Initialize C library for ALDR

Author: amorphedstar

.gitignore

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+*.a
+*.o
+*.out
+
+build/

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Makefile

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+CFLAGS ?= -O3 -flto -march=native
+
+all: libaldr.a sample.out
+	mkdir -p build/bin
+	cp sample.out build/bin/aldr
+	mkdir -p build/lib
+	cp libaldr.a build/lib
+	mkdir -p build/include
+	cp *.h build/include
+	$(MAKE) clean
+
+%.o: %.c
+	gcc $(CFLAGS) -c -o $@ $^
+
+libaldr.a: flip.o aldr.o
+	ar rcs $@ $^
+
+%.out: %.c libaldr.a
+	gcc $(CFLAGS) -o $@ $^ -lm
+
+.PHONY: clean
+clean:
+	rm -rf *.a *.o *.out

README.md

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+# The Amplified Loaded Dice Roller
+
+This repository contains a reference implementation in C
+of the Amplified Loaded Dice Roller (ALDR),
+a fast algorithm for rolling an $n$-sided die.
+
+## Building and Installing
+
+The library can be built by running
+
+    $ make all
+
+This command creates several artifacts in the `build/` directory:
+
+1. `build/lib/libaldr.a`: A static C library for C programs that use ALDR.
+
+1. `build/include`: Contains header files for C programs that use ALDR.
+
+1. `build/bin`: Contains the executable for a command line interface to ALDR.
+
+## Usage
+
+The following code from [examples/example.c](examples/example.c)
+shows how to use ALDR to sample from a distribution with given integer weights.
+
+```c
+#include <stdlib.h>
+#include <stdio.h>
+#include "aldr.h"
+
+int main(int argc, char **argv) {
+    int num_samples = 90;
+    int *samples = calloc(num_samples, sizeof(*samples));
+
+    int distribution[5] = { 1, 1, 2, 3, 2 };
+    struct aldr_s x = aldr_preprocess(distribution, 5);
+    for (int i = 0; i < num_samples; ++i) {
+        samples[i] = aldr_sample(&x);
+        printf("%d ", samples[i]);
+    }
+    printf("\n");
+
+    free(samples);
+    aldr_free(x);
+}
+```
+
+## Usage (Command Line Interface)
+
+The executable has the following command line interface:
+
+```
+usage: ./build/bin/aldr num_samples ...distribution...
+```
+
+where `num_samples` is the number of samples to draw;
+`...distribution...` is a space-separated list of positive integer weights.
+
+For example, to generate 90 samples from { 1, 1, 2, 3, 2 }, run the following:
+
+```sh
+./build/bin/aldr 90 1 1 2 3 2
+```
+
+To generate 9000 samples from { 1, 1, 2, 3, 2 }
+and count them as a histogram, run the following:
+
+```sh
+./build/bin/aldr 9000 1 1 2 3 2 | tr -d '\n' | tr ' ' '\n' | sort | uniq -c
+```
+
+<!-- ## Experiments
+
+Implementations of the experiments from the paper can be found at
+https://github.com/probsys/amplified-loaded-dice-roller-experiments. -->
+
+## Related Repositories
+
+For a more space-efficient but less entropy-efficient rejection sampler, see
+https://github.com/probsys/fast-loaded-dice-roller.

aldr.c

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+/*
+  Name:     aldr.c
+  Purpose:  Fast sampling of random integers.
+  Author:   CMU Probabilistic Computing Systems Lab
+  Copyright (C) 2025 CMU Probabilistic Computing Systems Lab, All Rights Reserved.
+
+  Released under Apache 2.0; refer to LICENSE.txt
+*/
+
+#include <stdlib.h>
+
+#include "flip.h"
+#include "aldr.h"
+
+void aldr_free (struct aldr_s x) {
+    free(x.breadths);
+    free(x.leaves_flat);
+}
+
+struct aldr_s aldr_preprocess(int* a, int n) {
+    // assume k <= 31
+    int m = 0;
+    for (int i = 0; i < n; ++i) {
+        m += a[i];
+    }
+    int k = 32 - __builtin_clz(m) - (1 == __builtin_popcount(m));
+    int K = k << 1;                         // depth
+    long long c = (1ll << K) / m;           // amplification factor
+    long long r = (1ll << K) % m;           // reject weight
+
+    int num_leaves = __builtin_popcountll(r);
+    for (int i = 0; i < n; ++i) {
+        num_leaves += __builtin_popcountll(c * a[i]);
+    }
+
+    int *breadths = calloc(K + 1, sizeof(int));
+    int *leaves_flat = calloc(num_leaves, sizeof(int));
+
+    int location = 0;
+    for(int j = 0; j <= K; j++) {
+        long long bit = (1ll << (K - j));
+        if (r & bit) {
+            leaves_flat[location] = 0;
+            ++breadths[j];
+            ++location;
+        }
+        for (int i = 0; i < n; ++i) {
+            long long Qi = c*a[i];
+            if (Qi & bit) {
+                leaves_flat[location] = i + 1;
+                ++breadths[j];
+                ++location;
+            }
+        }
+    }
+
+    return (struct aldr_s){
+            .length_breadths = K+1,
+            .length_leaves_flat = num_leaves,
+            .breadths = breadths,
+            .leaves_flat = leaves_flat
+        };
+}
+
+int aldr_sample(struct aldr_s* f) {
+    for (;;) {
+        int depth = 0;
+        int location = 0;
+        int val = 0;
+        for (;;) {
+            if (val < f->breadths[depth]) {
+                int ans = f->leaves_flat[location + val];
+                if (ans) return ans - 1;
+                else break;
+            }
+            location += f->breadths[depth];
+            val = ((val - f->breadths[depth]) << 1) | flip();
+            ++depth;
+        }
+    }
+}