Data update

Task/Partition-function-P/EasyLang/partition-function-p.easy

@@ -0,0 +1,66 @@
+func[] bnadd a[] b[] .
+   if len a[] < len b[] : swap a[] b[]
+   for i = 1 to len a[]
+      bi = 0
+      if i <= len b[] : bi = b[i]
+      h = a[i] + bi + c
+      r[] &= h mod 10000000
+      c = h div 10000000
+   .
+   if c > 0 : r[] &= c
+   return r[]
+.
+func[] bnsub a[] b[] .
+   for i = 1 to len a[]
+      ai = a[i]
+      bi = 0
+      if i <= len b[] : bi = b[i]
+      bi += c
+      c = 0
+      if bi > ai
+         ai += 10000000
+         c = 1
+      .
+      r[] &= ai - bi
+   .
+   while r[$] = 0 : len r[] -1
+   return r[]
+.
+func$ str bn[] .
+   s$ = bn[$]
+   for i = len bn[] - 1 downto 1
+      h$ = bn[i]
+      s$ &= substr "0000000" 1 (7 - len h$) & h$
+   .
+   return s$
+.
+proc calc i &p[][] .
+   subr upd
+      if k mod 2 = 1
+         h[] = bnadd p[i][] p[i - j][]
+      else
+         h[] = bnsub p[i][] p[i - j][]
+      .
+      p[i][] = h[]
+   .
+   while 1 = 1
+      k += 1
+      j = k * (3 * k - 1) div 2
+      if j > i : return
+      upd
+      j += k
+      if j > i : return
+      upd
+   .
+.
+proc partitions_p n &p[][] .
+   len p[][] n + 1
+   p[0][] = [ 1 ]
+   for i to n : calc i p[][]
+.
+t0 = systime
+nn = 6666
+partitions_p nn p[][]
+print str p[nn][]
+print ""
+print systime - t0 & "s"

Task/Partition-function-P/Pluto/partition-function-p.pluto

@@ -0,0 +1,35 @@
+local bigint = require "pluto:bigint"
+require "table2"
+
+local p = {}
+local pd = {}
+
+local part_diff_diff = |n| -> (n & 1 == 1) ? (n + 1) / 2 : n + 1
+
+local function part_diff(n)
+    if n < 2 then return 1 end
+    pd[n] = pd[n-1] + part_diff_diff(n - 1)
+    return pd[n]
+end
+
+local function partitions_p(n)
+    if n < 2 then return end
+    local psum = bigint.new(0)
+    for i = 1, n do
+        local pdi = part_diff(i)
+        if pdi > n then break end
+        local sign = (i - 1) % 4 < 2 ? 1 : -1
+        psum += p[n - pdi] * sign
+    end
+    p[n] = psum
+end
+
+local N = 6666
+p = table.rep(N, 0)
+pd = table.rep(N, 0)
+p[0] = bigint.new(1)
+p[1] = p[0]
+pd[0] = 1
+pd[1] = 1
+for n = 2, N do partitions_p(n) end
+print($"p[{N}] = {p[N]}")

Task/Partition-function-P/Uiua/partition-function-p.uiua

@@ -0,0 +1,5 @@
+P ← |1 memo(
+  Terms ← ⊂1+1\+♭⍉˜⊟+1⊸×2↘1⇡20
+  ⨬(⨬(/+ ≡(P-) Terms¤|1)⊸=₁|0)⊸≤₀
+)
+P69 # Bigger results look like they've already lost precision.