在函数式语言中，尾部调用优化就好像函数调用可以返回部分求值的表达式作为结果，然后由调用者求值。

f x = g x

f6变成了g6。因此，如果实现可以返回g6作为结果，然后调用该表达式，它将保存一个堆栈帧。

Also

f x = if c x then g x else h x.

还原到f6到g6或h6。所以如果实现计算c6，发现它是真的，那么它可以减少，

if true then g x else h x ---> g x

f x ---> h x

一个简单的非尾部调用优化解释器可能是这样的，

class simple_expresion
{
    ...
public:
    virtual ximple_value *DoEvaluate() const = 0;
};

class simple_value
{
    ...
};

class simple_function : public simple_expresion
{
    ...
private:
    simple_expresion *m_Function;
    simple_expresion *m_Parameter;

public:
    virtual simple_value *DoEvaluate() const
    {
        vector<simple_expresion *> parameterList;
        parameterList->push_back(m_Parameter);
        return m_Function->Call(parameterList);
    }
};

class simple_if : public simple_function
{
private:
    simple_expresion *m_Condition;
    simple_expresion *m_Positive;
    simple_expresion *m_Negative;

public:
    simple_value *DoEvaluate() const
    {
        if (m_Condition.DoEvaluate()->IsTrue())
        {
            return m_Positive.DoEvaluate();
        }
        else
        {
            return m_Negative.DoEvaluate();
        }
    }
}

尾部调用优化解释器可能是这样的，

class tco_expresion
{
    ...
public:
    virtual tco_expresion *DoEvaluate() const = 0;
    virtual bool IsValue()
    {
        return false;
    }
};

class tco_value
{
    ...
public:
    virtual bool IsValue()
    {
        return true;
    }
};

class tco_function : public tco_expresion
{
    ...
private:
    tco_expresion *m_Function;
    tco_expresion *m_Parameter;

public:
    virtual tco_expression *DoEvaluate() const
    {
        vector< tco_expression *> parameterList;
        tco_expression *function = const_cast<SNI_Function *>(this);
        while (!function->IsValue())
        {
            function = function->DoCall(parameterList);
        }
        return function;
    }

    tco_expresion *DoCall(vector<tco_expresion *> &p_ParameterList)
    {
        p_ParameterList.push_back(m_Parameter);
        return m_Function;
    }
};

class tco_if : public tco_function
{
private:
    tco_expresion *m_Condition;
    tco_expresion *m_Positive;
    tco_expresion *m_Negative;

    tco_expresion *DoEvaluate() const
    {
        if (m_Condition.DoEvaluate()->IsTrue())
        {
            return m_Positive;
        }
        else
        {
            return m_Negative;
        }
    }
}

递归函数方法有一个问题。它建立了一个大小为O(n)的调用堆栈，这使得我们的总内存开销为O(n)。这使得它很容易出现堆栈溢出错误，即调用堆栈变得太大而耗尽空间。

TCO (Tail call optimization)方案。它可以优化递归函数，以避免建立一个庞大的调用堆栈，从而节省内存成本。

有很多语言都在做TCO (JavaScript, Ruby和少数C)，而Python和Java不做TCO。

JavaScript语言已确认使用:)http://2ality.com/2015/06/tail-call-optimization.html

我们应该确保函数本身没有goto语句。函数调用是被调用函数的最后一个内容。 大规模递归可以使用它进行优化，但在小规模中，使函数调用成为尾部调用的指令开销降低了实际目的。 TCO可能导致一个永远运行的函数: 空白永恒() ｛ 永恒(); ｝

TCO (Tail Call Optimization) is the process by which a smart compiler can make a call to a function and take no additional stack space. The only situation in which this happens is if the last instruction executed in a function f is a call to a function g (Note: g can be f). The key here is that f no longer needs stack space - it simply calls g and then returns whatever g would return. In this case the optimization can be made that g just runs and returns whatever value it would have to the thing that called f.

这种优化可以使递归调用占用恒定的堆栈空间，而不是爆炸。

示例:这个阶乘函数不是TCOptimizable:

from dis import dis

def fact(n):
    if n == 0:
        return 1
    return n * fact(n-1)


dis(fact)
  2           0 LOAD_FAST                0 (n)
              2 LOAD_CONST               1 (0)
              4 COMPARE_OP               2 (==)
              6 POP_JUMP_IF_FALSE       12

  3           8 LOAD_CONST               2 (1)
             10 RETURN_VALUE

  4     >>   12 LOAD_FAST                0 (n)
             14 LOAD_GLOBAL              0 (fact)
             16 LOAD_FAST                0 (n)
             18 LOAD_CONST               2 (1)
             20 BINARY_SUBTRACT
             22 CALL_FUNCTION            1
             24 BINARY_MULTIPLY
             26 RETURN_VALUE

这个函数除了在它的return语句中调用另一个函数之外还做其他事情。

下面这个函数是TCOptimizable:

def fact_h(n, acc):
    if n == 0:
        return acc
    return fact_h(n-1, acc*n)

def fact(n):
    return fact_h(n, 1)


dis(fact)
  2           0 LOAD_GLOBAL              0 (fact_h)
              2 LOAD_FAST                0 (n)
              4 LOAD_CONST               1 (1)
              6 CALL_FUNCTION            2
              8 RETURN_VALUE

这是因为在这些函数中最后发生的事情是调用另一个函数。

看这里:

http://tratt.net/laurie/tech_articles/articles/tail_call_optimization

你可能知道，递归函数调用会对堆栈造成严重破坏;堆栈空间很容易很快用完。尾部调用优化是一种方法，通过它你可以创建一个使用常量堆栈空间的递归式算法，因此它不会不断增长，你会得到堆栈错误。

GCC C最小可运行示例与x86拆装分析

让我们看看GCC如何通过查看生成的程序集自动执行尾部调用优化。

这将作为一个非常具体的例子，说明其他答案(如https://stackoverflow.com/a/9814654/895245)中提到的优化可以将递归函数调用转换为循环。

这反过来又节省了内存并提高了性能，因为内存访问通常是现在使程序变慢的主要原因。

作为输入，我们给GCC一个基于阶乘的非优化朴素堆栈:

tail_call.c

#include <stdio.h>
#include <stdlib.h>

unsigned factorial(unsigned n) {
    if (n == 1) {
        return 1;
    }
    return n * factorial(n - 1);
}

int main(int argc, char **argv) {
    int input;
    if (argc > 1) {
        input = strtoul(argv[1], NULL, 0);
    } else {
        input = 5;
    }
    printf("%u\n", factorial(input));
    return EXIT_SUCCESS;
}

GitHub上游。

编译和分解:

gcc -O1 -foptimize-sibling-calls -ggdb3 -std=c99 -Wall -Wextra -Wpedantic \
  -o tail_call.out tail_call.c
objdump -d tail_call.out

其中-foptimize-sibling-calls是根据man gcc泛化尾部调用的名称:

   -foptimize-sibling-calls
       Optimize sibling and tail recursive calls.

       Enabled at levels -O2, -O3, -Os.

如上所述:我如何检查gcc是否执行尾递归优化?

我选择-O1是因为:

优化不是用-O0完成的。我怀疑这是因为缺少必要的中间转换。 -O3产生了非常高效的代码，虽然它也是尾部调用优化。

使用-fno-optimize-sibling-calls进行反汇编:

0000000000001145 <factorial>:
    1145:       89 f8                   mov    %edi,%eax
    1147:       83 ff 01                cmp    $0x1,%edi
    114a:       74 10                   je     115c <factorial+0x17>
    114c:       53                      push   %rbx
    114d:       89 fb                   mov    %edi,%ebx
    114f:       8d 7f ff                lea    -0x1(%rdi),%edi
    1152:       e8 ee ff ff ff          callq  1145 <factorial>
    1157:       0f af c3                imul   %ebx,%eax
    115a:       5b                      pop    %rbx
    115b:       c3                      retq
    115c:       c3                      retq

-foptimize-sibling-calls:

0000000000001145 <factorial>:
    1145:       b8 01 00 00 00          mov    $0x1,%eax
    114a:       83 ff 01                cmp    $0x1,%edi
    114d:       74 0e                   je     115d <factorial+0x18>
    114f:       8d 57 ff                lea    -0x1(%rdi),%edx
    1152:       0f af c7                imul   %edi,%eax
    1155:       89 d7                   mov    %edx,%edi
    1157:       83 fa 01                cmp    $0x1,%edx
    115a:       75 f3                   jne    114f <factorial+0xa>
    115c:       c3                      retq
    115d:       89 f8                   mov    %edi,%eax
    115f:       c3                      retq

两者之间的关键区别在于:

the -fno-optimize-sibling-calls uses callq, which is the typical non-optimized function call. This instruction pushes the return address to the stack, therefore increasing it. Furthermore, this version also does push %rbx, which pushes %rbx to the stack. GCC does this because it stores edi, which is the first function argument (n) into ebx, then calls factorial. GCC needs to do this because it is preparing for another call to factorial, which will use the new edi == n-1. It chooses ebx because this register is callee-saved: What registers are preserved through a linux x86-64 function call so the subcall to factorial won't change it and lose n. the -foptimize-sibling-calls does not use any instructions that push to the stack: it only does goto jumps within factorial with the instructions je and jne. Therefore, this version is equivalent to a while loop, without any function calls. Stack usage is constant.

在Ubuntu 18.10, GCC 8.2中测试。