The table below describes the list of built-in math functions. These functions can take scalar or vector arguments. Click an item in the table for details about that function.

The table below describes the list of built-in math functions that are defined with the
`half_`

or `native_`

prefix

The built-in math functions are categorized into the following:

- A list of built-in functions that have scalar or vector argument versions, and,
- A list of built-in functions that only take scalar float arguments.

The vector versions of the math functions operate component-wise. The description is per-component.

The built-in math functions are not affected by the prevailing rounding mode in the calling environment, and always return the same value as they would if called with the round to nearest even rounding mode.

The built-in math functions take scalar or vector arguments. For any specific use of these function, the actual type has to be the same for all arguments and the return type unless otherwise specified.

The generic type name gentype is used to indicate that the function can take float, float2, float3, float4, float8, float16, double, double2, double3, double4, double8, or double16 as the type for the arguments.

If extended with cl_khr_fp16, generic type name gentype may indicate half and half{2|3|4|8|16} as arguments and return values.

The generic type name gentypef is used to indicate that the function can take float, float2, float3, float4, float8, or float16 as the type for the arguments.

The generic type name gentyped is used to indicate that the function can take double, double2, double3, double4, double8, or double16 as the type for the arguments.

The math functions that are defined with the `half_`

prefix are
implemented with a minimum of 10-bits of accuracy i.e. an ULP value <= 8192 ulp.

The math functions that are defined with the `native_`

prefix may map
to one or more native device instructions and will typically have better performance
compared to the corresponding functions (without the `native_`

prefix) described. The accuracy (and in some cases the input range(s)) of these
functions is implementation-defined.

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