FROUND

Returns the closest 32-bit single precision float representation of a number.

Syntax:

FROUND(number)

Example:

If A1 contains 10:

FROUND(A1)

returns 10

If A1 contains -10:

FROUND(A1)

returns -10

Number:

Result:

10

Application:

Optimizing a 3D Graphics Engine

In 3D graphics, many calculations are performed on vectors and matrices. To save memory and increase rendering speed, some engines might choose to store position, rotation, and scale data in a single-precision floating-point format (32-bit) instead of a double-precision (64-bit). This is a common practice in game development and real-time simulations.

Problem: A physics engine calculates the position of an object using high-precision (double-precision) physics, but the rendering engine needs to display this object using low-precision (single-precision) coordinates. A simple ROUND() won't work correctly because it rounds to the nearest integer, not to the nearest single-precision float. Simply casting the number might not produce the most accurate single-precision representation.

Solution: The FROUND function can be used to convert the high-precision position data into the nearest single-precision representation, ensuring consistency between the physics and rendering engines.

Let's consider a scenario where an object's position is calculated in a physics simulation.

Initial Position (Double-Precision): 123.45678912345678

This number is very precise. When we need to pass this position to the graphics card for rendering, we want to use the most accurate single-precision representation.

Here's a table illustrating the difference between using no rounding, ROUND(), and FROUND():

	Method	Formula	Result	Description
	A	B	C	D
1	Original	123.45678912345678	123.45678912345679	The original double-precision number.
2	Simple Rounding	ROUND(123.45678912345678)	123	Rounds to the nearest integer. This loses a significant amount of precision and would cause the object to "jump" to a new location.
3	FROUND	FROUND(123.45678912345678)	123.456787109	Returns the single-precision floating-point representation closest to the original number. This is the value that would be stored in a 32-bit float, which is precisely what the graphics card expects.

As you can see, FROUND provides the most accurate conversion for this specific use case, preserving as much of the original value as possible within the constraints of the single-precision format. Without FROUND, the rendering could be inaccurate, leading to visual glitches or misalignment between the simulated and rendered positions.