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Angles (geometric), normalization and conversion

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

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


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

  •   degree
  •   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   of a turn   (or   0.5/   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   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 for ranging).


Positive and negative angles

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


Normalization

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

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

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


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[edit]

 
# syntax: GAWK -f ANGLES_(GEOMETRIC)_NORMALIZATION_AND_CONVERSION.AWK
# gawk starts showing discrepancies at test case number 7 when compared with C#
BEGIN {
pi = atan2(0,-1)
data_leng = split("-2,-1,0,1,2,6.2831853,16,57.2957795,359,399,6399,1000000",data_arr,",")
unit_leng = split("degree,gradian,mil,radian",unit_arr,",")
printf("%-10s %-10s %-8s %-12s %-12s %-12s %-12s test#\n","angle","normalized","unit","degrees","gradians","mils","radians")
for (a=1; a<=data_leng; a++) {
angle = data_arr[a]
arr["degree"] = normalize(angle,360)
arr["gradian"] = normalize(angle,400)
arr["mil"] = normalize(angle,6400)
arr["radian"] = normalize(angle,pi*2)
print("") # optional blank line between groupings
for (b=1; b<=unit_leng; b++) {
key1 = unit_arr[b]
printf("%-10s %-10s %-8s",angle,arr[key1],unit_arr[b])
for (c=1; c<=unit_leng; c++) {
key2 = unit_arr[c]
func_name = sprintf("%s2%s",key1,key2)
printf(" %-12s",(key1 == key2) ? arr[key2] : @func_name(arr[key2]))
}
printf(" %d\n",a)
}
}
# normalize_usage_stats()
exit(0)
}
function normalize(angle,n, a) {
a = angle
profile_arr[a][n]["+"] = 0
profile_arr[a][n]["-"] = 0
while (angle <= -n) { angle += n ; profile_arr[a][n]["+"]++ }
while (angle >= n) { angle -= n ; profile_arr[a][n]["-"]++ }
return(angle)
}
function normalize_usage_stats( a,b,c,n,total) {
print("")
PROCINFO["sorted_in"] = "@ind_num_asc"
for (a in profile_arr) {
for (b in profile_arr[a]) {
for (c in profile_arr[a][b]) {
n = profile_arr[a][b][c]
if (n == 0) { continue }
printf("%10s %10s %1s %7d\n",a,b,c,n)
total += n
}
}
}
printf("%31d total\n",total)
}
function degree2gradian(angle) { return(angle * 10 / 9) }
function degree2mil(angle) { return(angle * 160 / 9) }
function degree2radian(angle) { return(angle * pi / 180) }
function gradian2degree(angle) { return(angle * 9 / 10) }
function gradian2mil(angle) { return(angle * 16) }
function gradian2radian(angle) { return(angle * pi / 200) }
function mil2degree(angle) { return(angle * 9 / 160) }
function mil2gradian(angle) { return(angle / 16) }
function mil2radian(angle) { return(angle * pi / 3200) }
function radian2degree(angle) { return(angle * 180 / pi) }
function radian2gradian(angle) { return(angle * 200 / pi) }
function radian2mil(angle) { return(angle * 3200 / pi) }
 
Output:
angle      normalized unit     degrees      gradians     mils         radians      test#

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

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

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

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

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

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

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

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

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

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

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

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

C[edit]

#define PI 3.141592653589793
#define TWO_PI 6.283185307179586
 
double normalize2deg(double a) {
while (a < 0) a += 360;
while (a >= 360) a -= 360;
return a;
}
double normalize2grad(double a) {
while (a < 0) a += 400;
while (a >= 400) a -= 400;
return a;
}
double normalize2mil(double a) {
while (a < 0) a += 6400;
while (a >= 6400) a -= 6400;
return a;
}
double normalize2rad(double a) {
while (a < 0) a += TWO_PI;
while (a >= TWO_PI) a -= TWO_PI;
return a;
}
 
double deg2grad(double a) {return a * 10 / 9;}
double deg2mil(double a) {return a * 160 / 9;}
double deg2rad(double a) {return a * PI / 180;}
 
double grad2deg(double a) {return a * 9 / 10;}
double grad2mil(double a) {return a * 16;}
double grad2rad(double a) {return a * PI / 200;}
 
double mil2deg(double a) {return a * 9 / 160;}
double mil2grad(double a) {return a / 16;}
double mil2rad(double a) {return a * PI / 3200;}
 
double rad2deg(double a) {return a * 180 / PI;}
double rad2grad(double a) {return a * 200 / PI;}
double rad2mil(double a) {return a * 3200 / PI;}

C#[edit]

using System;
 
public static class Angles
{
public static void Main() => Print(-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 6399, 1_000_000);
 
public static void Print(params double[] angles) {
string[] names = { "Degrees", "Gradians", "Mils", "Radians" };
Func<double, double> rnd = a => Math.Round(a, 4);
Func<double, double>[] normal = { NormalizeDeg, NormalizeGrad, NormalizeMil, NormalizeRad };
 
Func<double, double>[,] convert = {
{ a => a, DegToGrad, DegToMil, DegToRad },
{ GradToDeg, a => a, GradToMil, GradToRad },
{ MilToDeg, MilToGrad, a => a, MilToRad },
{ RadToDeg, RadToGrad, RadToMil, a => a }
};
 
Console.WriteLine($@"{"Angle",-12}{"Normalized",-12}{"Unit",-12}{
"
Degrees",-12}{"Gradians",-12}{"Mils",-12}{"Radians",-12}");
 
foreach (double angle in angles) {
for (int i = 0; i < 4; i++) {
double nAngle = normal[i](angle);
 
Console.WriteLine($@"{
rnd(angle),-12}{
rnd(nAngle),-12}{
names[i],-12}{
rnd(convert[i, 0](nAngle)),-12}{
rnd(convert[i, 1](nAngle)),-12}{
rnd(convert[i, 2](nAngle)),-12}{
rnd(convert[i, 3](nAngle)),-12}"
);
}
}
}
 
public static double NormalizeDeg(double angle) => Normalize(angle, 360);
public static double NormalizeGrad(double angle) => Normalize(angle, 400);
public static double NormalizeMil(double angle) => Normalize(angle, 6400);
public static double NormalizeRad(double angle) => Normalize(angle, 2 * Math.PI);
 
private static double Normalize(double angle, double N) {
while (angle <= -N) angle += N;
while (angle >= N) angle -= N;
return angle;
}
 
public static double DegToGrad(double angle) => angle * 10 / 9;
public static double DegToMil(double angle) => angle * 160 / 9;
public static double DegToRad(double angle) => angle * Math.PI / 180;
 
public static double GradToDeg(double angle) => angle * 9 / 10;
public static double GradToMil(double angle) => angle * 16;
public static double GradToRad(double angle) => angle * Math.PI / 200;
 
public static double MilToDeg(double angle) => angle * 9 / 160;
public static double MilToGrad(double angle) => angle / 16;
public static double MilToRad(double angle) => angle * Math.PI / 3200;
 
public static double RadToDeg(double angle) => angle * 180 / Math.PI;
public static double RadToGrad(double angle) => angle * 200 / Math.PI;
public static double RadToMil(double angle) => angle * 3200 / Math.PI;
}
Output:
Angle       Normalized  Unit        Degrees     Gradians    Mils        Radians     
-2          -2          Degrees     -2          -2.2222     -35.5556    -0.0349     
-2          -2          Gradiens    -1.8        -2          -32         -0.0314     
-2          -2          Mils        -0.1125     -0.125      -2          -0.002      
-2          -2          Radians     -114.5916   -127.324    -2037.1833  -2          
-1          -1          Degrees     -1          -1.1111     -17.7778    -0.0175     
-1          -1          Gradiens    -0.9        -1          -16         -0.0157     
-1          -1          Mils        -0.0562     -0.0625     -1          -0.001      
-1          -1          Radians     -57.2958    -63.662     -1018.5916  -1          
0           0           Degrees     0           0           0           0           
0           0           Gradiens    0           0           0           0           
0           0           Mils        0           0           0           0           
0           0           Radians     0           0           0           0           
1           1           Degrees     1           1.1111      17.7778     0.0175      
1           1           Gradiens    0.9         1           16          0.0157      
1           1           Mils        0.0562      0.0625      1           0.001       
1           1           Radians     57.2958     63.662      1018.5916   1           
2           2           Degrees     2           2.2222      35.5556     0.0349      
2           2           Gradiens    1.8         2           32          0.0314      
2           2           Mils        0.1125      0.125       2           0.002       
2           2           Radians     114.5916    127.324     2037.1833   2           
6.2832      6.2832      Degrees     6.2832      6.9813      111.7011    0.1097      
6.2832      6.2832      Gradiens    5.6549      6.2832      100.531     0.0987      
6.2832      6.2832      Mils        0.3534      0.3927      6.2832      0.0062      
6.2832      6.2832      Radians     360         400         6400        6.2832      
16          16          Degrees     16          17.7778     284.4444    0.2793      
16          16          Gradiens    14.4        16          256         0.2513      
16          16          Mils        0.9         1           16          0.0157      
16          3.4336      Radians     196.7325    218.5916    3497.4662   3.4336      
57.2958     57.2958     Degrees     57.2958     63.662      1018.5916   1           
57.2958     57.2958     Gradiens    51.5662     57.2958     916.7325    0.9         
57.2958     57.2958     Mils        3.2229      3.581       57.2958     0.0562      
57.2958     0.7471      Radians     42.8063     47.5626     761.0018    0.7471      
359         359         Degrees     359         398.8889    6382.2222   6.2657      
359         359         Gradiens    323.1       359         5744        5.6392      
359         359         Mils        20.1938     22.4375     359         0.3524      
359         0.8584      Radians     49.1848     54.6498     874.3972    0.8584      
6399        279         Degrees     279         310         4960        4.8695      
6399        399         Gradiens    359.1       399         6384        6.2675      
6399        6399        Mils        359.9438    399.9375    6399        6.2822      
6399        2.7174      Radians     155.6931    172.9923    2767.8774   2.7174      
1000000     280         Degrees     280         311.1111    4977.7778   4.8869      
1000000     0           Gradiens    0           0           0           0           
1000000     1600        Mils        90          100         1600        1.5708      
1000000     5.9256      Radians     339.5132    377.2368    6035.7895   5.9256

Common Lisp[edit]

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

(defun DegToDeg (a) (rem a 360))
(defun GradToGrad (a) (rem a 400))
(defun MilToMil (a) (rem a 6400))
(defun RadToRad (a) (rem a (* 2 pi)))
 
(defun DegToGrad (a) (GradToGrad (* (/ a 360) 400)))
(defun DegToRad (a) (RadToRad (* (/ a 360) (* 2 pi))))
(defun DegToMil (a) (MilToMil (* (/ a 360) 6400)))
 
(defun GradToDeg (a) (DegToDeg (* (/ a 400) 360)))
(defun GradToRad (a) (RadToRad (* (/ a 400) (* 2 pi))))
(defun GradToMil (a) (MilToMil (* (/ a 400) 6400)))
 
(defun MilToDeg (a) (DegToDeg (* (/ a 6400) 360)))
(defun MilToGrad (a) (GradToGrad (* (/ a 6400) 400)))
(defun MilToRad (a) (RadToRad (* (/ a 6400) (* 2 pi))))
 
(defun RadToDeg (a) (DegToDeg (* (/ a (* 2 pi)) 360)))
(defun RadToGrad (a) (GradToGrad (* (/ a (* 2 pi)) 400)))
(defun RadToMil (a) (MilToMil (* (/ a (* 2 pi)) 6400)))
 
(defun angles (&rest angles)
(if (not angles) (setf angles '(-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000)))
(dolist (a angles)
(format t "UNIT [email protected] [email protected] [email protected] [email protected] [email protected]~%" "VAL*" "DEG" "GRAD" "MIL" "RAD")
(format t "Deg | ~15f | ~15f | ~15f | ~15f | ~15f~%" a (DegToDeg a) (DegToGrad a) (DegToMil a) (DegToRad a))
(format t "Grad | ~15f | ~15f | ~15f | ~15f | ~15f~%" a (GradToDeg a) (GradToGrad a) (GradToMil a) (GradToRad a))
(format t "Mil | ~15f | ~15f | ~15f | ~15f | ~15f~%" a (MilToDeg a) (MilToGrad a) (MilToMil a) (MilToRad a))
(format t "Rad | ~15f | ~15f | ~15f | ~15f | ~15f~%~%" a (RadToDeg a) (RadToGrad a) (RadToMil a) (RadToRad a))))
Output:
[CLISP]> (angles)
UNIT              VAL*               DEG              GRAD               MIL               RAD
Deg  |            -2.0 |            -2.0 |      -2.2222223 |      -35.555557 | -.0349065850399
Grad |            -2.0 |            -1.8 |            -2.0 |           -32.0 | -.0314159265359
Mil  |            -2.0 |         -0.1125 |          -0.125 |            -2.0 | -.0019634954085
Rad  |            -2.0 | -114.5915590262 | -127.3239544735 | -2037.183271576 |            -2.0

UNIT              VAL*               DEG              GRAD               MIL               RAD
Deg  |            -1.0 |            -1.0 |      -1.1111112 |      -17.777779 | -.0174532925199
Grad |            -1.0 |            -0.9 |            -1.0 |           -16.0 | -.0157079632679
Mil  |            -1.0 |        -0.05625 |         -0.0625 |            -1.0 | -.0009817477042
Rad  |            -1.0 | -57.29577951308 | -63.66197723676 | -1018.591635788 |            -1.0

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

UNIT              VAL*               DEG              GRAD               MIL               RAD
Deg  |             1.0 |             1.0 |       1.1111112 |       17.777779 | .01745329251994
Grad |             1.0 |             0.9 |             1.0 |            16.0 | .01570796326795
Mil  |             1.0 |         0.05625 |          0.0625 |             1.0 | .00098174770425
Rad  |             1.0 | 57.295779513082 | 63.661977236758 | 1018.5916357881 |             1.0

UNIT              VAL*               DEG              GRAD               MIL               RAD
Deg  |             2.0 |             2.0 |       2.2222223 |       35.555557 | .03490658503989
Grad |             2.0 |             1.8 |             2.0 |            32.0 | 0.0314159265359
Mil  |             2.0 |          0.1125 |           0.125 |             2.0 | .00196349540849
Rad  |             2.0 | 114.59155902616 | 127.32395447352 | 2037.1832715763 |             2.0

UNIT              VAL*               DEG              GRAD               MIL               RAD
Deg  |       6.2831855 |       6.2831855 |        6.981317 |       111.70107 |      0.10966227
Grad |       6.2831855 |        5.654867 |       6.2831855 |       100.53097 |     0.098696046
Mil  |       6.2831855 |       0.3534292 |       0.3926991 |       6.2831855 |     0.006168503
Rad  |       6.2831855 |             0.0 |             0.0 |             0.0 |             0.0

UNIT              VAL*               DEG              GRAD               MIL               RAD
Deg  |            16.0 |            16.0 |       17.777779 |       284.44446 | .27925268031909
Grad |            16.0 |            14.4 |            16.0 |           256.0 | .25132741228718
Mil  |            16.0 |             0.9 |             1.0 |            16.0 | .01570796326795
Rad  |            16.0 | 196.73247220932 | 218.59163578813 | 3497.4661726101 | 3.4336293856408

UNIT              VAL*               DEG              GRAD               MIL               RAD
Deg  |        57.29578 |       57.295784 |        63.66198 |       1018.5917 |      0.99999994
Grad |        57.29578 |       51.566204 |        57.29578 |        916.7325 |      0.90000004
Mil  |        57.29578 |       3.2228878 |       3.5809863 |        57.29578 |     0.056250002
Rad  |        57.29578 |        42.80651 |        47.56279 |       761.00464 |      0.74711454

UNIT              VAL*               DEG              GRAD               MIL               RAD
Deg  |           359.0 |           359.0 |        398.8889 |        6382.222 | 6.2657320146596
Grad |           359.0 |           323.1 |           359.0 |          5744.0 | 5.6391588131937
Mil  |           359.0 |        20.19375 |         22.4375 |           359.0 | 0.3524474258246
Rad  |           359.0 | 49.184845196553 |  54.64982799617 | 874.39724793872 | .85843749076357

UNIT              VAL*               DEG              GRAD               MIL               RAD
Deg  |           399.0 |            39.0 |       43.333332 |        693.3333 | .68067840827779
Grad |           399.0 |           359.1 |           399.0 |          6384.0 | 6.2674773439116
Mil  |           399.0 |        22.44375 |         24.9375 |           399.0 | .39171733399448
Rad  |           399.0 | 181.01602571985 |  201.1289174665 | 3218.0626794639 | 3.1593256476861

UNIT              VAL*               DEG              GRAD               MIL               RAD
Deg  |          6399.0 |           279.0 |           310.0 |          4960.0 | 4.8694686130642
Grad |          6399.0 |           359.1 |           399.0 |          6384.0 | 6.2674773439116
Mil  |          6399.0 |       359.94376 |        399.9375 |          6399.0 | 6.2822035594753
Rad  |          6399.0 | 155.69310421377 |  172.9923380153 | 2767.8774082448 |  2.717357291181

UNIT              VAL*               DEG              GRAD               MIL               RAD
Deg  |       1000000.0 |           280.0 |        311.1111 |        4977.778 | 4.8869219055841
Grad |       1000000.0 |             0.0 |             0.0 |             0.0 |             0.0
Mil  |       1000000.0 |            90.0 |           100.0 |          1600.0 | 1.5707963267949
Rad  |       1000000.0 | 339.51308232088 | 377.23675813431 | 6035.7881301489 | 5.9256211400939

Factor[edit]

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

USING: accessors combinators formatting inverse kernel math
math.constants quotations qw sequences units.si ;
IN: rosetta-code.angles
 
ALIAS: degrees arc-deg
: gradiens ( n -- d ) 9/10 * degrees ;
: mils ( n -- d ) 9/160 * degrees ;
: normalize ( d -- d' ) [ 2 pi * mod ] change-value ;
CONSTANT: units { degrees gradiens mils radians }
 
: .row ( angle unit -- )
2dup "%-12u%-12s" printf ( x -- x ) execute-effect
normalize units [ 1quotation [undo] call( x -- x ) ] with
map "%-12.4f%-12.4f%-12.4f%-12.4f\n" vprintf ;
 
: .header ( -- )
qw{ angle unit } units append
"%-12s%-12s%-12s%-12s%-12s%-12s\n" vprintf ;
 
: angles ( -- )
.header
{ -2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000 }
units [ .row ] cartesian-each ;
 
MAIN: angles
Output:
angle       unit        degrees     gradiens    mils        radians     
-2          degrees     -2.0000     -2.2222     -35.5556    -0.0349     
-2          gradiens    -1.8000     -2.0000     -32.0000    -0.0314     
-2          mils        -0.1125     -0.1250     -2.0000     -0.0020     
-2          radians     -114.5916   -127.3240   -2037.1833  -2.0000     
-1          degrees     -1.0000     -1.1111     -17.7778    -0.0175     
-1          gradiens    -0.9000     -1.0000     -16.0000    -0.0157     
-1          mils        -0.0563     -0.0625     -1.0000     -0.0010     
-1          radians     -57.2958    -63.6620    -1018.5916  -1.0000     
0           degrees     0.0000      0.0000      0.0000      0.0000      
0           gradiens    0.0000      0.0000      0.0000      0.0000      
0           mils        0.0000      0.0000      0.0000      0.0000      
0           radians     0.0000      0.0000      0.0000      0.0000      
1           degrees     1.0000      1.1111      17.7778     0.0175      
1           gradiens    0.9000      1.0000      16.0000     0.0157      
1           mils        0.0563      0.0625      1.0000      0.0010      
1           radians     57.2958     63.6620     1018.5916   1.0000      
2           degrees     2.0000      2.2222      35.5556     0.0349      
2           gradiens    1.8000      2.0000      32.0000     0.0314      
2           mils        0.1125      0.1250      2.0000      0.0020      
2           radians     114.5916    127.3240    2037.1833   2.0000      
6.2831853   degrees     6.2832      6.9813      111.7011    0.1097      
6.2831853   gradiens    5.6549      6.2832      100.5310    0.0987      
6.2831853   mils        0.3534      0.3927      6.2832      0.0062      
6.2831853   radians     360.0000    400.0000    6400.0000   6.2832      
16          degrees     16.0000     17.7778     284.4444    0.2793      
16          gradiens    14.4000     16.0000     256.0000    0.2513      
16          mils        0.9000      1.0000      16.0000     0.0157      
16          radians     196.7325    218.5916    3497.4662   3.4336      
57.2957795  degrees     57.2958     63.6620     1018.5916   1.0000      
57.2957795  gradiens    51.5662     57.2958     916.7325    0.9000      
57.2957795  mils        3.2229      3.5810      57.2958     0.0562      
57.2957795  radians     42.8063     47.5626     761.0018    0.7471      
359         degrees     359.0000    398.8889    6382.2222   6.2657      
359         gradiens    323.1000    359.0000    5744.0000   5.6392      
359         mils        20.1938     22.4375     359.0000    0.3524      
359         radians     49.1848     54.6498     874.3972    0.8584      
399         degrees     39.0000     43.3333     693.3333    0.6807      
399         gradiens    359.1000    399.0000    6384.0000   6.2675      
399         mils        22.4438     24.9375     399.0000    0.3917      
399         radians     181.0160    201.1289    3218.0627   3.1593      
6399        degrees     279.0000    310.0000    4960.0000   4.8695      
6399        gradiens    359.1000    399.0000    6384.0000   6.2675      
6399        mils        359.9438    399.9375    6399.0000   6.2822      
6399        radians     155.6931    172.9923    2767.8774   2.7174      
1000000     degrees     280.0000    311.1111    4977.7778   4.8869      
1000000     gradiens    0.0000      0.0000      0.0000      0.0000      
1000000     mils        90.0000     100.0000    1600.0000   1.5708      
1000000     radians     339.5131    377.2368    6035.7881   5.9256

Go[edit]

package main
 
import (
"fmt"
"math"
"strconv"
"strings"
)
 
func d2d(d float64) float64 { return math.Mod(d, 360) }
 
func g2g(g float64) float64 { return math.Mod(g, 400) }
 
func m2m(m float64) float64 { return math.Mod(m, 6400) }
 
func r2r(r float64) float64 { return math.Mod(r, 2*math.Pi) }
 
func d2g(d float64) float64 { return d2d(d) * 400 / 360 }
 
func d2m(d float64) float64 { return d2d(d) * 6400 / 360 }
 
func d2r(d float64) float64 { return d2d(d) * math.Pi / 180 }
 
func g2d(g float64) float64 { return g2g(g) * 360 / 400 }
 
func g2m(g float64) float64 { return g2g(g) * 6400 / 400 }
 
func g2r(g float64) float64 { return g2g(g) * math.Pi / 200 }
 
func m2d(m float64) float64 { return m2m(m) * 360 / 6400 }
 
func m2g(m float64) float64 { return m2m(m) * 400 / 6400 }
 
func m2r(m float64) float64 { return m2m(m) * math.Pi / 3200 }
 
func r2d(r float64) float64 { return r2r(r) * 180 / math.Pi }
 
func r2g(r float64) float64 { return r2r(r) * 200 / math.Pi }
 
func r2m(r float64) float64 { return r2r(r) * 3200 / math.Pi }
 
// Aligns number to decimal point assuming 7 characters before and after.
func s(f float64) string {
wf := strings.Split(strconv.FormatFloat(f, 'g', 15, 64), ".")
if len(wf) == 1 {
return fmt.Sprintf("%7s ", wf[0])
}
le := len(wf[1])
if le > 7 {
le = 7
}
return fmt.Sprintf("%7s.%-7s", wf[0], wf[1][:le])
}
 
func main() {
angles := []float64{-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795,
359, 399, 6399, 1000000}
ft := "%s %s %s %s %s\n"
fmt.Printf(ft, " degrees ", "normalized degs", " gradians ", " mils ", " radians")
for _, a := range angles {
fmt.Printf(ft, s(a), s(d2d(a)), s(d2g(a)), s(d2m(a)), s(d2r(a)))
}
fmt.Printf(ft, "\n gradians ", "normalized grds", " degrees ", " mils ", " radians")
for _, a := range angles {
fmt.Printf(ft, s(a), s(g2g(a)), s(g2d(a)), s(g2m(a)), s(g2r(a)))
}
fmt.Printf(ft, "\n mils ", "normalized mils", " degrees ", " gradians ", " radians")
for _, a := range angles {
fmt.Printf(ft, s(a), s(m2m(a)), s(m2d(a)), s(m2g(a)), s(m2r(a)))
}
fmt.Printf(ft, "\n radians ", "normalized rads", " degrees ", " gradians ", " mils ")
for _, a := range angles {
fmt.Printf(ft, s(a), s(r2r(a)), s(r2d(a)), s(r2g(a)), s(r2m(a)))
}
}
Output:
    degrees     normalized degs     gradians         mils            radians
     -2              -2              -2.2222222     -35.5555555      -0.0349065
     -1              -1              -1.1111111     -17.7777777      -0.0174532
      0               0               0               0               0        
      1               1               1.1111111      17.7777777       0.0174532
      2               2               2.2222222      35.5555555       0.0349065
      6.2831853       6.2831853       6.981317      111.701072        0.1096622
     16              16              17.7777777     284.4444444       0.2792526
     57.2957795      57.2957795      63.6619772    1018.5916355       0.9999999
    359             359             398.8888888    6382.2222222       6.2657320
    399              39              43.3333333     693.3333333       0.6806784
   6399             279             310            4960               4.8694686
1000000             280             311.1111111    4977.7777777       4.8869219

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

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

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

Groovy[edit]

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

import java.lang.reflect.Constructor
 
abstract class Angle implements Comparable<? extends Angle> {
double value
 
Angle(double value = 0) { this.value = normalize(value) }
 
abstract Number unitCircle()
abstract String unitName()
 
Number normalize(double n) { n % this.unitCircle() }
 
def <B extends Angle> B asType(Class<B> bClass){
if (bClass == this.class) return this
bClass.getConstructor(Number.class).newInstance(0).tap {
value = this.value * unitCircle() / this.unitCircle()
}
}
 
String toString() {
"${String.format('%14.8f',value)}${this.unitName()}"
}
 
int hashCode() {
value.hashCode() + 17 * unit().hashCode()
}
 
int compareTo(Angle that) {
this.value * that.unitCircle() <=> that.value * this.unitCircle()
}
 
boolean equals(that) {
this.is(that) ? true
 : that instanceof Angle ? (this <=> that) == 0
 : that instanceof Number ? this.value == this.normalize(that)
 : super.equals(that)
}
}
 
class Degrees extends Angle {
static final int UNIT_CIRCLE = 360
Number unitCircle() { UNIT_CIRCLE }
static final String UNIT = "º "
String unitName() { UNIT }
Degrees(Number value = 0) { super(value) }
}
 
class Gradians extends Angle {
static final int UNIT_CIRCLE = 400
Number unitCircle() { UNIT_CIRCLE }
static final String UNIT = " grad"
String unitName() { UNIT }
Gradians(Number value = 0) { super(value) }
}
 
class Mils extends Angle {
static final int UNIT_CIRCLE = 6400
Number unitCircle() { UNIT_CIRCLE }
static final String UNIT = " mil "
String unitName() { UNIT }
Mils(Number value = 0) { super(value) }
}
 
class Radians extends Angle {
static final double UNIT_CIRCLE = Math.PI*2
Number unitCircle() { UNIT_CIRCLE }
static final String UNIT = " rad "
String unitName() { UNIT }
Radians(Number value = 0) { super(value) }
}

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

class AngleCategory {
static Degrees getDeg(Number n) { new Degrees(n) }
static Gradians getGrad(Number n) { new Gradians(n) }
static Mils getMil(Number n) { new Mils(n) }
static Radians getRad(Number n) { new Radians(n) }
}

Test:

Number.metaClass.mixin AngleCategory
 
[ -2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000 ].each { rawAngle ->
println "\n raw angle normalized ------------------------------ conversions ------------------------------"
[rawAngle.deg, rawAngle.grad, rawAngle.mil, rawAngle.rad].each { angle ->
printf("%10s %20s %s %s %s %s\n", rawAngle.toString(), angle,
angle as Degrees, angle as Gradians,
angle as Mils, angle as Radians
)
}
}
 
// some additional checks implied in the task statement
// but not requested for solution demonstration
assert 360.deg == 0.deg
assert 90.deg == 100.grad
assert Math.PI.rad == 3200.mil
Output:
 raw angle      normalized       ------------------------------   conversions   ------------------------------
        -2     -2.00000000º        -2.00000000º        -2.22222222 grad   -35.55555556 mil     -0.03490659 rad 
        -2     -2.00000000 grad    -1.80000000º        -2.00000000 grad   -32.00000000 mil     -0.03141593 rad 
        -2     -2.00000000 mil     -0.11250000º        -0.12500000 grad    -2.00000000 mil     -0.00196350 rad 
        -2     -2.00000000 rad   -114.59155903º      -127.32395447 grad -2037.18327158 mil     -2.00000000 rad 

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

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

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

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

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

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

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

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

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

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

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

J[edit]

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

 
TAU =: 2p1 NB. tauday.com
 
normalize =: * * 1 | | NB. signum times the fractional part of absolute value
 
TurnTo=: &*
 
as_turn =: 1 TurnTo
as_degree =: 360 TurnTo
as_gradian =: 400 TurnTo
as_mil =: 6400 TurnTo
as_radian =: TAU TurnTo
 
Turn =: adverb def 'normalize as_turn inv m'
Degree =: adverb def 'normalize as_degree inv m'
Gradian =: adverb def 'normalize as_gradian inv m'
Mil =: adverb def 'normalize as_mil inv m'
Radian =: adverb def 'normalize as_radian inv m'
 

we can compose conversion sentences like

 
as_degree 100 Gradian
90
 

Presuming the following additional definitions:

 
NAMES =: > turn`degree`gradian`mil`radian
ALL =: as_turn`as_degree`as_gradian`as_mil`as_radian
to_all=: NAMES ; ALL`:0
 
VALUES =: _&".'-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000'
 
 
to_all VALUES Turn
+-------+------------------------------------+
|turn |0 0 0 0 0 0.283185 0 0.29578 0 0 0 0|
|degree |0 0 0 0 0 101.947 0 106.481 0 0 0 0|
|gradian|0 0 0 0 0 113.274 0 118.312 0 0 0 0|
|mil |0 0 0 0 0 1812.39 0 1892.99 0 0 0 0|
|radian |0 0 0 0 0 1.77931 0 1.85844 0 0 0 0|
+-------+------------------------------------+
 
to_all VALUES Degree
+-------+---------------------------------------------------------------------------------------------------------------+
|turn |_0.00555556 _0.00277778 0 0.00277778 0.00555556 0.0174533 0.0444444 0.159155 0.997222 0.108333 0.775 0.777778|
|degree | _2 _1 0 1 2 6.28319 16 57.2958 359 39 279 280|
|gradian| _2.22222 _1.11111 0 1.11111 2.22222 6.98132 17.7778 63.662 398.889 43.3333 310 311.111|
|mil | _35.5556 _17.7778 0 17.7778 35.5556 111.701 284.444 1018.59 6382.22 693.333 4960 4977.78|
|radian | _0.0349066 _0.0174533 0 0.0174533 0.0349066 0.109662 0.279253 1 6.26573 0.680678 4.86947 4.88692|
+-------+---------------------------------------------------------------------------------------------------------------+
 
to_all VALUES Gradian
+-------+----------------------------------------------------------------------------------------------+
|turn | _0.005 _0.0025 0 0.0025 0.005 0.015708 0.04 0.143239 0.8975 0.9975 0.9975 0|
|degree | _1.8 _0.9 0 0.9 1.8 5.65487 14.4 51.5662 323.1 359.1 359.1 0|
|gradian| _2 _1 0 1 2 6.28319 16 57.2958 359 399 399 0|
|mil | _32 _16 0 16 32 100.531 256 916.732 5744 6384 6384 0|
|radian |_0.0314159 _0.015708 0 0.015708 0.0314159 0.098696 0.251327 0.9 5.63916 6.26748 6.26748 0|
+-------+----------------------------------------------------------------------------------------------+
 
to_all VALUES Mil
+-------+-------------------------------------------------------------------------------------------------------------------+
|turn |_0.0003125 _0.00015625 0 0.00015625 0.0003125 0.000981748 0.0025 0.00895247 0.0560937 0.0623438 0.999844 0.25|
|degree | _0.1125 _0.05625 0 0.05625 0.1125 0.353429 0.9 3.22289 20.1937 22.4438 359.944 90|
|gradian| _0.125 _0.0625 0 0.0625 0.125 0.392699 1 3.58099 22.4375 24.9375 399.938 100|
|mil | _2 _1 0 1 2 6.28319 16 57.2958 359 399 6399 1600|
|radian |_0.0019635 _0.000981748 0 0.000981748 0.0019635 0.0061685 0.015708 0.05625 0.352447 0.391717 6.2822 1.5708|
+-------+-------------------------------------------------------------------------------------------------------------------+
 
to_all VALUES Radian
+-------+---------------------------------------------------------------------------------------------------+
|turn |_0.31831 _0.159155 0 0.159155 0.31831 1 0.546479 0.118907 0.136625 0.502822 0.432481 0.943092|
|degree |_114.592 _57.2958 0 57.2958 114.592 360 196.732 42.8063 49.1848 181.016 155.693 339.513|
|gradian|_127.324 _63.662 0 63.662 127.324 400 218.592 47.5626 54.6498 201.129 172.992 377.237|
|mil |_2037.18 _1018.59 0 1018.59 2037.18 6400 3497.47 761.002 874.397 3218.06 2767.88 6035.79|
|radian | _2 _1 0 1 2 6.28319 3.43363 0.747112 0.858437 3.15933 2.71736 5.92562|
+-------+---------------------------------------------------------------------------------------------------+
 

Java[edit]

 
import java.text.DecimalFormat;
 
// Title: Angles (geometric), normalization and conversion
 
public class AnglesNormalizationAndConversion {
 
public static void main(String[] args) {
DecimalFormat formatAngle = new DecimalFormat("######0.000000");
DecimalFormat formatConv = new DecimalFormat("###0.0000");
System.out.printf(" degrees gradiens mils radians%n");
for ( double angle : new double[] {-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000} ) {
for ( String units : new String[] {"degrees", "gradiens", "mils", "radians"}) {
double d = 0, g = 0, m = 0, r = 0;
switch (units) {
case "degrees":
d = d2d(angle);
g = d2g(d);
m = d2m(d);
r = d2r(d);
break;
case "gradiens":
g = g2g(angle);
d = g2d(g);
m = g2m(g);
r = g2r(g);
break;
case "mils":
m = m2m(angle);
d = m2d(m);
g = m2g(m);
r = m2r(m);
break;
case "radians":
r = r2r(angle);
d = r2d(r);
g = r2g(r);
m = r2m(r);
break;
}
System.out.printf("%15s  %8s = %10s  %10s  %10s  %10s%n", formatAngle.format(angle), units, formatConv.format(d), formatConv.format(g), formatConv.format(m), formatConv.format(r));
}
}
}
 
private static final double DEGREE = 360D;
private static final double GRADIAN = 400D;
private static final double MIL = 6400D;
private static final double RADIAN = (2 * Math.PI);
 
private static double d2d(double a) {
return a % DEGREE;
}
private static double d2g(double a) {
return a * (GRADIAN / DEGREE);
}
private static double d2m(double a) {
return a * (MIL / DEGREE);
}
private static double d2r(double a) {
return a * (RADIAN / 360);
}
 
private static double g2d(double a) {
return a * (DEGREE / GRADIAN);
}
private static double g2g(double a) {
return a % GRADIAN;
}
private static double g2m(double a) {
return a * (MIL / GRADIAN);
}
private static double g2r(double a) {
return a * (RADIAN / GRADIAN);
}
 
private static double m2d(double a) {
return a * (DEGREE / MIL);
}
private static double m2g(double a) {
return a * (GRADIAN / MIL);
}
private static double m2m(double a) {
return a % MIL;
}
private static double m2r(double a) {
return a * (RADIAN / MIL);
}
 
private static double r2d(double a) {
return a * (DEGREE / RADIAN);
}
private static double r2g(double a) {
return a * (GRADIAN / RADIAN);
}
private static double r2m(double a) {
return a * (MIL / RADIAN);
}
private static double r2r(double a) {
return a % RADIAN;
}
 
}
 
Output:
                               degrees    gradiens        mils     radians
      -2.000000   degrees =    -2.0000     -2.2222    -35.5556     -0.0349
      -2.000000  gradiens =    -1.8000     -2.0000    -32.0000     -0.0314
      -2.000000      mils =    -0.1125     -0.1250     -2.0000     -0.0020
      -2.000000   radians =  -114.5916   -127.3240  -2037.1833     -2.0000
      -1.000000   degrees =    -1.0000     -1.1111    -17.7778     -0.0175
      -1.000000  gradiens =    -0.9000     -1.0000    -16.0000     -0.0157
      -1.000000      mils =    -0.0563     -0.0625     -1.0000     -0.0010
      -1.000000   radians =   -57.2958    -63.6620  -1018.5916     -1.0000
       0.000000   degrees =     0.0000      0.0000      0.0000      0.0000
       0.000000  gradiens =     0.0000      0.0000      0.0000      0.0000
       0.000000      mils =     0.0000      0.0000      0.0000      0.0000
       0.000000   radians =     0.0000      0.0000      0.0000      0.0000
       1.000000   degrees =     1.0000      1.1111     17.7778      0.0175
       1.000000  gradiens =     0.9000      1.0000     16.0000      0.0157
       1.000000      mils =     0.0563      0.0625      1.0000      0.0010
       1.000000   radians =    57.2958     63.6620   1018.5916      1.0000
       2.000000   degrees =     2.0000      2.2222     35.5556      0.0349
       2.000000  gradiens =     1.8000      2.0000     32.0000      0.0314
       2.000000      mils =     0.1125      0.1250      2.0000      0.0020
       2.000000   radians =   114.5916    127.3240   2037.1833      2.0000
       6.283185   degrees =     6.2832      6.9813    111.7011      0.1097
       6.283185  gradiens =     5.6549      6.2832    100.5310      0.0987
       6.283185      mils =     0.3534      0.3927      6.2832      0.0062
       6.283185   radians =   360.0000    400.0000   6400.0000      6.2832
      16.000000   degrees =    16.0000     17.7778    284.4444      0.2793
      16.000000  gradiens =    14.4000     16.0000    256.0000      0.2513
      16.000000      mils =     0.9000      1.0000     16.0000      0.0157
      16.000000   radians =   196.7325    218.5916   3497.4662      3.4336
      57.295780   degrees =    57.2958     63.6620   1018.5916      1.0000
      57.295780  gradiens =    51.5662     57.2958    916.7325      0.9000
      57.295780      mils =     3.2229      3.5810     57.2958      0.0562
      57.295780   radians =    42.8063     47.5626    761.0018      0.7471
     359.000000   degrees =   359.0000    398.8889   6382.2222      6.2657
     359.000000  gradiens =   323.1000    359.0000   5744.0000      5.6392
     359.000000      mils =    20.1938     22.4375    359.0000      0.3524
     359.000000   radians =    49.1848     54.6498    874.3972      0.8584
     399.000000   degrees =    39.0000     43.3333    693.3333      0.6807
     399.000000  gradiens =   359.1000    399.0000   6384.0000      6.2675
     399.000000      mils =    22.4438     24.9375    399.0000      0.3917
     399.000000   radians =   181.0160    201.1289   3218.0627      3.1593
    6399.000000   degrees =   279.0000    310.0000   4960.0000      4.8695
    6399.000000  gradiens =   359.1000    399.0000   6384.0000      6.2675
    6399.000000      mils =   359.9438    399.9375   6399.0000      6.2822
    6399.000000   radians =   155.6931    172.9923   2767.8774      2.7174
 1000000.000000   degrees =   280.0000    311.1111   4977.7778      4.8869
 1000000.000000  gradiens =     0.0000      0.0000      0.0000      0.0000
 1000000.000000      mils =    90.0000    100.0000   1600.0000      1.5708
 1000000.000000   radians =   339.5131    377.2368   6035.7881      5.9256

Julia[edit]

using Formatting
 
d2d(d) = d % 360
g2g(g) = g % 400
m2m(m) = m % 6400
r2r(r) = r % 2π
d2g(d) = d2d(d) * 10 / 9
d2m(d) = d2d(d) * 160 / 9
d2r(d) = d2d(d) * π / 180
g2d(g) = g2g(g) * 9 / 10
g2m(g) = g2g(g) * 16
g2r(g) = g2g(g) * π / 200
m2d(m) = m2m(m) * 9 / 160
m2g(m) = m2m(m) / 16
m2r(m) = m2m(m) * π / 3200
r2d(r) = r2r(r) * 180 / π
r2g(r) = r2r(r) * 200 / π
r2m(r) = r2r(r) * 3200 / π
 
fmt(x::Real, width=16) = Int(round(x)) == x ? rpad(Int(x), width) :
rpad(format(x, precision=7), width)
fmt(x::String, width=16) = rpad(x, width)
 
const t2u = Dict("degrees" => [d2d, d2g, d2m, d2r],
"gradians" => [g2d, g2g, g2m, g2r], "mils" => [m2d, m2g, m2m, m2r],
"radians" => [r2d, r2g, r2m, r2r])
 
function testconversions(arr)
println("Number Units Degrees Gradians Mils Radians")
for num in arr, units in ["degrees", "gradians", "mils", "radians"]
print(fmt(num), fmt(units))
for f in t2u[units]
print(fmt(f(num)))
end
println()
end
end
 
testconversions([-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000])
 
Output:
Number          Units           Degrees          Gradians        Mils            Radians
-2              degrees         -2              -2.2222222      -35.5555556     -0.0349066
-2              gradians        -1.8000000      -2              -32             -0.0314159
-2              mils            -0.1125000      -0.1250000      -2              -0.0019635
-2              radians         -114.5915590    -127.3239545    -2037.1832716   -2
-1              degrees         -1              -1.1111111      -17.7777778     -0.0174533
-1              gradians        -0.9000000      -1              -16             -0.0157080
-1              mils            -0.0562500      -0.0625000      -1              -0.0009817
-1              radians         -57.2957795     -63.6619772     -1018.5916358   -1
0               degrees         0               0               0               0
0               gradians        0               0               0               0
0               mils            0               0               0               0
0               radians         0               0               0               0
1               degrees         1               1.1111111       17.7777778      0.0174533
1               gradians        0.9000000       1               16              0.0157080
1               mils            0.0562500       0.0625000       1               0.0009817
1               radians         57.2957795      63.6619772      1018.5916358    1
2               degrees         2               2.2222222       35.5555556      0.0349066
2               gradians        1.8000000       2               32              0.0314159
2               mils            0.1125000       0.1250000       2               0.0019635
2               radians         114.5915590     127.3239545     2037.1832716    2
6.2831853       degrees         6.2831853       6.9813170       111.7010720     0.1096623
6.2831853       gradians        5.6548668       6.2831853       100.5309648     0.0986960
6.2831853       mils            0.3534292       0.3926991       6.2831853       0.0061685
6.2831853       radians         359.9999996     399.9999995     6399.9999927    6.2831853
16              degrees         16              17.7777778      284.4444444     0.2792527
16              gradians        14.4000000      16              256             0.2513274
16              mils            0.9000000       1               16              0.0157080
16              radians         196.7324722     218.5916358     3497.4661726    3.4336294
57.2957795      degrees         57.2957795      63.6619772      1018.5916356    1.0000000
57.2957795      gradians        51.5662016      57.2957795      916.7324720     0.9000000
57.2957795      mils            3.2228876       3.5809862       57.2957795      0.0562500
57.2957795      radians         42.8063493      47.5626103      761.0017647     0.7471117
359             degrees         359             398.8888889     6382.2222222    6.2657320
359             gradians        323.1000000     359             5744            5.6391588
359             mils            20.1937500      22.4375000      359             0.3524474
359             radians         49.1848452      54.6498280      874.3972479     0.8584375
399             degrees         39              43.3333333      693.3333333     0.6806784
399             gradians        359.1000000     399             6384            6.2674773
399             mils            22.4437500      24.9375000      399             0.3917173
399             radians         181.0160257     201.1289175     3218.0626795    3.1593256
6399            degrees         279             310             4960            4.8694686
6399            gradians        359.1000000     399             6384            6.2674773
6399            mils            359.9437500     399.9375000     6399            6.2822036
6399            radians         155.6931042     172.9923380     2767.8774082    2.7173573
1000000         degrees         280             311.1111111     4977.7777778    4.8869219
1000000         gradians        0               0               0               0
1000000         mils            90              100             1600            1.5707963
1000000         radians         339.5130823     377.2367581     6035.7881302    5.9256211

Perl[edit]

Translation of: Raku
use strict;
use warnings;
use feature 'say';
use POSIX 'fmod';
 
my $tau = 2 * 4*atan2(1, 1);
my @units = (
{ code => 'd', name => 'degrees' , number => 360 },
{ code => 'g', name => 'gradians', number => 400 },
{ code => 'm', name => 'mills' , number => 6400 },
{ code => 'r', name => 'radians' , number => $tau },
);
 
my %cvt;
for my $a (@units) {
for my $b (@units) {
$cvt{ "${$a}{code}2${$b}{code}" } = sub {
my($angle) = shift;
my $norm = fmod($angle,${$a}{number}); # built-in '%' returns only integers
$norm -= ${$a}{number} if $angle < 0;
$norm * ${$b}{number} / ${$a}{number}
}
}
}
 
printf '%s'. '%12s'x4 . "\n", ' Angle Unit ', <Degrees Gradians Mills Radians>;
for my $angle (-2, -1, 0, 1, 2, $tau, 16, 360/$tau, 360-1, 400-1, 6400-1, 1_000_000) {
print "\n";
for my $from (@units) {
my @sub_keys = map { "${$from}{code}2${$_}{code}" } @units;
my @results = map { &{$cvt{$_}}($angle) } @sub_keys;
printf '%10g %-8s' . '%12g'x4 . "\n", $angle, ${$from}{name}, @results;
}
}
Output:
     Angle Unit         Degrees    Gradians       Mills     Radians

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

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

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

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

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

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

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

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

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

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

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

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

Phix[edit]

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[edit]

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

Raku[edit]

(formerly Perl 6)

 
my @units =
{ code => 'd', name => 'degrees' , number => 360 },
{ code => 'g', name => 'gradians', number => 400 },
{ code => 'm', name => 'mills' , number => 6400 },
{ code => 'r', name => 'radians' , number => tau },
;
 
my Code %cvt = (@units X @units).map: -> ($a, $b) {
"{$a.<code>}2{$b.<code>}" => sub ($angle) {
my $norm = $angle % $a.<number>
- ( $a.<number> if $angle < 0 );
$norm * $b.<number> / $a.<number>
}
}
 
say ' Angle Unit ', @units».<name>».tc.fmt('%11s');
 
for -2, -1, 0, 1, 2, tau, 16, 360/tau, 360-1, 400-1, 6400-1, 1_000_000 -> $angle {
say '';
for @units -> $from {
my @sub_keys = @units.map: { "{$from.<code>}2{.<code>}" };
 
my @results = %cvt{@sub_keys}».($angle);
 
say join ' ', $angle .fmt('%10g'),
$from.<name>.fmt('%-8s'),
@results .fmt('%11g');
}
}
Output:
     Angle Unit         Degrees    Gradians       Mills     Radians

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

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

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

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

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

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

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

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

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

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

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

   1000000 degrees          280     311.111     4977.78     4.88692
   1000000 gradians           0           0           0           0
   1000000 mills             90         100        1600      1.5708
   1000000 radians      339.513     377.237     6035.79     5.92562

Alternately, implemented as a series of postfix operators:

(Much of the complexity is due to the requirement that negative angles must normalize to a negative number.)

sub postfix:<t>( $t ) { my $a = $t % 1 * τ;           $t >=0 ?? $a !! $a - τ }
sub postfix:<d>( $d ) { my $a = $d % 360 * τ / 360; $d >=0 ?? $a !! $a - τ }
sub postfix:<g>( $g ) { my $a = $g % 400 * τ / 400; $g >=0 ?? $a !! $a - τ }
sub postfix:<m>( $m ) { my $a = $m % 6400 * τ / 6400; $m >=0 ?? $a !! $a - τ }
sub postfix:<r>( $r ) { my $a = $r % τ; $r >=0 ?? $a !! $a - τ }
 
sub postfix:«->($angle) { my $a = $angle / τ; ($angle < 0 and $a == -1) ?? -0 !! $a }
sub postfix:«->($angle) { my $a = $angle / τ * 360; ($angle < 0 and $a == -360) ?? -0 !! $a }
sub postfix:«->($angle) { my $a = $angle / τ * 400; ($angle < 0 and $a == -400) ?? -0 !! $a }
sub postfix:«->($angle) { my $a = $angle / τ * 6400; ($angle < 0 and $a == -6400) ?? -0 !! $a }
sub postfix:«->($angle) { my $a = $angle; ($angle < 0 and $a == -τ) ?? -0 !! $a }
 
for <-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000> -> $a {
say '';
say ' Quantity Unit ', <turns degrees gradians mils radians>.fmt('%15s');
for 'turns', &postfix:«t», 'degrees', &postfix:«d», 'gradians', &postfix:«g»,
'mils', &postfix:«m», 'radians', &postfix:«r»
-> $unit, &f {
printf "%10s %-10s %15s %15s %15s %15s %15s\n", $a, $unit,
|($a.&f->t, $a.&f->d, $a.&f->g, $a.&f->m, $a.&f->r)».round(.00000001);
}
}
 Quantity  Unit                turns         degrees        gradians            mils         radians
        -2 turns                    0               0               0               0               0
        -2 degrees        -0.00555556              -2     -2.22222222    -35.55555556     -0.03490659
        -2 gradians            -0.005            -1.8              -2             -32     -0.03141593
        -2 mils             -0.000313         -0.1125          -0.125              -2      -0.0019635
        -2 radians        -0.31830989   -114.59155903   -127.32395447  -2037.18327158              -2

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

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

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

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

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

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

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

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

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

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

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

REXX[edit]

/*REXX pgm normalizes an angle (in a scale), or converts angles from a scale to another.*/
numeric digits length( pi() ) - length(.) /*use the "length" of pi for precision.*/
parse arg x /*obtain optional arguments from the CL*/
if x='' | x="," then x= '-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000'
w= 20; w7= w+7 /*W: # dec digits past the dec. point.*/
@deg = 'degrees'; @grd= "gradians"; @mil = 'mils'; @rad = "radians"
# = words(x)
call hdr @deg @grd @mil @rad
do j=1 for #; y= word(x,j)
say shw(y) fmt(d2d(y)) fmt(d2g(y)) fmt(d2m(y)) fmt(d2r(y))
end /*j*/
 
call hdr @grd @deg @mil @rad
do j=1 for #; y= word(x,j)
say shw(y) fmt(g2g(y)) fmt(g2d(y)) fmt(g2m(y)) fmt(g2r(y))
end /*j*/
 
call hdr @mil @deg @grd @rad
do j=1 for #; y= word(x,j)
say shw(y) fmt(m2m(y)) fmt(m2d(y)) fmt(m2g(y)) fmt(m2r(y))
end /*j*/
 
call hdr @rad @deg @grd @mil
do j=1 for #; y= word(x,j)
say shw(y) fmt(r2r(y)) fmt(r2d(y)) fmt(r2g(y)) fmt(r2m(y))
end /*j*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
fmt: _= format(arg(1), 6,w); L= length(_); return left(format(_/1, 6),L) /*align a #*/
shw: _= format(arg(1),12,9); L= length(_); return left(format(_/1,12),L) /* " " "*/
pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923078; return pi
d2g: return d2d(arg(1)) * 10 / 9 /*convert degrees ───► gradians. */
d2m: return d2d(arg(1)) * 160 / 9 /*convert degrees ───► mils. */
d2r: return d2d(arg(1)) * pi() / 180 /*convert degrees ───► radians. */
g2d: return g2g(arg(1)) * 0.9 /*convert gradians ───► degrees. */
g2m: return g2g(arg(1)) * 16 /*convert gradians ───► mils. */
g2r: return g2g(arg(1)) * pi() * 0.005 /*convert gradians ───► radians. */
m2d: return m2m(arg(1)) * 9 * 0.00625 /*convert mils ───► degrees. */
m2g: return m2m(arg(1)) / 16 /*convert mils ───► gradians. */
m2r: return m2m(arg(1)) * pi() / 3200 /*convert mils ───► radians. */
r2d: return r2r(arg(1)) * 180 / pi() /*convert radians ───► degrees. */
r2g: return r2r(arg(1)) * 200 / pi() /*convert radians ───► gradians. */
r2m: return r2r(arg(1)) * 3200 / pi() /*convert radians ───► mils. */
d2d: return arg(1) // 360 /*normalize degrees ───► a unit circle.*/
g2g: return arg(1) // 400 /*normalize gradians───► a unit circle.*/
m2m: return arg(1) // 6400 /*normalize mils ───► a unit circle.*/
r2r: return arg(1) // (pi() * 2) /*normalize radians ───► a unit circle.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
hdr: parse arg #o #a #b #c .; _= '═'; say /* [↓] the header line*/
@n = 'normalized'
say center(#o,23 ) center(@n #o,w7) center(#a,w7 ) center(#b,w7 ) center(#c,w7 )
say center('',23,_) center('',w7, _) center('',w7,_) center('',w7,_) center('',w7,_)
return /* '↑' seperator line.*/
output   when using the default input:
        degrees             normalized degrees               gradians                      mils                       radians
═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
          -2               -2                          -2.22222222222222222222    -35.55555555555555555556     -0.03490658503988659154
          -1               -1                          -1.11111111111111111111    -17.77777777777777777778     -0.01745329251994329577
           0                0                           0                           0                           0
           1                1                           1.11111111111111111111     17.77777777777777777778      0.01745329251994329577
           2                2                           2.22222222222222222222     35.55555555555555555556      0.03490658503988659154
           6.2831853        6.2831853                   6.981317                  111.701072                    0.10966227099790767281
          16               16                          17.77777777777777777778    284.44444444444444444444      0.27925268031909273231
          57.2957795       57.2957795                  63.66197722222222222222   1018.59163555555555555556      0.9999999997716704269
         359              359                         398.88888888888888888889   6382.22222222222222222222      6.26573201465964318116
         399               39                          43.33333333333333333333    693.33333333333333333333      0.680678408277788535
        6399              279                         310                        4960                           4.86946861306417951962
     1000000              280                         311.11111111111111111111   4977.77777777777777777778      4.88692190558412281539

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

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

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

Ruby[edit]

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

module Angles
BASES = {"d" => 360, "g" => 400, "m" => 6400, "r" => Math::PI*2 ,"h" => 24 }
 
def self.method_missing(meth, angle)
from, to = BASES.values_at(*meth.to_s.split("2"))
raise NoMethodError, meth if (from.nil? or to.nil?)
mod = (angle.to_f * to / from) % to
angle < 0 ? mod - to : mod
end
 
end
 
#Demo
names = Angles::BASES.keys
puts " " + "%12s "*names.size % names
test = [-2, -1, 0, 1, 2*Math::PI, 16, 360/(2*Math::PI), 360-1, 400-1, 6400-1, 1_000_000]
 
test.each do |n|
names.each do |first|
res = names.map{|last| Angles.send((first + "2" + last).to_sym, n)}
puts first + "%12g "*names.size % res
end
puts
end
 
Output:
          d            g            m            r            h 
d          -2     -2.22222     -35.5556   -0.0349066    -0.133333 
g        -1.8           -2          -32   -0.0314159        -0.12 
m     -0.1125       -0.125           -2   -0.0019635      -0.0075 
r    -114.592     -127.324     -2037.18           -2     -7.63944 
h         -30     -33.3333     -533.333    -0.523599           -2 

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

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

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

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

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

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

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

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

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

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

Rust[edit]

use std::{
marker::PhantomData,
f64::consts::PI,
};
 
pub trait AngleUnit: Copy {
const TURN: f64;
const NAME: &'static str;
}
 
macro_rules! unit {
($name:ident, $value:expr, $string:expr) => (
#[derive(Debug, Copy, Clone)]
struct $name;
impl AngleUnit for $name {
const TURN: f64 = $value;
const NAME: &'static str = $string;
}
);
}
 
unit!(Degrees, 360.0, "Degrees");
unit!(Radians, PI * 2.0, "Radians");
unit!(Gradians, 400.0, "Gradians");
unit!(Mils, 6400.0, "Mils");
 
#[derive(Copy, Clone, PartialEq, PartialOrd)]
struct Angle<T: AngleUnit>(f64, PhantomData<T>);
 
impl<T: AngleUnit> Angle<T> {
pub fn new(val: f64) -> Self {
Self(val, PhantomData)
}
 
pub fn normalize(self) -> Self {
Self(self.0 % T::TURN, PhantomData)
}
 
pub fn val(self) -> f64 {
self.0
}
 
pub fn convert<U: AngleUnit>(self) -> Angle<U> {
Angle::new(self.0 * U::TURN / T::TURN)
}
 
pub fn name(self) -> &'static str {
T::NAME
}
}
 
fn print_angles<T: AngleUnit>() {
let angles = [-2.0, -1.0, 0.0, 1.0, 2.0, 6.2831853, 16.0, 57.2957795, 359.0, 399.0, 6399.0, 1000000.0];
println!("{:<12} {:<12} {:<12} {:<12} {:<12} {:<12}", "Angle", "Unit", "Degrees", "Gradians", "Mils", "Radians");
 
for &angle in &angles {
let deg = Angle::<T>::new(angle).normalize();
println!("{:<12} {:<12} {:<12.4} {:<12.4} {:<12.4} {:<12.4}",
angle,
deg.name(),
deg.convert::<Degrees>().val(),
deg.convert::<Gradians>().val(),
deg.convert::<Mils>().val(),
deg.convert::<Radians>().val(),
);
}
 
println!();
}
 
fn main() {
print_angles::<Degrees>();
print_angles::<Gradians>();
print_angles::<Mils>();
print_angles::<Radians>();
}
Output:
Angle        Unit         Degrees      Gradians     Mils         Radians
-2           Degrees      -2.0000      -2.2222      -35.5556     -0.0349
-1           Degrees      -1.0000      -1.1111      -17.7778     -0.0175
0            Degrees      0.0000       0.0000       0.0000       0.0000
1            Degrees      1.0000       1.1111       17.7778      0.0175
2            Degrees      2.0000       2.2222       35.5556      0.0349
6.2831853    Degrees      6.2832       6.9813       111.7011     0.1097
16           Degrees      16.0000      17.7778      284.4444     0.2793
57.2957795   Degrees      57.2958      63.6620      1018.5916    1.0000
359          Degrees      359.0000     398.8889     6382.2222    6.2657
399          Degrees      39.0000      43.3333      693.3333     0.6807
6399         Degrees      279.0000     310.0000     4960.0000    4.8695
1000000      Degrees      280.0000     311.1111     4977.7778    4.8869

Angle        Unit         Degrees      Gradians     Mils         Radians
-2           Gradians     -1.8000      -2.0000      -32.0000     -0.0314
-1           Gradians     -0.9000      -1.0000      -16.0000     -0.0157
0            Gradians     0.0000       0.0000       0.0000       0.0000
1            Gradians     0.9000       1.0000       16.0000      0.0157
2            Gradians     1.8000       2.0000       32.0000      0.0314
6.2831853    Gradians     5.6549       6.2832       100.5310     0.0987
16           Gradians     14.4000      16.0000      256.0000     0.2513
57.2957795   Gradians     51.5662      57.2958      916.7325     0.9000
359          Gradians     323.1000     359.0000     5744.0000    5.6392
399          Gradians     359.1000     399.0000     6384.0000    6.2675
6399         Gradians     359.1000     399.0000     6384.0000    6.2675
1000000      Gradians     0.0000       0.0000       0.0000       0.0000

Angle        Unit         Degrees      Gradians     Mils         Radians
-2           Mils         -0.1125      -0.1250      -2.0000      -0.0020
-1           Mils         -0.0563      -0.0625      -1.0000      -0.0010
0            Mils         0.0000       0.0000       0.0000       0.0000
1            Mils         0.0563       0.0625       1.0000       0.0010
2            Mils         0.1125       0.1250       2.0000       0.0020
6.2831853    Mils         0.3534       0.3927       6.2832       0.0062
16           Mils         0.9000       1.0000       16.0000      0.0157
57.2957795   Mils         3.2229       3.5810       57.2958      0.0562
359          Mils         20.1938      22.4375      359.0000     0.3524
399          Mils         22.4438      24.9375      399.0000     0.3917
6399         Mils         359.9438     399.9375     6399.0000    6.2822
1000000      Mils         90.0000      100.0000     1600.0000    1.5708

Angle        Unit         Degrees      Gradians     Mils         Radians
-2           Radians      -114.5916    -127.3240    -2037.1833   -2.0000
-1           Radians      -57.2958     -63.6620     -1018.5916   -1.0000
0            Radians      0.0000       0.0000       0.0000       0.0000
1            Radians      57.2958      63.6620      1018.5916    1.0000
2            Radians      114.5916     127.3240     2037.1833    2.0000
6.2831853    Radians      360.0000     400.0000     6400.0000    6.2832
16           Radians      196.7325     218.5916     3497.4662    3.4336
57.2957795   Radians      42.8063      47.5626      761.0018     0.7471
359          Radians      49.1848      54.6498      874.3972     0.8584
399          Radians      181.0160     201.1289     3218.0627    3.1593
6399         Radians      155.6931     172.9923     2767.8774    2.7174
1000000      Radians      339.5131     377.2368     6035.7881    5.9256

Swift[edit]

import Foundation
 
func normalize(_ f: Double, N: Double) -> Double {
var a = f
 
while a < -N { a += N }
while a >= N { a -= N }
 
return a
}
 
func normalizeToDeg(_ f: Double) -> Double {
return normalize(f, N: 360)
}
 
func normalizeToGrad(_ f: Double) -> Double {
return normalize(f, N: 400)
}
 
func normalizeToMil(_ f: Double) -> Double {
return normalize(f, N: 6400)
}
 
func normalizeToRad(_ f: Double) -> Double {
return normalize(f, N: 2 * .pi)
}
 
func d2g(_ f: Double) -> Double { f * 10 / 9 }
func d2m(_ f: Double) -> Double { f * 160 / 9 }
func d2r(_ f: Double) -> Double { f * .pi / 180 }
 
func g2d(_ f: Double) -> Double { f * 9 / 10 }
func g2m(_ f: Double) -> Double { f * 16 }
func g2r(_ f: Double) -> Double { f * .pi / 200 }
 
func m2d(_ f: Double) -> Double { f * 9 / 160 }
func m2g(_ f: Double) -> Double { f / 16 }
func m2r(_ f: Double) -> Double { f * .pi / 3200 }
 
func r2d(_ f: Double) -> Double { f * 180 / .pi }
func r2g(_ f: Double) -> Double { f * 200 / .pi }
func r2m(_ f: Double) -> Double { f * 3200 / .pi }
 
let angles = [-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 6399, 1_000_000]
let names = ["Degrees", "Gradians", "Mils", "Radians"]
let fmt = { String(format: "%.4f", $0) }
 
let normal = [normalizeToDeg, normalizeToGrad, normalizeToMil, normalizeToRad]
let convert = [
[{ $0 }, d2g, d2m, d2r],
[g2d, { $0 }, g2m, g2r],
[m2d, m2g, { $0 }, m2r],
[r2d, r2g, r2m, { $0 }]
]
 
let ans =
angles.map({ angle in
(0..<4).map({ ($0, normal[$0](angle)) }).map({
(fmt(angle),
fmt($0.1),
names[$0.0],
fmt(convert[$0.0][0]($0.1)),
fmt(convert[$0.0][1]($0.1)),
fmt(convert[$0.0][2]($0.1)),
fmt(convert[$0.0][3]($0.1))
)
})
})
 
print("angle", "normalized", "unit", "degrees", "grads", "mils", "radians")
 
for res in ans {
for unit in res {
print(unit)
}
 
print()
}
Output:
angle normalized unit degrees grads mils radians
("-2.0000", "-2.0000", "Degrees", "-2.0000", "-2.2222", "-35.5556", "-0.0349")
("-2.0000", "-2.0000", "Gradians", "-1.8000", "-2.0000", "-32.0000", "-0.0314")
("-2.0000", "-2.0000", "Mils", "-0.1125", "-0.1250", "-2.0000", "-0.0020")
("-2.0000", "-2.0000", "Radians", "-114.5916", "-127.3240", "-2037.1833", "-2.0000")

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

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

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

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

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

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

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

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

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

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

zkl[edit]

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

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

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

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

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

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

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

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

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

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

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

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

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