Math: Optimise 16-bit matrix multiplication functions.

Improve mat_multiply and mat_multiply_elementwise for 16-bit signed
integers by refactoring operations and simplifying handling of Q0 data.
Both functions now use incremented pointers in loop expressions for
better legibility and potential compiler optimisation.

Changes:
- Improved x pointer increments in mat_multiply.
- Integrating Q0 conditional logic into the main flow.
- Clean up the mat_multiply_elementwise loop structure.
- Ensure precision with appropriate fractional bit shifts.

These modifications aim to improve accuracy and efficiency in
fixed-point arithmetic operations.

Signed-off-by: Shriram Shastry <malladi.sastry@intel.com>

Author: ShriramShastry

src/math/matrix.c

@@ -3,93 +3,98 @@
 // Copyright(c) 2022 Intel Corporation. All rights reserved.
 //
 // Author: Seppo Ingalsuo <seppo.ingalsuo@linux.intel.com>
+//         Shriram Shastry <malladi.sastry@linux.intel.com>
 
 #include <sof/math/matrix.h>
 #include <errno.h>
 #include <stdint.h>
 
 int mat_multiply(struct mat_matrix_16b *a, struct mat_matrix_16b *b, struct mat_matrix_16b *c)
 {
-	int64_t s;
-	int16_t *x;
-	int16_t *y;
-	int16_t *z = c->data;
-	int i, j, k;
-	int y_inc = b->columns;
-	const int shift_minus_one = a->fractions + b->fractions - c->fractions - 1;
+	 /* check for NULL pointers */
+	if (!a || !b || !c)
+		return -EINVAL;
 
+	/* check for dimensions compatibility */
 	if (a->columns != b->rows || a->rows != c->rows || b->columns != c->columns)
 		return -EINVAL;
 
-	/* If all data is Q0 */
-	if (shift_minus_one == -1) {
-		for (i = 0; i < a->rows; i++) {
-			for (j = 0; j < b->columns; j++) {
-				s = 0;
-				x = a->data + a->columns * i;
-				y = b->data + j;
-				for (k = 0; k < b->rows; k++) {
-					s += (int32_t)(*x) * (*y);
-					x++;
-					y += y_inc;
-				}
-				*z = (int16_t)s; /* For Q16.0 */
-				z++;
-			}
-		}
+	int64_t acc;
+	int16_t *x, *y, *z = c->data;
+	int i, j, k;
+	/* Increment for pointer y to jump to the next row in matrix B */
+	int y_inc = b->columns;
+	const int shift_minus_one = a->fractions + b->fractions - c->fractions - 1;
+	/* Check for integer overflows during the shift operation. */
+	if (shift_minus_one < -1 || shift_minus_one > 62)
+		return -ERANGE;
 
-		return 0;
-	}
+	const int shift = shift_minus_one + 1;
+
+	/* Calculate offset for rounding. The offset is only needed when shift is
+	 * non-negative (> 0). Since shift = shift_minus_one + 1, the check for non-negative
+	 * value is (shift_minus_one >= -1)
+	 */
+	const int64_t offset = (shift_minus_one >= -1) ? (1LL << shift_minus_one) : 0;
 
 	for (i = 0; i < a->rows; i++) {
 		for (j = 0; j < b->columns; j++) {
-			s = 0;
+			acc = 0;
+			/* Position pointer x at the beginning of the ith row in matrix A */
 			x = a->data + a->columns * i;
+			/* Position pointer y at the beginning of the jth column in matrix B */
 			y = b->data + j;
 			for (k = 0; k < b->rows; k++) {
-				s += (int32_t)(*x) * (*y);
-				x++;
+				/* Multiply elements and add to sum */
+				acc += (int64_t)(*x++) * (*y);
+				/* Move pointer y to the next element in the column */
 				y += y_inc;
 			}
-			*z = (int16_t)(((s >> shift_minus_one) + 1) >> 1); /*Shift to Qx.y */
-			z++;
+			/* If shift == 0, then shift_minus_one == -1, which means the data is Q16.0
+			 * Otherwise, add the offset before the shift to round up if necessary
+			 */
+			*z++ = (shift == 0) ? (int16_t)acc : (int16_t)((acc + offset) >> shift);
 		}
 	}
+
 	return 0;
 }
 
 int mat_multiply_elementwise(struct mat_matrix_16b *a, struct mat_matrix_16b *b,
 			     struct mat_matrix_16b *c)
-{	int64_t p;
+{
+	/* check for NULL pointers */
+	if (!a || !b || !c)
+		return -EINVAL;
+	/* Validate dimensions match for elementwise multiplication */
+	if (a->columns != b->columns || a->rows != b->rows)
+		return -EINVAL;
+
+	const int total_elements = a->rows * a->columns;
+	/* Calculate shift for result Q format */
+	const int shift = a->fractions + b->fractions - c->fractions;
+	/* Check for integer overflows during the shift operation. */
+	if (shift < -1 || shift > 62)
+		return -ERANGE;
+	/* Offset for rounding */
+	const int64_t offset = (shift >= 0) ? (1LL << (shift - 1)) : 0;
+
 	int16_t *x = a->data;
 	int16_t *y = b->data;
 	int16_t *z = c->data;
+	int64_t acc;
 	int i;
-	const int shift_minus_one = a->fractions + b->fractions - c->fractions - 1;
 
-	if (a->columns != b->columns || b->columns != c->columns ||
-	    a->rows != b->rows || b->rows != c->rows) {
-		return -EINVAL;
-	}
-
-	/* If all data is Q0 */
-	if (shift_minus_one == -1) {
-		for (i = 0; i < a->rows * a->columns; i++) {
-			*z = *x * *y;
-			x++;
-			y++;
-			z++;
+	/* When no shifting is required (shift -1 indicated), simply multiply */
+	if (shift == -1) {
+		for (i = 0; i < total_elements; i++)
+			z[i] = x[i] * y[i]; /* Direct elementwise multiplication */
+	} else {
+		/* General case with shifting and offset for rounding */
+		for (i = 0; i < total_elements; i++) {
+			acc = (int64_t)x[i] * (int64_t)y[i]; /* Cast to int64_t to avoid overflow */
+			z[i] = (int16_t)((acc + offset) >> shift); /* Apply shift and offset */
 		}
-
-		return 0;
-	}
-
-	for (i = 0; i < a->rows * a->columns; i++) {
-		p = (int32_t)(*x) * *y;
-		*z = (int16_t)(((p >> shift_minus_one) + 1) >> 1); /*Shift to Qx.y */
-		x++;
-		y++;
-		z++;
 	}
 
 	return 0;