Mathematical Functions

abs

integer abs( integer arg );
long abs( long arg );
number abs( number arg );
decimal abs( decimal arg );

The abs() function returns the absolute value of a given argument of numeric data type (integer, long, number, or decimal).
If the given argument is null, the function fails with an error.
The abs() function behaves in the same way as the abs() function in Java or C/C++.
For the minimal integer, it returns minimal integer value: abs(-2147483648) returns -2147483648.
For the minimal long, it returns minimal long value: abs(-9223372036854775808L) returns -9223372036854775808.

Example 138. Usage of abs
The function abs(-123) returns 123 as integer.
The function abs(-1234L) returns 1234 as long.
The function abs(-1234.5) returns 1234.5 as number (double).
The function abs(-1234.6D) returns 1234.6 as decimal.

acos

number acos( decimal angle );
number acos( number angle );

The acos() function returns arc cosine of an angle.
If a given argument is null, the function fails with an error.

Example 139. Usage of acos
The function acos(0) returns 1.5707963267948966.
The function acos(1L) returns 0.0.
The function acos(sqrt(2)*0.5) returns 0.7853981633974483.
The function acos(0.5D)) returns 1.0471975511965979.
The function acos(5) returns null.
The function toDegrees(acos(0.5)) returns 60.

See also: asin, atan, cos, toDegrees

asin

number asin( decimal angle );
number asin( double angle );

The asin() function returns arc sine of an angle.
If a given argument is null, the function fails with an error.

Example 140. Usage of asin
The function asin(0) returns 0.0.
The function asin(1L) returns 1.5707963267948966.
The function asin(sqrt(2)*0.5) returns 0.7853981633974484.
The function asin(0.5D) returns 0.5235987755982989.
The function asin(5) returns null.
The function toDegrees(asin(0.5)) returns 30.

See also: acos, atan, sin, toDegrees

atan

number atan( decimal angle );
number atan( double angle );

The atan() function returns arc tangent of an angle.
If the given argument is null, the function fails with an error.

Example 141. Usage of atan
The function atan(0) returns 0.0.
The function atan(1L) returns 0.7853981633974483.
The function atan(sqrt(3)) returns 0.7853981633974483.
The function atan(0.5D) returns 0.4636476090008061.
The function toDegrees(atan(1)) returns 45.

bitAnd

integer bitAnd( integer arg1, integer arg2 );
long bitAnd( long arg1, long arg2 );
byte bitAnd( byte arg1, byte arg2 );

The bitAnd() function returns the number corresponding to the bitwise and of given integer, long or byte arguments.
For example, bitAnd(11,7) returns 3. As decimal 11 can be expressed as bitwise 1011, decimal 7 can be expressed as 111, thus the result is 11 which corresponds to decimal 3.
If one of the arguments is long, the function returns the long data type.
If one of the argument is null, the function fails with an error.
If the byte arguments are of different length, the length of returned byte is a minimum of the lengths of the arguments.

Example 142. Usage of bitAnd
The function bitAnd(6, 3) returns 2 as integer.
The function bitAnd(12L, 6L) returns 4 as long.
The function bitAnd(15L, 1) returns 1 as long.
Let b1 = hex2byte("4545") and b2 = hex2byte("464646"). The function bitAnd(b1, b2) returns a result that can be displayed in hexa as 4444.

See also: bitIsSet, bitLShift, bitNegate, bitOr, bitRShift, bitSet, bitXor, byteAt

bitIsSet

boolean bitIsSet( integer arg, integer index );
boolean bitIsSet( long arg, integer index );

The bitIsSet() function determines the value of the bit of the first argument located on the index and returns true or false, if the bit is 1 or 0, respectively.
If the index is greater than the number of bits in the data type, functions bitIsSet(integer, integer) and bitIsSet(long, integer) return false.
For example, bitIsSet(11,3) returns true. As decimal 11 can be expressed as bitwise 1011, the bit whose index is 3 (the fourth from the right) is 1, thus the result is true. And bitIsSet(11,2) would return false.
If one of the given arguments is null, the function fails with an error.

Example 143. Usage of bitIsSet
The function bitIsSet(19, 1) returns true.
The function bitIsSet(18, 0) returns false.
The function bitIsSet(18, 1) returns true.
The function bitIsSet(256, 8) returns true.

bitLShift

integer bitLShift( integer arg, integer shift );
long bitLShift( long arg, long shift );

The bitLShift() function returns the number corresponding to the original number with bits shifted to the left.
The new bits added to the number on the right side are set to 0. (Shift number of bits on the left side are added and set to 0.) For example, bitLShift(11,2) returns 44. As decimal 11 can be expressed as bitwise 1011, thus the two bits on the right side (00) are added and the result is 101100 which corresponds to decimal 44.
If one of the argument is long, the function returns the long data type.
If one of the arguments is null, the function fails with an error.

Example 144. Usage of bitLShift
The function bitLShift(4, 3) returns 32.
The function bitLShift(4, 28) returns 1073741824.
The function bitLShift(4, 29) returns null.
The function bitLShift(4, 29L) returns 2147483648.
The function bitLShift(4L, 60) returns 4611686018427387904.
The function bitLShift(5L, 61) returns -6917529027641081856.
The function bitLShift(4L, 61) returns null.

See also: bitAnd, bitIsSet, bitNegate, bitOr, bitRShift, bitSet, bitXor, byteAt

bitNegate

integer bitNegate( integer arg );
long bitNegate( long arg );
byte bitNegate( byte arg );

The bitNegate() function returns the number corresponding to its bitwise inverted number.
All ones are set up to zeros and all zeros are changed to ones.
If a given argument is null, the function fails with an error.

Example 145. Usage of bitNegate
The function bitNegate(11) returns -12. The function inverts all bits in an argument. The result is integer.
The function bitNegate(6L) returns -7. The result value is long.
Let b1 = hex2byte("989c9cdfd2a89e9393"). The function bitNegate(b1) returns 676363202d57616c6c.

See also: bitAnd, bitIsSet, bitLShift, bitOr, bitRShift, bitSet, bitXor, byteAt

bitOr

integer bitOr( integer arg1, integer arg2 );
long bitOr( long arg1, long arg2 );
byte bitOr( byte arg1, byte arg2 );

The bitOr() function returns the bitwise or of both arguments.
For example, bitOr(11,7) returns 15. As decimal 11 can be expressed as bitwise 1011, decimal 7 can be expressed as 111, thus the result is 1111 which corresponds to decimal 15.
If one of the given argument is long, the function returns the long data type.
If one of the given argument is null, the function fails with an error.
If the byte arguments are of different length, the length of returned byte is a minimum of the lengths of arguments.

Example 146. Usage of bitOr
The function bitOr(6, 3) returns 7 as integer.
The function bitOr(12L, 6L) returns 14 as long.
The function bitOr(15L, 1) returns 15 as long.
Let b1 = hex2byte("4545") and b2 = hex2byte("464646"). The function bitOr(b1, b2) returns a result that can be displayed in hexa as 4747.

See also: bitAnd, bitIsSet, bitLShift, bitNegate, bitRShift, bitSet, bitXor, byteAt

bitRShift

integer bitRShift( integer arg, integer shift );
long bitRShift( long arg, long shift );

The bitRShift() returns the number corresponding to the original number with bits shifted to the right.
Shift number of bits on the right side are removed. (For example, bitRShift(11,2) returns 2.) As decimal 11 can be expressed as bitwise 1011, thus the two bits on the right side are removed and the result is 10 which corresponds to decimal 2.
If one of the given arguments is long, the function returns long data type.
If one of the given argument is null, the function fails with an error.

Example 147. Usage of bitRShift
The function bitRShift(4, 2) returns 1.
The function bitRShift(129L, 3) returns 16.

See also: bitAnd, bitIsSet, bitLShift, bitNegate, bitSet, bitXor, byteAt

bitSet

integer bitSet( integer arg1, integer index, boolean setBitTo1 );
long bitSet( long arg1, integer index, boolean setBitTo1 );

The bitSet() function sets the value of the bit of the first argument located on the index specified as the second argument to 1 or 0 if the third argument is true or false, respectively, and returns the result as an integer or long.
If one of the given arguments is null, the function fails with an error.

Example 148. Usage of bitSet
The function bitSet(11,3,false) returns 3. As decimal 11 can be expressed as bitwise 1011, the bit whose index is 3 (the fourth from the right) is set to 0, thus the result is 11 which corresponds to decimal 3.
The function bitSet(11,2,true) returns 1111 which corresponds to decimal 15.
The function bitSet(0,1,33) returns 2.
The function bitSet(0,1,-23) returns 512.
The function bitSet(0L,1,33) returns 4294967296.

See also: bitAnd, bitIsSet, bitNegate, bitLShift, bitRShift, bitXor

bitXor

integer bitXor( integer arg, integer arg );
long bitXor( long arg, long arg );
byte bitXor( byte arg, byte arg );

The bitXor() function returns the bitwise exclusive or of both arguments.
For example, bitXor(11,7) returns 12. As decimal 11 can be expressed as bitwise 1011, decimal 7 can be expressed as111, thus the result is 1100 which corresponds to decimal 15.
If one of the given argument is long, the function returns the long data type.
If one of the given arguments is null, the function fails with an error.
If the byte arguments are of different length, the length of returned byte is a minimum of the lengths of arguments.

Example 149. Usage of bitXor
The function bitXor(3, 7) returns 4.
The function bitXor(4, 10L) returns 14.
Let b1 = hex2byte("4545") and b2 = hex2byte("464646"). The function bitXor(b1, b2) returns a result that can be displayed in hexa as 0303.

See also: bitAnd, bitIsSet, bitNegate, bitLShift, bitRShift, bitSet, byteAt

ceil

decimal ceil( decimal arg );
number ceil( number arg );

The ceil() function returns the smallest (closest to negative infinity) value that is greater than or equal to the argument and is equal to a mathematical integer.
It returns number (double) for integer, long and number. It returns decimal for decimal.
If the given argument is null, the function fails with an error.

Example 150. Usage of ceil
The function ceil(-3.45D) returns -3.0.
The function ceil(3) returns 3.0.
The function ceil(34L) returns 34.0.
The function ceil(35.5) returns 36.0.

See also: floor, round, roundHalfToEven

cos

number cos( number angle );
number cos( decimal angle );

The cos() function returns the trigonometric cosine of a given angle.
Angle is in radians.
If the given argument is null, the function fails with an error.

Example 151. Usage of cos
The function cos(0.0D) returns 1.0.
The function cos(pi()/4) returns 0.7071067811865476.
The function cos(toRadians(30)) returns 0.5773502691896257.

See also: acos, sin, tan, toRadians

e

number e(  );

The e() function returns the Euler number.

Example 152. Usage of e
The function e() returns 2.718281828459045.

See also: exp, pi

exp

number exp( decimal arg );
number exp( integer arg );
number exp( long arg );
number exp( number arg );

The exp() function returns the result of the exponential function of the given argument.
The argument can be of any numeric data type (integer, long, number, or decimal).
If the given argument is null, the function fails with an error.

Example 153. Usage of exp
The function exp(1) returns 2.7182818284590455.
The function exp(0L) returns 1.0.
The function exp(0.5D) returns 1.6487212707001282.
The function exp(2.5) returns 12.182493960703473.
The function exp(-5) returns 0.006737946999085467.

floor

decimal floor( decimal arg );
number floor( number arg );

The floor() function returns the largest (closest to positive infinity) value that is less than or equal to the argument and is equal to a mathematical integer.
It returns number (double) for integer, long and number and it returns decimal for decimal.
If the given argument is null, the function fails with an error.

Example 154. Usage of floor
The function floor(5) returns 5.0 as number (double).
The function floor(-10L) returns -10.0 as number (double).
The function floor(4.5D) returns 4.00 as decimal.
The function floor(-7.4) returns -8.0 as number (double).

See also: ceil, round, roundHalfToEven

log

number log( decimal arg );
number log( number arg );

The log() function returns the result of the natural logarithm of a given argument.
If the given argument is null, the function fails with an error. If the argument is negative, the function returns null.

Example 155. Usage of log
The function log(1) returns 0.0.
The function log(10L) returns 2.302585092994046.
The function log(4.5D) returns 1.5040773967762742.
The function log(7.5) returns 2.0149030205422647.
The function log(-7.4) returns null.
The function log(0) returns -Infinity.

See also: exp, log10

log10

number log10( decimal arg );
number log10( number arg );

The log10() function returns the result of the logarithm of a given argument to the base 10.
If the given argument is null, the function fails with an error. If the argument is negative, the function returns null.

Example 156. Usage of log10
The function log10(1) returns 0.0
The function log10(10L) returns 1.0.
The function log10(7.5D) returns 0.8750612633917001.
The function log10(0.5) returns -0.3010299956639812.
The function log10(0) returns -Infinity.
The function log10(-75) returns null.

See also: log, pow,

max

decimal max( decimal arg1, decimal arg2 );
integer max( integer arg1, integer arg2 );
long max( long arg1, long arg2 );
number max( number arg1, number arg2 );
<element type> max( <element type>[] list );

The max() function returns one of the given arguments which is bigger.
If one of the given arguments is null, the function returns the other argument. If both of the given arguments are null, the function returns null.
If a given list contains only null values or is empty, the function returns null. If the given list has a null reference, the function fails with an error. The returned element is the same data type as elements in the list.

Example 157. Usage of max
The function max(1, 2) returns 2 as integer.
The function max(3L, 4) returns 4 as long.
The function max(5.0, 8L) returns 8 as number (double).
The function max(5.25, 5.78D) returns 5.78 as decimal.
The function max(9, null) returns 9.
The list ints contains values null1, 3, 5, null, 4. The functions max(ints) returns 5.
The list nulls contains values null, null, null, null. The functions max(nulls) returns null.

See also: min

min

decimal min( decimal arg1, decimal arg2 );
integer min( integer arg1, integer arg2 );
long min( long arg1, long arg2 );
number min( number arg1, number arg2 );
<element type> min( <element type>[] list );

The min() function returns one of the given arguments which is smaller.
If one of the given arguments is null, the function returns the other argument. If both of the given arguments are null, the function returns null.
Null values in a list are omitted. The returned element is the same data type as elements in the list. If the given list contains only null values or is empty, the function returns null. If the given list has a null reference, the function fails with an error.

Example 158. Usage of min
The function min(2, 1) returns 1 as integer.
The function min(2L, 7) returns 2 as long.
The function min(4.5, 7L) returns 4.5 as number (double).
The function min(4.75, 5.6D) returns 4.75 as decimal.
The list ints contains values 1, 3, 5, null, 4. The functions min(ints) returns 1.
The list nulls contains values null, null, null, null. The functions min(nulls) returns null.

See also: max

pi

number pi()(  );

The pi function returns the pi number.

Example 159. Usage of pi
The pi() function returns 3.141592653589793.

See also: e

pow

decimal pow( decimal base, decimal exp );
number pow( number base, number exp );

The pow() function returns the exponential function of the first argument as the exponent with the second as the base.
The arguments can be of any numeric data type, data type do not need to be of the same type (integer, long, number or decimal).
If one of the given arguments is null, the function fails with an error.

The function pow with decimal arguments uses the integer part of the second argument only. Thus pow(4D, 2.5D) leads to a calculation of pow(4D, 2D).

Example 160. Usage of pow
The function pow(2L, 3) returns 8.0 as number (double).
The function pow(4, 3.5D) returns 64.00 as decimal. The integer part of second argument is used. The result is same as a result of pow(4, 3).
The function pow(4, 3.5) returns 128.0 as number (double).
The function pow(2.7, 3.89) returns 47.64365186615171 as number (double).
The function pow(2, -1D) fails.
The function pow(2, -1) returns 0.5 as number (double).

See also: exp, log, log10, sqrt

random

number random(  );

The random() function generates random positive double greater than or equal to 0.0 and less than 1.0.

Example 161. Usage of random
The function random() returns for example 0.23096784138492643. It can return another random value, e.g. 0.7559335772251974.

randomBoolean

boolean randomBoolean(  );

The randomBoolean() function generates true or false boolean values at random.
If these values are sent to any numeric data type field, they are converted to their numeric representation automatically (1 or 0, respectively).

Example 162. Usage of randomBoolean
The function randomBoolean() returns true for example. It can return false too as the result is random.

randomGaussian

number randomGaussian(  );

The randomGaussian() function generates at random both positive and negative values of number data type in a Gaussian distribution.
The mean value is 0. The standard deviation is 1.

Example 163. Usage of randomGaussian
The function randomGaussian() can return e.g. -1.7478412353643376.

randomInteger

integer randomInteger(  );
integer randomInteger( integer minimum, integer maximum );

The randomInteger() function generates both positive and negative integer values at random.
If the range of allowed values is specified, the result value will be greater than or equal to minimum and lower than or equal to maximum.
If one of the given arguments is null, the function fails with an error.

Example 164. Usage of randomInteger
The function randomInteger() returns for example -767954592.
The function randomInteger(0, 10) returns for example 7.

randomLong

long randomLong(  );
long randomLong( long minimum, long maximum );

The randomLong() function generates both positive and negative long values at random.
If the range of allowed values is specified, the result value will be greater than or equal to minimum and lower than or equal to maximum.
If one of the given arguments is null, the function fails with an error.

Example 165. Usage of randomLong
The function randomLong() returns for example -7985800599050861074.
The function randomLong(0, 5000000000L) returns for example 4594415452.

round

decimal round( decimal arg );
long round( number arg );
integer round( integer arg, integer precision );
long round( long arg, integer precision );
number round( number arg, integer precision );
decimal round( decimal arg, integer precision );

The round() function returns a rounded value using the "half up" rounding mode: if both neighbors are equidistant, rounds up.
Positive precision denotes the number of places after the decimal point and negative precision stands for the number of places before the decimal point. Therefore it only makes sense to use negative precision for integer and long data type arguments, since it signals to round to tens, hundreds, thousands and so on. So round(123, -2) will result in 100 and round(123.123, 2) will result in 123.12.
If the parameter precision is missing, the function rounds to nearest integer value.
If the given argument is null, the function fails with an error.
See also roundHalfToEven(decimal, integer).

Example 166. Usage of round
The function round(2.5D) returns 3.00 as decimal.
The function round(4.5) returns 5 as long.
The function round(6.25D, 1) returns 6.30 as decimal.
The function round(6.25, 1) returns 6.30 as number (double).
The function round(-124556.78D, -3) returns -125000.00 as decimal.
The function round(1253456.78, -6) returns 10000000 as double.

See also: ceil, floor, roundHalfToEven

roundHalfToEven

decimal roundHalfToEven( decimal arg );
decimal roundHalfToEven( decimal arg, integer precision );

The roundHalfToEven() function returns decimal value rounded to the closest integer value.
Uses the "half to even" rounding mode (also called banker’s rounding), i.e. if both the neighbors are equidistant, rounds to the nearest even number.
If a given argument is null, the function fails with an error.
Positive precision denotes the number of places after the decimal point and negative precision stands for the number of places before the decimal point (tens, hundreds, thousands and so on).

Example 167. Usage of roundHalfToEven
The function roundHalfToEven(2.5D) returns 2.
The function roundHalfToEven(3.5D) returns 4.
The function roundHalfToEven(2.25D, 1) returns 2.2.
The function roundHalfToEven(2.35D, 1) returns 2.4.
The function roundHalfToEven(12.25D, -1) returns 10.00.

See also: ceil, floor, round

setRandomSeed

void setRandomSeed( long arg );

The setRandomSeed() function generates the seed for all functions that generate values at random.
This function should be used in the init() function or method.
In such a case, all values generated at random do not change on different runs of the graph, they even remain the same after the graph is reset.
If the given argument is null, the function fails with an error.
The setRandomSeed() function sets random seed only for the CLT2 code of the component where it is used. It does not set the random seed for CTL2 functions in other components.

Example 168. Usage of setRandomSeed
function boolean init() { setRandomSeed(123456789012345678L); return true; }

signum

integer signum( integer arg );
long signum( long arg );
number signum( number arg );
integer signum( decimal arg );

The signum() function returns signum of the argument.
If the argument is negative, the function returns -1. If the argument is positive, the function returns 1. It the argument is 0, the function returns 0.
If the argument is null, the function fails.

Example 169. Usage of signum
The function signum(-2147483648) returns -1.
The function signum(-123456789012345L) returns -1.
The function signum(0.0) returns 0.
The function signum(123.45d) returns 1.
The function signum(null) fails.

sin

number sin( number angle );
number sin( decimal angle );

The sin() function returns the trigonometric sine of a given angle. The angle is in radians.
If the given argument is null, the function fails with an error.

Example 170. Usage of sin
The function sin(0D) returns 0.0.
The function sin(pi()*0.5) returns 1.0.
The function sin(toRadians(45)) returns 0.7071067811865475.

See also: asin, cos, tan, toRadians

sqrt

number sqrt( number arg );
number sqrt( decimal arg );

The sqrt() function returns the square root of a given argument.
The argument can be of any numeric data type; if the argument is integer or long, the argument will be converted to the number (double).
If a given argument is null, the function fails with an error.

Example 171. Usage of sqrt
The function sqrt(81) returns 9.0.
The function sqrt(40532396646334464L) returns 2.01326592E8.
The function sqrt(1.21) returns 1.1.
The function sqrt(1.44D) returns 1.2.
The function sqrt(0) returns 0.0.
The function sqrt(-1) returns null.

See also: log, log10, pow

tan

number tan( number angle );
number tan( decimal angle );

The tan() function returns the trigonometric tangent of a given angle. The angle is in radians.
If the given argument is null, the function fails with an error.

Example 172. Usage of tan
The function tan(0.0D) returns 0.0.
The function tan(pi()/3) returns 1.7320508075688767.
The function tan(toRadians(30)) returns 0.5773502691896257.

See also: atan, cos, sin, toRadians

toDegrees

double toDegrees( double angle );
double toDegrees( decimal angle );

The toDegrees function converts radians to degrees.
The angle is in radians. If the angle is null, the function fails.

Example 173. Usage of toDegrees
The function toDegrees(0) returns 0.0.
The function toDegrees(pi()) returns 180.0.

See also: acos, asin, atan, toRadians

toRadians

double toRadians( double angle );
double toRadians( decimal angle );

The toRadians function converts degrees to radians.
The angle is in degrees. If the angle is null, the function fails.

Example 174. Usage of toRadians
The function toRadians(0) returns 0.
The function toRadians(90d) returns 1.5707963267948966.

See also: cos, sin, tan, toDegrees

Updated 11 months ago