You are to write an assembly language program called subfaq.s that computes the generalized subfactorial function of nonnegative integer inputs i0 and n. The generalized subfactorial function is defined by the following recursion.
gs(0) = 1
inc(0) = i0
gs(n) = n gs(n-1) - inc(n-1)
inc(n) = -inc(n-1)
The generalized subfactorial function is closely related to the factorial function:
Factorial(n) can be written n! and is equal to gs(n) when i0 = 0.
Subfactorial(n) can be written !n and is equal to gs(n) when i0 = 1.
The values of both factorial and subfactorial get large very rapidly as n increases, so your program should return a 64-bit number representing gs(n) mod 264. In other words, just let your 64-bit register overflow. Try to make your code as short and efficient as possible. I recommend not using recursion, but rather writing a loop that starts from 0 and increments up to n. Write your assembly code from scratch rather than writing C and compiling to assembly. It takes only 10 to 20 instructions, and this will be your only assignment to write code in assembly. Don't miss out on the experience. You may copy your procedure entry and exit code from the textbook or the gcc compiler output without citing the source. Try to get your assembly code for subfac.s to occupy at most 50 bytes (30 is possible). To see your machine code, use
gcc64 -c subfaq.s
to produce object file subfaq.o , then use
objdump64 -d subfaq.o .
The following C program (called run_subfaq.c ) can be used to test your subfaq function. Do not include it with your submission; I already have it.
lli subfaq(int n, lli i0);
int main(int argc, char* argv[])
{
int i = 1, n;
lli i0, ans;
if(argc < 3) {printf("Usage: gs i0 n1 n2 n3 ... (list of non-negative integers)"); return -1;}
sscanf(argv[i++], "%lld", &i0);
while (i < argc) {
sscanf(argv[i], "%d", &n);
if(n < 0) printf("%d out of range\n", n);
else {
ans = subfaq(n, i0);
printf("gs(%d, %lld) = %lld\n", n, i0, ans);
}
i++;
}
return(0);
}
The compile command to test your programs will look like this:
gcc64 -Wall -std=gnu99 -o gs run_subfaq.c subfaq.s .
Here are two sample outputs to use in testing your programs.
C:>gs 0 0 1 2 3 4 5 6 13
gs(0, 0) = 1
gs(1, 0) = 1
gs(2, 0) = 2
gs(3, 0) = 6
gs(4, 0) = 24
gs(5, 0) = 120
gs(6, 0) = 720
gs(20, 0) = 2432902008176640000
gs(21, 0) = -4249290049419214848
gs(
C:>gs 1 0 1 2 3 4 5 6 13
gs(0, 1) = 1
gs(1, 1) = 0
gs(2, 1) = 1
gs(3, 1) = 2
gs(4, 1) = 9
gs(5, 1) = 44
gs(6, 1) = 265
gs(20, 1) = 895014631192902121
gs(21, 1) = 348563181341392924
(The outputs for n = 21 have overflowed the 64-bit word size.)