# java – How to determine if a number is positive or negative?-ThrowExceptions

Exception or error:

I was asked in an interview, how to determine whether a number is positive or negative. The rules are that we should not use conditional operators such as `<`, and `>`, built in java functions (like `substring`, `indexOf`, `charAt`, and `startsWith`), no regex, or API’s.

I did some homework on this and the code is given below, but it only works for integer type. But they asked me to write a generic code that works for `float`, `double`, and `long`.

`````` // This might not be better way!!

S.O.P ((( number >> 31 ) & 1) == 1 ? "- ve number " : "+ve number );
``````

How to solve:

The integer cases are easy. The double case is trickier, until you remember about infinities.

Note: If you consider the double constants “part of the api”, you can replace them with overflowing expressions like `1E308 * 2`.

``````int sign(int i) {
if (i == 0) return 0;
if (i >> 31 != 0) return -1;
return +1;
}
int sign(long i) {
if (i == 0) return 0;
if (i >> 63 != 0) return -1;
return +1;
}
int sign(double f) {
if (f != f) throw new IllegalArgumentException("NaN");
if (f == 0) return 0;
f *= Double.POSITIVE_INFINITY;
if (f == Double.POSITIVE_INFINITY) return +1;
if (f == Double.NEGATIVE_INFINITY) return -1;

//this should never be reached, but I've been wrong before...
throw new IllegalArgumentException("Unfathomed double");
}
``````

The following is a terrible approach that would get you fired at any job…

It depends on you getting a Stack Overflow Exception [or whatever Java calls it]… And it would only work for positive numbers that don’t deviate from 0 like crazy.

Negative numbers are fine, since you would overflow to positive, and then get a stack overflow exception eventually [which would return false, or “yes, it is negative”]

``````Boolean isPositive<T>(T a)
{
if(a == 0) return true;
else
{
try
{
return isPositive(a-1);
}catch(StackOverflowException e)
{
return false; //It went way down there and eventually went kaboom
}
}
}
``````

This will only works for everything except [0..2]

``````boolean isPositive = (n % (n - 1)) * n == n;
``````

You can make a better solution like this (works except for [0..1])

``````boolean isPositive = ((n % (n - 0.5)) * n) / 0.5 == n;
``````

You can get better precision by changing the 0.5 part with something like 2^m (m integer):

``````boolean isPositive = ((n % (n - 0.03125)) * n) / 0.03125 == n;
``````

You can do something like this:

``````((long) (num * 1E308 * 1E308) >> 63) == 0 ? "+ve" : "-ve"
``````

The main idea here is that we cast to a long and check the value of the most significant bit. As a double/float between -1 and 0 will round to zero when cast to a long, we multiply by large doubles so that a negative float/double will be less than -1. Two multiplications are required because of the existence of subnormals (it doesn’t really need to be that big though).

``````return ((num + "").charAt(0) == '-');
``````

``````// Returns 0 if positive, nonzero if negative
public long sign(long value) {
return value & 0x8000000000000000L;
}
``````

Call like:

``````long val1 = ...;
double val2 = ...;
float val3 = ...;
int val4 = ...;

sign((long) valN);
``````

Casting from double / float / integer to long should preserve the sign, if not the actual value…

You say

we should not use conditional operators

But this is a trick requirement, because `==` is also a conditional operator. There is also one built into `? :`, `while`, and `for` loops. So nearly everyone has failed to provide an answer meeting all the requirements.

The only way to build a solution without a conditional operator is to use lookup table vs one of a few other people’s solutions that can be boiled down to 0/1 or a character, before a conditional is met.

Here are the answers that I think might work vs a lookup table:

• Nabb
• Steven Schlansker
• Dennis Cheung
• Gary Rowe

This solution uses modulus. And yes, it also works for `0.5` (tests are below, in the main method).

``````public class Num {

public static int sign(long x) {
if (x == 0L || x == 1L) return (int) x;
return x == Long.MIN_VALUE || x % (x - 1L) == x ? -1 : 1;
}

public static int sign(double x) {
if (x != x) throw new IllegalArgumentException("NaN");
if (x == 0.d || x == 1.d) return (int) x;
if (x == Double.POSITIVE_INFINITY) return 1;
if (x == Double.NEGATIVE_INFINITY) return -1;
return x % (x - 1.d) == x ? -1 : 1;
}

public static int sign(int x) {
return Num.sign((long)x);
}

public static int sign(float x) {
return Num.sign((double)x);
}

public static void main(String args[]) {

System.out.println(Num.sign(Integer.MAX_VALUE)); // 1
System.out.println(Num.sign(1)); // 1
System.out.println(Num.sign(0)); // 0
System.out.println(Num.sign(-1)); // -1
System.out.println(Num.sign(Integer.MIN_VALUE)); // -1

System.out.println(Num.sign(Long.MAX_VALUE)); // 1
System.out.println(Num.sign(1L)); // 1
System.out.println(Num.sign(0L)); // 0
System.out.println(Num.sign(-1L)); // -1
System.out.println(Num.sign(Long.MIN_VALUE)); // -1

System.out.println(Num.sign(Double.POSITIVE_INFINITY)); // 1
System.out.println(Num.sign(Double.MAX_VALUE)); // 1
System.out.println(Num.sign(0.5d)); // 1
System.out.println(Num.sign(0.d)); // 0
System.out.println(Num.sign(-0.5d)); // -1
System.out.println(Num.sign(Double.MIN_VALUE)); // -1
System.out.println(Num.sign(Double.NEGATIVE_INFINITY)); // -1

System.out.println(Num.sign(Float.POSITIVE_INFINITY)); // 1
System.out.println(Num.sign(Float.MAX_VALUE)); // 1
System.out.println(Num.sign(0.5f)); // 1
System.out.println(Num.sign(0.f)); // 0
System.out.println(Num.sign(-0.5f)); // -1
System.out.println(Num.sign(Float.MIN_VALUE)); // -1
System.out.println(Num.sign(Float.NEGATIVE_INFINITY)); // -1
System.out.println(Num.sign(Float.NaN)); // Throws an exception

}
}
``````

This code covers all cases and types:

``````public static boolean isNegative(Number number) {
return (Double.doubleToLongBits(number.doubleValue()) & Long.MIN_VALUE) == Long.MIN_VALUE;
}
``````

This method accepts any of the wrapper classes (`Integer`, `Long`, `Float` and `Double`) and thanks to auto-boxing any of the primitive numeric types (`int`, `long`, `float` and `double`) and simply checks it the high bit, which in all types is the sign bit, is set.

It returns `true` when passed any of:

• any negative `int`/`Integer`
• any negative `long`/`Long`
• any negative `float`/`Float`
• any negative `double`/`Double`
• `Double.NEGATIVE_INFINITY`
• `Float.NEGATIVE_INFINITY`

and `false` otherwise.

Untested, but illustrating my idea:

``````boolean IsNegative<T>(T v) {
return (v & ((T)-1));
}
``````

It seems arbitrary to me because I don’t know how you would get the number as any type, but what about checking Abs(number) != number? Maybe && number != 0

Integers are trivial; this you already know. The deep problem is how to deal with floating-point values. At that point, you’ve got to know a bit more about how floating point values actually work.

The key is Double.doubleToLongBits(), which lets you get at the IEEE representation of the number. (The method’s really a direct cast under the hood, with a bit of magic for dealing with NaN values.) Once a double has been converted to a long, you can just use 0x8000000000000000L as a mask to select the sign bit; if zero, the value is positive, and if one, it’s negative.

If it is a valid answer

``````boolean IsNegative(char[] v) throws NullPointerException, ArrayIndexOutOfBoundException
{
return v[0]=='-';
}
``````

one more option I could think of

``````private static boolean isPositive(Object numberObject) {
Long number = Long.valueOf(numberObject.toString());
return Math.sqrt((number * number)) != number;
}

private static boolean isPositive(Object numberObject) {
Long number = Long.valueOf(numberObject.toString());
long signedLeftShifteredNumber = number << 1; // Signed left shift
long unsignedRightShifterNumber = signedLeftShifteredNumber >>> 1; // Unsigned right shift
return unsignedRightShifterNumber == number;
}
``````

This one is roughly based on ItzWarty’s answer, but it runs in logn time! Caveat: Only works for integers.

``````Boolean isPositive(int a)
{
if(a == -1) return false;
if(a == 0) return false;
if(a == 1) return true;
return isPositive(a/2);
}
``````

I think there is a very simple solution:

``````public boolean isPositive(int|float|double|long i){
return (((i-i)==0)? true : false);
}
``````

tell me if I’m wrong!

Try this without the code: `(x-SQRT(x^2))/(2*x)`

Write it using the conditional then take a look at the assembly code generated.

Why not get the square root of the number? If its negative – java will throw an error and we will handle it.

``````         try {
d = Math.sqrt(THE_NUMBER);
}
catch ( ArithmeticException e ) {
console.putln("Number is negative.");
}
``````

I don’t know how exactly Java coerces numeric values, but the answer is pretty simple, if put in pseudocode (I leave the details to you):

``````sign(x) := (x == 0) ? 0 : (x/x)
``````

If you are allowed to use “==” as seems to be the case, you can do something like that taking advantage of the fact that an exception will be raised if an array index is out of bounds. The code is for double, but you can cast any numeric type to a double (here the eventual loss of precision would not be important at all).

I have added comments to explain the process (bring the value in ]-2.0; -1.0] union [1.0; 2.0[) and a small test driver as well.

``````class T {

public static boolean positive(double f)
{
final boolean pos0[] = {true};
final boolean posn[] = {false, true};

if (f == 0.0)
return true;

while (true) {

// If f is in ]-1.0; 1.0[, multiply it by 2 and restart.
try {
if (pos0[(int) f]) {
f *= 2.0;
continue;
}
} catch (Exception e) {
}

// If f is in ]-2.0; -1.0] U [1.0; 2.0[, return the proper answer.
try {
return posn[(int) ((f+1.5)/2)];
} catch (Exception e) {
}

// f is outside ]-2.0; 2.0[, divide by 2 and restart.
f /= 2.0;

}

}

static void check(double f)
{
System.out.println(f + " -> " + positive(f));
}

public static void main(String args[])
{
for (double i = -10.0; i <= 10.0; i++)
check(i);
check(-1e24);
check(-1e-24);
check(1e-24);
check(1e24);
}
``````

The output is:

``````-10.0 -> false
-9.0 -> false
-8.0 -> false
-7.0 -> false
-6.0 -> false
-5.0 -> false
-4.0 -> false
-3.0 -> false
-2.0 -> false
-1.0 -> false
0.0 -> true
1.0 -> true
2.0 -> true
3.0 -> true
4.0 -> true
5.0 -> true
6.0 -> true
7.0 -> true
8.0 -> true
9.0 -> true
10.0 -> true
-1.0E24 -> false
-1.0E-24 -> false
1.0E-24 -> true
1.0E24 -> true
``````

Well, taking advantage of casting (since we don’t care what the actual value is) perhaps the following would work. Bear in mind that the actual implementations do not violate the API rules. I’ve edited this to make the method names a bit more obvious and in light of @chris’ comment about the {-1,+1} problem domain. Essentially, this problem does not appear to solvable without recourse to API methods within Float or Double that reference the native bit structure of the float and double primitives.

As everybody else has said: Stupid interview question. Grr.

``````public class SignDemo {

public static boolean isNegative(byte x) {
return (( x >> 7 ) & 1) == 1;
}

public static boolean isNegative(short x) {
return (( x >> 15 ) & 1) == 1;
}

public static boolean isNegative(int x) {
return (( x >> 31 ) & 1) == 1;
}

public static boolean isNegative(long x) {
return (( x >> 63 ) & 1) == 1;
}

public static boolean isNegative(float x) {
return isNegative((int)x);
}

public static boolean isNegative(double x) {
return isNegative((long)x);
}

public static void main(String[] args) {

// byte
System.out.printf("Byte %b%n",isNegative((byte)1));
System.out.printf("Byte %b%n",isNegative((byte)-1));

// short
System.out.printf("Short %b%n",isNegative((short)1));
System.out.printf("Short %b%n",isNegative((short)-1));

// int
System.out.printf("Int %b%n",isNegative(1));
System.out.printf("Int %b%n",isNegative(-1));

// long
System.out.printf("Long %b%n",isNegative(1L));
System.out.printf("Long %b%n",isNegative(-1L));

// float
System.out.printf("Float %b%n",isNegative(Float.MAX_VALUE));
System.out.printf("Float %b%n",isNegative(Float.NEGATIVE_INFINITY));

// double
System.out.printf("Double %b%n",isNegative(Double.MAX_VALUE));
System.out.printf("Double %b%n",isNegative(Double.NEGATIVE_INFINITY));

// interesting cases
// This will fail because we can't get to the float bits without an API and
// casting will round to zero
System.out.printf("{-1,1} (fail) %b%n",isNegative(-0.5f));

}

}
``````

This solution uses no conditional operators, but relies on catching two excpetions.

A division error equates to the number originally being “negative”. Alternatively, the number will eventually fall off the planet and throw a StackOverFlow exception if it is positive.

``````public static boolean isPositive( f)
{
int x;
try {
x = 1/((int)f + 1);
return isPositive(x+1);
} catch (StackOverFlow Error e) {
return true;

} catch (Zero Division Error e) {
return false;
}

}
``````

``````T sign(T x) {
if(x==0) return 0;
return x/Math.abs(x);
}
``````

Should work for every type T…

Alternatively, one can define abs(x) as Math.sqrt(x*x),
and if that is also cheating, implement your own square root function…

``````if (((Double)calcYourDouble()).toString().contains("-"))
doThis();
else doThat();
``````

Combined generics with double API. Guess it’s a bit of cheating, but at least we need to write only one method:

``````static <T extends Number> boolean isNegative(T number)
{
return ((number.doubleValue() * Double.POSITIVE_INFINITY) == Double.NEGATIVE_INFINITY);
}
``````

Two simple solutions. Works also for infinities and numbers -1 <= r <= 1
Will return “positive” for NaNs.

``````String positiveOrNegative(double number){
return (((int)(number/0.0))>>31 == 0)? "positive" : "negative";
}

String positiveOrNegative(double number){
return (number==0 || ((int)(number-1.0))>>31==0)? "positive" : "negative";
}
``````

There is a function is the math library called signnum.

It’s easy to do this like

``````private static boolean isNeg(T l) {
return (Math.abs(l-1)>Math.abs(l));
}
``````

`````` int number =0;