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{{task|geometry}}
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''', '''+0º''', '''0.000000''', or '''-0º''' should be shown as '''0º'''.
;Task: ::* write a function (or equivalent) to do the normalization for each scale :::::* Suggested names: :::::* '''d2d''', '''g2g''', '''m2m''', and '''r2r''' ::* write a function (or equivalent) to convert one scale to another :::::* Suggested names for comparison of different computer language function names: :::::* '''d2g''', '''d2m''', and '''d2r''' for degrees :::::* '''g2d''', '''g2m''', and '''g2r''' for gradians :::::* '''m2d''', '''m2g''', and '''m2r''' for mils :::::* '''r2d''', '''r2g''', and '''r2m''' for radians ::* normalize all angles used (except for the "original" or "base" angle) ::* show the angles in every scale and convert them to all other scales ::* show all output here on this page
For the (above) conversions, use these dozen numbers (in the order shown): :* '''-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000'''
C
#define PI 3.141592653589793
#define TWO_PI 6.283185307179586
double normalize2deg(double a) {
while (a < 0) a += 360;
while (a >= 360) a -= 360;
return a;
}
double normalize2grad(double a) {
while (a < 0) a += 400;
while (a >= 400) a -= 400;
return a;
}
double normalize2mil(double a) {
while (a < 0) a += 6400;
while (a >= 6400) a -= 6400;
return a;
}
double normalize2rad(double a) {
while (a < 0) a += TWO_PI;
while (a >= TWO_PI) a -= TWO_PI;
return a;
}
double deg2grad(double a) {return a * 10 / 9;}
double deg2mil(double a) {return a * 160 / 9;}
double deg2rad(double a) {return a * PI / 180;}
double grad2deg(double a) {return a * 9 / 10;}
double grad2mil(double a) {return a * 16;}
double grad2rad(double a) {return a * PI / 200;}
double mil2deg(double a) {return a * 9 / 160;}
double mil2grad(double a) {return a / 16;}
double mil2rad(double a) {return a * PI / 3200;}
double rad2deg(double a) {return a * 180 / PI;}
double rad2grad(double a) {return a * 200 / PI;}
double rad2mil(double a) {return a * 3200 / PI;}
C#
using System;
public static class Angles
{
public static void Main() => Print(-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 6399, 1_000_000);
public static void Print(params double[] angles) {
string[] names = { "Degrees", "Gradians", "Mils", "Radians" };
Func<double, double> rnd = a => Math.Round(a, 4);
Func<double, double>[] normal = { NormalizeDeg, NormalizeGrad, NormalizeMil, NormalizeRad };
Func<double, double>[,] convert = {
{ a => a, DegToGrad, DegToMil, DegToRad },
{ GradToDeg, a => a, GradToMil, GradToRad },
{ MilToDeg, MilToGrad, a => a, MilToRad },
{ RadToDeg, RadToGrad, RadToMil, a => a }
};
Console.WriteLine($@"{"Angle",-12}{"Normalized",-12}{"Unit",-12}{
"Degrees",-12}{"Gradians",-12}{"Mils",-12}{"Radians",-12}");
foreach (double angle in angles) {
for (int i = 0; i < 4; i++) {
double nAngle = normal[i](angle);
Console.WriteLine($@"{
rnd(angle),-12}{
rnd(nAngle),-12}{
names[i],-12}{
rnd(convert[i, 0](nAngle)),-12}{
rnd(convert[i, 1](nAngle)),-12}{
rnd(convert[i, 2](nAngle)),-12}{
rnd(convert[i, 3](nAngle)),-12}");
}
}
}
public static double NormalizeDeg(double angle) => Normalize(angle, 360);
public static double NormalizeGrad(double angle) => Normalize(angle, 400);
public static double NormalizeMil(double angle) => Normalize(angle, 6400);
public static double NormalizeRad(double angle) => Normalize(angle, 2 * Math.PI);
private static double Normalize(double angle, double N) {
while (angle <= -N) angle += N;
while (angle >= N) angle -= N;
return angle;
}
public static double DegToGrad(double angle) => angle * 10 / 9;
public static double DegToMil(double angle) => angle * 160 / 9;
public static double DegToRad(double angle) => angle * Math.PI / 180;
public static double GradToDeg(double angle) => angle * 9 / 10;
public static double GradToMil(double angle) => angle * 16;
public static double GradToRad(double angle) => angle * Math.PI / 200;
public static double MilToDeg(double angle) => angle * 9 / 160;
public static double MilToGrad(double angle) => angle / 16;
public static double MilToRad(double angle) => angle * Math.PI / 3200;
public static double RadToDeg(double angle) => angle * 180 / Math.PI;
public static double RadToGrad(double angle) => angle * 200 / Math.PI;
public static double RadToMil(double angle) => angle * 3200 / Math.PI;
}
{{out}}
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 ``` ## Factor Radians and degrees are already defined in theunits.sivocabulary. 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.) ```factor USING: accessors combinators formatting inverse kernel math math.constants quotations qw sequences units.si ; IN: rosetta-code.angles ALIAS: degrees arc-deg : gradiens ( n -- d ) 9/10 * degrees ; : mils ( n -- d ) 9/160 * degrees ; : normalize ( d -- d' ) [ 2 pi * mod ] change-value ; CONSTANT: units { degrees gradiens mils radians } : .row ( angle unit -- ) 2dup "%-12u%-12s" printf ( x -- x ) execute-effect normalize units [ 1quotation [undo] call( x -- x ) ] with map "%-12.4f%-12.4f%-12.4f%-12.4f\n" vprintf ; : .header ( -- ) qw{ angle unit } units append "%-12s%-12s%-12s%-12s%-12s%-12s\n" vprintf ; : angles ( -- ) .header { -2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000 } units [ .row ] cartesian-each ; MAIN: angles ``` {{out}} ```txt 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 ```go package main import ( "fmt" "math" "strconv" "strings" ) func d2d(d float64) float64 { return math.Mod(d, 360) } func g2g(g float64) float64 { return math.Mod(g, 400) } func m2m(m float64) float64 { return math.Mod(m, 6400) } func r2r(r float64) float64 { return math.Mod(r, 2*math.Pi) } func d2g(d float64) float64 { return d2d(d) * 400 / 360 } func d2m(d float64) float64 { return d2d(d) * 6400 / 360 } func d2r(d float64) float64 { return d2d(d) * math.Pi / 180 } func g2d(g float64) float64 { return g2g(g) * 360 / 400 } func g2m(g float64) float64 { return g2g(g) * 6400 / 400 } func g2r(g float64) float64 { return g2g(g) * math.Pi / 200 } func m2d(m float64) float64 { return m2m(m) * 360 / 6400 } func m2g(m float64) float64 { return m2m(m) * 400 / 6400 } func m2r(m float64) float64 { return m2m(m) * math.Pi / 3200 } func r2d(r float64) float64 { return r2r(r) * 180 / math.Pi } func r2g(r float64) float64 { return r2r(r) * 200 / math.Pi } func r2m(r float64) float64 { return r2r(r) * 3200 / math.Pi } // Aligns number to decimal point assuming 7 characters before and after. func s(f float64) string { wf := strings.Split(strconv.FormatFloat(f, 'g', 15, 64), ".") if len(wf) == 1 { return fmt.Sprintf("%7s ", wf[0]) } le := len(wf[1]) if le > 7 { le = 7 } return fmt.Sprintf("%7s.%-7s", wf[0], wf[1][:le]) } func main() { angles := []float64{-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000} ft := "%s %s %s %s %s\n" fmt.Printf(ft, " degrees ", "normalized degs", " gradians ", " mils ", " radians") for _, a := range angles { fmt.Printf(ft, s(a), s(d2d(a)), s(d2g(a)), s(d2m(a)), s(d2r(a))) } fmt.Printf(ft, "\n gradians ", "normalized grds", " degrees ", " mils ", " radians") for _, a := range angles { fmt.Printf(ft, s(a), s(g2g(a)), s(g2d(a)), s(g2m(a)), s(g2r(a))) } fmt.Printf(ft, "\n mils ", "normalized mils", " degrees ", " gradians ", " radians") for _, a := range angles { fmt.Printf(ft, s(a), s(m2m(a)), s(m2d(a)), s(m2g(a)), s(m2r(a))) } fmt.Printf(ft, "\n radians ", "normalized rads", " degrees ", " gradians ", " mils ") for _, a := range angles { fmt.Printf(ft, s(a), s(r2r(a)), s(r2d(a)), s(r2g(a)), s(r2m(a))) } } ``` {{out}} ```txt 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 ``` ## Julia ```julia using Formatting d2d(d) = d % 360 g2g(g) = g % 400 m2m(m) = m % 6400 r2r(r) = r % 2π d2g(d) = d2d(d) * 10 / 9 d2m(d) = d2d(d) * 160 / 9 d2r(d) = d2d(d) * π / 180 g2d(g) = g2g(g) * 9 / 10 g2m(g) = g2g(g) * 16 g2r(g) = g2g(g) * π / 200 m2d(m) = m2m(m) * 9 / 160 m2g(m) = m2m(m) / 16 m2r(m) = m2m(m) * π / 3200 r2d(r) = r2r(r) * 180 / π r2g(r) = r2r(r) * 200 / π r2m(r) = r2r(r) * 3200 / π fmt(x::Real, width=16) = Int(round(x)) == x ? rpad(Int(x), width) : rpad(format(x, precision=7), width) fmt(x::String, width=16) = rpad(x, width) const t2u = Dict("degrees" => [d2d, d2g, d2m, d2r], "gradians" => [g2d, g2g, g2m, g2r], "mils" => [m2d, m2g, m2m, m2r], "radians" => [r2d, r2g, r2m, r2r]) function testconversions(arr) println("Number Units Degrees Gradians Mils Radians") for num in arr, units in ["degrees", "gradians", "mils", "radians"] print(fmt(num), fmt(units)) for f in t2u[units] print(fmt(f(num))) end println() end end testconversions([-2, -1, 0, 1, 2, 6.2831853, 16, 57.2957795, 359, 399, 6399, 1000000]) ``` {{out}} ```txt 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 {{trans|Perl 6}} ```perl use strict; use warnings; use feature 'say'; use POSIX 'fmod'; my $tau = 2 * 4*atan2(1, 1); my @units = ( { code => 'd', name => 'degrees' , number => 360 }, { code => 'g', name => 'gradians', number => 400 }, { code => 'm', name => 'mills' , number => 6400 }, { code => 'r', name => 'radians' , number => $tau }, ); my %cvt; for my $a (@units) { for my $b (@units) { $cvt{ "${$a}{code}2${$b}{code}" } = sub { my($angle) = shift; my $norm = fmod($angle,${$a}{number}); # built-in '%' returns only integers $norm -= ${$a}{number} if $angle < 0; $norm * ${$b}{number} / ${$a}{number} } } } printf '%s'. '%12s'x4 . "\n", ' Angle Unit ',; 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; } } ``` {{out}} ```txt 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 ``` ## Perl 6 ```perl6 my @units = { code => 'd', name => 'degrees' , number => 360 }, { code => 'g', name => 'gradians', number => 400 }, { code => 'm', name => 'mills' , number => 6400 }, { code => 'r', name => 'radians' , number => tau }, ; my Code %cvt = (@units X @units).map: -> ($a, $b) { "{$a. }2{$b.}" => sub ($angle) { my $norm = $angle % $a.- ( $a. if $angle < 0 ); $norm * $b. / $a. } } say ' Angle Unit ', @units». ».tc.fmt('%11s'); for -2, -1, 0, 1, 2, tau, 16, 360/tau, 360-1, 400-1, 6400-1, 1_000_000 -> $angle { say ''; for @units -> $from { my @sub_keys = @units.map: { "{$from. }2{.}" }; my @results = %cvt{@sub_keys}».($angle); say join ' ', $angle .fmt('%10g'), $from..fmt('%-8s'), @results .fmt('%11g'); } } ``` {{out}} ```txt 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.)'' ```perl6>sub postfix: =0 ?? $a !! $a - τ } sub postfix: ( $d ) { my $a = $d % 360 * τ / 360; $d >=0 ?? $a !! $a - τ } sub postfix: ( $g ) { my $a = $g % 400 * τ / 400; $g >=0 ?? $a !! $a - τ } sub postfix: ( $m ) { my $a = $m % 6400 * τ / 6400; $m >=0 ?? $a !! $a - τ } sub postfix: ( $r ) { my $a = $r % τ; $r >=0 ?? $a !! $a - τ } sub postfix:«->t» ($angle) { my $a = $angle / τ; ($angle < 0 and $a == -1) ?? -0 !! $a } sub postfix:«->d» ($angle) { my $a = $angle / τ * 360; ($angle < 0 and $a == -360) ?? -0 !! $a } sub postfix:«->g» ($angle) { my $a = $angle / τ * 400; ($angle < 0 and $a == -400) ?? -0 !! $a } sub postfix:«->m» ($angle) { my $a = $angle / τ * 6400; ($angle < 0 and $a == -6400) ?? -0 !! $a } sub postfix:«->r» ($angle) { my $a = $angle; ($angle < 0 and $a == -τ) ?? -0 !! $a } for <-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000> -> $a { say ''; say ' Quantity Unit ', .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); } } ``` ```txt 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 ``` ## Phix Obviously if preferred you could define a long list of routines such as function d2g(atom a) return remainder(a/360,1)*400 end function ```Phix 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,-1,0,1,2,6.2831853,16,57.2957795,359,399,6399,1000000}, 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 ``` {{out}} ```txt 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 360 400 6400 6.28319 16 degrees 16 17.7778 284.444 0.279253 16 gradians 14.4 16 256 0.251327 16 mils 0.9 1 16 0.015708 16 radians 196.732 218.592 3497.47 3.43363 57.2958 degrees 57.2958 63.662 1018.59 1 57.2958 gradians 51.5662 57.2958 916.732 0.9 57.2958 mils 3.22289 3.58099 57.2958 0.05625 57.2958 radians 42.8063 47.5626 761.002 0.747112 359 degrees 359 398.889 6382.22 6.26573 359 gradians 323.1 359 5744 5.63916 359 mils 20.1937 22.4375 359 0.352447 359 radians 49.1848 54.6498 874.397 0.858437 399 degrees 39 43.3333 693.333 0.680678 399 gradians 359.1 399 6384 6.26748 399 mils 22.4438 24.9375 399 0.391717 399 radians 181.016 201.129 3218.06 3.15933 6399 degrees 279 310 4960 4.86947 6399 gradians 359.1 399 6384 6.26748 6399 mils 359.944 399.938 6399 6.2822 6399 radians 155.693 172.992 2767.88 2.71736 1e+6 degrees 280 311.111 4977.78 4.88692 1e+6 gradians 0 0 0 0 1e+6 mils 90 100 1600 1.5708 1e+6 radians 339.513 377.237 6035.79 5.92562 ``` ## Python ```python 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 ``` ## REXX ```rexx /*REXX pgm normalizes an angle (in a scale), or converts angles from a scale to another.*/ numeric digits length( pi() ) - length(.) /*use the "length" of pi for precision.*/ parse arg x /*obtain optional arguments from the CL*/ if x='' | x="," then x= '-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000' w= 20; w7= w+7 /*W: # dec digits past the dec. point.*/ @deg = 'degrees'; @grd= "gradians"; @mil = 'mils'; @rad = "radians" # = words(x) call hdr @deg @grd @mil @rad do j=1 for #; y= word(x,j) say shw(y) fmt(d2d(y)) fmt(d2g(y)) fmt(d2m(y)) fmt(d2r(y)) end /*j*/ call hdr @grd @deg @mil @rad do j=1 for #; y= word(x,j) say shw(y) fmt(g2g(y)) fmt(g2d(y)) fmt(g2m(y)) fmt(g2r(y)) end /*j*/ call hdr @mil @deg @grd @rad do j=1 for #; y= word(x,j) say shw(y) fmt(m2m(y)) fmt(m2d(y)) fmt(m2g(y)) fmt(m2r(y)) end /*j*/ call hdr @rad @deg @grd @mil do j=1 for #; y= word(x,j) say shw(y) fmt(r2r(y)) fmt(r2d(y)) fmt(r2g(y)) fmt(r2m(y)) end /*j*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ fmt: _= format(arg(1), 6,w); L= length(_); return left(format(_/1, 6),L) /*align a #*/ shw: _= format(arg(1),12,9); L= length(_); return left(format(_/1,12),L) /* " " "*/ pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923078; return pi d2g: return d2d(arg(1)) * 10 / 9 /*convert degrees ───► gradians. */ d2m: return d2d(arg(1)) * 160 / 9 /*convert degrees ───► mils. */ d2r: return d2d(arg(1)) * pi() / 180 /*convert degrees ───► radians. */ g2d: return g2g(arg(1)) * 0.9 /*convert gradians ───► degrees. */ g2m: return g2g(arg(1)) * 16 /*convert gradians ───► mils. */ g2r: return g2g(arg(1)) * pi() * 0.005 /*convert gradians ───► radians. */ m2d: return m2m(arg(1)) * 9 * 0.00625 /*convert mils ───► degrees. */ m2g: return m2m(arg(1)) / 16 /*convert mils ───► gradians. */ m2r: return m2m(arg(1)) * pi() / 3200 /*convert mils ───► radians. */ r2d: return r2r(arg(1)) * 180 / pi() /*convert radians ───► degrees. */ r2g: return r2r(arg(1)) * 200 / pi() /*convert radians ───► gradians. */ r2m: return r2r(arg(1)) * 3200 / pi() /*convert radians ───► mils. */ d2d: return arg(1) // 360 /*normalize degrees ───► a unit circle.*/ g2g: return arg(1) // 400 /*normalize gradians───► a unit circle.*/ m2m: return arg(1) // 6400 /*normalize mils ───► a unit circle.*/ r2r: return arg(1) // (pi() * 2) /*normalize radians ───► a unit circle.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ hdr: parse arg #o #a #b #c .; _= '═'; say /* [↓] the header line*/ @n = 'normalized' say center(#o,23 ) center(@n #o,w7) center(#a,w7 ) center(#b,w7 ) center(#c,w7 ) say center('',23,_) center('',w7, _) center('',w7,_) center('',w7,_) center('',w7,_) return /* '↑' seperator line.*/ ``` {{out|output|text= when using the default input:}} ```txt 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 ``` ## zkl {{trans|Perl6}} ```zkl var [const] tau=(0.0).pi*2, units=Dictionary( // code:(name, units in circle) "d", T("degrees", 360.0), "g",T("gradians",400.0), "m", T("mills", 6400.0), "r",T("radians", tau) ), cvtNm="%s-->%s".fmt, cvt= // "d-->r":fcn(angle){}, "r-->d":fcn(angle){} ... Walker.cproduct(units.keys,units.keys).pump(Dictionary(),fcn([(a,b)]){ return(cvtNm(a,b), // "d-->r" 'wrap(angle){ angle=angle.toFloat(); u:=units[a][1]; (angle%u)*units[b][1] / u }) }) ; ``` ```zkl codes:=units.keys; println(" Angle Unit ", codes.apply(fcn(k){ units[k][0] }).apply("%11s".fmt).concat(" ")); foreach angle in (T(-2.0,-1, 0, 1, 2, tau, 16, 360.0/tau, 360-1, 400-1, 6400-1, 1_000_000)){ println(); foreach from in (codes){ subKeys:=codes.apply(cvtNm.fp(from)); // ("d-->d","d-->g","d-->m","d-->r") r:=subKeys.pump(List,'wrap(k){ cvt[k](angle) }); println("%10g %-8s %s".fmt(angle,units[from][0], r.apply("%12g".fmt).concat(" "))); } } ``` {{out}} 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 ```