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bff4ec7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | /*@ 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;
}
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