```
gentype
```
| gentype `)` |

```
gentype
```
| gentype `)` |

```
gentype
```
| gentype `)` |

```
gentype
```
| gentype x`)` |

```
gentype
```
| gentype x`)` |

```
gentype
```
| gentype x`)` |

```
gentype
```
| gentype x`)` |

```
gentype
```
| gentype x`)` |

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gentype
```
| gentype x`)` |

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| gentype x`)` |

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| gentype x`)` |

`log`

computes natural logarithm.

`log2`

computes a base 2 logarithm.

`log10`

computes a base 10 logarithm.

`log1p`

computes log_{e}(1.0 + `x`

).

`logb`

computes the exponent of `x`

, which is
the integral part of log_{r} |`x`

|.

`half_log`

computes natural logarithm.

`half_log2`

computes a base 2 logarithm.

`half_log10`

computes a base 10 logarithm.

`native_log`

computes natural logarithm over an implementation-defined
range. The maximum error is implementation-defined.

`native_log2`

computes a base 2 logarithm over an
implementation-defined range. The maximum error is implementation-defined.

`native_log10`

computes a base 10 logarithm over an
implementation-defined range. The maximum error is implementation-defined.

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.

A subset of Math functions (table 6.8) are defined
with the `half_`

prefix. These
functions are implemented with a minimum of
10-bits of accuracy i.e. an ULP value ≤
8192 ulp.

A subset of Math functions (table 6.8) are
defined with the `native_`

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

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

For the half and native forms, we use the generic type name gentype to indicate that the functions (table 6.9) can take float, float2, float3, float4, float8 or float16 as the type for the arguments.

Support for denormal values is optional for
`half_`

functions. The `half_`

functions may return any
result allowed by section 7.5.3, even when
`-cl-denorms-are-zero`

(see section 5.8.4.2) is not in
force. Support for denormal values is
implementation-defined for `native_`

functions.

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