fmics21: update README, correct typos and add links to verified functions

README.md

 Frama-C Verification of Paparazzi
 =================================
-This GitLab project is a fork of Paparazzi UAV autopilot
-(https://github.com/paparazzi/paparazzi) that verify
-`pprz_algebra` library using Frama-C.
 
-This project adds the ACSL annotations in the code and provide a
-script to automatically launch the verification. Frama-C
-analyses the code and checks the absence of RTE (_RunTime
-Errors_) and some functional properties.
+This GitLab repository is a fork of Paparazzi UAV autopilot repository
+(https://github.com/paparazzi/paparazzi). The aim of this project is
+to verify the `pprz_algebra` library using Frama-C.
+
+This project adds ACSL annotations and provides a script to
+automatically launch Frama-C. Frama-C analyses the code, checks for
+the absence of RTE (_RunTime Errors_) and verify some functional
+properties.
 
 Required software
 -----------------
@@ -26,81 +27,102 @@ fixes a bug that prevented proving some goals. Also, the
 _statement contracts_ are used in the proofs, but this feature
 has been removed in newer versions.
 
-How to run the verification:
+How to launch the verification process
 -------------
+
+First, go to the `sw/airborne` directory:
+
 ```
 cd sw/airborne
 ```
 
 Update the variable `FRAMAC_PREFIX` in `frama-c-analysis.sh`
 with the path of the directory containing Frama-C binary. Then,
-launch the script that start the analysis:
+launch the script that starts the analysis:
 
 ```
 ./frama-c-analysis.sh
 ```
 
-The WP smoke tests can be enable with the environment variable
-`SMOKE` as follow:
+The WP smoke tests can be enabled with the environment variable
+`SMOKE` as follows:
 
 ```
 SMOKE=1 ./frama-c-analysis.sh
 ```
 
-Quick descritpion of modified files:
+Quick description of modified files
 ------------------------------------
 
-- `sw/airborne/frama-c-analysis.sh`: Script to automatically
-launch the verification using Frama-C.
-- `sw/airborne/output-frama-c-analysis.sh`: A python script
-used by `frama-c-analysis.sh` to read and analyse the results
-from Frama-C.
-- `sw/airborne/math/pprz_algebra_(int|float|double).(h|c)`:
-Mathematical library of Paparazzi that has been verified. These
-files have been annotated with ACSL.
-- `sw/airborne/math/pprz_algebra_(int|float|double)_frama_c.h`:
-Files containing definition of predicates, lemma and logical
-functions used to verify the absence of RTE in the library.
+- `sw/airborne/frama-c-analysis.sh`: a shell script that automatically
+launches the verification using Frama-C.
+- `sw/airborne/output-frama-c-analysis.sh`: a Python script used by
+`frama-c-analysis.sh` to read and analyse the results from Frama-C.
+- `sw/airborne/math/pprz_algebra_(int|float|double).(h|c)`: the
+mathematical library of Paparazzi that has been verified. These files
+have been annotated with ACSL.
+- `sw/airborne/math/pprz_algebra_(int|float|double)_frama_c.h`: files
+containing definition of predicates, lemmas and logical functions used
+to verify the absence of RTE in the library.
 - `sw/airborne/math/pprz_algebra_float_convert_rmat_frama_c.h`:
-Definition of predicates, lemma and logical functions for the
+definition of predicates, lemmas and logical functions for the
 verification of functional properties.
-- `sw/airborne/.frama-c/wp/interactive`: All the Coq scripts
-containing the proof of certain lemma.
-- `sw/airborne/.frama-c/wp/script`: All WP scripts containing
-the tactics used to prove some goals.
+- `sw/airborne/.frama-c/wp/interactive`: Coq scripts containing the
+proof lemmas.
+- `sw/airborne/.frama-c/wp/script`: WP scripts containing the tactics
+used to prove some goals.
 
-The verification:
------------------
-The Frama-C verification combines the analysis of the [EVA](https://frama-c.com/fc-plugins/eva.html) and
-[WP](https://frama-c.com/fc-plugins/wp.html) plugins. The
-plugin EVA requires a program entry point (a
-main or a function) to start its analysis. The script
-`frama-c-analysis.sh` find automatically all the function's
-name of the library using ctags. Then, the Frama-C verification is
-launched for every function `FUNCTION` with the following
-parameters:
-
-- `-rte`: Add RTE annotations in the code.
-- `-no-warn-left-shift-negative`: Allow left shift for negative values.
-- `-eva -lib-entry -main $FUNCTION`: Launch EVA analysis with
+Verification process
+---------------------
+
+The verification process combines the analysis of the
+[EVA](https://frama-c.com/fc-plugins/eva.html) and
+[WP](https://frama-c.com/fc-plugins/wp.html) plugins of Frama-C. The
+EVA plugin requires a program entry point (a `main` or a function) to
+start its analysis. The script `frama-c-analysis.sh` finds
+automatically all the names of the functions in the library using
+ctags. Then, verification is launched for every function `FUNCTION`
+with the following parameters:
+
+- `-rte`: adds RTE annotations in the code.
+- `-no-warn-left-shift-negative`: allows left shift for negative values.
+- `-eva -lib-entry -main $FUNCTION`: launches EVA analysis with
 `$FUNCTION` as the entry point. The initial state is determined by
-the _preconditions_ in the contract of the function.
-- `-wp-fct $FUNCTION`: Launch the WP verification with the options:
-  - `-wp-cache update`: Enable and use the cache.
-  - `-wp-model real+Cast`: Enable the real model to represent the
-  arithmetic on floating-point numbers. The `Cast` option enables
-  the usage of cast in the code.
+the _preconditions_ specified in the contract of the function.
+- `-wp-fct $FUNCTION`: launches the WP verification with the following
+  options:
+  - `-wp-cache update`: enables and uses cache.
+  - `-wp-model real+Cast`: enables the `real` model to represent the
+  arithmetic on floating-point numbers. The `Cast` option enables the
+  usage of cast in the code.
   - `-wp-prover alt-ergo,cvc4-strings-ce,z3,z3-ce,z3-nobv,tip`:
-  Add the different provers needed to verify the goals.
-- `-cpp-extra-args=-I../include`: Add the include directory of
+  adds the different provers needed to verify the goals.
+- `-cpp-extra-args=-I../include`: adds the include directory of
   Paparazzi.
-- `-cpp-extra-args=-DFRAMA_C_ANALYSIS`: Defined a C constant
-  in order to remove certain portions of code that are not
-  supported by Frama-C.
+- `-cpp-extra-args=-DFRAMA_C_ANALYSIS`: defines a C constant in order
+  to remove certain portions of code that are not supported by
+  Frama-C.
+
+Quick link to functions described in FMICS 2021 paper
+-----------------------------------------------------
+
+- the
+  [`float_rmat\_of_quat`](https://gitlab.isae-supaero.fr/b.pollien/paparazzi-frama-c/-/blob/fmics-2021/sw/airborne/math/pprz_algebra_float.h#L633)
+  function
+- the
+  [`float_quat_of_rmat`](https://gitlab.isae-supaero.fr/b.pollien/paparazzi-frama-c/-/blob/fmics-2021/sw/airborne/math/pprz_algebra_float.h#L946)
+  function
+- the
+  [`float_rmat_of_eulers_321`](https://gitlab.isae-supaero.fr/b.pollien/paparazzi-frama-c/-/blob/fmics-2021/sw/airborne/math/pprz_algebra_float.h#L612)
+  function
+- the
+  [`float_rmat_of_eulers_312`](https://gitlab.isae-supaero.fr/b.pollien/paparazzi-frama-c/-/blob/fmics-2021/sw/airborne/math/pprz_algebra_float.h#L620)
+  function
+
 
 More information about Paparazzi
 --------------------------------
 
 To have information about Paparazzi, go directly on the
-[website](https://wiki.paparazziuav.org/wiki/Main_Page) or on
-the [GitLab project](https://github.com/paparazzi/paparazzi).
\ No newline at end of file
+[website](https://wiki.paparazziuav.org/wiki/Main_Page) or on the
+[GitLab project](https://github.com/paparazzi/paparazzi).