Haversine formula

Haversine formula
You are encouraged to solve this task according to the task description, using any language you may know.

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The haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes. It is a special case of a more general formula in spherical trigonometry, the law of haversines, relating the sides and angles of spherical "triangles".

Task: Implement a haversine distance function, or use a library function, to show the haversine distance between Nashville International Airport (BNA) in Nashville, TN, USA: N 36°7.2', W 86°40.2' (36.12, -86.67) and Los Angeles International Airport (LAX) in Los Angeles, CA, USA: N 33°56.4', W 118°24.0' (33.94, -118.40).

C

<lang c>#include <stdio.h>

1. include <stdlib.h>
2. include <math.h>

1. define R 6371
2. define TO_RAD (3.1415926536 / 180)

double dist(double th1, double ph1, double th2, double ph2) { double dx, dy, dz; ph1 -= ph2; ph1 *= TO_RAD, th1 *= TO_RAD, th2 *= TO_RAD;

dz = sin(th1) - sin(th2); dx = cos(ph1) * cos(th1) - cos(th2); dy = sin(ph1) * cos(th1); return asin(sqrt(dx * dx + dy * dy + dz * dz) / 2) * 2 * R; }

int main() { double d = dist(36.12, -86.67, 33.94, -118.4); /* Americans don't know kilometers */ printf("dist: %.1f km (%.1f mi.)\n", d, d / 1.609344);

return 0; }</lang>

D

<lang d>import std.stdio, std.math;

real haversineDistance(in real dth1, in real dph1,

                      in real dth2, in real dph2) pure nothrow {

   enum real R = 6371;
   enum real TO_RAD = PI / 180;

   alias immutable(real) imr;
   imr ph1d = dph1 - dph2;
   imr ph1 = ph1d * TO_RAD;
   imr th1 = dth1 * TO_RAD;
   imr th2 = dth2 * TO_RAD;

   imr dz = sin(th1) - sin(th2);
   imr dx = cos(ph1) * cos(th1) - cos(th2);
   imr dy = sin(ph1) * cos(th1);
   return asin(sqrt(dx ^^ 2 + dy ^^ 2 + dz ^^ 2) / 2) * 2 * R;

}

void main() {

   immutable d = haversineDistance(36.12, -86.67, 33.94, -118.4);
   writefln("Haversine distance: %.1f km", d);

}</lang> Output:

Haversine distance: 2886.4 km

Go

<lang go>package main

import (

   "fmt"
   "math"

)

func haversine(θ float64) float64 {

   return .5 * (1 - math.Cos(θ))

}

type pos struct {

   φ float64 // latitude, radians
   ψ float64 // longitude, radians

}

func degPos(lat, lon float64) pos {

   return pos{lat * math.Pi / 180, lon * math.Pi / 180}

}

const rEarth = 6372.8 // km

func hsDist(p1, p2 pos) float64 {

   return 2 * rEarth * math.Asin(math.Sqrt(haversine(p2.φ-p1.φ)+
       math.Cos(p1.φ)*math.Cos(p2.φ)*haversine(p2.ψ-p1.ψ)))

}

func main() {

   fmt.Println(hsDist(degPos(36.12, -86.67), degPos(33.94, -118.40)))

}</lang> Output:

2887.2599506071097

Groovy

<lang Groovy>def haversine(lat1, lon1, lat2, lon2) {

 def R = 6372.8
 // In kilometers
 def dLat = Math.toRadians(lat2 - lat1)
 def dLon = Math.toRadians(lon2 - lon1)
 lat1 = Math.toRadians(lat1)
 lat2 = Math.toRadians(lat2)

 def a = Math.sin(dLat / 2) * Math.sin(dLat / 2) + Math.sin(dLon / 2) * Math.sin(dLon / 2) * Math.cos(lat1) * Math.cos(lat2)
 def c = 2 * Math.asin(Math.sqrt(a))
 R * c

}

haversine(36.12, -86.67, 33.94, -118.40)

> 2887.25995060711</lang>

Pascal

Works with: Free_Pascal

Library: Math

<lang pascal>Program HaversineDemo(output);

uses

 Math;

function haversineDist(th1, ph1, th2, ph2: double): double;

 const
  diameter = 2 * 6372.8;
 var
   dx, dy, dz: double;
 begin
   ph1 := degtorad(ph1 - ph2);
   th1 := degtorad(th1);
   th2 := degtorad(th2);

   dz := sin(th1) - sin(th2);
   dx := cos(ph1) * cos(th1) - cos(th2);
   dy := sin(ph1) * cos(th1);
   haversineDist := arcsin(sqrt(dx**2 + dy**2 + dz**2) / 2) * diameter;
 end;

begin

 writeln ('Haversine distance: ', haversineDist(36.12, -86.67, 33.94, -118.4):7:2, ' km.');

end.</lang> Output:

Haversine distance: 2887.26 km.

Perl 6

<lang perl6>class EarthPoint {

       has $.lat; # latitude
       has $.lon; # longitude

       has $earth_radius = 6371; # mean earth radius
       has $radian_ratio = pi / 180;

       # accessors for radians
       method latR { $.lat * $radian_ratio }
       method lonR { $.lon * $radian_ratio }

       method haversine-dist(EarthPoint $p) {

               my EarthPoint $arc .= new(
                       lat => $!lat - $p.lat,
                       lon => $!lon - $p.lon );

               my $a = sin($arc.latR/2) ** 2 + sin($arc.lonR/2) ** 2
                       * cos($.latR) * cos($p.latR);
               my $c = 2 * asin( sqrt($a) );

               return $earth_radius * $c;
       }

}

my EarthPoint $BNA .= new(lat => 36.12, lon => -86.67); my EarthPoint $LAX .= new(lat => 33.94, lon => -118.4);

say $BNA.haversine-dist($LAX); # 2886.44444099822</lang>

Python

Translation of: Groovy

<lang python>>>> import math >>> def haversine(lat1, lon1, lat2, lon2):

 R = 6372.8
 # In kilometers
 dLat = math.radians(lat2 - lat1)
 dLon = math.radians(lon2 - lon1)
 lat1 = math.radians(lat1)
 lat2 = math.radians(lat2)

 a = math.sin(dLat / 2) * math.sin(dLat / 2) + math.sin(dLon / 2) * math.sin(dLon / 2) * math.cos(lat1) * math.cos(lat2)
 c = 2 * math.asin(math.sqrt(a))
 return R * c

>>> haversine(36.12, -86.67, 33.94, -118.40) 2887.2599506071106 >>> </lang>

Tcl

Translation of: Groovy

<lang tcl>package require Tcl 8.5 proc haversineFormula {lat1 lon1 lat2 lon2} {

   set rads [expr atan2(0,-1)/180]
   set R 6372.8    ;# In kilometers

   set dLat [expr {($lat2-$lat1) * $rads}]
   set dLon [expr {($lon2-$lon1) * $rads}]
   set lat1 [expr {$lat1 * $rads}]
   set lat2 [expr {$lat2 * $rads}]

   set a [expr {sin($dLat/2)**2 + sin($dLon/2)**2*cos($lat1)*cos($lat2)}]
   set c [expr {2*asin(sqrt($a))}]
   return [expr {$R * $c}]

}

1. Don't bother with too much inappropriate accuracy!

puts [format "distance=%.1f km" [haversineFormula 36.12 -86.67 33.94 -118.40]]</lang> Output:

distance=2887.3 km