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Message-ID: <43q1qr20-9q83-74n7-no7p-n178p6s6p279@onlyvoer.pbz>
Date: Sat, 5 Apr 2025 21:46:25 -0400 (EDT)
From: Nicolas Pitre <npitre@...libre.com>
To: David Laight <david.laight.linux@...il.com>
cc: Andrew Morton <akpm@...ux-foundation.org>, linux-kernel@...r.kernel.org,
Uwe Kleine-König <u.kleine-koenig@...libre.com>,
Oleg Nesterov <oleg@...hat.com>, Peter Zijlstra <peterz@...radead.org>,
Biju Das <biju.das.jz@...renesas.com>
Subject: Re: [PATCH 1/3] lib: Add mul_u64_add_u64_div_u64() and
mul_u64_u64_div_u64_roundup()
On Sat, 5 Apr 2025, David Laight wrote:
> The existing mul_u64_u64_div_u64() rounds down, a 'rounding up'
> variant needs 'divisor - 1' adding in between the multiply and
> divide so cannot easily be done by a caller.
>
> Add mul_u64_add_u64_div_u64(a, b, c, d) that calculates (a * b + c)/d
> and implement the 'round down' and 'round up' using it.
>
> Update the x86-64 asm to optimise for 'c' being a constant zero.
>
> For architectures that support u128 check for a 64bit product after
> the multiply (will be cheap).
> Leave in the early check for other architectures (mostly 32bit) when
> 'c' is zero to avoid the multi-part multiply.
>
> Note that the cost of the 128bit divide will dwarf the rest of the code.
> This function is very slow on everything except x86-64 (very very slow
> on 32bit).
>
> Add kerndoc definitions for all three functions.
>
> Signed-off-by: David Laight <david.laight.linux@...il.com>
Reviewed-by: Nicolas Pitre <npitre@...libre.com>
Sidenote: The 128-bits division cost is proportional to the number of
bits in the final result. So if the result is 0x0080000000000000 then
the loop will execute only once and exit early.
> ---
> arch/x86/include/asm/div64.h | 19 +++++++++++-----
> include/linux/math64.h | 44 +++++++++++++++++++++++++++++++++++-
> lib/math/div64.c | 41 ++++++++++++++++++---------------
> 3 files changed, 79 insertions(+), 25 deletions(-)
>
> diff --git a/arch/x86/include/asm/div64.h b/arch/x86/include/asm/div64.h
> index 9931e4c7d73f..9322a35f6a39 100644
> --- a/arch/x86/include/asm/div64.h
> +++ b/arch/x86/include/asm/div64.h
> @@ -84,21 +84,28 @@ static inline u64 mul_u32_u32(u32 a, u32 b)
> * Will generate an #DE when the result doesn't fit u64, could fix with an
> * __ex_table[] entry when it becomes an issue.
> */
> -static inline u64 mul_u64_u64_div_u64(u64 a, u64 mul, u64 div)
> +static inline u64 mul_u64_add_u64_div_u64(u64 a, u64 mul, u64 add, u64 div)
> {
> u64 q;
>
> - asm ("mulq %2; divq %3" : "=a" (q)
> - : "a" (a), "rm" (mul), "rm" (div)
> - : "rdx");
> + if (statically_true(!add)) {
> + asm ("mulq %2; divq %3" : "=a" (q)
> + : "a" (a), "rm" (mul), "rm" (div)
> + : "rdx");
> + } else {
> + asm ("mulq %2; addq %4,%%rax; adcq $0,%%rdx; divq %3"
> + : "=a" (q)
> + : "a" (a), "rm" (mul), "rm" (div), "rm" (add)
> + : "rdx");
> + }
>
> return q;
> }
> -#define mul_u64_u64_div_u64 mul_u64_u64_div_u64
> +#define mul_u64_add_u64_div_u64 mul_u64_add_u64_div_u64
>
> static inline u64 mul_u64_u32_div(u64 a, u32 mul, u32 div)
> {
> - return mul_u64_u64_div_u64(a, mul, div);
> + return mul_u64_add_u64_div_u64(a, mul, 0, div);
> }
> #define mul_u64_u32_div mul_u64_u32_div
>
> diff --git a/include/linux/math64.h b/include/linux/math64.h
> index 6aaccc1626ab..e958170e64ab 100644
> --- a/include/linux/math64.h
> +++ b/include/linux/math64.h
> @@ -282,7 +282,49 @@ static inline u64 mul_u64_u32_div(u64 a, u32 mul, u32 divisor)
> }
> #endif /* mul_u64_u32_div */
>
> -u64 mul_u64_u64_div_u64(u64 a, u64 mul, u64 div);
> +/**
> + * mul_u64_add_u64_div_u64 - unsigned 64bit multiply, add, and divide
> + * @a: first unsigned 64bit multiplicand
> + * @b: second unsigned 64bit multiplicand
> + * @c: unsigned 64bit addend
> + * @d: unsigned 64bit divisor
> + *
> + * Multiply two 64bit values together to generate a 128bit product
> + * add a third value and then divide by a fourth.
> + * May BUG()/trap if @d is zero or the quotient exceeds 64 bits.
> + *
> + * Return: (@a * @b + @c) / @d
> + */
> +u64 mul_u64_add_u64_div_u64(u64 a, u64 b, u64 c, u64 d);
> +
> +/**
> + * mul_u64_u64_div_u64 - unsigned 64bit multiply and divide
> + * @a: first unsigned 64bit multiplicand
> + * @b: second unsigned 64bit multiplicand
> + * @d: unsigned 64bit divisor
> + *
> + * Multiply two 64bit values together to generate a 128bit product
> + * and then divide by a third value.
> + * May BUG()/trap if @d is zero or the quotient exceeds 64 bits.
> + *
> + * Return: @a * @b / @d
> + */
> +#define mul_u64_u64_div_u64(a, b, d) mul_u64_add_u64_div_u64(a, b, 0, d)
> +
> +/**
> + * mul_u64_u64_div_u64_roundup - unsigned 64bit multiply and divide rounded up
> + * @a: first unsigned 64bit multiplicand
> + * @b: second unsigned 64bit multiplicand
> + * @d: unsigned 64bit divisor
> + *
> + * Multiply two 64bit values together to generate a 128bit product
> + * and then divide and round up.
> + * May BUG()/trap if @d is zero or the quotient exceeds 64 bits.
> + *
> + * Return: (@a * @b + @d - 1) / @d
> + */
> +#define mul_u64_u64_div_u64_roundup(a, b, d) \
> + ({ u64 _tmp = (d); mul_u64_add_u64_div_u64(a, b, _tmp - 1, _tmp); })
>
> /**
> * DIV64_U64_ROUND_UP - unsigned 64bit divide with 64bit divisor rounded up
> diff --git a/lib/math/div64.c b/lib/math/div64.c
> index 5faa29208bdb..50e025174495 100644
> --- a/lib/math/div64.c
> +++ b/lib/math/div64.c
> @@ -183,26 +183,28 @@ u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder)
> }
> EXPORT_SYMBOL(iter_div_u64_rem);
>
> -#ifndef mul_u64_u64_div_u64
> -u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
> +#if !defined(mul_u64_add_u64_div_u64)
> +u64 mul_u64_add_u64_div_u64(u64 a, u64 b, u64 c, u64 d)
> {
> - if (ilog2(a) + ilog2(b) <= 62)
> - return div64_u64(a * b, c);
> -
> #if defined(__SIZEOF_INT128__)
>
> /* native 64x64=128 bits multiplication */
> - u128 prod = (u128)a * b;
> + u128 prod = (u128)a * b + c;
> u64 n_lo = prod, n_hi = prod >> 64;
>
> #else
>
> + if (!c && ilog2(a) + ilog2(b) <= 62)
> + return div64_u64(a * b, d);
> +
> /* perform a 64x64=128 bits multiplication manually */
> u32 a_lo = a, a_hi = a >> 32, b_lo = b, b_hi = b >> 32;
> u64 x, y, z;
>
> - x = (u64)a_lo * b_lo;
> + /* Since (x-1)(x-1) + 2(x-1) == x.x - 1 two u32 can be added to a u64 */
> + x = (u64)a_lo * b_lo + (u32)c;
> y = (u64)a_lo * b_hi + (u32)(x >> 32);
> + y += (u32)(c >> 32);
> z = (u64)a_hi * b_hi + (u32)(y >> 32);
> y = (u64)a_hi * b_lo + (u32)y;
> z += (u32)(y >> 32);
> @@ -212,36 +214,39 @@ u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
>
> #endif
>
> - /* make sure c is not zero, trigger exception otherwise */
> + if (!n_hi)
> + return div64_u64(n_lo, d);
> +
> + /* make sure d is not zero, trigger exception otherwise */
> #pragma GCC diagnostic push
> #pragma GCC diagnostic ignored "-Wdiv-by-zero"
> - if (unlikely(c == 0))
> + if (unlikely(d == 0))
> return 1/0;
> #pragma GCC diagnostic pop
>
> - int shift = __builtin_ctzll(c);
> + int shift = __builtin_ctzll(d);
>
> /* try reducing the fraction in case the dividend becomes <= 64 bits */
> if ((n_hi >> shift) == 0) {
> u64 n = shift ? (n_lo >> shift) | (n_hi << (64 - shift)) : n_lo;
>
> - return div64_u64(n, c >> shift);
> + return div64_u64(n, d >> shift);
> /*
> * The remainder value if needed would be:
> - * res = div64_u64_rem(n, c >> shift, &rem);
> + * res = div64_u64_rem(n, d >> shift, &rem);
> * rem = (rem << shift) + (n_lo - (n << shift));
> */
> }
>
> - if (n_hi >= c) {
> + if (n_hi >= d) {
> /* overflow: result is unrepresentable in a u64 */
> return -1;
> }
>
> /* Do the full 128 by 64 bits division */
>
> - shift = __builtin_clzll(c);
> - c <<= shift;
> + shift = __builtin_clzll(d);
> + d <<= shift;
>
> int p = 64 + shift;
> u64 res = 0;
> @@ -256,8 +261,8 @@ u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
> n_hi <<= shift;
> n_hi |= n_lo >> (64 - shift);
> n_lo <<= shift;
> - if (carry || (n_hi >= c)) {
> - n_hi -= c;
> + if (carry || (n_hi >= d)) {
> + n_hi -= d;
> res |= 1ULL << p;
> }
> } while (n_hi);
> @@ -265,5 +270,5 @@ u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
>
> return res;
> }
> -EXPORT_SYMBOL(mul_u64_u64_div_u64);
> +EXPORT_SYMBOL(mul_u64_add_u64_div_u64);
> #endif
> --
> 2.39.5
>
>
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