Audio: Optimize division by speed of sound using fixed-point reciprocal

This commit optimizes the division by the speed of sound in the
`theoretical_time_differences` function. By precomputing the fixed-point
reciprocal of the speed of sound, we eliminate the need for a costly
division operation in each iteration.

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

Author: ShriramShastry

src/audio/tdfb/tdfb_direction.c

@@ -406,8 +406,13 @@ static void theoretical_time_differences(struct tdfb_comp_data *cd, int16_t az)
 
 	for (i = 0; i < n_mic - 1; i++) {
 		delta_d = d[i + 1] - d[0]; /* Meters Q4.12 */
+		/* Multiply by the precomputed reciprocal in Q8 format, then adjust with
+		 * a right shift to correct scaling. The multiplication result is initially
+		 * in Q4.20 (12+8) format, and we want it back in Q4.12, so we shift right
+		 * by 8 positions.
+		 */
 		cd->direction.timediff_iter[i] =
-			(int32_t)((((int64_t)delta_d) << 19) / SPEED_OF_SOUND);
+			(int32_t)((((int64_t)delta_d) * RECIPROCAL_SPEED_OF_SOUND_Q8) >> 8);
 	}
 }
 

src/include/sof/math/numbers.h

@@ -117,5 +117,6 @@ uint32_t crc32(uint32_t base, const void *data, uint32_t bytes);
 
 /* Speed of sound (m/s) in 20 C temperature at standard atmospheric pressure */
 #define SPEED_OF_SOUND		343
+#define RECIPROCAL_SPEED_OF_SOUND_Q8 24458 /* Precomputed inverse in Q8 */
 
 #endif /* __SOF_MATH_NUMBERS_H__ */