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Message-Id: <20250405204530.186242-2-david.laight.linux@gmail.com>
Date: Sat, 5 Apr 2025 21:45:28 +0100
From: David Laight <david.laight.linux@...il.com>
To: Andrew Morton <akpm@...ux-foundation.org>,
linux-kernel@...r.kernel.org
Cc: David Laight <david.laight.linux@...il.com>,
Uwe Kleine-König <u.kleine-koenig@...libre.com>,
Nicolas Pitre <npitre@...libre.com>,
Oleg Nesterov <oleg@...hat.com>,
Peter Zijlstra <peterz@...radead.org>,
Biju Das <biju.das.jz@...renesas.com>
Subject: [PATCH 1/3] lib: Add mul_u64_add_u64_div_u64() and mul_u64_u64_div_u64_roundup()
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>
---
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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