LuaTeX - '>' 附近的意外符号

Question

我编写了我的第一个 Lua 代码，它在运行时按预期工作lua.exe。但是当我尝试包含 lua 文件或其完整源代码时，我总是收到错误 ! LuaTeX error mr.lua:11: unexpected symbol near '>' stack traceback: [C]: in function 'dofile' [\directlua]:1: in main chunk.

这是我的 tex 代码：

\documentclass{article}
\usepackage{luacode}
\begin{document}
\directlua{dofile("mr.lua")}
Is $1000003$ a prime number? \texttt{\directlua{tex.sprint(is_prime(1000003))}}
\end{document}

这是我的mr.lua：

-- This file provides the deterministic Miller-Rabin Algorithm.

-- http://en.wikipedia.org/wiki/Modular_exponentiation
function modular_pow(base, exponent, modulus)
    result = 1
    base = base % modulus
    while exponent > 0 do
        if (exponent % 2 == 1) then
            result = (result * base) % modulus
        end
        exponent = exponent >> 1
        base = (base * base) % modulus
    end
    return result
end

function is_composite(a, d, n, s)
    if modular_pow(a, d, n) == 1 then
        return false
    end
    for i = 0, s - 1 do
        if modular_pow(a, math.pow(2,i) * d, n) == n-1 then
            return false
        end
    end
    return true -- n  is definitely composite
end

-- Although Lua cannot handle big numbers without third party libs
-- this is proven to work correct for all numbers up to 100000000
-- bigger numbers not tested.
global function is_prime(n)
    if n < 5 then
        if n == 2 or n == 3 then
            return true
        end
        return false
    end
    p = n % 6 if p ~= 1 and p ~= 5 then return false end
    d, s = n - 1, 0
    while d % 2 == 0 do
        d, s = d >> 1, s + 1
    end
    -- Returns exact according to http://primes.utm.edu/prove/prove2_3.html
    if n < 2047 then
        if is_composite(2, d, n, s) then
            return false
        end
        return true
    end
    if n < 1373653 then
        for i,a in ipairs({2,3}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 9080191 then
        for i,a in ipairs({31,73}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 25326001 then
        for i,a in ipairs({2,3,5}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 118670087467 then
        if n == 3215031751 then
            return false
        end
        for i,a in ipairs({2,3,5,7}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 2152302898747 then
        for i,a in ipairs({2,3,5,7,11}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 3474749660383 then
        for i,a in ipairs({2,3,5,7,11,13}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 341550071728321 then
        for i,a in ipairs({2,3,5,7,11,13,17}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 3825123056546413051 then
        for i,a in ipairs({2,3,5,7,11,13,17,19,23}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    -- otherwise
    for i,a in ipairs({2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53}) do
        if is_composite(a, d, n, s) then
            return false
        end
    end
    return true
end

Answer 1

事实证明，附带的 Lua 版本LuaTeX不支持>> 从该行移位运算符exponent = exponent >> 1。

对于那些感兴趣的人，这里有旧 Lua 5.2 的完整工作代码（希望他们能尽快更新）：

特克斯：

\documentclass{article}
\usepackage{luacode}
\begin{document}
\directlua{dofile("mr.lua")}
Is $1000003$ a prime number? \texttt{\directlua{
if is_prime(1000003) then tex.sprint("true") else tex.sprint("false") end}}
\end{document}

mr.lua

-- This file provides the deterministic Miller-Rabin Algorithm.

-- http://en.wikipedia.org/wiki/Modular_exponentiation
function modular_pow(base, exponent, modulus)
    result = 1
    base = base % modulus
    while exponent > 0 do
        if (exponent % 2 == 1) then
            result = (result * base) % modulus
        end
        exponent = math.floor(exponent/2)
        base = (base * base) % modulus
    end
    return result
end

function is_composite(a, d, n, s)
    if modular_pow(a, d, n) == 1 then
        return false
    end
    for i = 0, s - 1 do
        if modular_pow(a, math.pow(2,i) * d, n) == n-1 then
            return false
        end
    end
    return true -- n  is definitely composite
end

-- Although Lua cannot handle big numbers without third party libs
-- this is proven to work correct for all numbers up to 100000000
-- bigger numbers not tested.
function is_prime(n)
    if n < 5 then
        if n == 2 or n == 3 then
            return true
        end
        return false
    end
    p = n % 6 if p ~= 1 and p ~= 5 then return false end
    d, s = n - 1, 0
    while d % 2 == 0 do
        d, s = math.floor(d/2), s + 1
    end
    -- Returns exact according to http://primes.utm.edu/prove/prove2_3.html
    if n < 2047 then
        if is_composite(2, d, n, s) then
            return false
        end
        return true
    end
    if n < 1373653 then
        for i,a in ipairs({2,3}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 9080191 then
        for i,a in ipairs({31,73}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 25326001 then
        for i,a in ipairs({2,3,5}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 118670087467 then
        if n == 3215031751 then
            return false
        end
        for i,a in ipairs({2,3,5,7}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 2152302898747 then
        for i,a in ipairs({2,3,5,7,11}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 3474749660383 then
        for i,a in ipairs({2,3,5,7,11,13}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 341550071728321 then
        for i,a in ipairs({2,3,5,7,11,13,17}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    if n < 3825123056546413051 then
        for i,a in ipairs({2,3,5,7,11,13,17,19,23}) do
            if is_composite(a, d, n, s) then
                return false
            end
        end
        return true
    end
    -- otherwise
    for i,a in ipairs({2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53}) do
        if is_composite(a, d, n, s) then
            return false
        end
    end
    return true
end