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Fibonacci and JIT compilers

June 18th, 2011 No comments

To maximize a compiler’s ability to generate high quality code many programming language standards do not specify the order in which the operands of a binary operator are evaluated. Most of the time the order of operand evaluation does not matter because all orders produce same final result. For instance in x + y the value of x may be obtained followed by obtaining the value of y and the two values added, alternatively the value of y may be obtained first followed by obtaining the value of x and the two values added; optimizers make use of local context information (e.g., holding one of the values in a register so it is immediately available for use in the evaluation of multiple instances of x) to work out which order produces the highest quality code.

If one of the operands is a function call that modifies the value of the other operand the result may depend on the order of evaluation. For instance, in:

int x;
 
int set_x(void)
{
x=1;
return 1;
}
 
int two_values(void)
{
x=0;
return x + set_x();
}

a left to right evaluation order of the return expression in two_values produces the value 1, while a right to left evaluation order produces the value 2. Every now and again developers accidentally write code that does something like this and are surprised to see program behavior change when they use different compiler options, a new version of the compiler or a different compiler (all things that can result in the order of evaluation changing for a given expression).

It is generally assumed that two calls to two_values within the same program will always produce the same answer, i.e., the decision on which order of evaluation to use is made at compile time and never changes while a program is running. Neither the C++ or C Standard requires that the evaluation order be fixed prior to program execution and use of a just-in-time compiler could result in the value returned by two_values alternating between 1 and 2. Some languages (e.g., Java) for which JIT compilers are expected to be used specify the exact order in which operands have to be evaluated.

One possible way of finding out whether a JIT compiler is being used for your C/C++ program is to test the values returned by two calls to two_values. A JIT compiler may, but is not required, to return different values on each call. Of course a decide-prior-to-execution C/C++ compiler does have the option of optimizing the following function to return true or false on the basis that the standard permits this behavior, but I would be very surprised to see this occur in practice:

bool Schrödinger(void)
{
return two_values() == two_values();
}

The runtime variability offered by JIT compilers makes it possible to write a program whose output can be any value between 1 and F_n (the n‘th Fibonacci number, where n is read from the input):

#include <stdio.h>
 
int x;
 
int set_x(int ret_val)
{
x=1;
return ret_val;
}
 
int two_unspec(void)
{
x=0;
return x + set_x(1);
}
 
int add_zero(val)
{
x=0;
return val - x + set_x(0);
}
 
int fib(int fib_num)
{
if (fib_num > 3)
   return fib(fib_num-2) + add_zero(fib(fib_num-1));
else
   if (fib_num == 3)
      return two_unspec();
   else
      return 1;
}
 
int main(void)
{
int n;
 
scanf("%d", &n);
printf("Fibonacci %d = %d\n", n, filb(n));
}

The C-semantics tool will ‘execute’ this program and produce a list of the F_n possible outputs (a PhD project under active development; the upper limit is currently around the 6th Fibonacci number which requires 11 hours and produces a 50G log file).

A decide-prior-to-execution compiler has a maximum choice of four possible outputs for a given input value and for a given executable the output produced by different input values will be perfectly correlated.