docs(frontend): massive modifications in the documentation

refs #812

docs/SUMMARY.md

@@ -7,7 +7,7 @@
 * [What is Concrete?](get-started/readme.md)
 * [Installation](get-started/installing.md)
 * [Quick start](get-started/quick_start.md)
-* [Limitations](get-started/limitations.md)
+* [Quick overview](get-started/quick_overview.md)
 * [Terminology](get-started/terminology.md)
 
 ## Operations
@@ -78,19 +78,19 @@
 ## Developers
 
 * [Contributing](dev/contributing.md)
+  * [Project layout](explanations/layout.md)
+  * [Compiler backend](explanations/backends/README.md)
+    * [Adding a new backend](explanations/backends/new_backend.md)
+  * [Optimizer](explanations/optimizer.md)
+  * [MLIR FHE dialects](explanations/dialects.md)
+    * [FHELinalg dialect](explanations/FHELinalgDialect.md)
+    * [FHE dialect](explanations/FHEDialect.md)
+    * [TFHE dialect](explanations/TFHEDialect.md)
+    * [Concrete dialect](explanations/ConcreteDialect.md)
+    * [Tracing dialect](explanations/TracingDialect.md)
+    * [Runtime dialect](explanations/RTDialect.md)
+    * [SDFG dialect](explanations/SDFGDialect.md)
+  * [Call FHE circuits from other languages](explanations/call_from_other_language.md)
 * [Release note](https://github.com/zama-ai/concrete/releases)
 * [Feature request](https://github.com/zama-ai/concrete/issues/new?assignees=\&labels=feature\&projects=\&template=features.md)
 * [Bug report](https://github.com/zama-ai/concrete/issues/new?assignees=\&labels=bug%2C+triage\&projects=\&template=bug_report.md)
-* [Project layout](explanations/layout.md)
-* [Compiler backend](explanations/backends/README.md)
-  * [Adding a new backend](explanations/backends/new_backend.md)
-* [Optimizer](explanations/optimizer.md)
-* [MLIR FHE dialects](explanations/dialects.md)
-  * [FHELinalg dialect](explanations/FHELinalgDialect.md)
-  * [FHE dialect](explanations/FHEDialect.md)
-  * [TFHE dialect](explanations/TFHEDialect.md)
-  * [Concrete dialect](explanations/ConcreteDialect.md)
-  * [Tracing dialect](explanations/TracingDialect.md)
-  * [Runtime dialect](explanations/RTDialect.md)
-  * [SDFG dialect](explanations/SDFGDialect.md)
-* [Call FHE circuits from other languages](explanations/call_from_other_language.md)

docs/get-started/quick_overview.md

@@ -0,0 +1,62 @@
+# Quick overview
+
+In this document, we give a quick overview of the philosophy behind Concrete.
+
+## Functions
+
+### Available FHE-friendly functions
+
+Concrete is a compiler, which aims to turn Python code into its FHE equivalent, in a process which is
+called the FHE compilation. The best efforts were made to simplify the process: in particular,
+exceptions apart, the same functions than the Python users are used to use are available. More complete
+list of available functions is given [in the reference section](../dev/compatibility.md).
+
+### Levelled vs non-levelled operations
+
+Basically, in the compiled circuit, there will be two kind of operations:
+- levelled operations, which are the additions, subtractions or multiplications by a constant; these
+operations are also called the linear operations
+- table lookup (TLU) operations, which are used to do anything which is not linear.
+
+TLU operations are essential to be able to compile complex functions. We explain their use in
+different sections of the documentation: [direct TLU use](../core-features/table_lookups.md) or
+[internal use to replace some non-linear functions](../core-features/non_linear_operations.md). We have
+tools in Concrete to replace univariate or multivariate non-linear functions (ie, functions of one
+or more inputs) by TLU.
+
+TLU are more costly that levelled operations, so we also explain how to limit their impact.
+
+Remark that matrix multiplication (aka Gemm -- General Matrix multiplication) and convolutions are
+levelled operations, since they imply only additions and multiplications by constant.
+
+### Conditional branches and loops
+
+Functions can't use conditional branches or non-constant-size loops,
+unless [modules](../compilation/composing_functions_with_modules.md) are used. However,
+control flow statements with constant values are allowed, for example,
+`for i in range(SOME_CONSTANT)`, `if os.environ.get("SOME_FEATURE") == "ON":`.
+
+## Data
+
+### Integers
+
+In Concrete, everything needs to be an integer. Users needing floats can quantize to integers before
+encryption, operate on integers and dequantize to floats after decryption: all of this is done for
+the user in Concrete ML. However, you can have floating-point intermediate values as long as they can
+be converted to an integer Table Lookup, for example, `(60 * np.sin(x)).astype(np.int64)`.
+
+### Scalars and tensors
+
+Functions can use scalar and tensors. As with Python, it is prefered to use tensorization, to make
+computations faster.
+
+### Inputs
+
+Inputs of a compiled function can be either encrypted or clear. Use of clear inputs is however
+quite limited. Remark that constants can appear in the program
+without much constraints, they are different from clear inputs which are dynamic.
+
+## Bit width constraints
+
+Bit width of encrypted values has a limit. We are constantly working on increasing the bit width limit.
+Exceeding this limit will trigger an error.