| /*@ Import Lean | |
| import Algorithms.modular_mul.lean.helper_lib | |
| open scoped SimpleC | |
| */ | |
| /*@ Extern Coq | |
| (ModularMul : Z -> Z -> Z -> Z -> Prop) | |
| (ModularMulProgress : Z -> Z -> Z -> Z -> Z -> Z -> Z -> Prop) | |
| */ | |
| int modular_mul(int a, int b, int modulus) | |
| /*@ Require | |
| 0 - modulus < a && a < modulus && | |
| INT_MIN < b && b <= INT_MAX && | |
| 0 < modulus && modulus * 2 <= INT_MAX && emp | |
| Ensure | |
| ModularMul(a, b, modulus, __return) && emp | |
| */ | |
| { | |
| int res = 0; | |
| int flag = 1; | |
| if (b < 0) { | |
| b = -b; | |
| flag = -1; | |
| } | |
| /*@ Inv Assert | |
| 0 - modulus@pre < a@pre && a@pre < modulus@pre && | |
| INT_MIN < b@pre && b@pre <= INT_MAX && | |
| modulus == modulus@pre && | |
| 0 < modulus@pre && modulus@pre * 2 <= INT_MAX && | |
| 0 <= b && b <= INT_MAX && | |
| (flag == 1 || flag == 0 - 1) && | |
| 0 - modulus@pre < a && a < modulus@pre && | |
| 0 - modulus@pre < res && res < modulus@pre && | |
| INT_MIN <= res + a && res + a <= INT_MAX && | |
| INT_MIN <= a + a && a + a <= INT_MAX && | |
| INT_MIN <= res * flag && res * flag <= INT_MAX && | |
| ModularMulProgress(a@pre, b@pre, modulus@pre, | |
| a, b, res, flag) && emp | |
| */ | |
| while (b > 0) { | |
| if (b % 2 == 1) { | |
| res = (res + a) % modulus; | |
| } | |
| b = b / 2; | |
| a = (a + a) % modulus; | |
| } | |
| return res * flag; | |
| } | |