Pre-compute reciprocals for sieving

Author: fjarri

src/hazmat/precomputed.rs

@@ -1,8 +1,12 @@
+use crypto_bigint::{Limb, Reciprocal, Word};
+
 /// The type that fits any small prime from the table.
 pub(crate) type SmallPrime = u16;
 
+const SMALL_PRIMES_SIZE: usize = 2047;
+
 /// The list of 2nd to 2048th primes (The 1st one, 2, is not included).
-pub(crate) const SMALL_PRIMES: [SmallPrime; 2047] = [
+pub(crate) const SMALL_PRIMES: [SmallPrime; SMALL_PRIMES_SIZE] = [
     3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
     101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193,
     197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307,
@@ -142,3 +146,15 @@ pub(crate) const SMALL_PRIMES: [SmallPrime; 2047] = [
     17599, 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737,
     17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863,
 ];
+
+const fn create_reciprocals() -> [Reciprocal; SMALL_PRIMES_SIZE] {
+    let mut arr = [Reciprocal::default(); SMALL_PRIMES_SIZE];
+    let mut i = 0;
+    while i < SMALL_PRIMES_SIZE {
+        arr[i] = Reciprocal::ct_new(Limb(SMALL_PRIMES[i] as Word)).0;
+        i += 1;
+    }
+    arr
+}
+
+pub(crate) const RECIPROCALS: [Reciprocal; SMALL_PRIMES_SIZE] = create_reciprocals();

src/hazmat/sieve.rs

@@ -7,7 +7,7 @@ use crypto_bigint::{Integer, Limb, NonZero, Random, Uint, Zero};
 use rand_core::CryptoRngCore;
 
 use crate::hazmat::{
-    precomputed::{SmallPrime, SMALL_PRIMES},
+    precomputed::{SmallPrime, RECIPROCALS, SMALL_PRIMES},
     Primality,
 };
 
@@ -151,10 +151,8 @@ impl<const L: usize> Sieve<L> {
         self.incr = 0;
 
         // Re-calculate residues.
-        for (i, small_prime) in SMALL_PRIMES.iter().enumerate().take(self.residues.len()) {
-            let (_quo, rem) = self
-                .base
-                .div_rem_limb(NonZero::new(Limb::from(*small_prime)).unwrap());
+        for (i, rec) in RECIPROCALS.iter().enumerate().take(self.residues.len()) {
+            let (_quo, rem) = self.base.ct_div_rem_limb_with_reciprocal(rec);
             self.residues[i] = rem.0 as SmallPrime;
         }