Is Floating-Point Division Really Slower Than Multiplication in Modern CPUs?

Performance Implications of Floating-Point Division vs. Multiplication

It has been stated that floating-point divisions are computationally slower than multiplications. This article delves into this assertion and examines its validity in modern PC architecture.

Division in floating-point operations often surpasses multiplication in terms of time complexity. CPUs typically execute multiplication within 1-2 clock cycles, while division demands a more prolonged process.

To illustrate the performance gap, consider the following code snippets:

float f1 = 200f / 2;
// vs.
float f2 = 200f * 0.5;

In many cases, f2 will be calculated faster due to the inherent efficiency of multiplication over division.

This performance distinction also manifests in more complex operations. For instance, the following loop:

float f1;
float f2 = 2;
float f3 = 3;
for(i = 0; i < 1e8; i++)
{
  f1 = (i * f2 + i / f3) * 0.5; //or divide by 2.0f, respectively
}

will execute more efficiently using multiplication by 0.5 instead of dividing by 2.0f, as division necessitates iterative steps.

The significant performance difference stems from the architectural complexities of division. Unlike multiplication, which can be parallelized by converting it into multiple additions, division involves iterative subtraction, a less parallelizable operation. To compensate, some floating-point units employ reciprocal approximations and multiplication, sacrificing some accuracy for efficiency.

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