Summary

This blog explains why simple right-shift truncation is often acceptable for fixed-point arithmetic in embedded systems and when it becomes a problem. It shows readers how to quantify the error and bias from right-shifts, when to apply cheap rounding hacks, and practical implementation notes for microcontroller firmware.

Key Takeaways

• Use right-shift truncation as an efficient default for many embedded fixed-point operations when error budgets permit.
• Quantify worst-case error and bias from truncation to decide if rounding is necessary for your application.
• Apply a cheap rounding technique (add half before shift) when you need unbiased results, and guard against overflow when doing so.
• Prefer arithmetic right shifts or explicit sign-extension for signed values to preserve correctness across compilers and architectures.
• Measure performance and test edge cases on target hardware to trade off accuracy versus speed in firmware.

Who Should Read This

Embedded firmware engineers working on microcontrollers who need practical guidance on fixed-point rounding trade-offs, accuracy budgeting, and performant numeric code.

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