Mesa (master): nir/algebraic: Make some notes about comparison rearrangements versus infinity

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Module: Mesa
Branch: master
Commit: aec0547838fa9d3d923a33755fb3aefe2dd81ba3
URL:    http://cgit.freedesktop.org/mesa/mesa/commit/?id=aec0547838fa9d3d923a33755fb3aefe2dd81ba3

Author: Ian Romanick <ian.d.romanick at intel.com>
Date:   Tue Jul  7 17:30:42 2020 -0700

nir/algebraic: Make some notes about comparison rearrangements versus infinity

The original comment was a little terse and a little incorrect.  The
rearrangements are fine w.r.t. NaN.  However, they produce incorrect
results if one operand is +Inf and the other is -Inf.

A later commit, "nir/algebraic: Add some compare-with-zero optimizations
that are exact", will add some more patterns here.  It may be reasonable
to squash this commit (forward) into that commit.

v2: Fix some incorrect comparisons operators in the comment (<= vs >=).
Add commentary that subtraction works like addition w.r.t. NaN.  Both
noticed / suggested by Caio.

Reviewed-by: Caio Marcelo de Oliveira Filho <caio.oliveira at intel.com>
Part-of: <https://gitlab.freedesktop.org/mesa/mesa/-/merge_requests/6358>

---

 src/compiler/nir/nir_opt_algebraic.py | 23 +++++++++++++++++++++--
 1 file changed, 21 insertions(+), 2 deletions(-)

diff --git a/src/compiler/nir/nir_opt_algebraic.py b/src/compiler/nir/nir_opt_algebraic.py
index d7577c5a2ac..7dd1820d584 100644
--- a/src/compiler/nir/nir_opt_algebraic.py
+++ b/src/compiler/nir/nir_opt_algebraic.py
@@ -2053,8 +2053,27 @@ before_ffma_optimizations = [
 # they help code generation but do not necessarily produce code that is
 # more easily optimizable.
 late_optimizations = [
-   # Most of these optimizations aren't quite safe when you get infinity or
-   # Nan involved but the first one should be fine.
+   # The rearrangements are fine w.r.t. NaN.  However, they produce incorrect
+   # results if one operand is +Inf and the other is -Inf.
+   #
+   # 1. Inf + -Inf = NaN
+   # 2. ∀x: x + NaN = NaN and x - NaN = NaN
+   # 3. ∀x: x != NaN = true
+   # 4. ∀x, ∀ cmp ∈ {<, >, ≤, ≥, =}: x cmp NaN = false
+   #
+   #               a=Inf, b=-Inf   a=-Inf, b=Inf    a=NaN    b=NaN
+   #  (a+b) < 0        false            false       false    false
+   #      a < -b       false            false       false    false
+   # -(a+b) < 0        false            false       false    false
+   #     -a < b        false            false       false    false
+   #  (a+b) >= 0       false            false       false    false
+   #      a >= -b      true             true        false    false
+   # -(a+b) >= 0       false            false       false    false
+   #     -a >= b       true             true        false    false
+   #  (a+b) == 0       false            false       false    false
+   #      a == -b      true             true        false    false
+   #  (a+b) != 0       true             true        true     true
+   #      a != -b      false            false       true     true
    (('flt',          ('fadd', a, b),  0.0), ('flt',          a, ('fneg', b))),
    (('flt', ('fneg', ('fadd', a, b)), 0.0), ('flt', ('fneg', a),         b)),
    (('~fge',          ('fadd', a, b),  0.0), ('fge',          a, ('fneg', b))),