Floating Point Math divergences between platforms

[mhofman]

Apparently the floating point Math functions do not return the same results on all platform / engines / architectures.

At this point we should probably also verify that all operations are actually fully deterministic on the same environment.

Some pointers:

• https://github.com/fingerprintjs/fingerprintjs/blob/master/src/sources/math.ts
• https://gitlab.torproject.org/legacy/trac/-/issues/13018
• https://bugzilla.mozilla.org/show_bug.cgi?id=531915
• https://randomascii.wordpress.com/2013/07/16/floating-point-determinism/

[mhofman]

Here are the eshost results of the fingerprint test:

$ eshost -s ./math-fp-fingerprint.js 
#### engine262, V8
acos= 1.4473588658278522
acosh= 709.889355822726
acoshPf= 355.291251501643
asin= 0.12343746096704435
asinh= 0.881373587019543
asinhPf= 0.8813735870195429
atanh= 0.5493061443340548
atanhPf= 0.5493061443340548
atan= 0.4636476090008061
sin= 0.8178819121159085
sinh= 1.1752011936438014
sinhPf= 2.534342107873324
cos= -0.8390715290095377
cosh= 1.5430806348152437
coshPf= 1.5430806348152437
tan= -1.4214488238747245
tanh= 0.7615941559557649
tanhPf= 0.7615941559557649
exp= 2.718281828459045
expm1= 1.718281828459045
expm1Pf= 1.718281828459045
log1p= 2.3978952727983707
log1pPf= 2.3978952727983707
powPI= 1.9275814160560204e-50

#### JavaScriptCore, Moddable XS
acos= 1.4473588658278522
acosh= 709.889355822726
acoshPf= 355.291251501643
asin= 0.12343746096704435
asinh= 0.881373587019543
asinhPf= 0.8813735870195429
atanh= 0.5493061443340548
atanhPf= 0.5493061443340549
atan= 0.4636476090008061
sin= 0.8178819121159085
sinh= 1.1752011936438014
sinhPf= 2.534342107873324
cos= -0.8390715290095377
cosh= 1.5430806348152437
coshPf= 1.5430806348152437
tan= -1.4214488238747245
tanh= 0.7615941559557649
tanhPf= 0.7615941559557649
exp= 2.718281828459045
expm1= 1.718281828459045
expm1Pf= 1.718281828459045
log1p= 2.3978952727983707
log1pPf= 2.3978952727983707
powPI= 1.9275814160560206e-50

#### SpiderMonkey
acos= 1.4473588658278522
acosh= 709.889355822726
acoshPf= 355.291251501643
asin= 0.12343746096704435
asinh= 0.881373587019543
asinhPf= 0.8813735870195429
atanh= 0.5493061443340548
atanhPf= 0.5493061443340548
atan= 0.4636476090008061
sin= 0.8178819121159085
sinh= 1.1752011936438014
sinhPf= 2.534342107873324
cos= -0.8390715290095377
cosh= 1.5430806348152437
coshPf= 1.5430806348152437
tan= -1.4214488238747245
tanh= 0.7615941559557649
tanhPf= 0.7615941559557649
exp= 2.718281828459045
expm1= 1.718281828459045
expm1Pf= 1.718281828459045
log1p= 2.3978952727983707
log1pPf= 2.3978952727983707
powPI= 1.9275814160560185e-50

Source

const M = Math; // To reduce the minified code size
const fallbackFn = () => 0;

function getMathFingerprint() {
  // Native operations
  const acos = M.acos || fallbackFn;
  const acosh = M.acosh || fallbackFn;
  const asin = M.asin || fallbackFn;
  const asinh = M.asinh || fallbackFn;
  const atanh = M.atanh || fallbackFn;
  const atan = M.atan || fallbackFn;
  const sin = M.sin || fallbackFn;
  const sinh = M.sinh || fallbackFn;
  const cos = M.cos || fallbackFn;
  const cosh = M.cosh || fallbackFn;
  const tan = M.tan || fallbackFn;
  const tanh = M.tanh || fallbackFn;
  const exp = M.exp || fallbackFn;
  const expm1 = M.expm1 || fallbackFn;
  const log1p = M.log1p || fallbackFn;

  // Operation polyfills
  const powPI = (value) => M.pow(M.PI, value);
  const acoshPf = (value) => M.log(value + M.sqrt(value * value - 1));
  const asinhPf = (value) => M.log(value + M.sqrt(value * value + 1));
  const atanhPf = (value) => M.log((1 + value) / (1 - value)) / 2;
  const sinhPf = (value) => M.exp(value) - 1 / M.exp(value) / 2;
  const coshPf = (value) => (M.exp(value) + 1 / M.exp(value)) / 2;
  const expm1Pf = (value) => M.exp(value) - 1;
  const tanhPf = (value) => (M.exp(2 * value) - 1) / (M.exp(2 * value) + 1);
  const log1pPf = (value) => M.log(1 + value);

  // Note: constant values are empirical
  return {
    acos: acos(0.123124234234234242),
    acosh: acosh(1e308),
    acoshPf: acoshPf(1e154), // 1e308 will not work for polyfill
    asin: asin(0.123124234234234242),
    asinh: asinh(1),
    asinhPf: asinhPf(1),
    atanh: atanh(0.5),
    atanhPf: atanhPf(0.5),
    atan: atan(0.5),
    sin: sin(-1e300),
    sinh: sinh(1),
    sinhPf: sinhPf(1),
    cos: cos(10.000000000123),
    cosh: cosh(1),
    coshPf: coshPf(1),
    tan: tan(-1e300),
    tanh: tanh(1),
    tanhPf: tanhPf(1),
    exp: exp(1),
    expm1: expm1(1),
    expm1Pf: expm1Pf(1),
    log1p: log1p(10),
    log1pPf: log1pPf(10),
    powPI: powPI(-100),
  };
}

(globalThis.print || console.log)(
  Object.entries(getMathFingerprint())
    .map(([key, value]) => `${key}= ${value}`)
    .join("\n")
);

Engine versions

┌────────────────┬───────────┬────────────────────────────────┬────────────────────────────┬────────────────────────────────────────────────┐
│ name           │ type      │ path                           │ args                       │ tags                                           │
├────────────────┼───────────┼────────────────────────────────┼────────────────────────────┼────────────────────────────────────────────────┤
│ JavaScriptCore │ jsc       │ /home/node/.esvu/bin/jsc       │                            │ 282686,web                                     │
├────────────────┼───────────┼────────────────────────────────┼────────────────────────────┼────────────────────────────────────────────────┤
│ Moddable XS    │ xs        │ /home/node/.esvu/bin/xs        │                            │ 10.5.0,embedded                                │
├────────────────┼───────────┼────────────────────────────────┼────────────────────────────┼────────────────────────────────────────────────┤
│ SpiderMonkey   │ jsshell   │ /home/node/.esvu/bin/sm        │                            │ 94.0a1#20210917093507,web                      │
├────────────────┼───────────┼────────────────────────────────┼────────────────────────────┼────────────────────────────────────────────────┤
│ V8             │ d8        │ /home/node/.esvu/bin/v8        │                            │ 9.6.56,web                                     │
├────────────────┼───────────┼────────────────────────────────┼────────────────────────────┼────────────────────────────────────────────────┤
│ engine262      │ engine262 │ /home/node/.esvu/bin/engine262 │ --features=top-level-await │ 0.0.1-14f50592362d889289e133fff4200e8e304c995a │
└────────────────┴───────────┴────────────────────────────────┴────────────────────────────┴────────────────────────────────────────────────┘

[erights]

Those are differences by engine, what about by instruction-set architecture? Are those engine differences all on the same architecture? Which?

fwiw, I am more surprised to see engine differences than I would be to see architecture differences.

[erights]

Math routines are OS fingerprintable

Even more surprising than by engine or by architecture. What OS were these on?