Fix factorial implementation

benches/benchmark.rs

@@ -13,7 +13,7 @@ use num_bigint::*;
 fn naive_factorial(n: &BigUint) -> BigUint {
     let mut acc = BigUint::from(1_usize);
     let mut i = BigUint::from(2_usize);
-    while &i <= &n {
+    while &i <= n {
         acc *= i.clone();
         i += BigUint::from(1_usize);
     }

examples/build.rs

@@ -11,16 +11,49 @@ fn checked_naive_factorial(n: u128) -> Option<u128> {
     Some(acc)
 }
 
+fn prime_range(
+    sieve: &Sieve,
+    lower_bound: u128,
+    upper_boud: u128,
+) -> impl Iterator<Item = u128> + '_ {
+    sieve
+        .primes_from(lower_bound as usize)
+        .map(|m| m as u128)
+        .take_while(move |m| *m <= upper_boud)
+}
+
+const SMALL_SWING: [u128; 33] = [
+    1, 1, 1, 3, 3, 15, 5, 35, 35, 315, 63, 693, 231, 3003, 429, 6435, 6435, 109395, 12155, 230945,
+    46189, 969969, 88179, 2028117, 676039, 16900975, 1300075, 35102025, 5014575, 145422675,
+    9694845, 300540195, 300540195,
+];
+
 fn prime_swing(n: u128, sieve: &Sieve) -> Option<u128> {
-    let mut product = 1u128;
-    for prime in sieve.primes_from(2).take_while(|x| *x < n as usize) {
-        let mut p = 1u128;
+    if n < 33 {
+        return Some(SMALL_SWING[n as usize]);
+    }
+    let sqrt = ((n as f64).sqrt().floor()) as u128;
+    let mut product: u128 = 1;
+    for prime in prime_range(sieve, n / 2 + 1, n) {
+        product = product.checked_mul(prime)?;
+    }
+
+    for prime in prime_range(sieve, sqrt + 1, n / 3) {
+        if (n / prime) & 1 == 1 {
+            product = product.checked_mul(prime)?;
+        }
+    }
+
+    for prime in prime_range(sieve, 3, sqrt) {
+        let mut p = 1;
         let mut q = n;
-        while q != 0 {
-            q /= prime as u128;
-            // q%2 == 1 if q is odd
-            if q % 2u128 == 1 {
-                p = p.checked_mul(prime as u128)?;
+        loop {
+            q /= prime;
+            if q == 0 {
+                break;
+            }
+            if q & 1 == 1 {
+                p *= prime;
             }
         }
         if p > 1 {
@@ -48,7 +81,7 @@ fn main() -> std::io::Result<()> {
     ));
 
     let sieve = Sieve::new(1_000);
-    file_content.push_str("pub const SMALL_PRIME_SWING: ");
+    file_content.push_str("pub const SMALL_ODD_SWING: ");
     let mut n = 0u128;
     let mut prime_swings = vec![];
     while let Some(swing) = prime_swing(n, &sieve) {

src/array.rs

@@ -35,134 +35,134 @@ pub const SMALL_FACTORIAL: [u128; 35] = [
     8683317618811886495518194401280000000,
     295232799039604140847618609643520000000,
 ];
-pub const SMALL_PRIME_SWING: [u128; 129] = [
+pub const SMALL_ODD_SWING: [u128; 129] = [
     1,
     1,
     1,
-    2,
-    6,
-    6,
-    20,
-    20,
-    70,
-    630,
-    252,
-    252,
-    924,
-    924,
-    3432,
-    51480,
-    12870,
-    12870,
-    48620,
-    48620,
-    184756,
-    3879876,
-    705432,
-    705432,
-    2704156,
-    67603900,
-    10400600,
-    280816200,
-    40116600,
-    40116600,
-    155117520,
-    155117520,
-    601080390,
-    19835652870,
-    2333606220,
-    81676217700,
-    9075135300,
-    9075135300,
-    35345263800,
-    1378465288200,
-    137846528820,
-    137846528820,
-    538257874440,
-    538257874440,
-    2104098963720,
-    94684453367400,
-    8233430727600,
-    8233430727600,
-    32247603683100,
-    1580132580471900,
-    126410606437752,
-    6446940928325352,
-    495918532948104,
-    495918532948104,
-    1946939425648112,
-    107081668410646160,
-    7648690600760440,
-    435975364243345080,
-    30067266499541040,
-    30067266499541040,
-    118264581564861424,
-    118264581564861424,
-    465428353255261088,
-    29321986255081448544,
-    1832624140942590534,
-    119120569161268384710,
-    7219428434016265740,
-    7219428434016265740,
-    28453041475240576740,
-    1963259861791599795060,
-    112186277816662845432,
-    112186277816662845432,
-    442512540276836779204,
-    442512540276836779204,
-    1746130564335626209832,
-    130959792325171965737400,
-    6892620648693261354600,
-    530731789949381124304200,
-    27217014869199032015600,
-    27217014869199032015600,
-    107507208733336176461620,
-    8708083907400230293391220,
-    424784580848791721628840,
-    424784580848791721628840,
-    1678910486211891090247320,
-    142707391328010742671022200,
-    6637553085023755473070800,
-    577467118397066726157159600,
-    26248505381684851188961800,
-    26248505381684851188961800,
-    103827421287553411369671120,
-    9448295337167360434640071920,
-    410795449442059149332177040,
-    38203976798111500887892464720,
-    1625701140345170250548615520,
-    154441608332791173802118474400,
-    6435067013866298908421603100,
-    6435067013866298908421603100,
-    25477612258980856902730428600,
-    2522283613639104833370312431400,
-    100891344545564193334812497256,
-    100891344545564193334812497256,
-    399608854866744452032002440112,
-    399608854866744452032002440112,
-    1583065848125949175357548128136,
-    166221914053224663412542553454280,
-    6272525058612251449529907677520,
-    6272525058612251449529907677520,
-    24857784491537440929618523018320,
-    24857784491537440929618523018320,
-    98527218530093856775578873054432,
-    10936521256840418102089254909041952,
-    390590044887157789360330532465784,
-    390590044887157789360330532465784,
-    1548655265692941410446222812934512,
-    178095355554688262201315623487468880,
-    6141219157058215937976400809912720,
-    718522641375811264743238894759788240,
-    24356699707654619143838606602026720,
-    2898447265210899678116794185641179680,
-    96614908840363322603893139521372656,
-    11690403969683962035071069882086091376,
-    383291933432261050330199012527412832,
-    47144907812168109190614478540871778336,
-    1520803477811874490019821888415218656,
-    190100434726484311252477736051902332000,
-    6034934435761406706427864636568328000,
-    6034934435761406706427864636568328000,
-    23951146041928082866135587776380551750,
+    3,
+    3,
+    15,
+    5,
+    35,
+    35,
+    315,
+    63,
+    693,
+    231,
+    3003,
+    429,
+    6435,
+    6435,
+    109395,
+    12155,
+    230945,
+    46189,
+    969969,
+    88179,
+    2028117,
+    676039,
+    16900975,
+    1300075,
+    35102025,
+    5014575,
+    145422675,
+    9694845,
+    300540195,
+    300540195,
+    9917826435,
+    583401555,
+    20419054425,
+    2268783825,
+    83945001525,
+    4418157975,
+    172308161025,
+    34461632205,
+    1412926920405,
+    67282234305,
+    2893136075115,
+    263012370465,
+    11835556670925,
+    514589420475,
+    24185702762325,
+    8061900920775,
+    395033145117975,
+    15801325804719,
+    805867616040669,
+    61989816618513,
+    3285460280781189,
+    121683714103007,
+    6692604275665385,
+    956086325095055,
+    54496920530418135,
+    1879204156221315,
+    110873045217057585,
+    7391536347803839,
+    450883717216034179,
+    14544636039226909,
+    916312070471295267,
+    916312070471295267,
+    59560284580634192355,
+    1804857108504066435,
+    120925426269772451145,
+    7113260368810144185,
+    490814965447899948765,
+    14023284727082855679,
+    995653215622882753209,
+    110628135069209194801,
+    8075853860052271220473,
+    218266320541953276229,
+    16369974040646495717175,
+    861577581086657669325,
+    66341473743672640538025,
+    1701063429324939500975,
+    134384010916670220577025,
+    26876802183334044115405,
+    2177020976850057573347805,
+    53098072606098965203605,
+    4407140026306214111899215,
+    209863810776486386280915,
+    17838423916001342833877775,
+    414847067813984717066925,
+    36091694899816670384822475,
+    3281063172710606398620225,
+    292014622371243969477200025,
+    6489213830472088210604445,
+    590518458572960027165004495,
+    25674715590128696833261065,
+    2387748549881968805493279045,
+    50803160635786570329644235,
+    4826300260399724181316202325,
+    1608766753466574727105400775,
+    156050375086257748529223875175,
+    3184701532372607112841303575,
+    315285451704888104171289053925,
+    12611418068195524166851562157,
+    1273753224887747940852007777857,
+    24975553429171528252000152507,
+    2572482003204667409956015708221,
+    197883231015743646919693516017,
+    20777739256653082926567819181785,
+    392032816163265715595619229845,
+    41947511329469431568731257593415,
+    1553611530721090058101157688645,
+    169343656848598816333026188062305,
+    3078975579065433024236839782951,
+    341766289276263065690289215907561,
+    48823755610894723670041316558223,
+    5517084384031103774714668771079199,
+    96790954105808838152888925808407,
+    11130959722168016387582226467966805,
+    383826197316138496123525050619545,
+    44907665085988204046452430922486765,
+    761146865864206848244956456313335,
+    90576477037840614941149818301286865,
+    6038431802522707662743321220085791,
+    730650248105247627191941867630380711,
+    11977872919758157822818719141481651,
+    1473278369130253412206702454402243073,
+    47525108681621077813119434012975583,
+    5940638585202634726639929251621947875,
+    94295850558771979787935384946380125,
+    11975573020964041433067793888190275875,
+    11975573020964041433067793888190275875,
 ];