Generate instead of hard coding factorial tables (#22096)

* Generate instead of hard coding factorial tables

* Preallocate factorial tables

* Add tests with old literal tables

Author: TotalVerb

base/combinatorics.jl

@@ -2,29 +2,17 @@
 
 # Factorials
 
-const _fact_table64 =
-    Int64[1,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600,6227020800,
-          87178291200,1307674368000,20922789888000,355687428096000,6402373705728000,
-          121645100408832000,2432902008176640000]
-
-const _fact_table128 =
-    UInt128[0x00000000000000000000000000000001, 0x00000000000000000000000000000002,
-            0x00000000000000000000000000000006, 0x00000000000000000000000000000018,
-            0x00000000000000000000000000000078, 0x000000000000000000000000000002d0,
-            0x000000000000000000000000000013b0, 0x00000000000000000000000000009d80,
-            0x00000000000000000000000000058980, 0x00000000000000000000000000375f00,
-            0x00000000000000000000000002611500, 0x0000000000000000000000001c8cfc00,
-            0x0000000000000000000000017328cc00, 0x0000000000000000000000144c3b2800,
-            0x00000000000000000000013077775800, 0x00000000000000000000130777758000,
-            0x00000000000000000001437eeecd8000, 0x00000000000000000016beecca730000,
-            0x000000000000000001b02b9306890000, 0x000000000000000021c3677c82b40000,
-            0x0000000000000002c5077d36b8c40000, 0x000000000000003ceea4c2b3e0d80000,
-            0x000000000000057970cd7e2933680000, 0x00000000000083629343d3dcd1c00000,
-            0x00000000000cd4a0619fb0907bc00000, 0x00000000014d9849ea37eeac91800000,
-            0x00000000232f0fcbb3e62c3358800000, 0x00000003d925ba47ad2cd59dae000000,
-            0x0000006f99461a1e9e1432dcb6000000, 0x00000d13f6370f96865df5dd54000000,
-            0x0001956ad0aae33a4560c5cd2c000000, 0x0032ad5a155c6748ac18b9a580000000,
-            0x0688589cc0e9505e2f2fee5580000000, 0xde1bc4d19efcac82445da75b00000000]
+const _fact_table64 = Vector{Int64}(20)
+_fact_table64[1] = 1
+for n in 2:20
+    _fact_table64[n] = _fact_table64[n-1] * n
+end
+
+const _fact_table128 = Vector{UInt128}(34)
+_fact_table128[1] = 1
+for n in 2:34
+    _fact_table128[n] = _fact_table128[n-1] * n
+end
 
 function factorial_lookup(n::Integer, table, lim)
     n < 0 && throw(DomainError())

test/combinatorics.jl

@@ -67,4 +67,34 @@ end
         @test factorial(Int32(12)) === Int32(479001600)
         @test_throws OverflowError factorial(Int32(13))
     end
+
+    _fact_table64 =
+        Int64[1,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600,6227020800,
+              87178291200,1307674368000,20922789888000,355687428096000,6402373705728000,
+              121645100408832000,2432902008176640000]
+
+    _fact_table128 =
+        UInt128[0x00000000000000000000000000000001, 0x00000000000000000000000000000002,
+                0x00000000000000000000000000000006, 0x00000000000000000000000000000018,
+                0x00000000000000000000000000000078, 0x000000000000000000000000000002d0,
+                0x000000000000000000000000000013b0, 0x00000000000000000000000000009d80,
+                0x00000000000000000000000000058980, 0x00000000000000000000000000375f00,
+                0x00000000000000000000000002611500, 0x0000000000000000000000001c8cfc00,
+                0x0000000000000000000000017328cc00, 0x0000000000000000000000144c3b2800,
+                0x00000000000000000000013077775800, 0x00000000000000000000130777758000,
+                0x00000000000000000001437eeecd8000, 0x00000000000000000016beecca730000,
+                0x000000000000000001b02b9306890000, 0x000000000000000021c3677c82b40000,
+                0x0000000000000002c5077d36b8c40000, 0x000000000000003ceea4c2b3e0d80000,
+                0x000000000000057970cd7e2933680000, 0x00000000000083629343d3dcd1c00000,
+                0x00000000000cd4a0619fb0907bc00000, 0x00000000014d9849ea37eeac91800000,
+                0x00000000232f0fcbb3e62c3358800000, 0x00000003d925ba47ad2cd59dae000000,
+                0x0000006f99461a1e9e1432dcb6000000, 0x00000d13f6370f96865df5dd54000000,
+                0x0001956ad0aae33a4560c5cd2c000000, 0x0032ad5a155c6748ac18b9a580000000,
+                0x0688589cc0e9505e2f2fee5580000000, 0xde1bc4d19efcac82445da75b00000000]
+
+    for expected in Any[_fact_table64, _fact_table128]
+        for (n, factn) in enumerate(expected)
+            @test factorial(oftype(factn, n)) === factn
+        end
+    end
 end