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Use when the code computes modular inverses via Fermat's little theorem using a power function with a data-dependent loop (pw(x, mod-2)) called repeatedly inside combinatorial helpers
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基于 SOC 职业分类
Use when printf statements output strings without trailing newlines
Use when array is accessed with direct user input as index (0-based indexing)
Use when the program accesses a precomputed table using an offset (e.g., arr[n-1]) that introduces an arithmetic operation between the symbolic input and the index
Use when loop variables iterate over character values (e.g., ASCII codes) to represent different operations or choices
Use when code uses a loop to search for an input value in an array and then uses the found index for further computation
Use when code reads a fixed number of characters into an array and only accesses individual elements
| name | avoid-recursive-modular-exponentiation-for-inverses |
| description | Use when the code computes modular inverses via Fermat's little theorem using a power function with a data-dependent loop (pw(x, mod-2)) called repeatedly inside combinatorial helpers |
A KLEE-coverage code transformation. Applying it rewrites C source so symbolic execution explores more of the program's behavior.
When the code computes modular inverses via Fermat's little theorem using a power function with a data-dependent loop (pw(x, mod-2)) called repeatedly inside combinatorial helpers
Precompute modular inverses, factorials, and inverse factorials in a single linear pass using the recurrence inv[i] = (mod - mod/i) * inv[mod%i] % mod, then implement comb() as a straight-line multiplication of table lookups
The pw() function executes ~30 iterations of branching on bits of (mod-2), and is invoked twice per combination call inside a symbolic loop, multiplying path counts exponentially; replacing it with table lookups eliminates these data-independent branches so KLEE spends its budget exploring input-dependent behavior instead of fixed arithmetic control flow
Before:
#include<stdio.h>
int H,W,A,B,fac[222222];
#define mod 1000000007
int add(int x,int y){
return (x+=y)<mod?x:x-mod;
}
int mul(int x,int y){
return (int)((long long int)x*y%mod);
}
int pw(int x,int y){
int r=1;
while(1){
if(y&1)r=mul(r,x);
if(y>>=1)x=mul(x,x);else
break;
}
return r;
}
int inv(int x){
return pw(x,mod-2);
}
int c(int x,int y){
--x;--y;
return mul(fac[x+y],inv(mul(fac[x],fac[y])));
}
int main(){
fac[0]=1;
for(int i=1; i<222222; i++)
fac[i] = mul(fac[i-1],i);
scanf("%d%d%d%d",&H,&W,&A,&B);
int res = 0;
for(int i=B+1; i<=W; i++)
res = add(res, mul(c(H-A,i),c(A, W-i+1)));
printf("%d\n",res);
return 0;
}
After:
#include <stdio.h>
const long long mod = 1000000007;
long long inv[200200],fact[200200],ifact[200200];
long long comb(int n, int k)
{
return fact[n] * ifact[k] % mod * ifact[n-k] % mod;
}
int main()
{
inv[1] = fact[0] = fact[1] = ifact[0] = ifact[1] = 1;
for (int i=2;i<200200;i++){
inv[i] = (mod - mod / i) * inv[mod % i] % mod;
fact[i] = fact[i-1] * i % mod;
ifact[i] = ifact[i-1] * inv[i] % mod;
}
int h,w,a,b; scanf ("%d %d %d %d",&h,&w,&a,&b);
long long ans = comb(h+w-2,h-1);
for (int i=0;i<b;i++){
long long u = comb(h-a-1+i,i);
long long v = comb(a-1+w-1-i,a-1);
ans = (ans - u * v % mod + mod) % mod;
}
printf ("%lld\n",ans);
return 0;
}
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