Is Floating-Point Multiplication Always Faster Than Division?

Comparing Floating Point Division and Multiplication Performance

Introduction:

In the realm of floating-point operations, the potential performance disparity between division and multiplication often sparks curiosity. This article aims to provide insights into this topic, addressing whether coding using division or multiplication yields performance advantages.

Performance Considerations:

Traditionally, division in floating-point computations was regarded as slower than multiplication. Modern processor architectures, however, offer varying levels of performance for these operations. Many CPUs can execute multiplication in a mere 1 or 2 clock cycles, while division typically requires more cycles.

For instance, divisions can surpass 24 cycles, as highlighted in an answer on the topic. This discrepancy stems from the algorithmic nature of these operations. Multiplication can be decomposed into numerous concurrent additions, whereas division involves iterative subtraction, a less efficient process in hardware.

Impact of Code Structure:

When analyzing the impact of code structure, the example provided in Update 1 demonstrates that division can have a notable performance overhead compared to multiplication. In the code snippet:

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

The division operation within the loop (i / f3) contributes to the increased execution time. Dividing by 2.0f (multiplication approach) would result in improved performance.

Underlying Reasons for Division's Complexity:

The architectural requirements for division are more complex than multiplication. Division involves finding the quotient of two numbers, a process that requires more intricate calculations. To mitigate this, some FP units employ an approximation technique called reciprocal multiplication, which speeds up division somewhat at the cost of accuracy.

Conclusion:

While floating-point division can be slower than multiplication on modern PC architectures, the performance disparity varies depending on the specific processor and the code structure being executed. For applications where performance is critical, opting for multiplication over division may provide a slight advantage. However, the relative performance impact of these operations should be assessed in the context of the overall algorithmic design.

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