```
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 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.

Functions with the `half_`

prefix are implemented with a minimum
of 10-bits of accuracy i.e. an ULP value less than or equal to 8192 ulp.

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

Copyright © 2007-2011 The Khronos Group Inc.
Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and/or associated documentation files (the
"Materials"), to deal in the Materials without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Materials, and to
permit persons to whom the Materials are furnished to do so, subject to
the condition that this copyright notice and permission notice shall be included
in all copies or substantial portions of the Materials.