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fix: Fix GaussianSampler
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@sp301415
sp301415 committed Sep 8, 2024
1 parent bdc11df commit 6384ca9
Showing 1 changed file with 128 additions and 125 deletions.
253 changes: 128 additions & 125 deletions math/csprng/gaussian_sampler.go
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Original file line number Diff line number Diff line change
Expand Up @@ -36,7 +36,7 @@ func (s *GaussianSampler[T]) uniformFloat() float64 {
}

// normFloat samples float64 from normal distribution.
func (s *GaussianSampler[T]) normFloat64() float64 {
func (s *GaussianSampler[T]) normFloat() float64 {
for {
var x, y float64

Expand Down Expand Up @@ -85,8 +85,7 @@ func (s *GaussianSampler[T]) Sample(stdDev float64) T {
panic("standard deviation not positive")
}

u := s.normFloat64() * stdDev
return T(int64(math.Round(u)))
return T(int64(math.Round(s.normFloat() * stdDev)))
}

// SampleSliceAssign samples rounded gaussian values
Expand All @@ -99,7 +98,7 @@ func (s *GaussianSampler[T]) SampleSliceAssign(stdDev float64, vOut []T) {
}

for i := range vOut {
vOut[i] = T(int64(math.Round(s.normFloat64() * stdDev)))
vOut[i] = T(int64(math.Round(s.normFloat() * stdDev)))
}
}

Expand All @@ -121,7 +120,7 @@ func (s *GaussianSampler[T]) SamplePolyAddAssign(stdDev float64, pOut poly.Poly[
}

for i := range pOut.Coeffs {
pOut.Coeffs[i] += T(int64(math.Round(s.normFloat64() * stdDev)))
pOut.Coeffs[i] += T(int64(math.Round(s.normFloat() * stdDev)))
}
}

Expand All @@ -135,145 +134,149 @@ func (s *GaussianSampler[T]) SamplePolySubAssign(stdDev float64, pOut poly.Poly[
}

for i := range pOut.Coeffs {
pOut.Coeffs[i] -= T(int64(math.Round(s.normFloat64() * stdDev)))
pOut.Coeffs[i] -= T(int64(math.Round(s.normFloat() * stdDev)))
}
}

/* Constants Generated by:
const (
blockSize = 128
scale = 1 << 24
)
var (
blockCount = 128
rn = 3.442619855899
area = 9.91256303526217e-3
q = float64(1 << 24)
qInv = 1.0 / (1 << 24)
wn [129]float64
kn [128]uint32
fn [128]float64
wn [128]float64
kn [128]uint32
fn [128]float64
dn = 3.442619855899
vn = 9.91256303526217e-3
)
wn[0] = area / gaussian(rn)
fn[0] = gaussian(wn[0])
q := vn / math.Exp(-.5*dn*dn)
wn[1] = rn
fn[1] = gaussian(wn[1])
for i := 2; i < blockCount; i++ {
wn[i] = gaussianInv(area/wn[i-1] + fn[i-1])
fn[i] = gaussian(wn[i])
}
kn[0] = uint32(math.Round((dn / q) * scale))
kn[1] = 0
for i := 0; i < blockCount; i++ {
kn[i] = uint32(math.Round((wn[i+1] / wn[i]) * q))
}
wn[0] = q / scale
wn[127] = dn / scale
fn[0] = 1.0
fn[127] = math.Exp(-.5 * dn * dn)
for i := range wn {
wn[i] *= qInv
tn := dn
for i := 126; i >= 1; i-- {
dn = math.Sqrt(-2.0 * math.Log(vn/dn+math.Exp(-.5*dn*dn)))
kn[i+1] = uint32((dn / tn) * scale)
tn = dn
wn[i] = dn / scale
fn[i] = math.Exp(-.5 * dn * dn)
}
*/

var (
rn = 3.442619855899
rnInv = 1 / rn
kn = [128]uint32{
0xed5a44, 0xefacca, 0xf4e443, 0xf75218,
0xf8c01e, 0xf9b369, 0xfa61c1, 0xfae542,
0xfb4c34, 0xfb9f19, 0xfbe355, 0xfc1c80,
0xfc4d18, 0xfc76e7, 0xfc9b3c, 0xfcbb14,
0xfcd732, 0xfcf02e, 0xfd0680, 0xfd1a89,
0xfd2c98, 0xfd3ced, 0xfd4bbe, 0xfd5938,
0xfd6581, 0xfd70b8, 0xfd7afa, 0xfd845e,
0xfd8cf8, 0xfd94da, 0xfd9c13, 0xfda2b1,
0xfda8bf, 0xfdae49, 0xfdb357, 0xfdb7f2,
0xfdbc20, 0xfdbfe8, 0xfdc351, 0xfdc65e,
0xfdc915, 0xfdcb79, 0xfdcd8f, 0xfdcf59,
0xfdd0da, 0xfdd215, 0xfdd30c, 0xfdd3c1,
0xfdd435, 0xfdd46b, 0xfdd463, 0xfdd41e,
0xfdd39d, 0xfdd2e1, 0xfdd1ea, 0xfdd0b8,
0xfdcf4c, 0xfdcda6, 0xfdcbc5, 0xfdc9a9,
0xfdc751, 0xfdc4bd, 0xfdc1ed, 0xfdbedd,
0xfdbb8f, 0xfdb800, 0xfdb42f, 0xfdb019,
0xfdabbe, 0xfda71b, 0xfda22d, 0xfd9cf2,
0xfd9767, 0xfd9189, 0xfd8b54, 0xfd84c4,
0xfd7dd6, 0xfd7685, 0xfd6ecb, 0xfd66a4,
0xfd5e0a, 0xfd54f6, 0xfd4b60, 0xfd4142,
0xfd3692, 0xfd2b48, 0xfd1f59, 0xfd12b9,
0xfd055c, 0xfcf734, 0xfce832, 0xfcd844,
0xfcc758, 0xfcb557, 0xfca22b, 0xfc8db7,
0xfc77de, 0xfc607c, 0xfc476b, 0xfc2c7e,
0xfc0f81, 0xfbf03a, 0xfbce63, 0xfba9ad,
0xfb81ba, 0xfb561d, 0xfb2651, 0xfaf1bb,
0xfab79d, 0xfa7711, 0xfa2efc, 0xf9ddfe,
0xf9825a, 0xf919d9, 0xf8a19a, 0xf815ce,
0xf77152, 0xf6ad05, 0xf5bec5, 0xf4979d,
0xf3208c, 0xf1344b, 0xee9244, 0xeac00a,
0xe4b68d, 0xd9c88f, 0xc01e37, 0x0,
0xed5a44, 0x0, 0xc01e36, 0xd9c88f,
0xe4b68d, 0xeac00a, 0xee9243, 0xf1344b,
0xf3208b, 0xf4979c, 0xf5bec5, 0xf6ad05,
0xf77151, 0xf815ce, 0xf8a199, 0xf919d8,
0xf98259, 0xf9ddfd, 0xfa2efc, 0xfa7711,
0xfab79c, 0xfaf1ba, 0xfb2651, 0xfb561c,
0xfb81ba, 0xfba9ad, 0xfbce63, 0xfbf039,
0xfc0f81, 0xfc2c7d, 0xfc476b, 0xfc607b,
0xfc77dd, 0xfc8db6, 0xfca22a, 0xfcb557,
0xfcc757, 0xfcd844, 0xfce832, 0xfcf734,
0xfd055b, 0xfd12b8, 0xfd1f58, 0xfd2b47,
0xfd3692, 0xfd4141, 0xfd4b60, 0xfd54f5,
0xfd5e09, 0xfd66a4, 0xfd6ecb, 0xfd7684,
0xfd7dd5, 0xfd84c4, 0xfd8b53, 0xfd9188,
0xfd9766, 0xfd9cf1, 0xfda22c, 0xfda71a,
0xfdabbe, 0xfdb019, 0xfdb42e, 0xfdb800,
0xfdbb8f, 0xfdbedd, 0xfdc1ec, 0xfdc4bd,
0xfdc751, 0xfdc9a8, 0xfdcbc4, 0xfdcda5,
0xfdcf4c, 0xfdd0b8, 0xfdd1e9, 0xfdd2e0,
0xfdd39c, 0xfdd41d, 0xfdd462, 0xfdd46a,
0xfdd435, 0xfdd3c0, 0xfdd30c, 0xfdd215,
0xfdd0da, 0xfdcf58, 0xfdcd8e, 0xfdcb79,
0xfdc914, 0xfdc65d, 0xfdc350, 0xfdbfe8,
0xfdbc1f, 0xfdb7f1, 0xfdb357, 0xfdae49,
0xfda8bf, 0xfda2b0, 0xfd9c12, 0xfd94d9,
0xfd8cf7, 0xfd845d, 0xfd7afa, 0xfd70b8,
0xfd6580, 0xfd5938, 0xfd4bbe, 0xfd3ced,
0xfd2c98, 0xfd1a89, 0xfd0680, 0xfcf02e,
0xfcd732, 0xfcbb14, 0xfc9b3b, 0xfc76e6,
0xfc4d18, 0xfc1c7f, 0xfbe354, 0xfb9f18,
0xfb4c34, 0xfae541, 0xfa61c1, 0xf9b369,
0xf8c01e, 0xf75217, 0xf4e442, 0xefacc9,
}
wn = [129]float64{
2.2131718675747815e-07, 2.0519613360756637e-07, 1.921108355868543e-07, 1.8377476085524966e-07,
1.7754413203285815e-07, 1.7251634639629894e-07, 1.6827138367586794e-07, 1.6457851960582595e-07,
1.6129693824778912e-07, 1.5833416052230356e-07, 1.5562607338618323e-07, 1.5312633668928968e-07,
1.5080032780103847e-07, 1.4862147105308605e-07, 1.4656890496086064e-07, 1.4462594065271317e-07,
1.427790092236437e-07, 1.4101692260012857e-07, 1.3933034189577322e-07, 1.3771138690106648e-07,
1.3615334389671515e-07, 1.346504434269189e-07, 1.3319768879359838e-07, 1.3179072194568535e-07,
1.3042571735835368e-07, 1.2909929715090525e-07, 1.2780846252205344e-07, 1.2655053786480287e-07,
1.2532312483723393e-07, 1.2412406432581048e-07, 1.2295140472104004e-07, 1.218033752831857e-07,
1.2067836364372882e-07, 1.1957489669105244e-07, 1.1849162424371361e-07, 1.1742730503406087e-07,
1.1638079461774568e-07, 1.1535103489736455e-07, 1.1433704500582873e-07, 1.1333791334063715e-07,
1.1235279057668203e-07, 1.1138088351455262e-07, 1.1042144964504784e-07, 1.0947379232993399e-07,
1.0853725651479514e-07, 1.0761122490282227e-07, 1.066951145291244e-07, 1.0578837368405278e-07,
1.0489047914144954e-07, 1.0400093365393879e-07, 1.0311926368258777e-07, 1.0224501733265326e-07,
1.0137776247083645e-07, 1.0051708500261117e-07, 9.966258729085928e-08, 9.881388669932032e-08,
9.797061424630097e-08, 9.713241335574595e-08, 9.629893869418865e-08, 9.54698550833093e-08,
9.464483647886372e-08, 9.382356500762706e-08, 9.300573005474621e-08, 9.219102739452782e-08,
9.137915835821887e-08, 9.056982903277516e-08, 8.976274948496838e-08, 8.895763300546134e-08,
8.815419536768938e-08, 8.735215409652654e-08, 8.655122774179126e-08, 8.575113515165824e-08,
8.495159474099038e-08, 8.415232374948604e-08, 8.335303748434811e-08, 8.255344854191848e-08,
8.17532660023774e-08, 8.09521945911731e-08, 8.014993380031266e-08, 7.934617696199576e-08,
7.85406102662929e-08, 7.773291171363688e-08, 7.692274999178623e-08, 7.610978326559989e-08,
7.529365786639572e-08, 7.447400686580345e-08, 7.365044851680766e-08, 7.282258454203579e-08,
7.198999824618987e-08, 7.115225242573783e-08, 7.030888704442901e-08, 6.945941663770386e-08,
6.860332740240491e-08, 6.774007392008063e-08, 6.686907545224076e-08, 6.598971173370091e-08,
6.510131817503429e-08, 6.420318036633099e-08, 6.329452775089875e-08, 6.237452630782386e-08,
6.144227004457674e-08, 6.049677105255892e-08, 5.953694781619198e-08, 5.856161138507287e-08,
5.7569448912212094e-08, 5.655900392003678e-08, 5.552865246624638e-08, 5.447657412427841e-08,
5.340071633940549e-08, 5.229875022845991e-08, 5.116801519357031e-08, 5.000544871673435e-08,
4.880749623181551e-08, 4.756999377274838e-08, 4.6288012736723265e-08, 4.4955650833490674e-08,
4.3565744795947436e-08, 4.210946627470455e-08, 4.0575737873861284e-08, 3.895036213040186e-08,
3.721467240667625e-08, 3.534334555098084e-08, 3.33006488328088e-08, 3.1033518240574354e-08,
2.8457512694399618e-08, 2.5424241206372792e-08, 2.162882274967572e-08, 1.6231588412162755e-08,
0,
wn = [128]float64{
2.2131718675747815e-07, 1.6231588412162755e-08, 2.162882274967572e-08, 2.5424241206372792e-08,
2.8457512694399618e-08, 3.1033518240574354e-08, 3.33006488328088e-08, 3.534334555098084e-08,
3.721467240667625e-08, 3.895036213040186e-08, 4.0575737873861284e-08, 4.210946627470455e-08,
4.3565744795947436e-08, 4.4955650833490674e-08, 4.6288012736723265e-08, 4.756999377274838e-08,
4.880749623181551e-08, 5.000544871673435e-08, 5.116801519357031e-08, 5.229875022845991e-08,
5.340071633940549e-08, 5.447657412427841e-08, 5.552865246624638e-08, 5.655900392003678e-08,
5.7569448912212094e-08, 5.856161138507287e-08, 5.953694781619198e-08, 6.049677105255892e-08,
6.144227004457674e-08, 6.237452630782386e-08, 6.329452775089875e-08, 6.420318036633099e-08,
6.510131817503429e-08, 6.598971173370091e-08, 6.686907545224076e-08, 6.774007392008063e-08,
6.860332740240491e-08, 6.945941663770386e-08, 7.030888704442901e-08, 7.115225242573783e-08,
7.198999824618987e-08, 7.282258454203579e-08, 7.365044851680766e-08, 7.447400686580345e-08,
7.529365786639572e-08, 7.610978326559989e-08, 7.692274999178623e-08, 7.773291171363688e-08,
7.85406102662929e-08, 7.934617696199576e-08, 8.014993380031266e-08, 8.09521945911731e-08,
8.17532660023774e-08, 8.255344854191848e-08, 8.335303748434811e-08, 8.415232374948604e-08,
8.495159474099038e-08, 8.575113515165824e-08, 8.655122774179126e-08, 8.735215409652654e-08,
8.815419536768938e-08, 8.895763300546134e-08, 8.976274948496838e-08, 9.056982903277516e-08,
9.137915835821887e-08, 9.219102739452782e-08, 9.300573005474621e-08, 9.382356500762706e-08,
9.464483647886372e-08, 9.54698550833093e-08, 9.629893869418865e-08, 9.713241335574595e-08,
9.797061424630097e-08, 9.881388669932032e-08, 9.966258729085928e-08, 1.0051708500261117e-07,
1.0137776247083645e-07, 1.0224501733265326e-07, 1.0311926368258777e-07, 1.0400093365393879e-07,
1.0489047914144954e-07, 1.0578837368405278e-07, 1.066951145291244e-07, 1.0761122490282227e-07,
1.0853725651479514e-07, 1.0947379232993399e-07, 1.1042144964504784e-07, 1.1138088351455262e-07,
1.1235279057668203e-07, 1.1333791334063715e-07, 1.1433704500582873e-07, 1.1535103489736455e-07,
1.1638079461774568e-07, 1.1742730503406087e-07, 1.1849162424371361e-07, 1.1957489669105244e-07,
1.2067836364372882e-07, 1.218033752831857e-07, 1.2295140472104004e-07, 1.2412406432581048e-07,
1.2532312483723393e-07, 1.2655053786480287e-07, 1.2780846252205344e-07, 1.2909929715090525e-07,
1.3042571735835368e-07, 1.3179072194568535e-07, 1.3319768879359838e-07, 1.346504434269189e-07,
1.3615334389671515e-07, 1.3771138690106648e-07, 1.3933034189577322e-07, 1.4101692260012857e-07,
1.427790092236437e-07, 1.4462594065271317e-07, 1.4656890496086064e-07, 1.4862147105308605e-07,
1.5080032780103847e-07, 1.5312633668928968e-07, 1.5562607338618323e-07, 1.5833416052230356e-07,
1.6129693824778912e-07, 1.6457851960582595e-07, 1.6827138367586794e-07, 1.7251634639629894e-07,
1.7754413203285815e-07, 1.8377476085524966e-07, 1.921108355868543e-07, 2.0519613360756637e-07,
}
fn = [128]float64{
0.0010143525641203774, 0.002669629083880923, 0.005548995220771345, 0.008624484412859885,
0.011839478657884862, 0.015167298010546568, 0.018592102737011288, 0.022103304615927098,
0.02569329193593427, 0.02935631744000685, 0.03308788614622575, 0.0368843887866562,
0.040742868074444175, 0.044660862200491425, 0.048636295859867805, 0.052667401903051005,
0.05675266348104985, 0.060890770348040406, 0.06508058521306807, 0.06932111739357791,
0.0736115018841134, 0.0779509825139734, 0.08233889824223567, 0.08677467189478019,
0.09125780082683026, 0.09578784912173144, 0.10036444102865587, 0.10498725540942132,
0.10965602101484027, 0.11437051244886601, 0.11913054670765083, 0.12393598020286782,
0.1287867061959432, 0.13368265258343937, 0.1386237799845946, 0.14361008009062776,
0.14864157424234226, 0.15371831220818166, 0.1588403711394793, 0.16400785468342038,
0.169220892237365, 0.17447963833078958, 0.17978427212329554, 0.18513499700899227,
0.19053204031913723, 0.1959756531162778, 0.20146611007431373, 0.2070037094399266,
0.21258877307173027, 0.21822164655430543, 0.22390269938500842, 0.22963232523211613,
0.23541094226347908, 0.24123899354543982, 0.2471169475123214, 0.25304529850732577,
0.25902456739620483, 0.2650553022555892, 0.2711380791383846, 0.2772735029191881,
0.283462208223233, 0.28970486044295984, 0.296002156846933, 0.30235482778648354,
0.3087636380061812, 0.31522938806501094, 0.3217529158759849, 0.3283350983728503,
0.33497685331358923, 0.3416791412315506, 0.3484429675463268, 0.35526938484791737,
0.3621594953693178, 0.36911445366447243, 0.3761354695105628, 0.38322381105590136,
0.39038080823731486, 0.39760785649387365, 0.40490642080722333, 0.4122780401026614,
0.41972433204957477, 0.42724699830499646, 0.4348478302499913, 0.44252871527546894,
0.4502916436820397, 0.4581387162678725, 0.4660721526894566, 0.47409430069301745,
0.4822076463294858, 0.4904148252838448, 0.49871863547098017, 0.5071220510755696,
0.5156282382440026, 0.5242405726729849, 0.5329626593838369, 0.5417983550254263,
0.5507517931146054, 0.5598274127040879, 0.569029991067952, 0.5783646811197644,
0.5878370544347078, 0.5974531509445181, 0.6072195366251217, 0.6171433708188824,
0.6272324852499288, 0.6374954773350439, 0.647941821110224, 0.6585820000500895,
0.6694276673488917, 0.6804918409973354, 0.6917891434366764, 0.7033360990161595,
0.7151515074105, 0.7272569183441863, 0.7396772436726488, 0.7524415591746129,
0.765584173897706, 0.7791460859296893, 0.7931770117713067, 0.8077382946829622,
0.8229072113814108, 0.8387836052959915, 0.8555006078694526, 0.8732430489100717,
0.8922816507840284, 0.9130436479717428, 0.9362826816850625, 0.9635996931270896,
1, 0.9635996931270896, 0.9362826816850625, 0.9130436479717428,
0.8922816507840284, 0.8732430489100717, 0.8555006078694526, 0.8387836052959915,
0.8229072113814108, 0.8077382946829622, 0.7931770117713067, 0.7791460859296893,
0.765584173897706, 0.7524415591746129, 0.7396772436726488, 0.7272569183441863,
0.7151515074105, 0.7033360990161595, 0.6917891434366764, 0.6804918409973354,
0.6694276673488917, 0.6585820000500895, 0.647941821110224, 0.6374954773350439,
0.6272324852499288, 0.6171433708188824, 0.6072195366251217, 0.5974531509445181,
0.5878370544347078, 0.5783646811197644, 0.569029991067952, 0.5598274127040879,
0.5507517931146054, 0.5417983550254263, 0.5329626593838369, 0.5242405726729849,
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}
)

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