Refactor times inverse of sqrt 2 calculation (#21293)

quantum/mousekey.c

@@ -25,11 +25,16 @@
 #include "mousekey.h"
 
 static inline int8_t times_inv_sqrt2(int8_t x) {
-    // 181/256 is pretty close to 1/sqrt(2)
-    // 0.70703125                 0.707106781
-    // 1 too small for x=99 and x=198
-    // This ends up being a mult and discard lower 8 bits
-    return (x * 181) >> 8;
+    // 181/256 (0.70703125) is used as an approximation for 1/sqrt(2)
+    // because it is close to the exact value which is 0.707106781
+    const int16_t  n = x * 181;
+    const uint16_t d = 256;
+
+    // To ensure that the integer result is rounded accurately after
+    // division, check the sign of the numerator:
+    // If negative, subtract half of the denominator before dividing
+    // Otherwise, add half of the denominator before dividing
+    return n < 0 ? (n - d / 2) / d : (n + d / 2) / d;
 }
 
 static report_mouse_t mouse_report = {0};