From 1fdf02ae5e0dc903f8ca179b8290469d643c27fa Mon Sep 17 00:00:00 2001
From: etienne <etienne.mdg@gmail.com>
Date: Thu, 19 Sep 2019 00:04:49 +0200
Subject: [PATCH 1/4] handling floating point errors

---
 src/push_relabel.jl | 19 +++++++++++++++++--
 1 file changed, 17 insertions(+), 2 deletions(-)

diff --git a/src/push_relabel.jl b/src/push_relabel.jl
index b4ed27a..060f49b 100644
--- a/src/push_relabel.jl
+++ b/src/push_relabel.jl
@@ -169,6 +169,21 @@ function relabel! end
     nothing
 end
 
+"""
+    is_zero(value)
+
+Test if the value is equal to zero. It handles floating point errors.
+"""
+function is_zero end
+function is_zero(
+        value::T
+    ) where {T}
+    if isa(value,AbstractFloat)
+        return isapprox(value, 0, atol = eps(T))
+    else
+        return value == 0
+    end
+end
 
 """
     discharge!(residual_graph, v, capacity_matrix, flow_matrix, excess, height, active, count, Q)
@@ -189,11 +204,11 @@ function discharge! end
         Q::AbstractVector                   # FIFO queue
     )
     for to in lg.outneighbors(residual_graph, v)
-        excess[v] == 0 && break
+        is_zero(excess[v]) && break
         push_flow!(residual_graph, v, to, capacity_matrix, flow_matrix, excess, height, active, Q)
     end
 
-    if excess[v] > 0
+    if ! is_zero(excess[v])
         if count[height[v] + 1] == 1
             gap!(residual_graph, height[v], excess, height, active, count, Q)
         else

From cc870147c74981a1a0ca9832954f5adf8db9d02b Mon Sep 17 00:00:00 2001
From: etienneINSA <depotetidg@gmail.com>
Date: Mon, 25 Nov 2019 14:24:01 +0100
Subject: [PATCH 2/4] handles floating point on dinic's algorithm

---
 src/dinic.jl        |  4 ++--
 src/maximum_flow.jl | 16 ++++++++++++++++
 src/push_relabel.jl | 16 ----------------
 3 files changed, 18 insertions(+), 18 deletions(-)

diff --git a/src/dinic.jl b/src/dinic.jl
index f10c1c8..681038d 100644
--- a/src/dinic.jl
+++ b/src/dinic.jl
@@ -21,7 +21,7 @@ function dinic_impl end
 
     while true
         augment = blocking_flow!(residual_graph, source, target, capacity_matrix, flow_matrix, P)
-        augment == 0 && break
+        is_zero(augment) && break
         flow += augment
     end
     return flow, flow_matrix
@@ -80,7 +80,7 @@ function blocking_flow! end
             end
         end
 
-        flow == 0 && continue                      # Flow cannot be augmented along path
+        is_zero(flow) && continue                      # Flow cannot be augmented along path
 
         v = target
         u = bv
diff --git a/src/maximum_flow.jl b/src/maximum_flow.jl
index 7b0fd1a..be1e1c1 100644
--- a/src/maximum_flow.jl
+++ b/src/maximum_flow.jl
@@ -178,3 +178,19 @@ function maximum_flow(
     end
     return maximum_flow(flow_graph, source, target, capacity_matrix, algorithm)
 end
+
+"""
+    is_zero(value)
+
+Test if the value is equal to zero. It handles floating point errors.
+"""
+function is_zero end
+function is_zero(
+        value::T
+    ) where {T}
+    if isa(value,AbstractFloat)
+        return isapprox(value, 0, atol = eps(T))
+    else
+        return value == 0
+    end
+end
diff --git a/src/push_relabel.jl b/src/push_relabel.jl
index 060f49b..e22d81b 100644
--- a/src/push_relabel.jl
+++ b/src/push_relabel.jl
@@ -169,22 +169,6 @@ function relabel! end
     nothing
 end
 
-"""
-    is_zero(value)
-
-Test if the value is equal to zero. It handles floating point errors.
-"""
-function is_zero end
-function is_zero(
-        value::T
-    ) where {T}
-    if isa(value,AbstractFloat)
-        return isapprox(value, 0, atol = eps(T))
-    else
-        return value == 0
-    end
-end
-
 """
     discharge!(residual_graph, v, capacity_matrix, flow_matrix, excess, height, active, count, Q)
 

From fe2aeff16636b31c8fdcce4b32457eb32d59c99d Mon Sep 17 00:00:00 2001
From: etienneINSA <depotetidg@gmail.com>
Date: Tue, 26 Nov 2019 09:47:31 +0100
Subject: [PATCH 3/4] wider tolerance for floating point

---
 src/maximum_flow.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/maximum_flow.jl b/src/maximum_flow.jl
index be1e1c1..093aaad 100644
--- a/src/maximum_flow.jl
+++ b/src/maximum_flow.jl
@@ -189,7 +189,7 @@ function is_zero(
         value::T
     ) where {T}
     if isa(value,AbstractFloat)
-        return isapprox(value, 0, atol = eps(T))
+        return isapprox(value, 0, atol = sqrt(eps(T)))
     else
         return value == 0
     end

From 60f2f8a3cd0847b2fa4b617c01d2c85543e46e3d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Mathieu=20Besan=C3=A7on?= <mathieu.besancon@gmail.com>
Date: Mon, 12 Oct 2020 17:43:08 +0200
Subject: [PATCH 4/4] Update src/push_relabel.jl

---
 src/push_relabel.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/push_relabel.jl b/src/push_relabel.jl
index e22d81b..88313b1 100644
--- a/src/push_relabel.jl
+++ b/src/push_relabel.jl
@@ -192,7 +192,7 @@ function discharge! end
         push_flow!(residual_graph, v, to, capacity_matrix, flow_matrix, excess, height, active, Q)
     end
 
-    if ! is_zero(excess[v])
+    if excess[v] ≉ zero(excess[v])
         if count[height[v] + 1] == 1
             gap!(residual_graph, height[v], excess, height, active, count, Q)
         else