rot kernel

apps/blas/rot/rot-alt.fil

@@ -0,0 +1,131 @@
+import "apps/blas/util.fil";
+import "primitives/signed.fil";
+
+// Applies a rotation to vectors x, y
+// W: element width
+// N: vector length
+// M: multiplier amount
+// A: adder amount
+// Tiles scalar-vector products based on multiplier count,
+// then does additions as multiplies finish
+comp Rot[W, N, M, A]<'G:II>(
+  go: interface['G],
+  c: ['G, 'G+1] W,
+  s: ['G, 'G+1] W,
+  x[N]: ['G, 'G+1] W,
+  y[N]: ['G, 'G+1] W,
+) -> (
+  out_1[N]: ['G+L, 'G+L+1] W,
+  out_2[N]: ['G+L, 'G+L+1] W
+) with {
+  some L where L > 0;
+  some II where II > 0;
+} where W > 0,
+        N > 0,
+        M > 0,
+        A > 0,
+        M % 4 == 0,   // need to do at least 4 multiplies at once
+        A % 2 == 0,   // need to do at least 2 adds at once
+        N % (M/4) == 0,
+        (M/4) % (A/2) == 0
+{
+  // partition mults into 4 groups, for 4 mults that need to happen at each time step
+  let m = M/4;
+
+  // same for adds, but only 2 adds to do
+  let a = A/2;
+
+  // reuse for a single scalar-vector computation
+  let mult_reuses = N / m;
+
+  // reuse for each of the adder groups
+  let add_reuses = m / a;
+
+  // dummy so we can get its params
+  M_ := new Multipliers[W, m];
+  let mult_latency = M_::L;
+  let mult_ii = M_::II;
+
+  A_ := new Adders[W, a];
+  let add_ii = A_::II;
+
+  // -s
+  negs := new Neg[W]<'G>(s);
+
+  // instantiate multipliers
+  let last_mult_invoke = (mult_reuses)*mult_ii;
+  M_cy := new Multipliers[W, m] in ['G, 'G+last_mult_invoke];
+  M_sy := new Multipliers[W, m] in ['G, 'G+last_mult_invoke];
+  M_cx := new Multipliers[W, m] in ['G, 'G+last_mult_invoke];
+  M_nsx := new Multipliers[W, m] in ['G, 'G+last_mult_invoke];
+
+  // instantiate adders
+  let add_end = last_mult_invoke + mult_latency + add_reuses*add_ii + (add_reuses-1)*(mult_reuses-1) + 1;
+  A_1 := new Adders[W, a] in ['G+mult_latency, 'G+add_end];
+  A_2 := new Adders[W, a] in ['G+mult_latency, 'G+add_end];
+
+  // check which stage is limiting the pipeline
+  let ii = if (add_end-mult_latency) < (last_mult_invoke) {(last_mult_invoke)} else {(add_end-mult_latency)};
+
+  bundle cy[mult_reuses][m]: for<k> ['G+k*mult_ii+mult_latency, 'G+k*mult_ii+mult_latency+1] W;
+  bundle sy[mult_reuses][m]: for<k> ['G+k*mult_ii+mult_latency, 'G+k*mult_ii+mult_latency+1] W;
+  bundle cx[mult_reuses][m]: for<k> ['G+k*mult_ii+mult_latency, 'G+k*mult_ii+mult_latency+1] W;
+  bundle nsx[mult_reuses][m]: for<k> ['G+k*mult_ii+mult_latency, 'G+k*mult_ii+mult_latency+1] W;
+
+  // scalar bundles for multiplications
+  bundle c_bundle[m]: ['G, 'G+1] W;
+  bundle s_bundle[m]: ['G, 'G+1] W;
+  bundle negs_bundle[m]: ['G, 'G+1] W;
+
+  // fill them
+  for i in 0..m {
+    c_bundle{i} = c;
+    s_bundle{i} = s;
+    negs_bundle{i} = negs.out;
+  }
+
+  // start multiplications
+  for i in 0..mult_reuses {
+    // some parameters
+    let mult_start = i*mult_ii;
+    let mult_end = i*mult_ii + mult_latency;
+
+    // register inputs
+    x_reg := new Shift[W, i*mult_ii, m]<'G>(x{i*m..(i+1)*m});
+    y_reg := new Shift[W, i*mult_ii, m]<'G>(y{i*m..(i+1)*m});
+    c_reg := new Shift[W, i*mult_ii, m]<'G>(c_bundle{0..m});
+    s_reg := new Shift[W, i*mult_ii, m]<'G>(s_bundle{0..m});
+    negs_reg := new Shift[W, i*mult_ii, m]<'G>(negs_bundle{0..m});
+
+    mult_cy := M_cy<'G+i*mult_ii>(c_reg.out{0..m}, y_reg.out{0..m});
+    mult_sy := M_sy<'G+i*mult_ii>(s_reg.out{0..m}, y_reg.out{0..m});
+    mult_cx := M_cx<'G+i*mult_ii>(c_reg.out{0..m}, x_reg.out{0..m});
+    mult_nsx := M_nsx<'G+i*mult_ii>(negs_reg.out{0..m}, x_reg.out{0..m});
+
+    cy{i}{0..m} = mult_cy.out{0..m};
+    sy{i}{0..m} = mult_sy.out{0..m};
+    cx{i}{0..m} = mult_cx.out{0..m};
+    nsx{i}{0..m} = mult_nsx.out{0..m};
+
+    for j in 0..add_reuses {
+      let offset = i*(add_reuses-1);
+      mult_cy_reg := new Shift[W, j*add_ii + offset, a]<'G+mult_end>(cy{i}{(j*a)..(j+1)*a});
+      mult_sy_reg := new Shift[W, j*add_ii + offset, a]<'G+mult_end>(sy{i}{(j*a)..(j+1)*a});
+      mult_cx_reg := new Shift[W, j*add_ii + offset, a]<'G+mult_end>(cx{i}{(j*a)..(j+1)*a});
+      mult_nsx_reg := new Shift[W, j*add_ii + offset, a]<'G+mult_end>(nsx{i}{(j*a)..(j+1)*a});
+
+      add_1 := A_1<'G + mult_end + j*add_ii + offset>(mult_cx_reg.out{0..a}, mult_sy_reg.out{0..a});
+      add_2 := A_2<'G + mult_end + j*add_ii + offset>(mult_nsx_reg.out{0..a}, mult_cy_reg.out{0..a});
+
+      add_1_reg := new Shift[W, latency - mult_end - j*add_ii - offset, a]<'G + mult_end + j*add_ii + offset>(add_1.out{0..a});
+      add_2_reg := new Shift[W, latency - mult_end - j*add_ii - offset, a]<'G + mult_end + j*add_ii + offset>(add_2.out{0..a});
+
+      out_1{(m*i)+(j*a)..(m*i)+(j+1)*a} = add_1_reg.out{0..a};
+      out_2{(m*i)+(j*a)..(m*i)+(j+1)*a} = add_2_reg.out{0..a};
+    }
+  }
+
+  let latency = (mult_reuses*mult_ii + mult_latency) + (add_reuses-1)*(mult_reuses-1) + (add_reuses-1)*add_ii;
+  L := latency;
+  II := ii;
+}

apps/blas/rot/rot.fil

@@ -0,0 +1,94 @@
+import "primitives/core.fil";
+import "apps/blas/scal/scal.fil";
+import "apps/blas/util.fil";
+import "primitives/signed.fil";
+
+// Applies a rotation to vectors x, y
+// W: element width
+// N: vector length
+// M: multiplier amount
+// A: adder amount
+// Uses scal to compute the scalar-vector products cy, sy, cx, -sx
+comp Rot[W, N, M, A]<'G:II>(
+  go: interface['G],
+  c: ['G, 'G+1] W,
+  s: ['G, 'G+1] W,
+  x[N]: ['G, 'G+1] W,
+  y[N]: ['G, 'G+1] W,
+) -> (
+  out_1[N]: ['G+L, 'G+L+1] W,
+  out_2[N]: ['G+L, 'G+L+1] W
+) with {
+  some L where L > 0;
+  some II where II > 0;
+} where W > 0,
+        L > 0,
+        N > 0,
+        M > 0,
+        A > 0,
+        M % 4 == 0,
+        A % 2 == 0
+{
+
+  scalex := new Scal[W, N, M/4];
+  let scale_latency = scalex::L;
+  let scale_ii = scalex::II;
+
+  zero := new Const[W, 0]<'G>();
+  neg_s := new Neg[W]<'G>(s);
+
+  bundle cy[N]:  ['G+scale_latency, 'G+scale_latency+1] W;
+  bundle sy[N]:  ['G+scale_latency, 'G+scale_latency+1] W;
+  bundle cx[N]:  ['G+scale_latency, 'G+scale_latency+1] W;
+  bundle msx[N]: ['G+scale_latency, 'G+scale_latency+1] W;
+
+  SCY := new Scal[W, N, M/4] in ['G, 'G+scale_ii];
+  scale_cy := SCY<'G>(y{0..N}, c);
+  cy{0..N} = scale_cy.out{0..N};
+
+  SSY := new Scal[W, N, M/4] in ['G, 'G+scale_ii];
+  scale_sy := SSY<'G>(y{0..N}, s);
+  sy{0..N} = scale_sy.out{0..N};
+
+  SCX := new Scal[W, N, M/4] in ['G, 'G+scale_ii];
+  scale_cx := SCX<'G>(x{0..N}, c);
+  cx{0..N} = scale_cx.out{0..N};
+
+  SMSX := new Scal[W, N, M/4] in ['G, 'G+scale_ii];
+  scale_msx := SMSX<'G>(x{0..N}, neg_s.out);
+  msx{0..N} = scale_msx.out{0..N};
+
+  // out_1{i} <- cx{i} + sy{i}
+  // out_2{i} <- msx{i} + cy{i}
+
+  let add_uses = N / (A/2);
+  let add_ii = 1;
+
+  // use half the adders for x, half for y
+  A_x := new Adders[W, A/2] in ['G+scale_latency, 'G+scale_latency+(add_uses-1)*add_ii+1];
+  A_y := new Adders[W, A/2] in ['G+scale_latency, 'G+scale_latency+(add_uses-1)*add_ii+1];
+
+  let latency = scale_latency + (add_uses-1) * add_ii; 
+  for k in 0..add_uses {
+    // save chunked arrays based on when we are ready to add them
+    cx_reg := new Shift[W, k*add_ii, A/2]<'G+scale_latency>(cx{k*(A/2)..(k+1)*(A/2)});
+    sy_reg := new Shift[W, k*add_ii, A/2]<'G+scale_latency>(sy{k*(A/2)..(k+1)*(A/2)});
+    cy_reg := new Shift[W, k*add_ii, A/2]<'G+scale_latency>(cy{k*(A/2)..(k+1)*(A/2)});
+    msx_reg := new Shift[W, k*add_ii, A/2]<'G+scale_latency>(msx{k*(A/2)..(k+1)*(A/2)});
+
+    ax := A_x<'G + scale_latency + k*add_ii>(cx_reg.out{0..(A/2)}, sy_reg.out{0..(A/2)});
+    ay := A_y<'G + scale_latency + k*add_ii>(msx_reg.out{0..(A/2)}, cy_reg.out{0..(A/2)});
+
+    // save add result
+    ax_reg := new Shift[W, latency - scale_latency - k*add_ii, A/2]<'G + scale_latency + k*add_ii>(ax.out{0..(A/2)});
+    ay_reg := new Shift[W, latency - scale_latency - k*add_ii, A/2]<'G + scale_latency + k*add_ii>(ay.out{0..(A/2)});
+
+    out_1{k*(A/2)..(k+1)*(A/2)} = ax_reg.out{0..(A/2)};
+    out_2{k*(A/2)..(k+1)*(A/2)} = ay_reg.out{0..(A/2)};
+  }
+
+  L := latency;
+  // this is a thing we can do now?
+  let ii = if (add_uses*add_ii) > (scale_ii) {add_uses*add_ii} else {scale_ii};
+  II := ii;
+}

apps/blas/rot/sim.py

@@ -0,0 +1,29 @@
+# for determining the right answer
+
+def rot(u, v, c, s):
+  assert len(u) == len(v)
+  x = [0] * len(u)
+  y = [0] * len(v)
+  for i in range(len(u)):
+    x[i] = c*u[i] + s*v[i]
+    y[i] = (-s)*u[i] + c*v[i]
+  return (x,y)
+
+if __name__ == '__main__':
+  u0 = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
+  v0 = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
+  c0 = 1
+  s0 = 1
+  (x0, y0) = rot(u0, v0, c0, s0)
+  print(f"x0: {x0}")
+  print(f"y0: {y0}")
+
+  print("\n======================\n")
+
+  u1 = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
+  v1 = [16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1]
+  c1 = 1
+  s1 = 1
+  (x1, y1) = rot(u1, v1, c1, s1)
+  print(f"x1: {x1}")
+  print(f"y1: {y1}")

apps/blas/rot/test.fil

@@ -0,0 +1,136 @@
+import "apps/blas/rot/rot-alt.fil";
+
+comp main<'G:II>(
+  go: interface['G],
+  c:   ['G, 'G+1] W,
+  s:   ['G, 'G+1] W,
+  u_0: ['G, 'G+1] W,
+  u_1: ['G, 'G+1] W,
+  u_2: ['G, 'G+1] W,
+  u_3: ['G, 'G+1] W,
+  u_4: ['G, 'G+1] W,
+  u_5: ['G, 'G+1] W,
+  u_6: ['G, 'G+1] W,
+  u_7: ['G, 'G+1] W,
+  u_8: ['G, 'G+1] W,
+  u_9: ['G, 'G+1] W,
+  u_10: ['G, 'G+1] W,
+  u_11: ['G, 'G+1] W,
+  u_12: ['G, 'G+1] W,
+  u_13: ['G, 'G+1] W,
+  u_14: ['G, 'G+1] W,
+  u_15: ['G, 'G+1] W,
+  v_0: ['G, 'G+1] W,
+  v_1: ['G, 'G+1] W,
+  v_2: ['G, 'G+1] W,
+  v_3: ['G, 'G+1] W,
+  v_4: ['G, 'G+1] W,
+  v_5: ['G, 'G+1] W,
+  v_6: ['G, 'G+1] W,
+  v_7: ['G, 'G+1] W,
+  v_8: ['G, 'G+1] W,
+  v_9: ['G, 'G+1] W,
+  v_10: ['G, 'G+1] W,
+  v_11: ['G, 'G+1] W,
+  v_12: ['G, 'G+1] W,
+  v_13: ['G, 'G+1] W,
+  v_14: ['G, 'G+1] W,
+  v_15: ['G, 'G+1] W,
+) -> (
+  x_0: ['G+L, 'G+L+1] W,
+  x_1: ['G+L, 'G+L+1] W,
+  x_2: ['G+L, 'G+L+1] W,
+  x_3: ['G+L, 'G+L+1] W,
+  x_4: ['G+L, 'G+L+1] W,
+  x_5: ['G+L, 'G+L+1] W,
+  x_6: ['G+L, 'G+L+1] W,
+  x_7: ['G+L, 'G+L+1] W,
+  x_8: ['G+L, 'G+L+1] W,
+  x_9: ['G+L, 'G+L+1] W,
+  x_10: ['G+L, 'G+L+1] W,
+  x_11: ['G+L, 'G+L+1] W,
+  x_12: ['G+L, 'G+L+1] W,
+  x_13: ['G+L, 'G+L+1] W,
+  x_14: ['G+L, 'G+L+1] W,
+  x_15: ['G+L, 'G+L+1] W,
+  y_0: ['G+L, 'G+L+1] W,
+  y_1: ['G+L, 'G+L+1] W,
+  y_2: ['G+L, 'G+L+1] W,
+  y_3: ['G+L, 'G+L+1] W,
+  y_4: ['G+L, 'G+L+1] W,
+  y_5: ['G+L, 'G+L+1] W,
+  y_6: ['G+L, 'G+L+1] W,
+  y_7: ['G+L, 'G+L+1] W,
+  y_8: ['G+L, 'G+L+1] W,
+  y_9: ['G+L, 'G+L+1] W,
+  y_10: ['G+L, 'G+L+1] W,
+  y_11: ['G+L, 'G+L+1] W,
+  y_12: ['G+L, 'G+L+1] W,
+  y_13: ['G+L, 'G+L+1] W,
+  y_14: ['G+L, 'G+L+1] W,
+  y_15: ['G+L, 'G+L+1] W,
+) with {
+  let M = 8;
+  let N = 16;
+  let W = 32;
+  let A = 2;
+  some L where L > 0;
+  some II where II > 0;
+} {
+  Rotx := new Rot[W, N, M, A];
+
+  bundle u[N]: ['G, 'G+1] W;
+  u{0} = u_0; u{1} = u_1; u{2} = u_2; u{3} = u_3; 
+  u{4} = u_4; u{5} = u_5; u{6} = u_6; u{7} = u_7;
+  u{8} = u_8; u{9} = u_9; u{10} = u_10; u{11} = u_11;
+  u{12} = u_12; u{13} = u_13; u{14} = u_14; u{15} = u_15;
+
+  bundle v[N]: ['G, 'G+1] W;
+  v{0} = v_0; v{1} = v_1; v{2} = v_2; v{3} = v_3; 
+  v{4} = v_4; v{5} = v_5; v{6} = v_6; v{7} = v_7;
+  v{8} = v_8; v{9} = v_9; v{10} = v_10; v{11} = v_11;
+  v{12} = v_12; v{13} = v_13; v{14} = v_14; v{15} = v_15;
+
+  r := Rotx<'G>(c, s, u{0..N}, v{0..N});
+
+  bundle x[N]: ['G+Rotx::L, 'G+Rotx::L+1] W;
+  x{0..N} = r.out_1{0..N};
+  x_0 = x{0};
+  x_1 = x{1};
+  x_2 = x{2};
+  x_3 = x{3};
+  x_4 = x{4};
+  x_5 = x{5};
+  x_6 = x{6};
+  x_7 = x{7};
+  x_8 = x{8};
+  x_9 = x{9};
+  x_10 = x{10};
+  x_11 = x{11};
+  x_12 = x{12};
+  x_13 = x{13};
+  x_14 = x{14};
+  x_15 = x{15};
+
+  bundle y[N]: ['G+Rotx::L, 'G+Rotx::L+1] W;
+  y{0..N} = r.out_2{0..N};
+  y_0 = y{0};
+  y_1 = y{1};
+  y_2 = y{2};
+  y_3 = y{3};
+  y_4 = y{4};
+  y_5 = y{5};
+  y_6 = y{6};
+  y_7 = y{7};
+  y_8 = y{8};
+  y_9 = y{9};
+  y_10 = y{10};
+  y_11 = y{11};
+  y_12 = y{12};
+  y_13 = y{13};
+  y_14 = y{14};
+  y_15 = y{15};
+
+  L := Rotx::L;
+  II := Rotx::II;
+}