diff --git a/include/mitsuba/core/constants.h b/include/mitsuba/core/constants.h
index 5ca9b397..52f8a2c9 100644
--- a/include/mitsuba/core/constants.h
+++ b/include/mitsuba/core/constants.h
@@ -47,31 +47,31 @@
 #undef INFINITY
 #endif
 
+#if defined(__WINDOWS__)
+#define ONE_MINUS_EPS_FLT 0.999999940395355225f
+#define ONE_MINUS_EPS_DBL 0.999999999999999888
+#else
+#define ONE_MINUS_EPS_FLT 0x1.fffffffffffff7p-1
+#define ONE_MINUS_EPS_DBL 0x1.fffffep-1f
+#endif
+
 #ifdef SINGLE_PRECISION
-#define M_E          2.71828182845904523536f
-#define M_PI         3.14159265358979323846f
-#define INV_PI       0.31830988618379067154f
-#define INV_TWOPI    0.15915494309189533577f
-#define INV_FOURPI   0.07957747154594766788f
-#define SQRT_TWO     1.41421356237309504880f
-#define INV_SQRT_TWO 0.70710678118654752440f
-#if defined(__WINDOWS__)
-#define ONE_MINUS_EPS 0.999999940395355225f
+#define M_E           2.71828182845904523536f
+#define M_PI          3.14159265358979323846f
+#define INV_PI        0.31830988618379067154f
+#define INV_TWOPI     0.15915494309189533577f
+#define INV_FOURPI    0.07957747154594766788f
+#define SQRT_TWO      1.41421356237309504880f
+#define INV_SQRT_TWO  0.70710678118654752440f
+#define ONE_MINUS_EPS ONE_MINUS_EPS_FLT
 #else
-#define ONE_MINUS_EPS 0x1.fffffep-1f
-#endif
-#else
-#define M_E          2.71828182845904523536
-#define M_PI         3.14159265358979323846
-#define INV_PI       0.31830988618379067154
-#define INV_TWOPI    0.15915494309189533577
-#define INV_FOURPI   0.07957747154594766788
-#define SQRT_TWO     1.41421356237309504880
-#define INV_SQRT_TWO 0.70710678118654752440
-#if defined(__WINDOWS__)
-#define ONE_MINUS_EPS 0.999999999999999888
-#else
-#define ONE_MINUS_EPS 0x1.fffffffffffff7p-1
-#endif
+#define M_E           2.71828182845904523536
+#define M_PI          3.14159265358979323846
+#define INV_PI        0.31830988618379067154
+#define INV_TWOPI     0.15915494309189533577
+#define INV_FOURPI    0.07957747154594766788
+#define SQRT_TWO      1.41421356237309504880
+#define INV_SQRT_TWO  0.70710678118654752440
+#define ONE_MINUS_EPS ONE_MINUS_EPS_DBL
 #endif
 #endif /* __MITSUBA_CORE_CONSTANTS_H */
diff --git a/src/samplers/sobolseq.h b/src/samplers/sobolseq.h
index 383beefb..4942136a 100644
--- a/src/samplers/sobolseq.h
+++ b/src/samplers/sobolseq.h
@@ -54,7 +54,7 @@ inline float sampleSingle(
 			result ^= Matrices::matrices32[i];
 	}
 
-	return result * (1.f / (1ULL << 32));
+	return std::min(result * (1.0f / (1ULL << 32)), ONE_MINUS_EPS_FLT);
 }
 
 // Compute one component of the Sobol'-sequence, where the component
@@ -77,7 +77,7 @@ inline double sampleDouble(
 			result ^= Matrices::matrices64[i];
 	}
 
-	return result * (1.0 / (1ULL << Matrices::size));
+	return std::min(result * (1.0 / (1ULL << Matrices::size)), ONE_MINUS_EPS_DBL);
 }
 
 // Call sampleSingle or sampleDouble depending on the compilation options