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Update SR to P3109 Release 3.1 definitions (#55)
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‎README.md‎

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@@ -7,7 +7,7 @@ handling various current and proposed floating point types:
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- [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754): Binary16, Binary32
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- [OCP Float8](https://www.opencompute.org/documents/ocp-8-bit-floating-point-specification-ofp8-revision-1-0-2023-06-20-pdf): E5M2, E4M3
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- [IEEE WG P3109](https://github.com/P3109/Public/blob/main/Shared%20Reports/IEEE%20WG%20P3109%20Interim%20Report.pdf): P3109_{K}p{P} for K > 2, and 1 <= P < K.
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- [IEEE WG P3109](https://github.com/P3109/Public/blob/main/IEEE%20WG%20P3109%20Interim%20Report%20(latest).pdf): P3109_{K}p{P} for K > 2, and 1 <= P < K.
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- [OCP MX Formats](https://www.opencompute.org/documents/ocp-microscaling-formats-mx-v1-0-spec-final-pdf): E2M1, M2M3, E3M2, E8M0, INT8, and the MX block formats.
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The library favours readability and extensibility over speed (although the *_ndarray functions are reasonably fast for large arrays, see the [benchmarking notebook](docs/source/04-benchmark.ipynb)).
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For example, here's a table from the [02-value-stats](docs/source/02-value-stats.ipynb) notebook:
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|name|B: Bits in the format|P: Precision in bits|E: Exponent field width in bits|Exact in float16?|Exact in float32?|0<x<1|1<x<Inf|minSubnormal|maxSubnormal|minNormal|maxNormal| |
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|--------------|-----|-----|-----|--------|--------|-------|-------|----------------|----------------|-------------|---------------|
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| p3109_k3p2sf | 3 | 2 | 1 | True | True | 1 | 1 | 0.5 | 0.5 | 1 | 1.5 |
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| ocp_e2m1 | 4 | 2 | 2 | True | True | 1 | 5 | 0.5 | 0.5 | 1 | 6 |
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| p3109_k4p2sf | 4 | 2 | 2 | True | True | 3 | 3 | 0.25 | 0.25 | 0.5 | 3 |
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| ocp_e2m3 | 6 | 4 | 2 | True | True | 7 | 23 | 0.125 | 0.875 | 1 | 7.5 |
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| ocp_e3m2 | 6 | 3 | 3 | True | True | 11 | 19 | 0.0625 | 0.1875 | 0.25 | 28 |
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| p3109_k6p3sf | 6 | 3 | 3 | True | True | 15 | 15 | 0.03125 | 0.09375 | 0.125 | 14 |
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| p3109_k6p4sf | 6 | 4 | 2 | True | True | 15 | 15 | 0.0625 | 0.4375 | 0.5 | 3.75 |
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| ocp_e4m3 | 8 | 4 | 4 | True | True | 55 | 70 | 2^-9 | 7/4*2^-7 | 0.015625 | 448 |
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| ocp_e5m2 | 8 | 3 | 5 | True | True | 59 | 63 | 2^-16 | 3/2*2^-15 | 2^-14 | 57344 |
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| p3109_k8p1se | 8 | 1 | 7 | False | True | 63 | 62 | n/a | n/a | 2^-63 | 2^62 |
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| p3109_k8p1ue | 8 | 1 | 8 | False | True | 127 | 125 | n/a | n/a | 2^-127 | 2^125 |
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| p3109_k8p3se | 8 | 3 | 5 | True | True | 63 | 62 | 2^-17 | 3/2*2^-16 | 2^-15 | 49152 |
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| p3109_k8p3sf | 8 | 3 | 5 | True | True | 63 | 63 | 2^-17 | 3/2*2^-16 | 2^-15 | 57344 |
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| p3109_k8p3ue | 8 | 3 | 6 | False | True | 127 | 125 | 2^-33 | 3/2*2^-32 | 2^-31 | 5/4*2^31 |
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| p3109_k8p3uf | 8 | 3 | 6 | False | True | 127 | 126 | 2^-33 | 3/2*2^-32 | 2^-31 | 3/2*2^31 |
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| p3109_k8p4se | 8 | 4 | 4 | True | True | 63 | 62 | 2^-10 | 7/4*2^-8 | 0.0078125 | 224 |
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| p3109_k8p4sf | 8 | 4 | 4 | True | True | 63 | 63 | 2^-10 | 7/4*2^-8 | 0.0078125 | 240 |
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| p3109_k8p4ue | 8 | 4 | 5 | True | True | 127 | 125 | 2^-18 | 7/4*2^-16 | 2^-15 | 53248 |
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| p3109_k8p4uf | 8 | 4 | 5 | True | True | 127 | 126 | 2^-18 | 7/4*2^-16 | 2^-15 | 57344 |
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| p3109_k8p7sf | 8 | 7 | 1 | True | True | 63 | 63 | 0.015625 | 63/32*2^-1 | 1 | 127/64*2^0 |
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| p3109_k8p8uf | 8 | 8 | 1 | True | True | 127 | 126 | 0.0078125 | 127/64*2^-1 | 1 | 127/64*2^0 |
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| binary16 | 16 | 11 | 5 | True | True | 15359 | 16383 | 2^-24 | 1023/512*2^-15 | 2^-14 | 65504 |
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| bfloat16 | 16 | 8 | 8 | False | True | 16255 | 16383 | 2^-133 | 127/64*2^-127 | 2^-126 | 255/128*2^127 |
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| ocp_e8m0 | 8 | 1 | 8 | False | True | 127 | 127 | n/a | n/a | 2^-127 | 2^127 |
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| ocp_int8 | 8 | 8 | 0 | True | True | 63 | 63 | 0.015625 | 127/64*2^0 | n/a | n/a |
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|name|B: Bits in the format|P: Precision in bits|E: Exponent field width in bits|0<x<1|1<x<Inf|minSubnormal|maxSubnormal|minNormal|maxNormal|Exact in float16?|Exact in float32?|
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|--------------|-----|-----|-----|-------|-------|----------------|----------------|-------------|---------------|--------|--------|
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| p3109_k3p2sf | 3 | 2 | 1 | 1 | 1 | 0.5 | 0.5 | 1 | 1.5 | True | True |
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| ocp_e2m1 | 4 | 2 | 2 | 1 | 5 | 0.5 | 0.5 | 1 | 6 | True | True |
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| p3109_k4p2sf | 4 | 2 | 2 | 3 | 3 | 0.25 | 0.25 | 0.5 | 3 | True | True |
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| ocp_e2m3 | 6 | 4 | 2 | 7 | 23 | 0.125 | 0.875 | 1 | 7.5 | True | True |
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| ocp_e3m2 | 6 | 3 | 3 | 11 | 19 | 0.0625 | 0.1875 | 0.25 | 28 | True | True |
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| p3109_k6p3sf | 6 | 3 | 3 | 15 | 15 | 0.03125 | 0.09375 | 0.125 | 14 | True | True |
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| p3109_k6p4sf | 6 | 4 | 2 | 15 | 15 | 0.0625 | 0.4375 | 0.5 | 3.75 | True | True |
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| ocp_e4m3 | 8 | 4 | 4 | 55 | 70 | 2^-9 | 7/4*2^-7 | 0.015625 | 448 | True | True |
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| ocp_e5m2 | 8 | 3 | 5 | 59 | 63 | 2^-16 | 3/2*2^-15 | 2^-14 | 57344 | True | True |
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| p3109_k8p1se | 8 | 1 | 7 | 63 | 62 | n/a | n/a | 2^-63 | 2^62 | False | True |
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| p3109_k8p1ue | 8 | 1 | 8 | 127 | 125 | n/a | n/a | 2^-127 | 2^125 | False | True |
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| p3109_k8p3se | 8 | 3 | 5 | 63 | 62 | 2^-17 | 3/2*2^-16 | 2^-15 | 49152 | True | True |
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| p3109_k8p3sf | 8 | 3 | 5 | 63 | 63 | 2^-17 | 3/2*2^-16 | 2^-15 | 57344 | True | True |
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| p3109_k8p3ue | 8 | 3 | 6 | 127 | 125 | 2^-33 | 3/2*2^-32 | 2^-31 | 5/4*2^31 | False | True |
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| p3109_k8p3uf | 8 | 3 | 6 | 127 | 126 | 2^-33 | 3/2*2^-32 | 2^-31 | 3/2*2^31 | False | True |
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| p3109_k8p4se | 8 | 4 | 4 | 63 | 62 | 2^-10 | 7/4*2^-8 | 0.0078125 | 224 | True | True |
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| p3109_k8p4sf | 8 | 4 | 4 | 63 | 63 | 2^-10 | 7/4*2^-8 | 0.0078125 | 240 | True | True |
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| p3109_k8p4ue | 8 | 4 | 5 | 127 | 125 | 2^-18 | 7/4*2^-16 | 2^-15 | 53248 | True | True |
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| p3109_k8p4uf | 8 | 4 | 5 | 127 | 126 | 2^-18 | 7/4*2^-16 | 2^-15 | 57344 | True | True |
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| p3109_k8p7sf | 8 | 7 | 1 | 63 | 63 | 0.015625 | 63/32*2^-1 | 1 | 127/64*2^0 | True | True |
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| p3109_k8p8uf | 8 | 8 | 1 | 127 | 126 | 0.0078125 | 127/64*2^-1 | 1 | 127/64*2^0 | True | True |
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| binary16 | 16 | 11 | 5 | 15359 | 16383 | 2^-24 | 1023/512*2^-15 | 2^-14 | 65504 | True | True |
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| bfloat16 | 16 | 8 | 8 | 16255 | 16383 | 2^-133 | 127/64*2^-127 | 2^-126 | 255/128*2^127 | False | True |
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| ocp_e8m0 | 8 | 1 | 8 | 127 | 127 | n/a | n/a | 2^-127 | 2^127 | False | True |
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| ocp_int8 | 8 | 8 | 0 | 63 | 63 | 0.015625 | 127/64*2^0 | n/a | n/a | True | True |
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#### Notes
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All NaNs are the same, with no distinction between signalling or quiet,

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