add new functions from recent releases (#60)

Adds functions from 8.1.2 and some that were added earlier.

reference/function/finance.md

@@ -28,9 +28,19 @@ Let's take the below order book as an example.
 A _buy market order_ with the size of 50 would wipe out the first two price levels of
 the _Ask_ side of the book, and would also trade on the third level.
 
-The full price of the trade: `14 * $14.50 + 16 * $14.60 + (50 - 14 - 16) * $14.80 = $732.6`
 
-The average price of the instrument in this trade: `$732.6 / 50 = $14.652`
+The full price of the trade:
+$$
+14 \cdot \$14.50 + 16 \cdot \$14.60 + (50 - 14 - 16) \cdot \$14.80 = \$732.60
+$$
+
+
+
+The average price of the instrument in this trade: 
+
+$$
+\$732.60 / 50 = \$14.652
+$$
 
 This average trade price is the output of the function when executed with the parameters taken from
 the above example:
@@ -115,11 +125,80 @@ SELECT ts, L2PRICE(100, askSize1, ask1, askSize2, ask2, askSize3, ask3)
 | 2024-05-22T09:40:15.175000Z | 0.565999999999 |
 | 2024-05-22T09:40:15.522000Z | 0.483          |
 
+
+## mid
+
+`mid(bid, ask)` - calculates the midpoint of a bidding price and asking price.
+
+Returns null if either argument is NaN or null.
+
+### Parameters
+
+- `bid` is any numeric bidding price value.
+- `ask` is any numeric asking price value.
+
+### Return value
+
+Return value type is `double`.
+
+### Examples
+
+```questdb-sql
+SELECT mid(1.5760, 1.5763)
+```
+
+| mid          |
+|:-------------|
+| 1.57615      |
+
+
+
+## spread_bps
+
+`spread_bps(bid, ask)` - calculates the quoted bid-ask spread, based on the highest bidding price,
+and the lowest asking price.
+
+The result is provided in basis points, and the calculation is:
+
+$$
+\frac
+{\text{spread}\left(\text{bid}, \text{ask}\right)}
+{\text{mid}\left(\text{bid}, \text{ask}\right)}
+\cdot
+10\,000
+$$
+
+
+### Parameters
+
+- `bid` is any numeric bidding price value.
+- `ask` is any numeric asking price value.
+
+### Return value
+
+Return value type is `double`.
+
+### Examples
+
+```questdb-sql
+SELECT spread_bps(1.5760, 1.5763)
+```
+
+| spread_bps     |
+|:---------------|
+| 1.903372140976 |
+
 ## vwap
 
 `vwap(price, quantity)` - Calculates the volume-weighted average price (VWAP)
-based on the given price and quantity columns. This is a handy replacement for
-the `sum(price * quantity) / sum(quantity)` expression.
+based on the given price and quantity columns. This is defined by the following formula:
+
+$$
+\text{vwap} =
+\frac
+{\text{sum}\left(\text{price} \cdot \text{quantity}\right)}
+{\text{sum}\left(\text{quantity}\right)}
+$$
 
 ### Parameters
 
@@ -140,3 +219,46 @@ FROM (SELECT x FROM long_sequence(100));
 | vwap |
 | :--- |
 | 67   |
+
+
+## wmid
+
+`wmid(bidSize, bidPrice, askPrice, askSize)` - calculates the weighted mid-price
+for a sized bid/ask pair.
+
+It is calculated with these formulae:
+
+$$
+\text{imbalance} = 
+\frac
+{ \text{bidSize} }
+{ \left(  \text{bidSize} + \text{askSize} \right) }
+$$
+
+$$
+\text{wmid} = \text{askPrice} \cdot \text{imbalance} 
++ \text{bidPrice} 
+\cdot \left( 1 - \text{imbalance} \right)
+$$
+
+### Parameters
+
+- `bidSize` is any numeric value representing the size of the bid offer.
+- `bidPrice` is any numeric value representing the bidding price.
+- `askPrice` is any numeric value representing the asking price.
+- `askSize` is any numeric value representing the size of the ask offer.
+
+### Return value
+
+Return value type is `double`.
+
+### Examples
+
+```questdb-sql
+SELECT wmid(100, 5, 6, 100)
+```
+
+| wmid |
+|:-----|
+| 5.5  |
+

reference/function/numeric.md

@@ -106,6 +106,56 @@ SELECT floor(15.75) as RoundedDown;
 | --------- |
 | 15        |
 
+
+## greatest
+
+`greatest(args...)` returns the largest entry in a series of numbers. 
+
+**Arguments:**
+
+- `args...` is a variable-size list of `long` or `double` values.
+
+**Return value:**
+
+Return value type is `double` or `long`.
+
+**Examples:**
+
+```questdb-sql
+SELECT greatest(11, 3, 8, 15)
+```
+
+| greatest |
+|----------|
+| 15       |
+
+
+
+## least
+
+`least(args...)` returns the smallest entry in a series of numbers.
+
+**Arguments:**
+
+- `args...` is a variable-size list of `long` or `double` values.
+
+**Return value:**
+
+Return value type is `double` or `long`.
+
+**Examples:**
+
+```questdb-sql
+SELECT least(11, 3, 8, 15)
+```
+
+| least |
+|-------|
+| 3     |
+
+
+
+
 ## ln
 
 `ln(value)` return the natural logarithm (**log*e***) of a given number.