List of mathematical $functions
As of Model 204 7.5, a set of high-performance, high-precision versions of the IBM mathematical $functions are built in to SOUL. These $functions, shown in the table below, eliminate the need to use external math libraries.
Your site could choose to use an external library instead of these integrated $functions. In such a case, these $functions would result in calls to the external library. To set up use of an external math library, contact Technical Support.
Before Model 204 7.5, these $functions were available as part of the Sirius Mods.
See Notation conventions for methods for information about the conventions followed in the $function descriptions.
Mathematical $function considerations
- Error handling
If invalid numerical values are passed to the mathematical functions (for example, a negative number to $Sqrt, an error message is printed at the user's terminal and 0 is returned as the function's value.
Table of mathematical $functions
| $Function | Description |
|---|---|
| $Abs(x) | Absolute value |
| $ArcCos(x) | Inverse cosine |
| $ArcSin(x) | Inverse sine |
| $ArcTan(x) | Arctangent |
| $ArcTan2(x,y) | Arctangent of x/y |
| $Cos(x) | Cosine of radian argument |
| $CosH(x) | Hyperbolic cosine |
| $Cotan(x) | Cotangent |
| $Erf(x) | Error function |
| $ErfC(x) | Complement error function |
| $Exp(x), $Exp_e(x) | Get natural exponent of a number |
| $Exp2(x), $Exp_2(x) | Get 2's exponent of a number |
| $Exp10(x), $Exp_10(x) | Get 10's exponent of a number |
| $Gamma(x) | Gamma function |
| $IxpI(x,y) | Integer base, integer exponent |
| $LGamma(x) | Log gamma function |
| $Log(x), $Log_e(x) | Get natural log of a number |
| $Log2(x), $Log_2(x) | Get log base 2 of a number |
| $Log10(x), $Log_10(x) | Get log base 10 of a number |
| $Max(x1,x2,x3,x4,x5,x6,x7,x8) | Return maximum of specified arguments |
| $Min(x1,x2,x3,x4,x5,x6,x7,x8) | Return minimum of specified arguments |
| $Pi | Value of pi |
| $RxpI(x,y) | Real base, integer exponent |
| $RxpR(x,y) | Real base, real exponent |
| $Sin(x) | Sine of radian argument |
| $SinH(x) | Hyperbolic sine |
| $Sqrt(x) | Square root of positive argument |
| $Tan(x) | Tangent |
| $TanH(x) | Hyperbolic tangent |