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.

Add kerndoc definitions for all three functions.

Link: https://lkml.kernel.org/r/20251105201035.64043-5-david.laight.linux@gmail.com
Signed-off-by: David Laight <david.laight.linux@gmail.com>
Reviewed-by: Nicolas Pitre <npitre@baylibre.com>
Cc: Biju Das <biju.das.jz@bp.renesas.com>
Cc: Borislav Betkov <bp@alien8.de>
Cc: "H. Peter Anvin" <hpa@zytor.com>
Cc: Ingo Molnar <mingo@redhat.com>
Cc: Jens Axboe <axboe@kernel.dk>
Cc: Li RongQing <lirongqing@baidu.com>
Cc: Oleg Nesterov <oleg@redhat.com>
Cc: Peter Zijlstra <peterz@infradead.org>
Cc: Thomas Gleinxer <tglx@linutronix.de>
Cc: Uwe Kleine-König <u.kleine-koenig@baylibre.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>

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
 

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

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