# log, log2, log10, log1p, logb

Logarithm functions.

 ``` gentype log (``` gentype `)`
 ``` gentype log2 (``` gentype `)`
 ``` gentype log10 (``` gentype `)`
 ``` gentype log1p (``` gentype x`)`
 ``` gentype logb (``` gentype x`)`
 ``` gentype half_log (``` gentype x`)`
 ``` gentype half_log2 (``` gentype x`)`
 ``` gentype half_log10 (``` gentype x`)`
 ``` gentype native_log (``` gentype x`)`
 ``` gentype native_log2 (``` gentype x`)`
 ``` gentype native_log10 (``` gentype x`)`

## Description

`log` computes natural logarithm.

`log2` computes a base 2 logarithm.

`log10` computes a base 10 logarithm.

`log1p` computes loge(1.0 + `x`).

`logb` computes the exponent of `x`, which is the integral part of logr |`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.

## Notes

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. The generic type name gentype is used to indicate that the function can take float, float2, float3, float4, float8, or float16 as the type for the arguments. For any specific use of these function, the actual type has to be the same for all arguments and the return type.

If extended with cl_khr_fp64, generic type name gentype may indicate double and double{2|3|4|8|16} as arguments and return values. 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.

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.

## Also see

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