N-body Force Calculation (NBODY)

Given n points in 3 dimensions calculate the gravitational force vector on each point due to all other points. This force vector can be an approximation. For this benchmark we use a gravitational constant of 1 giving the force between two particles located at r₁ and r₂ as:

F₁₂ = m₁ m₂ (r₂ - r₁)/ ||(r₂ - r₁)||³.

The input is a sequence of 3-d points, each coordinate which is a double-precision floating-point number. The output is a sequence of equal length containing a 3-d vector for each of the points, again in double-precision floating-point precision for each coordinate. We say a reported force F’ has error bound epsilon if

|| F - F’ || / || F || < epsilon,

where F is the actual force. By default all reported forces must have an error bound of epsilon = 10^-6. Ideally there should be a input parameter that gives an accuracy, time tradeoff.

Default Input Distributions

The default distributions are the following:

• Points chosen uniformly at random on the surface of a unit sphere. Should be generated with:
  randPoints -S -d 3 <n> <filename>

• Points chosen uniformly at random within a unit cube. Should be generated with:
  randPoints -d 3 <n> <filename>

• Points chosen at random from the Plummer distribution. Should be generated with:
  randPoints -k -d 3 <n> <filename>

The large size is n = 1 million, and the small size is n = .1 million.

Input and Output File Formats

The input and output need to be in the 3dpoints file format.