This section describes VML functions that compute values of mathematical functions on real and complex vector arguments with unit increment.
Each function is introduced by its short name, a brief description of its purpose, and the calling sequence for each type of data both for Fortran- and C-interfaces, as well as a description of the input/output arguments.
The input range of parameters is equal to the mathematical range of the input data type, unless the function description specifies input threshold values, which mark off the precision overflow, as follows:
FLT_MAX denotes the maximum number representable in single precision real data type
DBL_MAX denotes the maximum number representable in double precision real data type
Table "VML Mathematical Functions" lists available mathematical functions and associated data types.
| Function | Data Types | Description |
|---|---|---|
| Arithmetic Functions | ||
| v?Add | s, d, c, z | Addition of vector elements |
| v?Sub | s, d, c, z | Subtraction of vector elements |
| v?Sqr | s, d | Squaring of vector elements |
| v?Mul | s, d, c, z | Multiplication of vector elements |
| v?MulByConj | c, z | Multiplication of elements of one vector by conjugated elements of the second vector |
| v?Conj | c, z | Conjugation of vector elements |
| v?Abs | s, d, c, z | Computation of the absolute value of vector elements |
| v?Arg | c, z | Computation of the argument of vector elements |
| v?LinearFrac | s, d | Linear fraction transformation of vectors |
| Power and Root Functions | ||
| v?Inv | s, d | Inversion of vector elements |
| v?Div | s, d, c, z | Division of elements of one vector by elements of the second vector |
| v?Sqrt | s, d, c, z | Computation of the square root of vector elements |
| v?InvSqrt | s, d | Computation of the inverse square root of vector elements |
| v?Cbrt | s, d | Computation of the cube root of vector elements |
| v?InvCbrt | s, d | Computation of the inverse cube root of vector elements |
| v?Pow2o3 | s, d | Raising each vector element to the power of 2/3 |
| v?Pow3o2 | s, d | Raising each vector element to the power of 3/2 |
| v?Pow | s, d, c, z | Raising each vector element to the specified power |
| v?Powx | s, d, c, z | Raising each vector element to the constant power |
| v?Hypot | s, d | Computation of the square root of sum of squares |
| Exponential and Logarithmic Functions | ||
| v?Exp | s, d, c, z | Computation of the exponential of vector elements |
| v?Expm1 | s, d | Computation of the exponential of vector elements decreased by 1 |
| v?Ln | s, d, c, z | Computation of the natural logarithm of vector elements |
| v?Log10 | s, d, c, z | Computation of the denary logarithm of vector elements |
| v?Log1p | s, d | Computation of the natural logarithm of vector elements that are increased by 1 |
| Trigonometric Functions | ||
| v?Cos | s, d, c, z | Computation of the cosine of vector elements |
| v?Sin | s, d, c, z | Computation of the sine of vector elements |
| v?SinCos | s, d | Computation of the sine and cosine of vector elements |
| v?CIS | c, z | Computation of the complex exponent of vector elements (cosine and sine combined to complex value) |
| v?Tan | s, d, c, z | Computation of the tangent of vector elements |
| v?Acos | s, d, c, z | Computation of the inverse cosine of vector elements |
| v?Asin | s, d, c, z | Computation of the inverse sine of vector elements |
| v?Atan | s, d, c, z | Computation of the inverse tangent of vector elements |
| v?Atan2 | s, d | Computation of the four-quadrant inverse tangent of elements of two vectors |
| Hyperbolic Functions | ||
| v?Cosh | s, d, c, z | Computation of the hyperbolic cosine of vector elements |
| v?Sinh | s, d, c, z | Computation of the hyperbolic sine of vector elements |
| v?Tanh | s, d, c, z | Computation of the hyperbolic tangent of vector elements |
| v?Acosh | s, d, c, z | Computation of the inverse hyperbolic cosine of vector elements |
| v?Asinh | s, d, c, z | Computation of the inverse hyperbolic sine of vector elements |
| v?Atanh | s, d, c, z | Computation of the inverse hyperbolic tangent of vector elements. |
| Special Functions | ||
| v?Erf | s, d | Computation of the error function value of vector elements |
| v?Erfc | s, d | Computation of the complementary error function value of vector elements |
| v?CdfNorm | s, d | Computation of the cumulative normal distribution function value of vector elements |
| v?ErfInv | s, d | Computation of the inverse error function value of vector elements |
| v?ErfcInv | s, d | Computation of the inverse complementary error function value of vector elements |
| v?CdfNormInv | s, d | Computation of the inverse cumulative normal distribution function value of vector elements |
| v?LGamma | s, d | Computation of the natural logarithm for the absolute value of the gamma function of vector elements |
| v?TGamma | s, d | Computation of the gamma function of vector elements |
| Rounding Functions | ||
| v?Floor | s, d | Rounding towards minus infinity |
| v?Ceil | s, d | Rounding towards plus infinity |
| v?Trunc | s, d | Rounding towards zero infinity |
| v?Round | s, d | Rounding to nearest integer |
| v?NearbyInt | s, d | Rounding according to current mode |
| v?Rint | s, d | Rounding according to current mode and raising inexact result exception |
| v?Modf | s, d | Computation of the integer and fraction parts |