Improving 4bit quant mat mul performance by shifting position of -8 operation. (#15436)

Summary:

This diff introduces performance improvements in the 4-bit quant matrix multiplication operation by adjusting the position of the -8 operation. Resulting in overall reduction in math operation performed during shader runtime.

The thinking here is as follows:
* The 4 bit integer weights are unsigned ranging from 0 - 15, and thus to get unsigned number 8 is subtracted from the input.
* Assume WS[] is array of signed weights, M[] is matrix, S is the sum
The main loop essentially performs:
S += ( WS[i] - 8 ) * M[i],       for i = [0, N)
* This equation can rewritten as:
S += WS[i] * M[i] - 8 * M[i], for i = [0, N)
* 8 * M[i] need not be performed in the main loop.
Also 8 * M[i], for i = [0, N)
Can be substituted with A += M[i], for i = [0, N)
and A *= 8

Thus, splitting parts of this equation results in a significant reduction in math ops while producing the same result.

Reviewed By: SS-JIA

Differential Revision: D85721578

Author: trivedivivek

backends/vulkan/runtime/graph/ops/glsl/linear_qcsnw_tiled.glsl

@@ -64,6 +64,12 @@ void main() {
 
   T sums[TILE_ROWS * TILE_TXCOLS * 4];
 
+  $if QUANT_NBITS == 4:
+    // accumulate mat1 elements sum so -8 bias can be applied using it later.
+    T mat1_accum[TILE_ROWS];
+    $for r in range(TILE_ROWS):
+      mat1_accum[${r}] = T(0.0);
+
   for (int r = 0; r < TILE_ROWS; ++r) {
     $for c in range(TILE_TXCOLS):
       $for j in range(4):
@@ -86,6 +92,10 @@ void main() {
         VEC4_T mat1_vec4 = VEC4_T(texelFetch(t_in, ivec3(txpos, out_row + i, 0), 0));
       $for j in range(4):
           mat1[i * 4 + ${j}] = mat1_vec4[${j}];
+
+      $if QUANT_NBITS == 4:
+        // Accumulate mat1 element sum, this will be multiplied with -8 later for converting 4 bit data to a signed number.
+        mat1_accum[i] += mat1[i * 4 + 0] + mat1[i * 4 + 1] + mat1[i * 4 + 2] + mat1[i * 4 + 3];
     }
 
     $if WEIGHT_STORAGE == "buffer":
@@ -109,13 +119,13 @@ void main() {
             packed_weight_tex = texelFetch(
               t_weight, ivec2(weight_txcol + ${c}, pos + r), 0);
 
-          qmat2_vec4 = (VEC4_T(packed_weight_tex >> 4) - 8.0);
+          qmat2_vec4 = VEC4_T(packed_weight_tex >> 4);
           qmat2[${c} * 4 * TILE_TXCOLS + 0] = qmat2_vec4.x;
           qmat2[${c} * 4 * TILE_TXCOLS + 1] = qmat2_vec4.y;
           qmat2[${c} * 4 * TILE_TXCOLS + 2] = qmat2_vec4.z;
           qmat2[${c} * 4 * TILE_TXCOLS + 3] = qmat2_vec4.w;
 
-          qmat2_vec4 = (VEC4_T(packed_weight_tex & 0x0F) - 8.0);
+          qmat2_vec4 = VEC4_T(packed_weight_tex & 0x0F);
           qmat2[${c} * 4 * TILE_TXCOLS + 4] = qmat2_vec4.x;
           qmat2[${c} * 4 * TILE_TXCOLS + 5] = qmat2_vec4.y;
           qmat2[${c} * 4 * TILE_TXCOLS + 6] = qmat2_vec4.z;
@@ -156,10 +166,16 @@ void main() {
   for (int r = 0; r < TILE_ROWS; ++r) {
     VEC4_T scaled_sums;
     $for c in range(TILE_TXCOLS):
-      scaled_sums.x = sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 0] * scales[${c}].x;
-      scaled_sums.y = sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 1] * scales[${c}].y;
-      scaled_sums.z = sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 2] * scales[${c}].z;
-      scaled_sums.w = sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 3] * scales[${c}].w;
+      $if QUANT_NBITS == 4:
+        scaled_sums.x = (sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 0] + mat1_accum[r] * -8.0) * scales[${c}].x;
+        scaled_sums.y = (sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 1] + mat1_accum[r] * -8.0) * scales[${c}].y;
+        scaled_sums.z = (sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 2] + mat1_accum[r] * -8.0) * scales[${c}].z;
+        scaled_sums.w = (sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 3] + mat1_accum[r] * -8.0) * scales[${c}].w;
+      $else:
+        scaled_sums.x = sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 0] * scales[${c}].x;
+        scaled_sums.y = sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 1] * scales[${c}].y;
+        scaled_sums.z = sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 2] * scales[${c}].z;
+        scaled_sums.w = sums[r * TILE_TXCOLS * 4 + ${c} * 4 + 3] * scales[${c}].w;
 
       $if OUT_STORAGE == "buffer":
         if (out_row + r < out_sizes.y) {