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Mathematical Functions and Operators

Mathematical operators are provided for many Hyper types. For types without standard mathematical conventions (e.g., date/time types) we describe the actual behavior in subsequent sections.

The following mathematical operators are available:

+addition2 + 35
-subtraction2 - 3-1
*multiplication2 * 36
/division (integer division truncates the result)4 / 22
%modulo (remainder)5 % 41
^exponentiation (associates left to right)2.0 ^ 3.08
|/square root|/ 25.05
||/cube root||/ 27.03
@absolute value@ -5.05
&bitwise AND91 & 1511
|bitwise OR32 | 335
#bitwise XOR17 # 520
~bitwise NOT~1-2
<<bitwise shift left1 << 416
>>bitwise shift right8 >> 22

The bitwise operators work only on integral data types, whereas the others are available for all numeric data types.

The next table shows the available mathematical functions. In the table, dp indicates double precision. Many of these functions are provided in multiple forms with different argument types. Except where noted, any given form of a function returns the same data type as its argument. Note that every function, unless stated otherwise, returns an error in case of failures.

FunctionReturn TypeDescriptionExample
abs(x)same as inputabsolute valueabs(-17.4)17.4
cbrt(dp)dpcube rootcbrt(27.0)3.0
ceil(dp or numeric)same as inputnearest integer greater than or equal to argumentceil(-42.8)-42.0
ceiling(dp or numeric)same as inputnearest integer greater than or equal to argument (same as ceil)ceiling(-95.3)-95.0
degrees(dp)dpradians to degreesdegrees(0.5)28.6478897565412
div(y, x)same as input, bigint for numericinteger quotient of y/xdiv(9,4)2
floor(dp or numeric)same as inputnearest integer less than or equal to argumentfloor(-42.8)-43.0
ln(x)dpnatural logarithmln(2.0)0.693147180559945
log(x)dpbase 10 logarithmlog(100.0)2.0
log(b, x)dplogarithm to base blog(2.0, 64.0)6.0000000000
mod(y, x)same as input, bigint for numericremainder of y/xmod(9,4)1
pi()dp"𝜋" constantpi()3.14159265358979
power(a, b)dp or numerica raised to the power of bpower(9.0, 3.0)729
radians(x)dpdegrees to radiansradians(45.0)0.785398163397448
random()dprandom value in the range 0.0 <= x < 1.0random()0.6817331
round(dp or numeric)same as inputround to nearest integerround(42.4)42
round(v dp or numeric, s int)same as inputround to s decimal placesround(42.4382, 2)42.44
sign(x)same as inputsign of the argument (-1, 0, +1)sign(-8.4)-1
sqrt(x)dpsquare rootsqrt(2.0)1.4142135623731
trunc(dp or numeric)same as inputtruncate toward zerotrunc(42.8)42
trunc(v dp or numeric, s int)same as inputtruncate to s decimal placestrunc(42.4382, 2)42.43
width_bucket(operand, b1, b2, count int)intreturn the bucket number to which operand would be assigned in a histogram having count equal-width buckets spanning the range b1 to b2; returns 0 or count+1 for an input outside the rangewidth_bucket(5.35, 0.024, 10.06, 5)3

The characteristics of the values returned by random() depend on the system implementation. It is not suitable for cryptographic applications.

Finally, there are also trigonometric functions available:

Function (radians)Description
acos(x)inverse cosine
asin(x)inverse sine
atan(x)inverse tangent
atan2(y, x)inverse tangent of y/x

All trigonometric functions return values of type double precision.