From cb77b7c7cb744e1029a6ebd08b348dd7b1a751e2 Mon Sep 17 00:00:00 2001
From: blupper <33233478+TheBlupper@users.noreply.github.com>
Date: Thu, 6 Jun 2024 02:12:37 +0200
Subject: [PATCH 1/4] Fix norm calculation

---
 src/fpylll/algorithms/babai.py | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/fpylll/algorithms/babai.py b/src/fpylll/algorithms/babai.py
index b7942d86..5dd267d5 100644
--- a/src/fpylll/algorithms/babai.py
+++ b/src/fpylll/algorithms/babai.py
@@ -8,10 +8,10 @@
 """
 
 from fpylll import IntegerMatrix, LLL
-from math import ceil
+from math import isqrt
 
 
-def babai(B, t):
+def babai(B, t, *args, **kwargs):
     """
     Run Babai's Nearest Plane algorithm by running LLL.
 
@@ -46,13 +46,14 @@ def babai(B, t):
             A[i, j] = B[i, j]
 
     # make sure the input is LLL reduced before reading the norm of the last vector
-    LLL.reduction(A)
+    LLL.reduction(A, *args, **kwargs)
     # zero vector at the end
     A.swap_rows(0, B.nrows)
 
     for j in range(B.ncols):
         A[-1, j] = t[j]
-    A[-1, -1] = ceil(A[-2].norm())
+    # precise norm
+    A[-1, -1] = isqrt(sum(x**2 for x in A[-2])) + 1
 
     LLL.reduction(A)  # now call LLL to run Babai
 

From 0cf1973366483aef17bab6a10f00ca7933c52e7e Mon Sep 17 00:00:00 2001
From: blupper <33233478+TheBlupper@users.noreply.github.com>
Date: Thu, 6 Jun 2024 02:13:21 +0200
Subject: [PATCH 2/4] Pass on arguments to LLL.reduction

---
 src/fpylll/algorithms/babai.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/fpylll/algorithms/babai.py b/src/fpylll/algorithms/babai.py
index 5dd267d5..5b41a7b3 100644
--- a/src/fpylll/algorithms/babai.py
+++ b/src/fpylll/algorithms/babai.py
@@ -17,6 +17,8 @@ def babai(B, t, *args, **kwargs):
 
     :param B: Input lattice basis.
     :param target: Target point (∈ ZZ^n)
+    :param args: Passed onto LLL.reduction
+    :param kwargs: Passed onto LLL.reduction
     :returns coordinates of the solution vector:
 
     This implementation is more numerically stable compared to the one offered by `MatGSO.babai()`.

From e1b32b8278545719f95c20b4e28b6b2f7e89ca2a Mon Sep 17 00:00:00 2001
From: blupper <33233478+TheBlupper@users.noreply.github.com>
Date: Thu, 6 Jun 2024 02:17:24 +0200
Subject: [PATCH 3/4] Pass on arguments again

---
 src/fpylll/algorithms/babai.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/fpylll/algorithms/babai.py b/src/fpylll/algorithms/babai.py
index 5b41a7b3..c02263db 100644
--- a/src/fpylll/algorithms/babai.py
+++ b/src/fpylll/algorithms/babai.py
@@ -57,7 +57,7 @@ def babai(B, t, *args, **kwargs):
     # precise norm
     A[-1, -1] = isqrt(sum(x**2 for x in A[-2])) + 1
 
-    LLL.reduction(A)  # now call LLL to run Babai
+    LLL.reduction(A, *args, **kwargs)  # now call LLL to run Babai
 
     v = [0] * len(t)
     if A[-1, -1] > 0:

From ffe760dc97bc83a68243bac8b9643550e06b80d0 Mon Sep 17 00:00:00 2001
From: blupper <33233478+TheBlupper@users.noreply.github.com>
Date: Thu, 6 Jun 2024 11:02:50 +0200
Subject: [PATCH 4/4] Document +1

---
 src/fpylll/algorithms/babai.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/fpylll/algorithms/babai.py b/src/fpylll/algorithms/babai.py
index c02263db..9011b27f 100644
--- a/src/fpylll/algorithms/babai.py
+++ b/src/fpylll/algorithms/babai.py
@@ -54,7 +54,7 @@ def babai(B, t, *args, **kwargs):
 
     for j in range(B.ncols):
         A[-1, j] = t[j]
-    # precise norm
+    # precise norm, +1 to make sure it's not too small, too big doesn't matter
     A[-1, -1] = isqrt(sum(x**2 for x in A[-2])) + 1
 
     LLL.reduction(A, *args, **kwargs)  # now call LLL to run Babai