Angles (geometric), normalization and conversion

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
gradian
mil
radian

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:

gradian(s)
grad(s)
grade(s)
gon(s)
metric degree(s)
(Note that centigrade was used for ¹/₁₀₀^th 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:

radian(s)
rad(s)

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

Task

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(‘       Degrees        Normalized         Gradians          Mils            Radians’)
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(‘      Gradians        Normalized         Degrees           Mils            Radians’)
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(‘        Mils          Normalized         Degrees         Gradians          Radians’)
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(‘       Radians        Normalized         Degrees         Gradians          Mils’)
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

      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       51.5662015      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

        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

Ada

-- Rosetta Code Task written in Ada
-- Angles (geometric), normalization and conversion
-- https://rosettacode.org/wiki/Angles_(geometric),_normalization_and_conversion
-- translation from C (conversion functions) and (loosely) Lua (output table formatting)
-- July 2024, R. B. E.

-- To Do:
-- Specific float format/precision rather than generic?

with Ada.Text_IO; use Ada.Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
with Ada.Float_Text_IO; use Ada.Float_Text_IO;
with Ada.Strings.Fixed; use Ada.Strings.Fixed;
with Ada.Numerics;

procedure Angles_Geometric_Normalization_and_Conversion is
  Pi : constant := Ada.Numerics.Pi;
  Two_Pi : constant := 2.0 * Ada.Numerics.Pi;

  function Normalize_to_Deg (a : Float) return Float is 
    tmp : Float := a;
  begin
--    while (tmp < 0.0) loop
    while (tmp < -360.0) loop -- task description says to preserve negative input angles
      tmp := tmp + 360.0;
    end loop;
    while (tmp >= 360.0) loop
      tmp := tmp - 360.0;
    end loop;
    return tmp;    
  end Normalize_to_Deg;

  function Normalize_to_Grad (a : Float) return Float is 
    tmp : Float := a;
  begin
    while (tmp < 0.0) loop -- task description says to preserve negative input angles (punting)
      tmp := tmp + 400.0;
    end loop;
    while (tmp >= 400.0) loop
      tmp := tmp - 400.0;
    end loop;
    return tmp;    
  end Normalize_to_Grad;

  function Normalize_to_Mil (a : Float) return Float is 
    tmp : Float := a;
  begin
    while (tmp < 0.0) loop -- task description says to preserve negative input angles (punting)
      tmp := tmp + 6400.0;
    end loop;
    while (tmp >= 6400.0) loop
      tmp := tmp - 6400.0;
    end loop;
    return tmp;    
  end Normalize_to_Mil;

  function Normalize_to_Rad (a : Float) return Float is 
    tmp : Float := a;
  begin
    while (tmp < 0.0) loop -- task description says to preserve negative input angles (punting)
      tmp := tmp + Two_Pi;
    end loop;
    while (tmp >= Two_Pi) loop
      tmp := tmp - Two_Pi;
    end loop;
    return tmp;    
  end Normalize_to_Rad;

  function Deg_to_Grad (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a * (10.0 / 9.0);
    return tmp;
  end Deg_to_Grad;

  function Deg_to_Mil (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a * (160.0 / 9.0);
    return tmp;
  end Deg_to_Mil;

  function Deg_to_Rad (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a * (Pi / 180.0);
    return tmp;
  end Deg_to_Rad;

  function Grad_to_Deg (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a * (9.0 / 10.0);
    return tmp;
  end Grad_to_Deg;

  function Grad_to_Mil (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a * 16.0;
    return tmp;
  end Grad_to_Mil;

  function Grad_to_Rad (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a * (Pi / 200.0);
    return tmp;
  end Grad_to_Rad;

  function Mil_to_Deg (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a * (9.0 / 160.0);
    return tmp;
  end Mil_to_Deg;

  function Mil_to_Grad (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a / 16.0;
    return tmp;
  end Mil_to_Grad;

  function Mil_to_Rad (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a * (Pi / 3200.0);
    return tmp;
  end Mil_to_Rad;

  function Rad_to_Deg (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a * (180.0 / Pi);
    return tmp;
  end Rad_to_Deg;

  function Rad_to_Grad (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a * (200.0 / Pi);
    return tmp;
  end Rad_to_Grad;

  function Rad_to_Mil (a : Float) return Float is
    tmp : Float := a;
  begin
    tmp := a * (3200.0 / Pi);
    return tmp;
  end Rad_to_Mil;

  Three_Spaces : constant String := 3 * " ";

  type Index is range 1 .. 12;
  type Test_Values_Array is array (Index) of Float;
  Test_Values : Test_Values_Array :=
    (Float (-2), Float (-1), Float (0), Float (1), Float (2),
     6.2831853, Float (16), 57.2957795, Float (359),
     Float (399), Float (6399), Float (1000000));

begin
  Put_Line ("                        DEGREES         GRADIANS         MILS          RADIANS");
  Put_Line ("      TEST VALUE      Normalized       Converted       Converted      Converted");
  for I in Index loop
    Put (Test_Values (I), Exp => 0, Aft => 8, Fore => 8);
    Put (Three_Spaces);
    Put (Normalize_to_Deg (Test_Values (I)), Exp => 0, Aft => 8, Fore => 4);
    Put (Three_Spaces);
    Put (Deg_to_Grad (Normalize_to_Deg (Test_Values (I))), Exp => 0, Aft => 8, Fore => 4);
    Put (Three_Spaces);
    Put (Deg_to_Mil (Normalize_to_Deg (Test_Values (I))), Exp => 0, Aft => 8, Fore => 4);
    Put (Three_Spaces);
    Put (Deg_to_Rad (Normalize_to_Deg (Test_Values (I))), Exp => 0, Aft => 8, Fore => 2);
    New_Line;
  end loop;

  New_Line;
  Put_Line ("                       GRADIANS           MILS        RADIANS        DEGREES");
  Put_Line ("      TEST VALUE      Normalized       Converted     Converted      Converted");
  for I in Index loop
    Put (Test_Values (I), Exp => 0, Aft => 8, Fore => 8);
    Put (Three_Spaces);
    Put (Normalize_to_Grad (Test_Values (I)), Exp => 0, Aft => 8, Fore => 4);
    Put (Three_Spaces);
    Put (Grad_to_Mil (Normalize_to_Grad (Test_Values (I))), Exp => 0, Aft => 8, Fore => 4);
    Put (Three_Spaces);
    Put (Grad_to_Rad (Normalize_to_Grad (Test_Values (I))), Exp => 0, Aft => 8, Fore => 2);
    Put (Three_Spaces);
    Put (Grad_to_Deg (Normalize_to_Grad (Test_Values (I))), Exp => 0, Aft => 8, Fore => 4);
    New_Line;
  end loop;

  New_Line;
  Put_Line ("                         MILS           RADIANS       DEGREES        GRADIANS");
  Put_Line ("      TEST VALUE      Normalized       Converted     Converted      Converted");
  for I in Index loop
    Put (Test_Values (I), Exp => 0, Aft => 8, Fore => 8);
    Put (Three_Spaces);
    Put (Normalize_to_Mil (Test_Values (I)), Exp => 0, Aft => 8, Fore => 4);
    Put (Three_Spaces);
    Put (Mil_to_Rad (Normalize_to_Mil (Test_Values (I))), Exp => 0, Aft => 8, Fore => 2);
    Put (Three_Spaces);
    Put (Mil_to_Deg (Normalize_to_Mil (Test_Values (I))), Exp => 0, Aft => 8, Fore => 4);
    Put (Three_Spaces);
    Put (Mil_to_Grad (Normalize_to_Mil (Test_Values (I))), Exp => 0, Aft => 8, Fore => 4);
    New_Line;
  end loop;

  New_Line;
  Put_Line ("                         RADIANS          DEGREES       GRADIANS        MILS");
  Put_Line ("      TEST VALUE       Normalized        Converted     Converted      Converted");
  for I in Index loop
    Put (Test_Values (I), Exp => 0, Aft => 8, Fore => 8);
    Put (Three_Spaces);
    Put (Normalize_to_Rad (Test_Values (I)), Exp => 0, Aft => 8, Fore => 4);
    Put (Three_Spaces);
    Put (Rad_to_Deg (Normalize_to_Rad (Test_Values (I))), Exp => 0, Aft => 8, Fore => 4);
    Put (Three_Spaces);
    Put (Rad_to_Grad (Normalize_to_Rad (Test_Values (I))), Exp => 0, Aft => 8, Fore => 4);
    Put (Three_Spaces);
    Put (Rad_to_Mil (Normalize_to_Rad (Test_Values (I))), Exp => 0, Aft => 8, Fore => 4);
    New_Line;
  end loop;

end Angles_Geometric_Normalization_and_Conversion;

Output:

./angles_geometric_normalization_and_conversion
                        DEGREES         GRADIANS         MILS          RADIANS
      TEST VALUE      Normalized       Converted       Converted      Converted
      -2.00000000     -2.00000000     -2.22222233    -35.55555725   -0.03490658
      -1.00000000     -1.00000000     -1.11111116    -17.77777863   -0.01745329
       0.00000000      0.00000000      0.00000000      0.00000000    0.00000000
       1.00000000      1.00000000      1.11111116     17.77777863    0.01745329
       2.00000000      2.00000000      2.22222233     35.55555725    0.03490658
       6.28318548      6.28318548      6.98131752    111.70108032    0.10966227
      16.00000000     16.00000000     17.77777863    284.44445801    0.27925268
      57.29578018     57.29578018     63.66197968   1018.59167480    1.00000000
     359.00000000    359.00000000    398.88891602   6382.22265625    6.26573181
     399.00000000     39.00000000     43.33333588    693.33337402    0.68067843
    6399.00000000    279.00000000    310.00000000   4960.00000000    4.86946869
 1000000.00000000    280.00000000    311.11111450   4977.77783203    4.88692188

                       GRADIANS           MILS        RADIANS        DEGREES
      TEST VALUE      Normalized       Converted     Converted      Converted
      -2.00000000    398.00000000   6368.00000000    6.25176954    358.19998169
      -1.00000000    399.00000000   6384.00000000    6.26747751    359.09997559
       0.00000000      0.00000000      0.00000000    0.00000000      0.00000000
       1.00000000      1.00000000     16.00000000    0.01570796      0.89999998
       2.00000000      2.00000000     32.00000000    0.03141593      1.79999995
       6.28318548      6.28318548    100.53096771    0.09869605      5.65486670
      16.00000000     16.00000000    256.00000000    0.25132743     14.39999962
      57.29578018     57.29578018    916.73248291    0.90000004     51.56620026
     359.00000000    359.00000000   5744.00000000    5.63915920    323.10000610
     399.00000000    399.00000000   6384.00000000    6.26747751    359.09997559
    6399.00000000    399.00000000   6384.00000000    6.26747751    359.09997559
 1000000.00000000      0.00000000      0.00000000    0.00000000      0.00000000

                         MILS           RADIANS       DEGREES        GRADIANS
      TEST VALUE      Normalized       Converted     Converted      Converted
      -2.00000000   6398.00000000    6.28122234    359.88748169    399.87500000
      -1.00000000   6399.00000000    6.28220367    359.94372559    399.93750000
       0.00000000      0.00000000    0.00000000      0.00000000      0.00000000
       1.00000000      1.00000000    0.00098175      0.05625000      0.06250000
       2.00000000      2.00000000    0.00196350      0.11250000      0.12500000
       6.28318548      6.28318548    0.00616850      0.35342917      0.39269909
      16.00000000     16.00000000    0.01570796      0.89999998      1.00000000
      57.29578018     57.29578018    0.05625000      3.22288752      3.58098626
     359.00000000    359.00000000    0.35244745     20.19375038     22.43750000
     399.00000000    399.00000000    0.39171734     22.44374847     24.93750000
    6399.00000000   6399.00000000    6.28220367    359.94372559    399.93750000
 1000000.00000000   1600.00000000    1.57079637     90.00000000    100.00000000

                         RADIANS          DEGREES       GRADIANS        MILS
      TEST VALUE       Normalized        Converted     Converted      Converted
      -2.00000000      4.28318548    245.40844727    272.67605591   4362.81689453
      -1.00000000      5.28318548    302.70422363    336.33801270   5381.40820313
       0.00000000      0.00000000      0.00000000      0.00000000      0.00000000
       1.00000000      1.00000000     57.29578018     63.66197586   1018.59161377
       2.00000000      2.00000000    114.59156036    127.32395172   2037.18322754
       6.28318548      0.00000000      0.00000000      0.00000000      0.00000000
      16.00000000      3.43362856    196.73242188    218.59158325   3497.46533203
      57.29578018      0.74711514     42.80654526     47.56282425    761.00518799
     359.00000000      0.85856915     49.19239044     54.65820694    874.53131104
     399.00000000      3.15952921    181.02769470    201.14187622   3218.27001953
    6399.00000000      2.70112467    154.76304626    171.95893860   2751.34301758
 1000000.00000000      2.72260904    155.99400330    173.32667542   2773.22680664

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

      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       51.5662015      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

        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

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( heading );
        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

      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

AutoHotkey

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

result .= "Degrees    Degrees    Gradians    Mils    Radians`n"
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    Radians`n"
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    Radians`n"
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    Radians`n"
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)
}
Deg2Grad(Deg){
    return Deg2Deg(Deg) * 400 / 360
}
Deg2Mil(Deg){
    return Deg2Deg(Deg) * 6400 / 360
}
Deg2Rad(Deg){
    return Deg2Deg(Deg) * (π:=3.141592653589793) / 180
}
;-------------------------------------------------------
Grad2Grad(Grad){
    return Mod(Grad, 400)
}
Grad2Deg(Grad){
    return Grad2Grad(Grad) * 360 / 400
}
Grad2Mil(Grad){
    return Grad2Grad(Grad) * 6400 / 400
}
Grad2Rad(Grad){
    return Grad2Grad(Grad) * (π:=3.141592653589793) / 200
}
;-------------------------------------------------------
Mil2Mil(Mil){
    return Mod(Mil, 6400)
}
Mil2Deg(Mil){
    return Mil2Mil(Mil) * 360 / 6400
}
Mil2Grad(Mil){
    return Mil2Mil(Mil) * 400 / 6400
}
Mil2Rad(Mil){
    return Mil2Mil(Mil) * (π:=3.141592653589793) / 3200
}
;-------------------------------------------------------
Rad2Rad(Rad){
    return Mod(Rad, 2*(π:=3.141592653589793))
}
Rad2Deg(Rad){
    return Rad2Rad(Rad) * 180 / (π:=3.141592653589793)
}
Rad2Grad(Rad){
    return Rad2Rad(Rad) * 200 / (π:=3.141592653589793)
}
Rad2Mil(Rad){
    return Rad2Rad(Rad) * 3200 / (π:=3.141592653589793)
}
;-------------------------------------------------------

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

Gradians	Degrees		Gradians	Mils		Radians
-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

Mills		Degrees		Gradians	Mils		Radians
-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

Radians		Degrees		Gradians	Mils		Radians
-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,",")
    unit_leng = split("degree,gradian,mil,radian",unit_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["gradian"] = normalize(angle,400)
      arr["mil"]     = normalize(angle,6400)
      arr["radian"]  = normalize(angle,pi*2)
      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

Works with: BBC BASIC for Windows

      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
        READ Angle
        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

      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    339.5130824    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 },
            { GradToDeg, a => a, GradToMil, GradToRad },
            { MilToDeg, MilToGrad, a => a, MilToRad },
            { RadToDeg, RadToGrad, RadToMil, a => a }
        };

        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, "grad -> rad ", g2r);

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

    print(values, "rad -> deg ", r2d);
    print(values, "rad -> grad ", r2g);
    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 GradToGrad (a) (rem a 400))
(defun MilToMil (a) (rem a 6400))
(defun RadToRad (a) (rem a (* 2 pi)))

(defun DegToGrad (a) (GradToGrad (* (/ a 360) 400)))
(defun DegToRad (a) (RadToRad (* (/ a 360) (* 2 pi))))
(defun DegToMil (a) (MilToMil (* (/ a 360) 6400)))

(defun GradToDeg (a) (DegToDeg (* (/ a 400) 360)))
(defun GradToRad (a) (RadToRad (* (/ a 400) (* 2 pi))))
(defun GradToMil (a) (MilToMil (* (/ a 400) 6400)))

(defun MilToDeg (a) (DegToDeg (* (/ a 6400) 360)))
(defun MilToGrad (a) (GradToGrad (* (/ a 6400) 400)))
(defun MilToRad (a) (RadToRad (* (/ a 6400) (* 2 pi))))

(defun RadToDeg (a) (DegToDeg (* (/ a (* 2 pi)) 360)))
(defun RadToGrad (a) (GradToGrad (* (/ a (* 2 pi)) 400)))
(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 "Grad | ~15f | ~15f | ~15f | ~15f | ~15f~%" a (GradToDeg a) (GradToGrad a) (GradToMil a) (GradToRad a))
        (format t "Mil  | ~15f | ~15f | ~15f | ~15f | ~15f~%" a (MilToDeg a) (MilToGrad a) (MilToMil a) (MilToRad a))
        (format t "Rad  | ~15f | ~15f | ~15f | ~15f | ~15f~%~%" a (RadToDeg a) (RadToGrad a) (RadToMil a) (RadToRad a))))

Output:

[CLISP]> (angles)
UNIT              VAL*               DEG              GRAD               MIL               RAD
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

UNIT              VAL*               DEG              GRAD               MIL               RAD
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

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 |       1.1111112 |       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

UNIT              VAL*               DEG              GRAD               MIL               RAD
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

UNIT              VAL*               DEG              GRAD               MIL               RAD
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

UNIT              VAL*               DEG              GRAD               MIL               RAD
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

UNIT              VAL*               DEG              GRAD               MIL               RAD
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

UNIT              VAL*               DEG              GRAD               MIL               RAD
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

UNIT              VAL*               DEG              GRAD               MIL               RAD
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

UNIT              VAL*               DEG              GRAD               MIL               RAD
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

UNIT              VAL*               DEG              GRAD               MIL               RAD
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.SysUtils

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

  gradian    degree   gradian       mil    radian 
  ------------------------------------------------
        -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

      mil    degree   gradian       mil    radian 
  ------------------------------------------------
        -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

   radian    degree   gradian       mil    radian 
  ------------------------------------------------
        -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 ( -- )
    .header
    { -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

FutureBasic

include "NSLog.incl"

double local fn Normalize( f as double, n as double  )
  double a = f
  while ( a < -n ) : a += n : wend
  while ( a >= n ) : a -= n : wend
end fn = a
 
double local fn NormalizeToDegrees(  f as double ) return fn Normalize( f, 360  )      end fn = 0.0
double local fn NormalizeToGradians( f as double ) return fn Normalize( f, 400  )      end fn = 0.0
double local fn NormalizeToMils(     f as double ) return fn Normalize( f, 6400 )      end fn = 0.0
double local fn NormalizeToRadians(  f as double ) return fn Normalize( f, 2 * M_PI )  end fn = 0.0
  
double local fn d2g( f as double ) return f * 10 / 9       end fn = 0.0
double local fn d2m( f as double ) return f * 160 / 9      end fn = 0.0
double local fn d2r( f as double ) return f * M_PI / 180   end fn = 0.0
  
double local fn g2d( f as double ) return f * 9 / 10       end fn = 0.0
double local fn g2m( f as double ) return f * 16           end fn = 0.0
double local fn g2r( f as double ) return f * M_PI / 200   end fn = 0.0
  
double local fn m2d( f as double ) return f * 9 / 160      end fn = 0.0
double local fn m2g( f as double ) return f / 16           end fn = 0.0
double local fn m2r( f as double ) return f * M_PI / 3200  end fn = 0.0
  
double local fn r2d( f as double ) return f * 180  / M_PI  end fn = 0.0
double local fn r2g( f as double ) return f * 200  / M_PI  end fn = 0.0
double local fn r2m( f as double ) return f * 3200 / M_PI  end fn = 0.0
  
local fn CalculateDegrees
  CFArrayRef  angles = @[@-2, @-1, @0, @1, @2, @6.2831853, @16, @57.2957795, @359, @6399, @1000000]
  double      angle, degrees, gradians, mils, radians
  NSUInteger  i
  CFStringRef unit
  CFStringRef dashpad = fn StringByPaddingToLength( @"", 73, @"-", 0 )
  
  ptr anglePtr    = fn StringUTF8String( @"Angle"      )
  ptr unitPtr     = fn StringUTF8String( @"Unit"       )
  ptr normalPtr   = fn StringUTF8String( @"Normalized" )
  ptr gradiansPtr = fn StringUTF8String( @"Gradians"   )
  ptr milsPtr     = fn StringUTF8String( @"Mils"       )
  ptr radiansPtr  = fn StringUTF8String( @"Radians"    )
  
  // Header
  NSLog( @"\n%@", dashpad )
  NSLog( @"%13s  %5s  %15s %10s %7s %15s", anglePtr, unitPtr, normalPtr, gradiansPtr, milsPtr, radiansPtr )
  NSLog( @"%@", dashpad )
  
  // Degrees
  for i = 0 to fn ArrayCount( angles ) - 1
    angle    = dblval( angles[i] )
    unit     = @"Degrees"
    degrees  = fn NormalizeToDegrees( angle )
    gradians = fn NormalizeToGradians( fn d2g( degrees ) )
    mils     = fn NormalizeToMils(     fn d2m( degrees ) )
    radians  = fn NormalizeToRadians(  fn d2r( degrees ) )
    NSLog( @"%13.4f   %-10s % -12.4f % -11.4f % -12.4f % -13.4f", angle, fn StringUTF8String( unit ), degrees, gradians, mils, radians )
  next
  NSLog( @"" )
  
  // Gradians
  for i = 0 to fn ArrayCount( angles ) - 1
    angle    = dblval( angles[i] )
    unit     = @"Gradians"
    gradians = fn NormalizeToGradians( angle )
    degrees  = fn NormalizeToDegrees( fn g2d( gradians ) )
    mils     = fn NormalizeToMils(    fn g2m( gradians ) )
    radians  = fn NormalizeToRadians( fn g2r( gradians ) )
    NSLog( @"%13.4f   %-10s % -12.4f % -11.4f % -12.4f % -13.4f", angle, fn StringUTF8String( unit ), degrees, gradians, mils, radians )
  next
  NSLog( @"" )
  
  // Mils
  for i = 0 to fn ArrayCount( angles ) - 1
    angle    = dblval( angles[i] )
    unit     = @"Mils"
    mils     = fn NormalizeToMils( angle )
    degrees  = fn NormalizeToDegrees(  fn m2d( mils ) )
    gradians = fn NormalizeToGradians( fn m2g( mils ) )
    radians  = fn NormalizeToRadians(  fn m2r( mils ) )
    NSLog( @"%13.4f   %-10s % -12.4f % -11.4f % -12.4f % -13.4f", angle, fn StringUTF8String( unit ), degrees, gradians, mils, radians )
  next
  NSLog( @"" )
  
  // Radians
  for i = 0 to fn ArrayCount( angles ) - 1
    angle    = dblval( angles[i] )
    unit     = @"Radians"
    radians  = fn NormalizeToRadians( angle )
    degrees  = fn NormalizeToDegrees(  fn r2d( radians ) )
    gradians = fn NormalizeToGradians( fn r2g( radians ) )
    mils     = fn NormalizeToMils(     fn r2m( radians ) )
    NSLog( @"%13.4f   %-10s % -12.4f % -11.4f % -12.4f % -13.4f", angle, fn StringUTF8String( unit ), degrees, gradians, mils, radians )
  next
  NSLog( @"%@", dashpad )
end fn

fn CalculateDegrees

HandleEvents

Output:

-------------------------------------------------------------------------
        Angle   Unit       Normalized   Gradians    Mils         Radians
-------------------------------------------------------------------------
      -2.0000   Degrees    -2.0000      -2.2222     -35.5556     -0.0349      
      -1.0000   Degrees    -1.0000      -1.1111     -17.7778     -0.0175      
       0.0000   Degrees     0.0000       0.0000      0.0000       0.0000      
       1.0000   Degrees     1.0000       1.1111      17.7778      0.0175      
       2.0000   Degrees     2.0000       2.2222      35.5556      0.0349      
       6.2832   Degrees     6.2832       6.9813      111.7011     0.1097      
      16.0000   Degrees     16.0000      17.7778     284.4444     0.2793      
      57.2958   Degrees     57.2958      63.6620     1018.5916    1.0000      
     359.0000   Degrees     359.0000     398.8889    6382.2222    6.2657      
    6399.0000   Degrees     279.0000     310.0000    4960.0000    4.8695      
 1000000.0000   Degrees     280.0000     311.1111    4977.7778    4.8869      

      -2.0000   Gradians   -1.8000      -2.0000     -32.0000     -0.0314      
      -1.0000   Gradians   -0.9000      -1.0000     -16.0000     -0.0157      
       0.0000   Gradians    0.0000       0.0000      0.0000       0.0000      
       1.0000   Gradians    0.9000       1.0000      16.0000      0.0157      
       2.0000   Gradians    1.8000       2.0000      32.0000      0.0314      
       6.2832   Gradians    5.6549       6.2832      100.5310     0.0987      
      16.0000   Gradians    14.4000      16.0000     256.0000     0.2513      
      57.2958   Gradians    51.5662      57.2958     916.7325     0.9000      
     359.0000   Gradians    323.1000     359.0000    5744.0000    5.6392      
    6399.0000   Gradians    359.1000     399.0000    6384.0000    6.2675      
 1000000.0000   Gradians    0.0000       0.0000      0.0000       0.0000      

      -2.0000   Mils       -0.1125      -0.1250     -2.0000      -0.0020      
      -1.0000   Mils       -0.0563      -0.0625     -1.0000      -0.0010      
       0.0000   Mils        0.0000       0.0000      0.0000       0.0000      
       1.0000   Mils        0.0563       0.0625      1.0000       0.0010      
       2.0000   Mils        0.1125       0.1250      2.0000       0.0020      
       6.2832   Mils        0.3534       0.3927      6.2832       0.0062      
      16.0000   Mils        0.9000       1.0000      16.0000      0.0157      
      57.2958   Mils        3.2229       3.5810      57.2958      0.0562      
     359.0000   Mils        20.1938      22.4375     359.0000     0.3524      
    6399.0000   Mils        359.9438     399.9375    6399.0000    6.2822      
 1000000.0000   Mils        90.0000      100.0000    1600.0000    1.5708      

      -2.0000   Radians    -114.5916    -127.3240   -2037.1833   -2.0000      
      -1.0000   Radians    -57.2958     -63.6620    -1018.5916   -1.0000      
       0.0000   Radians     0.0000       0.0000      0.0000       0.0000      
       1.0000   Radians     57.2958      63.6620     1018.5916    1.0000      
       2.0000   Radians     114.5916     127.3240    2037.1833    2.0000      
       6.2832   Radians     360.0000     400.0000    6400.0000    6.2832      
      16.0000   Radians     196.7325     218.5916    3497.4662    3.4336      
      57.2958   Radians     42.8063      47.5626     761.0018     0.7471      
     359.0000   Radians     49.1848      54.6498     874.3972     0.8584      
    6399.0000   Radians     155.6931     172.9923    2767.8774    2.7174      
 1000000.0000   Radians     339.5132     377.2368    6035.7895    5.9256      
-------------------------------------------------------------------------

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

   gradians     normalized grds     degrees          mils            radians
     -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        

     mils       normalized mils     degrees        gradians          radians
     -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

    radians     normalized rads     degrees        gradians           mils  
     -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 Gradians getGrad(Number n) { new Gradians(n) }
    static Mils getMil(Number n) { new Mils(n) }
    static Radians getRad(Number n) { new Radians(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

Haskell

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
converting to radians
[∠-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°]

converting to grads
[-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'
   Gradian =: adverb def 'normalize as_gradian inv m'
   Mil     =: adverb def 'normalize as_mil inv m'
   Radian  =: adverb def 'normalize as_radian inv m'

we can compose conversion sentences like

   as_degree   100 Gradian
90

Presuming the following additional definitions:

   NAMES =: > turn`degree`gradian`mil`radian
   ALL =: as_turn`as_degree`as_gradian`as_mil`as_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|
+-------+---------------------------------------------------------------------------------------------------------------+

   to_all   VALUES Gradian
+-------+----------------------------------------------------------------------------------------------+
|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|
+-------+-------------------------------------------------------------------------------------------------------------------+

   to_all   VALUES Radian
+-------+---------------------------------------------------------------------------------------------------+
|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");
        System.out.printf("                               degrees    gradiens        mils     radians%n");
        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;
                case "gradiens":
                    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;
                case "radians":
                    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) {
        return a * (RADIAN / GRADIAN);
    }
    
    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) {
        return a * (GRADIAN / RADIAN);
    }
    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

Adapted from #Wren

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

PascalABC.NET

function fmod(x, y: real): real := x - trunc(x / y) * y;

function d2d(x: real): real := fmod(x, 360);
function g2g(x: real): real := fmod(x, 400);
function m2m(x: real): real := fmod(x, 6400);
function r2r(x: real): real := fmod(x, 2 * Pi);
function d2g(x: real): real := d2d(x) * 10 / 9;
function d2m(x: real): real := d2d(x) * 160 / 9;
function d2r(x: real): real := d2d(x) * Pi / 180;
function g2d(x: real): real := g2g(x) * 9 / 10;
function g2m(x: real): real := g2g(x) * 16;
function g2r(x: real): real := g2g(x) * Pi / 200;
function m2d(x: real): real := m2m(x) * 9 / 160;
function m2g(x: real): real := m2m(x) / 16;
function m2r(x: real): real := m2m(x) * Pi / 3200;
function r2d(x: real): real := r2r(x) * 180 / Pi;
function r2g(x: real): real := r2r(x) * 200 / Pi;
function r2m(x: real): real := r2r(x) * 3200 / Pi;

begin
  var Values: array of real := (-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000);
  writeln('       Degrees      Normalized       Gradians        Mils          Radians');
  writeln('———————————————————————————————————————————————————————————————————————————');
  foreach var val in Values do
    writeln(val:15:7, d2d(val):15:7, d2g(val):15:7, d2m(val):15:7, d2r(val):15:7);
  writeln;
  writeln( '      Gradians      Normalized       Degrees         Mils          Radians');
  writeln( '———————————————————————————————————————————————————————————————————————————');
  foreach var val in Values do
    writeln( val:15:7, g2g(val):15:7,  g2d(val):15:7,  g2m(val):15:7,  g2r(val):15:7);
  writeln;
  writeln( '        Mils        Normalized       Degrees       Gradians        Radians');
  writeln( '———————————————————————————————————————————————————————————————————————————');
  foreach var val in Values do
    writeln( val:15:7,  m2m(val):15:7,  m2d(val):15:7,  m2g(val):15:7, m2r(val):15:7);
  writeln;
  writeln( '       Radians      Normalized       Degrees       Gradians        Mils');
  writeln( '———————————————————————————————————————————————————————————————————————————');
  foreach var val in Values do
    writeln( val:15:7,  r2r(val):15:7,  r2d(val):15:7,  r2g(val):15:7,  r2m(val):15:7);
end.

Perl

Translation of: Raku

use strict;
use warnings;
use feature 'say';
use POSIX 'fmod';

my $tau = 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
def normalize2grad(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
def normalize2rad(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
    and radians.
'''

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,
                          padx=(8,8),
                          pady=(8,8))

        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)

        self.radiod = Radiobutton(self.su_fr,
                                  text='degree',
                                  font='arial 12 bold',
                                  fg='navy',
                                  bg='dodger blue',
                                  variable=self.unit,
                                  value='d')
        self.radiod.pack(side='top', anchor='w')

        self.radiog = Radiobutton(self.su_fr,
                                  text='gradian',
                                  font='arial 12 bold',
                                  fg='navy', 
                                  bg='dodger blue',
                                  variable=self.unit,
                                  value='g')
        self.radiog.pack(side='top', anchor='w')

        self.radiom = Radiobutton(self.su_fr,
                                  text='mil',
                                  font='arial 12 bold',
                                  fg='navy', 
                                  bg='dodger blue',
                                  variable=self.unit,
                                  value='m')
        self.radiom.pack(side='top', anchor='w')

        self.radior = Radiobutton(self.su_fr,
                                  text='radian',
                                  font='arial 12 bold',
                                  fg='navy', 
                                  bg='dodger blue',
                                  variable=self.unit,
                                  value='r')
        self.radior.pack(side='top', anchor='w')

        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,
                             padx = 3,
                             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,
                             text='   grads: ',
                             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,
                             padx = 3,
                             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,
                             padx = 3,
                             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
        self.rad_lbl = Label(self.res_fr,
                             text='radians: ',
                             anchor=E,
                             font='"Noto Mono" 12 bold',
                             fg='navy',
                             bg='lemon chiffon')
        self.rad_lbl.place(x=lblx, y=objy,
                           height=objh, width=lblw)

        self.rad_val = Label(self.res_fr,
                             text=' ',
                             anchor=E,
                             padx = 3,
                             font='"Noto Mono" 12 bold',
                             fg='navy',
                             bg='lemon chiffon')
        self.rad_val.place(x=valx, y=objy,
                           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)
        
        # convert to grads, mils, radians
        self.grad = self.d2g(self.deg)
        self.mil = self.d2m(self.deg)
        self.rad = self.d2r(self.deg)
        
        # show results
        self.deg_val.config(text=self.format_angle(self.deg))
        self.grd_val.config(text=self.format_angle(self.grad))
        self.mil_val.config(text=self.format_angle(self.mil))
        self.rad_val.config(text=self.format_angle(self.rad))
        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='')
        self.rad_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 (grad->grad a) (rem a 400))
(define (mil->mil a) (rem a 6400))
(define (rad->rad a) (rem a 2.pi))
 
(define (deg->grad a) (grad->grad (* (/ a 360) 400)))
(define (deg->rad a) (rad->rad (* (/ a 360) 2.pi)))
(define (deg->mil a) (mil->mil (* (/ a 360) 6400)))
 
(define (grad->deg a) (deg->deg (* (/ a 400) 360)))
(define (grad->rad a) (rad->rad (* (/ a 400) 2.pi)))
(define (grad->mil a) (mil->mil (* (/ a 400) 6400)))
 
(define (mil->deg a) (deg->deg (* (/ a 6400) 360)))
(define (mil->grad a) (grad->grad (* (/ a 6400) 400)))
(define (mil->rad a) (rad->rad (* (/ a 6400) 2.pi)))
 
(define (rad->deg a) (deg->deg (* (/ a 2.pi) 360)))
(define (rad->grad a) (grad->grad (* (/ a 2.pi) 400)))
(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 "Grad" a (grad->deg a) (grad->grad a) (grad->mil a) (grad->rad a))
    (tabulate "Mil" a (mil->deg a) (mil->grad a) (mil->mil a) (mil->rad a))
    (tabulate "Rad" a (rad->deg a) (rad->grad a) (rad->mil a) (rad->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

       gradians             normalized gradians               degrees                      mils                       radians
═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
          -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

         mils                 normalized mils                 degrees                    gradians                     radians
═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
          -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

        radians             normalized radians                degrees                    gradians                      mils
═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
          -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))} ${s(m2r(a))}')
    }
    println("\n    radians     normalized rads     degrees        gradians           mils  ")
    for a in angles {
        println('${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))
}
Fmt.print(f1, "radians", "normalized rads", "degrees", "gradians", "mils")
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

   gradians     normalized grds     degrees          mils           radians    
     -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      

     mils       normalized mils     degrees        gradians         radians    
     -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

    radians     normalized rads     degrees        gradians          mils      
     -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, "
     Degrees         Normalized      Gradians        Mils            Radians
");
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, "
     Gradians        Normalized      Degrees         Mils            Radians
");
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, "
     Mils            Normalized      Degrees         Gradians        Radians
");
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, "
     Radians         Normalized      Degrees         Gradians        Mils
");
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
     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

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