很简单，什么是尾部调用优化?
更具体地说，有哪些小代码段可以应用，哪些地方不可以，并解释原因?
当前回答
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。
其他回答
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。
让我们看一个简单的例子:用C实现的阶乘函数。
我们从显而易见的递归定义开始
unsigned fac(unsigned n)
{
if (n < 2) return 1;
return n * fac(n - 1);
}
如果函数返回前的最后一个操作是另一个函数调用，则函数以尾部调用结束。如果此调用调用相同的函数，则它是尾递归的。
尽管fac()乍一看是尾递归的，但实际情况并非如此
unsigned fac(unsigned n)
{
if (n < 2) return 1;
unsigned acc = fac(n - 1);
return n * acc;
}
即最后一个操作是乘法运算，而不是函数调用。
但是，可以将fac()重写为尾部递归，方法是将累积值作为附加参数向下传递调用链，并仅将最终结果作为返回值向上传递:
unsigned fac(unsigned n)
{
return fac_tailrec(1, n);
}
unsigned fac_tailrec(unsigned acc, unsigned n)
{
if (n < 2) return acc;
return fac_tailrec(n * acc, n - 1);
}
为什么这个有用呢?因为我们在尾部调用之后立即返回，所以我们可以在调用尾部位置的函数之前丢弃之前的堆栈框架，或者在递归函数的情况下，按原样重用堆栈框架。
尾部调用优化将我们的递归代码转换为
unsigned fac_tailrec(unsigned acc, unsigned n)
{
TOP:
if (n < 2) return acc;
acc = n * acc;
n = n - 1;
goto TOP;
}
这可以内联到fac()，我们得到
unsigned fac(unsigned n)
{
unsigned acc = 1;
TOP:
if (n < 2) return acc;
acc = n * acc;
n = n - 1;
goto TOP;
}
这相当于
unsigned fac(unsigned n)
{
unsigned acc = 1;
for (; n > 1; --n)
acc *= n;
return acc;
}
正如我们在这里看到的，一个足够先进的优化器可以用迭代代替尾递归，这是更有效的，因为您避免了函数调用开销，并且只使用固定数量的堆栈空间。
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;
}
}
}
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(); ｝
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。
