feat: add haversineDistance (#80)

* feat: add `haversineDistance`

* style: avoid `return`

Co-authored-by: Zoom <ZoomRmc@users.noreply.github.com>

* style: rename to `isClose`

---------

Co-authored-by: Zoom <ZoomRmc@users.noreply.github.com>

Author: vil02

maths/haversine_distance.nim

@@ -0,0 +1,53 @@
+# Haversine formula
+
+import std/math
+
+func haversineDistance(latitudeA, longitudeA, latitudeB,
+    longitudeB: float): float =
+  ## returns the length of the shortest path connecting the input points on an unit sphere.
+  ## The input points are represented by their spherical/geographical coordinates.
+  ## The inputs are expected to be in radians.
+  let
+    dLatitude = latitudeB - latitudeA
+    dLongitude = longitudeB - longitudeA
+    a = sin(dLatitude / 2.0)^2 + cos(latitudeA) * cos(latitudeB) * sin(
+        dLongitude / 2.0)^2
+  2.0 * arcsin(sqrt(a))
+
+when isMainModule:
+  import std/[unittest, sequtils, strformat]
+  suite "haversineDistance":
+    const testCases = [
+      (0.0, 0.0, 0.0, 0.0, 0.0),
+      (0.0, 0.0, PI / 2.0, 0.0, PI / 2.0),
+      (-PI / 2.0, 0.0, PI / 2.0, 0.0, PI),
+      (0.0, 0.0, 0.0, PI / 2.0, PI / 2.0),
+      (0.0, -PI / 2.0, 0.0, PI / 2.0, PI),
+      (1.0, -PI / 2.0, -1.0, PI / 2.0, PI),
+      (2.0, -PI / 2.0, -2.0, PI / 2.0, PI),
+      (3.0, -PI / 2.0, -3.0, PI / 2.0, PI),
+      (3.0, -PI / 2.0 + 0.5, -3.0, PI / 2.0 + 0.5, PI),
+      (0.0, 0.0, 0.0, PI, PI),
+      (PI / 2.0, 1.0, PI / 2.0, 2.0, 0.0),
+      (-PI / 2.0, 1.0, -PI / 2.0, 2.0, 0.0),
+      (0.0, 0.0, -PI / 4.0, 0.0, PI / 4.0),
+      (0.0, 1.0, PI / 4.0, 1.0, PI / 4.0),
+      (-PI / 2.0, 0.0, -PI / 4.0, 0.0, PI / 4.0),
+      (-PI / 2.0, 0.0, -PI / 4.0, 0.6, PI / 4.0),
+      (-PI / 2.0, 3.0, -PI / 4.0, 0.2, PI / 4.0),
+      ].mapIt:
+        (id: fmt"posA=({it[0]}, {it[1]}), posB=({it[2]}, {it[3]})",
+         latitudeA: it[0], longitudeA: it[1],
+         latitudeB: it[2], longitudeB: it[3],
+         expected: it[4])
+
+    func isClose(a, b: float): bool =
+      return abs(a-b) < 0.0000001
+
+    for tc in testCases:
+      test tc.id:
+        checkpoint("returns expected result")
+        check isClose(haversineDistance(tc.latitudeA, tc.longitudeA,
+            tc.latitudeB, tc.longitudeB), tc.expected)
+        check isClose(haversineDistance(tc.latitudeB, tc.longitudeB,
+            tc.latitudeA, tc.longitudeA), tc.expected)