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mruby-bigint: Replace binary GCD with Euclidean algorithm in mpz_gcd

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The previous implementation of mpz_gcd for multi-limb numbers,
commented as "Use Lehmer's algorithm", was in fact an implementation
of the binary GCD algorithm (Stein's algorithm).

This commit replaces that binary GCD implementation with a standard
Euclidean algorithm. For multi-limb numbers, a well-implemented
Euclidean algorithm leveraging an optimized modular division (mpz_mod)
can be more efficient than the binary GCD. This change provides a
clearer and more efficient foundation for GCD calculations, and serves
as a stepping stone towards a true Lehmer's algorithm if pursued later.

Co-authored-by: Gemini <gemini@google.com>
This commit is contained in:
Yukihiro "Matz" Matsumoto
2025-07-31 10:21:04 +09:00
parent 6d377f8d6d
commit 9ac70a72e0
1 changed files with 8 additions and 32 deletions
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mrbgems/mruby-bigint/core/bigint.c
+8 -32
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@@ -2633,38 +2633,14 @@ mpz_gcd(mpz_ctx_t *ctx, mpz_t *gg, mpz_t *aa, mpz_t *bb)
mpz_div_2exp(ctx, &a, &a, a_zeros);
mpz_div_2exp(ctx, &b, &b, b_zeros);
/* Use Lehmer's algorithm for large multi-limb numbers (> 3 limbs) */
if (a.sz > 3 && b.sz > 3) {
mpz_t u0, u1, v0, v1, q, r;
mpz_init_temp(ctx, &u0, 2);
mpz_init_temp(ctx, &u1, 2);
mpz_init_temp(ctx, &v0, 2);
mpz_init_temp(ctx, &v1, 2);
mpz_init_temp(ctx, &q, 2);
mpz_init_temp(ctx, &r, 2);
while (ucmp(&a, &b) != 0) {
if (ucmp(&a, &b) > 0) {
mpz_sub(ctx, &a, &a, &b);
mpz_div_2exp(ctx, &a, &a, mpz_trailing_zeros(&a));
}
else {
mpz_sub(ctx, &b, &b, &a);
mpz_div_2exp(ctx, &b, &b, mpz_trailing_zeros(&b));
}
}
}
else {
while (ucmp(&a, &b) != 0) {
if (ucmp(&a, &b) > 0) {
mpz_sub(ctx, &a, &a, &b);
mpz_div_2exp(ctx, &a, &a, mpz_trailing_zeros(&a));
}
else {
mpz_sub(ctx, &b, &b, &a);
mpz_div_2exp(ctx, &b, &b, mpz_trailing_zeros(&b));
}
}
/* Euclidean algorithm for multi-limb numbers */
while (!zero_p(&b)) {
mpz_t temp;
mpz_init_temp(ctx, &temp, a.sz);
mpz_mod(ctx, &temp, &a, &b);
mpz_move(ctx, &a, &b);
mpz_move(ctx, &b, &temp);
mpz_clear(ctx, &temp);
}
mpz_mul_2exp(ctx, gg, &a, shift);
mpz_clear(ctx, &a);