Exact UNORM8 to Float
The article discusses the conversion of 8-bit unsigned integers to floating-point numbers in GPUs. It highlights the challenges and methods for achieving exact conversions without using doubles or division. The author proposes using a geometric series to approximate the conversion while maintaining precision.
- ▪GPUs convert UNORM formats represented as 8-bit unsigned integers to floating-point numbers by dividing by 255.
- ▪Exact conversion is acknowledged as expensive, leading to alternative methods being explored.
- ▪The author suggests using a geometric series to achieve an exact conversion without relying on doubles or division.
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Record
| Original publisher | The ryg blog |
| Canonical URL | https://fgiesen.wordpress.com/2024/11/06/exact-unorm8-to-float/ |
| Publication time | Wed, 03 Jun 2026 08:29:46 +0000 |
| Retrieval time | 2026-06-03T08:41:59.255Z |
| Last seen | 2026-06-03T08:41:59.255Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | IIWl5WXnvJg6 |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
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| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
Opening excerpt (first ~120 words) tap to expand
GPUs support UNORM formats that represent a number inside [0,1] as an 8-bit unsigned integer. In exact arithmetic, the conversion to a floating-point number is straightforward: take the integer and divide it by 255. 8-bit integers are for sure machine numbers (exactly represented) in float32 and so is 255, so if you’re willing to do a “proper” divide, that’s the end of it; both inputs are exact, so the result of the division is the same as the result of the computation in exact arithmetic rounded to the nearest float32 (as per active rounding mode anyway), which is the best we can hope for.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at The ryg blog.
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