Angles (geometric), normalization and conversion: Difference between revisions

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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 $\pi$} of a turn (or ^0.5/_$\pi$ 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 $\pi$ 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)
° (a symbol)

Gradians are sometimes known or shown as:

gradian(s)
grad(s)
grade(s)
gon(s)
metric degree(s)

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

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) } </lang>

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

C

<lang 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;}</lang>

C#

<lang csharp>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;

}</lang>

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

<lang cpp>#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;

}</lang>

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. <lang lisp>(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))))</lang>

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

<lang Delphi> 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.</lang>

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.) <lang factor>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</lang>

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. <lang freebasic>#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 </lang>

Output:

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

Go

<lang 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)))
   }

}</lang>

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. <lang 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 asType(Class 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) }
}</lang>
This category class allows Angles to interoperate more easily with Numbers: <lang groovy>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) }
}</lang>
Test: <lang groovy>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</lang>

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
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: <lang>
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'
</lang> we can compose conversion sentences like <lang>
as_degree 100 Gradian
90 </lang> Presuming the following additional definitions: <lang>
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| +-------+---------------------------------------------------------------------------------------------------+ </lang>
Java
<lang 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; }
}</lang>

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
<lang javascript> </lang>
Julia
<lang 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])

</lang>

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
<lang scala>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))) }
}</lang>

Output:
See Java output
Lua
<lang 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</lang> Optionally: <lang lua>-- 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</lang>

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
<lang Mathematica>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}}]</lang>

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
<lang 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}"</lang>

Output:
Degrees Normalized Gradians Mils Radians ——————————————————————————————————————————————————————————————————————————————————— -2.0000000 -2.0000000 -2.2222222 -35.5555556 -0.0349066 -1.0000000 -1.0000000 -1.1111111 -17.7777778 -0.0174533 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 1.0000000 1.1111111 17.7777778 0.0174533 2.0000000 2.0000000 2.2222222 35.5555556 0.0349066 6.2831853 6.2831853 6.9813170 111.7010720 0.1096623 16.0000000 16.0000000 17.7777778 284.4444444 0.2792527 57.2957795 57.2957795 63.6619772 1018.5916356 1.0000000 359.0000000 359.0000000 398.8888889 6382.2222222 6.2657320 399.0000000 39.0000000 43.3333333 693.3333333 0.6806784 6399.0000000 279.0000000 310.0000000 4960.0000000 4.8694686 1000000.0000000 280.0000000 311.1111111 4977.7777778 4.8869219 Gradians Normalized Degrees Mils Radians ——————————————————————————————————————————————————————————————————————————————————— -2.0000000 -2.0000000 -1.8000000 -32.0000000 -0.0314159 -1.0000000 -1.0000000 -0.9000000 -16.0000000 -0.0157080 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 1.0000000 0.9000000 16.0000000 0.0157080 2.0000000 2.0000000 1.8000000 32.0000000 0.0314159 6.2831853 6.2831853 5.6548668 100.5309648 0.0986960 16.0000000 16.0000000 14.4000000 256.0000000 0.2513274 57.2957795 57.2957795 51.5662016 916.7324720 0.9000000 359.0000000 359.0000000 323.1000000 5744.0000000 5.6391588 399.0000000 399.0000000 359.1000000 6384.0000000 6.2674773 6399.0000000 399.0000000 359.1000000 6384.0000000 6.2674773 1000000.0000000 0.0000000 0.0000000 0.0000000 0.0000000 Mils Normalized Degrees Gradians Radians ——————————————————————————————————————————————————————————————————————————————————— -2.0000000 -2.0000000 -0.1125000 -0.1250000 -0.0019635 -1.0000000 -1.0000000 -0.0562500 -0.0625000 -0.0009817 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 1.0000000 0.0562500 0.0625000 0.0009817 2.0000000 2.0000000 0.1125000 0.1250000 0.0019635 6.2831853 6.2831853 0.3534292 0.3926991 0.0061685 16.0000000 16.0000000 0.9000000 1.0000000 0.0157080 57.2957795 57.2957795 3.2228876 3.5809862 0.0562500 359.0000000 359.0000000 20.1937500 22.4375000 0.3524474 399.0000000 399.0000000 22.4437500 24.9375000 0.3917173 6399.0000000 6399.0000000 359.9437500 399.9375000 6.2822036 1000000.0000000 1600.0000000 90.0000000 100.0000000 1.5707963 Radians Normalized Degrees Gradians Mils ——————————————————————————————————————————————————————————————————————————————————— -2.0000000 -2.0000000 -114.5915590 -127.3239545 -2037.1832716 -1.0000000 -1.0000000 -57.2957795 -63.6619772 -1018.5916358 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 1.0000000 57.2957795 63.6619772 1018.5916358 2.0000000 2.0000000 114.5915590 127.3239545 2037.1832716 6.2831853 6.2831853 359.9999996 399.9999995 6399.9999927 16.0000000 3.4336294 196.7324722 218.5916358 3497.4661726 57.2957795 0.7471117 42.8063493 47.5626103 761.0017647 359.0000000 0.8584375 49.1848452 54.6498280 874.3972479 399.0000000 3.1593256 181.0160257 201.1289175 3218.0626795 6399.0000000 2.7173573 155.6931042 172.9923380 2767.8774082 1000000.0000000 5.9256211 339.5130823 377.2367581 6035.7881302
Perl
Translation of: Raku
<lang perl>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; }
}</lang>

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
<lang python>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</lang>
Python: using tkinter
<lang python> 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.
</lang>
Racket
Translation of: Common Lisp
<lang racket>#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")))</lang>

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) <lang perl6> 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.}2{$b.}" => sub ($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.}2{.}" };my @results = %cvt{@sub_keys}».($angle);say join ' ', $angle .fmt('%10g'), $from.<name>.fmt('%-8s'), @results .fmt('%11g'); }}</lang>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 5.92562Alternately, 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.) <lang perl6>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); }}</lang>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 5.92562114REXX<lang 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 @raddo 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 @raddo 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 @raddo 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 @mildo 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 /*─────────── fmt: _= format(arg(1), 6,w); shw: _= format(arg(1),12,9); pi: pi= 3.1415926535897932384626 d2g: return d2d(arg(1)) * 10 / 9 d2m: return d2d(arg(1)) * 160 / 9 d2r: return d2d(arg(1)) * pi() / 180 g2d: return g2g(arg(1)) * 0.9 g2m: return g2g(arg(1)) * 16 g2r: return g2g(arg(1)) * pi() * 0.005 m2d: return m2m(arg(1)) * m2g: return m2m(arg(1)) / 16 m2r: return m2m(arg(1)) * pi() / 3200 r2d: return r2r(arg(1)) * 180 / pi() r2g: return r2r(arg(1)) * 200 / pi() r2m: return r2r(arg(1)) * 3200 / pi() d2d: return arg(1) // 360 g2g: return arg(1) // 400 m2m: return arg(1) // 6400 r2r: return arg(1) // (pi() * 2) /*─────────── hdr: parse arg #o #a #b #c .; /*stick a fork in it, we're all done. */ ───────────────────────────────────────────────────────────────────────────*/ L= length(_); return left(format(_/1, 6),L) /*align a #*/ L= length(_); return left(format(_/1,12),L) /* " " "*/ 433832795028841971693993751058209749445923078; return pi /*convert degrees ───► gradians. */ /*convert degrees ───► mils. */ /*convert degrees ───► radians. */ /*convert gradians ───► degrees. */ /*convert gradians ───► mils. */ /*convert gradians ───► radians. */ 9 * 0.00625 /*convert mils ───► degrees. */ /*convert mils ───► gradians. */ /*convert mils ───► radians. */ /*convert radians ───► degrees. */ /*convert radians ───► gradians. */ /*convert radians ───► mils. */ /*normalize degrees ───► a unit circle.*/ /*normalize gradians───► a unit circle.*/ /*normalize mils ───► a unit circle.*/ /*normalize radians ───► a unit circle.*/ ───────────────────────────────────────────────────────────────────────────*/ _= '═'; 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.*/</lang>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 6035.78813014892085608558RubyThis 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. <lang ruby>module AnglesBASES = {"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 endendDemonames = 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 putsend </lang>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 16Rust<lang 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 { 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>();}</lang>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 5.9256Swift<lang swift>import Foundation func normalize(_ f: Double, N: Double) -> Double {var a = fwhile 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()}</lang>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")WrenTranslation of: GoLibrary: Wren-fmt<lang ecmascript>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))}</lang>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 6035.7881302zklTranslation of: Raku<lang zkl>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 }) })</lang><lang zkl>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(" "))); }}</lang>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

@@ Line 1,561: / Line 1,561: @@
  1000000.000000   radians =   339.5131    377.2368   6035.7881      5.9256
 </pre>
+=={{header|Javascript}}==
+<lang javascript>
+</lang>
 =={{header|Julia}}==