Mathematical Functions
List of functions
You may also want to use some 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.
Example 61.50. 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 61.51. 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.
asin
number asin(decimal angle);
number asin(double angle);
The asin() function
returns arc sine of an angle.
If the given argument is null, the function
fails with an error.
Example 61.52. 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.
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 61.53. 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.
Compatibility notice: The function byte bitAnd(byte, byte) is available since CloverETL 4.0.0.
Example 61.54. 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 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 61.55. Usage of bitIsSet
The function isBitSet(19, 1) returns true.
The function isBitSet(18, 0) returns false.
The function isBitSet(18, 1) returns true.
The function isBitSet(256, 8) returns true.
See also: bitAnd, bitLShift, bitNegate, bitOr, bitRShift, bitSet, bitXor, byteAt,
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 argument is null, the function
fails with an error.
Example 61.56. 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 61.57. 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.
Compatibility notice: The function byte bitOr(byte, byte) is available since CloverETL 4.0.0.
Example 61.58. 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 as4747.
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 61.59. Usage of bitRShift
The function bitRShift(4, 2)returns 1.
The function bitRShift(129L, 3)returns 16.
See also: bitAnd, bitIsSet, bitLShift, bitNegate, bitLShift, 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 61.60. 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, bitLShift, 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 as 111, 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.
Compatibility notice: The function byte bitXor(byte, byte) is available since CloverETL 4.0.0.
Example 61.61. 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 result that can be displayed in hexa as 0303.
See also: bitAnd, bitIsSet, bitLShift, 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.
Compatibility notice: The function returns number for all input numeric data types in Clover 3.4 and older.
Example 61.62. 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 a given argument is null, the function fails with error.
Example 61.63. 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.
e
number e();
The e() function returns the Euler number.
Example 61.64. Usage of e
The function e() returns 2.718281828459045.
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 a 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 61.65. 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.
Compatibility notice: The function returns number for all input numeric data types in Clover 3.4 and older.
Example 61.66. 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 61.67. 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.
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 61.68. 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
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 61.69. 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 1, 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 61.70. 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 61.71. Usage of pi
the function pi() 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 error.
![[Important]](figures/important.png) | Important |
|---|---|
The function |
Example 61.72. 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).
random
number random();
The random() function
generates random positive double greater than or equal to
0.0 and less than
1.0.
Example 61.73. Usage of random
The function random() returns for example 0.23096784138492643.
It can return another random value, e.g. 0.7559335772251974.
See also: randomBoolean, randomDate, randomGaussian, randomInteger, randomLong, randomString, randomUUID, setRandomSeed
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 61.74. Usage of randomBoolean
The function randomBoolean() returns
true for example.
It can return false too as the result is random.
See also: random, randomDate, randomGaussian, randomInteger, randomLong, randomString, randomUUID, setRandomSeed
randomGaussian
number
randomGaussian();
The randomGaussian() function
generates at random both positive and negative values
of number data type in a Gaussian distribution.
Example 61.75. Usage of randomGaussian
The function randomGaussian() can return e.g. -1.7478412353643376.
See also: random, randomBoolean, randomDate, randomInteger, randomLong, randomString, randomUUID, setRandomSeed
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 61.76. Usage of randomInteger
The function randomInteger() returns for example -767954592.
The function randomInteger(0, 10) returns for example 7.
See also: random, randomBoolean, randomDate, randomGaussian, randomLong, randomString, randomUUID, setRandomSeed
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 61.77. Usage of randomLong
The function randomLong() returns for example -7985800599050861074.
The function randomLong(0, 5000000000L) returns for example 4594415452.
See also: random, randomBoolean, randomDate, randomGaussian, randomInteger, randomString, randomUUID, setRandomSeed
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 61.78. 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 61.79. 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.
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 preExecute() 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 resetted.
If the given argument is null, the function
fails with an error.
Example 61.80. Usage of setRandomSeed
function void preExecute() {
setRandomSeed(123456789012345678L);
}
See also: random, randomBoolean, randomDate, randomGaussian, randomInteger, randomLong, randomString, randomUUID, setRandomSeed
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 61.81. 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 a given argument is null, the function fails with an error.
Example 61.82. 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.
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 the given argument is null, the function fails
with an error.
Example 61.83. 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.
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 61.84. 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.
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 61.85. Usage of toDegrees
The function toDegrees(0) returns 0.0.
The function toDegrees(pi()) returns 180.0.
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 61.86. Usage of toRadians
The function toRadians(0) returns 0.
The function toRadians(90d) returns 1.5707963267948966.