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78 lines
1.9 KiB
Markdown
78 lines
1.9 KiB
Markdown
# Table Lookup
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In this tutorial, we are going to go over the ways to perform table lookups in **concrete**. Please read [Compiling and Executing](../howto/COMPILING_AND_EXECUTING.md) before reading further to see how you can compile the functions below.
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## Direct table lookup
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**concrete** provides a special class to allow direct table lookups. Here is how to import and use it:
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```python
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from concrete.common.extensions.table import LookupTable
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table = LookupTable([2, 1, 3, 0])
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def f(x):
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return table[x]
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```
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where
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- `x = EncryptedScalar(UnsignedInteger(2))`
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results in
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```python
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engine.run(0) == 2
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engine.run(1) == 1
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engine.run(2) == 3
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engine.run(3) == 0
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```
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## Fused table lookup
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Direct tables are tedious to prepare by hand. When possible, **concrete** fuses the floating point operations into a single table lookup automatically. There are some limitations on fusing operations, which you can learn more about on the next tutorial, [Working With Floating Points](./WORKING_WITH_FLOATING_POINTS.md).
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Here is an example function that results in fused table lookup:
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```python
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def f(x):
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return 127 - (50 * (np.sin(x) + 1)).astype(np.uint32) # astype is to go back to integer world
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```
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where
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- `x = EncryptedScalar(UnsignedInteger(3))`
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results in
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```python
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engine.run(0) == 77
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engine.run(1) == 35
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engine.run(2) == 32
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engine.run(3) == 70
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engine.run(4) == 115
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engine.run(5) == 125
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engine.run(6) == 91
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engine.run(7) == 45
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```
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Initially, the function is converted to this operation graph
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and after floating point operations are fused, we get the following operation graph
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Internally, it uses the following lookup table
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```python
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table = LookupTable([50, 92, 95, 57, 12, 2, 36, 82])
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```
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which is calculated by:
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```python
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[(50 * (np.sin(x) + 1)).astype(np.uint32) for x in range(2 ** 3)]
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```
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