From 22f9be6a47cee65f40db9dd5ee7eb34b91b19cf0 Mon Sep 17 00:00:00 2001
From: Simon Maertens <simon@slmaertens.dev>
Date: Fri, 12 Jul 2024 14:52:11 +0100
Subject: [PATCH 1/2] Added parentheses to multiplications to prevent compilers
 from using FMAs where the different rounding can lead to a change in control
 flow.

---
 SRC/dlanv2.f |  8 ++++++--
 SRC/slanv2.f | 10 +++++++---
 2 files changed, 13 insertions(+), 5 deletions(-)

diff --git a/SRC/dlanv2.f b/SRC/dlanv2.f
index c55b0ce510..a4bd262c98 100644
--- a/SRC/dlanv2.f
+++ b/SRC/dlanv2.f
@@ -248,10 +248,14 @@ SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
 *
 *           Compute [ A  B ] = [ CS  SN ] [ AA  BB ]
 *                   [ C  D ]   [-SN  CS ] [ CC  DD ]
+*
+*           Note: Some of the multiplications are wrapped in parentheses to
+*                 prevent compilers from using FMA instructions. See
+*                 https://github.com/Reference-LAPACK/lapack/issues/1031.
 *
             A = AA*CS + CC*SN
-            B = BB*CS + DD*SN
-            C = -AA*SN + CC*CS
+            B = ( BB*CS ) + ( DD*SN )
+            C = -( AA*SN ) + ( CC*CS )
             D = -BB*SN + DD*CS
 *
             TEMP = HALF*( A+D )
diff --git a/SRC/slanv2.f b/SRC/slanv2.f
index ac1a197822..40470867e7 100644
--- a/SRC/slanv2.f
+++ b/SRC/slanv2.f
@@ -144,7 +144,7 @@ SUBROUTINE SLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
 *     ..
 *     .. Local Scalars ..
       REAL               AA, BB, BCMAX, BCMIS, CC, CS1, DD, EPS, P, SAB,
-     $                   SAC, SCALE, SIGMA, SN1, TAU, TEMP, Z, SAFMIN, 
+     $                   SAC, SCALE, SIGMA, SN1, TAU, TEMP, Z, SAFMIN,
      $                   SAFMN2, SAFMX2
       INTEGER            COUNT
 *     ..
@@ -248,10 +248,14 @@ SUBROUTINE SLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
 *
 *           Compute [ A  B ] = [ CS  SN ] [ AA  BB ]
 *                   [ C  D ]   [-SN  CS ] [ CC  DD ]
+*
+*           Note: Some of the multiplications are wrapped in parentheses to
+*                 prevent compilers from using FMA instructions. See
+*                 https://github.com/Reference-LAPACK/lapack/issues/1031.
 *
             A = AA*CS + CC*SN
-            B = BB*CS + DD*SN
-            C = -AA*SN + CC*CS
+            B = ( BB*CS ) + ( DD*SN )
+            C = -( AA*SN ) + ( CC*CS )
             D = -BB*SN + DD*CS
 *
             TEMP = HALF*( A+D )

From 349b76a5ee8586c6cbddfee5a08ff536707fe2ff Mon Sep 17 00:00:00 2001
From: Simon Maertens <simon@slmaertens.dev>
Date: Fri, 12 Jul 2024 15:00:39 +0100
Subject: [PATCH 2/2] Remove trailing whitespace

---
 SRC/dlanv2.f | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/SRC/dlanv2.f b/SRC/dlanv2.f
index a4bd262c98..9008fdde08 100644
--- a/SRC/dlanv2.f
+++ b/SRC/dlanv2.f
@@ -144,7 +144,7 @@ SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
 *     ..
 *     .. Local Scalars ..
       DOUBLE PRECISION   AA, BB, BCMAX, BCMIS, CC, CS1, DD, EPS, P, SAB,
-     $                   SAC, SCALE, SIGMA, SN1, TAU, TEMP, Z, SAFMIN, 
+     $                   SAC, SCALE, SIGMA, SN1, TAU, TEMP, Z, SAFMIN,
      $                   SAFMN2, SAFMX2
       INTEGER            COUNT
 *     ..