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.

General information about built-in math functions: 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.

Half and Native forms

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.