bpf, docs: Define signed modulo as using truncated division

There's different mathematical definitions (truncated, floored, rounded,
etc.) and different languages have chosen different definitions [0][1].
E.g., languages/libraries that follow Knuth use a different mathematical
definition than C uses. This patch specifies which definition BPF uses,
as verified by Eduard [2] and others.

  [0] https://en.wikipedia.org/wiki/Modulo#Variants_of_the_definition
  [1] https://torstencurdt.com/tech/posts/modulo-of-negative-numbers/
  [2] https://lore.kernel.org/bpf/57e6fefadaf3b2995bb259fa8e711c7220ce5290.camel@gmail.com/

Signed-off-by: Dave Thaler <dthaler@microsoft.com>
Signed-off-by: Daniel Borkmann <daniel@iogearbox.net>
Acked-by: David Vernet <void@manifault.com>
Acked-by: Eduard Zingerman <eddyz87@gmail.com>
Link: https://lore.kernel.org/bpf/20231017203020.1500-1-dthaler1968@googlemail.com

diff --git a/Documentation/bpf/standardization/instruction-set.rst b/Documentation/bpf/standardization/instruction-set.rst
index c5d53a6e8c79f1a6c2d42b66b53d3b62796fff62..245b6defc298c2f26664b2f87dd5d2685c2b538c 100644 (file)
--- a/Documentation/bpf/standardization/instruction-set.rst
+++ b/Documentation/bpf/standardization/instruction-set.rst
@@ -283,6 +283,14 @@ For signed operations (``BPF_SDIV`` and ``BPF_SMOD``), for ``BPF_ALU``,
 is first :term:`sign extended<Sign Extend>` from 32 to 64 bits, and then
 interpreted as a 64-bit signed value.
 
+Note that there are varying definitions of the signed modulo operation
+when the dividend or divisor are negative, where implementations often
+vary by language such that Python, Ruby, etc.  differ from C, Go, Java,
+etc. This specification requires that signed modulo use truncated division
+(where -13 % 3 == -1) as implemented in C, Go, etc.:
+
+   a % n = a - n * trunc(a / n)
+
 The ``BPF_MOVSX`` instruction does a move operation with sign extension.
 ``BPF_ALU | BPF_MOVSX`` :term:`sign extends<Sign Extend>` 8-bit and 16-bit operands into 32
 bit operands, and zeroes the remaining upper 32 bits.