From b956e632e1d46c08500e759861462608272c5a87 Mon Sep 17 00:00:00 2001
From: nicoo <nicoo@debian.org>
Date: Tue, 16 Jun 2020 02:29:22 +0200
Subject: [PATCH 1/3] factor::table: Coalesce accesses to the `factors` table

~5.6% faster
---
 src/uu/factor/src/table.rs | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/src/uu/factor/src/table.rs b/src/uu/factor/src/table.rs
index e11b7198b..9d18c9d27 100644
--- a/src/uu/factor/src/table.rs
+++ b/src/uu/factor/src/table.rs
@@ -26,14 +26,18 @@ pub(crate) fn factor(mut num: u64) -> (Factors, u64) {
         // if (num * inv) mod 2^64 <= ceil, then prime divides num
         // See https://math.stackexchange.com/questions/1251327/
         // for a nice explanation.
+        let mut k = 0;
         loop {
             let Wrapping(x) = Wrapping(num) * Wrapping(inv);
 
             // While prime divides num
             if x <= ceil {
                 num = x;
-                factors.push(prime);
+                k += 1;
             } else {
+                if k > 0 {
+                    factors.add(prime, k);
+                }
                 break;
             }
         }

From 9d992b77b2840b4846e68700aff2c36d4ca24dbc Mon Sep 17 00:00:00 2001
From: nicoo <nicoo@debian.org>
Date: Sat, 20 Jun 2020 21:53:22 +0200
Subject: [PATCH 2/3] factor: Keep the primes table size in a single place

---
 src/uu/factor/build.rs | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/src/uu/factor/build.rs b/src/uu/factor/build.rs
index 1677e44eb..a045d66e6 100644
--- a/src/uu/factor/build.rs
+++ b/src/uu/factor/build.rs
@@ -39,12 +39,11 @@ fn main() {
     let mut file = File::create(&Path::new(&out_dir).join("prime_table.rs")).unwrap();
 
     // By default, we print the multiplicative inverses mod 2^64 of the first 1k primes
+    const DEFAULT_SIZE: usize = 1027;
     let n = args()
         .nth(1)
-        .unwrap_or_else(|| "1027".to_string())
-        .parse::<usize>()
-        .ok()
-        .unwrap_or(1027);
+        .and_then(|s| s.parse::<usize>().ok())
+        .unwrap_or(DEFAULT_SIZE);
 
     write!(file, "{}", PREAMBLE).unwrap();
     let mut cols = 3;

From 8e040bbf1adc0e1ea7d755c212eac94f5d3e2f72 Mon Sep 17 00:00:00 2001
From: nicoo <nicoo@debian.org>
Date: Sat, 20 Jun 2020 21:54:03 +0200
Subject: [PATCH 3/3] factor::table: Optimise the size of the precomputed table
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

A too-large precomputed table actually slows down the program: we spend
time fetching it from disk and from memory (into the CPU's cache), and
larger prime factors are more unlikely to occur in random integers (prime p
occurs with probability ~1/p when sampling 64b numbers uniformly-at-random)

The new value was chosen after measuring the execution time (for all
integers between 2 and 10⁷) for a broad set of values:

| n    | time (s) |
|------|----------|
| 16   | 40.84    |
| 32   | 34.491   |
| 64   | 29.044   |
| 128  | 25.121   |
| 192  | 23.98    |
| 256  | 23.102   |
| 256  | 24.93    |
| 272  | 23.57    |
| 288  | 23.85    |
| 304  | 23.91    |
| 320  | 23.24    |
| 329  | 23.45    |
| 336  | 23.55    |
| 352  | 23.09    |
| 368  | 23.65    |
| 384  | 23.32    |
| 384  | 23.36    |
| 400  | 23.30    |
| 416  | 23.38    |
| 432  | 23.42    |
| 448  | 23.95    |
| 448  | 24.00    |
| 464  | 23.81    |
| 480  | 23.55    |
| 496  | 24.10    |
| 512  | 24.101   |
| 512  | 24.23    |
| 1027 | 29.864   |
---
 src/uu/factor/build.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/uu/factor/build.rs b/src/uu/factor/build.rs
index a045d66e6..719ca63bb 100644
--- a/src/uu/factor/build.rs
+++ b/src/uu/factor/build.rs
@@ -39,7 +39,7 @@ fn main() {
     let mut file = File::create(&Path::new(&out_dir).join("prime_table.rs")).unwrap();
 
     // By default, we print the multiplicative inverses mod 2^64 of the first 1k primes
-    const DEFAULT_SIZE: usize = 1027;
+    const DEFAULT_SIZE: usize = 320;
     let n = args()
         .nth(1)
         .and_then(|s| s.parse::<usize>().ok())