[v1] mul_u64_u64_div_u64: Increase precision by conditionally swapping a and b

[PATCH] mul_u64_u64_div_u64: Increase precision by conditionally swapping a and b

Posted by Uwe Kleine-König 2 years, 4 months ago

As indicated in the added comment, the algorithm works better if b is
big. As multiplication is commutative, a and b can be swapped. Do this
If a is bigger than b.

Signed-off-by: Uwe Kleine-König <u.kleine-koenig@pengutronix.de>
---
 lib/math/div64.c | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/lib/math/div64.c b/lib/math/div64.c
index 55a81782e271..baf6f8681907 100644
--- a/lib/math/div64.c
+++ b/lib/math/div64.c
@@ -190,6 +190,23 @@ u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
 
 	/* can a * b overflow ? */
 	if (ilog2(a) + ilog2(b) > 62) {
+		/*
+		 * Note that the algorithm after the if block below might loose
+		 * some precision and the result is more exact for b > a. So
+		 * exchange a and b if a is bigger than b.
+		 *
+		 * For example with a = 43980465100800, b = 100000000, c = 1000000000
+		 * the below calculation doesn't modify b at all because div == 0
+		 * and then shift becomes 45 + 26 - 62 = 9 and so the result
+		 * becomes 4398035251080. However with a and b swapped the exact
+		 * result is calculated (i.e. 4398046510080).
+		 */
+		if (a > b) {
+			u64 tmp = a;
+			a = b;
+			b = tmp;
+		}
+
 		/*
 		 * (b * a) / c is equal to
 		 *

base-commit: 1870cdc0e8dee32e3c221704a2977898ba4c10e8
-- 
2.43.0

Re: [PATCH] mul_u64_u64_div_u64: Increase precision by conditionally swapping a and b

Posted by Marc Kleine-Budde 2 years, 4 months ago

On 02.03.2024 21:54:27, Uwe Kleine-König wrote:
> As indicated in the added comment, the algorithm works better if b is
> big. As multiplication is commutative, a and b can be swapped. Do this
> If a is bigger than b.
> 
> Signed-off-by: Uwe Kleine-König <u.kleine-koenig@pengutronix.de>
> ---
>  lib/math/div64.c | 17 +++++++++++++++++
>  1 file changed, 17 insertions(+)
> 
> diff --git a/lib/math/div64.c b/lib/math/div64.c
> index 55a81782e271..baf6f8681907 100644
> --- a/lib/math/div64.c
> +++ b/lib/math/div64.c
> @@ -190,6 +190,23 @@ u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
>  
>  	/* can a * b overflow ? */
>  	if (ilog2(a) + ilog2(b) > 62) {
> +		/*
> +		 * Note that the algorithm after the if block below might loose
> +		 * some precision and the result is more exact for b > a. So
> +		 * exchange a and b if a is bigger than b.
> +		 *
> +		 * For example with a = 43980465100800, b = 100000000, c = 1000000000
> +		 * the below calculation doesn't modify b at all because div == 0
> +		 * and then shift becomes 45 + 26 - 62 = 9 and so the result
> +		 * becomes 4398035251080. However with a and b swapped the exact
> +		 * result is calculated (i.e. 4398046510080).
> +		 */
> +		if (a > b) {
> +			u64 tmp = a;
> +			a = b;
> +			b = tmp;

You can use swap() from linux/minmax.h here.

Marc

> +		}
> +
>  		/*
>  		 * (b * a) / c is equal to
>  		 *
> 
> base-commit: 1870cdc0e8dee32e3c221704a2977898ba4c10e8
> -- 
> 2.43.0
> 
> 
> 

-- 
Pengutronix e.K.                 | Marc Kleine-Budde          |
Embedded Linux                   | https://www.pengutronix.de |
Vertretung Nürnberg              | Phone: +49-5121-206917-129 |
Amtsgericht Hildesheim, HRA 2686 | Fax:   +49-5121-206917-9   |

Re: [PATCH] mul_u64_u64_div_u64: Increase precision by conditionally swapping a and b

Posted by Randy Dunlap 2 years, 4 months ago


On 3/2/24 13:05, Marc Kleine-Budde wrote:
> On 02.03.2024 21:54:27, Uwe Kleine-König wrote:
>> As indicated in the added comment, the algorithm works better if b is
>> big. As multiplication is commutative, a and b can be swapped. Do this
>> If a is bigger than b.
>>
>> Signed-off-by: Uwe Kleine-König <u.kleine-koenig@pengutronix.de>
>> ---
>>  lib/math/div64.c | 17 +++++++++++++++++
>>  1 file changed, 17 insertions(+)
>>
>> diff --git a/lib/math/div64.c b/lib/math/div64.c
>> index 55a81782e271..baf6f8681907 100644
>> --- a/lib/math/div64.c
>> +++ b/lib/math/div64.c
>> @@ -190,6 +190,23 @@ u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
>>  
>>  	/* can a * b overflow ? */
>>  	if (ilog2(a) + ilog2(b) > 62) {
>> +		/*
>> +		 * Note that the algorithm after the if block below might loose

	s/loose/lose/

>> +		 * some precision and the result is more exact for b > a. So
>> +		 * exchange a and b if a is bigger than b.
>> +		 *
>> +		 * For example with a = 43980465100800, b = 100000000, c = 1000000000
>> +		 * the below calculation doesn't modify b at all because div == 0
>> +		 * and then shift becomes 45 + 26 - 62 = 9 and so the result
>> +		 * becomes 4398035251080. However with a and b swapped the exact
>> +		 * result is calculated (i.e. 4398046510080).
>> +		 */
>> +		if (a > b) {
>> +			u64 tmp = a;
>> +			a = b;
>> +			b = tmp;
> 
> You can use swap() from linux/minmax.h here.
> 
> Marc
> 
>> +		}
>> +
>>  		/*
>>  		 * (b * a) / c is equal to
>>  		 *
>>
>> base-commit: 1870cdc0e8dee32e3c221704a2977898ba4c10e8
>> -- 
>> 2.43.0
>>
>>
>>
> 

-- 
#Randy