# Arithmetic (float)

These functions return floating-point results.

## % (divide)¶

Syntax: x % y (atomic)

where x and y are numeric, returns a float. Note that this is different from some other programming languages, e.g. C++.

q)2%3
0.6666667


## exp¶

Syntax: exp x (atomic)

Returns ex, where e is the base of natural logarithms.

q)exp 1
2.718282
q)exp 0.5
1.648721
q)exp -4.2 0 0.1 0n 0w
0.01499558 1 1.105171 0n 0w


## log¶

Syntax: log x (atomic)

Returns the natural logarithm of x. Null is returned if the argument is negative, and negative infinity where x is 0.

q)log 1
0f
q)log 0.5
-0.6931472
q)log exp 42
42f
q)log -2 0n 0 0.1 1 42
0n 0n -0w -2.302585 0 3.73767


## prd¶

Syntax: prd x (aggregate)

Product: where x is

• a simple numeric list, returns the product of the items of x
• an atom, returns x
• a list of numeric lists, returns their products

Nulls are treated as 1s.

q)prd 7                    / product of atom (returned unchanged)
7
q)prd 2 3 5 7              / product of list
210
q)prd 2 3 0N 7             / 0N is treated as 1
42
q)prd (1 2 3 4;2 3 5 7)    / product of list of lists
2 6 15 28
q)prd "abc"
'type


## prds¶

Syntax: prds x (atomic)

Returns the cumulative products of the items of x. The product of an atom is itself. Nulls are treated as 1s.

q)prds 7                     / atom is returned unchanged
7
q)prds 2 3 5 7               / cumulative products of list
2 6 30 210
q)prds 2 3 0N 7              / 0N is treated as 1
2 6 6 42
q)prds (1 2 3;2 3 5)         / cumulative products of list of lists
1 2 3                        / same as (1 2 3;1 2 3 * 2 3 5)
2 6 15
q)prds "abc"                 / type error if list is not numeric
'type


## ratios¶

Syntax: ratios y (uniform)
Syntax: ratios[x;y] (uniform)

Returns the ratios of consecutive pairs of items of numeric list y.

Where applied as:

• a binary function, the result is
(%[y 0;x];%[y 1;y 0];%[y 2;y 1];…;%[y n-1;y n-2])

q)ratios[5;1 2 4 6 7 10]
0.2 2 2 1.5 1.166667 1.428571

• a unary function, 1 replaces the x in the binary application.
q)ratios 1 2 4 6 7 10
1 2 2 1.5 1.166667 1.428571


Example

In a query to get returns on prices:


q)update ret:ratios price by sym from trade
q)select log ratios price from trade


## reciprocal¶

Syntax: reciprocal x (atomic)

Returns the reciprocal of x.

q)reciprocal 0 0w 0n 3 10
0w 0 0n 0.3333333 0.1


## sqrt¶

Syntax: sqrt x (atomic)

Returns the square root of x. Where x is negative or null, the result is null.

q)sqrt -1 0n 0 25 50
0n 0n 0 5 7.071068


## xexp¶

Syntax: x xexp y (atomic)

To the power: returns xy.

q)2 xexp 8
256f
q)9 xexp 0.5
3f
q)1.5 xexp -4.2 0 0.1 0n 0w
0.1821448 1 1.04138 0n 0w


Note

The calculation is performed as exp y * log x. Note that if y is integer, this is not identical to prd y#x.


q)\P 0
q)prd 3#2
8
q)2 xexp 3
7.9999999999999982
q)exp 3 * log 2
7.9999999999999982


## xlog¶

Syntax: x xlog y (atomic)

Returns the base-x logarithm of y. Where y is negative or zero, the result is null and negative infinity respectively.

q)2 xlog 8
3f
q)2 xlog 0.125
-3f
q)1.5 xlog 0 0.125 1 3 0n
-0w -5.128534 0 2.709511 0n


xlog and xexp

xlog is the inverse of xexp. Where both are defined, y=x xexp x xlog y.


q)2 xexp 2 xlog -1 0 0.125 1 42
0n 0 0.125 1 42