diff --git a/milli/tests/assets/test_set.ndjson b/milli/tests/assets/test_set.ndjson
new file mode 100644
index 000000000..f219ab7e9
--- /dev/null
+++ b/milli/tests/assets/test_set.ndjson
@@ -0,0 +1,17 @@
+{"id":"A","word_rank":0,"typo_rank":1,"proximity_rank":15,"attribute_rank":505,"exact_rank":5,"asc_desc_rank":0,"title":"hell o","description":"hell o is the fourteenth episode of the american television series glee performing songs with this word","tag":"blue","":""}
+{"id":"B","word_rank":2,"typo_rank":0,"proximity_rank":0,"attribute_rank":0,"exact_rank":4,"asc_desc_rank":1,"title":"hello","description":"hello is a song recorded by english singer songwriter adele","tag":"red","":""}
+{"id":"C","word_rank":0,"typo_rank":1,"proximity_rank":8,"attribute_rank":336,"exact_rank":4,"asc_desc_rank":2,"title":"hell on earth","description":"hell on earth is the third studio album by american hip hop duo mobb deep","tag":"blue","":""}
+{"id":"D","word_rank":0,"typo_rank":1,"proximity_rank":10,"attribute_rank":757,"exact_rank":4,"asc_desc_rank":3,"title":"hell on wheels tv series","description":"the construction of the first transcontinental railroad across the united states in the world","tag":"red","":""}
+{"id":"E","word_rank":2,"typo_rank":0,"proximity_rank":0,"attribute_rank":0,"exact_rank":1,"asc_desc_rank":4,"title":"hello kitty","description":"also known by her full name kitty white is a fictional character produced by the japanese company sanrio","tag":"green","":""}
+{"id":"F","word_rank":2,"typo_rank":1,"proximity_rank":0,"attribute_rank":1017,"exact_rank":5,"asc_desc_rank":5,"title":"laptop orchestra","description":"a laptop orchestra lork or lo is a chamber music ensemble consisting primarily of laptops like helo huddersfield experimental laptop orchestra","tag":"blue","":""}
+{"id":"G","word_rank":1,"typo_rank":0,"proximity_rank":0,"attribute_rank":0,"exact_rank":3,"asc_desc_rank":5,"title":"hello world film","description":"hello world is a 2019 japanese animated sci fi romantic drama film directed by tomohiko ito and produced by graphinica","tag":"red","":""}
+{"id":"H","word_rank":1,"typo_rank":0,"proximity_rank":1,"attribute_rank":0,"exact_rank":3,"asc_desc_rank":4,"title":"world hello day","description":"holiday observed on november 21 to express that conflicts should be resolved through communication rather than the use of force","tag":"green","":""}
+{"id":"I","word_rank":0,"typo_rank":0,"proximity_rank":8,"attribute_rank":338,"exact_rank":3,"asc_desc_rank":3,"title":"hello world song","description":"hello world is a song written by tom douglas tony lane and david lee and recorded by american country music group lady antebellum","tag":"blue","":""}
+{"id":"J","word_rank":1,"typo_rank":0,"proximity_rank":1,"attribute_rank":1,"exact_rank":3,"asc_desc_rank":2,"title":"hello cruel world","description":"hello cruel world is an album by new zealand band tall dwarfs","tag":"green","":""}
+{"id":"K","word_rank":0,"typo_rank":2,"proximity_rank":9,"attribute_rank":670,"exact_rank":5,"asc_desc_rank":1,"title":"ello creation system","description":"in few word ello was a construction toy created by the american company mattel to engage girls in construction play","tag":"red","":""}
+{"id":"L","word_rank":0,"typo_rank":0,"proximity_rank":2,"attribute_rank":250,"exact_rank":4,"asc_desc_rank":0,"title":"good morning world","description":"good morning world is an american sitcom broadcast on cbs tv during the 1967 1968 season","tag":"blue","":""}
+{"id":"M","word_rank":0,"typo_rank":0,"proximity_rank":0,"attribute_rank":0,"exact_rank":0,"asc_desc_rank":0,"title":"hello world america","description":"a perfect match for a perfect engine using the query hello world america","tag":"red","":""}
+{"id":"N","word_rank":0,"typo_rank":0,"proximity_rank":0,"attribute_rank":0,"exact_rank":1,"asc_desc_rank":4,"title":"hello world america unleashed","description":"a very good match for a very good engine using the query hello world america","tag":"green","":""}
+{"id":"O","word_rank":0,"typo_rank":0,"proximity_rank":0,"attribute_rank":10,"exact_rank":0,"asc_desc_rank":6,"title":"a perfect match for a perfect engine using the query hello world america","description":"hello world america","tag":"blue","":""}
+{"id":"P","word_rank":0,"typo_rank":0,"proximity_rank":0,"attribute_rank":12,"exact_rank":1,"asc_desc_rank":3,"title":"a very good match for a very good engine using the query hello world america","description":"hello world america unleashed","tag":"red","":""}
+{"id":"Q","word_rank":1,"typo_rank":0,"proximity_rank":0,"attribute_rank":0,"exact_rank":3,"asc_desc_rank":2,"title":"hello world","description":"a hello world program generally is a computer program that outputs or displays the message hello world","tag":"green","":""}
diff --git a/milli/tests/mod.rs b/milli/tests/mod.rs
new file mode 100644
index 000000000..11095a6a9
--- /dev/null
+++ b/milli/tests/mod.rs
@@ -0,0 +1 @@
+mod search;
diff --git a/milli/tests/search/mod.rs b/milli/tests/search/mod.rs
new file mode 100644
index 000000000..609787712
--- /dev/null
+++ b/milli/tests/search/mod.rs
@@ -0,0 +1,137 @@
+use milli::{Criterion, Index, DocumentId};
+use milli::update::{IndexDocuments, UpdateFormat, Settings};
+
+use big_s::S;
+use heed::EnvOpenOptions;
+use maplit::{hashmap, hashset};
+use serde::Deserialize;
+use slice_group_by::GroupBy;
+
+mod query_criteria;
+
+pub const TEST_QUERY: &'static str = "hello world america";
+
+pub const EXTERNAL_DOCUMENTS_IDS: &[&str; 17] = &["A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q"];
+
+pub const CONTENT: &str = include_str!("../assets/test_set.ndjson");
+
+pub fn setup_search_index_with_criteria(criteria: &[Criterion]) -> Index {
+    let path = tempfile::tempdir().unwrap();
+    let mut options = EnvOpenOptions::new();
+    options.map_size(10 * 1024 * 1024); // 10 MB
+    let index = Index::new(options, &path).unwrap();
+
+    let mut wtxn = index.write_txn().unwrap();
+
+    let mut builder = Settings::new(&mut wtxn, &index, 0);
+
+    let criteria = criteria.iter().map(|c| c.to_string()).collect();
+    builder.set_criteria(criteria);
+    builder.set_filterable_fields(hashset!{
+        S("tag"),
+        S("unexisting_field"),
+        S("asc_desc_rank"),
+        S("unexisting_field"),
+    });
+    builder.set_synonyms(hashmap!{
+        S("hello") => vec![S("good morning")],
+        S("world") => vec![S("earth")],
+        S("america") => vec![S("the united states")],
+    });
+    builder.set_searchable_fields(vec![S("title"),S("description")]);
+    builder.execute(|_, _| ()).unwrap();
+
+    // index documents
+    let mut builder = IndexDocuments::new(&mut wtxn, &index, 0);
+    builder.update_format(UpdateFormat::JsonStream);
+    builder.enable_autogenerate_docids();
+    builder.execute(CONTENT.as_bytes(), |_, _| ()).unwrap();
+
+    wtxn.commit().unwrap();
+
+    index
+}
+
+#[allow(dead_code)]
+pub fn external_to_internal_ids(index: &Index, external_ids: &[&str]) -> Vec<DocumentId> {
+    let mut rtxn = index.read_txn().unwrap();
+    let docid_map = index.external_documents_ids(&mut rtxn).unwrap();
+    external_ids.iter().map(|id| docid_map.get(id).unwrap()).collect()
+}
+
+pub fn internal_to_external_ids(index: &Index, internal_ids: &[DocumentId]) -> Vec<String> {
+    let mut rtxn = index.read_txn().unwrap();
+    let docid_map = index.external_documents_ids(&mut rtxn).unwrap();
+    let docid_map: std::collections::HashMap<_, _> = EXTERNAL_DOCUMENTS_IDS.iter().map(|id| (docid_map.get(id).unwrap(), id)).collect();
+    internal_ids.iter().map(|id| docid_map.get(id).unwrap().to_string()).collect()
+}
+
+fn fetch_dataset() -> Vec<TestDocument> {
+    serde_json::Deserializer::from_str(CONTENT).into_iter().map(|r| r.unwrap()).collect()
+}
+
+pub fn expected_order(criteria: &[Criterion], autorize_typo: bool, optional_words: bool) -> Vec<TestDocument> {
+    let dataset = fetch_dataset();
+    let mut groups: Vec<Vec<TestDocument>> = vec![dataset];
+
+    for criterion in criteria {
+        let mut new_groups = Vec::new();
+        for group in groups.iter_mut() {
+            match criterion {
+                Criterion::Attribute => {
+                    group.sort_by_key(|d| d.attribute_rank);
+                    new_groups.extend(group.linear_group_by_key(|d| d.attribute_rank).map(Vec::from));
+                },
+                Criterion::Exactness => {
+                    group.sort_by_key(|d| d.exact_rank);
+                    new_groups.extend(group.linear_group_by_key(|d| d.exact_rank).map(Vec::from));
+                },
+                Criterion::Proximity => {
+                    group.sort_by_key(|d| d.proximity_rank);
+                    new_groups.extend(group.linear_group_by_key(|d| d.proximity_rank).map(Vec::from));
+                },
+                Criterion::Typo => {
+                    group.sort_by_key(|d| d.typo_rank);
+                    new_groups.extend(group.linear_group_by_key(|d| d.typo_rank).map(Vec::from));
+                },
+                Criterion::Words => {
+                    group.sort_by_key(|d| d.word_rank);
+                    new_groups.extend(group.linear_group_by_key(|d| d.word_rank).map(Vec::from));
+                },
+                Criterion::Asc(_) => {
+                    group.sort_by_key(|d| d.asc_desc_rank);
+                    new_groups.extend(group.linear_group_by_key(|d| d.asc_desc_rank).map(Vec::from));
+                },
+                Criterion::Desc(_) => {
+                    group.sort_by_key(|d| std::cmp::Reverse(d.asc_desc_rank));
+                    new_groups.extend(group.linear_group_by_key(|d| d.asc_desc_rank).map(Vec::from));
+                },
+            }
+        }
+        groups = std::mem::take(&mut new_groups);
+    }
+
+    if autorize_typo && optional_words {
+        groups.into_iter().flatten().collect()
+    } else if optional_words {
+        groups.into_iter().flatten().filter(|d| d.typo_rank == 0).collect()
+    } else if autorize_typo {
+        groups.into_iter().flatten().filter(|d| d.word_rank == 0).collect()
+    } else {
+        groups.into_iter().flatten().filter(|d| d.word_rank == 0 && d.typo_rank == 0).collect()
+    }
+}
+
+#[derive(Debug, Clone, Deserialize)]
+pub struct TestDocument {
+    pub id: String,
+    pub word_rank: u32,
+    pub typo_rank: u32,
+    pub proximity_rank: u32,
+    pub attribute_rank: u32,
+    pub exact_rank: u32,
+    pub asc_desc_rank: u32,
+    pub title: String,
+    pub description: String,
+    pub tag: String,
+}
diff --git a/milli/tests/search/query_criteria.rs b/milli/tests/search/query_criteria.rs
new file mode 100644
index 000000000..11d9b9e49
--- /dev/null
+++ b/milli/tests/search/query_criteria.rs
@@ -0,0 +1,531 @@
+use milli::{Search, SearchResult, Criterion};
+use big_s::S;
+
+use crate::search::{self, EXTERNAL_DOCUMENTS_IDS};
+
+#[test]
+fn none() {
+    let criteria = vec![];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, true, true).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn words() {
+    let criteria = vec![Criterion::Words];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, true, true).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn attribute() {
+    let criteria = vec![Criterion::Attribute];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, true, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn exactness() {
+    let criteria = vec![Criterion::Exactness];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, true, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn proximity() {
+    let criteria = vec![Criterion::Proximity];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, true, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn typo() {
+    let criteria = vec![Criterion::Typo];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, true, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn asc() {
+    let criteria = vec![Criterion::Asc(S("asc_desc_rank"))];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, true, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn desc() {
+    let criteria = vec![Criterion::Desc(S("asc_desc_rank"))];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, true, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn none_0_typo() {
+    let criteria = vec![];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.authorize_typos(false);
+    search.optional_words(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, false, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn attribute_0_typo() {
+    let criteria = vec![Criterion::Attribute];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+    search.authorize_typos(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, false, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn exactness_0_typo() {
+    let criteria = vec![Criterion::Exactness];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+    search.authorize_typos(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, false, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn proximity_0_typo() {
+    let criteria = vec![Criterion::Proximity];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+    search.authorize_typos(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, false, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn typo_0_typo() {
+    let criteria = vec![Criterion::Typo];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+    search.authorize_typos(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, false, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn asc_0_typo() {
+    let criteria = vec![Criterion::Asc(S("asc_desc_rank"))];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+    search.authorize_typos(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, false, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn desc_0_typo() {
+    let criteria = vec![Criterion::Desc(S("asc_desc_rank"))];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+    search.authorize_typos(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, false, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn test_desc_on_unexisting_field_should_return_all_1() {
+    let criteria = vec![Criterion::Desc(S("unexisting_field"))];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+    search.authorize_typos(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let criteria = vec![];
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, false, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn test_asc_on_unexisting_field_should_return_all_1() {
+    let criteria = vec![Criterion::Asc(S("unexisting_field"))];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+    search.optional_words(false);
+    search.authorize_typos(false);
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let criteria = vec![];
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, false, false).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn test_desc_on_unexisting_field_should_return_all_2() {
+    let criteria = vec![Criterion::Desc(S("unexisting_field"))];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let criteria = vec![];
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, true, true).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn test_asc_on_unexisting_field_should_return_all_2() {
+    let criteria = vec![Criterion::Asc(S("unexisting_field"))];
+    let index = search::setup_search_index_with_criteria(&criteria);
+    let mut rtxn = index.read_txn().unwrap();
+
+    let mut search = Search::new(&mut rtxn, &index);
+    search.query(search::TEST_QUERY);
+    search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+
+    let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+    let criteria = vec![];
+    let expected_external_ids: Vec<_> = search::expected_order(&criteria, true, true).into_iter().map(|d| d.id).collect();
+    let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+    assert_eq!(documents_ids, expected_external_ids);
+}
+
+#[test]
+fn criteria_mixup() {
+    use Criterion::*;
+    let index = search::setup_search_index_with_criteria(&vec![Words, Attribute, Desc(S("asc_desc_rank")), Exactness, Proximity, Typo]);
+
+
+    let criteria_mix = {
+        let desc = || Desc(S("asc_desc_rank"));
+        // all possible criteria order
+        vec![
+            vec![Words, Attribute,  desc(),     Exactness,  Proximity,  Typo],
+            vec![Words, Attribute,  desc(),     Exactness,  Typo,       Proximity],
+            vec![Words, Attribute,  desc(),     Proximity,  Exactness,  Typo],
+            vec![Words, Attribute,  desc(),     Proximity,  Typo,       Exactness],
+            vec![Words, Attribute,  desc(),     Typo,       Exactness,  Proximity],
+            vec![Words, Attribute,  desc(),     Typo,       Proximity,  Exactness],
+            vec![Words, Attribute,  Exactness,  desc(),     Proximity,  Typo],
+            vec![Words, Attribute,  Exactness,  desc(),     Typo,       Proximity],
+            vec![Words, Attribute,  Exactness,  Proximity,  desc(),     Typo],
+            vec![Words, Attribute,  Exactness,  Proximity,  Typo,       desc()],
+            vec![Words, Attribute,  Exactness,  Typo,       desc(),     Proximity],
+            vec![Words, Attribute,  Exactness,  Typo,       Proximity,  desc()],
+            vec![Words, Attribute,  Proximity,  desc(),     Exactness,  Typo],
+            vec![Words, Attribute,  Proximity,  desc(),     Typo,       Exactness],
+            vec![Words, Attribute,  Proximity,  Exactness,  desc(),     Typo],
+            vec![Words, Attribute,  Proximity,  Exactness,  Typo,       desc()],
+            vec![Words, Attribute,  Proximity,  Typo,       desc(),     Exactness],
+            vec![Words, Attribute,  Proximity,  Typo,       Exactness,  desc()],
+            vec![Words, Attribute,  Typo,       desc(),     Exactness,  Proximity],
+            vec![Words, Attribute,  Typo,       desc(),     Proximity,  Exactness],
+            vec![Words, Attribute,  Typo,       Exactness,  desc(),     Proximity],
+            vec![Words, Attribute,  Typo,       Exactness,  Proximity,  desc()],
+            vec![Words, Attribute,  Typo,       Proximity,  desc(),     Exactness],
+            vec![Words, Attribute,  Typo,       Proximity,  Exactness,  desc()],
+            vec![Words, desc(),     Attribute,  Exactness,  Proximity,  Typo],
+            vec![Words, desc(),     Attribute,  Exactness,  Typo,       Proximity],
+            vec![Words, desc(),     Attribute,  Proximity,  Exactness,  Typo],
+            vec![Words, desc(),     Attribute,  Proximity,  Typo,       Exactness],
+            vec![Words, desc(),     Attribute,  Typo,       Exactness,  Proximity],
+            vec![Words, desc(),     Attribute,  Typo,       Proximity,  Exactness],
+            vec![Words, desc(),     Exactness,  Attribute,  Proximity,  Typo],
+            vec![Words, desc(),     Exactness,  Attribute,  Typo,       Proximity],
+            vec![Words, desc(),     Exactness,  Proximity,  Attribute,  Typo],
+            vec![Words, desc(),     Exactness,  Proximity,  Typo,       Attribute],
+            vec![Words, desc(),     Exactness,  Typo,       Attribute,  Proximity],
+            vec![Words, desc(),     Exactness,  Typo,       Proximity,  Attribute],
+            vec![Words, desc(),     Proximity,  Attribute,  Exactness,  Typo],
+            vec![Words, desc(),     Proximity,  Attribute,  Typo,       Exactness],
+            vec![Words, desc(),     Proximity,  Exactness,  Attribute,  Typo],
+            vec![Words, desc(),     Proximity,  Exactness,  Typo,       Attribute],
+            vec![Words, desc(),     Proximity,  Typo,       Attribute,  Exactness],
+            vec![Words, desc(),     Proximity,  Typo,       Exactness,  Attribute],
+            vec![Words, desc(),     Typo,       Attribute,  Exactness,  Proximity],
+            vec![Words, desc(),     Typo,       Attribute,  Proximity,  Exactness],
+            vec![Words, desc(),     Typo,       Exactness,  Attribute,  Proximity],
+            vec![Words, desc(),     Typo,       Exactness,  Proximity,  Attribute],
+            vec![Words, desc(),     Typo,       Proximity,  Attribute,  Exactness],
+            vec![Words, desc(),     Typo,       Proximity,  Exactness,  Attribute],
+            vec![Words, Exactness,  Attribute,  desc(),     Proximity,  Typo],
+            vec![Words, Exactness,  Attribute,  desc(),     Typo,       Proximity],
+            vec![Words, Exactness,  Attribute,  Proximity,  desc(),     Typo],
+            vec![Words, Exactness,  Attribute,  Proximity,  Typo,       desc()],
+            vec![Words, Exactness,  Attribute,  Typo,       desc(),     Proximity],
+            vec![Words, Exactness,  Attribute,  Typo,       Proximity,  desc()],
+            vec![Words, Exactness,  desc(),     Attribute,  Proximity,  Typo],
+            vec![Words, Exactness,  desc(),     Attribute,  Typo,       Proximity],
+            vec![Words, Exactness,  desc(),     Proximity,  Attribute,  Typo],
+            vec![Words, Exactness,  desc(),     Proximity,  Typo,       Attribute],
+            vec![Words, Exactness,  desc(),     Typo,       Attribute,  Proximity],
+            vec![Words, Exactness,  desc(),     Typo,       Proximity,  Attribute],
+            vec![Words, Exactness,  Proximity,  Attribute,  desc(),     Typo],
+            vec![Words, Exactness,  Proximity,  Attribute,  Typo,       desc()],
+            vec![Words, Exactness,  Proximity,  desc(),     Attribute,  Typo],
+            vec![Words, Exactness,  Proximity,  desc(),     Typo,       Attribute],
+            vec![Words, Exactness,  Proximity,  Typo,       Attribute,  desc()],
+            vec![Words, Exactness,  Proximity,  Typo,       desc(),     Attribute],
+            vec![Words, Exactness,  Typo,       Attribute,  desc(),     Proximity],
+            vec![Words, Exactness,  Typo,       Attribute,  Proximity,  desc()],
+            vec![Words, Exactness,  Typo,       desc(),     Attribute,  Proximity],
+            vec![Words, Exactness,  Typo,       desc(),     Proximity,  Attribute],
+            vec![Words, Exactness,  Typo,       Proximity,  Attribute,  desc()],
+            vec![Words, Exactness,  Typo,       Proximity,  desc(),     Attribute],
+            vec![Words, Proximity,  Attribute,  desc(),     Exactness,  Typo],
+            vec![Words, Proximity,  Attribute,  desc(),     Typo,       Exactness],
+            vec![Words, Proximity,  Attribute,  Exactness,  desc(),     Typo],
+            vec![Words, Proximity,  Attribute,  Exactness,  Typo,       desc()],
+            vec![Words, Proximity,  Attribute,  Typo,       desc(),     Exactness],
+            vec![Words, Proximity,  Attribute,  Typo,       Exactness,  desc()],
+            vec![Words, Proximity,  desc(),     Attribute,  Exactness,  Typo],
+            vec![Words, Proximity,  desc(),     Attribute,  Typo,       Exactness],
+            vec![Words, Proximity,  desc(),     Exactness,  Attribute,  Typo],
+            vec![Words, Proximity,  desc(),     Exactness,  Typo,       Attribute],
+            vec![Words, Proximity,  desc(),     Typo,       Attribute,  Exactness],
+            vec![Words, Proximity,  desc(),     Typo,       Exactness,  Attribute],
+            vec![Words, Proximity,  Exactness,  Attribute,  desc(),     Typo],
+            vec![Words, Proximity,  Exactness,  Attribute,  Typo,       desc()],
+            vec![Words, Proximity,  Exactness,  desc(),     Attribute,  Typo],
+            vec![Words, Proximity,  Exactness,  desc(),     Typo,       Attribute],
+            vec![Words, Proximity,  Exactness,  Typo,       Attribute,  desc()],
+            vec![Words, Proximity,  Exactness,  Typo,       desc(),     Attribute],
+            vec![Words, Proximity,  Typo,       Attribute,  desc(),     Exactness],
+            vec![Words, Proximity,  Typo,       Attribute,  Exactness,  desc()],
+            vec![Words, Proximity,  Typo,       desc(),     Attribute,  Exactness],
+            vec![Words, Proximity,  Typo,       desc(),     Exactness,  Attribute],
+            vec![Words, Proximity,  Typo,       Exactness,  Attribute,  desc()],
+            vec![Words, Proximity,  Typo,       Exactness,  desc(),     Attribute],
+            vec![Words, Typo,       Attribute,  desc(),     Exactness,  Proximity],
+            vec![Words, Typo,       Attribute,  desc(),     Proximity,  Exactness],
+            vec![Words, Typo,       Attribute,  Exactness,  desc(),     Proximity],
+            vec![Words, Typo,       Attribute,  Exactness,  Proximity,  desc()],
+            vec![Words, Typo,       Attribute,  Proximity,  desc(),     Exactness],
+            vec![Words, Typo,       Attribute,  Proximity,  Exactness,  desc()],
+            vec![Words, Typo,       desc(),     Attribute,  Proximity,  Exactness],
+            vec![Words, Typo,       desc(),     Exactness,  Attribute,  Proximity],
+            vec![Words, Typo,       desc(),     Exactness,  Attribute,  Proximity],
+            vec![Words, Typo,       desc(),     Exactness,  Proximity,  Attribute],
+            vec![Words, Typo,       desc(),     Proximity,  Attribute,  Exactness],
+            vec![Words, Typo,       desc(),     Proximity,  Exactness,  Attribute],
+            vec![Words, Typo,       Exactness,  Attribute,  desc(),     Proximity],
+            vec![Words, Typo,       Exactness,  Attribute,  Proximity,  desc()],
+            vec![Words, Typo,       Exactness,  desc(),     Attribute,  Proximity],
+            vec![Words, Typo,       Exactness,  desc(),     Proximity,  Attribute],
+            vec![Words, Typo,       Exactness,  Proximity,  Attribute,  desc()],
+            vec![Words, Typo,       Exactness,  Proximity,  desc(),     Attribute],
+            vec![Words, Typo,       Proximity,  Attribute,  desc(),     Exactness],
+            vec![Words, Typo,       Proximity,  Attribute,  Exactness,  desc()],
+            vec![Words, Typo,       Proximity,  desc(),     Attribute,  Exactness],
+            vec![Words, Typo,       Proximity,  desc(),     Exactness,  Attribute],
+            vec![Words, Typo,       Proximity,  Exactness,  Attribute,  desc()],
+            vec![Words, Typo,       Proximity,  Exactness,  desc(),     Attribute],
+        ]
+    };
+
+    for criteria in criteria_mix {
+        eprintln!("Testing with criteria order: {:?}", &criteria);
+        //update criteria
+        let mut wtxn = index.write_txn().unwrap();
+        index.put_criteria(&mut wtxn, &criteria).unwrap();
+        wtxn.commit().unwrap();
+
+        let mut rtxn = index.read_txn().unwrap();
+
+        let mut search = Search::new(&mut rtxn, &index);
+        search.query(search::TEST_QUERY);
+        search.limit(EXTERNAL_DOCUMENTS_IDS.len());
+        search.optional_words(true);
+        search.authorize_typos(true);
+
+        let SearchResult { matching_words: _matching_words, candidates: _candidates, documents_ids } = search.execute().unwrap();
+
+        let expected_external_ids: Vec<_> = search::expected_order(&criteria, true, true).into_iter().map(|d| d.id).collect();
+        let documents_ids = search::internal_to_external_ids(&index, &documents_ids);
+
+        assert_eq!(documents_ids, expected_external_ids);
+    }
+}