This is an automated email from the ASF dual-hosted git repository.

alsay pushed a commit to branch no_tables
in repository https://gitbox.apache.org/repos/asf/datasketches-bigquery.git

commit dff7a6f55705723e607d49e3f066f90126b01f15
Author: AlexanderSaydakov <[email protected]>
AuthorDate: Mon Feb 10 18:46:19 2025 -0800

    render docs without tables
---
 cpc/README.md       | 51 +++++++++++++++++----------
 fi/README.md        | 21 +++++++-----
 hll/README.md       | 42 ++++++++++++++---------
 kll/README.md       | 54 ++++++++++++++++++-----------
 readme_generator.py | 31 +++++++++--------
 req/README.md       | 54 ++++++++++++++++++-----------
 tdigest/README.md   | 39 +++++++++++++--------
 theta/README.md     | 81 +++++++++++++++++++++++++++----------------
 tuple/README.md     | 99 ++++++++++++++++++++++++++++++++++-------------------
 9 files changed, 295 insertions(+), 177 deletions(-)

diff --git a/cpc/README.md b/cpc/README.md
index b55e9a3..fc71db7 100644
--- a/cpc/README.md
+++ b/cpc/README.md
@@ -37,25 +37,38 @@ If you are interested in making contributions to this 
project please see our
 [Community](https://datasketches.apache.org/docs/Community/) 
 page for how to contact us.
 
-| Function Name | Function Type | Signature | Description |
-|---|---|---|---|
-| [cpc_sketch_agg_union](../cpc/sqlx/cpc_sketch_agg_union.sqlx) | AGGREGATE | 
(sketch BYTES) -> BYTES | Creates a sketch that represents the union of the 
given column of sketches.<br><br>Param sketch: the column of sketches. Each as 
BYTES.<br>Defaults: lg\_k = 12, seed = 9001.<br>Returns: a Compact, Compressed 
CPC Sketch, as BYTES. |
-| [cpc_sketch_agg_string](../cpc/sqlx/cpc_sketch_agg_string.sqlx) | AGGREGATE 
| (str STRING) -> BYTES | Creates a sketch that represents the cardinality of 
the given STRING column.<br><br>Param str: the STRING column of 
identifiers.<br>Defaults: lg\_k = 12, seed = 9001.<br>Returns: a Compact, 
Compressed CPC Sketch, as BYTES  |
-| [cpc_sketch_agg_int64](../cpc/sqlx/cpc_sketch_agg_int64.sqlx) | AGGREGATE | 
(value INT64) -> BYTES | Creates a sketch that represents the cardinality of 
the given INT64 column.<br><br>Param value: the INT64 column of 
identifiers.<br>Defaults: lg\_k = 12, seed = 9001.<br>Returns: a Compact, 
Compressed CPC Sketch, as BYTES  |
-| 
[cpc_sketch_agg_string_lgk_seed](../cpc/sqlx/cpc_sketch_agg_string_lgk_seed.sqlx)
 | AGGREGATE | (str STRING, params STRUCT<lg_k BYTEINT, seed INT64> NOT 
AGGREGATE) -> BYTES | Creates a sketch that represents the cardinality of the 
given STRING column.<br><br>Param str: the STRING column of 
identifiers.<br>Param lg\_k: the sketch accuracy/size parameter as an integer 
in the range \[4, 26\].<br>Param seed: the seed to be used by the underlying 
hash function.<br>Returns: a Compact, Compre [...]
-| 
[cpc_sketch_agg_union_lgk_seed](../cpc/sqlx/cpc_sketch_agg_union_lgk_seed.sqlx) 
| AGGREGATE | (sketch BYTES, params STRUCT<lg_k BYTEINT, seed INT64> NOT 
AGGREGATE) -> BYTES | Creates a sketch that represents the union of the given 
column of sketches.<br><br>Param sketch: the column of sketches. Each as 
BYTES.<br>Param lg\_k: the sketch accuracy/size parameter as an integer in the 
range \[4, 26\].<br>Param seed: This is used to confirm that the given sketches 
were configured with the co [...]
-| 
[cpc_sketch_agg_int64_lgk_seed](../cpc/sqlx/cpc_sketch_agg_int64_lgk_seed.sqlx) 
| AGGREGATE | (value INT64, params STRUCT<lg_k BYTEINT, seed INT64> NOT 
AGGREGATE) -> BYTES | Creates a sketch that represents the cardinality of the 
given INT64 column.<br><br>Param value: the INT64 column of 
identifiers.<br>Param lg\_k: the sketch accuracy/size parameter as an integer 
in the range \[4, 26\].<br>Param seed: the seed to be used by the underlying 
hash function.<br>Returns: a Compact, Compres [...]
-| [cpc_sketch_get_estimate](../cpc/sqlx/cpc_sketch_get_estimate.sqlx) | SCALAR 
| (sketch BYTES) -> FLOAT64 | Gets cardinality estimate and bounds from given 
sketch.<br><br>Param sketch: The given sketch to query as BYTES.<br>Defaults: 
seed = 9001.<br>Returns: a FLOAT64 value as the cardinality estimate. |
-| [cpc_sketch_to_string](../cpc/sqlx/cpc_sketch_to_string.sqlx) | SCALAR | 
(sketch BYTES) -> STRING | Returns a summary string that represents the state 
of the given sketch.<br><br>Param sketch the given sketch as 
BYTES.<br>Defaults: seed = 9001.<br>Returns: a STRING that represents the state 
of the given sketch. |
-| 
[cpc_sketch_get_estimate_seed](../cpc/sqlx/cpc_sketch_get_estimate_seed.sqlx) | 
SCALAR | (sketch BYTES, seed INT64) -> FLOAT64 | Gets cardinality estimate and 
bounds from given sketch.<br><br>Param sketch: The given sketch to query as 
BYTES.<br>Param seed: This is used to confirm that the given sketch was 
configured with the correct seed.<br>Returns: a FLOAT64 value as the 
cardinality estimate. |
-| [cpc_sketch_to_string_seed](../cpc/sqlx/cpc_sketch_to_string_seed.sqlx) | 
SCALAR | (sketch BYTES, seed INT64) -> STRING | Returns a summary string that 
represents the state of the given sketch.<br><br>Param sketch the given sketch 
as BYTES.<br>Param seed: This is used to confirm that the given sketch was 
configured with the correct seed.<br>Returns: a STRING that represents the 
state of the given sketch. |
-| [cpc_sketch_union](../cpc/sqlx/cpc_sketch_union.sqlx) | SCALAR | (sketchA 
BYTES, sketchB BYTES) -> BYTES | Computes a sketch that represents the scalar 
union of the two given sketches.<br><br>Param sketchA: the first sketch as 
BYTES.<br>Param sketchB: the second sketch as BYTES.<br>Defaults: lg\_k = 12, 
seed = 9001.<br>Returns: a CPC Sketch, as BYTES. |
-| 
[cpc_sketch_get_estimate_and_bounds](../cpc/sqlx/cpc_sketch_get_estimate_and_bounds.sqlx)
 | SCALAR | (sketch BYTES, num_std_devs BYTEINT) -> STRUCT<estimate FLOAT64, 
lower_bound FLOAT64, upper_bound FLOAT64> | Gets cardinality estimate and 
bounds from given sketch.<br>  <br>Param sketch: The given sketch to query as 
bytes.<br>Param num\_std\_devs: The returned bounds will be based on the 
statistical confidence interval determined by the given number of standard 
deviations<br>  from the [...]
-| [cpc_sketch_union_lgk_seed](../cpc/sqlx/cpc_sketch_union_lgk_seed.sqlx) | 
SCALAR | (sketchA BYTES, sketchB BYTES, lg_k BYTEINT, seed INT64) -> BYTES | 
Computes a sketch that represents the scalar union of the two given 
sketches.<br><br>Param sketchA: the first sketch as BYTES.<br>Param sketchB: 
the second sketch as BYTES.<br>Param lg\_k: the sketch accuracy/size parameter 
as an integer in the range \[4, 26\].<br>Param seed: This is used to confirm 
that the given sketches were configure [...]
-| 
[cpc_sketch_get_estimate_and_bounds_seed](../cpc/sqlx/cpc_sketch_get_estimate_and_bounds_seed.sqlx)
 | SCALAR | (sketch BYTES, num_std_devs BYTEINT, seed INT64) -> STRUCT<estimate 
FLOAT64, lower_bound FLOAT64, upper_bound FLOAT64> | Gets cardinality estimate 
and bounds from given sketch.<br>  <br>Param sketch: The given sketch to query 
as bytes.<br>Param num\_std\_devs: The returned bounds will be based on the 
statistical confidence interval determined by the given number of standard de 
[...]
-
-**Examples:**
-
+## Aggregate Functions
+### [cpc_sketch_agg_union(sketch BYTES)](../cpc/sqlx/cpc_sketch_agg_union.sqlx)
+Creates a sketch that represents the union of the given column of 
sketches.<br><br>Param sketch: the column of sketches. Each as 
BYTES.<br>Defaults: lg\_k = 12, seed = 9001.<br>Returns: a Compact, Compressed 
CPC Sketch, as BYTES.
+### [cpc_sketch_agg_string(str STRING)](../cpc/sqlx/cpc_sketch_agg_string.sqlx)
+Creates a sketch that represents the cardinality of the given STRING 
column.<br><br>Param str: the STRING column of identifiers.<br>Defaults: lg\_k 
= 12, seed = 9001.<br>Returns: a Compact, Compressed CPC Sketch, as BYTES 
+### [cpc_sketch_agg_int64(value INT64)](../cpc/sqlx/cpc_sketch_agg_int64.sqlx)
+Creates a sketch that represents the cardinality of the given INT64 
column.<br><br>Param value: the INT64 column of identifiers.<br>Defaults: lg\_k 
= 12, seed = 9001.<br>Returns: a Compact, Compressed CPC Sketch, as BYTES 
+### [cpc_sketch_agg_string_lgk_seed(str STRING, params STRUCT<lg_k BYTEINT, 
seed INT64> NOT AGGREGATE)](../cpc/sqlx/cpc_sketch_agg_string_lgk_seed.sqlx)
+Creates a sketch that represents the cardinality of the given STRING 
column.<br><br>Param str: the STRING column of identifiers.<br>Param lg\_k: the 
sketch accuracy/size parameter as an integer in the range \[4, 26\].<br>Param 
seed: the seed to be used by the underlying hash function.<br>Returns: a 
Compact, Compressed CPC Sketch, as BYTES 
+### [cpc_sketch_agg_union_lgk_seed(sketch BYTES, params STRUCT<lg_k BYTEINT, 
seed INT64> NOT AGGREGATE)](../cpc/sqlx/cpc_sketch_agg_union_lgk_seed.sqlx)
+Creates a sketch that represents the union of the given column of 
sketches.<br><br>Param sketch: the column of sketches. Each as BYTES.<br>Param 
lg\_k: the sketch accuracy/size parameter as an integer in the range \[4, 
26\].<br>Param seed: This is used to confirm that the given sketches were 
configured with the correct seed.<br>Returns: a Compact, Compressed CPC Sketch, 
as BYTES.
+### [cpc_sketch_agg_int64_lgk_seed(value INT64, params STRUCT<lg_k BYTEINT, 
seed INT64> NOT AGGREGATE)](../cpc/sqlx/cpc_sketch_agg_int64_lgk_seed.sqlx)
+Creates a sketch that represents the cardinality of the given INT64 
column.<br><br>Param value: the INT64 column of identifiers.<br>Param lg\_k: 
the sketch accuracy/size parameter as an integer in the range \[4, 
26\].<br>Param seed: the seed to be used by the underlying hash 
function.<br>Returns: a Compact, Compressed CPC Sketch, as BYTES 
+
+## Scalar Functions
+### [cpc_sketch_get_estimate(sketch 
BYTES)](../cpc/sqlx/cpc_sketch_get_estimate.sqlx)
+Gets cardinality estimate and bounds from given sketch.<br><br>Param sketch: 
The given sketch to query as BYTES.<br>Defaults: seed = 9001.<br>Returns: a 
FLOAT64 value as the cardinality estimate.
+### [cpc_sketch_to_string(sketch BYTES)](../cpc/sqlx/cpc_sketch_to_string.sqlx)
+Returns a summary string that represents the state of the given 
sketch.<br><br>Param sketch the given sketch as BYTES.<br>Defaults: seed = 
9001.<br>Returns: a STRING that represents the state of the given sketch.
+### [cpc_sketch_get_estimate_seed(sketch BYTES, seed 
INT64)](../cpc/sqlx/cpc_sketch_get_estimate_seed.sqlx)
+Gets cardinality estimate and bounds from given sketch.<br><br>Param sketch: 
The given sketch to query as BYTES.<br>Param seed: This is used to confirm that 
the given sketch was configured with the correct seed.<br>Returns: a FLOAT64 
value as the cardinality estimate.
+### [cpc_sketch_to_string_seed(sketch BYTES, seed 
INT64)](../cpc/sqlx/cpc_sketch_to_string_seed.sqlx)
+Returns a summary string that represents the state of the given 
sketch.<br><br>Param sketch the given sketch as BYTES.<br>Param seed: This is 
used to confirm that the given sketch was configured with the correct 
seed.<br>Returns: a STRING that represents the state of the given sketch.
+### [cpc_sketch_union(sketchA BYTES, sketchB 
BYTES)](../cpc/sqlx/cpc_sketch_union.sqlx)
+Computes a sketch that represents the scalar union of the two given 
sketches.<br><br>Param sketchA: the first sketch as BYTES.<br>Param sketchB: 
the second sketch as BYTES.<br>Defaults: lg\_k = 12, seed = 9001.<br>Returns: a 
CPC Sketch, as BYTES.
+### [cpc_sketch_get_estimate_and_bounds(sketch BYTES, num_std_devs 
BYTEINT)](../cpc/sqlx/cpc_sketch_get_estimate_and_bounds.sqlx)
+Gets cardinality estimate and bounds from given sketch.<br>  <br>Param sketch: 
The given sketch to query as bytes.<br>Param num\_std\_devs: The returned 
bounds will be based on the statistical confidence interval determined by the 
given number of standard deviations<br>  from the returned estimate. This 
number may be one of {1,2,3}, where 1 represents 68% confidence, 2 represents 
95% confidence and 3 represents 99.7% confidence.<br>  For example, if the 
given num\_std\_devs = 2 and the r [...]
+### [cpc_sketch_get_estimate_and_bounds_seed(sketch BYTES, num_std_devs 
BYTEINT, seed INT64)](../cpc/sqlx/cpc_sketch_get_estimate_and_bounds_seed.sqlx)
+Gets cardinality estimate and bounds from given sketch.<br>  <br>Param sketch: 
The given sketch to query as bytes.<br>Param num\_std\_devs: The returned 
bounds will be based on the statistical confidence interval determined by the 
given number of standard deviations<br>  from the returned estimate. This 
number may be one of {1,2,3}, where 1 represents 68% confidence, 2 represents 
95% confidence and 3 represents 99.7% confidence.<br>  For example, if the 
given num\_std\_devs = 2 and the r [...]
+### [cpc_sketch_union_lgk_seed(sketchA BYTES, sketchB BYTES, lg_k BYTEINT, 
seed INT64)](../cpc/sqlx/cpc_sketch_union_lgk_seed.sqlx)
+Computes a sketch that represents the scalar union of the two given 
sketches.<br><br>Param sketchA: the first sketch as BYTES.<br>Param sketchB: 
the second sketch as BYTES.<br>Param lg\_k: the sketch accuracy/size parameter 
as an integer in the range \[4, 26\].<br>Param seed: This is used to confirm 
that the given sketches were configured with the correct seed.<br>Returns: a 
CPC Sketch, as BYTES.
+## Examples
 ```sql
 
 # using defaults
diff --git a/fi/README.md b/fi/README.md
index 3a51be0..04ebeea 100644
--- a/fi/README.md
+++ b/fi/README.md
@@ -36,15 +36,18 @@ If you are interested in making contributions to this 
project please see our
 [Community](https://datasketches.apache.org/docs/Community/) 
 page for how to contact us.
 
-| Function Name | Function Type | Signature | Description |
-|---|---|---|---|
-| 
[frequent_strings_sketch_merge](../fi/sqlx/frequent_strings_sketch_merge.sqlx) 
| AGGREGATE | (sketch BYTES, lg_max_map_size BYTEINT NOT AGGREGATE) -> BYTES | 
Merges sketches from the given column.<br><br>Param sketch: the column of 
values.<br>Param lg\_max\_map\_size: the sketch accuracy/size parameter as an 
integer not less than 3.<br>Returns: a serialized Frequent Strings sketch as 
BYTES. |
-| 
[frequent_strings_sketch_build](../fi/sqlx/frequent_strings_sketch_build.sqlx) 
| AGGREGATE | (item STRING, weight INT64, lg_max_map_size BYTEINT NOT 
AGGREGATE) -> BYTES | Creates a sketch that represents frequencies of the given 
column.<br><br>Param item: the column of STRING values.<br>Param weight: the 
amount by which the weight of the item should be increased.<br>Param 
lg\_max\_map\_size: the sketch accuracy/size parameter as a BYTEINT not less 
than 3.<br>Returns: a Frequent Strings [...]
-| 
[frequent_strings_sketch_to_string](../fi/sqlx/frequent_strings_sketch_to_string.sqlx)
 | SCALAR | (sketch BYTES) -> STRING | Returns a summary string that represents 
the state of the given sketch.<br><br>Param sketch: the given sketch as sketch 
encoded bytes.<br>Returns: a string that represents the state of the given 
sketch. |
-| 
[frequent_strings_sketch_get_result](../fi/sqlx/frequent_strings_sketch_get_result.sqlx)
 | SCALAR | (sketch BYTES, error_type STRING, threshold INT64) -> 
ARRAY<STRUCT<item STRING, estimate INT64, lower_bound INT64, upper_bound 
INT64>> | Returns an array of rows that include frequent items, estimates, 
lower and upper bounds<br>given an error\_type and a threshold.<br><br>Param 
sketch: the given sketch as sketch encoded bytes.<br>Param error\_type: 
determines whether no false positives o [...]
-
-**Examples:**
-
+## Aggregate Functions
+### [frequent_strings_sketch_merge(sketch BYTES, lg_max_map_size BYTEINT NOT 
AGGREGATE)](../fi/sqlx/frequent_strings_sketch_merge.sqlx)
+Merges sketches from the given column.<br><br>Param sketch: the column of 
values.<br>Param lg\_max\_map\_size: the sketch accuracy/size parameter as an 
integer not less than 3.<br>Returns: a serialized Frequent Strings sketch as 
BYTES.
+### [frequent_strings_sketch_build(item STRING, weight INT64, lg_max_map_size 
BYTEINT NOT AGGREGATE)](../fi/sqlx/frequent_strings_sketch_build.sqlx)
+Creates a sketch that represents frequencies of the given column.<br><br>Param 
item: the column of STRING values.<br>Param weight: the amount by which the 
weight of the item should be increased.<br>Param lg\_max\_map\_size: the sketch 
accuracy/size parameter as a BYTEINT not less than 3.<br>Returns: a Frequent 
Strings Sketch, as bytes.
+
+## Scalar Functions
+### [frequent_strings_sketch_to_string(sketch 
BYTES)](../fi/sqlx/frequent_strings_sketch_to_string.sqlx)
+Returns a summary string that represents the state of the given 
sketch.<br><br>Param sketch: the given sketch as sketch encoded 
bytes.<br>Returns: a string that represents the state of the given sketch.
+### [frequent_strings_sketch_get_result(sketch BYTES, error_type STRING, 
threshold INT64)](../fi/sqlx/frequent_strings_sketch_get_result.sqlx)
+Returns an array of rows that include frequent items, estimates, lower and 
upper bounds<br>given an error\_type and a threshold.<br><br>Param sketch: the 
given sketch as sketch encoded bytes.<br>Param error\_type: determines whether 
no false positives or no false negatives are desired.<br>Param threshold: a 
threshold to include items in the result list.<br>If NULL, the maximum error of 
the sketch is used as a threshold.<br>Returns: an array of frequent items with 
frequency estimates, low [...]
+## Examples
 ```sql
 
 select 
bqutil.datasketches.frequent_strings_sketch_to_string(bqutil.datasketches.frequent_strings_sketch_build(str,
 1, 5)) from unnest(["a", "b", "c"]) as str;
diff --git a/hll/README.md b/hll/README.md
index 127a88e..d8ee2f6 100644
--- a/hll/README.md
+++ b/hll/README.md
@@ -35,22 +35,32 @@ If you are interested in making contributions to this 
project please see our
 [Community](https://datasketches.apache.org/docs/Community/) 
 page for how to contact us.
 
-| Function Name | Function Type | Signature | Description |
-|---|---|---|---|
-| [hll_sketch_agg_string](../hll/sqlx/hll_sketch_agg_string.sqlx) | AGGREGATE 
| (str STRING) -> BYTES | Creates a sketch that represents the cardinality of 
the given STRING column.<br><br>Param str: the STRING column of 
identifiers.<br>Defaults: lg\_k = 12, tgt\_type = HLL\_4.<br>Returns: an HLL 
Sketch, as BYTES. |
-| [hll_sketch_agg_union](../hll/sqlx/hll_sketch_agg_union.sqlx) | AGGREGATE | 
(sketch BYTES) -> BYTES | Creates a sketch that represents the union of the 
given column of sketches.<br><br>Param sketch: the column of sketches. Each as 
BYTES.<br>Defaults: lg\_k = 12, tgt\_type = HLL\_4.<br>Returns: an HLL Sketch, 
as BYTES. |
-| [hll_sketch_agg_int64](../hll/sqlx/hll_sketch_agg_int64.sqlx) | AGGREGATE | 
(value INT64) -> BYTES | Creates a sketch that represents the cardinality of 
the given INT64 column.<br><br>Param value: the INT64 column of 
identifiers.<br>Defaults: lg\_k = 12, tgt\_type = HLL\_4.<br>Returns: an HLL 
Sketch, as BYTES. |
-| 
[hll_sketch_agg_string_lgk_type](../hll/sqlx/hll_sketch_agg_string_lgk_type.sqlx)
 | AGGREGATE | (str STRING, params STRUCT<lg_k BYTEINT, tgt_type STRING> NOT 
AGGREGATE) -> BYTES | Creates a sketch that represents the cardinality of the 
given STRING column.<br><br>Param str: the STRING column of 
identifiers.<br>Param lg\_k: the sketch accuracy/size parameter as an integer 
in the range \[4, 21\].<br>Param tgt\_type: The HLL type to use: one of 
{"HLL\_4", "HLL\_6", "HLL\_8"}.<br>Returns:  [...]
-| 
[hll_sketch_agg_union_lgk_type](../hll/sqlx/hll_sketch_agg_union_lgk_type.sqlx) 
| AGGREGATE | (sketch BYTES, params STRUCT<lg_k BYTEINT, tgt_type STRING> NOT 
AGGREGATE) -> BYTES | Creates a sketch that represents the union of the given 
column of sketches.<br><br>Param sketch: the column of sketches. Each as 
BYTES.<br>Param lg\_k: the sketch accuracy/size parameter as an integer in the 
range \[4, 21\].<br>Param tgt\_type: The HLL type to use: one of {"HLL\_4", 
"HLL\_6", "HLL\_8"}.<br>Re [...]
-| 
[hll_sketch_agg_int64_lgk_type](../hll/sqlx/hll_sketch_agg_int64_lgk_type.sqlx) 
| AGGREGATE | (value INT64, params STRUCT<lg_k BYTEINT, tgt_type STRING> NOT 
AGGREGATE) -> BYTES | Creates a sketch that represents the cardinality of the 
given INT64 column.<br><br>Param value: the INT64 column of 
identifiers.<br>Param lg\_k: the sketch accuracy/size parameter as an integer 
in the range \[4, 21\].<br>Param tgt\_type: The HLL type to use: one of 
{"HLL\_4", "HLL\_6", "HLL\_8"}.<br>Returns: a [...]
-| [hll_sketch_get_estimate](../hll/sqlx/hll_sketch_get_estimate.sqlx) | SCALAR 
| (sketch BYTES) -> FLOAT64 | Returns a summary string that represents the 
state of the given sketch.<br><br>Param sketch: the given sketch as 
BYTES.<br>Returns: the cardinality estimate as FLOAT64 value. |
-| [hll_sketch_to_string](../hll/sqlx/hll_sketch_to_string.sqlx) | SCALAR | 
(sketch BYTES) -> STRING | Returns a summary string that represents the state 
of the given sketch.<br><br>Param sketch: the given sketch as 
BYTES.<br>Returns: a STRING that represents the state of the given sketch. |
-| [hll_sketch_union](../hll/sqlx/hll_sketch_union.sqlx) | SCALAR | (sketchA 
BYTES, sketchB BYTES) -> BYTES | Computes a sketch that represents the union of 
the two given sketches.<br><br>Param sketchA: the first sketch as 
bytes.<br>Param sketchB: the second sketch as bytes.<br>Defaults: lg\_k = 12, 
tgt\_type = HLL\_4.<br>Returns: an HLL Sketch, as BYTES. |
-| [hll_sketch_union_lgk_type](../hll/sqlx/hll_sketch_union_lgk_type.sqlx) | 
SCALAR | (sketchA BYTES, sketchB BYTES, lg_k BYTEINT, tgt_type STRING) -> BYTES 
| Computes a sketch that represents the union of the two given 
sketches.<br><br>Param sketchA: the first sketch as bytes.<br>Param sketchB: 
the second sketch as bytes.<br>Param lg\_k: the sketch accuracy/size parameter 
as an integer in the range \[4, 21\].<br>Param tgt\_type: The HLL type to use: 
one of {"HLL\_4", "HLL\_6", "HLL\_8"}. [...]
-| 
[hll_sketch_get_estimate_and_bounds](../hll/sqlx/hll_sketch_get_estimate_and_bounds.sqlx)
 | SCALAR | (sketch BYTES, num_std_devs BYTEINT) -> STRUCT<estimate FLOAT64, 
lower_bound FLOAT64, upper_bound FLOAT64> | Gets cardinality estimate and 
bounds from given sketch.<br><br>Param sketch: The given sketch to query as 
BYTES.<br>Param num\_std\_devs: The returned bounds will be based on the 
statistical confidence interval determined by the given number of standard 
deviations<br>  from the r [...]
-
-**Examples:**
-
+## Aggregate Functions
+### [hll_sketch_agg_string(str STRING)](../hll/sqlx/hll_sketch_agg_string.sqlx)
+Creates a sketch that represents the cardinality of the given STRING 
column.<br><br>Param str: the STRING column of identifiers.<br>Defaults: lg\_k 
= 12, tgt\_type = HLL\_4.<br>Returns: an HLL Sketch, as BYTES.
+### [hll_sketch_agg_union(sketch BYTES)](../hll/sqlx/hll_sketch_agg_union.sqlx)
+Creates a sketch that represents the union of the given column of 
sketches.<br><br>Param sketch: the column of sketches. Each as 
BYTES.<br>Defaults: lg\_k = 12, tgt\_type = HLL\_4.<br>Returns: an HLL Sketch, 
as BYTES.
+### [hll_sketch_agg_int64(value INT64)](../hll/sqlx/hll_sketch_agg_int64.sqlx)
+Creates a sketch that represents the cardinality of the given INT64 
column.<br><br>Param value: the INT64 column of identifiers.<br>Defaults: lg\_k 
= 12, tgt\_type = HLL\_4.<br>Returns: an HLL Sketch, as BYTES.
+### [hll_sketch_agg_string_lgk_type(str STRING, params STRUCT<lg_k BYTEINT, 
tgt_type STRING> NOT 
AGGREGATE)](../hll/sqlx/hll_sketch_agg_string_lgk_type.sqlx)
+Creates a sketch that represents the cardinality of the given STRING 
column.<br><br>Param str: the STRING column of identifiers.<br>Param lg\_k: the 
sketch accuracy/size parameter as an integer in the range \[4, 21\].<br>Param 
tgt\_type: The HLL type to use: one of {"HLL\_4", "HLL\_6", 
"HLL\_8"}.<br>Returns: an HLL Sketch, as BYTES.
+### [hll_sketch_agg_union_lgk_type(sketch BYTES, params STRUCT<lg_k BYTEINT, 
tgt_type STRING> NOT AGGREGATE)](../hll/sqlx/hll_sketch_agg_union_lgk_type.sqlx)
+Creates a sketch that represents the union of the given column of 
sketches.<br><br>Param sketch: the column of sketches. Each as BYTES.<br>Param 
lg\_k: the sketch accuracy/size parameter as an integer in the range \[4, 
21\].<br>Param tgt\_type: The HLL type to use: one of {"HLL\_4", "HLL\_6", 
"HLL\_8"}.<br>Returns: an HLL Sketch, as BYTES.
+### [hll_sketch_agg_int64_lgk_type(value INT64, params STRUCT<lg_k BYTEINT, 
tgt_type STRING> NOT AGGREGATE)](../hll/sqlx/hll_sketch_agg_int64_lgk_type.sqlx)
+Creates a sketch that represents the cardinality of the given INT64 
column.<br><br>Param value: the INT64 column of identifiers.<br>Param lg\_k: 
the sketch accuracy/size parameter as an integer in the range \[4, 
21\].<br>Param tgt\_type: The HLL type to use: one of {"HLL\_4", "HLL\_6", 
"HLL\_8"}.<br>Returns: an HLL Sketch, as BYTES.
+
+## Scalar Functions
+### [hll_sketch_get_estimate(sketch 
BYTES)](../hll/sqlx/hll_sketch_get_estimate.sqlx)
+Returns a summary string that represents the state of the given 
sketch.<br><br>Param sketch: the given sketch as BYTES.<br>Returns: the 
cardinality estimate as FLOAT64 value.
+### [hll_sketch_to_string(sketch BYTES)](../hll/sqlx/hll_sketch_to_string.sqlx)
+Returns a summary string that represents the state of the given 
sketch.<br><br>Param sketch: the given sketch as BYTES.<br>Returns: a STRING 
that represents the state of the given sketch.
+### [hll_sketch_union(sketchA BYTES, sketchB 
BYTES)](../hll/sqlx/hll_sketch_union.sqlx)
+Computes a sketch that represents the union of the two given 
sketches.<br><br>Param sketchA: the first sketch as bytes.<br>Param sketchB: 
the second sketch as bytes.<br>Defaults: lg\_k = 12, tgt\_type = 
HLL\_4.<br>Returns: an HLL Sketch, as BYTES.
+### [hll_sketch_get_estimate_and_bounds(sketch BYTES, num_std_devs 
BYTEINT)](../hll/sqlx/hll_sketch_get_estimate_and_bounds.sqlx)
+Gets cardinality estimate and bounds from given sketch.<br><br>Param sketch: 
The given sketch to query as BYTES.<br>Param num\_std\_devs: The returned 
bounds will be based on the statistical confidence interval determined by the 
given number of standard deviations<br>  from the returned estimate. This 
number may be one of {1,2,3}, where 1 represents 68% confidence, 2 represents 
95% confidence and 3 represents 99.7% confidence.<br>  For example, if the 
given num\_std\_devs = 2 and the ret [...]
+### [hll_sketch_union_lgk_type(sketchA BYTES, sketchB BYTES, lg_k BYTEINT, 
tgt_type STRING)](../hll/sqlx/hll_sketch_union_lgk_type.sqlx)
+Computes a sketch that represents the union of the two given 
sketches.<br><br>Param sketchA: the first sketch as bytes.<br>Param sketchB: 
the second sketch as bytes.<br>Param lg\_k: the sketch accuracy/size parameter 
as an integer in the range \[4, 21\].<br>Param tgt\_type: The HLL type to use: 
one of {"HLL\_4", "HLL\_6", "HLL\_8"}.<br>Returns: an HLL Sketch, as BYTES.
+## Examples
 ```sql
 
 # expected 3
diff --git a/kll/README.md b/kll/README.md
index 30a707d..6ca9918 100644
--- a/kll/README.md
+++ b/kll/README.md
@@ -35,26 +35,40 @@ If you are interested in making contributions to this 
project please see our
 [Community](https://datasketches.apache.org/docs/Community/) 
 page for how to contact us.
 
-| Function Name | Function Type | Signature | Description |
-|---|---|---|---|
-| [kll_sketch_float_build](../kll/sqlx/kll_sketch_float_build.sqlx) | 
AGGREGATE | (value FLOAT64) -> BYTES | Creates a sketch that represents the 
distribution of the given column.<br><br>Param value: the column of FLOAT64 
values.<br>Defaults: k = 200.<br>Returns: a KLL Sketch, as bytes. |
-| [kll_sketch_float_merge](../kll/sqlx/kll_sketch_float_merge.sqlx) | 
AGGREGATE | (sketch BYTES) -> BYTES | Merges sketches from the given 
column.<br><br>Param sketch: the column of values.<br>Defaluts: k = 
200.<br>Returns: a serialized KLL sketch as BYTES. |
-| [kll_sketch_float_merge_k](../kll/sqlx/kll_sketch_float_merge_k.sqlx) | 
AGGREGATE | (sketch BYTES, k INT NOT AGGREGATE) -> BYTES | Merges sketches from 
the given column.<br><br>Param sketch: the column of values.<br>Param k: the 
sketch accuracy/size parameter as an integer in the range \[8, 
65535\].<br>Returns: a serialized KLL sketch as BYTES. |
-| [kll_sketch_float_build_k](../kll/sqlx/kll_sketch_float_build_k.sqlx) | 
AGGREGATE | (value FLOAT64, k INT NOT AGGREGATE) -> BYTES | Creates a sketch 
that represents the distribution of the given column.<br><br>Param value: the 
column of FLOAT64 values.<br>Param k: the sketch accuracy/size parameter as an 
INT in the range \[8, 65535\].<br>Returns: a KLL Sketch, as bytes. |
-| [kll_sketch_float_get_n](../kll/sqlx/kll_sketch_float_get_n.sqlx) | SCALAR | 
(sketch BYTES) -> INT64 | Returns the length of the input stream.<br><br>Param 
sketch: the given sketch as BYTES.<br>Returns: stream length as INT64 |
-| 
[kll_sketch_float_get_min_value](../kll/sqlx/kll_sketch_float_get_min_value.sqlx)
 | SCALAR | (sketch BYTES) -> FLOAT64 | Returns the minimum value of the input 
stream.<br><br>Param sketch: the given sketch as BYTES.<br>Returns: min value 
as FLOAT64 |
-| [kll_sketch_float_to_string](../kll/sqlx/kll_sketch_float_to_string.sqlx) | 
SCALAR | (sketch BYTES) -> STRING | Returns a summary string that represents 
the state of the given sketch.<br><br>Param sketch: the given sketch as sketch 
encoded bytes.<br>Returns: a string that represents the state of the given 
sketch. |
-| 
[kll_sketch_float_get_num_retained](../kll/sqlx/kll_sketch_float_get_num_retained.sqlx)
 | SCALAR | (sketch BYTES) -> INT64 | Returns the number of retained items 
\(samples\) in the sketch.<br><br>Param sketch: the given sketch as 
BYTES.<br>Returns: number of retained items as INT64 |
-| 
[kll_sketch_float_get_max_value](../kll/sqlx/kll_sketch_float_get_max_value.sqlx)
 | SCALAR | (sketch BYTES) -> FLOAT64 | Returns the maximum value of the input 
stream.<br><br>Param sketch: the given sketch as BYTES.<br>Returns: max value 
as FLOAT64 |
-| 
[kll_sketch_float_get_normalized_rank_error](../kll/sqlx/kll_sketch_float_get_normalized_rank_error.sqlx)
 | SCALAR | (sketch BYTES, pmf BOOL) -> FLOAT64 | Returns the approximate rank 
error of the given sketch normalized as a fraction between zero and 
one.<br>Param sketch: the given sketch as BYTES.<br>Param pmf: if true, returns 
the "double\-sided" normalized rank error for the get\_PMF\(\) 
function.<br>Otherwise, it is the "single\-sided" normalized rank error for all 
the other queri [...]
-| [kll_sketch_float_get_rank](../kll/sqlx/kll_sketch_float_get_rank.sqlx) | 
SCALAR | (sketch BYTES, value FLOAT64, inclusive BOOL) -> FLOAT64 | Returns an 
approximation to the normalized rank, on the interval \[0.0, 1.0\], of the 
given value.<br><br>Param sketch: the given sketch in serialized form.<br>Param 
value: value to be ranked.<br>Param inclusive: if true the weight of the given 
value is included into the rank.<br>Returns: an approximate rank of the given 
value. |
-| [kll_sketch_float_get_pmf](../kll/sqlx/kll_sketch_float_get_pmf.sqlx) | 
SCALAR | (sketch BYTES, split_points ARRAY<FLOAT64>, inclusive BOOL) -> 
ARRAY<FLOAT64> | Returns an approximation to the Probability Mass Function 
\(PMF\)<br>of the input stream as an array of probability masses defined by the 
given split\_points.<br><br>Param sketch: the given sketch as 
BYTES.<br><br>Param split\_points: an array of M unique, monotonically 
increasing values <br>  \(of the same type as the input va [...]
-| 
[kll_sketch_float_kolmogorov_smirnov](../kll/sqlx/kll_sketch_float_kolmogorov_smirnov.sqlx)
 | SCALAR | (sketchA BYTES, sketchB BYTES, pvalue FLOAT64) -> BOOL | Performs 
the Kolmogorov\-Smirnov Test between two KLL sketches of type FLOAT64.<br>If 
the given sketches have insufficient data or if the sketch sizes are too small, 
this will return false.<br><br>Param sketchA: sketch A in serialized 
form.<br>Param sketchB: sketch B in serialized form.<br>Param pvalue: Target 
p\-value. Typicall [...]
-| [kll_sketch_float_get_cdf](../kll/sqlx/kll_sketch_float_get_cdf.sqlx) | 
SCALAR | (sketch BYTES, split_points ARRAY<FLOAT64>, inclusive BOOL) -> 
ARRAY<FLOAT64> | Returns an approximation to the Cumulative Distribution 
Function \(CDF\) <br>of the input stream as an array of cumulative 
probabilities defined by the given split\_points.<br><br>Param sketch: the 
given sketch as BYTES.<br><br>Param split\_points: an array of M unique, 
monotonically increasing values<br>  \(of the same type as [...]
-| 
[kll_sketch_float_get_quantile](../kll/sqlx/kll_sketch_float_get_quantile.sqlx) 
| SCALAR | (sketch BYTES, rank FLOAT64, inclusive BOOL) -> FLOAT64 | Returns a 
value from the sketch that is the best approximation to a value from the 
original stream with the given rank.<br><br>Param sketch: the given sketch in 
serialized form.<br>Param rank: rank of a value in the hypothetical sorted 
stream.<br>Param inclusive: if true, the given rank is considered inclusive 
\(includes weight of a value\ [...]
-
-**Examples:**
-
+## Aggregate Functions
+### [kll_sketch_float_build(value 
FLOAT64)](../kll/sqlx/kll_sketch_float_build.sqlx)
+Creates a sketch that represents the distribution of the given 
column.<br><br>Param value: the column of FLOAT64 values.<br>Defaults: k = 
200.<br>Returns: a KLL Sketch, as bytes.
+### [kll_sketch_float_merge(sketch 
BYTES)](../kll/sqlx/kll_sketch_float_merge.sqlx)
+Merges sketches from the given column.<br><br>Param sketch: the column of 
values.<br>Defaluts: k = 200.<br>Returns: a serialized KLL sketch as BYTES.
+### [kll_sketch_float_merge_k(sketch BYTES, k INT NOT 
AGGREGATE)](../kll/sqlx/kll_sketch_float_merge_k.sqlx)
+Merges sketches from the given column.<br><br>Param sketch: the column of 
values.<br>Param k: the sketch accuracy/size parameter as an integer in the 
range \[8, 65535\].<br>Returns: a serialized KLL sketch as BYTES.
+### [kll_sketch_float_build_k(value FLOAT64, k INT NOT 
AGGREGATE)](../kll/sqlx/kll_sketch_float_build_k.sqlx)
+Creates a sketch that represents the distribution of the given 
column.<br><br>Param value: the column of FLOAT64 values.<br>Param k: the 
sketch accuracy/size parameter as an INT in the range \[8, 65535\].<br>Returns: 
a KLL Sketch, as bytes.
+
+## Scalar Functions
+### [kll_sketch_float_get_n(sketch 
BYTES)](../kll/sqlx/kll_sketch_float_get_n.sqlx)
+Returns the length of the input stream.<br><br>Param sketch: the given sketch 
as BYTES.<br>Returns: stream length as INT64
+### [kll_sketch_float_get_min_value(sketch 
BYTES)](../kll/sqlx/kll_sketch_float_get_min_value.sqlx)
+Returns the minimum value of the input stream.<br><br>Param sketch: the given 
sketch as BYTES.<br>Returns: min value as FLOAT64
+### [kll_sketch_float_to_string(sketch 
BYTES)](../kll/sqlx/kll_sketch_float_to_string.sqlx)
+Returns a summary string that represents the state of the given 
sketch.<br><br>Param sketch: the given sketch as sketch encoded 
bytes.<br>Returns: a string that represents the state of the given sketch.
+### [kll_sketch_float_get_num_retained(sketch 
BYTES)](../kll/sqlx/kll_sketch_float_get_num_retained.sqlx)
+Returns the number of retained items \(samples\) in the sketch.<br><br>Param 
sketch: the given sketch as BYTES.<br>Returns: number of retained items as INT64
+### [kll_sketch_float_get_max_value(sketch 
BYTES)](../kll/sqlx/kll_sketch_float_get_max_value.sqlx)
+Returns the maximum value of the input stream.<br><br>Param sketch: the given 
sketch as BYTES.<br>Returns: max value as FLOAT64
+### [kll_sketch_float_get_normalized_rank_error(sketch BYTES, pmf 
BOOL)](../kll/sqlx/kll_sketch_float_get_normalized_rank_error.sqlx)
+Returns the approximate rank error of the given sketch normalized as a 
fraction between zero and one.<br>Param sketch: the given sketch as 
BYTES.<br>Param pmf: if true, returns the "double\-sided" normalized rank error 
for the get\_PMF\(\) function.<br>Otherwise, it is the "single\-sided" 
normalized rank error for all the other queries.<br>Returns: normalized rank 
error as FLOAT64
+### [kll_sketch_float_get_rank(sketch BYTES, value FLOAT64, inclusive 
BOOL)](../kll/sqlx/kll_sketch_float_get_rank.sqlx)
+Returns an approximation to the normalized rank, on the interval \[0.0, 1.0\], 
of the given value.<br><br>Param sketch: the given sketch in serialized 
form.<br>Param value: value to be ranked.<br>Param inclusive: if true the 
weight of the given value is included into the rank.<br>Returns: an approximate 
rank of the given value.
+### [kll_sketch_float_get_pmf(sketch BYTES, split_points ARRAY<FLOAT64>, 
inclusive BOOL)](../kll/sqlx/kll_sketch_float_get_pmf.sqlx)
+Returns an approximation to the Probability Mass Function \(PMF\)<br>of the 
input stream as an array of probability masses defined by the given 
split\_points.<br><br>Param sketch: the given sketch as BYTES.<br><br>Param 
split\_points: an array of M unique, monotonically increasing values <br>  \(of 
the same type as the input values\)<br>  that divide the input value domain 
into M\+1 non\-overlapping intervals.<br>  <br>  Each interval except for the 
end intervals starts with a split\-poi [...]
+### [kll_sketch_float_kolmogorov_smirnov(sketchA BYTES, sketchB BYTES, pvalue 
FLOAT64)](../kll/sqlx/kll_sketch_float_kolmogorov_smirnov.sqlx)
+Performs the Kolmogorov\-Smirnov Test between two KLL sketches of type 
FLOAT64.<br>If the given sketches have insufficient data or if the sketch sizes 
are too small, this will return false.<br><br>Param sketchA: sketch A in 
serialized form.<br>Param sketchB: sketch B in serialized form.<br>Param 
pvalue: Target p\-value. Typically 0.001 to 0.1, e.g. 0.05.<br>Returns: boolean 
indicating whether we can reject the null hypothesis \(that the sketches<br>  
reflect the same underlying distribut [...]
+### [kll_sketch_float_get_cdf(sketch BYTES, split_points ARRAY<FLOAT64>, 
inclusive BOOL)](../kll/sqlx/kll_sketch_float_get_cdf.sqlx)
+Returns an approximation to the Cumulative Distribution Function \(CDF\) 
<br>of the input stream as an array of cumulative probabilities defined by the 
given split\_points.<br><br>Param sketch: the given sketch as 
BYTES.<br><br>Param split\_points: an array of M unique, monotonically 
increasing values<br>  \(of the same type as the input values to the 
sketch\)<br>  that divide the input value domain into M\+1 overlapping 
intervals.<br>  <br>  The start of each interval is below the lowes [...]
+### [kll_sketch_float_get_quantile(sketch BYTES, rank FLOAT64, inclusive 
BOOL)](../kll/sqlx/kll_sketch_float_get_quantile.sqlx)
+Returns a value from the sketch that is the best approximation to a value from 
the original stream with the given rank.<br><br>Param sketch: the given sketch 
in serialized form.<br>Param rank: rank of a value in the hypothetical sorted 
stream.<br>Param inclusive: if true, the given rank is considered inclusive 
\(includes weight of a value\)<br>Returns: an approximate quantile associated 
with the given rank.
+## Examples
 ```sql
 
 create or replace temp table kll_sketch(sketch bytes);
diff --git a/readme_generator.py b/readme_generator.py
index 4029422..196b750 100644
--- a/readme_generator.py
+++ b/readme_generator.py
@@ -87,10 +87,11 @@ def parse_sqlx(file_content: str, filename: str) -> dict:
   # Determine function type
   function_type = "AGGREGATE" if "AGGREGATE FUNCTION" in file_content else 
"SCALAR"
   return {
-      "function_name": filename[:-5],  # Remove file extension .sqlx
-      "signature": f"({', '.join([f'{arg[0]} {arg[1]}' for arg in arg_list])}) 
-> {return_type}",
+      "name": filename[:-5],  # Remove file extension .sqlx
+      "params": f"({', '.join([f'{arg[0]} {arg[1]}' for arg in arg_list])})",
+      "returns": return_type,
       "description": description,
-      "function_type": function_type,
+      "type": function_type,
   }
 
 # Function to walk through directories, parse SQLX files, and collect data for 
README
@@ -112,9 +113,10 @@ def process_folder(input_folder: str, sketch_type: str) -> 
dict:
         logging.info(f"Parsed data for {file}: {parsed_data}")
 
         function_index[sketch_type].append({
-            'function_name': parsed_data['function_name'],
-            'signature': parsed_data['signature'],
-            'function_type':parsed_data['function_type'],
+            'name': parsed_data['name'],
+            'params': parsed_data['params'],
+            'returns': parsed_data['returns'],
+            'type':parsed_data['type'],
             'description': parsed_data['description'],
             'path': sqlx_path
         })
@@ -126,21 +128,22 @@ def generate_readme(template_path: str, function_index: 
dict, examples_path: str
   with open(template_path, 'r') as template_file:
     output_lines = template_file.readlines()
 
-  # Generate the table content
-  output_lines += "\n"
-  output_lines += "| Function Name | Function Type | Signature | Description 
|\n"
-  output_lines += "|---|---|---|---|\n" # table header
+  output_lines += "\n## Aggregate Functions\n"
 
   # Sort functions by function type (AGGREGATE first, then SCALAR) and then by 
number of arguments
-  sorted_functions = sorted(function_index, key=lambda x: (x['function_type'], 
len(x['signature'].split(','))), reverse=False)
+  sorted_functions = sorted(function_index, key=lambda x: (x['type'], 
len(x['params'].split(','))), reverse=False)
+  is_aggregate = True
   for function in sorted_functions:
-    function_link = f"[{function['function_name']}](../{function['path']})"
-    output_lines += f"| {function_link} | {function['function_type']} | 
{function['signature']} | {function['description']} |\n"
+    if is_aggregate and function['type'] == 'SCALAR':
+      output_lines += "\n## Scalar Functions\n"
+      is_aggregate = False
+    function_link = 
f"[{function['name']}{function['params']}](../{function['path']})"
+    output_lines += f"### {function_link}\n{function['description']}\n"
 
   # Add examples section
   example_files = [f for f in os.listdir(examples_path) if 
f.endswith("_test.sql")]
   if example_files:
-    output_lines.append("\n**Examples:**\n\n")
+    output_lines.append("## Examples\n")
     for example_file in example_files:
       # Read the example SQL file
       with open(os.path.join(examples_path, example_file), 'r') as f:
diff --git a/req/README.md b/req/README.md
index 66dfafe..0abe1dc 100644
--- a/req/README.md
+++ b/req/README.md
@@ -37,26 +37,40 @@ If you are interested in making contributions to this 
project please see our
 [Community](https://datasketches.apache.org/docs/Community/) 
 page for how to contact us.
 
-| Function Name | Function Type | Signature | Description |
-|---|---|---|---|
-| [req_sketch_float_build](../req/sqlx/req_sketch_float_build.sqlx) | 
AGGREGATE | (value FLOAT64) -> BYTES | Creates a sketch that represents the 
distribution of the given column.<br><br>Param value: the column of FLOAT64 
values.<br>Defaults: k = 12, hra = true.<br>Returns: a serialized REQ Sketch as 
BYTES. |
-| [req_sketch_float_merge](../req/sqlx/req_sketch_float_merge.sqlx) | 
AGGREGATE | (sketch BYTES) -> BYTES | Merges sketches from the given 
column.<br><br>Param sketch: the column of sketches.<br>Defaults: k = 12, hra = 
true.<br>Returns: a serialized REQ sketch as BYTES. |
-| 
[req_sketch_float_build_k_hra](../req/sqlx/req_sketch_float_build_k_hra.sqlx) | 
AGGREGATE | (value FLOAT64, params STRUCT<k INT, hra BOOL> NOT AGGREGATE) -> 
BYTES | Creates a sketch that represents the distribution of the given 
column.<br><br>Param value: the column of FLOAT64 values.<br>Param k: the 
sketch accuracy/size parameter as an even INT in the range \[4, 
65534\].<br>Param hra: if true, the high ranks are prioritized for better 
accuracy. Otherwise the low ranks are prioritized  [...]
-| 
[req_sketch_float_merge_k_hra](../req/sqlx/req_sketch_float_merge_k_hra.sqlx) | 
AGGREGATE | (sketch BYTES, params STRUCT<k INT, hra BOOL> NOT AGGREGATE) -> 
BYTES | Merges sketches from the given column.<br><br>Param sketch: the column 
of values.<br>Param k: the sketch accuracy/size parameter as an even INT in the 
range \[4, 65534\].<br>Param hra: if true, the high ranks are prioritized for 
better accuracy. Otherwise the low ranks are prioritized for better 
accuracy.<br>Returns: a seria [...]
-| [req_sketch_float_get_n](../req/sqlx/req_sketch_float_get_n.sqlx) | SCALAR | 
(sketch BYTES) -> INT64 | Returns the length of the input stream.<br><br>Param 
sketch: the given sketch as BYTES.<br>Returns: stream length as INT64 |
-| 
[req_sketch_float_get_num_retained](../req/sqlx/req_sketch_float_get_num_retained.sqlx)
 | SCALAR | (sketch BYTES) -> INT64 | Returns the number of retained items 
\(samples\) in the sketch.<br><br>Param sketch: the given sketch as 
BYTES.<br>Returns: number of retained items as INT64 |
-| 
[req_sketch_float_get_min_value](../req/sqlx/req_sketch_float_get_min_value.sqlx)
 | SCALAR | (sketch BYTES) -> FLOAT64 | Returns the minimum value of the input 
stream.<br><br>Param sketch: the given sketch as BYTES.<br>Returns: min value 
as FLOAT64 |
-| [req_sketch_float_to_string](../req/sqlx/req_sketch_float_to_string.sqlx) | 
SCALAR | (sketch BYTES) -> STRING | Returns a summary string that represents 
the state of the given sketch.<br><br>Param sketch: the given sketch as 
BYTES.<br>Returns: a string that represents the state of the given sketch. |
-| 
[req_sketch_float_get_max_value](../req/sqlx/req_sketch_float_get_max_value.sqlx)
 | SCALAR | (sketch BYTES) -> FLOAT64 | Returns the maximum value of the input 
stream.<br><br>Param sketch: the given sketch as BYTES.<br>Returns: max value 
as FLOAT64 |
-| [req_sketch_float_get_cdf](../req/sqlx/req_sketch_float_get_cdf.sqlx) | 
SCALAR | (sketch BYTES, split_points ARRAY<FLOAT64>, inclusive BOOL) -> 
ARRAY<FLOAT64> | Returns an approximation to the Cumulative Distribution 
Function \(CDF\) <br>of the input stream as an array of cumulative 
probabilities defined by the given split\_points.<br><br>Param sketch: the 
given sketch as BYTES.<br><br>Param split\_points: an array of M unique, 
monotonically increasing values<br>  \(of the same type as [...]
-| 
[req_sketch_float_get_rank_lower_bound](../req/sqlx/req_sketch_float_get_rank_lower_bound.sqlx)
 | SCALAR | (sketch BYTES, rank FLOAT64, num_std_dev BYTEINT) -> FLOAT64 | 
Returns an approximate lower bound of the given normalized rank.<br>Param 
sketch: the given sketch as BYTES.<br>Param rank: the given rank, a value 
between 0 and 1.0.<br>Param num\_std\_dev: The returned bounds will be based on 
the statistical confidence interval determined by the given number of standard 
deviations<br [...]
-| [req_sketch_float_get_pmf](../req/sqlx/req_sketch_float_get_pmf.sqlx) | 
SCALAR | (sketch BYTES, split_points ARRAY<FLOAT64>, inclusive BOOL) -> 
ARRAY<FLOAT64> | Returns an approximation to the Probability Mass Function 
\(PMF\)<br>of the input stream as an array of probability masses defined by the 
given split\_points.<br><br>Param sketch: the given sketch as 
BYTES.<br><br>Param split\_points: an array of M unique, monotonically 
increasing values <br>  \(of the same type as the input va [...]
-| 
[req_sketch_float_get_quantile](../req/sqlx/req_sketch_float_get_quantile.sqlx) 
| SCALAR | (sketch BYTES, rank FLOAT64, inclusive BOOL) -> FLOAT64 | Returns a 
value from the sketch that is the best approximation to a value from the 
original stream with the given rank.<br><br>Param sketch: the given sketch in 
serialized form.<br>Param rank: rank of a value in the hypothetical sorted 
stream.<br>Param inclusive: if true, the given rank is considered inclusive 
\(includes weight of a value\ [...]
-| 
[req_sketch_float_get_rank_upper_bound](../req/sqlx/req_sketch_float_get_rank_upper_bound.sqlx)
 | SCALAR | (sketch BYTES, rank FLOAT64, num_std_dev BYTEINT) -> FLOAT64 | 
Returns an approximate upper bound of the given normalized rank.<br>Param 
sketch: the given sketch as BYTES.<br>Param rank: the given rank, a value 
between 0 and 1.0.<br>Param num\_std\_dev: The returned bounds will be based on 
the statistical confidence interval determined by the given number of standard 
deviations<br [...]
-| [req_sketch_float_get_rank](../req/sqlx/req_sketch_float_get_rank.sqlx) | 
SCALAR | (sketch BYTES, value FLOAT64, inclusive BOOL) -> FLOAT64 | Returns an 
approximation to the normalized rank, on the interval \[0.0, 1.0\], of the 
given value.<br><br>Param sketch: the given sketch in serialized form.<br>Param 
value: value to be ranked.<br>Param inclusive: if true the weight of the given 
value is included into the rank.<br>Returns: an approximate rank of the given 
value. |
-
-**Examples:**
-
+## Aggregate Functions
+### [req_sketch_float_build(value 
FLOAT64)](../req/sqlx/req_sketch_float_build.sqlx)
+Creates a sketch that represents the distribution of the given 
column.<br><br>Param value: the column of FLOAT64 values.<br>Defaults: k = 12, 
hra = true.<br>Returns: a serialized REQ Sketch as BYTES.
+### [req_sketch_float_merge(sketch 
BYTES)](../req/sqlx/req_sketch_float_merge.sqlx)
+Merges sketches from the given column.<br><br>Param sketch: the column of 
sketches.<br>Defaults: k = 12, hra = true.<br>Returns: a serialized REQ sketch 
as BYTES.
+### [req_sketch_float_build_k_hra(value FLOAT64, params STRUCT<k INT, hra 
BOOL> NOT AGGREGATE)](../req/sqlx/req_sketch_float_build_k_hra.sqlx)
+Creates a sketch that represents the distribution of the given 
column.<br><br>Param value: the column of FLOAT64 values.<br>Param k: the 
sketch accuracy/size parameter as an even INT in the range \[4, 
65534\].<br>Param hra: if true, the high ranks are prioritized for better 
accuracy. Otherwise the low ranks are prioritized for better 
accuracy.<br>Returns: a serialized REQ Sketch as BYTES.
+### [req_sketch_float_merge_k_hra(sketch BYTES, params STRUCT<k INT, hra BOOL> 
NOT AGGREGATE)](../req/sqlx/req_sketch_float_merge_k_hra.sqlx)
+Merges sketches from the given column.<br><br>Param sketch: the column of 
values.<br>Param k: the sketch accuracy/size parameter as an even INT in the 
range \[4, 65534\].<br>Param hra: if true, the high ranks are prioritized for 
better accuracy. Otherwise the low ranks are prioritized for better 
accuracy.<br>Returns: a serialized REQ sketch as BYTES.
+
+## Scalar Functions
+### [req_sketch_float_get_n(sketch 
BYTES)](../req/sqlx/req_sketch_float_get_n.sqlx)
+Returns the length of the input stream.<br><br>Param sketch: the given sketch 
as BYTES.<br>Returns: stream length as INT64
+### [req_sketch_float_get_num_retained(sketch 
BYTES)](../req/sqlx/req_sketch_float_get_num_retained.sqlx)
+Returns the number of retained items \(samples\) in the sketch.<br><br>Param 
sketch: the given sketch as BYTES.<br>Returns: number of retained items as INT64
+### [req_sketch_float_get_min_value(sketch 
BYTES)](../req/sqlx/req_sketch_float_get_min_value.sqlx)
+Returns the minimum value of the input stream.<br><br>Param sketch: the given 
sketch as BYTES.<br>Returns: min value as FLOAT64
+### [req_sketch_float_to_string(sketch 
BYTES)](../req/sqlx/req_sketch_float_to_string.sqlx)
+Returns a summary string that represents the state of the given 
sketch.<br><br>Param sketch: the given sketch as BYTES.<br>Returns: a string 
that represents the state of the given sketch.
+### [req_sketch_float_get_max_value(sketch 
BYTES)](../req/sqlx/req_sketch_float_get_max_value.sqlx)
+Returns the maximum value of the input stream.<br><br>Param sketch: the given 
sketch as BYTES.<br>Returns: max value as FLOAT64
+### [req_sketch_float_get_cdf(sketch BYTES, split_points ARRAY<FLOAT64>, 
inclusive BOOL)](../req/sqlx/req_sketch_float_get_cdf.sqlx)
+Returns an approximation to the Cumulative Distribution Function \(CDF\) 
<br>of the input stream as an array of cumulative probabilities defined by the 
given split\_points.<br><br>Param sketch: the given sketch as 
BYTES.<br><br>Param split\_points: an array of M unique, monotonically 
increasing values<br>  \(of the same type as the input values to the 
sketch\)<br>  that divide the input value domain into M\+1 overlapping 
intervals.<br>  <br>  The start of each interval is below the lowes [...]
+### [req_sketch_float_get_rank_lower_bound(sketch BYTES, rank FLOAT64, 
num_std_dev BYTEINT)](../req/sqlx/req_sketch_float_get_rank_lower_bound.sqlx)
+Returns an approximate lower bound of the given normalized rank.<br>Param 
sketch: the given sketch as BYTES.<br>Param rank: the given rank, a value 
between 0 and 1.0.<br>Param num\_std\_dev: The returned bounds will be based on 
the statistical confidence interval determined by the given number of standard 
deviations<br>  from the returned estimate. This number may be one of {1,2,3}, 
where 1 represents 68% confidence, 2 represents 95% confidence and 3 represents 
99.7% confidence.<br>Retur [...]
+### [req_sketch_float_get_pmf(sketch BYTES, split_points ARRAY<FLOAT64>, 
inclusive BOOL)](../req/sqlx/req_sketch_float_get_pmf.sqlx)
+Returns an approximation to the Probability Mass Function \(PMF\)<br>of the 
input stream as an array of probability masses defined by the given 
split\_points.<br><br>Param sketch: the given sketch as BYTES.<br><br>Param 
split\_points: an array of M unique, monotonically increasing values <br>  \(of 
the same type as the input values\)<br>  that divide the input value domain 
into M\+1 non\-overlapping intervals.<br>  <br>  Each interval except for the 
end intervals starts with a split\-poi [...]
+### [req_sketch_float_get_quantile(sketch BYTES, rank FLOAT64, inclusive 
BOOL)](../req/sqlx/req_sketch_float_get_quantile.sqlx)
+Returns a value from the sketch that is the best approximation to a value from 
the original stream with the given rank.<br><br>Param sketch: the given sketch 
in serialized form.<br>Param rank: rank of a value in the hypothetical sorted 
stream.<br>Param inclusive: if true, the given rank is considered inclusive 
\(includes weight of a value\)<br>Returns: an approximate quantile associated 
with the given rank.
+### [req_sketch_float_get_rank_upper_bound(sketch BYTES, rank FLOAT64, 
num_std_dev BYTEINT)](../req/sqlx/req_sketch_float_get_rank_upper_bound.sqlx)
+Returns an approximate upper bound of the given normalized rank.<br>Param 
sketch: the given sketch as BYTES.<br>Param rank: the given rank, a value 
between 0 and 1.0.<br>Param num\_std\_dev: The returned bounds will be based on 
the statistical confidence interval determined by the given number of standard 
deviations<br>  from the returned estimate. This number may be one of {1,2,3}, 
where 1 represents 68% confidence, 2 represents 95% confidence and 3 represents 
99.7% confidence.<br>Retur [...]
+### [req_sketch_float_get_rank(sketch BYTES, value FLOAT64, inclusive 
BOOL)](../req/sqlx/req_sketch_float_get_rank.sqlx)
+Returns an approximation to the normalized rank, on the interval \[0.0, 1.0\], 
of the given value.<br><br>Param sketch: the given sketch in serialized 
form.<br>Param value: value to be ranked.<br>Param inclusive: if true the 
weight of the given value is included into the rank.<br>Returns: an approximate 
rank of the given value.
+## Examples
 ```sql
 
 # using defaults
diff --git a/tdigest/README.md b/tdigest/README.md
index efb6bee..089a4d2 100644
--- a/tdigest/README.md
+++ b/tdigest/README.md
@@ -34,21 +34,30 @@ If you are interested in making contributions to this 
project please see our
 [Community](https://datasketches.apache.org/docs/Community/) 
 page for how to contact us.
 
-| Function Name | Function Type | Signature | Description |
-|---|---|---|---|
-| [tdigest_double_build](../tdigest/sqlx/tdigest_double_build.sqlx) | 
AGGREGATE | (value FLOAT64) -> BYTES | Creates a sketch that represents the 
distribution of the given column.<br><br>Param value: the column of FLOAT64 
values.<br>Defaults: k = 200.<br>Returns: a t\-Digest, as bytes. |
-| [tdigest_double_merge](../tdigest/sqlx/tdigest_double_merge.sqlx) | 
AGGREGATE | (sketch BYTES) -> BYTES | Merges sketches from the given 
column.<br><br>Param sketch: the column of values.<br>Defaults: k = 
200.<br>Returns: a serialized t\-Digest as BYTES. |
-| [tdigest_double_merge_k](../tdigest/sqlx/tdigest_double_merge_k.sqlx) | 
AGGREGATE | (sketch BYTES, k INT NOT AGGREGATE) -> BYTES | Merges sketches from 
the given column.<br><br>Param sketch: the column of values.<br>Param k: the 
sketch accuracy/size parameter as an integer in the range \[10, 
65535\].<br>Returns: a serialized t\-Digest as BYTES. |
-| [tdigest_double_build_k](../tdigest/sqlx/tdigest_double_build_k.sqlx) | 
AGGREGATE | (value FLOAT64, k INT NOT AGGREGATE) -> BYTES | Creates a sketch 
that represents the distribution of the given column.<br><br>Param value: the 
column of FLOAT64 values.<br>Param k: the sketch accuracy/size parameter as an 
INT in the range \[10, 65535\].<br>Returns: a t\-Digest, as bytes. |
-| 
[tdigest_double_get_max_value](../tdigest/sqlx/tdigest_double_get_max_value.sqlx)
 | SCALAR | (sketch BYTES) -> FLOAT64 | Returns the maximum value of the input 
stream.<br><br>Param sketch: the given sketch as BYTES.<br>Returns: max value 
as FLOAT64 |
-| [tdigest_double_to_string](../tdigest/sqlx/tdigest_double_to_string.sqlx) | 
SCALAR | (sketch BYTES) -> STRING | Returns a summary string that represents 
the state of the given sketch.<br><br>Param sketch: the given sketch as sketch 
encoded bytes.<br>Returns: a string that represents the state of the given 
sketch. |
-| 
[tdigest_double_get_total_weight](../tdigest/sqlx/tdigest_double_get_total_weight.sqlx)
 | SCALAR | (sketch BYTES) -> INT64 | Returns the total weight of the input 
stream.<br><br>Param sketch: the given sketch as BYTES.<br>Returns: total 
weight as INT64 |
-| 
[tdigest_double_get_min_value](../tdigest/sqlx/tdigest_double_get_min_value.sqlx)
 | SCALAR | (sketch BYTES) -> FLOAT64 | Returns the minimum value of the input 
stream.<br><br>Param sketch: the given sketch as BYTES.<br>Returns: min value 
as FLOAT64 |
-| [tdigest_double_get_rank](../tdigest/sqlx/tdigest_double_get_rank.sqlx) | 
SCALAR | (sketch BYTES, value FLOAT64) -> FLOAT64 | Returns an approximation to 
the normalized rank, on the interval \[0.0, 1.0\], of the given 
value.<br><br>Param sketch: the given sketch in serialized form.<br>Param 
value: value to be ranked.<br>Returns: an approximate rank of the given value. |
-| 
[tdigest_double_get_quantile](../tdigest/sqlx/tdigest_double_get_quantile.sqlx) 
| SCALAR | (sketch BYTES, rank FLOAT64) -> FLOAT64 | Returns a value from the 
sketch that is the best approximation to a value from the original stream with 
the given rank.<br><br>Param sketch: the given sketch in serialized 
form.<br>Param rank: rank of a value in the hypothetical sorted 
stream.<br>Returns: an approximate quantile associated with the given rank. |
-
-**Examples:**
-
+## Aggregate Functions
+### [tdigest_double_build(value 
FLOAT64)](../tdigest/sqlx/tdigest_double_build.sqlx)
+Creates a sketch that represents the distribution of the given 
column.<br><br>Param value: the column of FLOAT64 values.<br>Defaults: k = 
200.<br>Returns: a t\-Digest, as bytes.
+### [tdigest_double_merge(sketch 
BYTES)](../tdigest/sqlx/tdigest_double_merge.sqlx)
+Merges sketches from the given column.<br><br>Param sketch: the column of 
values.<br>Defaults: k = 200.<br>Returns: a serialized t\-Digest as BYTES.
+### [tdigest_double_merge_k(sketch BYTES, k INT NOT 
AGGREGATE)](../tdigest/sqlx/tdigest_double_merge_k.sqlx)
+Merges sketches from the given column.<br><br>Param sketch: the column of 
values.<br>Param k: the sketch accuracy/size parameter as an integer in the 
range \[10, 65535\].<br>Returns: a serialized t\-Digest as BYTES.
+### [tdigest_double_build_k(value FLOAT64, k INT NOT 
AGGREGATE)](../tdigest/sqlx/tdigest_double_build_k.sqlx)
+Creates a sketch that represents the distribution of the given 
column.<br><br>Param value: the column of FLOAT64 values.<br>Param k: the 
sketch accuracy/size parameter as an INT in the range \[10, 
65535\].<br>Returns: a t\-Digest, as bytes.
+
+## Scalar Functions
+### [tdigest_double_get_max_value(sketch 
BYTES)](../tdigest/sqlx/tdigest_double_get_max_value.sqlx)
+Returns the maximum value of the input stream.<br><br>Param sketch: the given 
sketch as BYTES.<br>Returns: max value as FLOAT64
+### [tdigest_double_to_string(sketch 
BYTES)](../tdigest/sqlx/tdigest_double_to_string.sqlx)
+Returns a summary string that represents the state of the given 
sketch.<br><br>Param sketch: the given sketch as sketch encoded 
bytes.<br>Returns: a string that represents the state of the given sketch.
+### [tdigest_double_get_total_weight(sketch 
BYTES)](../tdigest/sqlx/tdigest_double_get_total_weight.sqlx)
+Returns the total weight of the input stream.<br><br>Param sketch: the given 
sketch as BYTES.<br>Returns: total weight as INT64
+### [tdigest_double_get_min_value(sketch 
BYTES)](../tdigest/sqlx/tdigest_double_get_min_value.sqlx)
+Returns the minimum value of the input stream.<br><br>Param sketch: the given 
sketch as BYTES.<br>Returns: min value as FLOAT64
+### [tdigest_double_get_rank(sketch BYTES, value 
FLOAT64)](../tdigest/sqlx/tdigest_double_get_rank.sqlx)
+Returns an approximation to the normalized rank, on the interval \[0.0, 1.0\], 
of the given value.<br><br>Param sketch: the given sketch in serialized 
form.<br>Param value: value to be ranked.<br>Returns: an approximate rank of 
the given value.
+### [tdigest_double_get_quantile(sketch BYTES, rank 
FLOAT64)](../tdigest/sqlx/tdigest_double_get_quantile.sqlx)
+Returns a value from the sketch that is the best approximation to a value from 
the original stream with the given rank.<br><br>Param sketch: the given sketch 
in serialized form.<br>Param rank: rank of a value in the hypothetical sorted 
stream.<br>Returns: an approximate quantile associated with the given rank.
+## Examples
 ```sql
 
 create or replace temp table tdigest_double(sketch bytes);
diff --git a/theta/README.md b/theta/README.md
index cef3a08..a35a15d 100644
--- a/theta/README.md
+++ b/theta/README.md
@@ -36,35 +36,58 @@ If you are interested in making contributions to this 
project please see our
 [Community](https://datasketches.apache.org/docs/Community/) 
 page for how to contact us.
 
-| Function Name | Function Type | Signature | Description |
-|---|---|---|---|
-| [theta_sketch_agg_int64](../theta/sqlx/theta_sketch_agg_int64.sqlx) | 
AGGREGATE | (value INT64) -> BYTES | Creates a sketch that represents the 
cardinality of the given INT64 column.<br>  <br>Param value: the INT64 column 
of identifiers.<br>Defaults: lg\_k = 12, seed = 9001, p = 1.0.<br>Returns: a 
Compact, Compressed Theta Sketch, as BYTES.  |
-| [theta_sketch_agg_union](../theta/sqlx/theta_sketch_agg_union.sqlx) | 
AGGREGATE | (sketch BYTES) -> BYTES | Creates a sketch that represents the 
union of the given column of sketches.<br><br>Param sketch: the column of 
sketches. Each as BYTES.<br>Defaults: lg\_k = 12, seed = 9001.<br>Returns: a 
Compact, Compressed Theta Sketch, as BYTES. |
-| [theta_sketch_agg_string](../theta/sqlx/theta_sketch_agg_string.sqlx) | 
AGGREGATE | (str STRING) -> BYTES | Creates a sketch that represents the 
cardinality of the given STRING column.<br>  <br>Param str: the STRING column 
of identifiers.<br>Defaults: lg\_k = 12, seed = 9001, p = 1.0.<br>Returns: a 
Compact, Compressed Theta Sketch, as BYTES.  |
-| 
[theta_sketch_agg_union_lgk_seed](../theta/sqlx/theta_sketch_agg_union_lgk_seed.sqlx)
 | AGGREGATE | (sketch BYTES, params STRUCT<lg_k BYTEINT, seed INT64> NOT 
AGGREGATE) -> BYTES | Creates a sketch that represents the union of the given 
column of sketches.<br><br>Param sketch: the column of sketches. Each as 
BYTES.<br>Param lg\_k: the sketch accuracy/size parameter as a BYTEINT in the 
range \[4, 26\].<br>Param seed: This is used to confirm that the given sketches 
were configured with t [...]
-| 
[theta_sketch_agg_int64_lgk_seed_p](../theta/sqlx/theta_sketch_agg_int64_lgk_seed_p.sqlx)
 | AGGREGATE | (value INT64, params STRUCT<lg_k BYTEINT, seed INT64, p FLOAT64> 
NOT AGGREGATE) -> BYTES | Creates a sketch that represents the cardinality of 
the given INT64 column.<br><br>Param value: the INT64 column of 
identifiers.<br>Param lg\_k: the sketch accuracy/size parameter as a BYTEINT in 
the range \[4, 26\]. A NULL specifies the default of 12.<br>Param seed: the 
seed to be used by the  [...]
-| 
[theta_sketch_agg_string_lgk_seed_p](../theta/sqlx/theta_sketch_agg_string_lgk_seed_p.sqlx)
 | AGGREGATE | (str STRING, params STRUCT<lg_k BYTEINT, seed INT64, p FLOAT64> 
NOT AGGREGATE) -> BYTES | Creates a sketch that represents the cardinality of 
the given STRING column.<br><br>Param str: the STRING column of 
identifiers.<br>Param lg\_k: the sketch accuracy/size parameter as a BYTEINT in 
the range \[4, 26\]. A NULL specifies the default of 12.<br>Param seed: the 
seed to be used by the [...]
-| [theta_sketch_get_estimate](../theta/sqlx/theta_sketch_get_estimate.sqlx) | 
SCALAR | (sketch BYTES) -> FLOAT64 | Gets distinct count estimate from a  given 
sketch.<br><br>Param sketch: The given sketch to query as BYTES.<br>Defaults: 
seed = 9001.<br>Returns: distinct count estimate as FLOAT64. |
-| [theta_sketch_to_string](../theta/sqlx/theta_sketch_to_string.sqlx) | SCALAR 
| (sketch BYTES) -> STRING | Returns a summary string that represents the state 
of the given sketch.<br><br>Param sketch: the given sketch as 
BYTES.<br>Defaults: seed = 9001.<br>Returns: a STRING that represents the state 
of the given sketch. |
-| 
[theta_sketch_get_num_retained](../theta/sqlx/theta_sketch_get_num_retained.sqlx)
 | SCALAR | (sketch BYTES) -> INT | Returns the number of retained entries in 
the given sketch.<br>  <br>Param sketch: The given sketch to query as 
BYTES.<br>Defaults: seed = 9001.<br>Returns: number of retained entries as INT. 
|
-| [theta_sketch_get_theta](../theta/sqlx/theta_sketch_get_theta.sqlx) | SCALAR 
| (sketch BYTES) -> FLOAT64 | Returns theta \(effective sampling rate\) as a 
fraction from 0 to 1.<br>  <br>Param sketch: The given sketch to query as 
BYTES.<br>Defaults: seed = 9001.<br>Returns: theta as FLOAT64. |
-| 
[theta_sketch_get_num_retained_seed](../theta/sqlx/theta_sketch_get_num_retained_seed.sqlx)
 | SCALAR | (sketch BYTES, seed INT64) -> INT | Returns the number of retained 
entries in the given sketch.<br>  <br>Param sketch: The given sketch to query 
as BYTES.<br>Param seed: This is used to confirm that the given sketch was 
configured with the correct seed.<br>Returns: number of retained entries as 
INT. |
-| 
[theta_sketch_get_estimate_seed](../theta/sqlx/theta_sketch_get_estimate_seed.sqlx)
 | SCALAR | (sketch BYTES, seed INT64) -> FLOAT64 | Gets distinct count 
estimate from a given sketch.<br>  <br>Param sketch: The given sketch to query 
as BYTES.<br>Param seed: This is used to confirm that the given sketch was 
configured with the correct seed.<br>Returns: distinct count estimate as 
FLOA64. |
-| 
[theta_sketch_to_string_seed](../theta/sqlx/theta_sketch_to_string_seed.sqlx) | 
SCALAR | (sketch BYTES, seed INT64) -> STRING | Returns a summary string that 
represents the state of the given sketch.<br><br>Param sketch: the given sketch 
as BYTES.<br>Param seed: This is used to confirm that the given sketch was 
configured with the correct seed.<br>Returns: a STRING that represents the 
state of the given sketch. |
-| 
[theta_sketch_get_theta_seed](../theta/sqlx/theta_sketch_get_theta_seed.sqlx) | 
SCALAR | (sketch BYTES, seed INT64) -> FLOAT64 | Returns theta \(effective 
sampling rate\) as a fraction from 0 to 1.<br>  <br>Param sketch: The given 
sketch to query as BYTES.<br>Param seed: This is used to confirm that the given 
sketch was configured with the correct seed.<br>Returns: theta as FLOAT64. |
-| [theta_sketch_intersection](../theta/sqlx/theta_sketch_intersection.sqlx) | 
SCALAR | (sketchA BYTES, sketchB BYTES) -> BYTES | Computes a sketch that 
represents the scalar intersection of the two given sketches.<br><br>Param 
sketchA: the first sketch as BYTES.<br>Param sketchB: the second sketch as 
BYTES.<br>Defaults: seed = 9001.<br>Returns: a Compact, Compressed Theta 
Sketch, as BYTES. |
-| [theta_sketch_union](../theta/sqlx/theta_sketch_union.sqlx) | SCALAR | 
(sketchA BYTES, sketchB BYTES) -> BYTES | Computes a sketch that represents the 
scalar union of the two given sketches.<br><br>Param sketchA: the first sketch 
as BYTES.<br>Param sketchB: the second sketch as BYTES.<br>Defaults: lg\_k = 
12, seed = 9001.<br>Returns: a Compact, Compressed Theta Sketch, as BYTES. |
-| [theta_sketch_a_not_b](../theta/sqlx/theta_sketch_a_not_b.sqlx) | SCALAR | 
(sketchA BYTES, sketchB BYTES) -> BYTES | Computes a sketch that represents the 
scalar set difference: sketchA and not sketchB.<br><br>Param sketchA: the first 
sketch "A" as bytes.<br>Param sketchB: the second sketch "B" as 
bytes.<br>Defaults: seed = 9001.<br>Returns: a Compact, Compressed Theta 
Sketch, as BYTES. |
-| 
[theta_sketch_intersection_seed](../theta/sqlx/theta_sketch_intersection_seed.sqlx)
 | SCALAR | (sketchA BYTES, sketchB BYTES, seed INT64) -> BYTES | Computes a 
sketch that represents the scalar intersection of the two given 
sketches.<br><br>Param sketchA: the first sketch as BYTES.<br>Param sketchB: 
the second sketch as BYTES.<br>Param seed: This is used to confirm that the 
given sketches were configured with the correct seed.<br>Returns: a Compact, 
Compressed Theta Sketch, as BYTES. |
-| [theta_sketch_a_not_b_seed](../theta/sqlx/theta_sketch_a_not_b_seed.sqlx) | 
SCALAR | (sketchA BYTES, sketchB BYTES, seed INT64) -> BYTES | Computes a 
sketch that represents the scalar set difference: sketchA and not 
sketchB.<br><br>Param sketchA: the first sketch "A" as bytes.<br>Param sketchB: 
the second sketch "B" as bytes.<br>Param seed: This is used to confirm that the 
given sketches were configured with the correct seed.<br>Returns: a Compact, 
Compressed Theta Sketch, as BYTES. |
-| 
[theta_sketch_union_lgk_seed](../theta/sqlx/theta_sketch_union_lgk_seed.sqlx) | 
SCALAR | (sketchA BYTES, sketchB BYTES, lg_k BYTEINT, seed INT64) -> BYTES | 
Computes a sketch that represents the scalar union of the two given 
sketches.<br><br>Param sketchA: the first sketch as BYTES.<br>Param sketchB: 
the second sketch as BYTES.<br>Param lg\_k: the sketch accuracy/size parameter 
as an integer in the range \[4, 26\].<br>Param seed: This is used to confirm 
that the given sketches were con [...]
-| 
[theta_sketch_get_estimate_and_bounds](../theta/sqlx/theta_sketch_get_estimate_and_bounds.sqlx)
 | SCALAR | (sketch BYTES, num_std_devs BYTEINT) -> STRUCT<estimate FLOAT64, 
lower_bound FLOAT64, upper_bound FLOAT64> | Gets distinct count estimate and 
bounds from a given sketch.<br><br>Param sketch: The given sketch to query as 
BYTES.<br>Param num\_std\_devs: The returned bounds will be based on the 
statistical confidence interval<br>  determined by the given number of standard 
deviations [...]
-| 
[theta_sketch_jaccard_similarity](../theta/sqlx/theta_sketch_jaccard_similarity.sqlx)
 | SCALAR | (sketchA BYTES, sketchB BYTES) -> STRUCT<lower_bound FLOAT64, 
estimate FLOAT64, upper_bound FLOAT64> | Computes the Jaccard similarity index 
with upper and lower bounds.<br>The Jaccard similarity index J\(A,B\) = \(A ^ 
B\)/\(A U B\) is used to measure how similar the two sketches are to each 
other.<br>If J = 1.0, the sketches are considered equal. If J = 0, the two 
sketches are disjoint.<br [...]
-| 
[theta_sketch_get_estimate_and_bounds_seed](../theta/sqlx/theta_sketch_get_estimate_and_bounds_seed.sqlx)
 | SCALAR | (sketch BYTES, num_std_devs BYTEINT, seed INT64) -> STRUCT<estimate 
FLOAT64, lower_bound FLOAT64, upper_bound FLOAT64> | Gets distinct count 
estimate and bounds from a given sketch.<br><br>Param sketch: The given sketch 
to query as BYTES.<br>Param num\_std\_devs: The returned bounds will be based 
on the statistical confidence interval<br>  determined by the given number  
[...]
-| 
[theta_sketch_jaccard_similarity_seed](../theta/sqlx/theta_sketch_jaccard_similarity_seed.sqlx)
 | SCALAR | (sketchA BYTES, sketchB BYTES, seed INT64) -> STRUCT<lower_bound 
FLOAT64, estimate FLOAT64, upper_bound FLOAT64> | Computes the Jaccard 
similarity index with upper and lower bounds.<br>The Jaccard similarity index 
J\(A,B\) = \(A ^ B\)/\(A U B\) is used to measure how similar the two sketches 
are to each other.<br>If J = 1.0, the sketches are considered equal. If J = 0, 
the two ske [...]
-
-**Examples:**
-
+## Aggregate Functions
+### [theta_sketch_agg_int64(value 
INT64)](../theta/sqlx/theta_sketch_agg_int64.sqlx)
+Creates a sketch that represents the cardinality of the given INT64 
column.<br>  <br>Param value: the INT64 column of identifiers.<br>Defaults: 
lg\_k = 12, seed = 9001, p = 1.0.<br>Returns: a Compact, Compressed Theta 
Sketch, as BYTES. 
+### [theta_sketch_agg_union(sketch 
BYTES)](../theta/sqlx/theta_sketch_agg_union.sqlx)
+Creates a sketch that represents the union of the given column of 
sketches.<br><br>Param sketch: the column of sketches. Each as 
BYTES.<br>Defaults: lg\_k = 12, seed = 9001.<br>Returns: a Compact, Compressed 
Theta Sketch, as BYTES.
+### [theta_sketch_agg_string(str 
STRING)](../theta/sqlx/theta_sketch_agg_string.sqlx)
+Creates a sketch that represents the cardinality of the given STRING 
column.<br>  <br>Param str: the STRING column of identifiers.<br>Defaults: 
lg\_k = 12, seed = 9001, p = 1.0.<br>Returns: a Compact, Compressed Theta 
Sketch, as BYTES. 
+### [theta_sketch_agg_union_lgk_seed(sketch BYTES, params STRUCT<lg_k BYTEINT, 
seed INT64> NOT AGGREGATE)](../theta/sqlx/theta_sketch_agg_union_lgk_seed.sqlx)
+Creates a sketch that represents the union of the given column of 
sketches.<br><br>Param sketch: the column of sketches. Each as BYTES.<br>Param 
lg\_k: the sketch accuracy/size parameter as a BYTEINT in the range \[4, 
26\].<br>Param seed: This is used to confirm that the given sketches were 
configured with the correct seed.<br>Returns: a Compact, Compressed Theta 
Sketch, as BYTES.
+### [theta_sketch_agg_int64_lgk_seed_p(value INT64, params STRUCT<lg_k 
BYTEINT, seed INT64, p FLOAT64> NOT 
AGGREGATE)](../theta/sqlx/theta_sketch_agg_int64_lgk_seed_p.sqlx)
+Creates a sketch that represents the cardinality of the given INT64 
column.<br><br>Param value: the INT64 column of identifiers.<br>Param lg\_k: 
the sketch accuracy/size parameter as a BYTEINT in the range \[4, 26\]. A NULL 
specifies the default of 12.<br>Param seed: the seed to be used by the 
underlying hash function. A NULL specifies the default of 9001.<br>Param p: 
up\-front sampling probability. A NULL specifies the default of 
1.0.<br>Returns: a Compact, Compressed Theta Sketch, as BYTES.
+### [theta_sketch_agg_string_lgk_seed_p(str STRING, params STRUCT<lg_k 
BYTEINT, seed INT64, p FLOAT64> NOT 
AGGREGATE)](../theta/sqlx/theta_sketch_agg_string_lgk_seed_p.sqlx)
+Creates a sketch that represents the cardinality of the given STRING 
column.<br><br>Param str: the STRING column of identifiers.<br>Param lg\_k: the 
sketch accuracy/size parameter as a BYTEINT in the range \[4, 26\]. A NULL 
specifies the default of 12.<br>Param seed: the seed to be used by the 
underlying hash function. A NULL specifies the default of 9001.<br>Param p: 
up\-front sampling probability. A NULL specifies the default of 
1.0.<br>Returns: a Compact, Compressed Theta Sketch, as BYTES.
+
+## Scalar Functions
+### [theta_sketch_get_estimate(sketch 
BYTES)](../theta/sqlx/theta_sketch_get_estimate.sqlx)
+Gets distinct count estimate from a  given sketch.<br><br>Param sketch: The 
given sketch to query as BYTES.<br>Defaults: seed = 9001.<br>Returns: distinct 
count estimate as FLOAT64.
+### [theta_sketch_to_string(sketch 
BYTES)](../theta/sqlx/theta_sketch_to_string.sqlx)
+Returns a summary string that represents the state of the given 
sketch.<br><br>Param sketch: the given sketch as BYTES.<br>Defaults: seed = 
9001.<br>Returns: a STRING that represents the state of the given sketch.
+### [theta_sketch_get_num_retained(sketch 
BYTES)](../theta/sqlx/theta_sketch_get_num_retained.sqlx)
+Returns the number of retained entries in the given sketch.<br>  <br>Param 
sketch: The given sketch to query as BYTES.<br>Defaults: seed = 
9001.<br>Returns: number of retained entries as INT.
+### [theta_sketch_get_theta(sketch 
BYTES)](../theta/sqlx/theta_sketch_get_theta.sqlx)
+Returns theta \(effective sampling rate\) as a fraction from 0 to 1.<br>  
<br>Param sketch: The given sketch to query as BYTES.<br>Defaults: seed = 
9001.<br>Returns: theta as FLOAT64.
+### [theta_sketch_get_num_retained_seed(sketch BYTES, seed 
INT64)](../theta/sqlx/theta_sketch_get_num_retained_seed.sqlx)
+Returns the number of retained entries in the given sketch.<br>  <br>Param 
sketch: The given sketch to query as BYTES.<br>Param seed: This is used to 
confirm that the given sketch was configured with the correct seed.<br>Returns: 
number of retained entries as INT.
+### [theta_sketch_get_estimate_seed(sketch BYTES, seed 
INT64)](../theta/sqlx/theta_sketch_get_estimate_seed.sqlx)
+Gets distinct count estimate from a given sketch.<br>  <br>Param sketch: The 
given sketch to query as BYTES.<br>Param seed: This is used to confirm that the 
given sketch was configured with the correct seed.<br>Returns: distinct count 
estimate as FLOA64.
+### [theta_sketch_to_string_seed(sketch BYTES, seed 
INT64)](../theta/sqlx/theta_sketch_to_string_seed.sqlx)
+Returns a summary string that represents the state of the given 
sketch.<br><br>Param sketch: the given sketch as BYTES.<br>Param seed: This is 
used to confirm that the given sketch was configured with the correct 
seed.<br>Returns: a STRING that represents the state of the given sketch.
+### [theta_sketch_get_theta_seed(sketch BYTES, seed 
INT64)](../theta/sqlx/theta_sketch_get_theta_seed.sqlx)
+Returns theta \(effective sampling rate\) as a fraction from 0 to 1.<br>  
<br>Param sketch: The given sketch to query as BYTES.<br>Param seed: This is 
used to confirm that the given sketch was configured with the correct 
seed.<br>Returns: theta as FLOAT64.
+### [theta_sketch_intersection(sketchA BYTES, sketchB 
BYTES)](../theta/sqlx/theta_sketch_intersection.sqlx)
+Computes a sketch that represents the scalar intersection of the two given 
sketches.<br><br>Param sketchA: the first sketch as BYTES.<br>Param sketchB: 
the second sketch as BYTES.<br>Defaults: seed = 9001.<br>Returns: a Compact, 
Compressed Theta Sketch, as BYTES.
+### [theta_sketch_union(sketchA BYTES, sketchB 
BYTES)](../theta/sqlx/theta_sketch_union.sqlx)
+Computes a sketch that represents the scalar union of the two given 
sketches.<br><br>Param sketchA: the first sketch as BYTES.<br>Param sketchB: 
the second sketch as BYTES.<br>Defaults: lg\_k = 12, seed = 9001.<br>Returns: a 
Compact, Compressed Theta Sketch, as BYTES.
+### [theta_sketch_a_not_b(sketchA BYTES, sketchB 
BYTES)](../theta/sqlx/theta_sketch_a_not_b.sqlx)
+Computes a sketch that represents the scalar set difference: sketchA and not 
sketchB.<br><br>Param sketchA: the first sketch "A" as bytes.<br>Param sketchB: 
the second sketch "B" as bytes.<br>Defaults: seed = 9001.<br>Returns: a 
Compact, Compressed Theta Sketch, as BYTES.
+### [theta_sketch_get_estimate_and_bounds(sketch BYTES, num_std_devs 
BYTEINT)](../theta/sqlx/theta_sketch_get_estimate_and_bounds.sqlx)
+Gets distinct count estimate and bounds from a given sketch.<br><br>Param 
sketch: The given sketch to query as BYTES.<br>Param num\_std\_devs: The 
returned bounds will be based on the statistical confidence interval<br>  
determined by the given number of standard deviations from the returned 
estimate.<br>  This number may be one of {1,2,3}, where 1 represents 68% 
confidence,<br>  2 represents 95% confidence and 3 represents 99.7% 
confidence.<br>  For example, if the given num\_std\_devs  [...]
+### [theta_sketch_jaccard_similarity(sketchA BYTES, sketchB 
BYTES)](../theta/sqlx/theta_sketch_jaccard_similarity.sqlx)
+Computes the Jaccard similarity index with upper and lower bounds.<br>The 
Jaccard similarity index J\(A,B\) = \(A ^ B\)/\(A U B\) is used to measure how 
similar the two sketches are to each other.<br>If J = 1.0, the sketches are 
considered equal. If J = 0, the two sketches are disjoint.<br>A Jaccard of .95 
means the overlap between the two sets is 95% of the union of the two 
sets.<br><br>Param sketchA: the first sketch as bytes.<br>Param sketchB: the 
second sketch as bytes.<br>Defaults:  [...]
+### [theta_sketch_get_estimate_and_bounds_seed(sketch BYTES, num_std_devs 
BYTEINT, seed 
INT64)](../theta/sqlx/theta_sketch_get_estimate_and_bounds_seed.sqlx)
+Gets distinct count estimate and bounds from a given sketch.<br><br>Param 
sketch: The given sketch to query as BYTES.<br>Param num\_std\_devs: The 
returned bounds will be based on the statistical confidence interval<br>  
determined by the given number of standard deviations from the returned 
estimate.<br>  This number may be one of {1,2,3}, where 1 represents 68% 
confidence,<br>  2 represents 95% confidence and 3 represents 99.7% 
confidence.<br>  For example, if the given num\_std\_devs  [...]
+### [theta_sketch_intersection_seed(sketchA BYTES, sketchB BYTES, seed 
INT64)](../theta/sqlx/theta_sketch_intersection_seed.sqlx)
+Computes a sketch that represents the scalar intersection of the two given 
sketches.<br><br>Param sketchA: the first sketch as BYTES.<br>Param sketchB: 
the second sketch as BYTES.<br>Param seed: This is used to confirm that the 
given sketches were configured with the correct seed.<br>Returns: a Compact, 
Compressed Theta Sketch, as BYTES.
+### [theta_sketch_jaccard_similarity_seed(sketchA BYTES, sketchB BYTES, seed 
INT64)](../theta/sqlx/theta_sketch_jaccard_similarity_seed.sqlx)
+Computes the Jaccard similarity index with upper and lower bounds.<br>The 
Jaccard similarity index J\(A,B\) = \(A ^ B\)/\(A U B\) is used to measure how 
similar the two sketches are to each other.<br>If J = 1.0, the sketches are 
considered equal. If J = 0, the two sketches are disjoint.<br>A Jaccard of .95 
means the overlap between the two sets is 95% of the union of the two 
sets.<br><br>Param sketchA: the first sketch as bytes.<br>Param sketchB: the 
second sketch as bytes.<br>Param seed [...]
+### [theta_sketch_a_not_b_seed(sketchA BYTES, sketchB BYTES, seed 
INT64)](../theta/sqlx/theta_sketch_a_not_b_seed.sqlx)
+Computes a sketch that represents the scalar set difference: sketchA and not 
sketchB.<br><br>Param sketchA: the first sketch "A" as bytes.<br>Param sketchB: 
the second sketch "B" as bytes.<br>Param seed: This is used to confirm that the 
given sketches were configured with the correct seed.<br>Returns: a Compact, 
Compressed Theta Sketch, as BYTES.
+### [theta_sketch_union_lgk_seed(sketchA BYTES, sketchB BYTES, lg_k BYTEINT, 
seed INT64)](../theta/sqlx/theta_sketch_union_lgk_seed.sqlx)
+Computes a sketch that represents the scalar union of the two given 
sketches.<br><br>Param sketchA: the first sketch as BYTES.<br>Param sketchB: 
the second sketch as BYTES.<br>Param lg\_k: the sketch accuracy/size parameter 
as an integer in the range \[4, 26\].<br>Param seed: This is used to confirm 
that the given sketches were configured with the correct seed.<br>Returns: a 
Compact, Compressed Theta Sketch, as BYTES.
+## Examples
 ```sql
 
 # using defaults
diff --git a/tuple/README.md b/tuple/README.md
index 85a2e03..4867449 100644
--- a/tuple/README.md
+++ b/tuple/README.md
@@ -36,41 +36,70 @@ If you are interested in making contributions to this 
project please see our
 [Community](https://datasketches.apache.org/docs/Community/) 
 page for how to contact us.
 
-| Function Name | Function Type | Signature | Description |
-|---|---|---|---|
-| 
[tuple_sketch_int64_agg_union](../tuple/sqlx/tuple_sketch_int64_agg_union.sqlx) 
| AGGREGATE | (sketch BYTES) -> BYTES | Builds a Tuple Sketch that represents 
the UNION of the given column of Tuple Sketches.<br>Note that cardinality 
estimation accuracy, plots, and error tables are the same as the Theta 
Sketch.<br>This function only applies to Tuple Sketches with an INT64 summary 
column.<br><br>Param sketch: the given column of Tuple Sketches with an INT64 
summary column. This may not be [...]
-| 
[tuple_sketch_int64_agg_string](../tuple/sqlx/tuple_sketch_int64_agg_string.sqlx)
 | AGGREGATE | (key STRING, value INT64) -> BYTES | Builds a Tuple Sketch from 
a STRING Key column and an INT64 value column.<br>Multiple values for the same 
key are aggregated using the default mode.<br>Note that cardinality estimation 
accuracy, plots, error tables, and sampling probability p are the same as the 
Theta Sketch.<br>This function only applies to Tuple Sketches with a STRING Key 
column and an  [...]
-| 
[tuple_sketch_int64_agg_int64](../tuple/sqlx/tuple_sketch_int64_agg_int64.sqlx) 
| AGGREGATE | (key INT64, value INT64) -> BYTES | Builds a Tuple Sketch from an 
INT64 Key column and an INT64 value column.<br>Multiple values for the same key 
are aggregated using the default mode.<br>Note that cardinality estimation 
accuracy, plots, error tables, and sampling probability p are the same as the 
Theta Sketch.<br>This function only applies to Tuple Sketches with an INT64 Key 
column and an INT [...]
-| 
[tuple_sketch_int64_agg_union_lgk_seed_mode](../tuple/sqlx/tuple_sketch_int64_agg_union_lgk_seed_mode.sqlx)
 | AGGREGATE | (sketch BYTES, params STRUCT<lg_k BYTEINT, seed INT64, mode 
STRING> NOT AGGREGATE) -> BYTES | Builds a Tuple Sketch that represents the 
UNION of the given column of Tuple Sketches.<br>Note that cardinality 
estimation accuracy, plots, and error tables are the same as the Theta 
Sketch.<br>This function only applies to Tuple Sketches with an INT64 summary 
column.<br><b [...]
-| 
[tuple_sketch_int64_agg_int64_lgk_seed_p_mode](../tuple/sqlx/tuple_sketch_int64_agg_int64_lgk_seed_p_mode.sqlx)
 | AGGREGATE | (key INT64, value INT64, params STRUCT<lg_k BYTEINT, seed INT64, 
p FLOAT64, mode STRING> NOT AGGREGATE) -> BYTES | Builds a Tuple Sketch from an 
INT64 Key column and an INT64 value column.<br>Multiple values for the same key 
are aggregated using one of the selectable operations: { SUM, MIN, MAX, ONE 
\(constant 1\) }.<br>Note that cardinality estimation accuracy, [...]
-| 
[tuple_sketch_int64_agg_string_lgk_seed_p_mode](../tuple/sqlx/tuple_sketch_int64_agg_string_lgk_seed_p_mode.sqlx)
 | AGGREGATE | (key STRING, value INT64, params STRUCT<lg_k BYTEINT, seed 
INT64, p FLOAT64, mode STRING> NOT AGGREGATE) -> BYTES | Builds a Tuple Sketch 
from a STRING Key column and an INT64 value column.<br>Multiple values for the 
same key are aggregated using one of the selectable operations: SUM, MIN, MAX, 
ONE.<br>Note that cardinality estimation accuracy, plots, error ta [...]
-| 
[tuple_sketch_int64_to_string](../tuple/sqlx/tuple_sketch_int64_to_string.sqlx) 
| SCALAR | (sketch BYTES) -> STRING | Returns a human readable STRING that is a 
short summary of the state of this sketch.<br>  Note that cardinality 
estimation accuracy, plots, and error tables are the same as the Theta 
Sketch.<br>  This function only applies to Tuple Sketches with an INT64 summary 
column.<br><br>Param sketch: the sketch to be summarized. This may not be 
NULL.<br>Defaults: seed = 9001.<br> [...]
-| 
[tuple_sketch_int64_get_estimate](../tuple/sqlx/tuple_sketch_int64_get_estimate.sqlx)
 | SCALAR | (sketch BYTES) -> FLOAT64 | Returns the cardinality estimate of the 
given Tuple Sketch.<br>Note that cardinality estimation accuracy, plots, and 
error tables are the same as the Theta Sketch.<br>This function only applies to 
Tuple Sketches with an INT64 summary column.<br>  <br>Param sketch: the given 
Tuple Sketch. This may not be NULL.<br>Defaults: seed = 9001.<br>Returns: the 
cardinality  [...]
-| 
[tuple_sketch_int64_get_theta](../tuple/sqlx/tuple_sketch_int64_get_theta.sqlx) 
| SCALAR | (sketch BYTES) -> FLOAT64 | Returns theta \(effective sampling 
rate\) as a fraction from 0 to 1.<br>Note that cardinality estimation accuracy, 
plots, and error tables are the same as the Theta Sketch.<br>This function only 
applies to Tuple Sketches with an INT64 summary column.<br>  <br>Param sketch: 
the given Tuple Sketch. This may not be NULL.<br>Defaults: seed = 
9001.<br>Returns: theta as FLOAT64. |
-| 
[tuple_sketch_int64_get_num_retained](../tuple/sqlx/tuple_sketch_int64_get_num_retained.sqlx)
 | SCALAR | (sketch BYTES) -> INT | Returns the number of retained entries in 
the given sketch.<br>Note that cardinality estimation accuracy, plots, and 
error tables are the same as the Theta Sketch.<br>This function only applies to 
Tuple Sketches with an INT64 summary column.<br>  <br>Param sketch: the given 
Tuple Sketch. This may not be NULL.<br>Defaults: seed = 9001.<br>Returns: 
number of re [...]
-| 
[tuple_sketch_int64_get_theta_seed](../tuple/sqlx/tuple_sketch_int64_get_theta_seed.sqlx)
 | SCALAR | (sketch BYTES, seed INT64) -> FLOAT64 | Returns theta \(effective 
sampling rate\) as a fraction from 0 to 1.<br>Note that cardinality estimation 
accuracy, plots, and error tables are the same as the Theta Sketch.<br>This 
function only applies to Tuple Sketches with an INT64 summary column.<br>  
<br>Param sketch: the given Tuple Sketch. This may not be NULL.<br>Param seed: 
This is used t [...]
-| 
[tuple_sketch_int64_get_num_retained_seed](../tuple/sqlx/tuple_sketch_int64_get_num_retained_seed.sqlx)
 | SCALAR | (sketch BYTES, seed INT64) -> INT | Returns the number of retained 
entries in the given sketch.<br>Note that cardinality estimation accuracy, 
plots, and error tables are the same as the Theta Sketch.<br>This function only 
applies to Tuple Sketches with an INT64 summary column.<br>  <br>Param sketch: 
the given Tuple Sketch. This may not be NULL.<br>Param seed: This is used  [...]
-| 
[tuple_sketch_int64_to_string_seed](../tuple/sqlx/tuple_sketch_int64_to_string_seed.sqlx)
 | SCALAR | (sketch BYTES, seed INT64) -> STRING | Returns a human readable 
STRING that is a short summary of the state of this sketch.<br>  Note that 
cardinality estimation accuracy, plots, and error tables are the same as the 
Theta Sketch.<br>  This function only applies to Tuple Sketches with an INT64 
summary column.<br><br>Param sketch: the sketch to be summarized. This may not 
be NULL.<br>Para [...]
-| [tuple_sketch_int64_a_not_b](../tuple/sqlx/tuple_sketch_int64_a_not_b.sqlx) 
| SCALAR | (sketchA BYTES, sketchB BYTES) -> BYTES | Computes a sketch that 
represents the set difference of sketchA and not sketchB.<br>Note that 
cardinality estimation accuracy, plots, and error tables are the same as the 
Theta Sketch.<br>This function only applies to Tuple Sketches with an INT64 
summary column. <br>  <br>Param sketchA: the first sketch "A" as BYTES. This 
may not be NULL.<br>Param sketchB: th [...]
-| 
[tuple_sketch_int64_from_theta_sketch](../tuple/sqlx/tuple_sketch_int64_from_theta_sketch.sqlx)
 | SCALAR | (sketch BYTES, value INT64) -> BYTES | Converts the given Theta 
Sketch into a Tuple Sketch with a INT64 summary column set to the given INT64 
value.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br><br>Param sketch: the given Theta Sketch. 
This may not be NULL.<br>Param value: the given INT64 value. This may not be 
NULL.<br [...]
-| 
[tuple_sketch_int64_get_estimate_seed](../tuple/sqlx/tuple_sketch_int64_get_estimate_seed.sqlx)
 | SCALAR | (sketch BYTES, seed INT64) -> FLOAT64 | Returns the cardinality 
estimate of the given Tuple Sketch.<br>Note that cardinality estimation 
accuracy, plots, and error tables are the same as the Theta Sketch.<br>This 
function only applies to Tuple Sketches with an INT64 summary column.<br>  
<br>Param sketch: the given Tuple Sketch. This may not be NULL.<br>Param seed: 
This is used to c [...]
-| 
[tuple_sketch_int64_intersection](../tuple/sqlx/tuple_sketch_int64_intersection.sqlx)
 | SCALAR | (sketchA BYTES, sketchB BYTES) -> BYTES | Computes a sketch that 
represents the scalar intersection of sketchA and sketchB.<br>Note that 
cardinality estimation accuracy, plots, and error tables are the same as the 
Theta Sketch.<br>This function only applies to Tuple Sketches with an INT64 
summary column.<br><br>Param sketchA: the first sketch "A" as BYTES.<br>Param 
sketchB: the second sketc [...]
-| [tuple_sketch_int64_union](../tuple/sqlx/tuple_sketch_int64_union.sqlx) | 
SCALAR | (sketchA BYTES, sketchB BYTES) -> BYTES | Computes a Tuple Sketch that 
represents the UNION of sketchA and sketchB.<br>Note that cardinality 
estimation accuracy, plots, and error tables are the same as the Theta 
Sketch.<br>This function only applies to Tuple Sketches with an INT64 summary 
column.<br><br>Param sketchA: the first sketch "A" as BYTES. This may not be 
NULL.<br>Param sketchB: the second sketc [...]
-| 
[tuple_sketch_int64_from_theta_sketch_seed](../tuple/sqlx/tuple_sketch_int64_from_theta_sketch_seed.sqlx)
 | SCALAR | (sketch BYTES, value INT64, seed INT64) -> BYTES | Converts the 
given Theta Sketch into a Tuple Sketch with a INT64 summary column set to the 
given INT64 value.<br>Note that cardinality estimation accuracy, plots, and 
error tables are the same as the Theta Sketch.<br><br>Param sketch: the given 
Theta Sketch. This may not be NULL.<br>Param value: the given INT64 value. Th 
[...]
-| 
[tuple_sketch_int64_a_not_b_seed](../tuple/sqlx/tuple_sketch_int64_a_not_b_seed.sqlx)
 | SCALAR | (sketchA BYTES, sketchB BYTES, seed INT64) -> BYTES | Computes a 
sketch that represents the scalar set difference of sketchA and not 
sketchB.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketchA: the first sketch 
"A" as BYTES. This may not be  [...]
-| 
[tuple_sketch_int64_filter_low_high](../tuple/sqlx/tuple_sketch_int64_filter_low_high.sqlx)
 | SCALAR | (sketch BYTES, low INT64, high INT64) -> BYTES | Returns a Tuple 
Sketch computed from the given sketch filtered by the given low and high 
values. <br>This returns a compact tuple sketch that contains the subset of 
rows of the give sketch where the<br>summary column is greater\-than or equal 
to the given low and less\-than or equal to the given high.<br>Note that 
cardinality estimation [...]
-| 
[tuple_sketch_int64_get_estimate_and_bounds](../tuple/sqlx/tuple_sketch_int64_get_estimate_and_bounds.sqlx)
 | SCALAR | (sketch BYTES, num_std_devs BYTEINT) -> STRUCT<estimate FLOAT64, 
lower_bound FLOAT64, upper_bound FLOAT64> | Returns the cardinality estimate 
and bounds from the given Tuple Sketch.<br>Note that cardinality estimation 
accuracy, plots, and error tables are the same as the Theta Sketch.<br>This 
function only applies to Tuple Sketches with an INT64 summary column.<br>  <b 
[...]
-| 
[tuple_sketch_int64_filter_low_high_seed](../tuple/sqlx/tuple_sketch_int64_filter_low_high_seed.sqlx)
 | SCALAR | (sketch BYTES, low INT64, high INT64, seed INT64) -> BYTES | 
Returns a Tuple Sketch computed from the given sketch filtered by the given low 
and high values. <br>This returns a compact tuple sketch that contains the 
subset of rows of the give sketch where the<br>summary column is greater\-than 
or equal to the given low and less\-than or equal to the given high.<br>Note 
that  [...]
-| 
[tuple_sketch_int64_jaccard_similarity](../tuple/sqlx/tuple_sketch_int64_jaccard_similarity.sqlx)
 | SCALAR | (sketchA BYTES, sketchB BYTES) -> STRUCT<lower_bound FLOAT64, 
estimate FLOAT64, upper_bound FLOAT64> | Computes the Jaccard similarity index 
with upper and lower bounds.<br>The Jaccard similarity index J\(A,B\) = \(A ^ 
B\)/\(A U B\) is used to measure how similar the two sketches are to each 
other.<br>If J = 1.0, the sketches are considered equal. If J = 0, the two 
sketches are  [...]
-| 
[tuple_sketch_int64_get_sum_estimate_and_bounds](../tuple/sqlx/tuple_sketch_int64_get_sum_estimate_and_bounds.sqlx)
 | SCALAR | (sketch BYTES, num_std_devs BYTEINT) -> STRUCT<sum_estimate 
FLOAT64, sum_lower_bound FLOAT64, sum_upper_bound FLOAT64> | Returns the 
estimate and bounds for the sum of the INT64 summary column<br>scaled to the 
original population from the given Tuple Sketch.<br>Note that cardinality 
estimation accuracy, plots, and error tables are the same as the Theta Sketch.< 
[...]
-| 
[tuple_sketch_int64_intersection_seed_mode](../tuple/sqlx/tuple_sketch_int64_intersection_seed_mode.sqlx)
 | SCALAR | (sketchA BYTES, sketchB BYTES, seed INT64, mode STRING) -> BYTES | 
Computes a sketch that represents the scalar intersection of sketchA and 
sketchB.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketchA: the first sketch 
"A" [...]
-| 
[tuple_sketch_int64_get_sum_estimate_and_bounds_seed](../tuple/sqlx/tuple_sketch_int64_get_sum_estimate_and_bounds_seed.sqlx)
 | SCALAR | (sketch BYTES, num_std_devs BYTEINT, seed INT64) -> 
STRUCT<sum_estimate FLOAT64, sum_lower_bound FLOAT64, sum_upper_bound FLOAT64> 
| Returns the estimate and bounds for the sum of the INT64 summary 
column<br>scaled to the original population from the given Tuple 
Sketch.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same [...]
-| 
[tuple_sketch_int64_union_lgk_seed_mode](../tuple/sqlx/tuple_sketch_int64_union_lgk_seed_mode.sqlx)
 | SCALAR | (sketchA BYTES, sketchB BYTES, lg_k BYTEINT, seed INT64, mode 
STRING) -> BYTES | Computes a Tuple Sketch that represents the UNION of sketchA 
and sketchB.<br>Note that cardinality estimation accuracy, plots, and error 
tables are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketchA: the first sketch 
"A" [...]
-| 
[tuple_sketch_int64_get_estimate_and_bounds_seed](../tuple/sqlx/tuple_sketch_int64_get_estimate_and_bounds_seed.sqlx)
 | SCALAR | (sketch BYTES, num_std_devs BYTEINT, seed INT64) -> STRUCT<estimate 
FLOAT64, lower_bound FLOAT64, upper_bound FLOAT64> | Returns the cardinality 
estimate and bounds from the given Tuple Sketch.<br>Note that cardinality 
estimation accuracy, plots, and error tables are the same as the Theta 
Sketch.<br>This function only applies to Tuple Sketches with an INT64 s [...]
-| 
[tuple_sketch_int64_jaccard_similarity_seed](../tuple/sqlx/tuple_sketch_int64_jaccard_similarity_seed.sqlx)
 | SCALAR | (sketchA BYTES, sketchB BYTES, seed INT64) -> STRUCT<lower_bound 
FLOAT64, estimate FLOAT64, upper_bound FLOAT64> | Computes the Jaccard 
similarity index with upper and lower bounds.<br>The Jaccard similarity index 
J\(A,B\) = \(A ^ B\)/\(A U B\) is used to measure how similar the two sketches 
are to each other.<br>If J = 1.0, the sketches are considered equal. If J = 0, 
[...]
-
-**Examples:**
-
+## Aggregate Functions
+### [tuple_sketch_int64_agg_union(sketch 
BYTES)](../tuple/sqlx/tuple_sketch_int64_agg_union.sqlx)
+Builds a Tuple Sketch that represents the UNION of the given column of Tuple 
Sketches.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketch: the given column of 
Tuple Sketches with an INT64 summary column. This may not be NULL.<br>Defaults: 
lg\_k = 12, seed = 9001, mode = SUM.<br>Returns: a Compact Tuple Sketch as 
BYTES. 
+### [tuple_sketch_int64_agg_string(key STRING, value 
INT64)](../tuple/sqlx/tuple_sketch_int64_agg_string.sqlx)
+Builds a Tuple Sketch from a STRING Key column and an INT64 value 
column.<br>Multiple values for the same key are aggregated using the default 
mode.<br>Note that cardinality estimation accuracy, plots, error tables, and 
sampling probability p are the same as the Theta Sketch.<br>This function only 
applies to Tuple Sketches with a STRING Key column and an INT64 summary 
column.<br> <br>Param key: the STRING column of identifiers. This may not be 
NULL.<br>Param value: the INT64 value column [...]
+### [tuple_sketch_int64_agg_int64(key INT64, value 
INT64)](../tuple/sqlx/tuple_sketch_int64_agg_int64.sqlx)
+Builds a Tuple Sketch from an INT64 Key column and an INT64 value 
column.<br>Multiple values for the same key are aggregated using the default 
mode.<br>Note that cardinality estimation accuracy, plots, error tables, and 
sampling probability p are the same as the Theta Sketch.<br>This function only 
applies to Tuple Sketches with an INT64 Key column and an INT64 summary 
column.<br><br>Param key: the INT64 key column of identifiers. This may not be 
NULL.<br>Param value: the INT64 value colu [...]
+### [tuple_sketch_int64_agg_union_lgk_seed_mode(sketch BYTES, params 
STRUCT<lg_k BYTEINT, seed INT64, mode STRING> NOT 
AGGREGATE)](../tuple/sqlx/tuple_sketch_int64_agg_union_lgk_seed_mode.sqlx)
+Builds a Tuple Sketch that represents the UNION of the given column of Tuple 
Sketches.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketch: the given column of 
Tuple Sketches with an INT64 summary column. This may not be NULL.<br>Param 
lg\_k: the sketch accuracy/size parameter as an integer in the range \[4, 26\]. 
A NULL specifies the defau [...]
+### [tuple_sketch_int64_agg_int64_lgk_seed_p_mode(key INT64, value INT64, 
params STRUCT<lg_k BYTEINT, seed INT64, p FLOAT64, mode STRING> NOT 
AGGREGATE)](../tuple/sqlx/tuple_sketch_int64_agg_int64_lgk_seed_p_mode.sqlx)
+Builds a Tuple Sketch from an INT64 Key column and an INT64 value 
column.<br>Multiple values for the same key are aggregated using one of the 
selectable operations: { SUM, MIN, MAX, ONE \(constant 1\) }.<br>Note that 
cardinality estimation accuracy, plots, error tables, and sampling probability 
p are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 Key column and an INT64 summary column.<br><br>Param 
key: the INT64 key column of identifiers. Thi [...]
+### [tuple_sketch_int64_agg_string_lgk_seed_p_mode(key STRING, value INT64, 
params STRUCT<lg_k BYTEINT, seed INT64, p FLOAT64, mode STRING> NOT 
AGGREGATE)](../tuple/sqlx/tuple_sketch_int64_agg_string_lgk_seed_p_mode.sqlx)
+Builds a Tuple Sketch from a STRING Key column and an INT64 value 
column.<br>Multiple values for the same key are aggregated using one of the 
selectable operations: SUM, MIN, MAX, ONE.<br>Note that cardinality estimation 
accuracy, plots, error tables, and sampling probability p are the same as the 
Theta Sketch.<br>This function only applies to Tuple Sketches with a STRING Key 
column and an INT64 summary column.<br><br>Param key: the STRING key column of 
identifiers. This may not be NULL. [...]
+
+## Scalar Functions
+### [tuple_sketch_int64_to_string(sketch 
BYTES)](../tuple/sqlx/tuple_sketch_int64_to_string.sqlx)
+Returns a human readable STRING that is a short summary of the state of this 
sketch.<br>  Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>  This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketch: the sketch to be 
summarized. This may not be NULL.<br>Defaults: seed = 9001.<br>Returns: A human 
readable STRING that is a short summary of the state of this sketch.
+### [tuple_sketch_int64_get_estimate(sketch 
BYTES)](../tuple/sqlx/tuple_sketch_int64_get_estimate.sqlx)
+Returns the cardinality estimate of the given Tuple Sketch.<br>Note that 
cardinality estimation accuracy, plots, and error tables are the same as the 
Theta Sketch.<br>This function only applies to Tuple Sketches with an INT64 
summary column.<br>  <br>Param sketch: the given Tuple Sketch. This may not be 
NULL.<br>Defaults: seed = 9001.<br>Returns: the cardinality estimate of the 
given Tuple Sketch
+### [tuple_sketch_int64_get_theta(sketch 
BYTES)](../tuple/sqlx/tuple_sketch_int64_get_theta.sqlx)
+Returns theta \(effective sampling rate\) as a fraction from 0 to 1.<br>Note 
that cardinality estimation accuracy, plots, and error tables are the same as 
the Theta Sketch.<br>This function only applies to Tuple Sketches with an INT64 
summary column.<br>  <br>Param sketch: the given Tuple Sketch. This may not be 
NULL.<br>Defaults: seed = 9001.<br>Returns: theta as FLOAT64.
+### [tuple_sketch_int64_get_num_retained(sketch 
BYTES)](../tuple/sqlx/tuple_sketch_int64_get_num_retained.sqlx)
+Returns the number of retained entries in the given sketch.<br>Note that 
cardinality estimation accuracy, plots, and error tables are the same as the 
Theta Sketch.<br>This function only applies to Tuple Sketches with an INT64 
summary column.<br>  <br>Param sketch: the given Tuple Sketch. This may not be 
NULL.<br>Defaults: seed = 9001.<br>Returns: number of retained entries as INT.
+### [tuple_sketch_int64_get_theta_seed(sketch BYTES, seed 
INT64)](../tuple/sqlx/tuple_sketch_int64_get_theta_seed.sqlx)
+Returns theta \(effective sampling rate\) as a fraction from 0 to 1.<br>Note 
that cardinality estimation accuracy, plots, and error tables are the same as 
the Theta Sketch.<br>This function only applies to Tuple Sketches with an INT64 
summary column.<br>  <br>Param sketch: the given Tuple Sketch. This may not be 
NULL.<br>Param seed: This is used to confirm that the given sketches were 
configured with the correct seed. A NULL specifies the default seed = 
9001.<br>Returns: theta as FLOAT64.
+### [tuple_sketch_int64_get_num_retained_seed(sketch BYTES, seed 
INT64)](../tuple/sqlx/tuple_sketch_int64_get_num_retained_seed.sqlx)
+Returns the number of retained entries in the given sketch.<br>Note that 
cardinality estimation accuracy, plots, and error tables are the same as the 
Theta Sketch.<br>This function only applies to Tuple Sketches with an INT64 
summary column.<br>  <br>Param sketch: the given Tuple Sketch. This may not be 
NULL.<br>Param seed: This is used to confirm that the given sketches were 
configured with the correct seed. A NULL specifies the default seed = 
9001.<br>Returns: number of retained entrie [...]
+### [tuple_sketch_int64_to_string_seed(sketch BYTES, seed 
INT64)](../tuple/sqlx/tuple_sketch_int64_to_string_seed.sqlx)
+Returns a human readable STRING that is a short summary of the state of this 
sketch.<br>  Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>  This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketch: the sketch to be 
summarized. This may not be NULL.<br>Param seed: This is used to confirm that 
the given sketches were configured with the correct seed. A NULL specifies the 
default seed = 9001.<br>Re [...]
+### [tuple_sketch_int64_get_estimate_and_bounds(sketch BYTES, num_std_devs 
BYTEINT)](../tuple/sqlx/tuple_sketch_int64_get_estimate_and_bounds.sqlx)
+Returns the cardinality estimate and bounds from the given Tuple 
Sketch.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br>  <br>Param sketch: the given Tuple 
Sketch. This may not be NULL.<br>Param num\_std\_devs: The returned bounds will 
be based on the statistical confidence interval<br>  determined by the given 
number of standard deviations from the re [...]
+### [tuple_sketch_int64_jaccard_similarity(sketchA BYTES, sketchB 
BYTES)](../tuple/sqlx/tuple_sketch_int64_jaccard_similarity.sqlx)
+Computes the Jaccard similarity index with upper and lower bounds.<br>The 
Jaccard similarity index J\(A,B\) = \(A ^ B\)/\(A U B\) is used to measure how 
similar the two sketches are to each other.<br>If J = 1.0, the sketches are 
considered equal. If J = 0, the two sketches are disjoint.<br>A Jaccard of .95 
means the overlap between the two sets is 95% of the union of the two 
sets.<br>This function only applies to Tuple Sketches with an INT64 summary 
column.<br><br>Param sketchA: the firs [...]
+### [tuple_sketch_int64_a_not_b(sketchA BYTES, sketchB 
BYTES)](../tuple/sqlx/tuple_sketch_int64_a_not_b.sqlx)
+Computes a sketch that represents the set difference of sketchA and not 
sketchB.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column. <br>  <br>Param sketchA: the first 
sketch "A" as BYTES. This may not be NULL.<br>Param sketchB: the second sketch 
"B" as BYTES. This may not be NULL.<br>Defaults: seed = 9001.<br>Returns: a 
Compact Tuple Sketch as BYTES.
+### [tuple_sketch_int64_from_theta_sketch(sketch BYTES, value 
INT64)](../tuple/sqlx/tuple_sketch_int64_from_theta_sketch.sqlx)
+Converts the given Theta Sketch into a Tuple Sketch with a INT64 summary 
column set to the given INT64 value.<br>Note that cardinality estimation 
accuracy, plots, and error tables are the same as the Theta 
Sketch.<br><br>Param sketch: the given Theta Sketch. This may not be 
NULL.<br>Param value: the given INT64 value. This may not be NULL.<br>Defaults: 
seed = 9001.<br>Returns: a Tuple Sketch with an INT64 summary column as BYTES.
+### [tuple_sketch_int64_get_sum_estimate_and_bounds(sketch BYTES, num_std_devs 
BYTEINT)](../tuple/sqlx/tuple_sketch_int64_get_sum_estimate_and_bounds.sqlx)
+Returns the estimate and bounds for the sum of the INT64 summary 
column<br>scaled to the original population from the given Tuple 
Sketch.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br>  <br>Param sketch: the given Tuple 
Sketch. This may not be NULL.<br>Param num\_std\_devs: The returned bounds will 
be based on the statistical confidence interval<br>   [...]
+### [tuple_sketch_int64_get_estimate_seed(sketch BYTES, seed 
INT64)](../tuple/sqlx/tuple_sketch_int64_get_estimate_seed.sqlx)
+Returns the cardinality estimate of the given Tuple Sketch.<br>Note that 
cardinality estimation accuracy, plots, and error tables are the same as the 
Theta Sketch.<br>This function only applies to Tuple Sketches with an INT64 
summary column.<br>  <br>Param sketch: the given Tuple Sketch. This may not be 
NULL.<br>Param seed: This is used to confirm that the given sketches were 
configured with the correct seed. A NULL specifies the default seed = 
9001.<br>Returns: the cardinality estimate  [...]
+### [tuple_sketch_int64_intersection(sketchA BYTES, sketchB 
BYTES)](../tuple/sqlx/tuple_sketch_int64_intersection.sqlx)
+Computes a sketch that represents the scalar intersection of sketchA and 
sketchB.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketchA: the first sketch 
"A" as BYTES.<br>Param sketchB: the second sketch "B" as BYTES.<br>Defaults: 
seed = 9001.<br>Returns: a Compact Tuple Sketch as BYTES.
+### [tuple_sketch_int64_union(sketchA BYTES, sketchB 
BYTES)](../tuple/sqlx/tuple_sketch_int64_union.sqlx)
+Computes a Tuple Sketch that represents the UNION of sketchA and 
sketchB.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketchA: the first sketch 
"A" as BYTES. This may not be NULL.<br>Param sketchB: the second sketch "B" as 
BYTES. This may not be NULL.<br>Defaults: seed = 9001.<br>Returns: a Compact 
Tuple Sketch as BYTES.
+### [tuple_sketch_int64_from_theta_sketch_seed(sketch BYTES, value INT64, seed 
INT64)](../tuple/sqlx/tuple_sketch_int64_from_theta_sketch_seed.sqlx)
+Converts the given Theta Sketch into a Tuple Sketch with a INT64 summary 
column set to the given INT64 value.<br>Note that cardinality estimation 
accuracy, plots, and error tables are the same as the Theta 
Sketch.<br><br>Param sketch: the given Theta Sketch. This may not be 
NULL.<br>Param value: the given INT64 value. This may not be NULL.<br>Param 
seed: This is used to confirm that the given sketches were configured with the 
correct seed. A NULL specifies the default seed = 9001.<br>Ret [...]
+### [tuple_sketch_int64_get_sum_estimate_and_bounds_seed(sketch BYTES, 
num_std_devs BYTEINT, seed 
INT64)](../tuple/sqlx/tuple_sketch_int64_get_sum_estimate_and_bounds_seed.sqlx)
+Returns the estimate and bounds for the sum of the INT64 summary 
column<br>scaled to the original population from the given Tuple 
Sketch.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketch: the given Tuple 
Sketch. This may not be NULL.<br>Param num\_std\_devs: The returned bounds will 
be based on the statistical confidence interval<br>  de [...]
+### [tuple_sketch_int64_get_estimate_and_bounds_seed(sketch BYTES, 
num_std_devs BYTEINT, seed 
INT64)](../tuple/sqlx/tuple_sketch_int64_get_estimate_and_bounds_seed.sqlx)
+Returns the cardinality estimate and bounds from the given Tuple 
Sketch.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br>  <br>Param sketch: the given Tuple 
Sketch. This may not be NULL.<br>Param num\_std\_devs: The returned bounds will 
be based on the statistical confidence interval<br>  determined by the given 
number of standard deviations from the re [...]
+### [tuple_sketch_int64_a_not_b_seed(sketchA BYTES, sketchB BYTES, seed 
INT64)](../tuple/sqlx/tuple_sketch_int64_a_not_b_seed.sqlx)
+Computes a sketch that represents the scalar set difference of sketchA and not 
sketchB.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketchA: the first sketch 
"A" as BYTES. This may not be NULL.<br>Param sketchB: the second sketch "B" as 
BYTES. This may not be NULL.<br>Param seed: This is used to confirm that the 
given sketches were configu [...]
+### [tuple_sketch_int64_jaccard_similarity_seed(sketchA BYTES, sketchB BYTES, 
seed INT64)](../tuple/sqlx/tuple_sketch_int64_jaccard_similarity_seed.sqlx)
+Computes the Jaccard similarity index with upper and lower bounds.<br>The 
Jaccard similarity index J\(A,B\) = \(A ^ B\)/\(A U B\) is used to measure how 
similar the two sketches are to each other.<br>If J = 1.0, the sketches are 
considered equal. If J = 0, the two sketches are disjoint.<br>A Jaccard of .95 
means the overlap between the two sets is 95% of the union of the two 
sets.<br>This function only applies to Tuple Sketches with an INT64 summary 
column.<br><br>Param sketchA: the firs [...]
+### [tuple_sketch_int64_filter_low_high(sketch BYTES, low INT64, high 
INT64)](../tuple/sqlx/tuple_sketch_int64_filter_low_high.sqlx)
+Returns a Tuple Sketch computed from the given sketch filtered by the given 
low and high values. <br>This returns a compact tuple sketch that contains the 
subset of rows of the give sketch where the<br>summary column is greater\-than 
or equal to the given low and less\-than or equal to the given high.<br>Note 
that cardinality estimation accuracy, plots, and error tables are the same as 
the Theta Sketch.<br>This function only applies to Tuple Sketches with an INT64 
summary column.<br><br> [...]
+### [tuple_sketch_int64_filter_low_high_seed(sketch BYTES, low INT64, high 
INT64, seed INT64)](../tuple/sqlx/tuple_sketch_int64_filter_low_high_seed.sqlx)
+Returns a Tuple Sketch computed from the given sketch filtered by the given 
low and high values. <br>This returns a compact tuple sketch that contains the 
subset of rows of the give sketch where the<br>summary column is greater\-than 
or equal to the given low and less\-than or equal to the given high.<br>Note 
that cardinality estimation accuracy, plots, and error tables are the same as 
the Theta Sketch.<br>This function only applies to Tuple Sketches with an INT64 
summary column.<br><br> [...]
+### [tuple_sketch_int64_intersection_seed_mode(sketchA BYTES, sketchB BYTES, 
seed INT64, mode 
STRING)](../tuple/sqlx/tuple_sketch_int64_intersection_seed_mode.sqlx)
+Computes a sketch that represents the scalar intersection of sketchA and 
sketchB.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketchA: the first sketch 
"A" as BYTES.<br>Param sketchB: the second sketch "B" as BYTES.<br>Param seed: 
This is used to confirm that the given sketches were configured with the 
correct seed. A NULL specifies the de [...]
+### [tuple_sketch_int64_union_lgk_seed_mode(sketchA BYTES, sketchB BYTES, lg_k 
BYTEINT, seed INT64, mode 
STRING)](../tuple/sqlx/tuple_sketch_int64_union_lgk_seed_mode.sqlx)
+Computes a Tuple Sketch that represents the UNION of sketchA and 
sketchB.<br>Note that cardinality estimation accuracy, plots, and error tables 
are the same as the Theta Sketch.<br>This function only applies to Tuple 
Sketches with an INT64 summary column.<br><br>Param sketchA: the first sketch 
"A" as BYTES. This may not be NULL.<br>Param sketchB: the second sketch "B" as 
BYTES. This may not be NULL.<br>Param seed: This is used to confirm that the 
given sketches were configured with the c [...]
+## Examples
 ```sql
 
 # using defaults


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