initial attempt on bc

buggy because wrong base for log, but it's a start
This commit is contained in:
NunoSempere 2023-11-02 23:24:36 +00:00
parent 1a3099b7e4
commit 249a1ff434
6 changed files with 92 additions and 54 deletions

34
bc/estimate.bc Normal file
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@ -0,0 +1,34 @@
p_a = 0.8
p_b = 0.5
p_c = p_a * p_b
weights[0] = 1 - p_c
weights[1] = p_c / 2
weights[2] = p_c / 4
weights[3] = p_c / 4
/* We'll have to define the mixture manually */
define mixture(){
p = sample_unit_uniform()
if(p <= weights[0]){
return 0
}
if(p <= (weights[0] + weights[1])){
return 1
}
if(p<= (weights[0] + weights[1] + weights[2])){
return sample_to(1, 3)
}
return sample_to(2, 10)
}
/* n_samples = 1000000 */
n_samples = 10000
sum=0
for(i=0; i < n_samples; i++){
/* samples[i] = mixture() */
sum += mixture()
}
sum/n_samples
halt

51
bc/extra/beta.bc Normal file
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@ -0,0 +1,51 @@
define sample_gamma(alpha){
/*
A Simple Method for Generating Gamma Variables, Marsaglia and Wan Tsang, 2001
https://dl.acm.org/doi/pdf/10.1145/358407.358414
see also the references/ folder
Note that the Wikipedia page for the gamma distribution includes a scaling parameter
k or beta
https://en.wikipedia.org/wiki/Gamma_distribution
such that gamma_k(alpha, k) = k * gamma(alpha)
or gamma_beta(alpha, beta) = gamma(alpha) / beta
So far I have not needed to use this, and thus the second parameter is by default 1.
*/
if (alpha >= 1) {
d = alpha - (1/3);
c = 1.0 / sqrt(9.0 * d);
while (1) {
v=-1
while(v<=0) {
x = sample_unit_normal();
v = 1 + c * x;
}
v = v * v * v;
u = sample_unit_uniform();
if (u < (1 - (0.0331 * (x * x * x * x)))) { /* Condition 1 */
/*
the 0.0331 doesn't inspire much confidence
however, this isn't the whole story
by knowing that Condition 1 implies condition 2
we realize that this is just a way of making the algorithm faster
i.e., of not using the logarithms
*/
return d * v;
}
if (log(u, 2) < ((0.5 * (x * x)) + (d * (1 - v + log(v, 2))))) { /* Condition 2 */
return d * v;
}
}
} else {
return sample_gamma(1 + alpha) * p(sample_unit_uniform(), 1 / alpha);
/* see note in p. 371 of https://dl.acm.org/doi/pdf/10.1145/358407.358414 */
}
}
define sample_beta(a, b)
{
/* See: https://en.wikipedia.org/wiki/Gamma_distribution#Related_distributions */
gamma_a = sample_gamma(a);
gamma_b = sample_gamma(b);
return gamma_a / (gamma_a + gamma_b);
}

5
bc/makefile Normal file
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@ -0,0 +1,5 @@
compute:
ghbc -l squiggle.bc estimate.bc
time:
time ghbc -l squiggle.bc estimate.bc

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@ -6,7 +6,7 @@ https://pubs.opengroup.org/onlinepubs/9699919799.2018edition/utilities/bc.html
## gh-bc
To build
./configure
./configure.sh -O3
make
sudo cp bin/bc /usr/bin/ghbc

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@ -1,4 +1,4 @@
scale = 32
scale = 8
/* seed = 12345678910 */
pi = 4 * atan(1)
normal90confidence=1.6448536269514727148638489079916
@ -70,55 +70,3 @@ define sample_to(low, high){
loghigh = log(high, 2)
return e(sample_normal_from_90_confidence_interval(loglow, loghigh))
}
define sample_gamma(alpha){
/*
A Simple Method for Generating Gamma Variables, Marsaglia and Wan Tsang, 2001
https://dl.acm.org/doi/pdf/10.1145/358407.358414
see also the references/ folder
Note that the Wikipedia page for the gamma distribution includes a scaling parameter
k or beta
https://en.wikipedia.org/wiki/Gamma_distribution
such that gamma_k(alpha, k) = k * gamma(alpha)
or gamma_beta(alpha, beta) = gamma(alpha) / beta
So far I have not needed to use this, and thus the second parameter is by default 1.
*/
if (alpha >= 1) {
d = alpha - (1/3);
c = 1.0 / sqrt(9.0 * d);
while (1) {
v=-1
while(v<=0) {
x = sample_unit_normal();
v = 1 + c * x;
}
v = v * v * v;
u = sample_unit_uniform();
if (u < (1 - (0.0331 * (x * x * x * x)))) { /* Condition 1 */
/*
the 0.0331 doesn't inspire much confidence
however, this isn't the whole story
by knowing that Condition 1 implies condition 2
we realize that this is just a way of making the algorithm faster
i.e., of not using the logarithms
*/
return d * v;
}
if (log(u, 2) < ((0.5 * (x * x)) + (d * (1 - v + log(v, 2))))) { /* Condition 2 */
return d * v;
}
}
} else {
return sample_gamma(1 + alpha) * p(sample_unit_uniform(), 1 / alpha);
/* see note in p. 371 of https://dl.acm.org/doi/pdf/10.1145/358407.358414 */
}
}
define sample_beta(a, b)
{
/* See: https://en.wikipedia.org/wiki/Gamma_distribution#Related_distributions */
gamma_a = sample_gamma(a);
gamma_b = sample_gamma(b);
return gamma_a / (gamma_a + gamma_b);
}