diff --git a/Common/Constants/include/CommonConstants/MathConstants.h b/Common/Constants/include/CommonConstants/MathConstants.h
index 6870b8ddd5712..9ef3b4dba5ae0 100644
--- a/Common/Constants/include/CommonConstants/MathConstants.h
+++ b/Common/Constants/include/CommonConstants/MathConstants.h
@@ -22,7 +22,8 @@ namespace constants
 {
 namespace math
 {
-constexpr float Almost0 = 1.175494351e-38f;
+constexpr float Almost0 = 0x1.0p-126f;   // smallest non-denormal float
+constexpr float Epsilon = 0x0.000002p0f; // smallest float such that 1 != 1 + Epsilon
 constexpr float Almost1 = 1.f - 1.0e-6f;
 constexpr float VeryBig = 1.f / Almost0;
 
diff --git a/DataFormats/Reconstruction/src/TrackParametrizationWithError.cxx b/DataFormats/Reconstruction/src/TrackParametrizationWithError.cxx
index 0dd4a4441c0b3..81963adf79938 100644
--- a/DataFormats/Reconstruction/src/TrackParametrizationWithError.cxx
+++ b/DataFormats/Reconstruction/src/TrackParametrizationWithError.cxx
@@ -12,14 +12,9 @@
 #include "ReconstructionDataFormats/TrackParametrizationWithError.h"
 #include "ReconstructionDataFormats/Vertex.h"
 #include "ReconstructionDataFormats/DCA.h"
+#include "CommonConstants/MathConstants.h"
 #include <GPUCommonLogger.h>
 
-#ifndef __OPENCL__
-#include <cfloat>
-#else
-#include <float.h>
-#endif
-
 #ifndef GPUCA_GPUCODE_DEVICE
 #include <iostream>
 #endif
@@ -794,11 +789,11 @@ GPUd() auto TrackParametrizationWithError<value_T>::getPredictedChi2(const Track
   // get chi2 wrt other track, which must be defined at the same parameters X,alpha
   // Supplied non-initialized covToSet matrix is filled by inverse combined matrix for further use
 
-  if (gpu::CAMath::Abs(this->getAlpha() - rhs.getAlpha()) > FLT_EPSILON) {
+  if (gpu::CAMath::Abs(this->getAlpha() - rhs.getAlpha()) > o2::constants::math::Epsilon) {
     LOG(error) << "The reference Alpha of the tracks differ: " << this->getAlpha() << " : " << rhs.getAlpha();
     return 2.f * HugeF;
   }
-  if (gpu::CAMath::Abs(this->getX() - rhs.getX()) > FLT_EPSILON) {
+  if (gpu::CAMath::Abs(this->getX() - rhs.getX()) > o2::constants::math::Epsilon) {
     LOG(error) << "The reference X of the tracks differ: " << this->getX() << " : " << rhs.getX();
     return 2.f * HugeF;
   }
@@ -827,11 +822,11 @@ GPUd() bool TrackParametrizationWithError<value_T>::update(const TrackParametriz
   // update track with other track, the inverted combined cov matrix should be supplied
 
   // consider skipping this check, since it is usually already done upstream
-  if (gpu::CAMath::Abs(this->getAlpha() - rhs.getAlpha()) > FLT_EPSILON) {
+  if (gpu::CAMath::Abs(this->getAlpha() - rhs.getAlpha()) > o2::constants::math::Epsilon) {
     LOG(error) << "The reference Alpha of the tracks differ: " << this->getAlpha() << " : " << rhs.getAlpha();
     return false;
   }
-  if (gpu::CAMath::Abs(this->getX() - rhs.getX()) > FLT_EPSILON) {
+  if (gpu::CAMath::Abs(this->getX() - rhs.getX()) > o2::constants::math::Epsilon) {
     LOG(error) << "The reference X of the tracks differ: " << this->getX() << " : " << rhs.getX();
     return false;
   }
diff --git a/GPU/Common/GPUCommonConstants.h b/GPU/Common/GPUCommonConstants.h
index 883f64b7bdd12..f45aa05ed00ca 100644
--- a/GPU/Common/GPUCommonConstants.h
+++ b/GPU/Common/GPUCommonConstants.h
@@ -20,7 +20,7 @@
 #if !defined(__OPENCL1__)
 namespace GPUCA_NAMESPACE::gpu::gpu_common_constants
 {
-static CONSTEXPR const float kCLight = 0.000299792458f;
+static CONSTEXPR const float kCLight = 0.000299792458f; // TODO: Duplicate of MathConstants, fix this when OpenCL1 is removed
 }
 #endif