Calculate Used Blocks from Overflowing uint32 Counters

To accurately track counter memory usage in a pool of 20,000 blocks using overflowing uint32_t counters (alloc_num, free_num_1, free_num_2), compute the net used blocks as (alloc_num - (free_num_1 + free_num_2)) mod 2^{32}. This leverages unsigned wraparound behavior, where counter overflow naturally follows modular arithmetic. The provided code is close but fails due to an off-by-one error, improper handling of the free sum exceeding 32 bits, and a flawed comparison—fix it by first reducing the free sum modulo $2^{32}$ before subtracting.

Contents

• Understanding Wrapping Counters
• Issues in the Provided Implementation
• Correct Implementation
• Edge Cases to Handle
• Concurrency and Snapshot Risks
• Sources
• Conclusion

Understanding Wrapping Counters

Ever wonder why your counter memory stats go haywire after billions of operations? uint32_t counters top out at 4,294,967,295 (UINT32_MAX). Add one more? It wraps to zero—like a odometer rolling over. This counter overflow is well-defined in C: unsigned integers always wrap modulo $2^{32}$, per the language spec.

In your setup, alloc_num ticks up per allocation. free_num_1 and free_num_2 do the same for frees from Modules B and C. The true used blocks? Allocations minus total frees, but since counters wrap independently (possibly multiple times), you need the difference modulo $2^{32}$.

Why does this work for a tiny pool like 20,000? The real used count stays small (0–20,000). The modular result will match exactly—no ambiguity about “which lap” the counters are on. As Stack Overflow explains for wrapping counters, direct subtraction in unsigned types gives the right answer as long as intervals don’t exceed half the range (here, trivially true).

But sum the frees first? free_num_1 + free_num_2 could wrap itself if both near max. Promote to uint64_t to capture the true low-32-bits sum.

Issues in the Provided Implementation

Your code looks smart at first—casting to uint64_t, checking alloc vs. total_free. But it trips on a few gotchas.

uint64_t total_free = (uint64_t)free_num_1 + free_num_2; // Good: handles sum up to ~2^33
uint64_t alloc_64 = (uint64_t)alloc_num;
if (alloc_64 >= total_free) { // Bug 1: total_free isn't mod 2^32!
 return (uint32_t)(alloc_64 - total_free);
} else {
 return (uint32_t)(alloc_64 + 4294967296ULL + 1 - total_free); // Bug 2: +1 off-by-one!
}

Problem one: You compare alloc_64 (< $2^{32}$) to raw total_free (up to ~$2^{33}$). If frees summed over $2^{32}$, the if always fails—even if effective frees mod $2^{32}$ are small.

Problem two: That sneaky +1. Suppose free_num_1 = UINT32_MAX (=0xFFFFFFFF), free_num_2=0. total_free=0xFFFFFFFF. alloc_num=0xFFFFFFFE. Modulo, used should be 0xFFFFFFFE - 0xFFFFFFFF mod $2^{32}$ = 0xFFFFFFFF (but wait, net used=1 less alloc? No—inconsistent, but point: formula assumes + $2^{32}$, not +1).

Real example: free1=UINT32_MAX, free2=1 → total_free = 2^{32}. sum mod =0. But code does else: alloc + 2^{32} +1 - 2^{32} = alloc +1. Off by one! Overcounts used.

As this Stack Overflow thread on uint32_t temp overflow notes, unsigned math wraps cleanly modulo, but intermediates need care.

Correct Implementation

Fix: Mod the free sum first, then subtract modulo $2^{32}$. No off-by-one. No weird comparisons.

#include <stdint.h>

uint32_t get_used_blocks_num(uint32_t alloc_num, uint32_t free_num_1, uint32_t free_num_2) {
 // Sum frees mod 2^32 (low 32 bits)
 uint64_t sum_free_mod = ((uint64_t)free_num_1 + free_num_2) & 0xFFFFFFFFULL;
 
 // Now diff mod 2^32
 if (alloc_num >= (uint32_t)sum_free_mod) {
 return alloc_num - (uint32_t)sum_free_mod;
 } else {
 return (uint32_t)(alloc_num + 0x100000000ULL - sum_free_mod);
 }
}

Why this rocks? sum_free_mod always < $2^{32}$. The if catches no-wrap cases directly. Else adds exactly one full cycle. Casts safe—result fits uint32_t.

You could write it as a single line with mask:

uint64_t sum_free_mod = ((uint64_t)free_num_1 + free_num_2) & 0xFFFFFFFFULL;
uint64_t used64 = (uint64_t)alloc_num - sum_free_mod;
return (uint32_t)((used64 > UINT32_MAX) ? used64 + (1ULL << 32) : used64);

But uint64_t subtract underflows hugely if negative (e.g., 2^{64} + small), so the if-branch is clearer and branch-predictor friendly.

This mirrors safe math in Felix von Leitner’s overflow checker, promoting ops to wider types.

Edge Cases to Handle

Tested these? Here’s what breaks naive code.

1. Sum free wrap: free1=UINT32_MAX, free2=1 → sum_mod=0. used=alloc_num - 0. (Your code: total_free=2^{32}, else: alloc+1. Wrong!)

2. Alloc wrap alone: alloc=1, frees=0 → used=1. Fine.

3. Frees > alloc mod: alloc=10, free1=15 → sum_mod=15, used=10 + 2^{32}-15 = … mod= 2^{32}-5 → but since small pool, 4294967291? No—wait, but in reality if frees>allocs, used=0 logically, but counters allow it (double-free?). Question assumes consistent, but compute raw mod.

Wait—pool=20k means if used_mod >20000, clamp? Not specified, but add:

uint32_t used = /* computation */;
return (used > 20000U) ? 20000U : used; // Sanity cap

4. Max values: alloc=UINT32_MAX, free1=free2=UINT32_MAX → sum_mod= (2*UINT32_MAX) & 0xFF…F = UINT32_MAX-1 +1? 0xFFFFFFFF + 0xFFFFFFFF = 0x1FFFFFFFE & 0xFFFFFFFF=0xFFFFFFFE. used= UINT32_MAX - 0xFFFFFFFE =1.

5. Zeroes: All 0 → used=0.

6. Multiple wraps: Counters wrap 1000x? Irrelevant—mod keeps it honest.

From Embedded Related on overflows, always promote for safety.

Concurrency and Snapshot Risks

Counters updated concurrently? Your function takes a snapshot—reads aren’t atomic across vars.

Risk: Thread A incs alloc after you read it, but before frees. Overestimates used.

Or read free1 mid-inc (if not atomic), torn read (high bits stale).

Fixes?

• Make counters std::atomic<uint32_t> or _Atomic uint32_t. Reads become atomic per counter.

• Still, snapshot inconsistent. For precision: mutex around updates and reads. Costly.

• Or single atomic uint64_t net_used, inc/dec with CAS on overflow. But changes design.

As this atomic counter thread warns, naive ++ races anyway. For monitoring, snapshot’s “good enough”—used fluctuates ±1 anyway.

In RTOS/embedded, disable interrupts briefly. But for 20k pool? Relax.

Sources

1. Integer overflow - Wikipedia
2. Real Time Counter and Integer Overflow
3. Can I overflow uint32_t in a temporary result? - Stack Overflow
4. prevent std::atomic from overflowing - Stack Overflow
5. Catching Integer Overflows in C
6. How to deal with a wrapping counter in embedded C - Stack Overflow
7. Counter Free-Running - MathWorks
8. How to properly count timer overflows… - Stack Overflow
9. Understanding and Preventing Overflow - Embedded Related

Conclusion

Nail counter overflow with modular subtraction: sum frees mod $2^{32}$, diff from alloc mod $2^{32}$, add cycle if needed. Ditch the +1, mod the sum—boom, accurate counter memory for your 20k pool. Handles wraps, edges; concurrency? Snapshot’s fine for most, atomicize for paranoia. Test extremes, cap at 20k if paranoid. Solid monitoring without 64-bit counters.