From 60aee30548f427916274a7f99a6c7d342d991fdd Mon Sep 17 00:00:00 2001
From: ykiko <ykikoykikoykiko@gmail.com>
Date: Thu, 28 Mar 2024 16:54:47 +0800
Subject: [PATCH] adoping a more efficient division algorithm for bigint.

---
 python/_long.py  | 76 ++++++++++++++++++++++++++++++++++++++++++++----
 tests/09_long.py |  2 +-
 2 files changed, 72 insertions(+), 6 deletions(-)

diff --git a/python/_long.py b/python/_long.py
index e2ff938f..eac349c0 100644
--- a/python/_long.py
+++ b/python/_long.py
@@ -99,12 +99,78 @@ def ulong_divmodi(a: list, b: int):
     ulong_unpad_(res)
     return res, carry
 
+def ulong_lshift_(a: list, shift: int):
+    if shift == 0:
+        return
+    bits = shift % PyLong_SHIFT
+    carry = 0
+    for i in range(len(a) - 1, -1, -1):
+        new_carry = (a[i] >> (PyLong_SHIFT - bits)) & PyLong_MASK
+        a[i] = (a[i] << bits) & PyLong_MASK | carry
+        carry = new_carry
+    if carry != 0:
+        a.insert(0, carry)
+
+def ulong_rshift_(a: list, shift: int):
+    if shift == 0:
+        return
+    bits = shift % PyLong_SHIFT
+    carry = 0
+    for i in range(len(a)):
+        new_carry = (a[i] << (PyLong_SHIFT - bits)) & PyLong_MASK
+        a[i] = (a[i] >> bits) | carry
+        carry = new_carry
+    if carry != 0:
+        a.pop(0)
+
 def ulong_divmod(a: list, b: list):
-    q = [0]
-    while ulong_cmp(a, b) >= 0:
-        ulong_inc_(q)
-        a = ulong_sub(a, b)
-    return q, a
+
+    if ulong_cmp(a, b) < 0:
+        return [0], a
+
+    if len(b) == 1:
+        quotient = [0] * len(a)
+        remainder = 0
+        for i in range(len(a)-1, -1, -1):
+            temp = (remainder << PyLong_SHIFT) + a[i]
+            quotient[i] = temp // b[0]
+            remainder = temp % b[0]
+        return quotient, [remainder]
+
+    shift = PyLong_SHIFT - (b[-1].bit_length() - 1)
+    a = a.copy()
+    b = b.copy()
+    ulong_lshift_(a, shift)
+    ulong_lshift_(b, shift)
+
+    quotient = [0] * (len(a) - len(b) + 1)
+
+    for j in range(len(a)-len(b), -1, -1):
+        temp = ((a[j+len(b)] << PyLong_SHIFT) + a[j+len(b)-1]) // b[-1]
+        temp = min(temp, PyLong_MASK)
+        while temp*b[-1] > ((a[j+len(b)] << PyLong_SHIFT) + a[j+len(b)-1] - temp*a[j+len(b)-2] + (b[-2] if len(b) > 1 else 0)):
+            temp -= 1
+
+        carry = 0
+        for i in range(len(b)):
+            carry += a[i+j] - temp*b[i]
+            a[i+j] = carry & PyLong_MASK
+            carry >>= PyLong_SHIFT
+        a[j+len(b)] += carry
+
+        if a[j+len(b)] < 0:
+            carry = 0
+            for i in range(len(b)):
+                carry += a[i+j] + b[i]
+                a[i+j] = carry & PyLong_MASK
+                carry >>= PyLong_SHIFT
+            a[j+len(b)] += carry
+        else:
+            quotient[j] = temp
+
+    ulong_unpad_(a)
+    ulong_rshift_(a, shift)
+    return quotient, a
 
 def ulong_floordivi(a: list, b: int):
     # b > 0
diff --git a/tests/09_long.py b/tests/09_long.py
index 412a2d38..28d383b4 100644
--- a/tests/09_long.py
+++ b/tests/09_long.py
@@ -14,7 +14,7 @@ assert -a == -2
 assert 1 + a == 3L
 assert 1 - a == -1L
 assert 2 * a == 4L
-
+assert 2L**500 // 3333L
 
 # __lshift__ and __rshift__
 for i in range(29):