Math functions: Reduction

Probe an input-variable field at a sequence of positions then appy a reducation operator over the result.

In Action

The following code defines an variable input field and a sequence of positions field#3(1)[] F (r) = r*8; strand sample (int R) { real[5] X= {3,7,R,2,1}; ... } The following short-hand function probes the field at a sequence of positions then applies a reduction over the result. output tensor[] out= SUM(F, X);

The computation does the following:

  out = F(X<sub>0</sub>)+ X<sub>1</sub>)++ X<sub>2</sub>)..
  out = F(3)+ F(7)+F(R)+...
  out = 3*8+ 7*8+  R*8+...

Other reducation operators include getting the maximum and mininum.

output tensor[] out= MAX(F, X) output tensor[] out= MIN(F, X);

Implementation Details

• EIN Reduction operation wrapped inside probe terms and expanded in high-to mid
• High to mid creates variable binding in reduction operation and sequence EIN expression
• Easy translation from mid-to-low

Overview

• Branch: Diderot-Dev
• Syntax: SUM(), MAX(), MIN()
  • SUM : field#k(d)[] × tensor[d]{n} → real
  • MAX : field#k(d)[] × tensor[d]{n} → real
  • Min : field#k(d)[] × tensor[d]{n} → real

Directory Organization

• sequence of reals : X1
• sequence of vectors : X2
• Summation over a vector fields : X3