added Sqrt and SqrtRound functions

Author: Leonardo Cicconi

decimal.go

@@ -1360,6 +1360,52 @@ func RescalePair(d1 Decimal, d2 Decimal) (Decimal, Decimal) {
 	return d1, d2.rescale(baseScale)
 }
 
+// SqrtMaxIter sets a limit for number of iterations for the Sqrt function
+const SqrtMaxIter = 100000
+
+// Sqrt returns the square root of d, accurate to DivisionPrecision decimal places.
+func Sqrt(d Decimal) Decimal {
+	s, _ := SqrtRound(d, int32(DivisionPrecision))
+	return s
+}
+
+// SqrtRound returns the square root of d, accurate to precision decimal places.
+// The bool precise returns whether the precision was reached.
+func SqrtRound(d Decimal, precision int32) (Decimal, bool) {
+	maxError := New(1, -precision)
+	one := NewFromFloat(1)
+	var lo Decimal
+	var hi Decimal
+	// Handle cases where d < 0, d = 0, 0 < d < 1, and d > 1
+	if d.GreaterThanOrEqual(one) {
+		lo = Zero
+		hi = d
+	} else if d.Equal(one) {
+		return one, true
+	} else if d.LessThan(Zero) {
+		return NewFromFloat(-1), false // call this an error , cannot take sqrt of neg w/o imaginaries
+	} else if d.Equal(Zero) {
+		return Zero, true
+	} else {
+		// d is between 0 and 1. Therefore, 0 < d < Sqrt(d) < 1.
+		lo = d
+		hi = one
+	}
+	var mid Decimal
+	for i := 0; i < SqrtMaxIter; i++ {
+		mid = lo.Add(hi).Div(New(2, 0)) //mid = (lo+hi)/2;
+		if mid.Mul(mid).Sub(d).Abs().LessThan(maxError) {
+			return mid, true
+		}
+		if mid.Mul(mid).GreaterThan(d) {
+			hi = mid
+		} else {
+			lo = mid
+		}
+	}
+	return mid, false
+}
+
 func min(x, y int32) int32 {
 	if x >= y {
 		return y