bahaghari/lib: add math.sqrt function

subprojects/bahaghari/lib/default.nix

@@ -49,5 +49,5 @@ pkgs.lib.makeExtensible
 
     inherit (self.hex) isHexString;
     inherit (self.math) abs pow percentage factorial floor ceil round round'
-      summate product;
+      summate product sqrt;
   })

subprojects/bahaghari/lib/math.nix

@@ -48,6 +48,41 @@ rec {
     in
     if exponent < 0 then (1 / value) else value;
 
+  /* Given a number, find its square root. This method is implemented using
+     Newton's method.
+
+     Type: sqrt :: Number -> Number
+
+     Example:
+       sqrt 4
+       => 2
+
+       sqrt 169
+       => 13
+
+       sqrt 12
+       => 3.464101615
+  */
+  sqrt = number:
+    assert lib.assertMsg (number >= 0)
+      "bahaghariLib.math.sqrt: Only positive numbers are allowed";
+    let
+      # Changing this value can change the result drastically. A value of
+      # 10^-13 for tolerance seems to be the most balanced so far since we are
+      # dealing with floats and should be enough for most cases.
+      tolerance = pow 10 (-13);
+
+      iter = value:
+        let
+          root = 0.5 * (value + (number / value));
+        in
+          if (abs (root - value) > tolerance) then
+            iter root
+          else
+            value;
+    in
+      iter number;
+
   /* Implements the factorial function with the given value.
 
      Type: factorial :: Number -> Number

subprojects/bahaghari/tests/lib/math.nix

@@ -166,7 +166,7 @@ lib.runTests {
     expected = 10;
   };
 
-  testMathSummate22 = {
+  testMathSummate2 = {
     expr = self.math.summate [ 1 2 3 4.5 5.6 6.7 ];
     expected = 22.8;
   };
@@ -180,4 +180,26 @@ lib.runTests {
     expr = self.math.product [ 1.5 2 3 4.6 ];
     expected = 41.4;
   };
+
+  # All of the answers here should be sourced from another tool such as a
+  # calculator.
+  testMathSqrt = {
+    expr = self.math.sqrt 4;
+    expected = 2;
+  };
+
+  testMathSqrt2 = {
+    expr = self.math.sqrt 169;
+    expected = 13;
+  };
+
+  testMathSqrt3 = {
+    expr = self.math.round' (-9) (self.math.sqrt 12);
+    expected = 3.464101615;
+  };
+
+  testMathSqrt4 = {
+    expr = self.math.round' (-10) (self.math.sqrt 2);
+    expected = 1.4142135624;
+  };
 }