Replacing Floating-Point Arithmetic with Integer Arithmetic in C

In C programming, particularly for embedded systems, replacing floating-point arithmetic with integer arithmetic (often called fixed-point arithmetic) is a well-known technique to improve performance on processors that lack floating-point units (FPUs) or where execution speed and memory are limited.

Goal:

Use integer addition to approximate floating-point addition by scaling your numbers.

1. Concept of Fixed-Point Arithmetic

Instead of working directly with floats, multiply your floating-point values by a scaling factor (a power of 10 or 2) and treat them as integers.

For example:

This works because:

(1.234 + 2.000) ≈ (1234 + 2000) / 1000

2. Code Example

Output:

Approximate sum = 3.234

3. Why Use This?

• Speed: Integer addition is faster than float addition on most MCUs.
• Size: Integer arithmetic generates smaller machine code on systems without FPU.
• Determinism: Often more predictable timing than float operations.

4. Cautions

• Precision loss: Be careful with large numbers and small scales—overflow or rounding errors can occur.
• Overflow: Use larger types (e.g., int32_t or int64_t) if needed.
• Division artifacts: Only divide at the end to reduce cumulative error.

5. Conclusion

Approximating floating-point operations with scaled integer arithmetic is a powerful technique in C, especially for embedded systems where performance and memory efficiency are critical. By applying a fixed scaling factor, developers can perform precise and fast calculations using simple integer operations. While this method introduces some limitations in precision and range, it offers a reliable alternative to floating-point math on constrained hardware—making it an essential skill for embedded and systems-level programmers.