pwm: bcm2835: Improve period and duty cycle calculation

With an input clk rate bigger than 2000000000, scaler would have been
zero which then would have resulted in a division by zero.

Also the originally implemented algorithm divided by the result of a
division. This nearly always looses precision. Consider a requested period
of 1000000 ns. With an input clock frequency of 32786885 Hz the hardware
was configured with an actual period of 983869.007 ns (PERIOD = 32258)
while the hardware can provide 1000003.508 ns (PERIOD = 32787).
And note if the input clock frequency was 32786886 Hz instead, the hardware
was configured to 1016656.477 ns (PERIOD = 33333) while the optimal
setting results in 1000003.477 ns (PERIOD = 32787).

This patch implements proper range checking and only divides once for
the calculation of period (and similar for duty_cycle).

Signed-off-by: Uwe Kleine-König <u.kleine-koenig@pengutronix.de>
Reviewed-by: Lino Sanfilippo <LinoSanfilippo@gmx.de>
Tested-by: Lino Sanfilippo <LinoSanfilippo@gmx.de>
Signed-off-by: Thierry Reding <thierry.reding@gmail.com>

drivers/pwm/pwm-bcm2835.c

@@ -64,8 +64,9 @@ static int bcm2835_pwm_apply(struct pwm_chip *chip, struct pwm_device *pwm,
 
 	struct bcm2835_pwm *pc = to_bcm2835_pwm(chip);
 	unsigned long rate = clk_get_rate(pc->clk);
-	unsigned long long period;
-	unsigned long scaler;
+	unsigned long long period_cycles;
+	u64 max_period;
+
 	u32 val;
 
 	if (!rate) {
@@ -73,18 +74,36 @@ static int bcm2835_pwm_apply(struct pwm_chip *chip, struct pwm_device *pwm,
 		return -EINVAL;
 	}
 
-	scaler = DIV_ROUND_CLOSEST(NSEC_PER_SEC, rate);
-	/* set period */
-	period = DIV_ROUND_CLOSEST_ULL(state->period, scaler);
+	/*
+	 * period_cycles must be a 32 bit value, so period * rate / NSEC_PER_SEC
+	 * must be <= U32_MAX. As U32_MAX * NSEC_PER_SEC < U64_MAX the
+	 * multiplication period * rate doesn't overflow.
+	 * To calculate the maximal possible period that guarantees the
+	 * above inequality:
+	 *
+	 *     round(period * rate / NSEC_PER_SEC) <= U32_MAX
+	 * <=> period * rate / NSEC_PER_SEC < U32_MAX + 0.5
+	 * <=> period * rate < (U32_MAX + 0.5) * NSEC_PER_SEC
+	 * <=> period < ((U32_MAX + 0.5) * NSEC_PER_SEC) / rate
+	 * <=> period < ((U32_MAX * NSEC_PER_SEC + NSEC_PER_SEC/2) / rate
+	 * <=> period <= ceil((U32_MAX * NSEC_PER_SEC + NSEC_PER_SEC/2) / rate) - 1
+	 */
+	max_period = DIV_ROUND_UP_ULL((u64)U32_MAX * NSEC_PER_SEC + NSEC_PER_SEC / 2, rate) - 1;
 
-	/* dont accept a period that is too small or has been truncated */
-	if ((period < PERIOD_MIN) || (period > U32_MAX))
+	if (state->period > max_period)
 		return -EINVAL;
 
-	writel(period, pc->base + PERIOD(pwm->hwpwm));
+	/* set period */
+	period_cycles = DIV_ROUND_CLOSEST_ULL(state->period * rate, NSEC_PER_SEC);
+
+	/* don't accept a period that is too small */
+	if (period_cycles < PERIOD_MIN)
+		return -EINVAL;
+
+	writel(period_cycles, pc->base + PERIOD(pwm->hwpwm));
 
 	/* set duty cycle */
-	val = DIV_ROUND_CLOSEST_ULL(state->duty_cycle, scaler);
+	val = DIV_ROUND_CLOSEST_ULL(state->duty_cycle * rate, NSEC_PER_SEC);
 	writel(val, pc->base + DUTY(pwm->hwpwm));
 
 	/* set polarity */