[PATCH 1/3] lib: Add mul_u64_add_u64_div_u64() and mul_u64_u64_div_u64_roundup()

[David Laight <david.laight.linux@gmail.com>]

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@gmail.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