Checking If All Variables Have the Same Sign

Recently, I encountered a task that required determining whether all variables have the same sign (positive or negative), or even zero. A straightforward approach involves multiple comparisons, but a more elegant and potentially efficient solution utilizes the bitwise XOR operator.

Disclaimer: The problem I had actually prevented the value to be zero, but I leave it in to illustrate the problem.

Problem Statement

Given a set of variables (e.g., value1, value2, value3), determine if they all have the same sign.

Initial Approach

A common approach involves checking each variable explicitly:

if (
	( value1 >= 0 && value2 >= 0 && value3 >= 0 ) ||
	( value1 <= 0 && value2 <= 0 && value3 <= 0 )
) {
	// do something here
}

And in more strict way would be:

if (
	( value1 > 0 && value2 > 0 && value3 > 0 ) ||
	( value1 < 0 && value2 < 0 && value3 < 0 ) ||
	( value1 == value2 == value3 )
) {
	// do something here
}

This approach works but becomes cumbersome and error-prone when dealing with more variables..

XOR-Based Solution

A more compact way to solve this problem is by leveraging the bitwise XOR operator.

The XOR (exclusive OR) operator compares corresponding bits of two numbers and returns 1 if the bits are different and 0 if they are the same. This property makes XOR useful for detecting differences in sign bits. In the case of signed integers, the leftmost bit (most significant bit) represents the sign: 0 for positive numbers and 1 for negative numbers. When XOR is applied to two numbers with different signs, the result will have its sign bit set to 1, making it negative. If all numbers share the same sign, the XOR result will be non-negative.

if ( value1 ^ value2 ^ value3 >= 0) {
	// do something here
}

And again, more strict way (for last time, you get the idea :)):

if (
	( value1 ^ value2 ^ value3 >= 0 ) ||
	( value1 == value2 == value3 )
) {
	// do something here
}

This works in JavaScript because numbers are stored as 32-bit integers when performing bitwise operations. However, this method does not work directly with floating-point numbers in Python or Java due to how these languages handle bitwise operations on non-integer types.

Alternative Solutions for Python and Java

Python Approach (Using copysign)

Since floating-point numbers do not support bitwise operations directly, we can use the copysign function from the math module:

from math import copysign

if copysign(1, -value1) == copysign(1, -value2) == copysign(1, -value3):
	// do something here

This method effectively normalizes the sign of each number and compares them directly.

Java Approach (Using Raw Integer Bits)

In Java, we can convert floating-point values into their raw integer bit representations before applying XOR:

if ( 
	Float.floatToRawIntBits(value1) ^ 	
	Float.floatToRawIntBits(value2) ^
	Float.floatToRawIntBits(value3) >= 0
) {
	// do something here
}

For double values, we use doubleToRawLongBits instead:

if (
	Double.doubleToRawLongBits(value1) ^ 
	Double.doubleToRawLongBits(value2) ^ 
	Double.doubleToRawLongBits(value3) >= 0
) {
	// do something here
}

Handling Mixed Types

If dealing with a mix of integers, floats, and doubles, the approach remains similar:

if (
	value1 ^ 
	Float.floatToRawIntBits(value2) ^ 
	Double.doubleToRawLongBits(value3) >= 0
) {
	// do something here
}

Conclusion

Although this bitwise approach makes the code slightly longer, it is still more efficient than performing multiple explicit comparisons. Additionally, from an optimization perspective, bitwise operations are generally faster than conditional branching.

By leveraging language-specific techniques, we can ensure the solution works reliably across different programming environments.