diff --git a/tex/generic/pgf/libraries/pgflibraryintersections.code.tex b/tex/generic/pgf/libraries/pgflibraryintersections.code.tex
index 6bed3e47..1f30b257 100644
--- a/tex/generic/pgf/libraries/pgflibraryintersections.code.tex
+++ b/tex/generic/pgf/libraries/pgflibraryintersections.code.tex
@@ -552,13 +552,13 @@
             % <=>  |s| * ||#2 - #1|| < eps
             % and, since s< 0  here:
             % <=>  -s * ||#2 - #1|| < eps
-            \pgf@xa=-\pgf@intersect@len@a\pgf@x
-            \ifdim\pgf@xa<\pgfintersectiontolerance\relax
-                % close enough to first endpoint of line 1:
-                \def\pgf@marshal{1}%
-            \else
-                \def\pgf@marshal{0}%
-            \fi
+            \begingroup
+                \pgfkeys{/pgf/fpu,/pgf/fpu/output format=float}%
+                \pgfmathfloatparse{-\pgf@intersect@len@a*\pgf@x<\pgfintersectiontolerance}%
+                \pgfmath@smuggleone{\pgfmathresult}%
+            \endgroup
+            \pgfmathfloattoint{\pgfmathresult}%
+            \let\pgf@marshal\pgfmathresult
         \else
             \ifdim\pgf@x>1pt
                 % let it count as hit if
@@ -566,14 +566,13 @@
                 % <=>  |s-1| * ||#2 - #1|| < eps
                 % and, since s > 1  here:
                 % <=>  s * ||#2 - #1|| - ||#2 - #1|| < eps
-                \pgf@xa=\pgf@intersect@len@a\pgf@x
-                \advance\pgf@xa by-\pgf@intersect@len@a pt %
-                \ifdim\pgf@xa<\pgfintersectiontolerance\relax
-                    % close enough to second endpoint of line 1:
-                    \def\pgf@marshal{1}%
-                \else
-                    \def\pgf@marshal{0}%
-                \fi
+                \begingroup
+                    \pgfkeys{/pgf/fpu,/pgf/fpu/output format=float}%
+                    \pgfmathfloatparse{\pgf@intersect@len@a*\pgf@x-\pgf@intersect@len@a<\pgfintersectiontolerance}%
+                    \pgfmath@smuggleone{\pgfmathresult}%
+                \endgroup
+                \pgfmathfloattoint{\pgfmathresult}%
+                \let\pgf@marshal\pgfmathresult
             \else
                 % 0<= s <= 1: we have an intersection within line 1.
                 \def\pgf@marshal{1}%
@@ -584,24 +583,23 @@
         \if1\pgf@marshal
             \ifdim\pgf@y<0sp
                 % see remarks for line 1. same applies here.
-                \pgf@xa=-\pgf@intersect@len@b\pgf@y
-                \ifdim\pgf@xa<\pgfintersectiontolerance\relax
-                    % close enough to first endpoint of line 2:
-                    \def\pgf@marshal{1}%
-                \else
-                    \def\pgf@marshal{0}%
-                \fi
+                \begingroup
+                \pgfkeys{/pgf/fpu,/pgf/fpu/output format=float}%
+                \pgfmathfloatparse{-\pgf@intersect@len@b*\pgf@y<\pgfintersectiontolerance}%
+                \pgfmath@smuggleone{\pgfmathresult}%
+                \endgroup
+                \pgfmathfloattoint{\pgfmathresult}%
+                \let\pgf@marshal\pgfmathresult
             \else
                 \ifdim\pgf@y>1pt
                     % see remarks for line 1. same applies here.
-                    \pgf@xa=\pgf@intersect@len@b\pgf@y
-                    \advance\pgf@xa by-\pgf@intersect@len@b pt %
-                    \ifdim\pgf@xa<\pgfintersectiontolerance\relax
-                        % close enough to second endpoint of line 2:
-                        \def\pgf@marshal{1}%
-                    \else
-                        \def\pgf@marshal{0}%
-                    \fi
+                    \begingroup
+                        \pgfkeys{/pgf/fpu,/pgf/fpu/output format=float}%
+                        \pgfmathfloatparse{\pgf@intersect@len@b*\pgf@y-\pgf@intersect@len@b<\pgfintersectiontolerance}%
+                        \pgfmath@smuggleone{\pgfmathresult}%
+                    \endgroup
+                    \pgfmathfloattoint{\pgfmathresult}%
+                    \let\pgf@marshal\pgfmathresult
                 \else
                     % 0<= t <= 1: we have an intersection within line 2.
                     \def\pgf@marshal{1}%