File size: 1,176 Bytes
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 | /*@ Import Lean
import Algorithms.modular_power.lean.helper_lib
open scoped SimpleC
*/
/*@ Extern Coq
(ModularPower : Z -> Z -> Z -> Z -> Prop)
(ModularPowerProgress : Z -> Z -> Z -> Z -> Z -> Z -> Prop)
*/
int modular_power(int a, int b, int modulus)
/*@ Require
0 <= a && a < modulus &&
0 <= b &&
2 <= modulus && modulus <= 46341 && emp
Ensure
0 <= __return && __return < modulus &&
ModularPower(a, b, modulus, __return) && emp
*/
{
int result = 1;
/*@ Inv Assert
0 <= a@pre && a@pre < modulus@pre &&
0 <= b@pre &&
modulus == modulus@pre &&
2 <= modulus@pre && modulus@pre <= 46341 &&
0 <= a && a < modulus@pre &&
0 <= b && b <= b@pre &&
0 <= result && result < modulus@pre &&
0 <= a * a && a * a <= INT_MAX &&
0 <= result * a && result * a <= INT_MAX &&
ModularPowerProgress(a@pre, b@pre, modulus@pre,
a, b, result) && emp
*/
while (b > 0) {
if (b % 2 == 1) {
result = result * a % modulus;
}
a = a * a % modulus;
b /= 2;
}
return result;
}
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