Merge PR cosmos#5219: Added sqrt function to sdk.Decimal type

types/decimal.go

@@ -318,6 +318,32 @@ func (d Dec) QuoInt64(i int64) Dec {
 	return Dec{mul}
 }
 
+// ApproxSqrt returns an approximate sqrt estimation using Newton's method to
+// compute square roots x=√d for d > 0. The algorithm starts with some guess and
+// computes the sequence of improved guesses until an answer converges to an
+// approximate answer. It returns -(sqrt(abs(d)) if input is negative.
+func (d Dec) ApproxSqrt() Dec {
+	if d.IsNegative() {
+		return d.MulInt64(-1).ApproxSqrt().MulInt64(-1)
+	}
+
+	if d.IsZero() {
+		return ZeroDec()
+	}
+
+	z := OneDec()
+	// first guess
+	z = z.Sub((z.Mul(z).Sub(d)).Quo(z.MulInt64(2)))
+
+	// iterate until change is very small
+	for zNew, delta := z, z; delta.GT(SmallestDec()); z = zNew {
+		zNew = zNew.Sub((zNew.Mul(zNew).Sub(d)).Quo(zNew.MulInt64(2)))
+		delta = z.Sub(zNew)
+	}
+
+	return z
+}
+
 // is integer, e.g. decimals are zero
 func (d Dec) IsInteger() bool {
 	return new(big.Int).Rem(d.Int, precisionReuse).Sign() == 0

types/decimal_test.go

@@ -424,3 +424,22 @@ func TestDecCeil(t *testing.T) {
 		require.Equal(t, tc.expected, res, "unexpected result for test case %d, input: %v", i, tc.input)
 	}
 }
+
+func TestApproxSqrt(t *testing.T) {
+	testCases := []struct {
+		input    Dec
+		expected Dec
+	}{
+		{OneDec(), OneDec()},                                                // 1.0 => 1.0
+		{NewDecWithPrec(25, 2), NewDecWithPrec(5, 1)},                       // 0.25 => 0.5
+		{NewDecWithPrec(4, 2), NewDecWithPrec(2, 1)},                        // 0.09 => 0.3
+		{NewDecFromInt(NewInt(9)), NewDecFromInt(NewInt(3))},                // 9 => 3
+		{NewDecFromInt(NewInt(-9)), NewDecFromInt(NewInt(-3))},              // -9 => -3
+		{NewDecFromInt(NewInt(2)), NewDecWithPrec(1414213562373095049, 18)}, // 2 => 1.414213562373095049
+	}
+
+	for i, tc := range testCases {
+		res := tc.input.ApproxSqrt()
+		require.Equal(t, tc.expected, res, "unexpected result for test case %d, input: %v", i, tc.input)
+	}
+}