.3333333 0.6806784 399.0000000 gradians = 359.1000000 399.0000000 6384.0000000 6.2674773 399.0000000 mils = 22.4437500 24.9375000 399.0000000 0.3917173 399.0000000 radians = 181.0160257 201.1289175 3218.0626795 3.1593256 6399.0000000 degrees = 279.0000000 310.0000000 4960.0000000 4.8694686 6399.0000000 gradians = 359.1000000 399.0000000 6384.0000000 6.2674773 6399.0000000 mils = 359.9437500 399.9375000 6399.0000000 6.2822036 6399.0000000 radians = 155.6931042 172.9923380 2767.8774082 2.7173573 1000000.0000000 degrees = 280.0000000 311.1111111 4977.7777778 4.8869219 1000000.0000000 gradians = 0.0000000 0.0000000 0.0000000 0.0000000 1000000.0000000 mils = 90.0000000 100.0000000 1600.0000000 1.5707963 1000000.0000000 radians = 339.5130823 377.2367581 6035.7881302 5.9256211 ## Mathematica/Wolfram Language ClearAll[NormalizeAngle, NormalizeDegree, NormalizeGradian, NormalizeMil, NormalizeRadian] NormalizeAngle[d_, full_] := Module[{a = d}, If[Abs[a/full] > 4, a = a - Sign[a] full (Quotient[Abs[a], full] - 4) ]; While[a < -full, a += full]; While[a > full, a -= full]; a ] ClearAll[Degree2Gradian, Degree2Mil, Degree2Radian, Gradian2Degree, Gradian2Mil, Gradian2Radian, Mil2Degree, Mil2Gradian, Mil2Radian, Radian2Degree, Radian2Gradian, Radian2Mil] NormalizeDegree[d_] := NormalizeAngle[d, 360] NormalizeGradian[d_] := NormalizeAngle[d, 400] NormalizeMil[d_] := NormalizeAngle[d, 6400] NormalizeRadian[d_] := NormalizeAngle[d, 2 Pi] Degree2Gradian[d_] := d 400/360 Degree2Mil[d_] := d 6400/360 Degree2Radian[d_] := d Pi/180 Gradian2Degree[d_] := d 360/400 Gradian2Mil[d_] := d 6400/400 Gradian2Radian[d_] := d 2 Pi/400 Mil2Degree[d_] := d 360/6400 Mil2Gradian[d_] := d 400/6400 Mil2Radian[d_] := d 2 Pi/6400 Radian2Degree[d_] := d 180/Pi Radian2Gradian[d_] := d 400/(2 Pi) Radian2Mil[d_] := d 6400/(2 Pi) MapThread[Construct, {{Degree2Gradian, Degree2Mil, Degree2Radian, Gradian2Degree, Gradian2Mil, Gradian2Radian, Mil2Degree, Mil2Gradian, Mil2Radian, Radian2Degree, Radian2Gradian, Radian2Mil}, {-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000}}]  Output: {-(20/9),-(160/9),0,9/10,32,0.098696,9/10,3.58099,(359 \[Pi])/3200,71820/\[Pi],1279800/\[Pi],3200000000/\[Pi]} ## Nim import math import strformat const Values = [float -2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000] func d2d(x: float): float {.inline.} = x mod 360 func g2g(x: float): float {.inline.} = x mod 400 func m2m(x: float): float {.inline.} = x mod 6400 func r2r(x: float): float {.inline.} = x mod (2 * Pi) func d2g(x: float): float {.inline.} = d2d(x) * 10 / 9 func d2m(x: float): float {.inline.} = d2d(x) * 160 / 9 func d2r(x: float): float {.inline.} = d2d(x) * Pi / 180 func g2d(x: float): float {.inline.} = g2g(x) * 9 / 10 func g2m(x: float): float {.inline.} = g2g(x) * 16 func g2r(x: float): float {.inline.} = g2g(x) * Pi / 200 func m2d(x: float): float {.inline.} = m2m(x) * 9 / 160 func m2g(x: float): float {.inline.} = m2m(x) / 16 func m2r(x: float): float {.inline.} = m2m(x) * Pi / 3200 func r2d(x: float): float {.inline.} = r2r(x) * 180 / Pi func r2g(x: float): float {.inline.} = r2r(x) * 200 / Pi func r2m(x: float): float {.inline.} = r2r(x) * 3200 / Pi # Normalizing and converting degrees. echo " Degrees Normalized Gradians Mils Radians" echo "———————————————————————————————————————————————————————————————————————————————————" for val in Values: echo fmt"{val:15.7f} {d2d(val):15.7f} {d2g(val):15.7f} {d2m(val):15.7f} {d2r(val):15.7f}" # Normalizing and converting gradians. echo "" echo " Gradians Normalized Degrees Mils Radians" echo "———————————————————————————————————————————————————————————————————————————————————" for val in Values: echo fmt"{val:15.7f} {g2g(val):15.7f} {g2d(val):15.7f} {g2m(val):15.7f} {g2r(val):15.7f}" # Normalizing and converting mils. echo "" echo " Mils Normalized Degrees Gradians Radians" echo "———————————————————————————————————————————————————————————————————————————————————" for val in Values: echo fmt"{val:15.7f} {m2m(val):15.7f} {m2d(val):15.7f} {m2g(val):15.7f} {m2r(val):15.7f}" # Normalizing and converting radians. echo "" echo " Radians Normalized Degrees Gradians Mils" echo "———————————————————————————————————————————————————————————————————————————————————" for val in Values: echo fmt"{val:15.7f} {r2r(val):15.7f} {r2d(val):15.7f} {r2g(val):15.7f} {r2m(val):15.7f}"  Output:  Degrees Normalized Gradians Mils Radians ——————————————————————————————————————————————————————————————————————————————————— -2.0000000 -2.0000000 -2.2222222 -35.5555556 -0.0349066 -1.0000000 -1.0000000 -1.1111111 -17.7777778 -0.0174533 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 1.0000000 1.1111111 17.7777778 0.0174533 2.0000000 2.0000000 2.2222222 35.5555556 0.0349066 6.2831853 6.2831853 6.9813170 111.7010720 0.1096623 16.0000000 16.0000000 17.7777778 284.4444444 0.2792527 57.2957795 57.2957795 63.6619772 1018.5916356 1.0000000 359.0000000 359.0000000 398.8888889 6382.2222222 6.2657320 399.0000000 39.0000000 43.3333333 693.3333333 0.6806784 6399.0000000 279.0000000 310.0000000 4960.0000000 4.8694686 1000000.0000000 280.0000000 311.1111111 4977.7777778 4.8869219 Gradians Normalized Degrees Mils Radians ——————————————————————————————————————————————————————————————————————————————————— -2.0000000 -2.0000000 -1.8000000 -32.0000000 -0.0314159 -1.0000000 -1.0000000 -0.9000000 -16.0000000 -0.0157080 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 1.0000000 0.9000000 16.0000000 0.0157080 2.0000000 2.0000000 1.8000000 32.0000000 0.0314159 6.2831853 6.2831853 5.6548668 100.5309648 0.0986960 16.0000000 16.0000000 14.4000000 256.0000000 0.2513274 57.2957795 57.2957795 51.5662016 916.7324720 0.9000000 359.0000000 359.0000000 323.1000000 5744.0000000 5.6391588 399.0000000 399.0000000 359.1000000 6384.0000000 6.2674773 6399.0000000 399.0000000 359.1000000 6384.0000000 6.2674773 1000000.0000000 0.0000000 0.0000000 0.0000000 0.0000000 Mils Normalized Degrees Gradians Radians ——————————————————————————————————————————————————————————————————————————————————— -2.0000000 -2.0000000 -0.1125000 -0.1250000 -0.0019635 -1.0000000 -1.0000000 -0.0562500 -0.0625000 -0.0009817 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 1.0000000 0.0562500 0.0625000 0.0009817 2.0000000 2.0000000 0.1125000 0.1250000 0.0019635 6.2831853 6.2831853 0.3534292 0.3926991 0.0061685 16.0000000 16.0000000 0.9000000 1.0000000 0.0157080 57.2957795 57.2957795 3.2228876 3.5809862 0.0562500 359.0000000 359.0000000 20.1937500 22.4375000 0.3524474 399.0000000 399.0000000 22.4437500 24.9375000 0.3917173 6399.0000000 6399.0000000 359.9437500 399.9375000 6.2822036 1000000.0000000 1600.0000000 90.0000000 100.0000000 1.5707963 Radians Normalized Degrees Gradians Mils ——————————————————————————————————————————————————————————————————————————————————— -2.0000000 -2.0000000 -114.5915590 -127.3239545 -2037.1832716 -1.0000000 -1.0000000 -57.2957795 -63.6619772 -1018.5916358 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 1.0000000 57.2957795 63.6619772 1018.5916358 2.0000000 2.0000000 114.5915590 127.3239545 2037.1832716 6.2831853 6.2831853 359.9999996 399.9999995 6399.9999927 16.0000000 3.4336294 196.7324722 218.5916358 3497.4661726 57.2957795 0.7471117 42.8063493 47.5626103 761.0017647 359.0000000 0.8584375 49.1848452 54.6498280 874.3972479 399.0000000 3.1593256 181.0160257 201.1289175 3218.0626795 6399.0000000 2.7173573 155.6931042 172.9923380 2767.8774082 1000000.0000000 5.9256211 339.5130823 377.2367581 6035.7881302 ## Perl Translation of: Raku use strict; use warnings; use feature 'say'; use POSIX 'fmod'; mytau = 2 * 4*atan2(1, 1);
my @units = (
{ code => 'd', name => 'degrees' , number =>  360 },
{ code => 'g', name => 'gradians', number =>  400 },
{ code => 'm', name => 'mills'   , number => 6400 },
{ code => 'r', name => 'radians' , number => $tau }, ); my %cvt; for my$a (@units) {
for my $b (@units) {$cvt{ "${$a}{code}2${$b}{code}" } = sub {
my($angle) = shift; my$norm = fmod($angle,${$a}{number}); # built-in '%' returns only integers$norm -= ${$a}{number} if $angle < 0;$norm * ${$b}{number} / ${$a}{number}
}
}
}

printf '%s'. '%12s'x4 . "\n", '     Angle Unit    ', <Degrees Gradians Mills Radians>;
for my $angle (-2, -1, 0, 1, 2,$tau, 16, 360/$tau, 360-1, 400-1, 6400-1, 1_000_000) { print "\n"; for my$from (@units) {
my @sub_keys = map { "${$from}{code}2${$_}{code}" } @units;
my @results  = map { &{$cvt{$_}}($angle) } @sub_keys; printf '%10g %-8s' . '%12g'x4 . "\n",$angle, ${$from}{name}, @results;
}
}

Output:
     Angle Unit         Degrees    Gradians       Mills     Radians

-2 degrees         -362    -402.222    -6435.56    -6.31809
-2 gradians      -361.8        -402       -6432     -6.3146
-2 mills       -360.113    -400.125       -6402    -6.28515
-2 radians     -474.592    -527.324    -8437.18    -8.28319

-1 degrees         -361    -401.111    -6417.78    -6.30064
-1 gradians      -360.9        -401       -6416    -6.29889
-1 mills       -360.056    -400.062       -6401    -6.28417
-1 radians     -417.296    -463.662    -7418.59    -7.28319

0 degrees            0           0           0           0
0 gradians           0           0           0           0
0 mills              0           0           0           0
0 radians            0           0           0           0

1 degrees            1     1.11111     17.7778   0.0174533
1 gradians         0.9           1          16    0.015708
1 mills        0.05625      0.0625           1 0.000981748
1 radians      57.2958      63.662     1018.59           1

2 degrees            2     2.22222     35.5556   0.0349066
2 gradians         1.8           2          32   0.0314159
2 mills         0.1125       0.125           2   0.0019635
2 radians      114.592     127.324     2037.18           2

6.28319 degrees      6.28319     6.98132     111.701    0.109662
6.28319 gradians     5.65487     6.28319     100.531    0.098696
6.28319 mills       0.353429    0.392699     6.28319   0.0061685
6.28319 radians            0           0           0           0

16 degrees           16     17.7778     284.444    0.279253
16 gradians        14.4          16         256    0.251327
16 mills            0.9           1          16    0.015708
16 radians      196.732     218.592     3497.47     3.43363

57.2958 degrees      57.2958      63.662     1018.59           1
57.2958 gradians     51.5662     57.2958     916.732         0.9
57.2958 mills        3.22289     3.58099     57.2958     0.05625
57.2958 radians      42.8064     47.5626     761.002    0.747112

359 degrees          359     398.889     6382.22     6.26573
359 gradians       323.1         359        5744     5.63916
359 mills        20.1938     22.4375         359    0.352447
359 radians      49.1848     54.6498     874.397    0.858437

399 degrees           39     43.3333     693.333    0.680678
399 gradians       359.1         399        6384     6.26748
399 mills        22.4438     24.9375         399    0.391717
399 radians      181.016     201.129     3218.06     3.15933

6399 degrees          279         310        4960     4.86947
6399 gradians       359.1         399        6384     6.26748
6399 mills        359.944     399.938        6399      6.2822
6399 radians      155.693     172.992     2767.88     2.71736

1e+06 degrees          280     311.111     4977.78     4.88692
1e+06 gradians           0           0           0           0
1e+06 mills             90         100        1600      1.5708
1e+06 radians      339.513     377.237     6035.79     5.92562

## Phix

Obviously if preferred you could define a long list of routines such as function d2g(atom a) return remainder(a/360,1)*400 end function

constant units = {"degrees","gradians","mils","radians"},
turns = {1/360,1/400,1/6400,0.5/PI}

function convert(atom a, integer fdx, tdx)
return remainder(a*turns[fdx],1)/turns[tdx]
end function

constant tests = {-2,-1,0,1,2,2*PI,16,57.2957795,359,399,6399,1000000}
printf(1,"    angle unit     %9s %9s %9s %9s\n",units)
for i=1 to length(tests) do
for fdx=1 to length(units) do
printf(1,"%9g %-8s",{tests[i],units[fdx]})
for tdx=1 to length(units) do
printf(1," %9g",convert(tests[i],fdx,tdx))
end for
puts(1,"\n")
end for
puts(1,"\n")
end for

Output:
    angle unit       degrees  gradians      mils   radians
-2 degrees         -2  -2.22222  -35.5556 -0.034907
-2 gradians      -1.8        -2       -32 -0.031416
-2 mils       -0.1125    -0.125        -2 -0.001963
-2 radians   -114.592  -127.324  -2037.18        -2

-1 degrees         -1  -1.11111  -17.7778 -0.017453
-1 gradians      -0.9        -1       -16 -0.015708
-1 mils      -0.05625   -0.0625        -1 -0.000982
-1 radians   -57.2958   -63.662  -1018.59        -1

0 degrees          0         0         0         0
0 gradians         0         0         0         0
0 mils             0         0         0         0
0 radians          0         0         0         0

1 degrees          1   1.11111   17.7778  0.017453
1 gradians       0.9         1        16  0.015708
1 mils       0.05625    0.0625         1  0.000982
1 radians    57.2958    63.662   1018.59         1

2 degrees          2   2.22222   35.5556  0.034907
2 gradians       1.8         2        32  0.031416
2 mils        0.1125     0.125         2  0.001963
2 radians    114.592   127.324   2037.18         2

6.28319 degrees    6.28319   6.98132   111.701  0.109662
6.28319 gradians   5.65487   6.28319   100.531  0.098696
6.28319 mils      0.353429  0.392699   6.28319  0.006169
6.28319 radians          0         0         0         0

16 degrees         16   17.7778   284.444  0.279253
16 gradians      14.4        16       256  0.251327
16 mils           0.9         1        16  0.015708
16 radians    196.732   218.592   3497.47   3.43363

57.2958 degrees    57.2958    63.662   1018.59         1
57.2958 gradians   51.5662   57.2958   916.732       0.9
57.2958 mils       3.22289   3.58099   57.2958   0.05625
57.2958 radians    42.8063   47.5626   761.002  0.747112

359 degrees        359   398.889   6382.22   6.26573
359 gradians     323.1       359      5744   5.63916
359 mils       20.1937   22.4375       359  0.352447
359 radians    49.1848   54.6498   874.397  0.858437

399 degrees         39   43.3333   693.333  0.680678
399 gradians     359.1       399      6384   6.26748
399 mils       22.4438   24.9375       399  0.391717
399 radians    181.016   201.129   3218.06   3.15933

6399 degrees        279       310      4960   4.86947
6399 gradians     359.1       399      6384   6.26748
6399 mils       359.944   399.938      6399    6.2822
6399 radians    155.693   172.992   2767.88   2.71736

1e+6 degrees        280   311.111   4977.78   4.88692
1e+6 gradians         0         0         0         0
1e+6 mils            90       100      1600    1.5708
1e+6 radians    339.513   377.237   6035.79   5.92562


## Python

### Python: Original

PI = 3.141592653589793
TWO_PI = 6.283185307179586

def normalize2deg(a):
while a < 0: a += 360
while a >= 360: a -= 360
return a
while a < 0: a += 400
while a >= 400: a -= 400
return a
def normalize2mil(a):
while a < 0: a += 6400
while a >= 6400: a -= 6400
return a
while a < 0: a += TWO_PI
while a >= TWO_PI: a -= TWO_PI
return a

def deg2grad(a): return a * 10.0 / 9.0
def deg2mil(a): return a * 160.0 / 9.0
def deg2rad(a): return a * PI / 180.0

def grad2deg(a): return a * 9.0 / 10.0
def grad2mil(a): return a * 16.0
def grad2rad(a): return a * PI / 200.0

def mil2deg(a): return a * 9.0 / 160.0
def mil2grad(a): return a / 16.0
def mil2rad(a): return a * PI / 3200.0

def rad2deg(a): return a * 180.0 / PI
def rad2grad(a): return a * 200.0 / PI
def rad2mil(a): return a * 3200.0 / PI


### Python: using tkinter

''' Python 3.6.5 code using Tkinter graphical user interface.
Angles (geometric), normalization and conversion challenge.
User enteres value for angle and selects a unit, then
presses 'Convert' button.
Values for that angle are shown in degrees, grads, mils
'''

from tkinter import *
from tkinter import messagebox
import math

class Angle:
def __init__(self, gw):
self.window = gw
self.unit = StringVar()
self.unit.set(' ')

a1 = "(Enter 'Angle' & select 'Unit',"
a2 = "then click 'Convert')"
self.msga = a1 + '\n' + a2

# dictionary of functions to execute depending
# on which radio button was selected:
self.d_to_deg = {'d':self.d2d,
'g':self.g2d,
'm':self.m2d,
'r':self.r2d}

# top frame:
self.top_fr = Frame(gw,
width=600,
height=100,
bg='dodger blue')
self.top_fr.pack(fill=X)

self.hdg = Label(self.top_fr,
text='  Angle Conversion  ',
font='arial 22 bold',
fg='navy',
bg='lemon chiffon')
self.hdg.place(relx=0.5, rely=0.5,
anchor=CENTER)

self.close_btn = Button(self.top_fr,
text='Quit',
bd=5,
bg='navy',
fg='lemon chiffon',
font='arial 12 bold',
command=self.close_window)
self.close_btn.place(relx=0.07, rely=0.5,
anchor=W)

self.clear_btn = Button(self.top_fr,
text='Clear',
bd=5,
bg='navy',
fg='lemon chiffon',
font='arial 12 bold',
command=self.clear_screen)
self.clear_btn.place(relx=0.92, rely=0.5,
anchor=E)

# bottom frame:
self.btm_fr = Frame(gw,
width=600,
height=500,
bg='lemon chiffon')
self.btm_fr.pack(fill=X)

self.msg = Label(self.btm_fr,
text=self.msga,
font='arial 16 bold',
fg='navy',
bg='lemon chiffon')
self.msg.place(relx=0.5, rely=0.1,
anchor=CENTER)

self.nbr_fr = LabelFrame(self.btm_fr,
text='     Angle   ',
bg='dodger blue',
fg='navy',
bd=4,
relief=RIDGE,
font='arial 12 bold')
self.nbr_fr.place(relx=0.17, rely=0.27,
anchor=CENTER)

self.nbr_ent = Entry(self.nbr_fr,
justify='center',
font='arial 12 bold',
fg='navy',
bg='lemon chiffon',
bd=4,
width=10)
self.nbr_ent.grid(row=0, column=0,

self.su_fr = LabelFrame(self.btm_fr,
text='  Select Unit  ',
bg='dodger blue',
fg='navy',
bd=8,
relief=RIDGE,
font='arial 12 bold')
self.su_fr.place(relx=0.48, rely=0.35,
anchor=CENTER)

text='degree',
font='arial 12 bold',
fg='navy',
bg='dodger blue',
variable=self.unit,
value='d')

font='arial 12 bold',
fg='navy',
bg='dodger blue',
variable=self.unit,
value='g')

text='mil',
font='arial 12 bold',
fg='navy',
bg='dodger blue',
variable=self.unit,
value='m')

font='arial 12 bold',
fg='navy',
bg='dodger blue',
variable=self.unit,
value='r')

self.convert_btn = Button(self.btm_fr,
text='Convert',
width=14,
bd=5,
bg='dodger blue',
fg='navy',
font='arial 12 bold',
command=self.convert)
self.convert_btn.place(relx=0.93, rely=.25,
anchor=E)

self.res_fr = LabelFrame(self.btm_fr,
text='   Results  ',
bg='dodger blue',
fg='navy',
bd=8,
width=230,
height=130,
relief=RIDGE,
font='arial 12 bold')
self.res_fr.place(relx=0.48, rely=0.74,
anchor=CENTER)

objh = 20   # widget height
lblw = 80   # label width
valw = 100  # value width
lblx = 15   # x-position of label in frame
valx = 100  # x-position of value in frame
objy = 5    # y-position of widget in frame

self.deg_lbl = Label(self.res_fr,
text=' degrees: ',
anchor=E,
font='"Noto Mono" 12 bold',
fg='navy',
bg='lemon chiffon')
self.deg_lbl.place(x=lblx, y=objy,
height=objh, width=lblw)

self.deg_val = Label(self.res_fr,
text=' ',
anchor=E,
font='"Noto Mono" 12 bold',
fg='navy',
bg='lemon chiffon')
self.deg_val.place(x=valx, y=objy,
height=objh, width=valw)

objy = objy + objh   # next row
self.grd_lbl = Label(self.res_fr,
anchor=E,
font='"Noto Mono" 12 bold',
fg='navy',
bg='lemon chiffon')
self.grd_lbl.place(x=lblx, y=objy,
height=objh, width=lblw)

self.grd_val = Label(self.res_fr,
text=' ',
anchor=E,
font='"Noto Mono" 12 bold',
fg='navy',
bg='lemon chiffon')
self.grd_val.place(x=valx, y=objy,
height=objh, width=valw)

objy = objy + objh   # next row
self.mil_lbl = Label(self.res_fr,
text='    mils: ',
anchor=E,
font='"Noto Mono" 12 bold',
fg='navy',
bg='lemon chiffon')
self.mil_lbl.place(x=lblx, y=objy,
height=objh, width=lblw)

self.mil_val = Label(self.res_fr,
text=' ',
anchor=E,
font='"Noto Mono" 12 bold',
fg='navy',
bg='lemon chiffon')
self.mil_val.place(x=valx, y=objy,
height=objh, width=valw)

objy = objy + objh   # next row
anchor=E,
font='"Noto Mono" 12 bold',
fg='navy',
bg='lemon chiffon')
height=objh, width=lblw)

text=' ',
anchor=E,
font='"Noto Mono" 12 bold',
fg='navy',
bg='lemon chiffon')
height=objh, width=valw)

# process conversion request:
def convert(self):
# edit requested angle and unit:
try:
a = float(self.nbr_ent.get())
except:
self.err_msg('Angle entry must be numeric')
return
u = self.unit.get()
if u not in self.d_to_deg:
self.err_msg('Unit must be selected')
return

# convert request to degrees:
deg = self.d_to_deg[u](a)

# normalize:
self.deg = self.normalize(deg)

self.mil = self.d2m(self.deg)

# show results
self.deg_val.config(text=self.format_angle(self.deg))
self.mil_val.config(text=self.format_angle(self.mil))
return

def d2d(self, a):
return a

def g2d(self, a):
return .9 * a

def r2d(self, a):
return 180 * a / math.pi

def m2d(self, a):
return .05625 * a

def normalize(self, a):
if a >= 0:
x = a % 360
else:
x = -(-a % 360)
if x == -0.0:
x = 0.0
return x

def d2g(self, a):
return 10 * a / 9

def d2m(self, a):
return 160 * a / 9

def d2r(self, a):
return math.pi * a / 180

def format_angle(self, a):
return f'{a:.4f}'

def err_msg(self, msg):
messagebox.showerror('Error Message', msg)
return

# restore screen to it's 'initial' state:
def clear_screen(self):
self.nbr_ent.delete(0, 'end')
self.unit.set(' ')
self.deg_val.config(text='')
self.grd_val.config(text='')
self.mil_val.config(text='')
return

def close_window(self):
self.window.destroy()

# ************************************************

root = Tk()
root.title('ANGLES')
root.geometry('600x600+100+50')
root.resizable(False, False)
a = Angle(root)
root.mainloop()

# ************************************************

##  I wish I could show a screenshot of the tkinter window
##  to show how the input and output appear, but I don't know
##  if that is possible here.
##  I have processed all of the suggested angles and the
##  results matched those from a few other languages on this
##  page.


## Racket

Translation of: Common Lisp
#lang racket

(define (rem n m)
(let* ((m (abs m)) (-m (- m)))
(let recur ((n n))
(cond [(< n -m) (recur (+ n m))]
[(>= n m) (recur (- n m))]
[else n]))))

(define 2.pi (* 2 pi))

(define (deg->deg a) (rem a 360))
(define (mil->mil a) (rem a 6400))

(define (deg->mil a) (mil->mil (* (/ a 360) 6400)))

(define (grad->deg a) (deg->deg (* (/ a 400) 360)))
(define (grad->mil a) (mil->mil (* (/ a 400) 6400)))

(define (mil->deg a) (deg->deg (* (/ a 6400) 360)))

(define (rad->deg a) (deg->deg (* (/ a 2.pi) 360)))
(define (rad->mil a) (mil->mil (* (/ a 2.pi) 6400)))

(define (tabulate #:fmt (fmt (λ (v) (~a (exact->inexact v) #:align 'right #:width 15))) head . vs)
(string-join (cons (~a #:width 6 head) (map fmt vs)) " | "))

(define (report-angle a)
(string-join
(list
(tabulate #:fmt (λ (x) (~a x #:width 15 #:align 'center)) "UNIT" "VAL*" "DEG" "GRAD" "MIL" "RAD")
(tabulate "Deg" a (deg->deg a) (deg->grad a) (deg->mil a) (deg->rad a))
(tabulate "Mil" a (mil->deg a) (mil->grad a) (mil->mil a) (mil->rad a))
"\n"))

(module+ test
(displayln
(string-join (map report-angle '(-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000))
"\n\n")))

Output:
UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |            -2.0 |            -2.0 | -2.222222222222 | -35.55555555555 | -0.034906585039
Grad   |            -2.0 |            -1.8 |            -2.0 |           -32.0 | -0.031415926535
Mil    |            -2.0 |         -0.1125 |          -0.125 |            -2.0 | -0.001963495408
Rad    |            -2.0 | -114.5915590261 | -127.3239544735 | -2037.183271576 |            -2.0

UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |            -1.0 |            -1.0 | -1.111111111111 | -17.77777777777 | -0.017453292519
Grad   |            -1.0 |            -0.9 |            -1.0 |           -16.0 | -0.015707963267
Mil    |            -1.0 |        -0.05625 |         -0.0625 |            -1.0 | -0.000981747704
Rad    |            -1.0 | -57.29577951308 | -63.66197723675 | -1018.591635788 |            -1.0

UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |             0.0 |             0.0 |             0.0 |             0.0 |             0.0
Grad   |             0.0 |             0.0 |             0.0 |             0.0 |             0.0
Mil    |             0.0 |             0.0 |             0.0 |             0.0 |             0.0
Rad    |             0.0 |             0.0 |             0.0 |             0.0 |             0.0

UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |             1.0 |             1.0 | 1.1111111111111 | 17.777777777777 | 0.0174532925199
Grad   |             1.0 |             0.9 |             1.0 |            16.0 | 0.0157079632679
Mil    |             1.0 |         0.05625 |          0.0625 |             1.0 | 0.0009817477042
Rad    |             1.0 | 57.295779513082 | 63.661977236758 | 1018.5916357881 |             1.0

UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |             2.0 |             2.0 | 2.2222222222222 | 35.555555555555 | 0.0349065850398
Grad   |             2.0 |             1.8 |             2.0 |            32.0 | 0.0314159265358
Mil    |             2.0 |          0.1125 |           0.125 |             2.0 | 0.0019634954084
Rad    |             2.0 | 114.59155902616 | 127.32395447351 | 2037.1832715762 |             2.0

UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |       6.2831853 |       6.2831853 | 6.9813170000000 | 111.70107200000 | 0.1096622709979
Grad   |       6.2831853 | 5.6548667700000 |       6.2831853 |     100.5309648 | 0.0986960438981
Mil    |       6.2831853 | 0.3534291731250 |   0.39269908125 |       6.2831853 | 0.0061685027436
Rad    |       6.2831853 | 359.99999958864 | 399.99999954293 | 6399.9999926869 |       6.2831853

UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |            16.0 |            16.0 | 17.777777777777 | 284.44444444444 | 0.2792526803190
Grad   |            16.0 |            14.4 |            16.0 |           256.0 | 0.2513274122871
Mil    |            16.0 |             0.9 |             1.0 |            16.0 | 0.0157079632679
Rad    |            16.0 | 196.73247220931 | 218.59163578813 | 3497.4661726100 | 3.4336293856408

UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |      57.2957795 |      57.2957795 | 63.661977222222 | 1018.5916355555 | 0.9999999997716
Grad   |      57.2957795 |     51.56620155 |      57.2957795 |      916.732472 | 0.8999999997945
Mil    |      57.2957795 |  3.222887596875 |   3.58098621875 |      57.2957795 | 0.0562499999871
Rad    |      57.2957795 | 42.806349262182 | 47.562610291313 | 761.00176466102 | 0.7471117353837

UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |           359.0 |           359.0 | 398.88888888888 | 6382.2222222222 | 6.2657320146596
Grad   |           359.0 |           323.1 |           359.0 |          5744.0 | 5.6391588131936
Mil    |           359.0 |        20.19375 |         22.4375 |           359.0 | 0.3524474258246
Rad    |           359.0 | 49.184845196556 | 54.649827996174 | 874.39724793878 | 0.8584374907637

UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |           399.0 |            39.0 | 43.333333333333 | 693.33333333333 | 0.6806784082777
Grad   |           399.0 |           359.1 |           399.0 |          6384.0 | 6.2674773439116
Mil    |           399.0 |        22.44375 |         24.9375 |           399.0 | 0.3917173339944
Rad    |           399.0 | 181.01602571984 | 201.12891746649 | 3218.0626794639 | 3.1593256476863

UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |          6399.0 |           279.0 |           310.0 |          4960.0 | 4.8694686130641
Grad   |          6399.0 |           359.1 |           399.0 |          6384.0 | 6.2674773439116
Mil    |          6399.0 |       359.94375 |        399.9375 |          6399.0 | 6.2822035594753
Rad    |          6399.0 | 155.69310421380 | 172.99233801534 | 2767.8774082455 | 2.7173572912109

UNIT   |      VAL*       |       DEG       |      GRAD       |       MIL       |       RAD
Deg    |       1000000.0 |           280.0 | 311.11111111111 | 4977.7777777777 | 4.8869219047104
Grad   |       1000000.0 |             0.0 |             0.0 |             0.0 | 6.2831853064904
Mil    |       1000000.0 |            90.0 |           100.0 |          1600.0 | 1.5707963267971
Rad    |       1000000.0 | 339.51308232545 | 377.23675813525 | 6035.7881301641 | 5.9256225262850

## Raku

(formerly Perl 6)

my @units =
{ code => 'd', name => 'degrees' , number =>  360 },
{ code => 'g', name => 'gradians', number =>  400 },
{ code => 'm', name => 'mills'   , number => 6400 },
{ code => 'r', name => 'radians' , number =>  tau },
;

my Code %cvt = (@units X @units).map: -> ($a,$b) {
"{$a.<code>}2{$b.<code>}" => sub ($angle) { my$norm = $angle %$a.<number>
- ( $a.<number> if$angle < 0 );
$norm *$b.<number> / $a.<number> } } say ' Angle Unit ', @units».<name>».tc.fmt('%11s'); for -2, -1, 0, 1, 2, tau, 16, 360/tau, 360-1, 400-1, 6400-1, 1_000_000 ->$angle {
say '';
for @units -> $from { my @sub_keys = @units.map: { "{$from.<code>}2{.<code>}" };

my @results = %cvt{@sub_keys}».($angle); say join ' ',$angle      .fmt('%10g'),
$from.<name>.fmt('%-8s'), @results .fmt('%11g'); } }  Output:  Angle Unit Degrees Gradians Mills Radians -2 degrees -2 -2.22222 -35.5556 -0.0349066 -2 gradians -1.8 -2 -32 -0.0314159 -2 mills -0.1125 -0.125 -2 -0.0019635 -2 radians -114.592 -127.324 -2037.18 -2 -1 degrees -1 -1.11111 -17.7778 -0.0174533 -1 gradians -0.9 -1 -16 -0.015708 -1 mills -0.05625 -0.0625 -1 -0.000981748 -1 radians -57.2958 -63.662 -1018.59 -1 0 degrees 0 0 0 0 0 gradians 0 0 0 0 0 mills 0 0 0 0 0 radians 0 0 0 0 1 degrees 1 1.11111 17.7778 0.0174533 1 gradians 0.9 1 16 0.015708 1 mills 0.05625 0.0625 1 0.000981748 1 radians 57.2958 63.662 1018.59 1 2 degrees 2 2.22222 35.5556 0.0349066 2 gradians 1.8 2 32 0.0314159 2 mills 0.1125 0.125 2 0.0019635 2 radians 114.592 127.324 2037.18 2 6.28319 degrees 6.28319 6.98132 111.701 0.109662 6.28319 gradians 5.65487 6.28319 100.531 0.098696 6.28319 mills 0.353429 0.392699 6.28319 0.0061685 6.28319 radians 0 0 0 0 16 degrees 16 17.7778 284.444 0.279253 16 gradians 14.4 16 256 0.251327 16 mills 0.9 1 16 0.015708 16 radians 196.732 218.592 3497.47 3.43363 57.2958 degrees 57.2958 63.662 1018.59 1 57.2958 gradians 51.5662 57.2958 916.732 0.9 57.2958 mills 3.22289 3.58099 57.2958 0.05625 57.2958 radians 42.8064 47.5626 761.002 0.747112 359 degrees 359 398.889 6382.22 6.26573 359 gradians 323.1 359 5744 5.63916 359 mills 20.1938 22.4375 359 0.352447 359 radians 49.1848 54.6498 874.397 0.858437 399 degrees 39 43.3333 693.333 0.680678 399 gradians 359.1 399 6384 6.26748 399 mills 22.4438 24.9375 399 0.391717 399 radians 181.016 201.129 3218.06 3.15933 6399 degrees 279 310 4960 4.86947 6399 gradians 359.1 399 6384 6.26748 6399 mills 359.944 399.938 6399 6.2822 6399 radians 155.693 172.992 2767.88 2.71736 1000000 degrees 280 311.111 4977.78 4.88692 1000000 gradians 0 0 0 0 1000000 mills 90 100 1600 1.5708 1000000 radians 339.513 377.237 6035.79 5.92562 Alternately, implemented as a series of postfix operators: (Much of the complexity is due to the requirement that negative angles must normalize to a negative number.) sub postfix:<t>($t ) { my $a =$t % 1 * τ;           $t >=0 ??$a !! $a - τ } sub postfix:<d>($d ) { my $a =$d % 360 * τ / 360;   $d >=0 ??$a !! $a - τ } sub postfix:<g>($g ) { my $a =$g % 400 * τ / 400;   $g >=0 ??$a !! $a - τ } sub postfix:<m>($m ) { my $a =$m % 6400 * τ / 6400; $m >=0 ??$a !! $a - τ } sub postfix:<r>($r ) { my $a =$r % τ;               $r >=0 ??$a !! $a - τ } sub postfix:«->t» ($angle) { my $a =$angle / τ;        ($angle < 0 and$a == -1)    ?? -0 !! $a } sub postfix:«->d» ($angle) { my $a =$angle / τ * 360;  ($angle < 0 and$a == -360)  ?? -0 !! $a } sub postfix:«->g» ($angle) { my $a =$angle / τ * 400;  ($angle < 0 and$a == -400)  ?? -0 !! $a } sub postfix:«->m» ($angle) { my $a =$angle / τ * 6400; ($angle < 0 and$a == -6400) ?? -0 !! $a } sub postfix:«->r» ($angle) { my $a =$angle;            ($angle < 0 and$a == -τ)    ?? -0 !! $a } for <-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000> ->$a {
say '';
say '  Quantity  Unit      ', <turns degrees gradians mils radians>.fmt('%15s');
for 'turns', &postfix:«t», 'degrees', &postfix:«d», 'gradians', &postfix:«g»,
'mils',  &postfix:«m», 'radians', &postfix:«r»
-> $unit, &f { printf "%10s %-10s %15s %15s %15s %15s %15s\n",$a, $unit, |($a.&f->t, $a.&f->d,$a.&f->g, $a.&f->m,$a.&f->r)».round(.00000001);
}
}

 Quantity  Unit                turns         degrees        gradians            mils         radians
-2 turns                    0               0               0               0               0
-2 degrees        -0.00555556              -2     -2.22222222    -35.55555556     -0.03490659
-2 gradians            -0.005            -1.8              -2             -32     -0.03141593
-2 mils             -0.000313         -0.1125          -0.125              -2      -0.0019635
-2 radians        -0.31830989   -114.59155903   -127.32395447  -2037.18327158              -2

Quantity  Unit                turns         degrees        gradians            mils         radians
-1 turns                    0               0               0               0               0
-1 degrees        -0.00277778              -1     -1.11111111    -17.77777778     -0.01745329
-1 gradians           -0.0025            -0.9              -1             -16     -0.01570796
-1 mils             -0.000156        -0.05625         -0.0625              -1     -0.00098175
-1 radians        -0.15915494    -57.29577951    -63.66197724  -1018.59163579              -1

Quantity  Unit                turns         degrees        gradians            mils         radians
0 turns                    0               0               0               0               0
0 degrees                  0               0               0               0               0
0 gradians                 0               0               0               0               0
0 mils                     0               0               0               0               0
0 radians                  0               0               0               0               0

Quantity  Unit                turns         degrees        gradians            mils         radians
1 turns                    0               0               0               0               0
1 degrees         0.00277778               1      1.11111111     17.77777778      0.01745329
1 gradians            0.0025             0.9               1              16      0.01570796
1 mils              0.000156         0.05625          0.0625               1      0.00098175
1 radians         0.15915494     57.29577951     63.66197724   1018.59163579               1

Quantity  Unit                turns         degrees        gradians            mils         radians
2 turns                    0               0               0               0               0
2 degrees         0.00555556               2      2.22222222     35.55555556      0.03490659
2 gradians             0.005             1.8               2              32      0.03141593
2 mils              0.000313          0.1125           0.125               2       0.0019635
2 radians         0.31830989    114.59155903    127.32395447   2037.18327158               2

Quantity  Unit                turns         degrees        gradians            mils         radians
6.2831853 turns            0.2831853      101.946708       113.27412      1812.38592      1.77930572
6.2831853 degrees         0.01745329       6.2831853        6.981317      111.701072      0.10966227
6.2831853 gradians        0.01570796      5.65486677       6.2831853     100.5309648      0.09869604
6.2831853 mils            0.00098175      0.35342917      0.39269908       6.2831853       0.0061685
6.2831853 radians                  1    359.99999959    399.99999954   6399.99999269       6.2831853

Quantity  Unit                turns         degrees        gradians            mils         radians
16 turns                    0               0               0               0               0
16 degrees         0.04444444              16     17.77777778    284.44444444      0.27925268
16 gradians              0.04            14.4              16             256      0.25132741
16 mils                0.0025             0.9               1              16      0.01570796
16 radians         0.54647909    196.73247221    218.59163579   3497.46617261      3.43362939

Quantity  Unit                turns         degrees        gradians            mils         radians
57.2957795 turns            0.2957795       106.48062        118.3118       1892.9888      1.85843741
57.2957795 degrees         0.15915494      57.2957795     63.66197722   1018.59163556               1
57.2957795 gradians        0.14323945     51.56620155      57.2957795      916.732472             0.9
57.2957795 mils            0.00895247       3.2228876      3.58098622      57.2957795         0.05625
57.2957795 radians         0.11890653     42.80634926     47.56261029    761.00176466      0.74711174

Quantity  Unit                turns         degrees        gradians            mils         radians
359 turns                    0               0               0               0               0
359 degrees         0.99722222             359    398.88888889   6382.22222222      6.26573201
359 gradians            0.8975           323.1             359            5744      5.63915881
359 mils              0.056094        20.19375         22.4375             359      0.35244743
359 radians         0.13662457      49.1848452       54.649828    874.39724794      0.85843749

Quantity  Unit                turns         degrees        gradians            mils         radians
399 turns                    0               0               0               0               0
399 degrees         0.10833333              39     43.33333333    693.33333333      0.68067841
399 gradians            0.9975           359.1             399            6384      6.26747734
399 mils              0.062344        22.44375         24.9375             399      0.39171733
399 radians         0.50282229    181.01602572    201.12891747   3218.06267946      3.15932565

Quantity  Unit                turns         degrees        gradians            mils         radians
6399 turns                    0               0               0               0               0
6399 degrees              0.775             279             310            4960      4.86946861
6399 gradians            0.9975           359.1             399            6384      6.26747734
6399 mils              0.999844       359.94375        399.9375            6399      6.28220356
6399 radians         0.43248085    155.69310421    172.99233802   2767.87740825      2.71735729

Quantity  Unit                turns         degrees        gradians            mils         radians
1000000 turns                    0               0               0               0               0
1000000 degrees         0.77777778             280    311.11111111   4977.77777778      4.88692191
1000000 gradians                 0               0               0               0               0
1000000 mils                  0.25              90             100            1600      1.57079633
1000000 radians          0.9430919    339.51308233    377.23675814   6035.78813022      5.92562114

## REXX

/*REXX pgm normalizes an angle (in a scale), or converts angles from a scale to another.*/
numeric digits length( pi() )   -   length(.)    /*use the "length" of pi for precision.*/
parse arg x                                      /*obtain optional arguments from the CL*/
if x='' | x=","  then x= '-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000'
w= 20;                                 w7= w+7   /*W:  # dec digits past the dec. point.*/
@deg = 'degrees';       @grd= "gradians";        @mil = 'mils';           @rad = "radians"
# = words(x)
call hdr @deg @grd @mil @rad
do j=1  for #;            y= word(x,j)
say shw(y)        fmt(d2d(y))              fmt(d2g(y))    fmt(d2m(y))    fmt(d2r(y))
end   /*j*/

call hdr @grd @deg @mil @rad
do j=1  for #;            y= word(x,j)
say shw(y)        fmt(g2g(y))              fmt(g2d(y))    fmt(g2m(y))    fmt(g2r(y))
end   /*j*/

call hdr @mil @deg @grd @rad
do j=1  for #;            y= word(x,j)
say shw(y)        fmt(m2m(y))              fmt(m2d(y))    fmt(m2g(y))    fmt(m2r(y))
end   /*j*/

call hdr @rad @deg @grd @mil
do j=1  for #;            y= word(x,j)
say shw(y)        fmt(r2r(y))              fmt(r2d(y))    fmt(r2g(y))    fmt(r2m(y))
end   /*j*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
fmt: _= format(arg(1), 6,w);  L= length(_);  return left(format(_/1, 6),L)   /*align a #*/
shw: _= format(arg(1),12,9);  L= length(_);  return left(format(_/1,12),L)   /*  "   " "*/
pi:  pi= 3.1415926535897932384626433832795028841971693993751058209749445923078;  return pi
d2g: return d2d(arg(1)) *   10  /    9           /*convert degrees   ───► gradians.     */
d2m: return d2d(arg(1)) *  160  /    9           /*convert degrees   ───► mils.         */
d2r: return d2d(arg(1)) * pi()  /  180           /*convert degrees   ───► radians.      */
g2d: return g2g(arg(1)) *    0.9                 /*convert gradians  ───► degrees.      */
g2m: return g2g(arg(1)) *   16                   /*convert gradians  ───► mils.         */
g2r: return g2g(arg(1)) * pi()  *    0.005       /*convert gradians  ───► radians.      */
m2d: return m2m(arg(1)) *    9  *    0.00625     /*convert mils      ───► degrees.      */
m2g: return m2m(arg(1)) /   16                   /*convert mils      ───► gradians.     */
m2r: return m2m(arg(1)) * pi()  / 3200           /*convert mils      ───► radians.      */
r2d: return r2r(arg(1)) *  180  / pi()           /*convert radians   ───► degrees.      */
r2g: return r2r(arg(1)) *  200  / pi()           /*convert radians   ───► gradians.     */
r2m: return r2r(arg(1)) * 3200  / pi()           /*convert radians   ───► mils.         */
d2d: return     arg(1) //  360                   /*normalize degrees ───► a unit circle.*/
g2g: return     arg(1) //  400                   /*normalize gradians───► a unit circle.*/
m2m: return     arg(1) // 6400                   /*normalize mils    ───► a unit circle.*/
r2r: return     arg(1) // (pi() * 2)             /*normalize radians ───► a unit circle.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
hdr: parse arg #o #a #b #c .;         _= '═';              say   /* [↓]  the header line*/
@n  = 'normalized'
say center(#o,23  )  center(@n #o,w7) center(#a,w7  ) center(#b,w7  ) center(#c,w7  )
say center('',23,_)  center('',w7, _) center('',w7,_) center('',w7,_) center('',w7,_)
return                                                      /* '↑'  seperator line.*/

output   when using the default input:
        degrees             normalized degrees               gradians                      mils                       radians
═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
-2               -2                          -2.22222222222222222222    -35.55555555555555555556     -0.03490658503988659154
-1               -1                          -1.11111111111111111111    -17.77777777777777777778     -0.01745329251994329577
0                0                           0                           0                           0
1                1                           1.11111111111111111111     17.77777777777777777778      0.01745329251994329577
2                2                           2.22222222222222222222     35.55555555555555555556      0.03490658503988659154
6.2831853        6.2831853                   6.981317                  111.701072                    0.10966227099790767281
16               16                          17.77777777777777777778    284.44444444444444444444      0.27925268031909273231
57.2957795       57.2957795                  63.66197722222222222222   1018.59163555555555555556      0.9999999997716704269
359              359                         398.88888888888888888889   6382.22222222222222222222      6.26573201465964318116
399               39                          43.33333333333333333333    693.33333333333333333333      0.680678408277788535
6399              279                         310                        4960                           4.86946861306417951962
1000000              280                         311.11111111111111111111   4977.77777777777777777778      4.88692190558412281539

═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
-2               -2                          -1.8                       -32                          -0.03141592653589793238
-1               -1                          -0.9                       -16                          -0.01570796326794896619
0                0                           0                           0                           0
1                1                           0.9                        16                           0.01570796326794896619
2                2                           1.8                        32                           0.03141592653589793238
6.2831853        6.2831853                   5.65486677                100.5309648                   0.09869604389811690553
16               16                          14.4                       256                           0.25132741228718345908
57.2957795       57.2957795                  51.56620155                916.732472                    0.89999999979450338421
359              359                         323.1                      5744                           5.63915881319367886304
399              399                         359.1                      6384                           6.26747734391163751073
6399              399                         359.1                      6384                           6.26747734391163751073
1000000                0                           0                           0                           0

═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
-2               -2                          -0.1125                     -0.125                      -0.00196349540849362077
-1               -1                          -0.05625                    -0.0625                     -0.00098174770424681039
0                0                           0                           0                           0
1                1                           0.05625                     0.0625                      0.00098174770424681039
2                2                           0.1125                      0.125                       0.00196349540849362077
6.2831853        6.2831853                   0.353429173125              0.39269908125               0.0061685027436323066
16               16                           0.9                         1                           0.01570796326794896619
57.2957795       57.2957795                   3.222887596875              3.58098621875               0.05624999998715646151
359              359                          20.19375                    22.4375                      0.35244742582460492894
399              399                          22.44375                    24.9375                      0.39171733399447734442
6399             6399                         359.94375                   399.9375                      6.28220355947533966654
1000000             1600                          90                         100                           1.57079632679489661923

═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
-2               -2                        -114.5915590261646417536    -127.32395447351626861511  -2037.18327157626029784171
-1               -1                         -57.2957795130823208768     -63.66197723675813430755  -1018.59163578813014892086
0                0                           0                           0                           0
1                1                          57.2957795130823208768      63.66197723675813430755   1018.59163578813014892086
2                2                         114.5915590261646417536     127.32395447351626861511   2037.18327157626029784171
6.2831853        6.2831853                 359.99999958863999622298    399.99999954293332913665   6399.99999268693326618633
16                3.43362938564082704615    196.73247220931713402877    218.59163578813014892086   3497.4661726100823827337
57.2957795        0.74711173538372170767     42.80634926218202230527     47.56261029131335811697    761.00176466101372987153
359                0.85843749076357081526     49.18484519655319477054     54.64982799617021641171    874.39724793872346258733
399                3.15932564768605195371    181.01602571984602984246    201.12891746649558871385   3218.06267946392941942158
6399                2.71735729118096649006    155.69310421377129063139    172.99233801530143403488   2767.87740824482294455809
1000000                5.92562114009385143291    339.51308232087679815481    377.23675813430755350535   6035.78813014892085608558


## Ruby

This Angles module responds to methods like r2d. Adding an element (like "h"=>24, for a clock-like angle system) to the BASES hash adds 9 more methods, totaling to 25 methods. None of these methods are actually implemented.

module Angles
BASES = {"d" => 360, "g" => 400, "m" => 6400, "r" => Math::PI*2 ,"h" => 24 }

def self.method_missing(meth, angle)
from, to = BASES.values_at(*meth.to_s.split("2"))
raise NoMethodError, meth if (from.nil? or to.nil?)
mod = (angle.to_f * to / from) % to
angle < 0 ? mod - to : mod
end

end

#Demo
names = Angles::BASES.keys
puts " " + "%12s "*names.size % names
test = [-2, -1, 0, 1, 2*Math::PI, 16, 360/(2*Math::PI), 360-1, 400-1, 6400-1, 1_000_000]

test.each do |n|
names.each do |first|
res = names.map{|last| Angles.send((first + "2" + last).to_sym, n)}
puts first + "%12g "*names.size % res
end
puts
end

Output:
          d            g            m            r            h
d          -2     -2.22222     -35.5556   -0.0349066    -0.133333
g        -1.8           -2          -32   -0.0314159        -0.12
m     -0.1125       -0.125           -2   -0.0019635      -0.0075
r    -114.592     -127.324     -2037.18           -2     -7.63944
h         -30     -33.3333     -533.333    -0.523599           -2

d          -1     -1.11111     -17.7778   -0.0174533   -0.0666667
g        -0.9           -1          -16    -0.015708        -0.06
m    -0.05625      -0.0625           -1 -0.000981748     -0.00375
r    -57.2958      -63.662     -1018.59           -1     -3.81972
h         -15     -16.6667     -266.667    -0.261799           -1

d           0            0            0            0            0
g           0            0            0            0            0
m           0            0            0            0            0
r           0            0            0            0            0
h           0            0            0            0            0

d           1      1.11111      17.7778    0.0174533    0.0666667
g         0.9            1           16     0.015708         0.06
m     0.05625       0.0625            1  0.000981748      0.00375
r     57.2958       63.662      1018.59            1      3.81972
h          15      16.6667      266.667     0.261799            1

d     6.28319      6.98132      111.701     0.109662     0.418879
g     5.65487      6.28319      100.531     0.098696     0.376991
m    0.353429     0.392699      6.28319    0.0061685    0.0235619
r           0            0            0            0            0
h     94.2478       104.72      1675.52      1.64493      6.28319

d          16      17.7778      284.444     0.279253      1.06667
g        14.4           16          256     0.251327         0.96
m         0.9            1           16     0.015708         0.06
r     196.732      218.592      3497.47      3.43363      13.1155
h         240      266.667      4266.67      4.18879           16

d     57.2958       63.662      1018.59            1      3.81972
g     51.5662      57.2958      916.732          0.9      3.43775
m     3.22289      3.58099      57.2958      0.05625     0.214859
r     42.8064      47.5626      761.002     0.747112      2.85376
h     139.437       154.93      2478.87      2.43363      9.29578

d         359      398.889      6382.22      6.26573      23.9333
g       323.1          359         5744      5.63916        21.54
m     20.1938      22.4375          359     0.352447      1.34625
r     49.1848      54.6498      874.397     0.858437      3.27899
h         345      383.333      6133.33      6.02139           23

d          39      43.3333      693.333     0.680678          2.6
g       359.1          399         6384      6.26748        23.94
m     22.4438      24.9375          399     0.391717      1.49625
r     181.016      201.129      3218.06      3.15933      12.0677
h         225          250         4000      3.92699           15

d         279          310         4960      4.86947         18.6
g       359.1          399         6384      6.26748        23.94
m     359.944      399.938         6399       6.2822      23.9962
r     155.693      172.992      2767.88      2.71736      10.3795
h         225          250         4000      3.92699           15

d         280      311.111      4977.78      4.88692      18.6667
g           0            0            0  3.69482e-13            0
m          90          100         1600       1.5708            6
r     339.513      377.237      6035.79      5.92562      22.6342
h         240      266.667      4266.67      4.18879           16


## Rust

use std::{
marker::PhantomData,
f64::consts::PI,
};

pub trait AngleUnit: Copy {
const TURN: f64;
const NAME: &'static str;
}

macro_rules! unit {
($name:ident,$value:expr, $string:expr) => ( #[derive(Debug, Copy, Clone)] struct$name;
impl AngleUnit for $name { const TURN: f64 =$value;
const NAME: &'static str = $string; } ); } unit!(Degrees, 360.0, "Degrees"); unit!(Radians, PI * 2.0, "Radians"); unit!(Gradians, 400.0, "Gradians"); unit!(Mils, 6400.0, "Mils"); #[derive(Copy, Clone, PartialEq, PartialOrd)] struct Angle<T: AngleUnit>(f64, PhantomData<T>); impl<T: AngleUnit> Angle<T> { pub fn new(val: f64) -> Self { Self(val, PhantomData) } pub fn normalize(self) -> Self { Self(self.0 % T::TURN, PhantomData) } pub fn val(self) -> f64 { self.0 } pub fn convert<U: AngleUnit>(self) -> Angle<U> { Angle::new(self.0 * U::TURN / T::TURN) } pub fn name(self) -> &'static str { T::NAME } } fn print_angles<T: AngleUnit>() { let angles = [-2.0, -1.0, 0.0, 1.0, 2.0, 6.2831853, 16.0, 57.2957795, 359.0, 399.0, 6399.0, 1000000.0]; println!("{:<12} {:<12} {:<12} {:<12} {:<12} {:<12}", "Angle", "Unit", "Degrees", "Gradians", "Mils", "Radians"); for &angle in &angles { let deg = Angle::<T>::new(angle).normalize(); println!("{:<12} {:<12} {:<12.4} {:<12.4} {:<12.4} {:<12.4}", angle, deg.name(), deg.convert::<Degrees>().val(), deg.convert::<Gradians>().val(), deg.convert::<Mils>().val(), deg.convert::<Radians>().val(), ); } println!(); } fn main() { print_angles::<Degrees>(); print_angles::<Gradians>(); print_angles::<Mils>(); print_angles::<Radians>(); }  Output: Angle Unit Degrees Gradians Mils Radians -2 Degrees -2.0000 -2.2222 -35.5556 -0.0349 -1 Degrees -1.0000 -1.1111 -17.7778 -0.0175 0 Degrees 0.0000 0.0000 0.0000 0.0000 1 Degrees 1.0000 1.1111 17.7778 0.0175 2 Degrees 2.0000 2.2222 35.5556 0.0349 6.2831853 Degrees 6.2832 6.9813 111.7011 0.1097 16 Degrees 16.0000 17.7778 284.4444 0.2793 57.2957795 Degrees 57.2958 63.6620 1018.5916 1.0000 359 Degrees 359.0000 398.8889 6382.2222 6.2657 399 Degrees 39.0000 43.3333 693.3333 0.6807 6399 Degrees 279.0000 310.0000 4960.0000 4.8695 1000000 Degrees 280.0000 311.1111 4977.7778 4.8869 Angle Unit Degrees Gradians Mils Radians -2 Gradians -1.8000 -2.0000 -32.0000 -0.0314 -1 Gradians -0.9000 -1.0000 -16.0000 -0.0157 0 Gradians 0.0000 0.0000 0.0000 0.0000 1 Gradians 0.9000 1.0000 16.0000 0.0157 2 Gradians 1.8000 2.0000 32.0000 0.0314 6.2831853 Gradians 5.6549 6.2832 100.5310 0.0987 16 Gradians 14.4000 16.0000 256.0000 0.2513 57.2957795 Gradians 51.5662 57.2958 916.7325 0.9000 359 Gradians 323.1000 359.0000 5744.0000 5.6392 399 Gradians 359.1000 399.0000 6384.0000 6.2675 6399 Gradians 359.1000 399.0000 6384.0000 6.2675 1000000 Gradians 0.0000 0.0000 0.0000 0.0000 Angle Unit Degrees Gradians Mils Radians -2 Mils -0.1125 -0.1250 -2.0000 -0.0020 -1 Mils -0.0563 -0.0625 -1.0000 -0.0010 0 Mils 0.0000 0.0000 0.0000 0.0000 1 Mils 0.0563 0.0625 1.0000 0.0010 2 Mils 0.1125 0.1250 2.0000 0.0020 6.2831853 Mils 0.3534 0.3927 6.2832 0.0062 16 Mils 0.9000 1.0000 16.0000 0.0157 57.2957795 Mils 3.2229 3.5810 57.2958 0.0562 359 Mils 20.1938 22.4375 359.0000 0.3524 399 Mils 22.4438 24.9375 399.0000 0.3917 6399 Mils 359.9438 399.9375 6399.0000 6.2822 1000000 Mils 90.0000 100.0000 1600.0000 1.5708 Angle Unit Degrees Gradians Mils Radians -2 Radians -114.5916 -127.3240 -2037.1833 -2.0000 -1 Radians -57.2958 -63.6620 -1018.5916 -1.0000 0 Radians 0.0000 0.0000 0.0000 0.0000 1 Radians 57.2958 63.6620 1018.5916 1.0000 2 Radians 114.5916 127.3240 2037.1833 2.0000 6.2831853 Radians 360.0000 400.0000 6400.0000 6.2832 16 Radians 196.7325 218.5916 3497.4662 3.4336 57.2957795 Radians 42.8063 47.5626 761.0018 0.7471 359 Radians 49.1848 54.6498 874.3972 0.8584 399 Radians 181.0160 201.1289 3218.0627 3.1593 6399 Radians 155.6931 172.9923 2767.8774 2.7174 1000000 Radians 339.5131 377.2368 6035.7881 5.9256 ## Swift import Foundation func normalize(_ f: Double, N: Double) -> Double { var a = f while a < -N { a += N } while a >= N { a -= N } return a } func normalizeToDeg(_ f: Double) -> Double { return normalize(f, N: 360) } func normalizeToGrad(_ f: Double) -> Double { return normalize(f, N: 400) } func normalizeToMil(_ f: Double) -> Double { return normalize(f, N: 6400) } func normalizeToRad(_ f: Double) -> Double { return normalize(f, N: 2 * .pi) } func d2g(_ f: Double) -> Double { f * 10 / 9 } func d2m(_ f: Double) -> Double { f * 160 / 9 } func d2r(_ f: Double) -> Double { f * .pi / 180 } func g2d(_ f: Double) -> Double { f * 9 / 10 } func g2m(_ f: Double) -> Double { f * 16 } func g2r(_ f: Double) -> Double { f * .pi / 200 } func m2d(_ f: Double) -> Double { f * 9 / 160 } func m2g(_ f: Double) -> Double { f / 16 } func m2r(_ f: Double) -> Double { f * .pi / 3200 } func r2d(_ f: Double) -> Double { f * 180 / .pi } func r2g(_ f: Double) -> Double { f * 200 / .pi } func r2m(_ f: Double) -> Double { f * 3200 / .pi } let angles = [-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 6399, 1_000_000] let names = ["Degrees", "Gradians", "Mils", "Radians"] let fmt = { String(format: "%.4f",$0) }

let normal = [normalizeToDeg, normalizeToGrad, normalizeToMil, normalizeToRad]
let convert = [
[{ $0 }, d2g, d2m, d2r], [g2d, {$0 }, g2m, g2r],
[m2d, m2g, { $0 }, m2r], [r2d, r2g, r2m, {$0 }]
]

let ans =
angles.map({ angle in
(0..<4).map({ ($0, normal[$0](angle)) }).map({
(fmt(angle),
fmt($0.1), names[$0.0],
fmt(convert[$0.0][0]($0.1)),
fmt(convert[$0.0][1]($0.1)),
fmt(convert[$0.0][2]($0.1)),
fmt(convert[$0.0][3]($0.1))
)
})
})

print("angle", "normalized", "unit", "degrees", "grads", "mils", "radians")

for res in ans {
for unit in res {
print(unit)
}

print()
}

Output:
angle normalized unit degrees grads mils radians
("-2.0000", "-2.0000", "Degrees", "-2.0000", "-2.2222", "-35.5556", "-0.0349")
("-2.0000", "-2.0000", "Gradians", "-1.8000", "-2.0000", "-32.0000", "-0.0314")
("-2.0000", "-2.0000", "Mils", "-0.1125", "-0.1250", "-2.0000", "-0.0020")
("-2.0000", "-2.0000", "Radians", "-114.5916", "-127.3240", "-2037.1833", "-2.0000")

("-1.0000", "-1.0000", "Degrees", "-1.0000", "-1.1111", "-17.7778", "-0.0175")
("-1.0000", "-1.0000", "Gradians", "-0.9000", "-1.0000", "-16.0000", "-0.0157")
("-1.0000", "-1.0000", "Mils", "-0.0563", "-0.0625", "-1.0000", "-0.0010")
("-1.0000", "-1.0000", "Radians", "-57.2958", "-63.6620", "-1018.5916", "-1.0000")

("0.0000", "0.0000", "Degrees", "0.0000", "0.0000", "0.0000", "0.0000")
("0.0000", "0.0000", "Gradians", "0.0000", "0.0000", "0.0000", "0.0000")
("0.0000", "0.0000", "Mils", "0.0000", "0.0000", "0.0000", "0.0000")
("0.0000", "0.0000", "Radians", "0.0000", "0.0000", "0.0000", "0.0000")

("1.0000", "1.0000", "Degrees", "1.0000", "1.1111", "17.7778", "0.0175")
("1.0000", "1.0000", "Gradians", "0.9000", "1.0000", "16.0000", "0.0157")
("1.0000", "1.0000", "Mils", "0.0563", "0.0625", "1.0000", "0.0010")
("1.0000", "1.0000", "Radians", "57.2958", "63.6620", "1018.5916", "1.0000")

("2.0000", "2.0000", "Degrees", "2.0000", "2.2222", "35.5556", "0.0349")
("2.0000", "2.0000", "Gradians", "1.8000", "2.0000", "32.0000", "0.0314")
("2.0000", "2.0000", "Mils", "0.1125", "0.1250", "2.0000", "0.0020")
("2.0000", "2.0000", "Radians", "114.5916", "127.3240", "2037.1833", "2.0000")

("6.2832", "6.2832", "Degrees", "6.2832", "6.9813", "111.7011", "0.1097")
("6.2832", "6.2832", "Gradians", "5.6549", "6.2832", "100.5310", "0.0987")
("6.2832", "6.2832", "Mils", "0.3534", "0.3927", "6.2832", "0.0062")
("6.2832", "6.2832", "Radians", "360.0000", "400.0000", "6400.0000", "6.2832")

("16.0000", "16.0000", "Degrees", "16.0000", "17.7778", "284.4444", "0.2793")
("16.0000", "16.0000", "Gradians", "14.4000", "16.0000", "256.0000", "0.2513")
("16.0000", "16.0000", "Mils", "0.9000", "1.0000", "16.0000", "0.0157")
("16.0000", "3.4336", "Radians", "196.7325", "218.5916", "3497.4662", "3.4336")

("57.2958", "57.2958", "Degrees", "57.2958", "63.6620", "1018.5916", "1.0000")
("57.2958", "57.2958", "Gradians", "51.5662", "57.2958", "916.7325", "0.9000")
("57.2958", "57.2958", "Mils", "3.2229", "3.5810", "57.2958", "0.0562")
("57.2958", "0.7471", "Radians", "42.8063", "47.5626", "761.0018", "0.7471")

("359.0000", "359.0000", "Degrees", "359.0000", "398.8889", "6382.2222", "6.2657")
("359.0000", "359.0000", "Gradians", "323.1000", "359.0000", "5744.0000", "5.6392")
("359.0000", "359.0000", "Mils", "20.1938", "22.4375", "359.0000", "0.3524")
("359.0000", "0.8584", "Radians", "49.1848", "54.6498", "874.3972", "0.8584")

("6399.0000", "279.0000", "Degrees", "279.0000", "310.0000", "4960.0000", "4.8695")
("6399.0000", "399.0000", "Gradians", "359.1000", "399.0000", "6384.0000", "6.2675")
("6399.0000", "6399.0000", "Mils", "359.9438", "399.9375", "6399.0000", "6.2822")
("6399.0000", "2.7174", "Radians", "155.6931", "172.9923", "2767.8774", "2.7174")

("1000000.0000", "280.0000", "Degrees", "280.0000", "311.1111", "4977.7778", "4.8869")
("1000000.0000", "0.0000", "Gradians", "0.0000", "0.0000", "0.0000", "0.0000")
("1000000.0000", "1600.0000", "Mils", "90.0000", "100.0000", "1600.0000", "1.5708")
("1000000.0000", "5.9256", "Radians", "339.5132", "377.2368", "6035.7895", "5.9256")

## V (Vlang)

Translation of: Go
import math
import strconv
fn d2d(d f64) f64 { return math.mod(d, 360) }
fn g2g(g f64) f64 { return math.mod(g, 400) }
fn m2m(m f64) f64 { return math.mod(m, 6400) }
fn r2r(r f64) f64 { return math.mod(r, 2*math.pi) }
fn d2g(d f64) f64 { return d2d(d) * 400 / 360 }
fn d2m(d f64) f64 { return d2d(d) * 6400 / 360 }
fn d2r(d f64) f64 { return d2d(d) * math.pi / 180 }
fn g2d(g f64) f64 { return g2g(g) * 360 / 400 }
fn g2m(g f64) f64 { return g2g(g) * 6400 / 400 }
fn g2r(g f64) f64 { return g2g(g) * math.pi / 200 }
fn m2d(m f64) f64 { return m2m(m) * 360 / 6400 }
fn m2g(m f64) f64 { return m2m(m) * 400 / 6400 }
fn m2r(m f64) f64 { return m2m(m) * math.pi / 3200 }
fn r2d(r f64) f64 { return r2r(r) * 180 / math.pi }
fn r2g(r f64) f64 { return r2r(r) * 200 / math.pi }
fn r2m(r f64) f64 { return r2r(r) * 3200 / math.pi }

fn s(f f64) string {
wf := strconv.format_fl(f, strconv.BF_param{
len0: 15
len1: 7
positive: f>=0
}).split('.')
if wf[1] == '0000000' {
return "${wf[0]:7} " } mut le := wf[1].len if le > 7 { le = 7 } return "${wf[0]:7}.${wf[1][..le]:-7}" } fn main() { angles := [-2.0, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000] println(" degrees normalized degs gradians mils radians") for a in angles { println('${s(a)} ${s(d2d(a))}${s(d2g(a))} ${s(d2m(a))}${s(d2r(a))}')
}
println("\n   gradians     normalized grds     degrees          mils            radians")
for a in angles {
println('${s(a)}${s(g2g(a))} ${s(g2d(a))}${s(g2m(a))} ${s(g2r(a))}') } println("\n mils normalized mils degrees gradians radians") for a in angles { println('${s(a)} ${s(m2m(a))}${s(m2d(a))} ${s(m2g(a))}${s(m2r(a))}')
}
for a in angles {
println('${s(a)}${s(r2r(a))} ${s(r2d(a))}${s(r2g(a))} ${s(r2m(a))}') } } Output: Same as Go entry ## Wren Translation of: Go Library: Wren-fmt import "./fmt" for Fmt var d2d = Fn.new { |d| d % 360 } var g2g = Fn.new { |g| g % 400 } var m2m = Fn.new { |m| m % 6400 } var r2r = Fn.new { |r| r % (2*Num.pi) } var d2g = Fn.new { |d| d2d.call(d) * 400 / 360 } var d2m = Fn.new { |d| d2d.call(d) * 6400 / 360 } var d2r = Fn.new { |d| d2d.call(d) * Num.pi / 180 } var g2d = Fn.new { |g| g2g.call(g) * 360 / 400 } var g2m = Fn.new { |g| g2g.call(g) * 6400 / 400 } var g2r = Fn.new { |g| g2g.call(g) * Num.pi / 200 } var m2d = Fn.new { |m| m2m.call(m) * 360 / 6400 } var m2g = Fn.new { |m| m2m.call(m) * 400 / 6400 } var m2r = Fn.new { |m| m2m.call(m) * Num.pi / 3200 } var r2d = Fn.new { |r| r2r.call(r) * 180 / Num.pi } var r2g = Fn.new { |r| r2r.call(r) * 200 / Num.pi } var r2m = Fn.new { |r| r2r.call(r) * 3200 / Num.pi } var f1 = "$15m $15m$15m $15m$15m"
var f2 = "$15.7g$15.7g $15.7g$15.7g \$15.7g"
var angles = [-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000]
Fmt.print(f1, "degrees", "normalized degs", "gradians", "mils", "radians")
for (a in angles) {
Fmt.print(f2, a, d2d.call(a), d2g.call(a), d2m.call(a), d2r.call(a))
}
f1 = "\n" + f1
Fmt.print(f1, "gradians", "normalized grds", "degrees", "mils", "radians")
for (a in angles) {
Fmt.print(f2, a, g2g.call(a), g2d.call(a), g2m.call(a), g2r.call(a))
}
Fmt.print(f1, "mils", "normalized mils", "degrees", "gradians", "radians")
for (a in angles) {
Fmt.print(f2, a, m2m.call(a), m2d.call(a), m2g.call(a), m2r.call(a))
}
for (a in angles) {
Fmt.print(f2, a, r2r.call(a), r2d.call(a), r2g.call(a), r2m.call(a))
}

Output:
    degrees     normalized degs    gradians          mils           radians
-2.0            -2.0            -2.2222222     -35.5555556      -0.0349066
-1.0            -1.0            -1.1111111     -17.7777778      -0.0174533
0.0             0.0             0.0             0.0             0.0
1.0             1.0             1.1111111      17.7777778       0.0174533
2.0             2.0             2.2222222      35.5555556       0.0349066
6.2831853       6.2831853       6.981317      111.701072        0.1096623
16.0            16.0            17.7777778     284.4444444       0.2792527
57.2957795      57.2957795      63.6619772    1018.5916356       1.0
359.0           359.0           398.8888889    6382.2222222       6.265732
399.0            39.0            43.3333333     693.3333333       0.6806784
6399.0           279.0           310.0          4960.0             4.8694686
1000000.0           280.0           311.1111111    4977.7777778       4.8869219

-2.0            -2.0            -1.8           -32.0            -0.0314159
-1.0            -1.0            -0.9           -16.0            -0.015708
0.0             0.0             0.0             0.0             0.0
1.0             1.0             0.9            16.0             0.015708
2.0             2.0             1.8            32.0             0.0314159
6.2831853       6.2831853       5.6548668     100.5309648       0.098696
16.0            16.0            14.4           256.0             0.2513274
57.2957795      57.2957795      51.5662016     916.732472        0.9
359.0           359.0           323.1          5744.0             5.6391588
399.0           399.0           359.1          6384.0             6.2674773
6399.0           399.0           359.1          6384.0             6.2674773
1000000.0             0.0             0.0             0.0             0.0

-2.0            -2.0            -0.1125         -0.125          -0.0019635
-1.0            -1.0            -0.05625        -0.0625         -0.0009817
0.0             0.0             0.0             0.0             0.0
1.0             1.0             0.05625         0.0625          0.0009817
2.0             2.0             0.1125          0.125           0.0019635
6.2831853       6.2831853       0.3534292       0.3926991       0.0061685
16.0            16.0             0.9             1.0             0.015708
57.2957795      57.2957795       3.2228876       3.5809862       0.05625
359.0           359.0            20.19375        22.4375          0.3524474
399.0           399.0            22.44375        24.9375          0.3917173
6399.0          6399.0           359.94375       399.9375          6.2822036
1000000.0          1600.0            90.0           100.0             1.5707963

-2.0            -2.0          -114.591559     -127.3239545   -2037.1832716
-1.0            -1.0           -57.2957795     -63.6619772   -1018.5916358
0.0             0.0             0.0             0.0             0.0
1.0             1.0            57.2957795      63.6619772    1018.5916358
2.0             2.0           114.591559      127.3239545    2037.1832716
6.2831853       6.2831853     359.9999996     399.9999995    6399.9999927
16.0             3.4336294     196.7324722     218.5916358    3497.4661726
57.2957795       0.7471117      42.8063493      47.5626103     761.0017647
359.0             0.8584375      49.1848452      54.649828      874.3972479
399.0             3.1593256     181.0160257     201.1289175    3218.0626795
6399.0             2.7173573     155.6931042     172.992338     2767.8774082
1000000.0             5.9256211     339.5130823     377.2367581    6035.7881302


## XPL0

def Pi = 3.14159265358979323846, N=12, Tab=9;
func real D2D;  real D;  return Mod(D, 360.);
func real G2G;  real G;  return Mod(G, 400.);
func real M2M;  real M;  return Mod(M, 6400.);
func real R2R;  real R;  return Mod(R, 2.*Pi);
func real D2G;  real D;  return 400. * D2D(D) / 360.;
func real D2M;  real D;  return 6400.* D2D(D) / 360.;
func real D2R;  real D;  return 2.*Pi* D2D(D) / 360.;
func real G2D;  real G;  return 360. * G2G(G) / 400.;
func real G2M;  real G;  return 6400.* G2G(G) / 400.;
func real G2R;  real G;  return 2.*Pi* G2G(G) / 400.;
func real M2D;  real M;  return 360. * M2M(M) / 6400.;
func real M2G;  real M;  return 400. * M2M(M) / 6400.;
func real M2R;  real M;  return 2.*Pi* M2M(M) / 6400.;
func real R2D;  real R;  return 360. * R2R(R) / (2.*Pi);
func real R2G;  real R;  return 400. * R2R(R) / (2.*Pi);
func real R2M;  real R;  return 6400.* R2R(R) / (2.*Pi);

real Angle;  int I;
[Angle:=
[-2., -1., 0., 1., 2., 6.2831853, 16., 57.2957795, 359., 399., 6399., 1000000.];
Format(7, 7);
Text(0, "
");
for I:= 0 to N-1 do
[RlOut(0, Angle(I));  ChOut(0, Tab);
RlOut(0, D2D(Angle(I)));  ChOut(0, Tab);
RlOut(0, D2G(Angle(I)));  ChOut(0, Tab);
RlOut(0, D2M(Angle(I)));  ChOut(0, Tab);
RlOut(0, D2R(Angle(I)));  CrLf(0);
];
Text(0, "
");
for I:= 0 to N-1 do
[RlOut(0, Angle(I));  ChOut(0, Tab);
RlOut(0, G2G(Angle(I)));  ChOut(0, Tab);
RlOut(0, G2D(Angle(I)));  ChOut(0, Tab);
RlOut(0, G2M(Angle(I)));  ChOut(0, Tab);
RlOut(0, G2R(Angle(I)));  CrLf(0);
];
Text(0, "
");
for I:= 0 to N-1 do
[RlOut(0, Angle(I));  ChOut(0, Tab);
RlOut(0, M2M(Angle(I)));  ChOut(0, Tab);
RlOut(0, M2D(Angle(I)));  ChOut(0, Tab);
RlOut(0, M2G(Angle(I)));  ChOut(0, Tab);
RlOut(0, M2R(Angle(I)));  CrLf(0);
];
Text(0, "
");
for I:= 0 to N-1 do
[RlOut(0, Angle(I));  ChOut(0, Tab);
RlOut(0, R2R(Angle(I)));  ChOut(0, Tab);
RlOut(0, R2D(Angle(I)));  ChOut(0, Tab);
RlOut(0, R2G(Angle(I)));  ChOut(0, Tab);
RlOut(0, R2M(Angle(I)));  CrLf(0);
];
]
Output:
     Degrees         Normalized      Gradians        Mils            Radians
-2.0000000      -2.0000000      -2.2222222     -35.5555556      -0.0349066
-1.0000000      -1.0000000      -1.1111111     -17.7777778      -0.0174533
0.0000000       0.0000000       0.0000000       0.0000000       0.0000000
1.0000000       1.0000000       1.1111111      17.7777778       0.0174533
2.0000000       2.0000000       2.2222222      35.5555556       0.0349066
6.2831853       6.2831853       6.9813170     111.7010720       0.1096623
16.0000000      16.0000000      17.7777778     284.4444444       0.2792527
57.2957795      57.2957795      63.6619772    1018.5916356       1.0000000
359.0000000     359.0000000     398.8888889    6382.2222222       6.2657320
399.0000000      39.0000000      43.3333333     693.3333333       0.6806784
6399.0000000     279.0000000     310.0000000    4960.0000000       4.8694686
1000000.0000000     280.0000000     311.1111111    4977.7777778       4.8869219
-2.0000000      -2.0000000      -1.8000000     -32.0000000      -0.0314159
-1.0000000      -1.0000000      -0.9000000     -16.0000000      -0.0157080
0.0000000       0.0000000       0.0000000       0.0000000       0.0000000
1.0000000       1.0000000       0.9000000      16.0000000       0.0157080
2.0000000       2.0000000       1.8000000      32.0000000       0.0314159
6.2831853       6.2831853       5.6548668     100.5309648       0.0986960
16.0000000      16.0000000      14.4000000     256.0000000       0.2513274
57.2957795      57.2957795      51.5662016     916.7324720       0.9000000
359.0000000     359.0000000     323.1000000    5744.0000000       5.6391588
399.0000000     399.0000000     359.1000000    6384.0000000       6.2674773
6399.0000000     399.0000000     359.1000000    6384.0000000       6.2674773
1000000.0000000       0.0000000       0.0000000       0.0000000       0.0000000
-2.0000000      -2.0000000      -0.1125000      -0.1250000      -0.0019635
-1.0000000      -1.0000000      -0.0562500      -0.0625000      -0.0009817
0.0000000       0.0000000       0.0000000       0.0000000       0.0000000
1.0000000       1.0000000       0.0562500       0.0625000       0.0009817
2.0000000       2.0000000       0.1125000       0.1250000       0.0019635
6.2831853       6.2831853       0.3534292       0.3926991       0.0061685
16.0000000      16.0000000       0.9000000       1.0000000       0.0157080
57.2957795      57.2957795       3.2228876       3.5809862       0.0562500
359.0000000     359.0000000      20.1937500      22.4375000       0.3524474
399.0000000     399.0000000      22.4437500      24.9375000       0.3917173
6399.0000000    6399.0000000     359.9437500     399.9375000       6.2822036
1000000.0000000    1600.0000000      90.0000000     100.0000000       1.5707963
-2.0000000      -2.0000000    -114.5915590    -127.3239545   -2037.1832716
-1.0000000      -1.0000000     -57.2957795     -63.6619772   -1018.5916358
0.0000000       0.0000000       0.0000000       0.0000000       0.0000000
1.0000000       1.0000000      57.2957795      63.6619772    1018.5916358
2.0000000       2.0000000     114.5915590     127.3239545    2037.1832716
6.2831853       6.2831853     359.9999996     399.9999995    6399.9999927
16.0000000       3.4336294     196.7324722     218.5916358    3497.4661726
57.2957795       0.7471117      42.8063493      47.5626103     761.0017647
359.0000000       0.8584375      49.1848452      54.6498280     874.3972479
399.0000000       3.1593256     181.0160257     201.1289175    3218.0626795
6399.0000000       2.7173573     155.6931042     172.9923380    2767.8774082
1000000.0000000       5.9256211     339.5130823     377.2367581    6035.7881302


## zkl

Translation of: Raku
var [const]
tau=(0.0).pi*2,
units=Dictionary(	// code:(name, units in circle)
"d", T("degrees", 360.0), "g",T("gradians",400.0),
"m", T("mills",  6400.0), "r",T("radians", tau) ),
cvtNm="%s-->%s".fmt,
cvt=  // "d-->r":fcn(angle){}, "r-->d":fcn(angle){} ...
Walker.cproduct(units.keys,units.keys).pump(Dictionary(),fcn([(a,b)]){
return(cvtNm(a,b),  // "d-->r"
'wrap(angle){ angle=angle.toFloat();
u:=units[a][1];
(angle%u)*units[b][1] / u
})
})
;
codes:=units.keys;
println("     Angle Unit     ",
codes.apply(fcn(k){ units[k][0] }).apply("%11s".fmt).concat(" "));
foreach angle in (T(-2.0,-1, 0, 1, 2, tau, 16, 360.0/tau, 360-1, 400-1, 6400-1, 1_000_000)){
println();
foreach from in (codes){
subKeys:=codes.apply(cvtNm.fp(from)); // ("d-->d","d-->g","d-->m","d-->r")
r:=subKeys.pump(List,'wrap(k){ cvt[k](angle) });
println("%10g %-8s %s".fmt(angle,units[from][0],
r.apply("%12g".fmt).concat(" ")));
}
}
Output:
     Angle Unit         degrees    gradians       mills     radians

-2 degrees            -2     -2.22222     -35.5556   -0.0349066
-2 gradians         -1.8           -2          -32   -0.0314159
-2 mills         -0.1125       -0.125           -2   -0.0019635
-2 radians      -114.592     -127.324     -2037.18           -2

-1 degrees            -1     -1.11111     -17.7778   -0.0174533
-1 gradians         -0.9           -1          -16    -0.015708
-1 mills        -0.05625      -0.0625           -1 -0.000981748
-1 radians      -57.2958      -63.662     -1018.59           -1

0 degrees             0            0            0            0
0 gradians            0            0            0            0
0 mills               0            0            0            0
0 radians             0            0            0            0

1 degrees             1      1.11111      17.7778    0.0174533
1 gradians          0.9            1           16     0.015708
1 mills         0.05625       0.0625            1  0.000981748
1 radians       57.2958       63.662      1018.59            1

2 degrees             2      2.22222      35.5556    0.0349066
2 gradians          1.8            2           32    0.0314159
2 mills          0.1125        0.125            2    0.0019635
2 radians       114.592      127.324      2037.18            2

6.28319 degrees       6.28319      6.98132      111.701     0.109662
6.28319 gradians      5.65487      6.28319      100.531     0.098696
6.28319 mills        0.353429     0.392699      6.28319    0.0061685
6.28319 radians             0            0            0            0

16 degrees            16      17.7778      284.444     0.279253
16 gradians         14.4           16          256     0.251327
16 mills             0.9            1           16     0.015708
16 radians       196.732      218.592      3497.47      3.43363

57.2958 degrees       57.2958       63.662      1018.59            1
57.2958 gradians      51.5662      57.2958      916.732          0.9
57.2958 mills         3.22289      3.58099      57.2958      0.05625
57.2958 radians       42.8064      47.5626      761.002     0.747112

359 degrees           359      398.889      6382.22      6.26573
359 gradians        323.1          359         5744      5.63916
359 mills         20.1938      22.4375          359     0.352447
359 radians       49.1848      54.6498      874.397     0.858437

399 degrees            39      43.3333      693.333     0.680678
399 gradians        359.1          399         6384      6.26748
399 mills         22.4438      24.9375          399     0.391717
399 radians       181.016      201.129      3218.06      3.15933

6399 degrees           279          310         4960      4.86947
6399 gradians        359.1          399         6384      6.26748
6399 mills         359.944      399.938         6399       6.2822
6399 radians       155.693      172.992      2767.88      2.71736

1e+06 degrees           280      311.111      4977.78      4.88692
1e+06 gradians            0            0            0            0
1e+06 mills              90          100         1600       1.5708
1e+06 radians       339.513      377.237      6035.79      5.92562