Half precision math functions

In SYCL the half precision math functions are defined in the namespace sycl::half_precision. The functions that are available within this namespace are specified in the list below. These functions are implemented with a minimum of 10-bits of accuracy i.e. the maximum error is less than or equal to 8192 ulp.

cos

Overload 1

float cos(float x);

Preconditions: The value of x must be in the range [-216, +216].

Returns: The cosine of x.

Overload 2

template<typename NonScalar>
/*return-type*/ cos(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Preconditions: The value of each element of x must be in the range [-216, +216].

Returns: For each element of x, the cosine of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

divide

Overload 1

float divide(float x, float y);

Returns: The value x / y.

Overload 2

template<typename NonScalar1, typename NonScalar2>
/*return-type*/ divide(NonScalar1 x, NonScalar2 y);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Returns: For each element of x and y, the value x[i] / y[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

exp

Overload 1

float exp(float x);

Returns: The base-e exponential of x.

Overload 2

template<typename NonScalar>
/*return-type*/ exp(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Returns: For each element of x, the base-e exponential of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

exp2

Overload 1

float exp2(float x);

Returns: The base-2 exponential of x.

Overload 2

template<typename NonScalar>
/*return-type*/ exp2(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Returns: For each element of x, the base-2 exponential of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

exp10

Overload 1

float exp10(float x);

Returns: The base-10 exponential of x.

Overload 2

template<typename NonScalar>
/*return-type*/ exp10(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Returns: For each element of x, the base-10 exponential of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

log

Overload 1

float log(float x);

Returns: The natural logarithm of x.

Overload 2

template<typename NonScalar>
/*return-type*/ log(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Returns: For each element of x, the natural logarithm of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

log2

Overload 1

float log2(float x);

Returns: The base 2 logarithm of x.

Overload 2

template<typename NonScalar>
/*return-type*/ log2(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Returns: For each element of x, the base 2 logarithm of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

log10

float log10(float x)                (1)

template<typename NonScalar>        (2)
/*return-type*/ log10(NonScalar x)

Overload 1

float log10(float x);

Returns: The base 10 logarithm of x.

Overload 2

template<typename NonScalar>
/*return-type*/ log10(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Returns: For each element of x, the base 10 logarithm of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

powr

Overload 1

float powr(float x, float y);

Preconditions: The value of x must be greater than or equal to zero.

Returns: The value of x raised to the power y.

Overload 2

template<typename NonScalar1, typename NonScalar2>
/*return-type*/ powr(NonScalar1 x, NonScalar2 y);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Preconditions: Each element of x must be greater than or equal to zero.

Returns: For each element of x and y, the value of x[i] raised to the power y[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

recip

Overload 1

float recip(float x);

Returns: The reciprocal of x.

Overload 2

template<typename NonScalar>
/*return-type*/ recip(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Returns: For each element of x, the reciprocal of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

rsqrt

Overload 1

float rsqrt(float x);

Returns: The inverse square root of x.

Overload 2

template<typename NonScalar>
/*return-type*/ rsqrt(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Returns: For each element of x, the inverse square root of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

sin

Overload 1

float sin(float x);

Preconditions: The value of x must be in the range [-216, +216].

Returns: The sine of x.

Overload 2

template<typename NonScalar>
/*return-type*/ sin(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Preconditions: The value of each element of x must be in the range [-216, +216].

Returns: For each element of x, the sine of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

sqrt

Overload 1

float sqrt(float x);

Returns: The square root of x.

Overload 2

template<typename NonScalar>
/*return-type*/ sqrt(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Returns: For each element of x, the square root of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.

tan

float tan(float x)                (1)

template<typename NonScalar>      (2)
/*return-type*/ tan(NonScalar x)

Overload 1

float tan(float x);

Preconditions: The value of x must be in the range [-216, +216].

Returns: The tangent of x.

Overload 2

template<typename NonScalar>
/*return-type*/ tan(NonScalar x);

Constraints: Available only if all of the following conditions are met:

• NonScalar is marray, vec, or the __swizzled_vec__ type; and

• The element type is float.

Preconditions: The value of each element of x must be in the range [-216, +216].

Returns: For each element of x, the tangent of x[i].

The return type is NonScalar unless NonScalar is the __swizzled_vec__ type, in which case the return type is the corresponding vec.