Added Sqrt and SqrtRound functionality

decimal.go

@@ -19,6 +19,7 @@ package decimal
 import (
 	"database/sql/driver"
 	"encoding/binary"
+	"errors"
 	"fmt"
 	"math"
 	"math/big"
@@ -1677,3 +1678,59 @@ func (d Decimal) Tan() Decimal {
 	}
 	return y
 }
+
+// More math
+
+// Sqrt returns the square root of d, accurate to DivisionPrecision decimal places.
+// Sqrt is only valid for non-negative numbers; it will return an error otherwise.
+func (d Decimal) Sqrt() (Decimal, error) {
+	s, _, err := d.SqrtRound(int32(DivisionPrecision))
+	return s, err
+}
+
+// ErrImaginaryResult indicates an operation that would produce an imaginary result.
+var ErrImaginaryResult = errors.New("The result of this operation is imaginary.")
+
+// SqrtMaxIter sets a limit for number of iterations for the Sqrt function
+const SqrtMaxIter = 1000000
+
+// SqrtRound returns the square root of d, accurate to precision decimal places.
+// The bool precise returns whether the precision was achieved.
+// SqrtRound is only valid for non-negative numbers; it will return an error otherwise.
+func (d Decimal) SqrtRound(precision int32) (Decimal, bool, error) {
+	var (
+		maxError = New(1, -precision)
+		one      = NewFromFloat(1)
+		lo, 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, nil
+	} else if d.LessThan(Zero) {
+		return Zero, false, ErrImaginaryResult
+	} else if d.Equal(Zero) {
+		return Zero, true, nil
+	} 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, nil
+		}
+		if mid.Mul(mid).GreaterThan(d) {
+			hi = mid
+		} else {
+			lo = mid
+		}
+	}
+	return mid, false, nil
+}

decimal_test.go

@@ -2881,6 +2881,40 @@ func TestAvg(t *testing.T) {
 	}
 }
 
+func TestSqrtRound(t *testing.T) {
+	i := NewFromFloat(-1)
+	if _, err := i.Sqrt(); err != ErrImaginaryResult {
+		t.Errorf("Square root of -1 should produce error")
+	}
+
+	var vals = map[string]string{
+		// value : Sqrt(value)
+		"0.0":       "0.0",
+		"0.002342":  "0.0483942145302514",
+		"1.0":       "1.0",
+		"3.0":       "1.7320508075688773",
+		"4.0":       "2.0",
+		"4.5":       "2.1213203435596426",
+		"3289854.0": "1813.7954680724064485",
+	}
+
+	for val, expected := range vals {
+		v, err := NewFromString(val)
+		if err != nil {
+			t.Errorf("error parsing test value into Decimal")
+		}
+
+		e, err := NewFromString(expected)
+		if err != nil {
+			t.Errorf("error parsing test expected value into Decimal")
+		}
+
+		if sqrt, err := v.Sqrt(); err != nil || !sqrt.Equal(e) {
+			t.Errorf("Square root of %s should be %s, not %s (error: %s)", v, e, sqrt, err)
+		}
+	}
+}
+
 func TestRoundBankAnomaly(t *testing.T) {
 	a := New(25, -1)
 	b := New(250, -2)