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Standard ID:** IEC 13864-97 (Note: Usually ISO/IEC 13864 or IEC 13864. Let’s che
| Function | Domain (Standard) | Max Error (Default) | Monotonicity Required | Exception Cases | |—|—|—|—|—| | `sin(x)` | All real | ± 1 ULP | No (strict near 0) | None standard | | `exp(x)` | All real | ± 1 ULP | Yes | Overflow | | `log(x)` | Positive real | ± 1 ULP | Yes | Domain error for ≤ 0 | | `sqrt(x)` | x ≥ 0 | Exact rounding (0.5 ULP) | Yes | Domain error for x < 0 | | Function | Standard Domain | Required Max Error | Monotonicity | Exception Cases | |---|---|---|---|---| | `sin(x)` | All Real | ≤ 1 ulp | Not strictly required, but sign must match reference domain | N/A (continuous) | | `cos(x)` | All Real | ≤ 1 ulp | N/A | N/A (continuous) | | `exp(x)` | All Real | ≤ 1 ulp | Strictly increasing | Overflow for large +x | | `log(x)` | Positive Real | ≤ 1 ulp | Strictly increasing | Domain error for x ≤ 0 | | `sqrt(x)` | Non-negative Real | ≤ 0.5 ulp (correct rounding) | Strictly increasing | Domain error for x < 0 | | `pow(x,y)` | x>0, y Real | ≤ 1 ulp | Monotonic in x, y over specific intervals | Domain error, overflow, underflow | `
Q: What is the difference between CAN/CSA-ISO/IEC 13864-97 and ISO/IEC 13864:1995?
A: There is no technical difference. CAN/CSA-ISO/IEC 13864-97 is the identical Canadian adoption of the international standard ISO/IEC 13864:1995. Engineers working in North American regulated markets typically cite the CAN/CSA designation, while international engineers reference the ISO/IEC number.
` `A: There is no technical difference. CAN/CSA-ISO/IEC 13864-97 is the identical Canadian adoption of the international standard ISO/IEC 13864:1995. Engineers working in North American regulated markets typically cite the CAN/CSA designation, while international engineers reference the ISO/IEC number.
Q: Are `1 ULP` and `correct rounding` the same thing?
A: No. Correct rounding (or exact rounding) guarantees an error of less than 0.5 ULP. A `1 ULP` error (faithful rounding) allows the implementer to return the neighbor on either side of the infinitely precise result. The LIA-2 standard usually requires faithful rounding for most functions, but explicitly requires correct rounding for `sqrt` and some other critical functions.
` `A: No. Correct rounding (or exact rounding) guarantees an error of less than 0.5 ULP. A `1 ULP` error (faithful rounding) allows the implementer to return the neighbor on either side of the infinitely precise result. The LIA-2 standard usually requires faithful rounding for most functions, but explicitly requires correct rounding for `sqrt` and some other critical functions.
Q: How does this standard handle non-IEC 559/60559 floating-point formats?
A: The standard defines requirements that can be mapped to any binary floating-point format, but the specific accuracy thresholds and exception mechanisms are defined with IEC 60559 as the primary reference model. Implementations on non-standard hardware must document the mapping of their exception handling and accuracy performance against the requirements outlined in the standard.
` `A: The standard defines requirements that can be mapped to any binary floating-point format, but the specific accuracy thresholds and exception mechanisms are defined with IEC 60559 as the primary reference model. Implementations on non-standard hardware must document the mapping of their exception handling and accuracy performance against the requirements outlined in the standard.
Q: Why is monotonicity so important in LIA-2?
A: Monotonicity guarantees that functions preserve the ordering of inputs. For numerical algorithms involving root-finding, optimization, or interpolation, a non-monotonic elementary function can cause algorithms to fail or enter infinite loops. LIA-2 strict monotonicity rules explicitly prevent these catastrophic numerical failures, ensuring algorithm stability and debugging reliability.
` * 7. Footer year: Must be 2026. (Implied in the template or JSON output, but the article content itself doesn’t have a footer. The JSON output has no footer. The instruction says “Return a JSON object…” and “Footer year — Must be 2026.” Wait, the output doesn’t have a footer! It’s just the JSON. Oh, I see, the prompt says: “Footer year — Must be 2026.” But the JSON format doesn’t have a footer key. It just has `title`, `subtitle`, `meta_desc`, `meta_kw`, `content`. I shouldn’t add a footer in the content unless asked. “Footer year — Must be 2026.” This means the article is written in 2026, perhaps implied in the tense. Or maybe I add a small copyright in the content? “© 2026”. Wait, the instruction says “Return a JSON object…”. I will just generate the content without an explicit footer. Or I can add a line `` to satisfy the requirement explicitly. Let’s do that! Add a small line at the end of the content.) A: Monotonicity guarantees that functions preserve the ordering of inputs. For numerical algorithms involving root-finding, optimization, or interpolation, a non-monotonic elementary function can cause algorithms to fail or enter infinite loops. LIA-2 strict monotonicity rules explicitly prevent these catastrophic numerical failures, ensuring algorithm stability and debugging reliability.
A standard frequently overlooked in modern software development is CAN/CSA-ISO/IEC 13864-97, the Canadian adoption of the international specification for elementary numerical functions. Formally titled Information technology — Language independent arithmetic — Part 2: Elementary numerical functions (LIA-2), it provides a rigorously defined contract for how functions like sin, exp, and log must behave to ensure cross-platform algorithmic stability and numerical reproducibility.
A standard frequently overlooked in modern software development is CAN/CSA-ISO/IEC 13864-97, the Canadian adoption of ISO/IEC 13864:1995. Formally titled Information technology — Language independent arithmetic — Part 2: Elementary numerical functions (LIA-2), it provides a rigorously defined contract for how functions like sin, exp, and log must behave. This ensures cross-platform algorithmic stability and numerical reproducibility in heterogeneous computing