drivers/sensor: si7006: Fix math for calculating sensor values

The existing code rounded the result to an integer, then multiplied that
integer by 1000000 to get micro-degrees or micro-percent, and then
divided by 1000000 to get whole degrees/percent and took the modulus to
get fractional degrees/percent.

Obviously, multiplying and then dividing an integer by the same value
has no effect!

The result is the humidity and temperature were always rounded down to
the nearest integer.

Fix this to properly keep the fractional component.  This is done in a
way that avoids any integer divisions, which are slow on all CPUs, but
especially most microcontrollers, e.g. Cortex-M, lack any integer
division instruction.

Avoiding the base 10 math does not require more code.  One just needs to
think in binary and use binary fractions instead of base 10 fractions.

Signed-off-by: Trent Piepho <[email protected]>

Author: xyzzy42

drivers/sensor/silabs/si7006/si7006.c

@@ -14,6 +14,7 @@
 #include <zephyr/drivers/i2c.h>
 #include <stdio.h>
 #include <stdlib.h>
+#include <zephyr/sys/util.h>
 #include "si7006.h"
 #include <zephyr/logging/log.h>
 
@@ -112,25 +113,58 @@ static int si7006_channel_get(const struct device *dev,
 	struct si7006_data *si_data = dev->data;
 
 	if (chan == SENSOR_CHAN_AMBIENT_TEMP) {
-
-		int32_t temp_ucelcius = (((17572 * (int32_t)si_data->temperature)
-					/ 65536) - 4685) * 10000;
-
-		val->val1 = temp_ucelcius / 1000000;
-		val->val2 = temp_ucelcius % 1000000;
-
-		LOG_DBG("temperature = val1:%d, val2:%d", val->val1, val->val2);
+		/* Raw formula: (temp * 175.72) / 65536 - 46.85
+		 * To use integer math, scale the 175.72 factor by 128 and move the offset to
+		 * inside the division.  This gives us:
+		 *
+		 * (temp * 175.72 * 128 - 46.86 * 128 * 65536) / (65536 * 128)
+		 * The constants can be calculated now:
+		 * (temp * 22492 - 393006285) / 2^23
+		 *
+		 * There is a very small amount of round-off error in the factor of 22492.  To
+		 * compenstate, a constant of 5246 is used to center the error about 0, thus
+		 * reducing the overall MSE.
+		 */
+
+		/* Temperature value times two to the 23rd power, i.e. temp_23 = temp << 23 */
+		const int32_t temp_23 = si_data->temperature * 22492 - (393006285 - 5246);
+		/* Integer component of temperature */
+		int32_t temp_int = temp_23 >> 23;
+		/* Fractional component of temperature */
+		int32_t temp_frac = temp_23 & BIT_MASK(23);
+
+		/* Deal with the split twos-complement / BCD format oddness with negatives */
+		if (temp_23 < 0) {
+			temp_int += 1;
+			temp_frac -= BIT(23);
+		}
+		val->val1 = temp_int;
+		/* Remove a constant factor of 64 from (temp_frac * 1000000) >> 23 */
+		val->val2 = (temp_frac * 15625ULL) >> 17;
+
+		LOG_DBG("temperature %u = val1:%d, val2:%d", si_data->temperature,
+			val->val1, val->val2);
 
 		return 0;
 	} else if (chan == SENSOR_CHAN_HUMIDITY) {
-
-		int32_t relative_humidity = (((125 * (int32_t)si_data->humidity)
-					    / 65536) - 6) * 1000000;
-
-		val->val1 = relative_humidity / 1000000;
-		val->val2 = relative_humidity % 1000000;
-
-		LOG_DBG("humidity = val1:%d, val2:%d", val->val1, val->val2);
+		/* Humidity times two to the 16th power.  Offset of -6 not applied yet. */
+		const uint32_t rh_16 = si_data->humidity * 125U;
+		/* Integer component of humidity */
+		const int16_t rh_int = rh_16 >> 16;
+		/* Fraction component of humidity */
+		const uint16_t rh_frac = rh_16 & BIT_MASK(16);
+
+		val->val1 = rh_int - 6; /* Apply offset now */
+		/* Remove a constant factor of 64 from (rh_frac * 1000000) >> 16 */
+		val->val2 = (rh_frac * 15625) >> 10;
+
+		/* Deal with the split twos-complement / BCD format oddness with negatives */
+		if (val->val1 < 0) {
+			val->val1 += 1;
+			val->val2 -= 1000000;
+		}
+
+		LOG_DBG("humidity %u = val1:%d, val2:%d", si_data->humidity, val->val1, val->val2);
 
 		return 0;
 	} else {