Re: [PATCH v5 next 4/9] lib: Add mul_u64_add_u64_div_u64() and mul_u64_u64_div_u64_roundup()

H. Peter Anvin
2025-11-06T00:26:58Z

On November 5, 2025 12:10:30 PM PST, David Laight <david.laight.linux@gmail.com> 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.
>
>Add kerndoc definitions for all three functions.
>
>Signed-off-by: David Laight <david.laight.linux@gmail.com>
>Reviewed-by: Nicolas Pitre <npitre@baylibre.com>
>---
>
>Changes for v2 (formally patch 1/3):
>- Reinstate the early call to div64_u64() on 32bit when 'c' is zero.
> Although I'm not convinced the path is common enough to be worth
> the two ilog2() calls.
>
>Changes for v3 (formally patch 3/4):
>- The early call to div64_u64() has been removed by patch 3.
> Pretty much guaranteed to be a pessimisation.
>
>Changes for v4:
>- For x86-64 split the multiply, add and divide into three asm blocks.
> (gcc makes a pigs breakfast of (u128)a * b + c)
>- Change the kerndoc since divide by zero will (probably) fault.
>
>Changes for v5:
>- Fix test that excludes the add/adc asm block for constant zero 'add'.
>
> arch/x86/include/asm/div64.h | 20 +++++++++------
> include/linux/math64.h | 48 +++++++++++++++++++++++++++++++++++-
> lib/math/div64.c | 14 ++++++-----
> 3 files changed, 67 insertions(+), 15 deletions(-)
>
>diff --git a/arch/x86/include/asm/div64.h b/arch/x86/include/asm/div64.h
>index 9931e4c7d73f..6d8a3de3f43a 100644
>--- a/arch/x86/include/asm/div64.h
>+++ b/arch/x86/include/asm/div64.h
>@@ -84,21 +84,25 @@ 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 rax, u64 mul, u64 add, u64 div)
> {
>- u64 q;
>+ u64 rdx;
>
>- asm ("mulq %2; divq %3" : "=a" (q)
>- : "a" (a), "rm" (mul), "rm" (div)
>- : "rdx");
>+ asm ("mulq %[mul]" : "+a" (rax), "=d" (rdx) : [mul] "rm" (mul));
>
>- return q;
>+ if (!statically_true(!add))
>+ asm ("addq %[add], %[lo]; adcq $0, %[hi]" :
>+ [lo] "+r" (rax), [hi] "+r" (rdx) : [add] "irm" (add));
>+
>+ asm ("divq %[div]" : "+a" (rax), "+d" (rdx) : [div] "rm" (div));
>+
>+ return rax;
> }
>-#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..e889d850b7f1 100644
>--- a/include/linux/math64.h
>+++ b/include/linux/math64.h
>@@ -282,7 +282,53 @@ 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.
>+ * The Generic code divides by 0 if @d is zero and returns ~0 on overflow.
>+ * Architecture specific code may trap on zero or overflow.
>+ *
>+ * 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.
>+ * The Generic code divides by 0 if @d is zero and returns ~0 on overflow.
>+ * Architecture specific code may trap on zero or overflow.
>+ *
>+ * 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.
>+ * The Generic code divides by 0 if @d is zero and returns ~0 on overflow.
>+ * Architecture specific code may trap on zero or overflow.
>+ *
>+ * 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 4a4b1aa9e6e1..a88391b8ada0 100644
>--- a/lib/math/div64.c
>+++ b/lib/math/div64.c
>@@ -183,13 +183,13 @@ 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 d)
>+#ifndef mul_u64_add_u64_div_u64
>+u64 mul_u64_add_u64_div_u64(u64 a, u64 b, u64 c, u64 d)
> {
> #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
>@@ -198,8 +198,10 @@ u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 d)
> 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;
>- y = (u64)a_lo * b_hi + (u32)(x >> 32);
>+ /* 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)(c >> 32);
>+ y += (u32)(x >> 32);
> z = (u64)a_hi * b_hi + (u32)(y >> 32);
> y = (u64)a_hi * b_lo + (u32)y;
> z += (u32)(y >> 32);
>@@ -265,5 +267,5 @@ u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 d)
>
> return res;
> }
>-EXPORT_SYMBOL(mul_u64_u64_div_u64);
>+EXPORT_SYMBOL(mul_u64_add_u64_div_u64);
> #endif

For the roundup case, I'm somewhat curious how this compares with doing:

cmp $1, %rdx
sbb $-1, %rax

... after the division. At least it means not needing to compute d - 1, saving an instruction as well as a register. Unfortunately using an lea instruction to compute %rax (which otherwise would incorporate both) isn't possible since it doesn't set the flags.

The cmp; sbb sequence should be no slower than add; adc – I'm saying "no slower" because %rdx is never written to, so I think this is provably a better sequence; whether or not it is measurable is another thing (but if we are tweaking this stuff...)