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Mathematics and statistics

function rank ƒ semantics
+ 2 a add
- 2 a subtract
* 2 a multiply
% 2 a divide
$ 2 A dot product, matrix multiply
& 2 a lesser
| 2 a greater
abs 1 a absolute value
acos 1 a arccosine
asin 1 a arcsine
atan 1 a arctangent
avg 1 A arithmetic mean
avgs 1 u arithmetic means
ceiling 1 a round up to integer
cor 2 A correlation
cos 1 a cosine
cov 2 A covariance
deltas 1 u differences
dev 1 A standard deviation
div 2 a integer division
ema 2 m exponential moving average
exp 1 a ex
floor 1 a round down to integer
inv 1 u matrix inverse
log 1 a natural logarithm
lsq 2 matrix divide
mavg 2 m moving average
max 1 A greatest
maxs 1 u maximums
mcount 2 m moving count
mdev 2 m moving deviation
med 1 A median
min 1 A least
mins 1 u minimums
mmax 2 m moving maximum
mmin 2 m moving minimum
mmu 2 matrix multiply
mod 2 a modulo
msum 2 m moving sum
prd 1 A product
prds 1 u products
ratios 1 u ratios
reciprocal 1 a reciprocal
scov 2 A statistical covariance
sdev 1 A statistical standard deviation
signum 1 a sign
sin 1 a sine
sqrt 1 a square root
sum 1 A sum
sums 1 u sums
svar 1 A statistical variance
tan 1 a tangent
til 1 natural numbers till
var 1 A variance
wavg 2 A weighted average
wsum 2 A weighted sum
xbar 2 A round down
xexp 2 a xy
xlog 2 a base-x logarithm of y

ƒ – a: atomic; u: uniform; A: aggregate; m: moving

Domains and ranges

The domains and ranges of the mathematical functions have boolean, numeric, and temporal datatypes.

q)2+3 4 5
5 6 7
q)2012.05 2012.06m-2
2012.03 2012.04m
q)3.3 4.4 5.5*1b
3.3 4.4 5.5

Individual function articles tabulate non-obvious domain and range datatypes.

Dictionaries and tables

The domains and ranges also extend to:

  • dictionaries where the value of the dictionary is in the domain
    
        q)3+`a`b`c!(42;2012.09.15;1b)
        a| 45
        b| 2012.09.18
        c| 4
        
  • simple tables where the value of the flip of the table is in the domain
    
        q)3%([]b:1 2 3;c:45 46 47)
        b   c
        --------------
        3   0.06666667
        1.5 0.06521739
        1   0.06382979
        
  • keyed tables where the value of the table is in the domain
    
        q)show v:([sym:`ibm`goog`msoft]qty:1000 2000 3000;p:1550 375 98)
        sym  | qty  p
        -----| ---------
        ibm  | 1000 1550
        goog | 2000 375
        msoft| 3000 98
        q)v+5
        sym  | qty  p
        -----| ---------
        ibm  | 1005 1555
        goog | 2005 380
        msoft| 3005 103
        

Exceptions to the above:

cor                  scov
cov                  sdev
dev                  svar
div  (tables)        til
ema                  var
inv                  wavg (tables)
lsq                  wsum (tables)
mmu                  xbar (tables)
mod  (tables)        xexp (tables)

Mathematics with temporals

Temporal datatypes (timestamp, month, date, datetime, timespan, minute, second, time) are encoded as integer or float offsets from 2000.01.01 or 00:00.

Mathematical functions on temporals are applied to the underlying numerics. See domain/range tables for individual functions for the result datatypes.

Beyond addition and subtraction

Results for addition and subtraction are generally intuitive and useful; not always for other arithmetic functions.


q)2017.12.31+0 1 2
2017.12.31 2018.01.01 2018.01.02
q)2017.12m-0 1 2
2017.12 2017.11 2017.10m
q)2017.12m*0 1 2
2000.01 2017.12 2035.11m
q)2017.12m% 1 2 3
215 107.5 71.66667
q)00:10%2
5f
q)00:10:00%2
300f
q)00:10:00.000%2
300000f
q)00:10:00.000000000%2
3e+11

Aggregating nulls

avg, min, max and sum are special: they ignore nulls, in order to be similar to SQL92. But for nested x these functions preserve the nulls.

q)avg (1 2;0N 4)
0n 3