vector_ops.mdwn

   1 # Vector Operations Extension to SV
   2
   3 This extension is usually dependent on SV SUBVL being implemented. When SUBVL is set to define the length of a subvector the operations in this extension interpret the elements as a single vector.
   4
   5 Normally in SV all operations are scalar and independent, and the operations on them may inherently be independently parallelised, with the result being a vector of length exactly equal to the input vectors.
   6
   7 In this extension, the subvector itself is typically the unit, although some operations will work on scalars or standard vectors as well, or the result is a scalar that is dependent on all elements within the vector arguments.
   8
   9 Examples which can require SUBVL include cross product and may in future involve complex numbers.
  10
  11 ## Vector cross product
  12
  13 Result is the cross product of x and y, i.e., the resulting components are, in order:
  14
  15     x[1] * y[2] - y[1] * x[2]
  16     x[2] * y[0] - y[2] * x[0]
  17     x[0] * y[1] - y[0] * x[1]
  18
  19 All the operands must be vectors of 3 components of a floating-point type.
  20
  21 ## Vector dot product
  22
  23 Computes the dot product of two vectors. Internal accuracy must be greater than the
  24 input vectors and the result.
  25
  26 ## Vector length
  27
  28 The scalar length of a vector:
  29
  30     sqrt(x[0]^2 + x[1]^2 + ...).
  31
  32 ## Vector distance
  33
  34 The scalar distance between two vectors. Subtracts one vector from the other and returns length
  35
  36 ## Vector LERP
  37
  38 Known as **fmix** in GLSL.
  39
  40 <https://en.m.wikipedia.org/wiki/Linear_interpolation>
  41
  42 ## Vector SLERP
  43
  44 <https://en.m.wikipedia.org/wiki/Slerp>