Mathematical functions and operators
Mathematical operators
| Operator | Expression & Description | Example |
|---|---|---|
| + | operand1 + operand2 Addition. | 1 + 2 → 3 |
| - | operand1 - operand2 Subtraction. | 1 - 2 → -1 |
| - | - operand Negation. | - (-1) → 1 |
| * | operand1 * operand2 Multiplication. | 2 * 3 → 6 |
| / | operand1 / operand2 Division (results are truncated for integers). | 3 / 2 → 1 3.0 / 2 → 1.5 3 / 1.8 → 1.666... |
| % | operand1 % operand2 Remainder (valid for smallint/int/bigint/numeric). | 3 % 2 → 1 |
| ^ | operand1 ^ operand2 Exponent. | 2.0 ^ -2 → 0.25 |
| ||/ | ||/ operand Cube root. | ||/ 27 → 3 |
| @ | @ operand Absolute value. | @ -10 → 10 |
| & | operand1 & operand2 Bitwise AND | 91 & 15 → 11 |
| | | operand1 | operand2 Bitwise OR | 32 | 3 → 35 |
| # | operand1 # operand2 Bitwise exclusive OR | 17 # 5 → 20 |
| ~ | ~ operand Bitwise NOT | ~1 → -2 |
| << | operand1 << operand2 Bitwise shift left | 1 << 4 → 16 |
| >> | operand1 >> operand2 Bitwise shift right | 8 >> 2 → 2 |
Mathematical functions
| Function | Description | Example |
|---|---|---|
| abs ( input_value ) → absolute_value @ ( input_value ) → absolute_value | Returns the absolute value of input_value. The input_value can be type int or decimal. The return type is the same as the input_value type. | abs(-3) → 3 @(-3) → 3 |
| cbrt ( double_precision_input ) → double_precision_output | Returns the cube root of the input. | cbrt(27) → 3 |
| ceil ( numeric_input ) → integer_output ceil ( double_precision_input ) → integer_output | Returns the nearest integer greater than or equal to the argument. ceiling() can also be used as an alias for ceil(). | ceil(1.23559) → 2 ceiling(-1.23559) → -1 |
| exp ( double_precision_input ) → double_precision_output exp ( numeric_input ) → numeric_output | Returns the exponential value of numeric. | exp(2.0) → 7.38905609893065 |
| floor ( numeric_input ) → integer_output floor ( double_precision_input ) → integer_output | Returns the nearest integer less than or equal to the argument. | floor(1.23559) → 1 floor(-1.23559) → -2 |
| ln ( double_precision_input ) → double_precision_output ln ( numeric_input ) → numeric_output | Returns the natural logarithmic value of the input. | ln(10) → 2.302585092994046 |
| log10 ( double_precision_input ) → double_precision_output log10 ( numeric_input ) → numeric_output | Returns the log base 10 value of the input value. log() can also be used and accepts the same input types. | log10(25) → 1.3979400086720377 |
| min_scale ( numeric_input ) → integer_output | Minimum scale (number of fractional decimal digits) needed to represent the supplied value precisely | min_scale(8.4100) → 2 |
| pow ( x_double_precision, y_double_precision ) → double_precision pow ( x_numeric, y_numeric ) → numeric | Returns x_double_precision or x_numeric raised to the power of y_double_precision or y_numeric. power() can also be used as an alias for pow(). | pow(2.0, 3.0) → 8 power(2.0, 3.0) → 8 |
| round ( x_numeric, y_int ) → output_value | Rounds x_numeric to y_int decimal places. y_int can be negative. | round(1.23559, 2) → 1.24 |
| round ( numeric_input ) → integer_output round ( double_precision_input ) → integer_output | Rounds to the nearest integer. | round(1.23559) → 1 |
| scale ( numeric_input ) → integer_output | Scale of the argument (the number of decimal digits in the fractional part) | scale(8.4100) → 4 |
| sign(double_precision_input or decimal_input) -> same_as_input | Returns the sign of the input value as -1 if the input is negative, 1 if the input is positive, or 0 if the input is 0. | sign(8.64) → 1 sign(-8.64) → -1 |
| sqrt ( numeric_input ) → numeric_output sqrt ( double_precision_input ) → double_precision_output | Returns the square root of the input. | sqrt(16) → 4 |
| trim_scale ( numeric_input ) → numeric_output | Reduces the value's scale (number of fractional decimal digits) by removing trailing zeroes | trim_scale(8.4100) → 8.41 |
| trunc ( double_precision_input ) → double_precision_output trunc ( numeric_input ) → numeric_output | Truncate the input value to zero decimal places. | trunc(-20.0932) → -20 |
Trigonometric functions
| Function | Description | Example |
|---|---|---|
| sin ( radians ) → sine | Returns the trigonometric sine (in double precision) of an angle measured in radians (in double precision). | sin(1) → 0.8414709848078965 |
| cos ( radians ) → cosine | Returns the trigonometric cosine (in double precision) of an angle measured in radians (in double precision). | cos(1) → 0.5403023058681398 |
| tan ( radians ) → tangent | Returns the trigonometric tangent (in double precision) of an angle measured in radians (in double precision). | tan(1) → 1.5574077246549021 |
| cot ( radians ) → cotangent | Returns the trigonometric cotangent (in double precision) of an angle measured in radians (in double precision). | cot(1) → 0.6420926159343308 |
| asin ( input_value ) → radians | Returns the inverse sine (in radians and double precision) of a given value (in double precision). | asin(0.5) → 0.5235987755982989 |
| acos ( input_value ) → radians | Returns the inverse cosine (in radians and double precision) of a given value (in double precision). | acos(0.5) → 1.0471975511965976 |
| atan ( input_value ) → radians | Returns the inverse tangent (in radians and double precision) of a given value (in double precision). | atan(1.0) → 0.7853981633974483 |
| atan2 ( y_value, x_value ) → radians | Returns the inverse tangent (in radians and double precision) of the quotient of two given values (y_value divided by x_value). | atan2(1.0, 1.0) → 0.7853981633974483 |
| sinh ( input_value ) → hyperbolic_sine | Returns the hyperbolic sine (in double precision) of a given value (in double precision). | sinh(1.0) → 1.1752011936438014 |
| cosh ( input_value ) → hyperbolic_cosine | Returns the hyperbolic cosine (in double precision) of a given value (in double precision). | cosh(1.0) → 1.5430806348152437 |
| tanh ( input_value ) → hyperbolic_tangent | Returns the hyperbolic tangent (in double precision) of a given value (in double precision). | tanh(1.0) → 0.7615941559557649 |
| coth ( input_value ) → hyperbolic_cotangent | Returns the hyperbolic cotangent (in double precision) of a given value (in double precision). | coth(2) → 1.0373147207275481 |
| asinh ( input_value ) → inverse_hyperbolic_sine | Returns the inverse hyperbolic sine (in double precision) of a given value (in double precision). | asinh(1.0) → 0.881373587019543 |
| acosh ( input_value ) → inverse_hyperbolic_cosine | Returns the inverse hyperbolic cosine (in double precision) of a given value (in double precision). | acosh(2.0) → 1.3169578969248166 |
| atanh ( input_value ) → inverse_hyperbolic_tangent | Returns the inverse hyperbolic tangent (in double precision) of a given value (in double precision). | atanh(0.5) → 0.5493061443340549 |
| sind ( degrees ) → sine | Returns the trigonometric sine (in double precision) of an angle measured in degrees (in double precision). | sind(15) → 0.2588190451025208 |
| cosd ( degrees ) → cosine | Returns the trigonometric cosine (in double precision) of an angle measured in degrees (in double precision). | cosd(15) → 0.9659258262890683 |
| tand ( degrees ) → tangent | Returns the trigonometric tangent (in double precision) of an angle measured in degrees (in double precision). | tand(15) → 0.26794919243112275 |
| cotd ( degrees ) → cotangent | Returns the trigonometric cotangent (in double precision) of an angle measured in degrees (in double precision) | cotd(45) → 1 |
Degrees and radians functions
| Function | Description | Example |
|---|---|---|
| degrees ( radians ) → degrees | Returns the conversion (in double precision) of an angle measured in radians (in double precision) to degrees. | degrees(pi()/2) → 90 |
| radians ( degrees ) → radians | Returns the conversion (in double precision) of an angle measured in degrees (in double precision) to radians. | radians(180) → 3.141592653589793 |
