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mod_inv.c
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mod_inv.c
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// return a modular multiplicative inverse of n with respect to the modulus.
// return 0 if the linear congruence has no solutions.
unsigned mod_inv(unsigned ra, unsigned rb) {
unsigned rc, sa = 1, sb = 0, sc, i = 0;
if (rb > 1) do {
rc = ra % rb;
sc = sa - (ra / rb) * sb;
sa = sb, sb = sc;
ra = rb, rb = rc;
} while (++i, rc);
sa *= (i *= ra == 1) != 0;
sa += (i & 1) * sb;
return sa;
}
#include <assert.h>
int main(void) {
unsigned n, mod, res;
n = 52, mod = 107;
res = mod_inv(n, mod);
assert(res == 35); // 35 is a solution of the linear congruence.
n = 66, mod = 123;
res = mod_inv(n, mod);
assert(res == 0); // 66 does note have an inverse modulo 123.
}
/*
n = 7 and mod = 45 then res = 13 so 1 == ( 13 * 7 ) % 45
n = 52 and mod = 107 then res = 35 so 1 == ( 35 * 52 ) % 107
n = 213 and mod = 155 then res = 147 so 1 == ( 147 * 213 ) % 155
n = 392 and mod = 45 then res = 38 so 1 == ( 38 * 392 ) % 45
n = 687 and mod = 662 then res = 53 so 1 == ( 53 * 687 ) % 662
n = 451 and mod = 799 then res = 512 so 1 == ( 512 * 451 ) % 799
n = 1630 and mod = 259 then res = 167 so 1 == ( 167 * 1630 ) % 259
n = 4277 and mod = 4722 then res = 191 so 1 == ( 191 * 4277 ) % 4722
n = 4135054603 and mod = 3212775958 then res = 1220502011 so 1 == (1220502011 * 4135054603) % 3212775958
*/