Merge branch 'bpf-nfp-mul-div-support'

Jiong Wang says:

====================
NFP supports u16 and u32 multiplication. Multiplication is done 8-bits per
step, therefore we need 2 steps for u16 and 4 steps for u32.

We also need one start instruction to initialize the sequence and one or
two instructions to fetch the result depending on either you need the high
halve of u32 multiplication.

For ALU64, if either operand is beyond u32's value range, we reject it. One
thing to note, if the source operand is BPF_K, then we need to check "imm"
field directly, and we'd reject it if it is negative.  Because for ALU64,
"imm" (with s32 type) is expected to be sign extended to s64 which NFP mul
doesn't support. For ALU32, it is fine for "imm" be negative though,
because the result is 32-bits and here is no difference on the low halve
of result for signed/unsigned mul, so we will get correct result.

NFP doesn't have integer divide instruction, this patch set uses reciprocal
algorithm (the basic one, reciprocal_div) to emulate it.

For each u32 divide, we would need 11 instructions to finish the operation.

   7 (for multiplication) + 4 (various ALUs) = 11

Given NFP only supports multiplication no bigger than u32, we'd require
divisor and dividend no bigger than that as well.

Also eBPF doesn't support signed divide and has enforced this on C language
level by failing compilation. However LLVM assembler hasn't enforced this,
so it is possible for negative constant to leak in as a BPF_K operand
through assembly code, we reject such cases as well.

Meanwhile reciprocal_div.h only implemented the basic version of:

   "Division by Invariant Integers Using Multiplication"
                          - Torbjörn Granlund and Peter L. Montgomery

This patch set further implements the optimized version (Figure 4.2 in the
paper) inside existing reciprocal_div.h. When the divider is even and the
calculated reciprocal magic number doesn't fit u32, we could reduce the
required ALU instructions from 4 to 2 or 1 for some cases.

The advanced version requires more complex calculation to get the
reciprocal multiplier and other control variables, but then could reduce
the required emulation operations. It makes sense to use it for JIT divide
code generation (for example eBPF JIT backends) for which we are willing to
trade performance of JITed code with that of host.

v2:
  - add warning in l == 32 code path. (Song Liu/Jakub)
  - jit separate insn sequence for l == 32. (Jakub/Edwin)
  - should use unrestricted operand for mul.
  - once place should use "1U << exp" instead of "1 << exp".
====================

Signed-off-by: Daniel Borkmann <daniel@iogearbox.net>

1 files changed, 68 insertions, 0 deletions

diff --git a/include/linux/reciprocal_div.h b/include/linux/reciprocal_div.h
index e031e9f2f9d8..585ce89c0f33 100644
--- a/include/linux/reciprocal_div.h
+++ b/include/linux/reciprocal_div.h
@@ -25,6 +25,9 @@ struct reciprocal_value {
 	u8 sh1, sh2;
 };
 
+/* "reciprocal_value" and "reciprocal_divide" together implement the basic
+ * version of the algorithm described in Figure 4.1 of the paper.
+ */
 struct reciprocal_value reciprocal_value(u32 d);
 
 static inline u32 reciprocal_divide(u32 a, struct reciprocal_value R)
@@ -33,4 +36,69 @@ static inline u32 reciprocal_divide(u32 a, struct reciprocal_value R)
 	return (t + ((a - t) >> R.sh1)) >> R.sh2;
 }
 
+struct reciprocal_value_adv {
+	u32 m;
+	u8 sh, exp;
+	bool is_wide_m;
+};
+
+/* "reciprocal_value_adv" implements the advanced version of the algorithm
+ * described in Figure 4.2 of the paper except when "divisor > (1U << 31)" whose
+ * ceil(log2(d)) result will be 32 which then requires u128 divide on host. The
+ * exception case could be easily handled before calling "reciprocal_value_adv".
+ *
+ * The advanced version requires more complex calculation to get the reciprocal
+ * multiplier and other control variables, but then could reduce the required
+ * emulation operations.
+ *
+ * It makes no sense to use this advanced version for host divide emulation,
+ * those extra complexities for calculating multiplier etc could completely
+ * waive our saving on emulation operations.
+ *
+ * However, it makes sense to use it for JIT divide code generation for which
+ * we are willing to trade performance of JITed code with that of host. As shown
+ * by the following pseudo code, the required emulation operations could go down
+ * from 6 (the basic version) to 3 or 4.
+ *
+ * To use the result of "reciprocal_value_adv", suppose we want to calculate
+ * n/d, the pseudo C code will be:
+ *
+ *   struct reciprocal_value_adv rvalue;
+ *   u8 pre_shift, exp;
+ *
+ *   // handle exception case.
+ *   if (d >= (1U << 31)) {
+ *     result = n >= d;
+ *     return;
+ *   }
+ *
+ *   rvalue = reciprocal_value_adv(d, 32)
+ *   exp = rvalue.exp;
+ *   if (rvalue.is_wide_m && !(d & 1)) {
+ *     // floor(log2(d & (2^32 -d)))
+ *     pre_shift = fls(d & -d) - 1;
+ *     rvalue = reciprocal_value_adv(d >> pre_shift, 32 - pre_shift);
+ *   } else {
+ *     pre_shift = 0;
+ *   }
+ *
+ *   // code generation starts.
+ *   if (imm == 1U << exp) {
+ *     result = n >> exp;
+ *   } else if (rvalue.is_wide_m) {
+ *     // pre_shift must be zero when reached here.
+ *     t = (n * rvalue.m) >> 32;
+ *     result = n - t;
+ *     result >>= 1;
+ *     result += t;
+ *     result >>= rvalue.sh - 1;
+ *   } else {
+ *     if (pre_shift)
+ *       result = n >> pre_shift;
+ *     result = ((u64)result * rvalue.m) >> 32;
+ *     result >>= rvalue.sh;
+ *   }
+ */
+struct reciprocal_value_adv reciprocal_value_adv(u32 d, u8 prec);
+
 #endif /* _LINUX_RECIPROCAL_DIV_H */