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Gaussian sampler improvements #22

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Gaussian sampler improvements #22

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2b9f32a
recalibrate ramez coeffs
osdnk Jun 19, 2026
a08dac0
cdfsampler ct
osdnk Jun 19, 2026
90e7390
exp_small ct
osdnk Jun 19, 2026
a2134df
remove 0ULL,0ULL extry from CDF
osdnk Jun 19, 2026
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54 changes: 35 additions & 19 deletions src/grandom.c
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Original file line number Diff line number Diff line change
Expand Up @@ -30,12 +30,10 @@ static const z128 CDF155[]
{ 0ULL, 1055215183460ULL },
{ 0ULL, 724109373ULL },
{ 0ULL, 327744ULL },
{ 0ULL, 98ULL },
{ 0ULL, 0ULL } };
{ 0ULL, 98ULL } };

/*
* Compute exp(x) for x such that |x| <= 0.5*ln 2
* FIXME: Recompute Remez coefficients for interval [-ln 2,0]
* Compute exp(x) for x in [-ln 2, 0]
*
* The algorithm used below is derived from the public domain
* library fdlibm (http://www.netlib.org/fdlibm/e_exp.c).
Expand All @@ -44,38 +42,56 @@ static const z128 CDF155[]
static inline double
exp_small (double x)
{
#define C1 (1.66666666666666019037e-01)
#define C2 (-2.77777777770155933842e-03)
#define C3 (6.61375632143793436117e-05)
#define C4 (-1.65339022054652515390e-06)
#define C5 (4.13813679705723846039e-08)
#define C1 ( 1.66666666666666657415e-01)
#define C2 (-2.77777777777722060387e-03)
#define C3 ( 6.61375660702744565646e-05)
#define C4 (-1.65343769616898187644e-06)
#define C5 ( 4.17431906195525278958e-08)
#define C6 (-1.02842107821646284274e-09)

double t;
double t, d, y;

t = x * x;
t = x - t * (C1 + t * (C2 + t * (C3 + t * (C4 + t * C5)))); // R1
t = 1.0 - ((x * t) / (t - 2.0) - x);
t = x - t * (C1 + t * (C2 + t * (C3 + t * (C4 + t * (C5 + t * C6))))); // R1

/* 1/(t - 2) via Newton (y <- y*(2 - d*y)) */
d = t - 2.0;
y = -0.4193;
y *= 2.0 - d * y;
y *= 2.0 - d * y;
y *= 2.0 - d * y;
y *= 2.0 - d * y;
y *= 2.0 - d * y;
t = 1.0 - (x * t * y - x); // == 1.0 - ((x * t) / (t - 2.0) - x)
return t;

#undef C1
#undef C2
#undef C3
#undef C4
#undef C5
#undef C6
}

static inline unsigned int
cdfsampler (rng_state_t state, const z128 CDF[])
cdfsampler (rng_state_t state, const z128 CDF[], unsigned int len)
{
uint64_t buf[2];
const uint64_t *hi = buf, *lo = buf + 1;
unsigned int z;
uint64_t buf[2], hi, lo, d;
unsigned int z, i;
int b0, b1, b2;

rng_urandom (state, (unsigned char *)buf, 16);
hi = buf[0];
lo = buf[1];

z = 0;
while (*hi <= CDF[z].hi && (*hi < CDF[z].hi || *lo < CDF[z].lo))
++z;
for (i = 0; i < len; i++)
{
b0 = __builtin_sub_overflow (lo, CDF[i].lo, &d); // b0 = (lo < CDF[i].lo)
b1 = __builtin_sub_overflow (hi, CDF[i].hi, &d); // b1 = (hi < CDF[i].hi)
b2 = __builtin_sub_overflow (d, (uint64_t)b0, &d); // d = 0 if (hi = CDF[i].hi). then, if b0 = 1, b2 = 1
z += (unsigned int)(b1 | b2);
}

return z;
}
Expand Down Expand Up @@ -122,7 +138,7 @@ gaussian155 (rng_state_t state, double c)
b = bits & 1;
bits >>= 1;
pos += 1;
k = cdfsampler (state, CDF155);
k = cdfsampler (state, CDF155, sizeof (CDF155) / sizeof (CDF155[0]));
k = (-b & (2 * k)) - k + b; // bimodal Gaussian
x = ((k - c) * (k - c) - (k - b) * (k - b)) * dss;
}
Expand Down