optimize sieve of Eratosthenes

lib/primes/src/lib.rs

@@ -33,10 +33,14 @@ where
     }
 
     fn from_array(array: Vec<bool>, min_value: &usize, max_value: &usize) -> Self {
-        let mut vector = Vec::new();
-        let mut set = HashSet::new();
+        let number_of_primes = array.iter().filter(|b| **b).count();
+        let mut vector = Vec::with_capacity(number_of_primes);
+        let mut set = HashSet::with_capacity(number_of_primes);
+
         for number in *min_value..*max_value {
-            if array[(number - min_value) as usize] {
+            let idx = number - min_value;
+            // SAFETY: see considerations in get_prime_numbers_array
+            if unsafe { *array.get_unchecked(idx) } {
                 let prime = FromPrimitive::from_usize(number).unwrap();
                 vector.push(prime);
                 set.insert(prime);
@@ -51,18 +55,30 @@ where
         let length = *max_value - *min_value;
         let mut result = vec![true; length];
 
-        let upper_limit = f64::sqrt(*max_value as f64).ceil() as usize;
+        let upper_limit = Self::calc_upper_limit(max_value);
         for i in 2..upper_limit {
-            for multiple in ((i * i)..*max_value).step_by(i) {
-                if &multiple < min_value {
-                    continue;
-                }
-                result[multiple - min_value] = false;
+            let skip = Self::find_number_to_skip_until_min_value(min_value, i);
+
+            for multiple in (i * i..*max_value).step_by(i).skip(skip) {
+                let idx = multiple - min_value;
+                // SAFETY: `multiple` will always be between min_value and max_value
+                // (which define the length of the array), therfore idx is always smaller than the
+                // length of result, therefore this access is always in bounds.
+                // This is slightly faster than the bounds-checked write.
+                unsafe { *result.get_unchecked_mut(idx) = false };
             }
         }
         result
     }
 
+    fn calc_upper_limit(max_value: &usize) -> usize {
+        f64::sqrt(*max_value as f64).ceil() as usize
+    }
+
+    fn find_number_to_skip_until_min_value(min_value: &usize, i: usize) -> usize {
+        ((min_value.saturating_sub(i * i)) as f64 / i as f64).ceil() as usize
+    }
+
     pub fn remove(&mut self, num: &T) {
         if let Some(index) = self.vector.iter().position(|x| x == num) {
             self.vector.remove(index);
@@ -75,6 +91,11 @@ where
         self.vector.len()
     }
 
+    pub fn is_empty(&self) -> bool {
+        debug_assert_eq!(self.vector.len(), self.set.len());
+        self.vector.is_empty()
+    }
+
     pub fn pop(&mut self) -> Option<T> {
         let result = self.vector.pop();
         if let Some(value) = result {
@@ -139,4 +160,11 @@ mod test {
         let primes = Primes::get_between(2, 10_000_000);
         assert_eq!(primes.len(), 664_579);
     }
+
+    //     #[ignore]
+    //     #[test]
+    //     fn test_performance_2() {
+    //         let primes = Primes::get_between(2, 1_000_000_000);
+    //         assert_eq!(primes.len(), 50_847_534);
+    //     }
 }