From cf9d0892bf2eec31c3cec42d3d6ee92f852d3acf Mon Sep 17 00:00:00 2001
From: Reza Behzadan <rbehzadan@gmail.com>
Date: Wed, 13 May 2020 15:37:40 +0430
Subject: [PATCH] initial commit: import bigint

---
 .gitignore      |  48 ++++++
 README.md       |   0
 bigint.lua      | 384 ++++++++++++++++++++++++++++++++++++++++++++++++
 bigint_test.lua |  91 ++++++++++++
 4 files changed, 523 insertions(+)
 create mode 100644 .gitignore
 create mode 100644 README.md
 create mode 100644 bigint.lua
 create mode 100644 bigint_test.lua

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..68efd84
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,48 @@
+
+# Created by https://www.gitignore.io/api/lua
+# Edit at https://www.gitignore.io/?templates=lua
+
+### Lua ###
+# Compiled Lua sources
+luac.out
+
+# luarocks build files
+*.src.rock
+*.zip
+*.tar.gz
+
+# Object files
+*.o
+*.os
+*.ko
+*.obj
+*.elf
+
+# Precompiled Headers
+*.gch
+*.pch
+
+# Libraries
+*.lib
+*.a
+*.la
+*.lo
+*.def
+*.exp
+
+# Shared objects (inc. Windows DLLs)
+*.dll
+*.so
+*.so.*
+*.dylib
+
+# Executables
+*.exe
+*.out
+*.app
+*.i*86
+*.x86_64
+*.hex
+
+
+# End of https://www.gitignore.io/api/lua
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..e69de29
diff --git a/bigint.lua b/bigint.lua
new file mode 100644
index 0000000..b750539
--- /dev/null
+++ b/bigint.lua
@@ -0,0 +1,384 @@
+BigInt = {}
+BigInt.__index = BigInt
+
+
+local function trim(a)
+    for i = #a, 2, -1 do
+        if a[i] ~= 0 then break end
+        table.remove(a)
+    end
+    if #a == 1 and a[1] == 0 then a.sign = 1 end
+end
+
+local function num2tab(n)
+    local t = {sign=1}
+    local i = 1
+    if n < 0 then
+        n = -n
+        t.sign = -1
+    end
+    repeat
+        local r = math.fmod(n, 10)
+        n = math.floor(n / 10)
+        t[i] = r
+        i = i + 1
+    until n == 0
+    return t
+end
+
+local function str2tab(s)
+    local s = string.match(s, "^[+-]?%d+$") or "0"
+    local t = {sign=1}
+    local i = #s
+    local j = 1
+    local first = 1
+    if s:sub(1, 1) == '-' then t.sign=-1;first=2 end
+    if s:sub(1, 1) == '+' then first=2 end
+    while i >= first do
+        t[j] = s:sub(i, i):byte()-48
+        j = j + 1
+        i = i - 1
+    end
+    return t
+end
+
+local function iterZip(a, b)
+    local a = BigInt(a)
+    local b = BigInt(b)
+    local i = 1
+    return function()
+        if not a[i] and not b[i] then return end
+        local ai = a[i] or 0
+        local bi = b[i] or 0
+        i = i + 1
+        return ai, bi, i-1
+    end
+end
+
+local function iterZipRev(a, b, n)
+    local a = BigInt(a)
+    local b = BigInt(b)
+    local i = n
+    if not i then
+        i = #a
+        if #b > i then i = #b end
+    end
+    return function()
+        if i<1 then return end
+        local ai = a[i] or 0
+        local bi = b[i] or 0
+        i = i - 1
+        return ai, bi, i+1
+    end
+end
+
+local function concat(a, b)
+    if not b then return a:clone() end
+    local c = b:clone()
+    local n = #c
+    for i in ipairs(a) do
+        n = n + 1
+        c[n] = a[i]
+    end
+    c.sign = a.sign
+    trim(c)
+    return c
+end
+
+local function append(a, d)
+    table.insert(a, 1, d)
+    trim(a)
+end
+
+local function uadd(a, b)
+    local c = BigInt()
+    local carry = 0
+    for ai, bi, i in iterZip(a, b) do
+        local ci = ai + bi + carry
+        if ci > 9 then
+            ci = ci - 10
+            carry = 1
+        else
+            carry = 0
+        end
+        c[i] = ci
+    end
+    trim(c)
+    return c
+end
+
+local function ult(a, b)
+    for ai, bi in iterZipRev(a, b) do
+        if ai < bi then return true end
+        if bi < ai then return false end
+    end
+    return false
+end
+
+local function usub(a, b)
+    local c = BigInt()
+    if ult(a, b) then a, b = b, a; c.sign = -1 end
+    local borrow = 0
+    local ci
+    for ai, bi, i in iterZip(a, b) do
+        ci = (ai - borrow) - bi
+        if ci < 0 then
+            -- ci = 10 + ai - borrow - bi
+            ci = ci + 10
+            borrow = 1
+        else
+            borrow = 0
+        end
+        c[i] = ci
+    end
+    trim(c)
+    return c
+end
+
+local function udiv(a, b)
+    local a = BigInt(a):clone()
+    local b = BigInt(b):clone()
+    local q = BigInt()
+    local d = BigInt()
+    local r
+    a.sign = 1
+    b.sign = 1
+    if b == q then return end
+    if a == q then return q, q end
+    -- if a < b then return q, a:clone() end
+    if a < b then return q, a end
+    if a == b then return BigInt(1), q end
+    -- if #b == 1 and b[1] == 1 then return a:clone(), q end
+    if #b == 1 and b[1] == 1 then return a, q end
+    for k = #a, 1, -1 do
+        -- d:append(a[k])
+        append(d, a[k])
+        if d >= b then
+            for i = 10, 1, -1 do
+                r = d - i * b
+                if r.sign == 1 then 
+                    -- q = q:concat(BigInt(i))
+                    q = concat(q, BigInt(i))
+                    break
+                end
+            end
+            d = r
+        else
+            q = q * 10
+        end
+    end
+    return q, r
+end
+
+local function uinc(a)
+    -- in place
+    local i = 1
+    local c = 1
+    repeat
+        if not a[i] then a[i] = 0 end
+        a[i] = a[i] + c
+        c = 0
+        if a[i] > 9 then
+            a[i] = a[i] - 10
+            c = 1
+        end
+        i = i + 1
+    until c == 0
+end
+
+local function udec(a)
+    -- in place
+    if #a == 1 and a[1] == 0 then
+        a[1] = 1
+        a.sign = -1
+        return
+    end
+    local i = 1
+    local c = 1
+    repeat
+        a[i] = a[i] - c
+        c = 0
+        if a[i] < 0 then
+            a[i] = a[i] + 10
+            c = 1
+        end
+        i = i + 1
+    until c == 0
+    trim(a)
+end
+
+function BigInt.__eq(a, b)
+    if #a ~= #b then return false end
+    if a.sign ~= b.sign then return false end
+    local i = 1
+    local r = true
+    while a[i] do
+        if a[i] ~= b[i] then
+            r = false
+            break
+        end
+        i = i + 1
+    end
+    return r
+end
+
+function BigInt.__lt(a, b)
+    return BigInt.__sub(a, b).sign == -1
+end
+
+function BigInt.__unm(a)
+    local b = BigInt.clone(a)
+    b.sign = a.sign * -1
+    return b
+end
+
+function BigInt.__add(a, b)
+    local a = BigInt(a)
+    local b = BigInt(b)
+    if a.sign == 1 and b.sign == 1 then
+        return uadd(a, b)
+    elseif a.sign == 1 and b.sign == -1 then
+        return usub(a, b)
+    elseif a.sign == -1 and b.sign == 1 then
+        return usub(b, a)
+    else
+        local r = uadd(a, b)
+        r.sign = -1
+        return r
+    end
+end
+
+function BigInt.__sub(a, b)
+    local a = BigInt(a)
+    local b = BigInt(b)
+    if a.sign == 1 and b.sign == 1 then
+        return usub(a, b)
+    elseif a.sign == 1 and b.sign == -1 then
+        return uadd(a, b)
+    elseif a.sign == -1 and b.sign == 1 then
+        local c = uadd(a, b)
+        c.sign = -1
+        return c
+    else
+        return usub(b, a)
+    end
+end
+
+function BigInt.__mul(a, b)
+    local a = BigInt(a)
+    local b = BigInt(b)
+    local c = BigInt()
+    for i = 1, #a do
+        local carry = 0
+        for j = 1, #b do
+            local k = i + j - 1
+            local ai = a[i] or 0
+            local bj = b[j] or 0
+            local ck = c[k] or 0
+            ck = ck + carry + ai * bj
+            -- carry = ck // 10
+            -- c[k] = ck % 10
+            carry = math.floor(ck / 10)
+            c[k] = math.fmod(ck, 10)
+        end
+        c[i+#b] = carry
+    end
+    c.sign = a.sign * b.sign
+    trim(c)
+    return c
+end
+
+function BigInt.__div(a, b)
+    local q = udiv(a, b)
+    q.sign = a.sign * b.sign
+    trim(q)
+    return q
+end
+
+function BigInt.__pow(a, b)
+    local a = BigInt(a)
+    local b = BigInt(b):clone()
+    local c = BigInt(1)
+    local i = BigInt(1)
+    if b.sign == -1 then b.sign = 1 end
+    while i <= b do
+        c = c * a
+        i:inc()
+    end
+    return c
+end
+
+function BigInt:__tostring()
+    local l = {}
+    local i = 1
+    -- trim(self)
+    -- if #self == 1 and self[1] == "0" then return "0" end
+    for j = #self, 1, -1 do
+        l[i] = self[j]
+        i = i + 1
+    end
+    -- trim(l)
+    if self.sign == -1 then
+        return "-"..table.concat(l)
+    end
+    return table.concat(l)
+end
+
+function BigInt:inc()
+    -- in place
+    if self.sign == -1 then
+        udec(self)
+    else
+        uinc(self)
+    end
+end
+
+function BigInt:dec()
+    -- in place
+    if self.sign == -1 then
+        uinc(self)
+    else
+        udec(self)
+    end
+end
+
+function BigInt:toBase()
+end
+
+function BigInt:fromBase()
+end
+
+function BigInt.divmod(a, b)
+    local q, r = udiv(a, b)
+    q.sign = a.sign * b.sign
+    trim(q)
+    trim(r)
+    return q, r
+end
+
+function BigInt.clone(a)
+    local o = {unpack(a)}
+    o.sign = a.sign
+    setmetatable(o, BigInt)
+    return o
+end
+
+function BigInt:new(n)
+    local o
+    local t = type(n)
+    if t == "number" then
+        o = num2tab(math.floor(n))
+    elseif t == "string" then
+        o = str2tab(n)
+    elseif t == "table" then
+        if n.__tostring == self.__tostring then return n end
+        o = {unpack(n)}
+    else
+        o = {0, sign=1}
+    end
+    setmetatable(o, BigInt)
+    return o
+end
+
+setmetatable(BigInt, {__call=BigInt.new})
+return BigInt
diff --git a/bigint_test.lua b/bigint_test.lua
new file mode 100644
index 0000000..c3f45af
--- /dev/null
+++ b/bigint_test.lua
@@ -0,0 +1,91 @@
+B = require("bigint")
+local S = string.format
+
+function printf(...)
+    io.write(string.format(...))
+end
+
+function bc(exp)
+    local cmd = string.format('echo "%s" | bc', exp)
+    f = io.popen(cmd, 'r')
+    s = f:read('*a')
+    f:close()
+    return s:gsub("\\", ""):gsub("\n", "")
+end
+
+ops = {
+    ['+'] = function(a, b) return a + b end,
+    ['-'] = function(a, b) return a - b end,
+    ['*'] = function(a, b) return a * b end,
+    ['/'] = function(a, b) return a / b end,
+    ['^'] = function(a, b) return a ^ b end,
+}
+
+local signs = {"", "-", "+"}
+
+function test_op(a, b, op, msg)
+    local sa = tostring(a):gsub("%s+", ""):gsub("^+", "")
+    local sb = tostring(b):gsub("%s+", ""):gsub("^+", "")
+    local r = ops[op](B(a), B(b))
+    local sr = tostring(r)
+    local s = S('%s %s %s', sa, op, sb)
+    local s2 = msg or S('%s %s %s', a, op, b)
+    local br = bc(s)
+    assert(sr==br, S("%s: '%s' != '%s'", s2, sr, br))
+    print(S("[PASSED] %s", s2))
+end
+
+function test_four(a, b)
+    print(("-"):rep(50))
+    print(S("A = '%s'", a))
+    print(S("B = '%s'", b))
+    for op in pairs(ops) do
+        if op == '^' then goto continue end
+        for _, s1 in ipairs(signs) do
+            for _, s2 in ipairs(signs) do
+                local sa = s1..a
+                local sb = s2..b
+                local ma = s1.."A"
+                local mb = s2.."B"
+                test_op(sa, sb, op, S("%s %s %s", ma, op, mb))
+                test_op(sb, sa, op, S("%s %s %s", mb, op, ma))
+            end
+        end
+::continue::
+    end
+end
+
+function test_divmod(a, b)
+    local q, r = B(a):divmod(B(b))
+    local calculatedQuotient = tostring(q)
+    local calculatedRemainder = tostring(r)
+    local sq = S("%s / %s", a, b)
+    local sr = S("%s %% %s", a, b)
+    local expectedQuotient = bc(sq)
+    local expectedRemainder = bc(sr)
+    assert(calculatedQuotient==expectedQuotient,
+        S("%s: '%s' != '%s'", sq, calculatedQuotient, expectedQuotient))
+    print(S("[PASSED] %s", sq))
+    assert(calculatedRemainder == expectedRemainder,
+        S("%s: '%s' != '%s'", sr, calculatedRemainder, expectedRemainder))
+    print(S("[PASSED] %s", sr))
+end
+
+
+test_four(
+    "432094820938402398402983415987430593923832340",
+    "234290830983245674250132908423290489320329209458645349721"
+)
+
+test_four("123", "12")
+
+test_four(
+    "10000000000000000000000000000000000000000000000000000000000000000",
+    "99999999999999999999999999999999999999999999999999999999"
+)
+
+test_divmod("12312321", "322")
+test_divmod("322", "12312321")
+
+test_op("2", "100", "^")
+test_op("5", "1024", "^")