Re: [PATCH v2 2/3] lib/string_helpers.c: don't lose precision in string_get_size()

[Rasmus Villemoes]

On Tue, Oct 27 2015, Vitaly Kuznetsov <vkuznets@xxxxxxxxxx> wrote:

> string_get_size() loses precision when there is a remainder for
> blk_size / divisor[units] and size is big enough. E.g
> string_get_size(8192, 4096, STRING_UNITS_10, ...) returns "32.7 MB"
> while it is supposed to return "33.5 MB". For some artificial inputs
> the result can be ridiculously wrong, e.g.
> string_get_size(3000, 1900, STRING_UNITS_10, ...) returns "3.00 MB"
> when "5.70 MB" is expected.
>
> The issues comes from the fact than we through away
> blk_size / divisor[units] remainder when size is > exp. This can be fixed
> by saving it and doing some non-trivial calculations later to fix the error
> but that would make this function even more cumbersome. Slightly re-factor
> the function to not lose the precision for all inputs.
>
> The overall complexity of this function comes from the fact that size can
> be huge and we don't want to do size * blk_size as it can overflow. Do the
> math in two steps:
> 1) Reduce size to something < blk_size * divisor[units]
> 2) Multiply the result (and the remainder) by blk_size and do final
>    calculations.
>
> Reported-by: Rasmus Villemoes <linux@xxxxxxxxxxxxxxxxxx>
> Signed-off-by: Vitaly Kuznetsov <vkuznets@xxxxxxxxxx>
> ---
> Changes since v1:
> - Check against blk_size == 0 [Rasmus Villemoes]
> - Do not rename 'i' to 'order' [Andy Shevchenko]
> ---
>  lib/string_helpers.c | 37 ++++++++++++++++++++++++-------------
>  1 file changed, 24 insertions(+), 13 deletions(-)
>
> diff --git a/lib/string_helpers.c b/lib/string_helpers.c
> index f6c27dc..eba8e82 100644
> --- a/lib/string_helpers.c
> +++ b/lib/string_helpers.c
> @@ -44,7 +44,8 @@ void string_get_size(u64 size, u32 blk_size, const enum string_size_units units,
>  		[STRING_UNITS_2] = 1024,
>  	};
>  	int i, j;
> -	u32 remainder = 0, sf_cap, exp;
> +	u64 remainder = 0;
> +	u32 sf_cap;
>  	char tmp[8];
>  	const char *unit;
>  
> @@ -53,28 +54,36 @@ void string_get_size(u64 size, u32 blk_size, const enum string_size_units units,
>  	if (!size)
>  		goto out;
>  
> -	while (blk_size >= divisor[units]) {
> -		remainder = do_div(blk_size, divisor[units]);
> -		i++;
> +	if (!blk_size) {
> +		WARN_ON(1);
> +		size = 0;
> +		goto out;
>  	}

I don't think we need to handle that, but if you want, please put the
WARN inside the conditional (so say "if (WARN_ON(!blk_size)) {...}". And
don't make it _ONCE; the ordinary version is slightly cheaper (since
there's no static bool __warned and no code to manage that).

>  
> -	exp = divisor[units] / blk_size;
>  	/*
> -	 * size must be strictly greater than exp here to ensure that remainder
> -	 * is greater than divisor[units] coming out of the if below.
> +	 * size can be huge and doing size * blk_size right away can overflow.
> +	 * As a first step reduce huge size to something less than
> +	 * blk_size * divisor[units].
>  	 */
> -	if (size > exp) {
> +	while (size > (u64)blk_size * divisor[units]) {

It seems weird that we reduce _more_ for smaller block sizes - indeed,
for blk_size==1 we end up reducing size to <= 1000 (or 1024), which is
certainly a good way to lose some precision. Also, this relies on
blk_size being smaller than (roughly) sqrt(U64_MAX/divisor[units]),
which is of course true in practice, but a slightly annoying implicit
assumption.

I do think that my approach of reducing size till it's smaller than
U64_MAX/blk_size is simpler and better. There's much less fixup
code. It's simply

  while (size > div_u64(U64_MAX, blk_size) {
    do_div(size, divisor[units]);
    ++i;
  }
  size *= blk_size;
  while (size > divisor[units]) {
    remainder = do_div(size, divisor[units]);
    ++i;
  }

which is as self-explaining as it gets.

And yes, one needs to use the include/linux/math64.h functions/macros
for u64/u32 divisions - otherwise I'm pretty sure one will get friendly
mails from the build bot.

  while (size > )
>  		remainder = do_div(size, divisor[units]);
> -		remainder *= blk_size;
>  		i++;
> -	} else {
> -		remainder *= size;
>  	}
>  
> +	/* Now we're OK with doing size * blk_size, it won't overflow. */
>  	size *= blk_size;
> +	remainder *= blk_size;
> +	/*
> +	 * We were doing partial multiplication by blk_size.
> +	 * remainder >= divisor[units] here means size should be increased.
> +	 */
>  	size += remainder / divisor[units];
> -	remainder %= divisor[units];
> +	remainder -= (remainder / divisor[units]) * divisor[units];
>  
> +	/*
> +	 * Normalize. size >= divisor[units] means we still have enough
> +	 * precision and dropping remainder is fine.
> +	 */
>  	while (size >= divisor[units]) {
>  		remainder = do_div(size, divisor[units]);
>  		i++;
> @@ -87,7 +96,8 @@ void string_get_size(u64 size, u32 blk_size, const enum string_size_units units,
>  	if (j) {
>  		remainder *= 1000;
>  		remainder /= divisor[units];
> -		snprintf(tmp, sizeof(tmp), ".%03u", remainder);
> +		/* remainder is < divisor[units] here, (u32) is legit */

What is actually important is that remainder is < 1000. remainder was
initially < divisor[units], but then the multiplication and division
transformed that into "1/1000s" of whatever unit we're using. 

> +		snprintf(tmp, sizeof(tmp), ".%03u", (u32)remainder);
>  		tmp[j+1] = '\0';
>  	}
>  
> @@ -97,6 +107,7 @@ void string_get_size(u64 size, u32 blk_size, const enum string_size_units units,
>  	else
>  		unit = units_str[units][i];
>  
> +	/* size is < divisor[units] here, (u32) is legit */
>  	snprintf(buf, len, "%u%s %s", (u32)size,
>  		 tmp, unit);
>  }
--
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