diff --git a/include/constants.h b/include/constants.h
index 8b02018..4543f03 100644
--- a/include/constants.h
+++ b/include/constants.h
@@ -11,6 +11,17 @@ extern "C" {
 #define DAQP_UNCONSTRAINED_OPTIMAL -2
 #define DAQP_INF ((c_float)1e30)
 
+// PRECISION-DEPENDENT TOLERANCES
+#ifdef DAQP_SINGLE_PRECISION
+#define DAQP_LU_SING_TOL   ((c_float)1e-6)  // pivot magnitude below this is singular (daqp_lu)
+#define DAQP_INIT_PRIM_TOL ((c_float)1e-5)  // slack "on bound" band for primal warm start
+#define DAQP_INIT_DUAL_TOL ((c_float)1e-6)  // multiplier sign threshold for dual warm start
+#else
+#define DAQP_LU_SING_TOL   ((c_float)1e-12)
+#define DAQP_INIT_PRIM_TOL ((c_float)1e-9)
+#define DAQP_INIT_DUAL_TOL ((c_float)1e-12)
+#endif
+
 // DEFAULT SETTINGS
 #define DAQP_DEFAULT_PRIM_TOL 1e-6
 #define DAQP_DEFAULT_DUAL_TOL 1e-12
diff --git a/src/api.c b/src/api.c
index 8ef4754..73efa99 100644
--- a/src/api.c
+++ b/src/api.c
@@ -539,7 +539,7 @@ int daqp_first_violating(c_float* x, c_float* A, c_float* bu, c_float* bl, int n
 void daqp_primal_init_active(DAQPProblem* qp, c_float* x){
     int i,disp;
     c_float Ax, slack;
-    c_float tol= 1e-9;
+    c_float tol= DAQP_INIT_PRIM_TOL;
 
     // Simple constraints
     for(i=0; i < qp->ms; i++){
@@ -579,7 +579,7 @@ void daqp_primal_init_active(DAQPProblem* qp, c_float* x){
 // based on a dual iterate
 void daqp_dual_init_active(DAQPProblem* qp, c_float* lam){
     int i;
-    c_float tol = 1e-12;
+    c_float tol = DAQP_INIT_DUAL_TOL;
     for(i=0; i < qp->m; i++){
         if(qp->sense[i] & DAQP_IMMUTABLE) continue;
         if(lam[i] > tol){
diff --git a/src/utils.c b/src/utils.c
index c551dba..7af1dd3 100644
--- a/src/utils.c
+++ b/src/utils.c
@@ -534,7 +534,7 @@ int daqp_lu(c_float* A, int* P, int n) {
         }
 
         // Check for singularity
-        if (max_val < 1e-12) return -1;
+        if (max_val < DAQP_LU_SING_TOL) return -1;
 
         // Swap rows in A
         for (int k = 0; k < n; k++) {