Your Browser Does Math Differently on Every OS, and Anti-Bot Systems Read the Bits

Fingerprinting is usually about canvas, WebGL, fonts, audio. There is a quieter signal, and it lives in the last bits of a number.

Run this in any console:

Math.tanh(0.8)
// 0.6640367702678491   genuine Linux Chrome    (glibc)
// 0.664036770267849    genuine macOS Chrome     (libsystem_m)
// 0.6640367702678489   genuine Windows Chrome   (UCRT)

That is not a constant. It is an approximation, and the exact bits depend on the OS that computed it. A genuine Mac runs Math.tanh through Apple’s math library. Linux runs it through glibc¹. The two disagree on about a quarter of all inputs, usually by one unit in the last place (1 ULP²). Windows, through the Universal C Runtime, disagrees with both on a few percent, and on the input above all three land on a different bit.

The same call, run on genuine Chrome 150 across three real machines:

Measured over the DevTools protocol on Chrome 150: Linux (glibc), macOS 26 on Apple Silicon (libsystem_m), Windows 11 (ucrtbase.dll). tanh(0.5) is one of the roughly three-in-four inputs where everyone agrees, which is exactly why it makes a useless probe. tanh(0.8) is one that separates all three at once.

One tanh call on the right input is a per-OS signature. Claim macOS, return Linux math bits, and you have contradicted your own User-Agent.

Scrapfly ships a browser that has to match a real one across hundreds of signals. Math is one of the harder ones. Here is why, and how we close it.

Why one function returns different bits

IEEE 754³ defines how a double is stored. It does not require sin, cos, tanh, or exp to be correctly rounded. Correct rounding is expensive, so every vendor ships a libm⁴ that trades a fraction of a ULP for speed, with its own minimax⁵ coefficients, lookup tables, and reduction constants.

Three implementations, three sets of bits:

• Linux: glibc
• macOS: Apple libsystem_m
• Windows: UCRT⁶ (ucrtbase.dll)

They agree almost everywhere and split just often enough to classify the OS. A detector needs no math. It needs a table: genuine macOS Chrome returns this pattern for cos(1), genuine Linux Chrome returns that one. One probe, one comparison.

Four traps

“Just reimplement the Mac functions” breaks on contact. Four reasons.

1. Only some math leaks. V8⁷ ships its own math and links it statically: Math.exp, Math.pow, Math.atan, and most of the rest come from bundled llvm-libc⁸, and Math.sin / Math.cos from a bundled glibc-derived dbl-64 routine. All of them are identical on every OS, so spoofing them creates an inconsistency. The exception is Math.tanh: none of the bundled libraries export it, so V8 falls back to the platform std::tanh. It is the only Math.* that leaks the OS, and that asymmetry is itself checkable.

2. JavaScript math and CSS math are different code paths. CSS sin(), cos(), and atan2() do not share code with Math.sin. The layout engine reduces the angle in degrees, then calls platform std::sin on the reduced value. That gives a different result than a direct radian sin(), and it hits the host libm, so all seven CSS trig functions leak. We reproduced the degree reduction and the radians-to-degrees step bit-for-bit, not just the leaf function.

3. macOS has two math libraries that disagree. Apple Silicon carries scalar libsystem_m and the Accelerate framework⁹’s vector routines (vvsin, vvtanh). They are different code. Across a million inputs they diverge on 10 to 89 percent, depending on the function. Take cos(0): scalar returns exactly 1.0, Accelerate returns 0.9999999999999999. So “reproduce Apple’s math” is undefined until you know which library the browser calls, at which site. We resolved it by driving real Chrome on a real Mac over the debugging protocol and reading the exact double. Answer: scalar libsystem_m backs Math.tanh, CSS trig, and the audio compressor’s per-sample transcendentals. Accelerate backs Chrome’s Web Audio DSP on Mac, the FFT, the vector math, and the biquad filters (fft_frame_mac.cc, vector_math_mac.h, biquad.cc, all BUILDFLAG(IS_MAC)). Pick the wrong library for a given call site and you land 1 ULP off on most inputs, worse than not spoofing.

4. Architecture leaks. ARM and x86 differ on fused-multiply-add and on NaN sign propagation. A reproduction that is correct on paper drifts if the compiler fuses a multiply-add on one target and not the other.

The map: what leaks where

Put the routing on one page. Bold is the host libm (glibc, Apple libsystem_m, or UCRT), the code that leaks the OS. Everything else is identical on every machine and safe to leave alone.

V8 bundled = statically linked and identical on every OS: llvm-libc for most functions, a glibc-derived dbl-64 routine for sin/cos. host libm = the platform library that leaks the OS (libsystem_m on Mac, glibc on Linux, UCRT on Windows). Accelerate = Apple’s vDSP, which Chrome uses for the Mac Web Audio DSP.

Three things stand out. First, V8 routes almost everything through its own bundled math, so JavaScript Math is a tell in exactly one place: Math.tanh. Second, CSS is a tell everywhere, because Blink calls the host libm directly for every trig function. Third, Web Audio on Mac runs on Accelerate for the FFT and the vector stages, while the DynamicsCompressor’s per-sample transcendentals stay scalar libsystem_m. Three different libraries in one audio graph.

WASM is not in the table because it has no transcendental opcodes. sin and friends come from whatever libm the module bundled, and its arithmetic (f64.sqrt, f64.mul) is hardware, so WASM math is identical on every OS. Its only fingerprint axis is the ARM-versus-x86 split in NaN canonicalization and a few SIMD roundings.

The tells cluster in three surfaces: Math.tanh, every CSS trig function, and Web Audio (the Accelerate FFT, which carries the CPU architecture, plus the compressor’s scalar libsystem_m, which carries the OS). That is the whole target.

How to close it

No noise. Perturbing the output fails twice. A reference comparison sees a value that matches no real OS, and per-call randomness breaks determinism, which is its own tell. The target is not “different from Linux.” It is “identical to the OS you claim.”

Reproduce the algorithm exactly. Recover the target’s minimax coefficients, exponent tables, and reduction constants from its libm, and transcribe them to portable C. Match every bit, including the inputs where the target rounds the wrong way. You are not building a good tanh. You are building theirs. Here is Apple’s sin polynomial, coefficients pulled straight out of libsystem_m:

// Every fused multiply-add Apple emits is written as an explicit fma(). The
// bit pattern of each coefficient is copied verbatim; a decimal transcription
// would round differently.
static const double P[6] = {
     0x1.5d8fd1fd19ccdp-33, -0x1.ae5e5a9291f5dp-26,  0x1.71de3567d48a1p-19,
    -0x1.a01a019bfdf03p-13,  0x1.111111110f7d0p-7,  -0x1.5555555555548p-3,
};
static double sin_poly(double x2) {
  double p = fma(x2, P[0], P[1]);
  p = fma(x2, p, P[2]);
  p = fma(x2, p, P[3]);
  p = fma(x2, p, P[4]);
  p = fma(x2, p, P[5]);
  return x2 * p;                 // caller finishes: sin(x) = fma(x, x2*p, x)
}

Make it deterministic. That explicit fma() matters. Compile with FMA contraction off (-ffp-contract=off) so the compiler never invents or drops a fusion of its own. Now the fused ops are exactly the ones Apple fuses, and the result is identical on FMA¹⁰ and non-FMA CPUs, and identical between the ARM machine you imitate and the x86 fleet you run on. Hardware FMA and correctly-rounded software FMA return the same bits.

When reproduction is not worth it, lift the original. Windows UCRT is x86-64, the same ISA as a Linux server, and position-independent. Map the genuine ucrtbase.dll into memory at runtime and call its exports directly. The bits are genuine because the code is genuine, no reverse-engineering required.

Calling into Windows code from a Linux binary hits the ABI boundary. UCRT is compiled for the Windows x64 convention: the callee owns 32 bytes of shadow space above the return address, and the callee-saved register set differs from System V. Declare the function pointers ms_abi or clang’s frame layout gets corrupted by the callee’s shadow-space writes, and the indirect call jumps into garbage.

// Windows x64 ABI, not System V. Without ms_abi the call crashes.
typedef double(__attribute__((ms_abi)) * D1)(double);          // tanh, sin, ...
typedef double(__attribute__((ms_abi)) * D2)(double, double);  // atan2

// The mapped DLL code is not a CFI-registered indirect-call target, so
// -fsanitize=cfi-icall (on in production) #UD-traps every call -> SIGILL at
// startup. Opt the wrappers that call through the pointers out of that check.
[[clang::no_sanitize("cfi-icall")]]
double ucrt_tanh(double x) {
  return ucrt.loaded ? ucrt.tanh(x) : std::tanh(x);
}

One more detail decides correctness. Every UCRT math function starts with mov eax, [rip+disp32], reading a CPU-dispatch flag that selects the scalar or the FMA/AVX2 code path. A fresh mapping leaves it at zero, so you get the slow path, whose bits differ from what a modern Windows box produces. Extract the flag’s address from the tanh prologue and force it to the FMA path before the first call, and the lifted library matches a real Windows machine bit-for-bit.

Patch the chokepoint, gate it. Hook the single function that owns the value, where the engine calls libm. Gate on the claimed OS: Linux keeps glibc, Mac gets the reproduction.

Watch the clock. A perfect reproduction that runs slow is still a tell. Our first build lowered every fma() to a software call, because the default x86 baseline predates hardware FMA. That ran 2.5 to 6 times slower than native. A loop timing Math.tanh against Math.sin would show a ratio no real browser has. Turning on hardware FMA cut each fused op to one instruction: about 6 times faster, faster than glibc, and bit-identical.

Validation

None of this ships without proof. Our harness runs 871,000 inputs per release across every branch and domain: dense grids, interval boundaries, subnormals, signed zeros, infinities, NaNs. Two ground truths back it:

1. A genuine-device oracle: a real Mac computing both scalar and Accelerate results for every input, so we know exactly where the two disagree.
2. A genuine-browser anchor: real Chrome on a real Mac over the debugging protocol, computing Math.tanh and every CSS trig function at full precision. This is the surface a fingerprinter reads.

We ship at bit-for-bit parity with genuine Mac Chrome on Math.tanh and on CSS sin, cos, tan, asin, acos, atan, and atan2, with the reproduction verified identical to the machine code in the shipped binary. Domain edges get checked too: asin(2) on a real Mac resolves to 0 (out of domain is NaN, and CSS clamps NaN to zero), not the 90 degrees a naive reproduction returns.

Why it matters

Math is deterministic, cheap to probe, hard to fake, and almost never on a spoofing stack’s radar. That makes it a strong signal for a defender and a liability for a scraper. Getting it right takes reverse-engineering vendor libm internals, mapping how three engines route math per call site, matching algorithms to the last bit, holding determinism across architectures, and proving it against real hardware.

That is the work behind Scrapfly’s browser. Send a request through our API and ask to present as macOS, and the identity holds down to the rounding of a cosine.

Scrapium is Scrapfly’s scraping browser, built to stay indistinguishable from real traffic. Our engineering blog goes deep on the rest of the stack.