diff --git a/include/linux/bpf.h b/include/linux/bpf.h
index 4001d11be1516..583c4477a0e39 100644
--- a/include/linux/bpf.h
+++ b/include/linux/bpf.h
@@ -909,10 +909,14 @@ bpf_ctx_record_field_size(struct bpf_insn_access_aux *aux, u32 size)
 	aux->ctx_field_size = size;
 }
 
+static bool bpf_is_ldimm64(const struct bpf_insn *insn)
+{
+	return insn->code == (BPF_LD | BPF_IMM | BPF_DW);
+}
+
 static inline bool bpf_pseudo_func(const struct bpf_insn *insn)
 {
-	return insn->code == (BPF_LD | BPF_IMM | BPF_DW) &&
-	       insn->src_reg == BPF_PSEUDO_FUNC;
+	return bpf_is_ldimm64(insn) && insn->src_reg == BPF_PSEUDO_FUNC;
 }
 
 struct bpf_prog_ops {
diff --git a/kernel/bpf/verifier.c b/kernel/bpf/verifier.c
index 9ae6eae134716..83d659c14b291 100644
--- a/kernel/bpf/verifier.c
+++ b/kernel/bpf/verifier.c
@@ -3662,12 +3662,29 @@ static int push_jmp_history(struct bpf_verifier_env *env,
 
 /* Backtrack one insn at a time. If idx is not at the top of recorded
  * history then previous instruction came from straight line execution.
+ * Return -ENOENT if we exhausted all instructions within given state.
+ *
+ * It's legal to have a bit of a looping with the same starting and ending
+ * insn index within the same state, e.g.: 3->4->5->3, so just because current
+ * instruction index is the same as state's first_idx doesn't mean we are
+ * done. If there is still some jump history left, we should keep going. We
+ * need to take into account that we might have a jump history between given
+ * state's parent and itself, due to checkpointing. In this case, we'll have
+ * history entry recording a jump from last instruction of parent state and
+ * first instruction of given state.
  */
 static int get_prev_insn_idx(struct bpf_verifier_state *st, int i,
 			     u32 *history)
 {
 	u32 cnt = *history;
 
+	if (i == st->first_insn_idx) {
+		if (cnt == 0)
+			return -ENOENT;
+		if (cnt == 1 && st->jmp_history[0].idx == i)
+			return -ENOENT;
+	}
+
 	if (cnt && st->jmp_history[cnt - 1].idx == i) {
 		i = st->jmp_history[cnt - 1].prev_idx;
 		(*history)--;
@@ -4547,10 +4564,10 @@ static int __mark_chain_precision(struct bpf_verifier_env *env, int regno)
 				 * Nothing to be tracked further in the parent state.
 				 */
 				return 0;
-			if (i == first_idx)
-				break;
 			subseq_idx = i;
 			i = get_prev_insn_idx(st, i, &history);
+			if (i == -ENOENT)
+				break;
 			if (i >= env->prog->len) {
 				/* This can happen if backtracking reached insn 0
 				 * and there are still reg_mask or stack_mask
@@ -15546,15 +15563,16 @@ static int visit_func_call_insn(int t, struct bpf_insn *insns,
 				struct bpf_verifier_env *env,
 				bool visit_callee)
 {
-	int ret;
+	int ret, insn_sz;
 
-	ret = push_insn(t, t + 1, FALLTHROUGH, env, false);
+	insn_sz = bpf_is_ldimm64(&insns[t]) ? 2 : 1;
+	ret = push_insn(t, t + insn_sz, FALLTHROUGH, env, false);
 	if (ret)
 		return ret;
 
-	mark_prune_point(env, t + 1);
+	mark_prune_point(env, t + insn_sz);
 	/* when we exit from subprog, we need to record non-linear history */
-	mark_jmp_point(env, t + 1);
+	mark_jmp_point(env, t + insn_sz);
 
 	if (visit_callee) {
 		mark_prune_point(env, t);
@@ -15576,15 +15594,17 @@ static int visit_func_call_insn(int t, struct bpf_insn *insns,
 static int visit_insn(int t, struct bpf_verifier_env *env)
 {
 	struct bpf_insn *insns = env->prog->insnsi, *insn = &insns[t];
-	int ret, off;
+	int ret, off, insn_sz;
 
 	if (bpf_pseudo_func(insn))
 		return visit_func_call_insn(t, insns, env, true);
 
 	/* All non-branch instructions have a single fall-through edge. */
 	if (BPF_CLASS(insn->code) != BPF_JMP &&
-	    BPF_CLASS(insn->code) != BPF_JMP32)
-		return push_insn(t, t + 1, FALLTHROUGH, env, false);
+	    BPF_CLASS(insn->code) != BPF_JMP32) {
+		insn_sz = bpf_is_ldimm64(insn) ? 2 : 1;
+		return push_insn(t, t + insn_sz, FALLTHROUGH, env, false);
+	}
 
 	switch (BPF_OP(insn->code)) {
 	case BPF_EXIT:
@@ -15714,11 +15734,21 @@ static int check_cfg(struct bpf_verifier_env *env)
 	}
 
 	for (i = 0; i < insn_cnt; i++) {
+		struct bpf_insn *insn = &env->prog->insnsi[i];
+
 		if (insn_state[i] != EXPLORED) {
 			verbose(env, "unreachable insn %d\n", i);
 			ret = -EINVAL;
 			goto err_free;
 		}
+		if (bpf_is_ldimm64(insn)) {
+			if (insn_state[i + 1] != 0) {
+				verbose(env, "jump into the middle of ldimm64 insn %d\n", i);
+				ret = -EINVAL;
+				goto err_free;
+			}
+			i++; /* skip second half of ldimm64 */
+		}
 	}
 	ret = 0; /* cfg looks good */
 
diff --git a/tools/testing/selftests/bpf/progs/verifier_precision.c b/tools/testing/selftests/bpf/progs/verifier_precision.c
index 193c0f8272d05..6b564d4c09866 100644
--- a/tools/testing/selftests/bpf/progs/verifier_precision.c
+++ b/tools/testing/selftests/bpf/progs/verifier_precision.c
@@ -91,3 +91,43 @@ __naked int bpf_end_bswap(void)
 }
 
 #endif /* v4 instruction */
+
+SEC("?raw_tp")
+__success __log_level(2)
+/*
+ * Without the bug fix there will be no history between "last_idx 3 first_idx 3"
+ * and "parent state regs=" lines. "R0_w=6" parts are here to help anchor
+ * expected log messages to the one specific mark_chain_precision operation.
+ *
+ * This is quite fragile: if verifier checkpointing heuristic changes, this
+ * might need adjusting.
+ */
+__msg("2: (07) r0 += 1                       ; R0_w=6")
+__msg("3: (35) if r0 >= 0xa goto pc+1")
+__msg("mark_precise: frame0: last_idx 3 first_idx 3 subseq_idx -1")
+__msg("mark_precise: frame0: regs=r0 stack= before 2: (07) r0 += 1")
+__msg("mark_precise: frame0: regs=r0 stack= before 1: (07) r0 += 1")
+__msg("mark_precise: frame0: regs=r0 stack= before 4: (05) goto pc-4")
+__msg("mark_precise: frame0: regs=r0 stack= before 3: (35) if r0 >= 0xa goto pc+1")
+__msg("mark_precise: frame0: parent state regs= stack=:  R0_rw=P4")
+__msg("3: R0_w=6")
+__naked int state_loop_first_last_equal(void)
+{
+	asm volatile (
+		"r0 = 0;"
+	"l0_%=:"
+		"r0 += 1;"
+		"r0 += 1;"
+		/* every few iterations we'll have a checkpoint here with
+		 * first_idx == last_idx, potentially confusing precision
+		 * backtracking logic
+		 */
+		"if r0 >= 10 goto l1_%=;"	/* checkpoint + mark_precise */
+		"goto l0_%=;"
+	"l1_%=:"
+		"exit;"
+		::: __clobber_common
+	);
+}
+
+char _license[] SEC("license") = "GPL";
diff --git a/tools/testing/selftests/bpf/verifier/ld_imm64.c b/tools/testing/selftests/bpf/verifier/ld_imm64.c
index f9297900cea6d..78f19c255f20b 100644
--- a/tools/testing/selftests/bpf/verifier/ld_imm64.c
+++ b/tools/testing/selftests/bpf/verifier/ld_imm64.c
@@ -9,8 +9,8 @@
 	BPF_MOV64_IMM(BPF_REG_0, 2),
 	BPF_EXIT_INSN(),
 	},
-	.errstr = "invalid BPF_LD_IMM insn",
-	.errstr_unpriv = "R1 pointer comparison",
+	.errstr = "jump into the middle of ldimm64 insn 1",
+	.errstr_unpriv = "jump into the middle of ldimm64 insn 1",
 	.result = REJECT,
 },
 {
@@ -23,8 +23,8 @@
 	BPF_LD_IMM64(BPF_REG_0, 1),
 	BPF_EXIT_INSN(),
 	},
-	.errstr = "invalid BPF_LD_IMM insn",
-	.errstr_unpriv = "R1 pointer comparison",
+	.errstr = "jump into the middle of ldimm64 insn 1",
+	.errstr_unpriv = "jump into the middle of ldimm64 insn 1",
 	.result = REJECT,
 },
 {