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Geometric functions

Geometric functions#

In SYCL the OpenCL geometric functions are available in the namespace sycl on host and device as defined in the OpenCL 1.2 specification document par. 6.12.5. On the host the vector types use the sycl::vec class and on a SYCL device use the corresponding native SYCL backend vector types. All of the geometric functions use round-to-nearest-even rounding mode.

The function descriptions in this section use two terms that refer to a specific list of types. The term generic geometric type represents the following types:

  • float

  • double

  • half

  • sycl::marray<float, N>, where N is 2, 3, or 4

  • sycl::marray<double, N>, where N is 2, 3, or 4

  • sycl::marray<half, N>, where N is 2, 3, or 4

  • sycl::vec<float, N>, where N is 2, 3, or 4

  • sycl::vec<double, N>, where N is 2, 3, or 4

  • sycl::vec<half, N>, where N is 2, 3, or 4

  • __swizzled_vec__ that is convertible to sycl::vec<float, N>, where N is 2, 3, or 4

  • __swizzled_vec__ that is convertible to sycl::vec<double, N>, where N is 2, 3, or 4

  • __swizzled_vec__ that is convertible to sycl::vec<half, N>, where N is 2, 3, or 4

The term float geometric type represents these types:

  • float

  • sycl::marray<float, N>, where N is 2, 3, or 4

  • sycl::vec<float, N>, where N is 2, 3, or 4

  • __swizzled_vec__ that is convertible to sycl::vec<float, N>, where N is 2, 3, or 4

See also

SYCL Specification Section 4.17.9

sycl::cross#

template<typename Geo3or4Float1, typename Geo3or4Float2>
/*return-type*/ cross(Geo3or4Float1 p0, Geo3or4Float2 p1);

Available only if all of the following conditions are met:

  • Geo3or4Float1 is one of the following types:

    • sycl::marray<float, 3>

    • sycl::marray<double, 3>

    • sycl::marray<half, 3>

    • sycl::marray<float, 4>

    • sycl::marray<double, 4>

    • sycl::marray<half, 4>

    • sycl::vec<float, 3>

    • sycl::vec<double, 3>

    • sycl::vec<half, 3>

    • sycl::vec<float, 4>

    • sycl::vec<double, 4>

    • sycl::vec<half, 4>

    • __swizzled_vec__ that is convertible to sycl::vec<float, 3>

    • __swizzled_vec__ that is convertible to sycl::vec<double, 3>

    • __swizzled_vec__ that is convertible to sycl::vec<half, 3>

    • __swizzled_vec__ that is convertible to sycl::vec<float, 4>

    • __swizzled_vec__ that is convertible to sycl::vec<double, 4>

    • __swizzled_vec__ that is convertible to sycl::vec<half, 4>

  • If Geo3or4Float1 is sycl::marray, then Geo3or4Float2 must be the same as Geo3or4Float1;

  • If Geo3or4Float1 is sycl::vec or the __swizzled_vec__ type, then Geo3or4Float2 must also be sycl::vec or the __swizzled_vec__ type, and both must have the same element type and the same number of elements.

Returns the cross product of first 3 components of p0 and p1. When the inputs have 4 components, the 4th component of the result is 0.0.

The return type is Geo3or4Float1 unless Geo3or4Float1 is the __swizzled_vec__ type, in which case the return type is the corresponding sycl::vec.

sycl::dot#

template<typename GeoFloat1, typename GeoFloat2>
/*return-type*/ dot(GeoFloat1 p0, GeoFloat2 p1);

Available only if all of the following conditions are met:

  • GeoFloat1 is a generic geometric type as defined above;

  • If GeoFloat1 is not sycl::vec or the __swizzled_vec__ type, then GeoFloat2 must be the same as GeoFloat1;

  • If GeoFloat1 is sycl::vec or the __swizzled_vec__ type, then GeoFloat2 must also be sycl::vec or the __swizzled_vec__ type, and both must have the same element type and the same number of elements.

Returns the dot product of p0 and p1.

The return type is GeoFloat1 if the input types are scalar. Otherwise, the return type is GeoFloat1::value_type.

sycl::distance#

template<typename GeoFloat1, typename GeoFloat2>
/*return-type*/ distance(GeoFloat1 p0, GeoFloat2 p1);

Available only if all of the following conditions are met:

  • GeoFloat1 is a generic geometric type as defined above;

  • If GeoFloat1 is not sycl::vec or the __swizzled_vec__ type, then GeoFloat2 must be the same as GeoFloat1;

  • If GeoFloat1 is sycl::vec or the __swizzled_vec__ type, then GeoFloat2 must also be sycl::vec or the __swizzled_vec__ type, and both must have the same element type and the same number of elements.

Returns the distance between p0 and p1. This is calculated as sycl::length(p0 - p1).

The return type is GeoFloat1 if the input types are scalar. Otherwise, the return type is GeoFloat1::value_type.

sycl::length#

template<typename GeoFloat>
/*return-type*/ length(GeoFloat p);

Available only if GeoFloat is a generic geometric type as defined above.

Returns the length of vector p, i.e., sycl::sqrt(sycl::pow(p[0],2) + sycl::pow(p[1],2) + ...).

The return type is GeoFloat if the input type is scalar. Otherwise, the return type is GeoFloat::value_type.

sycl::normalize#

template<typename GeoFloat>
/*return-type*/ normalize(GeoFloat p);

Available only if GeoFloat is a generic geometric type as defined above.

Returns a vector in the same direction as p but with a length of 1.

The return type is GeoFloat unless GeoFloat is the __swizzled_vec__ type, in which case the return type is the corresponding sycl::vec.

sycl::fast_distance#

template<typename GeoFloat1, typename GeoFloat2>
/*return-type*/ fast_distance(GeoFloat1 p0, GeoFloat2 p1);

Available only if all of the following conditions are met:

  • GeoFloat1 is a float geometric type as defined above;

  • If GeoFloat1 is not sycl::vec or the __swizzled_vec__ type, then GeoFloat2 must be the same as GeoFloat1;

  • If GeoFloat1 is sycl::vec or the __swizzled_vec__ type, then GeoFloat2 must also be sycl::vec or the __swizzled_vec__ type, and both must have the same element type and the same number of elements.

Returns the value sycl::fast_length(p0 - p1).

The return type is GeoFloat1 if the input types are scalar. Otherwise, the return type is GeoFloat1::value_type.

sycl::fast_length#

template<typename GeoFloat>
/*return-type*/ fast_length(GeoFloat p);

Available only if GeoFloat is a float geometric type as defined above.

Returns the length of vector p computed as:

sycl::half_precision::sqrt(sycl::pow(p[0],2) + sycl::pow(p[1],2) + ...).

The return type is GeoFloat if the input type is scalar. Otherwise, the return type is GeoFloat::value_type.

sycl::fast_normalize#

template<typename GeoFloat>
/*return-type*/ fast_normalize(GeoFloat p);

Available only if GeoFloat is a float geometric type as defined above.

Returns a vector in the same direction as p but with a length of 1 computed as:

p * sycl::half_precision::rsqrt(sycl::pow(p[0],2) + sycl::pow(p[1],2) + ...).

The result shall be within 8192 ulps error from the infinitely precise result of:

if (sycl::all(p == 0.0f))
  result = p;
else
  result = p / sycl::sqrt(sycl::pow(p[0], 2) + sycl::pow(p[1], 2) + ...);

with the following exceptions:

  1. If the sum of squares is greater than FLT_MAX then the value of the floating-point values in the result vector are undefined.

  2. If the sum of squares is less than FLT_MIN then the implementation may return back p.

The return type is GeoFloat unless GeoFloat is the __swizzled_vec__ type, in which case the return type is the corresponding sycl::vec.

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